Technical University of Denmark Graz University of Technology · TECHNICAL UNIVERSITY OF DENMARK...

TECHNICAL UNIVERSITY

OF DENMARK

Master Thesis

written at the

Technical University of Denmark

and

Graz University of Technology

Department of Buildings and Energy Technical University of Denmark Building 118, Brovej DK-2800 Kgs. Lyngby Denmark

Department of Electrical Power Systems Graz University of Technology Inffeldgasse 18/I A-8010 Graz Austria

Andreas Lugmaier

Optimisation of Energy Efficiency Methods

in Buildings regarding Life Cycle Costs

Master Thesis

Supervisors: Denmark: Prof. Svend Svendsen Toke Rammer Nielsen

Austria: Prof. Manfred Sakulin

Ernst Schmautzer

Graz, December 2000

Acknowledgements

I would like to thank the following people for their help creating this report:

First mention is to my supervisors at the Technical University of Denmark, Toke Rammer

Nielsen and Svend Svendsen, who encouraged me to undertake this project, provided

assistance with the programming and gave valuable advice on it.

Second mention must go to my supervisors at my home university, the Technical University

of Graz, Manfred Sakulin and Ernst Schmautzer, who made it possible to write this thesis in

Denmark and supported me with their help.

I would also like to thank my family, relatives and friends, who gave me support during my

study time and especially for their help in the final phase of my thesis.

Graz, December 2000

.......................................................

Andreas Lugmaier

Title:

Optimisation of Energy Efficiency Methods in Buildings regarding Life Cycle Costs

Abstract:

In this thesis it was desired to develop a program which finds the optimum building

design by minimising the total Life Cycle Costs (LCC), by given design options and

project specific boundary conditions.

The program uses a simplified dynamically heat load and consumption calculation,

taking the outdoor temperature and solar radiation variations under consideration. It

optimises a building regarding the LCC minimum by taking different heat insulation

levels, the aspect ratio of the building, window areas and types, solar shading systems,

orientation possibilities, heating systems, solar hot water production systems,

ventilation and cooling systems under consideration.

The most sensible parameters for the chosen energy saving level are the type of

heating used and the price paid for the energy. In addition a rise of the energy price

will greatly influence the result.

The program can be used to find a successful realisation strategy for building design

by detecting, evaluating and sorting the economical and ecological measures.

This thesis demonstrates the merit in using the developed program, which considers

the life time for a building and the connected life cycle costs, for future choice of

energy saving methods.

Keywords:

optimisation, life cycle cost, energy consumption, optimal building design

Titel:

Optimierung von Methoden zur Steigerung der Energieeffizienz in Gebäuden unter

Berücksichtigung der Lebenszykluskosten

Kurzfassung:

Mit dieser Diplomarbeit wurde ein Programm entwickelt, welches die totalen

Lebenszykluskosten eines Gebäudes unter Berücksichtigung der projektspezifischen

Grenzen und gegebenen Designmöglichkeiten minimiert.

Das Programm verwendet eine vereinfachte dynamische Wärmebedarfsberechnung in

welchem die jahreszeitlichen Schwankungen der Außentemperatur und die

Sonneneinstrahlung berücksichtigt werden. Das Programm optimiert ein Gebäude

hinsichtlich der Lebenszykluskosten unter Berücksichtigung der Wärmedämmung,

Geometrie, Fensterflächen und Fenstertypen, Beschattungssysteme,

Orientierungsmöglichkeit, solare Warmwassersysteme, Ventilationssysteme und Air

Conditioning Systeme.

Der gewählte Heizungstyp und die davon abhängigen Energiekosten üben den größten

Einfluß auf das Ergebnis der Optimierung aus. Zusätzlich wirkt sich auch eine

Energiepreissteigerung stark auf das Ergebnis aus.

Dieses Programm ermöglicht es dem Benutzer ökonomische und ökologische

Einsparmöglichkeiten in Gebäuden zu erkennen, zu evaluieren und zu sortieren und

damit eine erfolgreiche Strategie für die Realisierung solcher Gebäude zu entwickeln.

Diese Diplomarbeit demonstriert in anschaulicher Weise den Vorteil des entwickelten

Programmes, welches die Lebenszykluszeit des Gebäudes und den damit verbundenen

Kosten berücksichtigt, für die zukünftige Auswahl von Energiesparmöglichkeiten in

Gebäuden.

Stichwörter:

Optimierung, Lebenszykluskosten, Energieverbrauch, Optimales Gebäudedesign

Warum beglückt uns die herrliche, das Leben

erleichternde, Arbeit ersparende Technik so wenig?

Weil wir noch nicht gelernt haben,

vernünftigen Gebrauch von ihr zu machen!

[ Albert Einstein ]

Optimisation of Energy Efficiency Methods in Buildings regarding Life Cycle Costs Report

Page: 1

Table of Contents:

1 INTRODUCTION................................................................................................. 4

1.1 Background ............................................................................................................................................. 4

1.2 Hypothesis ............................................................................................................................................... 4

1.3 System Boundaries and Limitations...................................................................................................... 6

1.4 Energy demand ....................................................................................................................................... 7

1.4.1 Climate of the surrounding.............................................................................................................. 7

1.4.2 Indoor climate and function of the building .................................................................................... 8

1.4.3 Building envelope ........................................................................................................................... 8

1.4.4 Heating and ventilation system, lighting, appliances ...................................................................... 9

1.5 Life Cycle Cost (LCC) ............................................................................................................................ 9

1.6 Building Costs ......................................................................................................................................... 9

1.6.1 Investment Costs ........................................................................................................................... 10

1.6.2 Operational costs ........................................................................................................................... 10

1.6.3 Maintenance Costs ........................................................................................................................ 11

1.6.4 Other Costs.................................................................................................................................... 11

1.7 Optimisation technique ........................................................................................................................ 11

2 METHODS ........................................................................................................ 12

2.1 Principles ............................................................................................................................................... 12

2.2 Discount rate ......................................................................................................................................... 13

2.2.1 Theory ........................................................................................................................................... 13

2.2.2 Database input and calculations .................................................................................................... 13

2.3 Life Cycle Costs (LCC)......................................................................................................................... 14

2.3.1 Theory ........................................................................................................................................... 14


2.4 Geometrical considerations.................................................................................................................. 19

2.4.1 Theory ........................................................................................................................................... 19



Page: 2

2.5 Indoor climate model............................................................................................................................ 21

2.5.1 Theory ........................................................................................................................................... 21

2.5.1.1 Indoor Climate.......................................................................................................................... 22

2.5.1.2 Heat storage ability................................................................................................................... 25

2.5.1.3 Heat losses:............................................................................................................................... 28

2.5.1.4 Solar heat gain .......................................................................................................................... 31

2.5.1.5 Internal heat sources ................................................................................................................. 31

2.5.1.6 Air and wall temperature .......................................................................................................... 32

2.5.2 Model ............................................................................................................................................ 32


2.6 Outer wall .............................................................................................................................................. 35

2.6.1 Theory ........................................................................................................................................... 35


2.7 Inner wall............................................................................................................................................... 38

2.7.1 Theory ........................................................................................................................................... 38


2.8 Floor....................................................................................................................................................... 39

2.8.1 Theory ........................................................................................................................................... 39


2.9 Ceiling .................................................................................................................................................... 41

2.9.1 Theory ........................................................................................................................................... 41


2.10 Window............................................................................................................................................. 43

2.10.1 Theory ........................................................................................................................................... 43


2.11 Other basic calculations of the rooms ............................................................................................ 50


2.12 Solar shading .................................................................................................................................... 52

2.12.1 Theory ........................................................................................................................................... 52


2.13 Orientation ....................................................................................................................................... 54

2.13.1 Theory ........................................................................................................................................... 54



Page: 3

2.14 Heating System................................................................................................................................. 57

2.14.1 Theory ........................................................................................................................................... 57


2.15 Hot water system.............................................................................................................................. 60

2.15.1 Theory ........................................................................................................................................... 60


2.16 Ventilation ........................................................................................................................................ 64

2.16.1 Theory ........................................................................................................................................... 64


2.17 Cooling .............................................................................................................................................. 69

2.17.1 Theory ........................................................................................................................................... 69


2.18 Optimisation ..................................................................................................................................... 72

2.18.1 Theory ........................................................................................................................................... 72

2.18.2 Database input............................................................................................................................... 73

3 CASE STUDY AND SENSITIVITY ANALYSIS................................................. 75

3.1 Input data .............................................................................................................................................. 75

3.2 Results.................................................................................................................................................... 78

3.3 Sensitivity analysis ................................................................................................................................ 81

3.3.1 Analysis of the optimisation results .............................................................................................. 81

3.3.2 Scenarios with different starting points......................................................................................... 85

3.4 Discussion .............................................................................................................................................. 88

4 CONCLUSION .................................................................................................. 92

5 REFERENCES.................................................................................................. 94

APPENDIX ............................................................................................................... 97


Page: 4

1 Introduction

1.1 Background The environmental problems we are facing today constitute new constraints on development

all over the world. Most of the severe environmental problems are related to the use of

energy. In Denmark about 70% of the end energy consumption of households is used for

heating.1 The connection between environmental impacts and the energy consumption is very

close. One environmental problem, the emission of carbon dioxide from burning fuel, has

come to dominate the energy debate and policies in the last two decades. Each year the global

burning of fossil fuel results in the emission of around 30 billion tons of CO2. These

additional, manmade CO2 emissions lead to a higher CO2 concentration in the atmosphere and

therefore to the so called Global Warming Effect.2

This increasingly leads towards the conclusion that it would be advantageous to reduce the

energy consumption of buildings to a more environmentally friendly level and to a more

energy cost efficient level.

1.2 Hypothesis The energy conscious building designer has a number of energy conservation options and

technologies to choose from. This results in a higher potential of reducing the energy

requirements. The implementation of this approach is complicated by the fact that the design

options are often strongly coupled and may give contradictory design applications. Therefore,

the key design issue is to get an optimum technology mix, whereby the total energy

requirements have to be considered as a whole, together with economy and the optimisation

of the comfort conditions.

To find the optimum solution means that the best possible solution under the given conditions

is required. A starting point would be to define these conditions.

An optimisation for conditioning in an economic way will be to keep the Life Cycle Costs as

low as possible. The meaning of the costs can differ, for example the builder of a house will

look for the lowest investment cost for building, whereas the user (if he is not the builder, too)

will look for the lowest total Life Cycle Energy Costs. Whether the individual user owns or

1 Pages 8 and 28, Energistatistik 98 2 Page 6, Note 1, Energy and Environment


Page: 5

rents the building is rather a financing question which, ideally speaking, should not influence

the principle of the optimisation process.

The costs of a building are:

• Investment costs (e.g. interests, depreciation and maintenance)

• Operational costs (e.g. energy costs)

• Maintenance costs (e.g. service costs)

• Other costs (e.g. insurance, taxes)

For an economical optimisation the Life Cycle Costs have to be minimised. Other parameters

may be used for optimisation, e.g. CO2 emissions and highest interest rate.

Accordingly, the fundamental low energy building design problem may be formulated as

follows:

What is the optimum building design that minimises the total Life Cycle Costs,

given the design options and the project specific boundary conditions?

The answer to this question may be found with an optimisation program. This program will be

able to solve the problem in an appropriate way. In a first step it will show the direction of the

cost and energy saving possibilities, concerning less borders and restrictions. As a second step

the program can be used to deliver more detailed results, including stricter requirements and

borders. Therefore, a dynamical consideration of the problem (especially for the indoor

climate) will be born in mind.

This work shall give a base for energy engineers and architects for choosing optimal building

design and the most cost effective energy saving modifications. This shall support the

decisions regarding the installation of energy saving technology.

It will be probably hard to find realistic and reliable data for all applications to include in the

formulas. Therefore it will be better to determine the power and energy demand and give the

possibility of changing and updating the costs for the different parts of the calculation.


Page: 6

1.3 System Boundaries and Limitations At the beginning certain limitations must be made in order to reduce the number of

parameters that could be applied to energy system considerations. It shall be mentioned that

for many calculations and considerations a lot of simplifications will have to be made. The

backbone of this program will be the database which should be able to handle values for:

• Aspect ratio (length divided by the width of the building)

• Outer wall types (certain insulation levels)

• Inner wall types

• Floor types (certain insulation levels)

• Ceiling types (certain insulation levels)

• Window types

• Window areas (percentage factor)

• Solar shading systems

• Orientation possibilities

• Heating systems

• Solar hot water production (yearly solar hot water share levels)

• Ventilation systems

• Cooling systems

Limitations have also been set to make the calculations feasible.

• A simplified indoor climate model will be used.3

• All chosen windows will have the same area and will be the same model

• Easy estimation for the load of appliances and the occupancy in the room. The load is

considered to be the same in all rooms.

• Daylight consideration is not directly included in the calculation

• The energy enclosed in the building material and used for production of the building parts

will not be included in this calculation.4

Other limitations will be also made during defining the project and these parameters will be

described in more detail further on in the thesis.

3 Vinsim program, computer program from the Institute for Buildings and Energy, DTU 4 Page 328, Energy use during the Life Cycle of Single Unit Dwellings


Page: 7

1.4 Energy demand5 The energy consumption of a building is influenced by many different quantities. They can be

devided into four groups:

Figure 1: Energy demand

All four groups influence the energy demand of a building. Each group has an effect on the

others. For example, a building with only a heating system cannot guarantee that the indoor

climate will be within the allowed range in hot summer periods, unless there is a cooling

facility available.

1.4.1 Climate of the surrounding

The method of construction, especially the form of the building; the choice of materials, the

type and shape of windows and the solar shading facilities all influence the indoor climate. If

the building concept, the indoor climate and the method of construction are initially set, then

the range of energy saving methods available will be rather small.

The influence of the energy demand of the building on the outdoor climate will not be directly

considered. Only if the suggestions for energy optimisation given later in this thesis are

widely used there will be an influence on the Earth’s CO2 content and therefore on the

climate. However, a detailed survey of these suggestions will not be part of this thesis.

The relations of the surrounding climate can be described by parameters, such as: air

temperature, moisture, wind speed, pressure and cleanliness of the outdoor air; solar radiation,

precipitation and radiant temperature.

5 Pages 18 – 19, Raumkonditionierung


Page: 8

The most important factor of the surrounding climate is obviously the temperature of the

outdoor air. A lot of common rules for dimensioning the yearly heating demand only use

mean and maximum temperatures for dimensioning the heating power, and the so called

degree-day method. The use of such values and the degree-day method can lead to mistakes in

the calculation, especially in the case of modern high insulated and light construction

buildings. Therefore, the relationship between the heat gains from solar radiation, lighting and

people and the capacity of the heating system will change.

It is therefore necessary to get sufficiently precise values for the energy demand of buildings

and it will often be necessary to consider the changes in the outdoor climate. Reference to the

room temperature and the solar radiation are the most important parts to consider.

1.4.2 Indoor climate and function of the building

For the indoor climate of the building the most important factors are the temperature,

moisture content, fresh air supply, natural and artificial lighting, internal heat sources, time

schedules of occupation and the working periods of the installations in the building. To get an

adequate measure of the indoor climate the surrounding climate has to be analysed

dynamically over at least one whole year.

1.4.3 Building envelope

The design of a building has a big influence on the energy balance. The different capabilities

of the building envelope to store heat in the walls, roof or floor has a significant effect on the

heating and cooling energy demand. Even for buildings which are only heated, not only the

heat transmission factors for the different outdoor parts like outer walls, windows, roof and

floor construction factors are enough to consider, also the heat storage capacity of the

different parts have to be taken into account. Because these factors also influence the cooling

of the building during the night, or the possibility of storing and using, for example, solar heat

gain and losses during the night. The effects on the indoor climate in the summer will also be

highly influenced by the storage capacity of the building.

It is often possible to avoid an air conditioning system, simply by changing the construction

materials of the building. The shape and orientation of the house are also influencing factors

on the energy consumption. The ratio between the volume and the outdoor surface, especially,

determines the energy demand of building. For large buildings this relation can be overlapped

by the bigger lighting and cooling energy demand for interior rooms; windows and solar

shading have an additional impact.


Page: 9

1.4.4 Heating and ventilation system, lighting, appliances

The influence of the energy consumption design is driven by: the type of the conditioning

system (e.g. heating-, cooling-, air conditioning); type of system (air conditioning system with

water and air or only with water); heat recovery system and energy transfer within the

building; lighting system and the general appliances.

These four groups influence the household energy balance and cannot be easily demarcated

from each other. Therefore it can be seen that it is essential to look at these parameters at a

very early stage of planning a building.

1.5 Life Cycle Cost (LCC) For the comparison of cost effectiveness of energy saving, various methods with different

economical characteristics can be used, e. g. life cycle cost, annual cost, pay back period,

internal rate of invest, specific cost of saved energy etc. In this thesis the LCC method is used

as a tool to define the best overall energy saving possibilities in a building. It shall be possible

to compare the different Life Cycle Cost savings with the additional investment for the

savings. The different appearing costs do not emerge at the same time and therefore the

method of the Net Present Value, NPV, has been used for calculating the Life Cycle Costs

throughout this thesis. This is to make the cost flow comparable at one special occasion, the

base year.

1.6 Building Costs6 Having found a suitable method for evaluating the different combination of energy saving

measurements, it is necessary to find the different values of the parts in the Life Cycle Cost

function.

In this thesis it shall be shown how mathematical expressions can be found in order to

calculate the LCC. It is necessary to find a mathematical expression for how the building cost

varies with the ability of the components to save energy. This ability raises when e. g. more

insulation are put on the external walls, floor or ceiling, etc. and therefore, it would be a

proper way including the different investment costs of the thermal insulation and comparing

them with the effects on the operational costs.

6 Page 17-22, Optimal energy retrofits on existing multifamily buildings


Page: 10

1.6.1 Investment Costs

The investment costs will include the costs for the production, delivery and fitting of the

building parts.

The costs will have to refer to different units of the building, for example floor area, wall area

or m³ of air flow per hour to include them in a good way in the calculation.

For the insulation it is possible to calculate how much a certain amount of extra insulation

will cost, when it is added to for example the wall. The steps will be given gradually with the

corresponding U-values, because it is not possible to use insulation material in all wanted

thickness.

In the same manner it shall be possible to find mathematical expressions that approximately

reflect the real costs for buying and installing e. g. heating, ventilation or cooling equipment.

Investigating the price lists e.g. heating systems, the costs to a great deal depend on the power

that has to be installed. If it is not possible to find the right values right now, it shall be at least

possible to put them in the program in an appropriate way later on.

The price book used in this thesis is called “Husbygning – Brutto”7 and the prices given in

this book are including the material price and wages for the installation. After some

discussion with the supervisor, a decision was made to use the values for 200 pieces in the

book, because these numbers meet the real prices in Denmark in a better way.

1.6.2 Operational costs

In order to get lower energy costs, two different methods can be used. One method is to install

energy conserving measures in the house. The heat transmitted through e. g. the external wall

can be diminished by adding more insulation to it.

The other method is to make the energy losses cheaper and to install a heat producing

equipment with lower running costs. An example of this is to install a solar hot water system,

which takes major parts of its energy from the sun. Changing the heating equipment in order

to get lower running costs can be done in two ways. The first is to choose a system with a

higher efficiency and the second is to choose other “fuels” for the heating system, e. g. gas

instead of electricity. It might also be cheaper to produce the energy somewhere else, e. g.

district heating systems.

Combinations of these different strategies can, of course, be the solution to the optimisation

problem.

7 Husbygning Brutto


Page: 11

1.6.3 Maintenance Costs

Some parts of the house will have some maintenance costs, which means that something has

to be changed or repaired during the lifetime. These costs will be given as an percentage of

the investment costs per year or as a fixed value per area and year.

1.6.4 Other Costs

Some other costs will appear for building a house. This could be e. g. insurance or cleaning

costs. These costs are not included in the calculation, if they are not considered in the selling

price of the building parts.

Also taxes (VAT) are not included in the calculations to make them more comparable, but

they can be easily added by multiplying the results with the VAT rate.

1.7 Optimisation technique It is possible to optimise different parts to get a better household energy consumption, like:

• Technical measures in the building (e.g. choice of the installation systems for heating,

cooling, lighting, air conditioning and the source of energy)

• Architectural measures (e.g. choice of the insulation and thermal performance)

• Technical supply measures (e.g. choosing where to get the various energy forms from)

• Internal measures (e.g. choosing an energy saving control and regulation)

It should be mentioned that there is a big influence on the results of the optimisation by many

uncertain factors, like: Lifetime, discount rates, energy costs, investment costs, maintenance

costs, personal costs, availability of energy supply, availability of personnel, form and time of

using the building; technical development for facilities, valuation of the working area, time of

work, care for the environment, taxes, and so on.

Therefore it is important to do a sensitivity analysis on the project. This sensitivity analysis

will be done by checking the results of a case study to ensure that the given solution is “the

optimised version”. A change of the input factors will then show the influence of the chosen

figures. In an additional analysis the influence of the energy rise rate, the assumed lifetime of

the building or the heating systems on the optimisation results will be examined.


Page: 12

2 Methods In this part the theoretical background and the mathematical model of the building will be

formulated, to show which methods were used in this thesis.

2.1 Principles The program is written in MATLAB. The basis for Matlab is the mathematics associated with

matrices and linear algebra calculations. It is therefore well suited for producing highly

complex numerical computations and graphical representations. Matlab can also be used by

less experienced users to produce simple but effective programs. The functions in Matlab

allow many mathematical operations to be performed, including linear algebra, data analysis,

signal processing, numerical solution of ordinary differential equations, of course

optimisation and many others.

To use and give an example for the function of this program a database has to be created and

some fixed variables are needed as an input data (Appendix A). The background of this

database and the fixed variables influenced the selection of the calculation methods.

Sometimes it was not possible to get data in the required form. If this happened the equations

in the model were changed to use this new available input data in an appropriate way.

Each input variable will be stated with the name, which is used in the database, the term,

which is used in the program, the unit, the format and a description of it.

The input data was received from many different places, and some of this data is more reliable

than the rest. The sources of the data will be mentioned and also assumptions, related to

information given from people will be stated in the chapters.

The creation of the database will be such that it can be easily expanded, if necessary.

The methods used in this thesis will be described as follows:

• A description of the chosen method of economic ranking, the Life Cycle Cost method,

will be described in detail.

• The possible geometrical considerations of the building will be described.

• The requirements on the mathematical indoor model will have to be described.

• All needed input data of different building parts have to be discussed.

• Finally, a suitable optimisation program must be found to fulfil the requirements and will

be described in more detail.


Page: 13

2.2 Discount rate8

2.2.1 Theory

In order to find an optimal energy and financial strategy it is necessary to have an accurate

ranking criterion. The Life Cycle Cost is such a criterion, and in the next chapter this is

discussed in more detail. However, before this can be done, it is necessary to explain the

discount rate, which will be needed to calculate the LCC.

It is not so easy to choose the proper discount rate. Using a high rate makes investments less

profitable and the reverse is true for low rates.

2.2.2 Database input and calculations

The input from the database has to include the following variables:

Name: Program term: Unit: Format: Description:interest_rate: iint [ % ] value Interest rateinflation_rate: iinf [ % ] value Inflation rateenergy_rise_rate: iene [ % ] value Energy price rising rateTable 1: Discount rate variables

The normal discount rate (id), which is calculated by subtracting the inflation (iinf) from the

interest rate (iint), is used for the calculations which are not greatly influenced by a rising

energy price, for example investment or maintenance costs.

• Discount rate: infint iiid −= [ % ] Equation 1

For energy related costs, the energy price dependent discount rate (ide), which is calculated by

subtracting the inflation and the energy price rising rate (iene) of the interest rate, must be used

to calculate the variable energy costs, of the total Life Cycle Costs.

• Energy price dependent discount rate: enede iiii −−= infint [ % ] Equation 2

These formulae were used for the calculation of the discount rate in this thesis.

8 Page 15, Optimal energy retrofits on existing multifamily buildings


Page: 14

2.3 Life Cycle Costs (LCC)

2.3.1 Theory9

The Life Cycle Costs are calculated as the sum of the Net Present Values (NPV)10 of the

Investment Costs (IC), Periodical Costs (PC) and Operating Costs (OC) minus the Scrap

Values (SV) over the lifetime. In the case of a building, the LCC depends on many factors,

such as the insulation performance of the walls, floor and ceiling; the building shape,

windows, heating and hot water consumption, ventilation and air conditioning. A better

performance of the insulation leads to an increase in purchase price, on the one hand, but

leads to a reduction in heat losses and therefore operating costs. The operating costs are

multiplied by the Present Value Factor (PVF), which depend on the discount rates (ide,id) and

the calculated lifetime. Id is used for the maintenance cost calculation and ide is used for the

operating cost calculation, including the rate of energy price increase.

( )dde

tLC

dde

dde ii

itLCPVF/

/

/

11),(

−+−

=

Equation 3

OCPVF idetLCtLCSVPCICLCC ∗+−+= ∑∑∑ ),()((tLC)(tLC) Equation 4

LCC

0 10 20 30 40 50 60 70 80 90 100

Insulation thickness [ mm ]

LCC

Energy Cost

Building Cost

Total Cost

Figure 2: Draft Life Cycle Costs

9 Methods to compare the economic effectiveness of energy savings of warm water supply systems 10 Page 12-15, Optimal energy retrofits on existing multifamily buildings


Page: 15

Principally, as shown in Figure 2 for the example of a wall, the LCC are a function of the

insulation performance. The curve starts from the uninsulated wall with very high operating

cost, a fixed purchase price for the wall and a zero purchase price for the insulation.

From here the Life Cycle Costs curve decreases down to its minimum point, because the

operational costs are decreasing faster than the costs for insulation are increasing. For the

costs of the insulation a fixed rising rate for thicker insulation is assumed. Beyond this

optimum the LCC increase again because high additional purchase prices for improvements

are necessary for only small operating cost savings.

The economic optimum with the lowest LCC are reached at the optimum insulation

performance. Each centimetre of additional insulation beyond the optimum leads to an

increase of the LCC.

The sum of all the costs for the house, during its life cycle period, is called the LCC, or the

sum of the NPV for the entire house. If there are many energy saving possibilities, then those

which give the building the lowest possible LCC should be chosen.

There are a number of methods which can be used for ranking different investment strategies.

Some of these strategies are for example savings- to investment ratio, the internal rate of

return on investment, the Net Present Value, the Discounted Pay Back Period and some

varieties of “the quantity of energy saved per investment dollar spent”.

The two first methods are technically correct when having a limited amount of money to

invest, but the methods do not give the optimal solution for the entire house without a

cumbersome iterative procedure.

In this case, where the best energy saving strategies with the lowest costs over the lifetime for

a building shall be found, the method of the NPV seems to be the best. A building is a system

with many different details and equipment that depend on each other. Therefore the method

used has to be superimposed e. g. it must be possible to sum the different costs. This sum

should show the total cost for the building. Only the NPV method does this.

When investing money into something, this is done because of the benefit that comes out

from the investment. Not only the normal building costs, as it is still often done nowadays,

also the energy costs of the house over the whole lifetime should be taken into account in the

investment decision. In this thesis the costs come from investing in energy conserving

measures e. g. insulation on an external wall. The benefit is the reduction in the energy cost

that comes from heating or cooling the building to a suitable temperature.


Page: 16

The problem in evaluating this analysis is the time lag between the cost and the benefit.

Fortunately, there is a method that solves this, called the Net Present Value (NPV) method.

Figure 3: Draft Net Present Value method

Figure 3 shows the LCC calculation using the Net Present Value method and includes:

• IC: Initial investment costs.

• PC: Periodic costs, which recur on a periodic basis throughout the life of a project.

• OC: Operational or annual recurring costs, which accur each year in an equal

amount or by an amount that is increasing/decreasing at a constant rate

throughout the study period. These operational costs are included in the

maintenance costs (MC), which have to be multiplied by the normal discount

rate and the energy costs (EC). These have to be multiplied by the increase in

energy price dependent discount rate.

• SV: Scrap value of the last investment.

Some examples for Figure 3 from the energy saving terminology can be the cost for insulation

to an external wall as a type IC investment. A type PC investment could be the investment of

windows, where the lifetime is shorter than the insulation of the wall. Therefore the windows

have to be changed for example every 20 years. The energy cost of heating or cooling of the


Page: 17

house could be an example of a type OC investment. And the Scrap value appears in the

calculation if the lifetime of the calculation is shorter than the lifetime of the considered part.

In this case the part of the building still has a value, and this has to be considered in the

calculation.

In this figure the scrap value arrow is on the positive side of the graph but facing to the zero

line, and therefore counting as negative costs.

According to economic theory, the discount rate tells us how much better the first alternative

is. The money paid next year can be transferred to this year by use of the discount rate and

this new value is called the Present Value, PV.

For Figure 3 the LCC would be:

( ) ( )[ ] ( ){ }( ) ( )

de

tLCde

d

tLCd

tLCd

2*tpartd

tpartd

ii11EC

ii11MC

i1SVi1i1PCICLCC−−

−−−

+−∗+

+−∗+

+∗−+++∗+=

Equation 5

tpart: [ year ] Lifetime of the considered part of the building

It is rather hard to find or assume the proper lifetime and optimisation time for a building. The

building consists of so many materials, so an overall lifetime cannot be assumed. It was

decided to consider 30 years as the calculation life and optimisation time for a building as a

starting point.


The input from the database has to include the following variable:

Name: Program term: Unit: Format: Description:totalLC_time: tLC [ years ] value Considered life time of the calcualtionTable 2: Life Cycle Cost variable

The calculation of the LCC have to be done, related to the theory given before.


Page: 18

1. Investment and scrap values: First of all it has to be checked how often the investment costs have to appear in the

calculation. Then the costs can be calculated as follows:

( )

( ) ( )tLCd

part

partpartLCpartpart

ztz

dpartpart

i1t

tztttmentcostInves

i1tmentcostInvesLCC part

+

−−−

+= ∑ −

**

*

*0

*

Equation 6 The factor z is the value how often the investment costs have to be reinvested. The first part

of the equation are the investment and reinvestment costs and the second term is the scrap

value. This calculation has to be done for all building parts used for the building.

2. Maintenance costs: The maintenance costs have to be quoted on a yearly basis and are therefore only to be

summed and multiplied with the corresponding present value factor.

( ) ( )d

tLCd

part ii11ecostMaintenancLCCeMaintenanc

−+−= ∑ *

Equation 7

It is clear that thicker insulation between the walls do not influence the maintenance costs of

the walls. A facade in very bad condition has to be repaired and painted whether you put extra

insulation on the wall or not. Therefore these maintenance costs can be considered as constant

in the calculations. These costs will be given as a percentage of the investment costs per year

or as a fixed value per area and year.

3. Running costs: The running or operational costs have to be quoted on a yearly basis, and will be multiplied

with the present value factor, which includes the energy price depending discount rate. The

energy price rising rate will only affect energy costs (for example gas, oil or electricity). The

energy costs will be added as a type of energy tax on fossil fuel reliant products.

( )de

tLCde

ii11

econsumepricehwconsumhwpricehpricefixhconsumhprice

LCCRunning−+−

++

+= *

***

Equation 8


Page: 19

The consumption of heat (hconsum), hot water (hwconsum) and electricity (econsum) have to

be multiplied with the corresponding prices for heat (hprice), hot water (hwprice) and

electricity (eprice). For some heating systems an additional fixed price (hpricefix) has to be

paid every year.

The total Life Cycle Costs are then found by summing the building parts, the maintenance and

the running costs.

The calculation of the LCC are done in a separate program which is called “LCC.m” and can

be found in Appendix B. It is difficult to find reliable relations between the different building

parts and their LCC, and the way this was achieved can be seen in the next chapters. In order

to use the LCC method for a building it is necessary to define the basic geometrical borders

and see which parts are used in such a building.

2.4 Geometrical considerations

2.4.1 Theory

Under the principles of a low energy building the shape of the building will have a big

influence on the consumption. However, the shape is not only a factor for lowering the energy

consumption, it is also an important factor for the total building costs, because a more

compact house can save a lot of investment costs.

Building a compact house means to reduce the areas facing the outside temperature to a

minimum. However, it should be mentioned that the reduction of the outer wall area will also

reduce the size of the possible window area, and therefore the daylight factor and the possible

solar gain. The daylight factor has an influence on how pleasant the room will be.

One factor which can describe the geometry of a building is the so called aspect ratio. The

aspect ratio for this thesis is defined as the length divided by the width of the building.

The net-area and height of the building have to be given as an input in the program, and it is

assumed that the height will always be given for one floor. These values are usually known in

the beginning of the planning. It will be also necessary to define whether the building will

have more than one floor, because then the heat losses will of course be different. This feature

of the program can be used with the floor- and ceiling-flag. If the ground is connected to the

floor or the ceiling is connected to the roof, the respective flags have to be set to “Yes”.

It should be mentioned that there will have to be a special calculation for each floor of the

building.


Page: 20

As can be seen in the following Figure 4, at least 6 rooms will have to exist. It is assumed that

all rooms of the building will have the same size. Four “outer rooms”, which will have one

length and one width of a room connected to the outside, are necessary. Any even number of

so called “inner rooms” can be used in this calculation model.

Figure 4: Ground plan of the building


The input data given in the beginning will have to include:

Name: Program term: Unit: Format: Description:building_area: AB [ m² ] value Area of the buildingheight: heightR [ m ] value Height of a roomroomnumber: rooms [ 1 ] value Number of rooms inside the building.Aspect ratio building: AspectRB [ m/m ] value Aspect ratio of the building Table 3: Geometric variables It can be seen that the net building area, the height of the room and the room number have to

be defined by the user as an input. The range for the aspect ratio will have to be given as an

input too and the optimisation program can then calculate the optimum aspect ratio. The basic

calculations of the building will therefore be:

• Length of the Building: ABAspectRBlengthB *= [ m ] Equation 9

• Width of the building: AspectRB

ABwidthB =

[ m ] Equation 10

• Area of the room: rooms

ABAR =

[ m² ] Equation 11 All rooms in the building have the same area.


Page: 21

• Volume of the building: ABheightRVB *= [ m³ ] Equation 12

The basic calculations of the rooms will therefore be:

• Aspect ratio of the room:

=

roomsAspectRBAspectRR 4*

[ 1 ] Equation 13

• Length of the room: ARAspectRRlengthR *= [ m ] Equation 14

• Width of the room: AR

AspectRRwidthR =

[ m ] Equation 15

• Volume of the room: ARheightRVR *= [ m³ ] Equation 16

2.5 Indoor climate model

2.5.1 Theory11

The standard for a mathematical indoor climate model used in this thesis was quite ambitious.

The program should be fast, because a lot of iterations will have to be done until a final

optimised result can be given.

The model has to guarantee that the indoor climate requirements are considered under

dynamic conditions. In addition the heat storage ability and the heat losses of the building, the

solar heat gain and the influence of shading, the additional interior heat production, the air

and wall temperatures, and the heating-, ventilation-, or cooling system have to be considered

in hourly values over a whole reference year to match the requirements of a dynamic model.

The precise description of the shading and heating-, ventilation- and cooling-system is done in

the corresponding chapters and is mentioned here only if necessary.

11 Page 33-53, Environmental science in building


Page: 22

2.5.1.1 Indoor Climate

The purpose of room conditioning in offices and residential buildings is to obtain comfortable

living and working conditions for humans and to fulfil the requirements of objects stored in

buildings. What people find to be comfortable is naturally strongly influenced by a lot of

personal factors for each person.

Nevertheless, starting from the physiological mechanisms of human beings in combination

with experience, certain essential preconditions for comfort can be defined. Comfort relies on

four components, namely thermal comfort, air hygiene, optics and acoustics:

a ) Thermal comfort12

As mentioned above the thermal comfort of human beings is governed by many physiological

mechanisms of the body and these vary from person to person. In any particular thermal

environment it is difficult to get more than 50 % of the people affected to agree that the

conditions are comfortable!

The body constantly produces heat energy from the food energy it consumes. The transfer of

the heat form the body is mainly by the processes of convection, radiation and evaporation.

The total quantity of heat produced by a person depends upon the size, the age, the sex, the

activity and the clothing of the person (Range: 70 – 250 W/person). A further complication is

the ability of the body to become accustomed to the surrounding conditions and to adapt to

them. This adaptation can be influenced by the type of climate and the social habits in a

country.

b ) Air hygiene13

The normal process of breathing gives significant quantities of CO2, latent heat and water

vapour to the air. Household air is contaminated by body odours, bacteria, and the products of

smoking, cooking and washing. In places of work, contamination may be increased by a

variety of gases and dusts. A number of statutory regulations specify minimum rates of air

supply in occupied spaces. Recommended rates of ventilation depend upon the volume of a

room, the number of occupants, the type of activity and whether smoking is expected. More

data can be found under the chapter of the ventilation system.

12 Pages 56 – 60, Environmental science in building


Page: 23

c ) Optics14

It is often necessary to provide a room with natural light from the sun or the sky. The qualities

of this natural light may be thought desirable for a pleasant environment or they may be

needed to perform certain tasks, such as exacting work with colour. The natural light can be

used as the basic source of interior lighting or can be combined with artificial light.

The quantity of natural light inside a room is governed by the factors listed below. By

analysing these factors it is possible to describe daylight numerically and to predict its effects

in a room:

• The nature and brightness of the sky.

• The size, shape and position of the windows.

• Reflections from surfaces inside the room.

• Reflections and obstructions from objects outside and inside the room.

If the natural lighting is not enough, artificial lighting has to be added. The type of lighting for

a building is closely linked to other design decisions for the building, such as the basic plan

shape or the type and extent of windows. The main function of lighting is to provide optical

comfort and therefore:

• to provide enough light for people to carry out particular activities,

• to provide enough light for people to move about with ease and safety,

• to display the feature of the building in a manner suitable for its character and purpose.

d ) Acoustics15

The term “Acoustics” can be used to describe the study of sound in general, but the subject of

room acoustics is concerned with the control of sound within an enclosed space.

Good building design invariably involves a consideration of the presence of sound in the

environment. Common topics of concern are the exclusion of external noise, the reduction of

sound passing between the rooms and the quality of sound inside rooms. Noise is an

unwanted sound in buildings.

13 Page 61 Environmental science in building 14 Pages 132 and 153, Environmental science in building 15 Pages 166, 189 and 214 Environmental science in building


Page: 24

This is an environmental definition of sound that takes account of the effect of a sound rather

than its nature. Even if a sound consists of the finest music it can be considered as noise if it

occurs in the middle of the night! Many of the reasons for not wanting a particular sound can

be identified by the effects that it can have on the listener or on the environment. Some of

these effects are described below:

• Quality of life: Noisy environments, such as areas near busy roads or airports,

are considered unpleasant and undesirable.

• Interference: Interference with significant sounds such as speech or music can

be annoying.

• Expense: Businesses may suffer loss of revenue in a noisy environment.

The detailed acoustic requirements for a particular room depend upon the nature and the

purpose of the space and the exact nature of a “good” sound is partly a matter of personal

preference. The general requirements for good acoustics are summarised as follows:

• adequate levels of sound,

• even distribution to all listeners in the room,

• background noise and external noise reduced to acceptable levels,

• absence of echoes and similar acoustic defects.

It shall be mentioned here that air hygiene, optical and acoustic requirements are only

included in this thesis, if they go hand in hand with other requirements. For example the

ventilation rate in a building is required by the Danish building restrictions and therefore air

hygiene requirements must be fulfilled.


Page: 25

2.5.1.2 Heat storage ability

The heat storage ability of a building or room depends on the thermal conductivity and heat

capacity of the materials used.

Thermal conductivity: The term lambda (λ) or k is used; it is a measure of the rate at

[ W/m K ] which heat is conducted through a particular material under

specific conditions.

Figure 5: Thermal conductivity

The thermal conductivities of some building materials used in this thesis are given in the

following Table 4. These values are a selection of measured values commonly used for

standard calculations. It is important to remember that the thermal conductivity of practical

building materials varies with moisture content as the presence of water increases conduction.

Type: lambda[ W / mK ]

Pore concrete: 0,2Concrete 2300 1,600Plaster: 0,170Mineral wool kl. 39 0,039light concrete 1200 0,400Bricks 0,780 Table 416: Thermal conductivity of selected materials

16 TSBI3 program database


Page: 26

The specific heat transfer through a wall will be called heat transfer coefficient in this thesis

and the term Kw will be used. The unit will be given in Watt per m² and Kelvin because this

will be more useful for the method of calculation.

• Heat transfer coefficient:

∆

=

2x

Kw λ

Kw: [ W/m²K ] Equation 17 λ: [ W/m K ] Material thermal conductivity ∆x: [ m ] Thickness of the building part, connected to indoor17.

The ∆x used for this calculation is the thickness of the building part, for example the inner

wall fraction of the outer wall which has the biggest influence on the thermal conductivity.

The Kw values are given in the database for walls, floors and ceilings and have to be

multiplied with the connected areas as it can be seen in Equation 49.

Heat capacity: The same mass of different materials can “hold” different

[ J/kg K ] quantities of heat.

The heat capacity of a particular material is measured by a value of specific heat capacity

(Cp), and Table 5 gives values for some materials.

Material: Specific heat capacity Specific heat capacity

[ Wh/ kgK ] [ J / kgK ]Wood 0,4722 1700Water 1,164 4190 Table 5: Heat capacity of selected materials

The heat capacities of different materials are compared on the basis of equal masses.

However, the same mass of different materials may occupy different volumes of space,

depending upon their densities.

Heavyweight masonry materials, such as brick, concrete and stone, have high densities. This

means that relatively small volumes of these materials have a large mass and therefore

provide a relatively high heat capacity within a small volume.

17 Simplification for the calculation was done with agreement of Toke Rammer Nielsen.


Page: 27

The heat storage provided by the brick, concrete or stone used in construction is called the

thermal capacity of the building. It is possible for two types of wall to have the same thermal

insulation, as measured by the U-values, but to absorb or dissipate heat at different rates.

As a result the rooms inside such walls would take different times to warm or to cool, as

indicated in Figure 6.

Figure 6: Influence of thermal conductivity on temperature changes

In general, lightweight structures respond more quickly to surrounding temperature changes

than do heavyweight structures. This is because heavyweight materials have a higher thermal

capacity. This effect has to be included in a mathematical building indoor model, because it

affects the indoor climate to a high degree.

The term for the heat capacity used in this thesis will be Cw and will be given in J per Kelvin

and m², because this will be more useful for the calculation method.

Heat capacity: xCCw p ∆∗∗= ρ Cw: [ J/(K m²) ] Equation 18 ρ: [ kg/m³ ] Density of the material Cp: [ J/kg K ] Specific heat capacity ∆x: [ m ] Thickness of the building part, connected to indoor18.

The ∆x used for this calculation is the thickness of the building part, for example the inner

wall fraction of the outer wall which has the biggest influence on the thermal capacity. The

Cw values are given in the database for walls, floors and ceilings and have to be multiplied

with the connected areas as it can be seen in Equation 48.

18 Simplification for the calculation was done with agreement of Toke Rammer Nielsen.


Page: 28

The next table gives important values which will be used the heat capacity in this thesis:

Type: Density: Specific heat capacity:[ kg/m³ ] [ J/(kg K) ]

Pore concrete: 645 1000Concrete 2300 2300 800Plaster: 800 1006Mineral wool kl. 39 50 840light concrete 1200 1200 1000Bricks 1800 880 Table 619: Density and specific heat capacity values

2.5.1.3 Heat losses:

The U-values and thermal bridges are responsible for heat losses in a building.

U value: A U-value is a measure of the overall rate of heat transfer, by all

[ W/m² K ] mechanisms under standard conditions, through a particular

section of construction.

Heat is transferred through an element of a building by a number of mechanisms. Layers of

different materials conduct heat at different rates; in any cavity there is heat transfer by

conduction and convection in the air and by radiation. At the inside and outside surfaces the

heat transfer by radiation and convection is affected too, by factors such as surface colour and

exposure to climate.

It is convenient to combine all these factors in a single figure which describes the air to air

behaviour of a particular construction. This figure is called the overall thermal transmittance

coefficient or U-value.

• U-value: CD

U∗+

=λλ

U: [ W/(m² K) ] Equation 19 D: [ m ] Insulation thickness λ: [ W/m K ] Thermal Conductivity C: [ m² K/W ] Constant factor

19 TSBI 3 program database


Page: 29

Standard U-values are calculated by making certain assumptions about moisture contents of

materials and about rates of heat transfer at surfaces and in cavities. Although the standard

assumptions represent practical conditions as far as possible, they will not always agree

exactly with U-values measured on site.

Standard U-values are needed as a common basis for comparing the thermal insulation of

different types of structure and for predicting the heat loss from buildings, and they are also

used to specify the amount of thermal insulation required by regulations. The maximum U-

values for building parts (Table 7) that can be used in Denmark are given by the Danish

Building Regulations.20 Building part: Max. U-value

[ W / m²K ]Light wall 0,2Heavy wall 0,3Floor 0,2Ceiling 0,15Window 1,8 Table 7: U-value limits ( Danish Building Regulations )

The U values of the building parts facing the outside have a big influence on the heat loss of

the building. These parts of the building are the outer walls, the ceiling, the floor and the

windows. The door is of course also such a part, but the influence is neglected in this thesis.

The sum of the heat transfer components, calculated on the basis of the different U-values will

be used in the indoor climate model.

It will be decisive to reduce these heat losses to lower the heat costs. A temperature difference

appears in the building parts placed between the outdoor and the indoor temperature due to

the fact that during the autumn, winter and spring period the indoor temperature is often

higher than the outside temperature in North and Central Europe.

Heat energy always tends to transfer from high temperature to low temperature regions

(Second law of Thermodynamics).

In order to maintain a constant temperature within a building it is necessary to restrict the rate

at which heat energy is exchanged with the surroundings, e. g. thickness of insulation or the

rate of natural and artificial ventilation. Keeping heat inside a building for as long as possible

conserves energy and reduces heating costs.

Thermal insulation is the major factor in reducing the loss of heat from buildings. Adequate

insulation should therefore be a feature of good initial design.

20 Page 11, Danish Building Regulations


Page: 30

Good insulation can also reduce the time taken for a room to heat up to a comfortable

temperature; for example, in a room that is unoccupied during the day.

In the summer period it is also useful to have good thermal insulation, because this will also

reduce the flow of heat into a building, when the temperature outside is greater than the

temperature inside.

It shall be mentioned that it is necessary to get prices for the different parts of the building in

relation to the existing U-values (which is of course related to the thickness of the insulation).

Thermal bridges, cold bridges: A thermal bridge is a portion of a structure whose

[ W/m K ] high thermal conductivity lowers the overall

thermal insulation of the structure.

When a material of high thermal conductivity passes completely through a wall, floor or

ceiling then the insulation in that area is said to be “bridged” and thus its effective U-value is

reduced.

There is increased heat flow across the thermal bridge and the surfaces on the interior side of

the bridge therefore become cooler, giving rise to the informal term of “cold bridge”. There is

an increased risk of condensation and mould growth on these internal surfaces around cold

bridges, such as the lintel above a window.

Figure 7: Thermal bridges

Thermal bridges can easily occur when the insulation of a wall is bridged at the junctions with

the floor, the roof, or the windows. Some examples of thermal bridges are shown in Figure 7.


Page: 31

The remedy for thermal bridging is the correct design and installation of thermal insulation.

The thermal bridge losses in this thesis are divided into corner, floor-wall, ceiling-wall,

window glass-frame and window frame-wall linear losses. This distribution is made, because

these values are usually easy to obtain from the building parts manufacturers. It was discussed

where to include the linear losses; for example, the floor-wall linear losses could be counted

half to the floor and half to the wall, or everything could be counted to the wall or in any other

relationship. The problem also exists that different walls combined with different floors,

ceiling or windows will give varying linear losses.

This problem will probably have to be considered later on in a database where different

combination linear losses will be available to be used. In this thesis all linear losses, except

the window glass-frame losses will be saved in the outer wall database.

2.5.1.4 Solar heat gain21

Most of the solar heat gain in buildings in middle and northern Europe is by direct radiation

through windows. The maximum gains through south facing windows tend to occur in spring

and autumn when the lower angle of the Sun causes radiation to fall more directly onto

vertical surfaces. This heat gain via windows can be useful for winter heating, if used

correctly.

The rate at which heat from the Sun can be used is dependent on many factors, including the

time of day and year, and will be further described in the orientation chapter. The input in this

model has to include the total solar radiation in hourly values.

2.5.1.5 Internal heat sources22

Casual heat gains take account of the heat given off by various activities and equipment in a

building that are not primarily designed to give heat. The major sources of such heat are as

follows:

• Heat from people

• Heat from lighting

• Heat from cooking and water heating.

• Heat from machinery, refrigerators, electrical appliances.

21 Pages 70-71, Environmental Science in Building. 22 Page 73, Environmental Science in Building.


Page: 32

This type of heat gain must be considered in the design of the heating / cooling design. Where

possible this heat should be used rather than wasted. The combined heat output of the various

sources varies from hour to hour and should therefore be included in hourly values in a room

model.

2.5.1.6 Air and wall temperature

The temperature of the surrounding surfaces can affect the thermal comfort of people as much

as the temperature of the surrounding air. This is because the rate at which heat is radiated

from a person is affected by the radiant properties of the surroundings. For example, when

sitting near the cold surface of a window the heat radiated from the body increases and can

cause discomfort. Therefore it is important to include these values in a room model.

2.5.2 Model

The model used in this program comes from the Danish program “Vinsim”23 which was

developed at the Institute of Building and Energy at the Technical University of Denmark.

The program “Vinsim” gives hourly results for the heating and cooling demand of a room and

the air temperature in the room.

This model does not match all the requirements specified previously, so it had to be changed

to fulfil the criteria. This changing was done by the supervisor Toke Rammer Nielsen. The

model was transferred in a Matlab file and the temperature calculations were modified. The

original model was also expanded with two weighting factors for the solar heat gain and an

additional load factor for the heat gain of appliances and people inside the room.

The two weighting factors are introduced as:

wa: weighting factor for the amount of solar energy gains to the air nodes

ww: weighting factor for the amount of solar energy gains to the wall nodes

wa + ww = 1 the total amount of solar energy gains splits between the two nodes

In addition, the influence of shading was included in the model as a possibility which can be

chosen.

23 Vinsim model, program at the IBE, DTU


Page: 33

The thermal model including solar gains used in this thesis is given in the next figure:

Figure 8: Thermal room model

The following equations will be used for this model:

LoadTTKTTUAQwdt

dTC wairwoutairsolaair

a +−∗−−∗−=∗ )()(*

Equation 20

)( wairwsolww

w TTKQwdt

dTC −∗+∗=∗

Equation 21

Ca, Cw: [ J/K ] Total heat capacity for air and wall. Tair, Tw, Tout: [ °C ] Temperatures for the air, wall and outside. UA: [ W/K ] Rooms total heat loss coefficient Kw: [ W/K ] Total heat transfer coefficient t: [ h ] Time Load: [ W ] Internal heat sources

The UA value is the sum of the room heat losses. The Kw value is the sum of the heat transfer

coefficients in the room and the Cw value is the sum of the room heat capacities. Qsol

considers the total transmitted solar radiation in the room in hourly values and the Load factor

gives the interior heat production.

The right side of the model, including the UA value of the room, is responsible for modelling

the heat losses and the left side, including the Kw and Cw values, is responsible for modelling

the heat storage ability.


Page: 34


The additional input data used for this model is given in the next table:

Name: Program term: Unit: Format: Description:Outdoor temperature: Tout [ °C ] row Temperature of the outsidetemperature_set: Tset [ °C ] value Set point of the minimum room temperatureload: Load [ W ] row Heat load in one room per hoursolarradiation_air: wa [ 1 ] value Solar radiation to air node factorsolarradiation_wall: ww [ 1 ] value Solar radiation to wall node factor Table 8: Indoor climate model variables

The outdoor temperature for the chosen climate is given in hourly values for a reference year.

Tset is the minimum temperature wanted in the room. The load is also given as a row with

hourly values for one year and gives a profile for the production of heat in the room from

people and appliances. The solar radiation is divided into two factors and the proportion can

be changed as mentioned in the theory.

The solutions of the solved differential equations (Equation 20,Equation 21)give results for

the heating and cooling demand, the maximum heating and cooling values, the air

temperature in the room and the use of the shading possibility.

• Mean temperature of the building: ( ) ( )

rooms

roomstempintempin

tempouttempout

midtemp

−

+

++

= 24*21

2*22*1

Equation 22

The different temperatures in the rooms are used to get a mean temperature value for the

whole building. Because the areas and therefore volumes of the rooms are equal, the mean

value can be calculated as shown in Equation 22. It should be mentioned that this is a simple

method of calculating a mean temperature of the building and it should probably be examined

further if it is feasible to do it this way.

In order to obtain the input data needed for this model and to make use of the output data, the

parts of the building have to be described in detail.

The input data for the model are given by the outer and inner walls, floor, ceiling, window,

solar shading and orientation. The output will be used for the heating, hot water, ventilation

and cooling systems.


Page: 35

2.6 Outer wall

2.6.1 Theory

Two different sizes of outer wall calculations will occur in this program. The outer wall of an

outer room will include the length and width of the room, multiplied with the height of the

room, and the outer wall of the inner room will include only the area, given by the length and

the height of the room. The window area has to be subtracted from the outer area to get the

right values. Entrance door(s) will not be included in the calculation.


The database input of the outer wall has to include the following data.

Name: Program term: Unit: Format: Description:name: string Name of the wall typedescription: string Description of the wall typeLC_time: toutwall [ year ] value Life time of the outer wallinsulation_thickness: [ m ] row Thickness of the insulationu_value: UAmoutwall [ W/(m² K) ] row U value of the outer wall per m²investmentcosts: Invoutwallm [ DKK/m² ] row Investment costs of the outer wall per m²maintenancecosts: Maintoutwallm [ DKK/(m² year) ] value Maintenance costs of the outer wall per m²linloss_tofloor: flinloss [ W/(m K) ] row Floor linear losses per mlinloss_towindow: wwlinloss [ W/(m K) ] row Window - Wall linear losses per mlinloss_toceiling: celinloss [ W/(m K) ] row Ceiling linear losses per mlinloss_tocorner: colinloss [ W/(m K) ] row Corner linear losses per mheattrans_wall: Kwouterwall [ W/(m² K) ] value Heat transfer coefficient outer wall per m²heatcap_wall: Cwouterwall [ J/(m² K) ] value Heat capacity of the outer wall per m²Table 9: Outer wall variables

Values for the six insulation levels, with a thickness ranging between 125 mm to 400 mm and

a corresponding U-value range between 0,25 to 0,09 Watt per m² outer wall area and Kelvin

are included in the database. Six different wall types are also given in the database, which will

already give 36 possible combinations just for the outer wall. The investment costs of an outer

wall therefore include the costs of the wall plus the additional costs for the insulation

thickness. The maintenance cost was found as a percentage of the investment cost in the

Danish reference book “Renovering & Drift – BRUTTO”24. This given data was used to

calculate the maintenance cost for the wall with the lowest insulation thickness and was then

added as a fixed value to the database. This is done because it is assumed that the

maintenance cost will only rely on repairing the outside of the outer wall, and therefore given

per m² of the outer wall area. The Kw and Cw values are also related to the outer wall area

and the different linear losses are given per metre of the connection.

24 Handbook for lifetimes and maintenance costs of building parts, Renovering & Drift – BRUTTO 1997


Page: 36

The different walls and most of the corresponding values are given from the report

“Udvikling af Klimaskærmskonstruktioner”, written at the Danish Technical University,

Institute for Building and Energy.25

Outer wall types: T1a, T1b and T1c

Figure 9: Two walls connected to the foundation Figure 10: Outline two walls house-type

As can be seen in the two figures above, the first group of three outer wall types consists of

two walls, connected to the foundation, on each side of the insulation. The inner part of the

outer wall of this construction can be made of bricks, pore concrete or light concrete.

Outer wall types: T2.1a, T2.1b and T2.1c

Figure 11: One wall connected to the foundation Figure 12: Outline one wall house-type

25 Udvikling af Klimaskærmskonstruktioner


Page: 37

As can be seen in the two figures above, the second group of three outer wall types consists of

one wall, which is used to carry the static load, connected to the foundation and a second wall,

which is only used as a protection for the insulation. The insulation is again located between

these walls. The inner part of the outer wall of this construction can again be made of bricks,

pore concrete or light concrete.

The calculations for the outer walls of the rooms will therefore be:

• UA value of the outer wall: [ ]( )widthRheightRAwinlengthRheightRUAmoutwallin/outUAoutwall(

***)

+−=

[ W/K ] Equation 23 The term in the brackets is only used if the calculation is for an outer room, because then the outer wall area will be bigger.

• Investment costs outer wall: [ ]( )( ) ** AwinwidthRlengthRheightRmInvoutwall(in/out)Invoutwall−+

=

[ money ] Equation 24 The term in the brackets is only used if the calculation is for an outer room, then the outer wall area will be bigger.

• Maintenance costs outer wall: [ ]( )( ) ** AwinwidthRlengthRheightRlmlMaintoutwa(in/out)llMaintoutwa

−+=

[ money/year ] Equation 25 The term in the brackets is only used if the calculation is for an outer room, then the outer wall area will be bigger.

The calculations for the outer wall of the whole building:

• Investment costs outer wall: ( ) loutInvoutwalroomslinInvoutwallInvoutwal

*44*

+−=

[ money ] Equation 26

• Maintenance costs outer wall: ( ) loutlMaintoutwaroomslinlMaintoutwallMaintoutwa

*44*

+−=

[ money/year ] Equation 27


Page: 38

2.7 Inner wall

2.7.1 Theory

Since there are two different sizes of outer wall area there will also be two different sizes of

inner wall area occurring in this program. The inner wall of an outer room will include the

length and width of the room, multiplied with the height of the room. The inner wall of the

inner room is given by the length and two times the width of the room multiplied by the

height. Doors are not included in the calculation. A reduction factor of 0,5 has to be used in

the investment calculations, because two rooms share one inner wall.


The database input of the inner wall has to include the following data.

Name: Program term: Unit: Format: Description:name: string Name of the wall typedescription: string Description of the wall typeLC_time: tinwall [ year ] value Life time of the inner wallinvestmentcosts: Invinwallm [ DKK/m² ] row Investment costs of the inner wall per m²maintenancecosts: Maintinwallm [ DKK/(m² year) ] value Maintenance costs of the inner wall per m²heattrans_wall: Kwinnerwall [ W/(m² K) ] value Heat transfer coefficient inner wall per m²heatcap_wall: Cwinnerwall [ J/(m² K) ] value Heat capacity of the inner wall per m²Table 10: Inner wall variables

To make it possible to choose between different kinds of inner walls, three different types are

considered in the database. It is assumed that the thickness of the inner wall will be 0,1 m and

that it can consist either of plaster (with mineral wool inside), pore concrete or bricks. This

leads of course to different values for the heat transfer coefficient and heat capacity. The

investment cost of an inner wall is therefore including the cost of building the wall. The

maintenance cost was found as a percentage of the investment cost in the Danish reference

book. This given data was used to calculate the maintenance cost for the wall, and then added

as a fixed value to the database. Therefore the value given for the maintenance cost is given

per m² of the inner wall area. The Kw and Cw values are also related to the inner wall area.

The calculations for the inner walls of the rooms will therefore be:

• Investment costs inner wall: [ ]( ) 5,0* **)/(

widthRlengthRheightRInvinwallmoutinInvinwall

+=

[ money ] Equation 28 The term in the brackets is only used if the calculation is for an inner room, then the inner wall area will be bigger.


Page: 39

• Maintenance costs inner wall: [ ]( ) 5,0* **

widthRlengthRheightRinwallmMaintinwallMaint

+=

[ money/year ] Equation 29 The term in the brackets is only used if the calculation is for an inner room, then the inner wall area will be bigger.

The calculations for the inner wall of the whole building are similar to the outer wall

calculations of the whole building.

2.8 Floor

2.8.1 Theory

The floor is a crucial part in a building, because people have the most “direct” contact with

this part.

If the floor is connected to the ground (ground floor) the considered U-value is multiplied

with a reduction factor of 0,6 because the ground temperature is different from the outdoor

temperature.26 In this case the floor_to_outerside_flag in the fixed variable database will have

to be set to “Yes”. If the calculations do not take place for a ground floor the flag has to be set

to “No “ and no U-value will be calculated. Then the costs will have to be split up, because

then this floor is also the ceiling of the room underneath. The heat capacity of the floor still

has to be added to the room heat capacity, because the storage ability is not lower.


The database input of the floor has to include the following data:

Name: Program term: Unit: Format: Description:name: string Name of the floor typedescription: string Description of the floor typeLC_time: tfloor [ year ] value Life time of the floorinsulation_thickness: [ m ] row Thickness of the insulationu_value: Uamfloor [ W/(m² K) ] row U value of the floor per m²investmentcosts: Invfloorm [ DKK/m² ] row Investment costs of the floor per m²maintenancecosts: Maintfloorm [ DKK/(m² year) ] value Maintenance costs of the floor per m²heattrans_wall: Kwfloor [ W/(m² K) ] value Heat transfer coefficient floor per m²heatcap_wall: Cwfloor [ J/(m² K) ] value Heat capacity of the floor per m²Table 11: Floor variables

26 Assumption was taken from the program Vinsim.


Page: 40

Values for the six insulation levels, with a thickness ranging between 70 mm to 300 mm and a

corresponding U-value range between 0,199 to 0,09 Watt per m² floor area and Kelvin are

included in the database. The investment cost of a floor is therefore including the cost of the

floor plus the additional cost for the insulation thickness. The maintenance cost was found as

a percentage of the investment cost in the Danish reference book. This given data was used to

calculate the maintenance cost for the floor with the lowest insulation thickness and was then

added as a fixed value to the database. This is done because it is assumed that the

maintenance cost will only rely on repairing the outside of the floor, and therefore given per

m² of the floor area. The Kw and Cw values are also related to the floor area.

For the use of the program only one floor is included in the database right now, but additional

floors can be added if wanted.

Figure 13: Outline floor type

As can be seen in Figure 13 this floor is built up in different layers, the one connected to the

ground consists of a granulate called “Leca concrete”. The other layers consist of a membrane

to avoid water and moisture, insulation and heavy concrete. The cover of the concrete is not

included in this calculation. The thickness of the insulation and therefore the U-value and

costs can be chosen between 6 possibilities.

The calculations for the floor of the rooms will therefore be: • UA value of the floor: 6,0** ARUAmfloorUAfloor =

[ W/K ] Equation 30 AR is the area of the room.

• Investment costs floor: [ ]5,0** ARInvfloormInvfloorR = [ money ] Equation 31

• Maintenance costs floor: [ ]0,5*AR*mMaintfloorRMaintfloor =

[ money/year ] Equation 32


Page: 41

The reduction factor 0,5 is used if the floor is not connected to the ground, since the floor of

the one room will be the ceiling of the room beneath.

The calculations for the floor of the whole building:

• Investment costs floor: roomsloorRfInvloorfInv *= [ money ] Equation 33

• Maintenance costs floor: roomsloorRfMaintloorfMaint *= [ money/year ] Equation 34

2.9 Ceiling

2.9.1 Theory

If they ceiling is connected to the outside (roof), the ceiling_to_outerside_flag in the fixed

variable database will have to be set to “Yes” and a U-value calculation will take place. If the

flag is set to “No” the ceiling of this floor is the bottom of the next floor and therefore the

costs will have to been split up.


The database input of the ceiling has to include the following data.

Name: Program term: Unit: Format: Description:name: string Name of the ceiling typedescription: string Description of the ceiling typeLC_time: tceiling [ year ] value Life time of the ceilinginsulation_thickness: [ m ] row Thickness of the insulationu_value: Uamceiling [ W/(m² K) ] row U value of the ceiling per m²investmentcosts: Invceilingm [ DKK/m² ] row Investment costs of the ceiling per m²maintenancecosts: Maintceilingm [ DKK/(m² year) ] value Maintenance costs of the ceiling per m²heattrans_wall: Kwceiling [ W/(m² K) ] value Heat transfer coefficient ceiling per m²heatcap_wall: Cwceiling [ J/(m² K) ] value Heat capacity of the ceiling per m²Table 12: Ceiling variables

Values for the eight insulation levels, with a thickness ranging between 250 mm to 600 mm

and a corresponding U-value range between 0,144 to 0,063 Watt per m² ceiling area and

Kelvin are included in the database. The investment cost of a ceiling is therefore including the

cost of the ceiling plus the additional cost for the insulation thickness. The maintenance cost

was found as a percentage of the investment cost in the Danish reference book. This given

data was used to calculate the maintenance cost for the ceiling with the lowest insulation

thickness and was then added as a fixed value to the database. This is done because it is

assumed that the maintenance cost will only rely on repairing the outside of the ceiling, and is


Page: 42

therefore given per m² of the ceiling area. The Kw and Cw values are also related to the

ceiling area.

For the use of the program only one ceiling is currently included in the database, but

additional ceilings can be added if wanted.

Figure 14: Outline ceiling type

As can be seen in Figure 14 this ceiling is built up in different layers; the insulation is the

uppermost layer. The other layers consist of an isolation foil, a wooden bar construction, also

filled with insulation, and plaster plates. The plaster plates are the sealing of the roof and they

can be seen from the inside of the room.

The calculations for the ceiling of the rooms will therefore be:

• UA value of the ceiling: AR*UAmceilingUAceiling = [ W/K ] Equation 35 AR is the area of the room.

• Investment costs ceiling: [ ]5,0** ARmInvceilingRInvceiling = [ money ] Equation 36

• Maintenance costs ceiling: [ ]0,5*AR*ngmMaintceilingRMaintceili = [ money/year ] Equation 37

The reduction factor 0,5 is used if the ceiling is not connected to the outer side. Because then

the ceiling of this room will be the floor of the room above.

The calculations of the investment and maintenance costs for the ceiling of the whole building

is the same as for the floor.


Page: 43

2.10 Window

2.10.1 Theory

Daylight is usually admitted into a building by means of windows or skylights; but these

windows also transmit heat, sound and air. So the design of windows for a building, called

fenestration, affects almost all the comfort variables. The provision of natural lighting in a

building must not be designed without also considering questions of artificial lighting,

heating, ventilation and sound control. As already mentioned in this thesis, daylight is not

included as a direct requirement or cost factor, and noise protection is also not included.

These requirements have to been checked later on by the engineer or architect or could be

implemented in the program later on. The next two figures show the basic principles of a

window in a building.

Figure 15: Heat loss through windows Figure 16: Solar heat gain

High performance windows should be an integral part of an energy – efficient building

envelope. A high performance window must have low heat losses and air leakages, but high

solar transmission. This allows windows, with regards to the heat losses and the orientation,

to make positive heat balances possible. In Denmark high performance windows can be

defined as any window system that has a U-value of 1,5 W/m² K or lower (Danish building

regulation requires 1,8 W/m² K!).27 For south facing windows with a U-value lower than 1

W/m² K a positive heat balance can be reached. For east and west facing windows heat gains

and losses compensate each other, and for north facing windows the energy balance is

27 Page 23 – 26, Solar energy houses


Page: 44

negative. A conclusion of these results could be to make the windows to the south as big as

possible, without neglecting solar shading, to the east and west a normal size, and the north

facing windows as small as possible.28

In addition, the windows should be designed for high solar and visible-light transmission and

low air leakages. Low heat-loss values are achieved through a combination of multiple

glazing, low-emissivity coatings, inert-gas fills, insulating edge spacers, low conductivity

frames and insulating shutters. High solar and daylight transmission is achieved by carefully

selecting glazing systems and coatings, and by minimising the frame area. Examples for a

reduction of window losses are:

• Radiative heat loss can be reduced by choosing glazing with low emissivity (low-E)

coating. Low-E coating can be applied to the inner surfaces of each glazing (on glass

planes or thin plastic films). These coating can reduce radiative heat transfer by up to

96%.

• Convective losses are reduced by replacing the air between the panes with an inert gas.

Argon is the cheapest and most common. Krypton, and more recently Xenon, are

sometimes used. They are more expensive, but provide lower convective losses and have

a much smaller optimum glazing spacing. The use of low-E coatings without gas fill is a

false economy, because decreased radiative heat transfer is offset by increased convective

heat transfer.

• The most straightforward approach to achieving a high-performance glazing system is to

use multiple panes of low-E films and gas fills, an example of how such a window looks

can be seen in the next figure. The number of radiative and convective transfers occurring

in series is thereby increased, reducing the overall U-value. Each extra layer, however,

reduces solar gains and adds to the bulk of the window unit. Multiple layers of inert gas

fills and low-E coatings are so effective that the glazing typically has a lower heat loss

than the frame and edge components of a window. Such an example of a window is

shown in the next figure.

28 Page 18, Niedrig-Energie-Häuser


Page: 45

Figure 17: Draft of a high performance window


The database input of the window has to include the following data.

Name: Program term: Unit: Format: Description:name: string Name of the windowdescription: string Description of the windowLC_time: twindow [ year ] value Life time of the windowglas_u_value: UVglas [ W/(m² K) ] value U value of the window glass per m²frame_u_value: UVframe [ W/(m² K) ] value U value of the window frame per m²g_value: gvalue [ 1 ] value G value of the window glass per m²frame_thickness: framet [ m ] value Thickness of the frameprice.fix_costs Invwindowfix [ DKK ] value Fixed investment costs of the windowprice.var_costs Invwindowm [ DKK/m² ] value Variable investment costs of the window per m²maintenancecosts: Maintwindowm [ % Investmentcosts ] value Maintenance costs in % of Investment costslinear_losses: gwlinloss [ W/(m K) ] value Glas - Window linear losses per mframe_factor: p [ 1 ] value Angular dependency factorTable 13: Window variables In the database the glass U-value and g-value is given per m² of glass area and the frame U-

value is given per m² of frame area. The g-value is the total solar energy transmittance and has

a value ranging between zero and one to specify how much energy can pass through the

window area. The unit of the given investment costs are related to the window area. The

maintenance cost of the window was found in the Danish reference book as a percentage of

investment cost. This percentage is used because the maintenance cost will also depend on the

size of the window area. The linear loss factor gives the value for the linear losses between

the glass and the frame. The frame factor p stands for the g-value dependency on the

incidence angle, which describes the nature of the window and influences the solar radiation.

The use of this factor can be seen in Equation 53. If no value is given for a window a factor 3

will be used in the database.29

29 The factor comes from the program Soldia


Page: 46

The difficulty in this part of the task lies in the fact that the window costs should be able to be

given as a function related to the window area. This demand was set up because the program

should be able to choose a window out of a wide range. This range was made with the

window percentage factor, which is defined in this thesis as the window area given as a

percentage of the outer wall area, given by the length and the height of the room. It was a

difficult way to get the needed values. Data given in the next figures and tables show the

exact development of the functions and the sources.

It was easy to get data for window glasses with different u-values (prices), but hard to get data

on different windows (including the frame and glass).

Therefore as can be seen in the next table and figure the prices for a window [frame (U-value:

1.5) and glass (U-value: 1)] from one company (Domus)30 were taken and compared with the

prices for a similar window glass (U-value: 1) from another company (Pilkington).31

Rationel: Domus window (glass U value 1.0) Pilkington: Klar float - Optima klar/neutralArea: Costs: Costs: Area: Glascosts: Windowcosts Costs:

excl. Work incl. Work excl. Work excl.Work incl. Work[ m² ] [ DKK ] [ DKK ] [ m² ] [ DKK ] [ DKK ] [ DKK ]0,346 1414 1886 0,09 336 1052 15040,46 1577 2058 0,16 376 1092 15490,58 1694 2185 0,25 459 1175 16390,69 1824 2324 0,36 623 1339 18120,774 1897 2403 0,49 760 1476 19590,877 1905 2419 0,64 922 1638 21341,055 2048 2577 0,81 1064 1780 22891,17 2132 2670 1 1241 1957 24811,25 2184 2728 1,21 1437 2153 26941,315 2241 2790 1,44 1645 2361 29201,41 2280 2837 1,69 1936 2652 32311,505 2381 2945 1,96 2209 2925 35261,565 2372 2941 2,25 2578 3294 39181,724 2464 3046 2,56 3092 3808 44571,815 2529 3118 2,89 3469 4185 4860

3,24 3847 4563 5266Final cost fucntion: Final cost fucntions:

Price =715,5 [DKK/m²] * area + 1274 [DKK] Price = 1186,6 [DKK/m²] * area + 1330 [DKK]

Table 14: Comparison of a “Domus” and a “Pilkington” window

30 Paper ”Vinduer & Døre” ; Company Rationel 31 Paper “Pilkingtion Brand Names”, Company Pilkington


Page: 47

C ost comparison (W in dow an d w in dow glass)

Price (glass) = 1090,5 [DKK/m²] * area + 182,27 [DKK]

Price (w indow ) = 715,5 [DKK/m²] * area + 1274 [DKK]

0

500

1000

1500

2000

2500

3000

3500

4000

0 0,5 1 1,5 2 2,5 3 3,5

W indow area [ m² ]

Cos

t [ D

KK

]

Pilkington Glass

Domus Frame + Glass

Linear (Pilkington Glass)

Linear (Domus Frame +Glass)

Figure 18: Comparison glass and frame costs (“Domus”) and glass costs (“Pilkington”)

With this method it was possible to calculate an average frame price, which was done by

comparing the costs for 1m² window area and leads to frame costs of 715 DKK per window.

This made it possible to create five different types of windows, where the frames are the same

but the glasses are different. Additional working costs for the installation of the window in the

wall had to be added to these costs, to make it comparable with the other prices used in this

program. An additional price function was created by values found in the Danish price book

[ 04.31.51.01-04 and 09-12)] and the results can be seen in the figure beneath this text.

Working Costs: Area: Areacosts:[ DKK ] [ m² ] [ DKK/m² ]

500 1 500,00500 1,35 370,37540 1,32 409,09620 1,65 375,76500 0,36 1388,89540 1 540,00540 1,44 375,00620 1,95 317,95

Installation working costs for windows

WorkCosts = 79,908 * area + 444,42

0

100

200

300

400

500

600

700

0 0,5 1 1,5 2 2,5 Window area [ m² ]

[ DK

K ]

Work cost per m² window

Linear (Work cost per m² window)

Table 15 : Working costs window Figure 19: Working costs window

This final cost functions for windows could now be calculated and has been given for five

different Types. Two of them can be found in table 12 and the other three can be found in the

following:


Page: 48

Pilkington: Klar float - Energi klar Pilkington: Klar float - Klar float Pilkington: Klar float - Energi superArea: Glascosts: Windowcosts Costs: Glascosts: Windowcosts Costs: Glascosts: Windowcosts Costs:

excl. Work excl.Work incl. Work excl. Work excl.Work incl. Work excl. Work excl.Work incl. Work[ m² ] [ DKK ] [ DKK ] [ DKK ] [ DKK ] [ DKK ] [ DKK ] [ DKK ] [ DKK ] [ DKK ]0,09 192 908 1360 107 823 1275 202 918 13700,16 215 931 1388 119 835 1292 227 943 14000,25 262 978 1442 146 862 1326 277 993 14570,36 356 1072 1545 198 914 1387 377 1093 15660,49 434 1150 1634 240 956 1440 458 1174 16580,64 527 1243 1739 293 1009 1505 557 1273 17690,81 608 1324 1833 339 1055 1564 642 1358 18671 709 1425 1949 393 1109 1633 748 1464 1988

1,21 821 1537 2078 456 1172 1713 867 1583 21241,44 940 1656 2215 522 1238 1797 993 1709 22681,69 1106 1822 2401 615 1331 1910 1168 1884 24631,96 1262 1978 2579 701 1417 2018 1333 2049 26502,25 1473 2189 2813 818 1534 2158 1556 2272 28962,56 1767 2483 3132 982 1698 2347 1866 2582 32312,89 1982 2698 3373 1101 1817 2492 2092 2808 34833,24 2198 2914 3617 1221 1937 2640 2322 3038 3741

Final cost fucntion: Final cost fucntion: Final cost fucntions:Price = 712 [DKK/m²] * area + 1257 [DKK] Price = 431 [DKK/m²] * area + 1214 [DKK] Price = 748 [DKK/m²] * area + 1262 [DKK]

Table 16: Comparison “Pilkington” windows

The frame values were assumed to be 1,5 W/m² K for the U-value, 11,5 cm for the thickness

of the frame and 0,06 W/m K for the linear losses between the glass and the frame. These

values were found in the data given for the “Domus” window from the company Rationel.

This window type has a wooden frame and it was also assumed that only the whole window

area is surrounded with a frame.

Therefore the difference comes from the different glasses, fillings and coatings used, which

leads to a different value for the U- and g-value of the glass and daylight transmittance factor.

These values were calculated with the Danish program “Glas 98”32 and are given in the

following Table.

Name: U-value: Daylight transmittance: g-value:[ W/(m² K) ] [ % ] [ 1 ]

Pilkington: Klar float - Energi klar: 1,3 77 0,66Pilkington: Klar float - Optima klar: 1,1 65 0,54Pilkington: Klar float - Optima neutral: 1,3 56 0,61Pilkington: Klar float - Klar float: 2,8 82 0,76Pilkington: Klar float - Energi super: 1,1 75 0,59 Table 17: U-values, Daylight transmittance factors and g-values of “Pilkington” windows

This assumption made it possible to get the desired functions for five different windows, with

reasonably realistic and comparable prices and figures. The next figure gives an example for

this price function, which is used for the window database in this thesis.

32 Glas 98, Danish Program


Page: 49

Pilkington Windows

Price Klar float - Klar float = 431,21 * area + 1214,1

Price Klar float - Energi super = 747,76 * area + 1262,5

0

500

1000

1500

2000

2500

3000

3500

4000

0 0,5 1 1,5 2 2,5 3 3,5

Area [ m² ]

[ DK

K ]

Klar float - Klar float

Klar float - Energi super

Linear (Klar float - Klar float)

Linear (Klar float - Energi super)

Figure 20: Total costs comparison of a double klar-float and a klar-float energi-super “Pilkington” window Because it is not easy to implement the window part in the optimisation program, it will be

assumed that the same windows are used for each room in the building. This decision was

made due to the lack of time for this project, but could and maybe should be changed in

future.

The basic calculations of the window for a room will therefore be:

• Area of the window:

=

100** windowperclengthRheightRAwin

[ m² ] Equation 38 The window area is given as a percentage of the outer wall area, given by the length and height of the room.

• Width of the window: Awinswin = [ m ] Equation 39

• Width of the glass: frametswinsglas *2−= [ m ] Equation 40

• Length of the glass: sglashglasslengt *4= [ m ] Equation 41

• Area of the glass: ( )2sglasAglas = [ m² ] Equation 42


Page: 50

• Area of the frame: AglasAwinAframe −= [ m² ] Equation 43

• UA value of the window: gwlinlosshglasslengt

UVframeAframeUVglasAglasUAwin*

**+

+=

[ W/K ] Equation 44

• Investment costs window: *ARInvwindowm

ixInvwindowfInvwindowR+

=

[ money ] Equation 45 The investment costs for a window are depending on the window area.

• Maintenance costs window:

=

100* windowmMaintInvwindowRindowRwMaint

[ money/year ] Equation 46 The maintenance costs are given as percentage of the investment costs, because the window area is changing.

For the whole building the costs of the windows will again be the cost of one window

multiplied with the number of rooms.

2.11 Other basic calculations of the rooms


As mentioned in the indoor climate model chapter, the input for the heat capacities and heat

transfer coefficients have to be calculated by summing the different values of the room parts.

In addition the overall U-values of the rooms, including the existing linear losses, need to be

calculated.

It is important to know the heat capacity value of the air which is calculated in the next

equation. The volume related air heat capacity value (Cam, [ J/(K m³) ]) has to be given as

input data for this calculation from the database.

• Heat capacity of air in the room: VRCamCa *= [ J/K ] Equation 47

The heat capacity of the whole room also has to be calculated. The values for the different

parts are given per m² and therefore have to be multiplied with the corresponding areas.


Page: 51

• Calculation of the room heat capacity:

[ ]( )( )[ ]( )

ARCwceilingARCwfloor2or 1widthRlenghtRheightRlCwinnerwal

AwinwidthRlengthRheightRlCwouterwalCw

** ***

**

++++

−+=

[ J/K ] Equation 4833 If the calculation is for an outer room the width of the room has to be multiplied with the height and the Cw value of the outer wall. If it is for an inner room the width has to be multiplied twice with the inner wall Cw value and the height.

The values for the heat transfer coefficient are given per m² and also have to be multiplied

with the corresponding areas. It can be seen that the heat transfer coefficients for the inner

wall, the floor and the ceiling are always considered for the entire wall. This assumption was

made after a discussion with the supervisor.

• Calculation of the room heat transfer coefficient:

[ ]( )( )

[ ]( )

AR

Kwceiling

AR

Kwfloor

2or 1widthRlengthRheightR

lKwinnerwal

AwinwidthRlengthRheightR

lKwouterwal

Kw

*113,0

1*113,0

1

***113,0

1

**113,0

1

++

++

+

++

−+

+=

[ W/K ] Equation 4934 If the calculation is for an outer room the width of the room has to be multiplied with the height and the Kw value of the outer wall. If it is for an inner room the width has to be multiplied twice with the inner wall Kw value and the height.

All linear losses are multiplied with the corresponding lengths and summed up to be included

in a U-value for the whole room. For the heat transfer coefficients of the inner wall, floor and

ceiling the entire values are considered and multiplied with the corresponding lengths. This

was also done after discussion with the supervisor and can of course lead to further

discussions.

33 Equation was given by the supervisor 34 Equation was given by the supervisor


Page: 52

• Calculation of the room linear losses:

[ ][ ]( )[ ]( )

wwlinlossswinwidthRlenghtRcelinloss

widthRlengthRflinloss3or 2*heightR*colinlossUAlinloss

**4*

*

+++++

=

[ W/K ] Equation 50 The factor 2 is used for an inner room and the factor 3 is used for an outer room. The width is only added to the floor and ceiling linear losses, if it is an outer room.

The total UA-value is calculated by summing up the UA-values of the floor, ceiling, outer

wall windows and linear losses.

2.12 Solar shading35

2.12.1 Theory

Since ordinary windows have traditionally been the primary source of heat gain and daylight,

especially in the summer any effort to shade them has had great benefits in terms of comfort

and energy use. Sun controls are parts of a building that help to prevent excessive heat gain

and glare caused by direct sunshine.

The best place to shade a window is on the outside, before the sun strikes the window: • Using landscape elements to provide shade is probably the best, because nothing can be

much better at providing a cool shade in the summer than a great broad-leafed tree. In

addition to shading the building from direct sun, trees have been found to reduce the

temperature of air immediately around them by as much as 5°C below the temperature of

the surrounding air due to the evaporation of moisture. A window shaded with a high tree

can have full shade in the summer and trees and bushes can provide strategic shade from

low east or west sun angle which is extremely difficult to shade architecturally.

• The most common artificial outside shading device is the fixed overhang. For south-

facing windows, overhangs can be sized to block out much of the summer sun but still

permit lower-angled winter sun to enter. Other exterior devices include grills, awnings,

roll down shutters, canopies, Bermuda shutters, and bamboo shades. The choice of the

shade type is often distinctly regional, based on local traditions.

35 Pages 127-138, Residential Windows


Page: 53

Figure 21: Shading by a tree Figure 22: Shading by an overhang

The shading device can also be installed inside the building: • Internal controls such as blinds give protection against glare and direct radiation. The

system is less effective than controls outside the glass because the blind will absorb some

solar heat and re-emit this heat into the room. Examples are curtains and internal shutters.

• Special glasses are available which prevent the transmission of most heat radiation with

only some loss of light transmission. A similar effect is given by special film which sticks

onto plain glass.


The input in the program for the calculation of the shading has to include the following

values:

Name: Program term: Unit: Format: Description:name: string Name of the shadingdescription: string Description of the shadingLC_time: tshading [ year ] value Life time of the shadingminimum_shading_factor: Smin [ 1 ] value Minimum shading coefficientprice.fix_costs Invshadingfix [ DKK ] value Fixed investment costs for shadingprice.var_costs Invshadingm [ DKK/m² ] value Variable investment costs of the shading per m²maintenancecosts: Maintshadingm [ % ] value Maintenance costs of the shadingTable 18: Shading variables

The most important factor needed for this program will be the minimum shading factor. This

factor gives the value [0 to 1] corresponding to the minimum amount of solar radiation that

can be blocked. A value of 1 means that none of the radiation will be blocked, and 0 means

that all radiation can be blocked from the shading device. The investment costs are related to

the window area and the maintenance costs are given as a percentage of the investment costs.


Page: 54

The calculations in the program will therefore be:

• Investment costs room shading: AwinmInvshading

fixInvshadingoutinInvshading*

)/( +=


For the whole building the costs will be:

• Investment costs window: ( ) outInvshadingroomsinInvshadingInvshading

*44* +−=


The maintenance costs for the shading system are calculated as a percentage of investment

costs per year.

2.13 Orientation

2.13.1 Theory

The solar heat gained in a building by radiation from the sun depends on the following

factors:36

• The geographical latitude of the site, which determines the height of the sun in the sky.

• The orientation of the building on the site, such as whether rooms are facing north or

south.

• The season in the year, which also affects the height of the sun in the sky.

• The local cloud conditions, which can block solar radiation.

• The angles between the sun and the building surfaces, because maximum gain occurs

when surfaces are at right angles to the rays of the sun.

• The nature of the window glass and whether it absorbs or reflects any radiation.

• The nature of the roof and walls, because heavyweight materials behave differently to

lightweight materials.

36 Page 71, Environmental Science in Building


Page: 55

Figure 23: Height of the sun throughout a year in Denmark

In Figure 23 the height of the sun is given for some specific days in Denmark. It is clear, that

if the latitude is given by the chosen country (for this thesis values for Denmark are used), the

orientation of the building will have a big influence on the solar heat gains. Therefore the

orientation was desired to be included in the program as an option. It is clear that it will of

course not always be possible to choose the orientation of the building, but the program

should be able to handle it, if needed. For example the solar radiation values on a 90° wall per

year are given for this Danish sun profile given before.

Total solar radiation on a 90° wall:

0

100

200

300

400

500

600

700

800

900

1000

South East West NorthOrientation

[ kW

h / m

² ]

Figure 24: Total solar radiation on a 90° wall


Page: 56

Orientation: Total solar radiation on a 90° wall: Difference:[ kWh / m² ] [ % ]

South 900 0East 622 -31West 693 -23North 330 -63

Table 19: Total solar radiation on a 90° wall

The results of the program soldia37 show that there is, as expected, a high dependency on the

orientation of the building (e.g. direction of the window).


The data for the direction the room is facing to, has to be given in the database as an

additional input to calculate the Solar radiation (Qsun).

Name: Program term Unit: Format: Descrip tion:direction1 direction1 [ ] matrix Solar data base in one directiondirection2 direction2 [ ] matrix Solar data base in the opposite direction Table 20: Orientation variables

For each of the main orientations, south, north, east and west different matrixes containing

solar radiation data are given. It is arranged, that if direction1 is facing to the south, direction2

is facing to the north (combination 1) and if direction1 is facing to the east, direction2 is

facing to the west (combination 2). It is currently only possible to choose between these two

orientation combinations.

The direction vectors are build up as followed:

Direction vector: Hour: Diffuse solar radiation: Reflected solar radiaton: Direct solar radiation: Solar radiation angle:[ 1 ] [ W/m² ] [ W/m² ] [ W/m² ] [ ° ]

Each direction matrix consists of 8760 rows with these corresponding hourly values.

Later on the program could be expanded to be able to choose between more orientations.

( ) ( )

( )

−++

−

=p

p

radiation solar reflected radiation solar diffuse

angle radiationsolar radiation solar direct

gvalueAglasQsun

36060*tan1*

360*tan1*

**π

π

Equation 53: Calculation of the total transmitted solar radiation in hourly values from the program “Soldia”

37 Soldia program, IBE, DTU


Page: 57

This equation calculates the total transmitted solar radiation in hourly values. This equation

was provided by the supervisor, and was taken from the Danish computer program “Soldia”,

developed at the Institute for Buildings and Energy, Technical University of Denmark.38

The nature of the window and influence on the solar radiation is included in the frame

condition or angular dependency factor (p) and it is assumed that the window will be set in at

an angle of 90°.

2.14 Heating System

2.14.1 Theory39

If heat gains in a room are too few to keep the indoor climate acceptable, additional heating

will be needed.

In principle there are three different kinds of heating systems in use.

• The first possibility is to use a single room heater, which is placed and designed only for

this room.

• The second possibility is to use a central heating system in a building. This heating system

is commonly placed in the cellar of a building.

• The third possibility is to use a district heating system, where some or most buildings are

supplied with heat from a heating system which is built in a central place.

a ) Single room heating system:

The advantage of this system is that the heat is directly produced on site and an expensive

distribution system is not needed. Therefore single heaters are often easy to install and have

less expensive installation costs. The lower efficiency can lead to a higher fuel consumption

and therefore higher operating costs.

In addition, the control of such a heating system is hard to adjust and therefore quite

uncomfortable for the user. Examples of such a system are single gas or oil heaters, tiled

stoves or electrical heating.

38 Soldia program, IBE, DTU 39 Diplomarbeit TU-Graz


Page: 58

b ) Central heating:

The main characteristic of such a system is that the heat is produced on a site which lies

outside of the heated rooms. The heat can be transferred from this place to the needed areas

by water or air distribution system. The advantage of such systems is that small room heating

systems are not necessary - central heating is therefore more comfortable. The efficiency of a

central heating system is also better, which means less fuel costs and therefore also less

environmental pollution. Examples of such a system are gas, oil or coal heaters, but also

electricity or the environmentally friendly biomass heating systems.

c ) District heating:

In district heating systems water is heated on a central site, such as power or incineration

plants and then transported via pipes to the consumers. The big advantage of this system is the

continuous availability of the heat and that people do not have to take care of the heat

production. In case of oil, coal and wood heating systems the replacement by a district heating

system leads to a reduction in the space needed in the building. Another advantage is that heat

produced due to other processes such as electricity production can be used in such systems.

This leads to higher efficiency for these production sites, up to 90%, and also reduces the

environmental pollution. However, high costs of the heat distribution system have to be

considered.


The input data from the database has to include:

Name: Program term: Unit: Format: Description:name: string Name of the heating systemdescription: string Description of the heating systemLC_time: theating [ year ] value Life time of the heating systemfueltype hsyfuel [ ene,gas,oil,dih ] string Fuel type of the heating systemefficiency eheatingsy [ % ] value Efficiency of the heating systemprice.fix_costs Invheatsyfix [ DKK/m² ] value Fixed investment costs for the heating systemprice.var_costs Invheatsym [ (DKK/m²)/m² ] value Variable investment costs of the heating systemmaintenancecosts: Maintheatsym [ % ] value Maintenance costs of the heating systemgas_fixprice: gasfix [ DKK/year ] value Fixed price for gasgas_price: gas [ DKK/kWh ] value Variable price for gasoil_fixprice: oilfix [ DKK/year ] value Fixed price for oiloil_price: oil [ DKK/kWh ] value Variable price for oilelectricity_price: eprice [ DKK/kWh ] value Variable price for electricityelectricity_fixprice_night: epricefixnight [ DKK/year ] value Fixed price for electricity during nighttimeelectricity_price_night: epricenight [ DKK/kWh ] value Variable price for electricity during nighttimedistrictheat_price: districth [ DKK/kWh ] value Variable price for district heatingdistrictheat_fixprice: districthfix [ DKK/(kW year) ] value Fixed price for district heatingTable 21: Heating variables


Page: 59

It can be seen that the heating system costs are related to the area of the building. This is

probably not the best way to consider this, but the only one where comparable prices could be

found. A price function using values from the Danish reference book was created as follow: Type: Area: Price: Formula:

[ m² ] [ DKK/m² ]Detached House 80 582 Price = -0,6143 * area + 626,57

120 546200 506

Traditional heating system: Terraced House 80 500 Price = -0,5482 * area + 539,43Oil or Gas: 120 467

200 432Apartment house: 80 401 Price = -0,2196 * area + 417,29

120 389200 374

Detached House 80 508 Price = -0,5482 * area + 547,43120 475200 440

Traditional heating system: Terraced House 80 437 Price = -0,5089 * area + 473,86District Heating: 120 407

200 374Apartment house: 80 365 Price = -0,4429 * area + 396,71

120 338200 310

Traditional heating system: Office building 500 386 Price = -0,0546 * area + 405Oil or Gas: 1000 338

2000 300Traditional heating system: Office building 500 328 Price = -0,047 * area + 344,5

District Heating: 1000 2872000 254

Table 22: Price function for heating systems per m² floor area

The heating system defines which fuel type is chosen. A lot of variables for the different

prices are needed. Because gas, oil and district heating are the most common forms in

Denmark, only values for these categories were taken under consideration. The electricity

prices will be needed for the ventilation or cooling system. However, as a source for heating,

electricity it is not so often used in Denmark.40 It will be possible to add other variables to the

program in the future.

Energy prices:41

Change Rates: 1 DKK = 100 øre = 1,85 ÖS = 0,135 € Gas: Heating price: 202 øre / m³ 1 m³ Gas = 4,2 kWh 48 øre / kWh

Extra costs for heating: 340 DKK DH: Water price: 350 DKK / MWh 35 øre / kWh Connection fee: 113 DKK / kW year Electricity: Normal price 124 øre / kWh Night price: 98 øre / kWh (Time: 2130 – 0630)

Extra costs for two counter: 504 DKK

40 Page 27, Energistatitik 98 41 htttp://www.kb.kk.dk, Københavns Energi


Page: 60

Oil:42 Heating oil price: 4526 DKK / m³ 45 øre / kWh

All prices are given excluding taxes. The choice of the fuel type defines which variable and

fixed price for heating is used in the calculation. It should be mentioned here that for the

district heating system the fixed price will rely on the maximum kW needed by the heating

system. Therefore the maximum building heating consumption will have to be calculated by

summing the maximum heating demand from the different rooms.

The investment costs are calculated as follow:

• Investment costs heating system: ( ) ABABInvheatsymixInvheatsyfInvheatsy

**+=


The maintenance cost for the heating system are calculated as a percentage of the investment

cost per year.

The heating demand of the whole building will be the sum of the heating of the rooms and is

given as an output from the indoor climate model. The real heating demand will have to

consider the efficiency of the heating system.

• Heating consumption:

=

100eheatingsy

Heatinghconsum

[ kWh/year ] Equation 55 To receive the real consumption, the heating demand has to be divided by the efficiency of the heating system.

2.15 Hot water system43

2.15.1 Theory

For the energy costs it will be important to include the production of hot water needed in this

building. In locations with high solar irradiation, very simple systems combining the function

of collecting and storing solar energy are feasible. High utilisation of solar energy with for

42 http://www.q8.dk,Oil company 43 Page 45-47, Solar energy houses


Page: 61

example collectors on the roof, requires distribution within the building. For hot water

production a water based collector-type is mostly used.

In this project the hot water can either be produced with the normal heating system or by a

mixture of the heating system and a solar hot water system.


The input data from the database has to include: Name: Program term: Unit: Format: Description:

name: string Name of the solar hot water systemdescription: string Description of the solar hot water systemLC_time: tsolsy [ year ] value Life time of the solar hot water systemprice.fix_costs Invsolsyfix [ DKK ] value Fixed investment costs for the solar hot water systemprice.var_costs Invsolsym [ DKK/m² ] value Variable investment costs of the solar hot water system per m²maintenancecosts: Maintsolsym [ % ] value Maintenance costs of the solar hot water systemDaily water consumption: Wconsum [ l/day ] value Water consumption of the building per dayTemp. Difference water: DT [ °C ] value Temperature difference between cold and hot waterSolar share factor: solarshare [ % ] row Yearly share of hot water produced by solar energyNet area factor: nettoareafac [ (m² day)/l ] row Net area factor of the solar hot water systemTable 23: Hot water system variables

The investment costs are related to the size of the solar area. The way this relationship is

defined can be seen in the description below.

The data used for these calculations relies on the experience of a solar hot water system

installation company44 and is therefore less scientific but more practical.

First of all it is important to define how much hot water and therefore energy is needed. The

next table gives values which can be used for the calculation of the water consumption.

Name: Mean water consumption:[ l/(day*person) ]

Residential building: 45Office building: 15 Table 24: Mean water consumption

The temperature difference of the water is important for the energy consumption. It is

assumed that the water is heated up by 50°45. This leads to the mathematical expression:

• Hot water energy consumption: TWconsumQw ∆= *1000

16,1**365

[ kWh/year ] Equation 5646 The factor ∆T is used for the temperature difference between the cold and the hot water.

44 Ernst Grim Ges. m. b. H, Melk 45 Page 13, Diplomarbeit Türk Jürgen, TU Graz 46 Page 13, Diplomarbeit Türk Jürgen, TU Graz


Page: 62

The Qw is the yearly energy consumption value to produce the amount of hot water needed.

The amount of the energy which has to be produced by the normal heating system is called

hwconsum and depends on the yearly solar cover factor (solarshare) and of course on the

efficiency of the heating system.

• Real hot water energy consumption:

−

=

100

*100

1

eheatingsy

Qwsolarshare

hwconsum

[ kWh/year ] Equation 57

Data for the required solar area needed for the different yearly solar cover factors was also

given in these information paper from the Ernst Grim Ges. m. b.H. Equations for the different

cover factors could be created with these numbers.

Solar share factor: Mean water consumption: Solar Area (Sun): Equation:[ % ] [ l/day ] [ m² ]30 0 0 Solar Area = 0,016 * Watercons.

200 3,2400 6,4

40 0 0 Solar Area = 0,02 * Watercons.200 4400 8

50 0 0 Solar Area = 0,025 * Watercons.200 5400 10

60 0 0 Solar Area = 0,031 * Watercons.200 6,2400 12,4

70 0 0 Solar Area = 0,042 * Watercons.200 8,4400 16,8

Table 25: Solar area dependency on the water consumption and solar share factor for the SUN 2 system

Because all these factors are only valid for the solar system SUN 2, an additional factor has to

be found for other solar systems. This was enabled with the introduction of a reduction factor.

This factor reduces the size of the solar area needed in relation to the average yearly

production factor of the SUN 2 solar system.

Name: Average Yearly production factor: Reduction factor:[ kW/(m² solar area) ]

SUN 2: 400 1SUN 3: 410 0,976SUN-GEO: 480 0,833SUN-VAC: 580 0,69

Table 26: Reduction factors of different solar systems


Page: 63

This made it possible to use different types of solar systems in the program. The final

equations and reduction factors are given in the next table.

TYPE: SUN 2: SUN 3: SUN-GEO: SUN-VAC:

Average Yearly production factor: [ kW/m² ] Original Equation: 400 410 480 580Reduction factor: 1,0000 0,9756 0,8333 0,6896Solar share factor (30%): [ (m² day)/ l ] Solar Area = 0,016 * Wcon. 0,0160 0,0156 0,0133 0,0110Solar share factor (40%): [ (m² day)/ l ] Solar Area = 0,02 * Wcon. 0,0200 0,0195 0,0167 0,0138Solar share factor (50%): [ (m² day)/ l ] Solar Area = 0,025 * Wcon. 0,0250 0,0244 0,0208 0,0173Solar share factor (60%): [ (m² day)/ l ] Solar Area = 0,031 * Wcon. 0,0310 0,0303 0,0258 0,0214Solar share factor (70%): [ (m² day)/ l ] Solar Area = 0,042 * Wcon. 0,0420 0,4100 0,0350 0,0290Table 27: Solar area dependency on the reduced water consumption and solar share factors

These solar area factors were multiplied with the corresponding reduction factors to get the

net area factors, and these factors were placed in the database. With these factors it is possible

to calculate the corresponding solar area for each solar system.

The net prices for the installation were also found in the given paper and were compared with

net prices found in the Danish price book to see if these systems are comparable.

Solar heating Comparison

PriceDK = 1318,2 * area + 12000PriceSUN2 = 1982 * area + 5531,5

PriceSUN-GEO = 2094,6 * area + 7333,3

PriceSUN3 = 2162,2 * area + 5891,9

PriceSUN-VAC = 3891,9 * area + 6432,4

0

5000

10000

15000

20000

25000

30000

35000

40000

0 2 4 6 8 10 12

Area [m²]

Pric

e [D

KK

]

SUN2DanskSUN3SUN-GEOSUN-VACLinear (Dansk)Linear (SUN2)Linear (SUN-GEO)Linear (SUN3)Linear (SUN-VAC)

Figure 25: Comparison of prices for solar heating systems

As can be seen the prices for these systems should be able to be used in this thesis. It is clear

that in reality it is not possible to use all solar area fractions claimed by this program. It was

not possible to include this in a different way and if a fraction is returned the next higher or

lower possible area could be chosen.


Page: 64

The values for the cost of the solar system are therefore:

• Investment costs solar hot w. system: InvsolsymWconsumacnettoareaf

xInvsolsyfiInvsolsy**

+=


The maintenance costs for the solar hot water system are calculated as a percentage of

investment costs per year.

2.16 Ventilation

2.16.1 Theory47

In any occupied space, ventilation is necessary to provide oxygen and to remove

contaminated air. Fresh air contains 21% oxygen and 0,04% carbon dioxide, while exhaled air

contains about 16% oxygen and 4% carbon dioxide. The body requires a constant supply of

oxygen but the air would be unacceptable well before there is a danger to life. It is therefore

necessary to consider the rate of ventilation as a comfort requirement in buildings.

The rate of ventilation has also a great effect on the part of ventilation heat losses in buildings.

Typical design temperatures and infiltration rates:

Table 2848: Design temperatures and inflation rates for Buildings

The air outside a building usually has a much lower moisture content than the air inside,

because cool air cannot hold as much moisture as warm air. Ventilating a building therefore

reduces the risk of condensation. It is theoretically possible to avoid all condensation by

adequate ventilation but as the ventilation rate increases, the heat loss in the staled air also

increases.

47 Page Pages 65 – 97, Environmental Science in Building 48 Page 60, Table 3.3, Environmental Science in Building


Page: 65

The air change needed can either be supplied by a high infiltration rate, which requires a less

air-tight building and therefore produces higher heat losses. Alternatively, a higher ventilation

rate and a low infiltration rate can be used in a house, which requires an air-tight building and

gives the possibility of saving energy with a heat recovery system.

The natural ventilation rates in dwellings have been decreasing over the years from typically

four air changes per hour to less than one air change per hour. The construction of modern

doors, windows, and floors usually provide better seals against the entry of outside air than in

the past.

The warm air released from a building contains valuable heat energy, even if the air is

considered “stale” for ventilation purposes. The heat lost during the opening of doors and

windows becomes a significant area of energy conservation, especially when the cladding of

buildings is insulated to high standards. These ventilation losses are reduced by better seals in

the construction of the building, by air-sealed door lobbies, and the use of controlled

ventilation. Some of the heat contained in exhausted air can be recovered by a heat exchanger.

There are two main different types of heat exchangers used in order to increase the thermal

efficiency.49

• Plate heat exchanger:

For dwellings, cross-flow and counter-flow plate heat exchangers are the most common type

of heat-recovery systems. Plate heat exchangers are fairly simple so-called static devices, with

no moving parts, and thus require minimal maintenance, chiefly cleaning of filters. Driven by

one or two fans, supply and exhaust air passes through the unit on either side of a series of

thin plates, across which heat is exchanged. Among the disadvantages are that balanced

ventilation systems require a lot of ducting because the air supply and extraction need to be

brought together, while the supply and exhaust grills need to be placed sufficiently far apart to

avoid the re-entry of some of the exhaust air. The systems are also sensitive to occupant

behaviour, for example opening of windows. It is possible to construct plate heat exchangers

with a thermal efficiency of close to 80-85%.

49 Pages 31-34, Solar Energy Houses


Page: 66

Figure 26: Plate heat exchanger

• Thermal wheels:

A thermal wheel consists of a revolving cylinder divided into a number of segments packed

with a coarsely knitted metal mesh. It operates by rotating between 10 and 20 revolutions per

minute, picking up heat from the warmer exhaust air stream and discharging it to the cooler

supply side. These wheels have higher efficiencies than plate heat exchanger units, typically

80-90%. Generally, thermal wheels are not used very much in dwellings, one of the major

reasons being the risk of cross-contamination, another being cost.

Figure 27: Thermal wheel


Page: 67



Name: Program term: Unit: Format: Description:name: string Name of the ventilation systemdescription: string Description of the ventilation systemLC_time: tvent [ year ] value Life time of the ventilation systeminvestmentcosts: Invventm [ DKK/(m³/s) ] value Investment costs of the ventilation system per m³/smaintenancecosts: Maintventm [ % ] value Maintenance costs of the ventilation systempressure_drop ventilation appliance: Dpsystem [ pa ] value Pressure drop of the ventilation appliancepressure_drop: Dpduct [ pa ] value Pressure drop of the ductingheatcap_air: Cam [ J/(K m³) ] value Heat capacity of the air per m³mech_ventrate: n [ 1/h ] value Mechanical ventilation rateinfilrate_with_ventilation: infil [ 1/h ] value Infiltration rateinfilrate_without_ventilation: infil [ 1/h ] value Infiltration ratesystem efficiency: eventsy [ % ] value Efficiency of the ventilation systemheat recovery efficiency: eheatrec [ % ] value Efficiency of the heat recoveryTable 29: Ventilation system variables

As can be seen the investment costs of the ventilation system are related to the volume change

per second, since this was the only method found to relate these two terms. The maintenance

costs are given again in percentage form, because of the changing investment costs. The

pressure drop of the whole system is dependent on the pressure drop of both the ducting and

the ventilation appliances, and influences the system efficiency (eventsy). The efficiency of

the heat recovery (eheatrec) is an important factor for the heat consumption. The way the

electricity consumption of the ventilation system is calculated can be seen in this chapter.

The next equation was given in the indoor model and was therefore used to calculate the

losses caused by the ventilation. As it can be seen the ventilation losses can be added to the

building UA-value.

• Additional ventilation UA-value: ( )( )3600

**1* VneheatrecinfilCamUAv−+

=

[ W/K ] Equation 59

The value for the heat capacity of the air is 1213 J/(K m³) at 20 degree Celsius.50

It was hard to find data for ventilation systems, therefore data from the Master Thesis

“Forwarming af Ventilationsluft”51 of the supervisor was chosen to be used.

50 Page 20, Environmental Science in Building 51 Pages 44, 49,50; “Forvarming af Ventilationsluft”


Page: 68

Type: Efficiency heat recovery: Motor effect: Number Motors: Costs:[ % ] [ W ] [ 1 ] [ DKK ]

Exhausto: 66 40 1 40895Genvex: 63 80 2 34675Temovex: 83 64 2 40700 Table 30: Motor effect and heat recovery efficiency of three ventilation systems

The values given in Table 30 come from the above-mentioned thesis and are used to calculate

usable values for this thesis. The motor effect can be used to calculate the relationship

between the system efficiency and electricity consumption. The electricity consumption

depends on the pressure drop of the ventilation system.

The data in the thesis of my supervisor [Nielsen, Toke Rammer] was given for a room with a

volume of 300m³ and an air change rate of 0,5 1/h. A pressure drop of 200 pa was given for

each of the exhaust and supply air ventilation system parts.

The electricity needed for the ventilation system can be calculated as follow:

• Electricity consumption:

∆=

100

***2eventsy

pVnPm

[ W ] Equation 60 The factor 2 is used because only one part of the ventilation system is used for the pressure

drop. In other words, if only one motor is used this gives a higher system efficiency. It was

necessary to make the given prices comparable, therefore they were divided by the volume

change per second.

Type: Efficiency Ventilation system: Costs:[ % ] [ DKK/(m³/s) ]

Exhausto: 41,7 981480Genvex: 20,9 832000Temovex: 25,7 976000 Table 31: Efficiency and costs of three ventilation systems

With these assumptions it was possible to define the investment and running costs of the used

ventilation systems.

• Investment costs ventilation system: ( ) InvventmVBnInvvent *

3600*

=

[ DKK ] Equation 61 The investment factor is multiplied with the ventilation rate and the Volume of the building.

The maintenance costs for the ventilation system are calculated as a percentage of investment

costs per year. The electricity needed for the ventilation system can then be calculated as

follow:


Page: 69

• Ventilation electricity consumption: 1000

24*365*

100

3600***2

∆

=eventsy

VBnp

teconsumven

[ kWh/year ] Equation 6252 The power of the ventilation is multiplied with the number of hours per year and divided by 1000 to get the electricity consumption in kWh per year. It is assumed that the ventilation system is running the whole year.

It shall be mentioned again that these assumptions were the only way these values could be

included in comparable form.

2.17 Cooling

2.17.1 Theory

An air conditioning system should only be used if it is not possible to avoid over heating and

cannot be accepted by the user.

There are many possibilities to reduce the risk of over heating. Some example have been

already given in the last chapters. The type of construction, the shading system, the

ventilation system and last but not least the load in a room will have the biggest influences on

the indoor temperature and over heating periods. Therefore most of the over heating can be

avoided by using the right techniques.

But if a cooling system is still needed or wanted high running costs will appear.

The cooling demand of an air conditioning system is not only the sum of the cooling demand

of the rooms in a building, it is also dependent upon which type of system is used.

Almost all air conditioning systems can be reduced to 4 basic types.53 The difference can be

defined by the way the cooling is delivered into the room.

• Four conductor induction air conditioning system

• Two channel air conditioning system

• One channel air conditioning system with constant air change

• One channel air conditioning system with variable air change

52 Page 165, Varme og Klimateknik 53 Page 65, Raumkonditionierung


Page: 70

In terms of technical performance these four basic types can differ in:

• Type and number of elements used in the centre of the system

• Type of the local distribution of the post heater or post cooler in the system

• Type of air supply into the rooms

• Type of air controlling component

• Losses of the system

• Method of moistening the air



Name: Program term: Unit: Format: Description:name: string Name of the cooling systemdescription: string Description of the cooling systemLC_time: tcool [ year ] value Life time of the cooling systeminvestmentcosts: Invcoolsym [ DKK/(m³/s) ] value Investment costs of the cooling system per m³/smaintenancecosts: Maintcoolsym [ % ] value Maintenance costs of the cooling systemCOP_factor: ecoolingsy [ % ] value Efficiency of the cooling systemtemperature_cooling: Tempcool [ °C ] value Set temperature of the cooling systemTable 32: Cooling system variables

Because it was very difficult to get realistic data for the cooling systems, values for two

different types have been chosen in relation to the existing ventilation system. This data will

therefore not be realistic, but should indicate how the systems could be implemented. In this

thesis the cooling system can only be chosen if the ventilation is chosen as well.

The cooling system should be included in a better way if it is desired to use such a system

more often, but in terms of saving energy and money the best way will be to avoid using such

systems.

Therefore the investment costs of the cooling system are assumed to be also related to the

volume change per second, as used in the ventilation system. The maintenance costs are given

again in a percentage, because of the changing investment costs. The efficiency of the cooling

system (ecoolingsy) uses the so called Coefficient Of Performance (COP ) and is an important

factor for the electricity consumption. The way how the electricity consumption of the

ventilation system is calculated can be seen in this chapter.


Page: 71

The following calculations will be done in the program:

• Investment costs cooling system: ( ) InvcoolmVBncoolInvcool *

3600*

=

[ money ] Equation 63 If there is no cooling consumption in the calculation, even when the cooling system is chosen the investment costs are set to zero and a warning will be given in the end of the program.

The maintenance costs for the cooling system are calculated as a percentage of investment

costs per year. The cooling demands for the rooms are given by the indoor model

calculations, and are summed to get the cooling demand for the whole building.

• Cooling electricity consumption:

=

100ecoolingsy

Coolingleconsumcoo

[ kWh/year ] Equation 64 To calculate the real electricity consumption of the system the cooling demand of the building has to be divided by the efficiency of the cooling system, which depends very much on which type is chosen.


Page: 72

2.18 Optimisation

2.18.1 Theory

To minimise the LCC, with given design options and project specific boundary conditions it

is important to find a program which can do this in an appropriate way.

The energy conscious building designer has a number of energy saving options with this

database and the program should help to choose the values which fit best the given

requirements.

In an overall run the database will give a high number of possibilities for the program to

choose from and therefore the program has to find the solution in a very complex way.

If fractional values are also to be included in the optimisation program, this will make it even

more difficult to find a solution in an appropriate calculation time.

In the first step the program should be used to seek for an overview of the energy saving

options of the planned building. This should be done with less borders and regulations, to

show the direction of the saving possibilities. Secondly, the program could be used to deliver

more detailed results, including stricter requirements and borders.

A program to handle such problems is the MATLAB routine gclSolve, which is a part of the

optimisation environment TOMLAB, and was developed 1999 at a Swedish university.54 The

program solves general global optimisation problems of the form:

Min f(x) x s/t x_L <= x <= x_U

b_L <= A x <= b_U c_L <= c(x) <= c_U x(i) integer, for i in I

INPUT PARAMETERS: x_L Lower bounds for x x_U Upper bounds for x b_L Lower bounds for linear constraints b_U Upper bounds for linear constraints A Linear constraint matrix c_L Lower bounds for non linear constraints. c_U Upper bounds for non linear constraints. p_f Name of m-file computing the function value. p_c Name of m-file computing the nonlinear constraints. I Set of integer variables, default I=[]. GLOBAL Global definitions (e.g. max. number of function evaluations) PriLev Printing level

54 Program gclSolve


Page: 73

Calling syntax:

function Result = gclSolve(p_f,p_c,x_L,x_U,A,b_L,b_U,c_L,c_U,I,GLOBAL,PriLev)

More data about the program used can be found in Appendix C.

2.18.2 Database input

The vector X includes all possible varying factors from the database and gives possible

numbers, which can be used in the optimisation program.

=

=

=

∞

2-1100.0000-0.0001

-0.00012-15-14-03-02-0

12-15-18-11- 06-11-03-16- 16 - 1

norientatiopercentage window

ratio aspect systemingsolar shad

factor re water shahotsolar type water hotsolar

type nventilatiotype systemcoolingtype systemheating

type windowtype ceiling level insulation

type ceilingtypefloor level insulation

typefloor type inner wall

type outer wall level insulationtype outer wall

x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

X

As can be seen, 17 different parts exist, and for each part an unlimited number of comparable

input data can be added later on.

Each of these parts was described in the previous chapters. It is important to mention that the

vectors inside the different parts must have the same size (for example 6 types of outer wall

insulation thickness), otherwise the optimisation program can not handle the task.

The program “startprog.m” gives the option to check the important input data, to load the

outdoor temperature file, to start the optimisation program, to prepare and display the output

data and finally to check the output data.

In the beginning the solar radiation factors are checked whether the sum is equal to 1. Then

the interest, inflation and energy price rising rate are checked whether the numbers are given

in the right percentage area; otherwise a warning will appear on the screen.

Next the number of rooms will be checked whether they are an equal number and at least 6.


Page: 74

The next step is to load the climate data with the outdoor temperatures of the country in which

the calculation should take place.

Then the optimisation program is started with the term:

LCCcostroom = gclSolve(‘Optimise’,’dummi’,[ minimum variables (X) ],

[ maximum variables (X) ],0,0,0,0,0,[1 2 3 4 5 6 7 8 9 10 11 12 13 14 17])

Wherein the LCCcostroom returns the values for the optimisation, the “Optimise.m” program

(Appendix A and B) includes the database and its calculations, the “dummi.m” is only needed

for the syntax of the gclSolve program. Then the wanted minimum and maximum values of

the 17 variables are given as an input. The following five zeroes are also needed from the

gclSolve program. Finally all variables which can only choose between integer variables have

to be mentioned.

Because of the high number of possibilities which can be combined together, it is wise to

choose a way of stepwise optimisation. This means that after the first run, when the direction

of the result can be seen from the output data, a new run should be done where the borders are

smaller.

After the results from the optimisation program are returned in the LCCcostroom data file, the

graphical indoor temperature simulation takes place. This was done to satisfy the requirement

of checking the indoor climate (by measuring the temperature) and therefore making it visible

to the user. The different room temperatures are given in different colours as follow:

Yellow: Temperature of the outer room with direction 1

Green: Temperature of the outer room with direction 2

Red: Temperature of the inner room with direction 1

Blue: Temperature of the inner room with direction 2

Black: Mean temperature of the building

Magenta: Outdoor temperature

The number of hours where the temperatures in the rooms are over 26, 28 and 30°C are also

stated in numbers for the 4 different rooms and for the whole building.

At the end a check is done and a warning will be given, if the cooling system was chosen but

did not have any consumption. Another check tells the user that if the solar heating is not

chosen, the solar area will be 0, even if another value will be given in the optimised result.


Page: 75

3 Case study and sensitivity analysis

3.1 Input data In accordance with the supervisor it was decided to do a case study on an office building. The

input data was taken from the Danish book “Bygningers energibehov” where construction and

calculation examples are given.55

This example gives values for a typical office building in Denmark.

For the single storey building, a net area of 612 m² and a height of 2,5 m is given. Therefore

the floor and ceiling to the outside flags have to be set to “Yes”. The number of rooms is

assumed to be 10, which meets the division used in the book at best.

The values for the size of the building can be seen in the following drawings:

Front side plan:

Figure 28: Building front side plan

Ground plan:

Figure 29: Building ground plan

An easy load profile was produced for the rooms. It was defined that in each room 6 people

(100 Watt) and electrical appliances with 600 Watt are placed. This load is given every day

between 8°° and 17°°, for the rest of the time the load is set to 0 Watt.

55 Page 51, “Bygnigers energibehov


Page: 76

In the thesis it was decided to set the solar radiation to the air and to the wall note to 0,5, this

means that one half of the solar radiation goes into the air and the other half goes into the

wall.

For this project the infiltration rate or the mechanical ventilation rate are set to one change per

hour. This can be seen in Table 28. If the mechanical ventilation system is used, still a small

additional natural infiltration rate of 0,2 changes per hour is existing. This gives a total

number of changes of air per hour of 1,2 for a room with a ventilation system and 1 for the

natural ventilated house.

The minimum indoor temperature was set to 20° C, which was given as a standard condition

for this building in this book and the starting temperature for shading or cooling was set to

26°C. The optimisation program shall not use the cooling system, because of energy and

investment cost savings.

The hot water consumption is calculated after the given value in Table 24. The result for the

hot water consumption of 60 people is therefore 900 litres per day and the temperature

difference assumption of 50° Celsius is used.

For the ducting of the ventilation system in the office building a pressure drop of 500 Pascal

is assumed. This assumption was made after a discussion with the supervisor and was chosen

related to previous experience on such projects.

The lifetime of the whole building was set to be 30 years for the first calculation and the

interest rate was set to 5%, the inflation rate to 2% and the energy price rising rate to 0%.

The influence of the lifetime of the building and the economical factors on the optimised

results will have to be investigated with the sensitivity analysis and can be seen in chapter 3.3.


Page: 77

The possible choices in the data base will be:

=

=

=

2-150.0000-30.00004.0000 -1.7500

25-14-03-0

011-105-18-1

16-1

13-16- 16 - 1

norientatiopercentage window

ratio aspect systemingsolar shad

factor re water shahotsolar type water hotsolar

type nventilatiotype systemcoolingtype systemheating

type windowtype ceiling level insulation

type ceilingtypefloor level insulation

typefloor type inner wall

type outer wall level insulationtype outer wall

x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

X

• The floor and ceiling type have to be set to a value (in this case 1), because the flags are

set to “Yes”.

• The heating system can only choose between an oil and gas heating system, because it is

assumed that no district heating is available.

• The cooling system is set to zero, because as mentioned before, it is not wanted to have

cooling, and if the ventilation is not chosen, it would give an error in the program.

• The solar shading factor is set to two because a high shading factor should be used

(possible to shade up to 80% of the radiation).

• For the aspect ratio a value between 1,75 and 4 is possible, because it is not wanted to get

a room length less than 70% of the room width. This is done due to the lack of a daylight

factor to give a minimum for the daylight.

• For the window a percentage between 30 and 50 percent is wanted. This is done due to

have a minimum of window area, but reduce the risk of overheating if the windows would

get too big.


Page: 78

3.2 Results In the gclSolve program a maximum of 900 iterations was given as an input. This

corresponded to a calculation time of about 11 hours and gave the following results:

LCC: 2271191 DKK [ 5 3 1 1 2 1 1 1 10 0 0 3 4 2 1,7501 49,9985 1 ] This result shows that the program tried to use the lowest aspect ratio, but the highest window

area and orientation 1 (south-north) has been chosen. With these results new input data was

created and according to the result the aspect ratio was set to be 1,75; the window area was set

to 50 and the orientation to 1. It is clear that these assumptions had to be checked by the

sensitivity analysis after the second run.

At this time 600 iterations were given as an input in the optimisation program and the

following results were achieved:

LCC: 2259984 DKK [ 4 3 1 1 2 1 1 1 10 0 0 3 4 2 1,75 50 1 ] This data means that T2a will be chosen for the outer wall type with an insulation thickness of

250 mm, which leads to a U-value of 0,135 Watt per Kelvin and m².

Inner wall type 1 will be used, which is the lightest and cheapest of the three types.

For the floor an insulation thickness of 100 mm is chosen, which gives a U-value of 0,173

W/(K m²).

For the ceiling the lowest insulation of 250 mm is chosen, which could mean that even a

lower insulation would have been chosen by the program, if the data would have been

available. The U-value of the ceiling is therefore 0,144 W/(K m²).

Window type number one is chosen which is the Pilkington window with a glass U-value of

1,28 W/(K m²), a frame U-value of 1,5W/(K m²) and a g-value of 0,66. This window has the

highest g-value and also the lowest costs in this range of window U-values.

The gas heating system is probably chosen by the program because the maintenance costs are

lower than for the oil heating system, even though the combined fixed and energy costs are

higher than for oil.

No cooling will be included, because a cooling system shall be avoided and is not wanted to

be in the solution. The ventilation system has not been chosen by the program.


Page: 79

A solar hot water system SUN-GEO is chosen with a solar share factor of 60 % per year,

which means that it will be cheaper to produce hot water with the solar system than with the

normal heating system, and that this system is the cheapest for this demand.

The shading type was defined to be able to shade up to 80% of the radiation and as mentioned

in the shading chapter, no costs were available for this factor.

The aspect ratio is set to 1,75 which gives a length of 32,7 metres and a width of 18,7 metres

for the building. Therefore the room length will be about 6,5 metres and the room width will

be about 9,35 metres. As can be seen the program tries to use the lowest aspect ratio, this is

done due to the fact that the outer wall is more expensive than the inner wall and no daylight

factor is used as a requirement.

The highest window area is chosen, probably because the total cost for a window (including

the savings through solar gain) are lower than for the wall.

The temperature distribution of the building is given in the next figures where the hourly

values for February (Figure 30) and June (Figure 31) and daily values over the whole year

(Figure 32) can be seen:

800 900 1000 1100 1200 1300 140020

21

22

23

24

25

26

Hours in the month [ h ]

Tem

pera

ture

s [ °

C ]

Temperature distribution of the building in February

Figure 30: Temperature distribution of the building in February


Page: 80

Yellow: Temperature of the outer room with direction 1 Green: Temperature of the outer room with direction 2 Red: Temperature of the inner room with direction 1 Blue: Temperature of the inner room with direction 2 Black: Mean temperature of the building Magenta: Out door temperature

3700 3800 3900 4000 4100 4200 430020

21

22

23

24

25

26

27

28

29

30

Hours in the month [ h ]

Tem

pera

ture

s [ °

C ]

Temperature distribution of the building in June

Figure 31: Temperature distribution of the building in June

50 100 150 200 250 300 350

10

15

20

25

30

Days of the year [ d ]

Tem

pera

ture

s [ °

C ]

Mean and outdoor temperature distribution of the building

Figure 32: Mean and outdoor temperature distribution of the building


Page: 81

It can be seen that as expected in February the temperature never exceeds 26° C, but for the

period in June when the outdoor temperatures are higher than 26 °C the shading will not be

enough to prevent the building from over heating. With the temperature distribution over the

whole year it will be possible to see how often the mean temperature in the building will

exceed the wanted 26° C. The client will have to decide if he want to accept or change this

proposal for the building.

3.3 Sensitivity analysis

3.3.1 Analysis of the optimisation results

To ensure that the given solution is “the optimised version” within the given borders a

variation of the factors will be done, but also the influence of the given borders will be

examined. This survey will also look more closely at which factors have a big and which have

a small influence on the LCC. Also the cost gradient could be seen from the 17 different input

data ranges. LCC: LCC Dif.: Elec. Con.: Heat + HW con.: Heat + HW Dif.: > 26°C >28°C >30°C

[ DKK ] [ % ] [ kWh / year ] [ kWh / year ] [ % ] [ h ] [ h ] [ h ]Name:Original 2259984 0,00% 0 56763 0,00% 472 79 0Wallinsulation 4-1 2268400 0,37% 0 59088 4,10% 426 69 0Wallinsulation 4-5 2263900 0,17% 0 55974 -1,39% 487 83 0Wall type 1-3 2317800 2,56% 0 56976 0,38% 468 79 0Wall type 2-3 2323900 2,83% 0 56861 0,17% 445 70 0Wall type 3-3 2321800 2,74% 0 56819 0,10% 433 63 0Wall type 5-3 2271200 0,50% 0 56754 -0,02% 448 70 0Wall type 6-3 2289100 1,29% 0 56544 -0,39% 431 62 0Inner wall type 2 2268300 0,37% 0 56364 -0,70% 440 65 0Inner wall type 3 2298900 1,72% 0 55636 -1,99% 394 37 0Floorinsulation 1-1 2261300 0,06% 0 57780 1,79% 449 74 0Floorinsulation 1-3 2268700 0,39% 0 55557 -2,12% 492 84 0Ceilinginsulation 1-3 2278700 0,83% 0 54239 -4,45% 515 87 0Window 2 2327100 2,97% 0 57221 0,81% 403 61 0Window 3 2330600 3,12% 0 57597 1,47% 423 69 0Window 4 2327600 2,99% 0 67903 19,63% 366 56 0Window 5 2260600 0,03% 0 56317 -0,79% 437 72 0Heating 11 2313100 2,35% 0 56763 0,00% 472 79 0Heating 12 2049100 -9,33% 0 49234 -13,26% 472 79 0Solar hot water 0, share 0 2300000 1,77% 0 70213 23,70% 472 79 0Solar hot water 3, share 50 2266500 0,29% 0 59005 3,95% 472 79 0Solar hot water 3, share 70 2265600 0,25% 0 54522 -3,95% 472 79 0Solar hot water 1, share 60 2267400 0,33% 0 56763 0,00% 472 79 0Solar hot water 2, share 60 2273500 0,60% 0 56763 0,00% 472 79 0Solar hot water 4, share 60 2299100 1,73% 0 56763 0,00% 472 79 0Ventilation 1 3121900 38,14% 10714 32956 -41,94% 1257 357 58Cooling 1 3983200 76,25% 11528 32962 -41,93% 0 0 0Shading 1 2258600 -0,06% 0 56615 -0,26% 977 384 106Aspect ratio 1,35 2256000 -0,18% 0 56666 -0,17% 420 68 0Aspect ratio 2 2265200 0,23% 0 56886 0,22% 492 85 0Window perc. 40 2263100 0,14% 0 56939 0,31% 400 60 0Window perc. 56,5 2259400 -0,03% 0 56810 0,08% 516 88 0Window perc. 60 2259600 -0,02% 0 56882 0,21% 539 92 1Orientation 2 2271400 0,51% 0 57976 2,14% 697 132 6Low heat consumption 2577900 14,07% 0 43681 -23,05% 579 61 0

Table 33: Comparison of the LCC and HHW consumption results by changing of the input factors


Page: 82

Life Cycle Cost comparison

1980000

2080000

2180000

2280000

2380000

2480000

2580000

Orig

inal

Wal

linsu

latio

n 4-

1

Wal

linsu

latio

n 4-

5

Wal

l typ

e 1-

3

Wal

l typ

e 2-

3

Wal

l typ

e 3-

3

Wal

l typ

e 5-

3

Wal

l typ

e 6-

3

Inne

r wal

l typ

e 2

Inne

r wal

l typ

e 3

Floo

rinsu

latio

n 1-

1

Floo

rinsu

latio

n 1-

3

Cei

lingi

nsul

atio

n 1-

3

Win

dow

2

Win

dow

3

Win

dow

4

Win

dow

5

Hea

ting

11

Hea

ting

12

Sol

ar h

ot w

ater

0, s

hare

0

Sol

ar h

ot w

ater

3, s

hare

50

Sol

ar h

ot w

ater

3, s

hare

70

Sol

ar h

ot w

ater

1, s

hare

60

Sol

ar h

ot w

ater

2, s

hare

60

Sol

ar h

ot w

ater

4, s

hare

60

Sha

ding

1

Asp

ect r

atio

1,3

5

Asp

ect r

atio

2

Win

dow

per

c. 4

0

Win

dow

per

c. 5

6,5

Win

dow

per

c. 6

0

Orie

ntat

ion

2

Low

hea

t con

sum

ptio

n

Type

Cos

ts [

DK

K ]

Figure 33: Life Cycle Cost comparison (Changing of the input factors)

Comparison yearly heat energy consumption

43000

48000

53000

58000

63000

68000

Orig

inal

Wal

linsu

latio

n 4-

1

Wal

linsu

latio

n 4-

5

Wal

l typ

e 1-

3

Wal

l typ

e 2-

3

Wal

l typ

e 3-

3

Wal

l typ

e 5-

3

Wal

l typ

e 6-

3

Inne

r wal

l typ

e 2

Inne

r wal

l typ

e 3

Floo

rinsu

latio

n 1-

1

Floo

rinsu

latio

n 1-

3

Cei

lingi

nsul

atio

n 1-

3

Win

dow

2

Win

dow

3

Win

dow

4

Win

dow

5

Hea

ting

11

Hea

ting

12

Sol

ar h

ot w

ater

0, s

hare

0

Sol

ar h

ot w

ater

3, s

hare

50

Sol

ar h

ot w

ater

3, s

hare

70

Sol

ar h

ot w

ater

1, s

hare

60

Sol

ar h

ot w

ater

2, s

hare

60

Sol

ar h

ot w

ater

4, s

hare

60

Sha

ding

1

Asp

ect r

atio

1,3

5

Asp

ect r

atio

2

Win

dow

per

c. 4

0

Win

dow

per

c. 5

6,5

Win

dow

per

c. 6

0

Orie

ntat

ion

2

Low

hea

t con

sum

ptio

n

Type

Hea

t ene

rgy

cons

umpt

ion

[ kW

h/ye

ar ]

Figure 34: Comparison of the yearly heat energy consumption (Changing of the input factors)


Page: 83

The data from Table 33 show the difference in the Life Cycle Costs (LCC) and the difference

in heating and hot water (HHW) consumption in figures and percentage. The amount of hours

with over temperature in the building is also stated there.

The two graphic diagrams make it possible to compare the change of the LCC with the

demand for HHW production in the different variants.

The optimised figures for the LCC and HHW consumption are shown and put into the x-axes

to make the comparison feasible.

The first figures worthy of note are the five values with lower LCC than in the optimum

version.

One result where lower LCC occur are in the Heating 12 case, where it is now assumed to

have the option of district heating, and this leads to much lower LCC and less HHW

consumption. This is because the system is cheaper and has a higher efficiency in end use

than the one optimised with the gas heating system.

It can be seen that the program would, if possible, optimise the window area to 56,5% (if the

other values are fixed). However, the influence of the window area on the LCC and HHW

consumption is rather low, but great on the temperature. This is probably due to the effect that

the window has a small U-value and therefore the heat loss will be small, even if a bigger area

is used, but the influence of the solar radiation in summer will depend very much on the used

area.

Again, when shading type one is used the LCC is a little bit lower, but the temperatures in the

rooms are getting much higher. This would reduce the comfort in the room and is not wanted.

Finally, if the aspect ratio has the chance to be reduced, the program would use an optimum

rate of 1,35 (other values are fixed) to achieve lower LCC, but as mentioned before this

reduces the daylight in the room and is therefore not wanted, too.

On one hand it can be seen that varying the amount of insulation does not influence the LCC

to a high degree, but gives a noticeable change in the HHW use. This can support the

important decision of choosing or not choosing a higher insulation thickness.


Page: 84

On the other hand the comparison of the different wall types, gives a big range of higher

LCC, even if the change of the HHW demand is very small. This can support the decision of

which wall type to choose to get the same HHW demand, but maintain low LCC.

The different types of windows also have a big influence on the LCC and HHW demand. For

window type 4 (High U-value/low investment cost) the heating demand is much higher, but

the LCC is not much higher as for a window with a better U-value. Therefore it can be seen

that it is worth using a more efficient window, without paying more over the lifetime.

By taking a closer look at the changing of the solar system factors it can be seen that it is

worth installing a solar hot water system, to reduce the heating costs and therefore

environmental pollution per year. The yearly solar share factor has less influence on the total

LCC than the type of the solar system.

If the dynamically calculated value for the heating demand of 40628 kWh/year (excluding the

system efficiency factor) is compared with the statically calculated heating demand of 38425

kWh/year for this building given in the reference book, it can be seen that the model fits for

these calculations. This difference particularly exists because only the U-values, and not the

type of the building parts, are given in the reference book. If it is compared with the

maximum allowed energy consumption of 63250 kWh/year by the Danish regulations for this

building, it can be seen that the optimised building has about 35% less energy consumption.

For the “low heat consumption” model the lowest U-values for the outer wall, ceiling, floor,

and window were chosen. Inner wall type 3, a yearly solar share factor of 70% and the

optimum for the window area were also chosen. This made it possible to compare the

optimised LCC office building with a possible lower energy consuming variation. This result

shows that the heat consumption per year can be reduced by 24% while only having 14%

more LCC in the considered period. So if reductions in heating demand and emissions are

wanted, the extra costs over the lifetime will be about 300.000 DKK.

For the cooling and ventilation options it can be seen that the LCC are much higher and that

the HHW use are lower. Instead of the lower HHW use, which are reduced because the heat

exchanger will reduce the losses, electricity is used for the motors of the ventilation or cooling

system. The temperatures given for the ventilation option are higher than for the optimised


Page: 85

version, which could rely on the fact that in the given indoor model the option to turn off the

heat exchanger in the summertime was not included. This is of course not wanted and was

changed from the supervisor after finishing these analysis (in the Appendix C already the new

version is given). There is no over heating in the cooling version but as mentioned before the

costs are much higher, although this is not principally because of the running costs which are

quite small, but because of the high investment costs.

The cost sensitivity analysis applied to the optimised building design results in only small

Life Cycle Cost differences. This is due to the fact that in the sensitivity analysis only one

factor is changed while all other factors are kept unchanged.

3.3.2 Scenarios with different starting points

Another sensitivity analysis was done to compare the optimised reference case with other

optimised scenarios, where the given borders in the beginning are changed. The influence of

the rise on the energy price, the expected lifetime and the influence of the available heating

system on the optimisation results were investigated.

The method of optimisation was the same as for the first calculation, and will therefore not be

explained in detail. The results can be seen in the next table. Outer wall type: [ 1 ] T2a (pore concrete) T2a (pore concrete) T2a (pore concrete) T2b (light concrete)Outer wall insulation level: [ mm ] 250,00 300,00 250,00 200,00Inner wall type: [ 1 ] Plaster Plaster Plaster PlasterFloor type: [ 1 ] Concrete 2300 Concrete 2300 Concrete 2300 Concrete 2300Floor insulation level: [ mm ] 100,00 100,00 100,00 70,00Ceiling type: [ 1 ] Ceiling 1 Ceiling 1 Ceiling 1 Ceiling 1Ceiling insulation level: [ mm ] 250,00 300,00 250,00 250,00Window type: [ 1 ] Plikington UV 1.3 Plikington UV 1.1 Plikington UV 1.3 Plikington UV 1.3Heating system type: [ 1 ] Gas Gas Gas District heatingCooling system type: [ 1 ] None None None NoneVentilation system type: [ 1 ] None None None NoneSolar hot water type: [ 1 ] SUN-GEO SUN-GEO SUN-GEO NoneSolar hot water share factor: [ % ] 60,00 70,00 60,00 NoneSolar shading system: [ 1 ] Up to 80% Up to 80% Up to 80% Up to 80%Aspect ratio: [ m/m ] 1,75 1,75 1,75 1,75Window area: [ % ] 50,00 50,00 50,00 50,00Orientation: [ 1 ] South - North South - North South - North South - North

Name: Original Energy rise rate 2% Lifetime 20 years District HeatLife cycle cost: [ DKK ] 2259984 2427288 1735776 2052504Difference life cycle cost: [ % ] 0,00% 7,40% -23,20% -9,18%Heat and hot water consumption: [ kWh / year ] 56763 52176 56763 62470Difference heat and hot water consumption: [ % ] 0,00% -8,08% 0,00% 10,05%Mean indoor temperature over 26 degrees C.: [ ºC ] 472 481 472 409Difference temperature: [ % ] 0,00% 1,91% 0,00% -13,35%Mean indoor temperature over 28 degrees C.: [ ºC ] 79 80 79 60Difference temperature: [ % ] 0,00% 1,27% 0,00% -24,05%Mean indoor temperature over 30 degrees C.: [ ºC ] 0 0 0 0Difference temperature: [ % ] 0,00% 0,00% 0,00% 0,00%Table 34: Comparing the results of the scenarios with different starting conditions


Page: 86

The comparison was done by changing one input factor, but leaving all others as they had

been defined before.

For the first comparison the energy rise rate was introduced with a rise of 2% in energy costs

per year. Therefore the overall LCC rise by about 7,4 % in this period of 30 years, but the

HHW consumption is reduced by 8%. The reduction in the consumption is due to the fact that

it now seems to be more economical to use a thicker outer wall and ceiling insulation, to

change to a window with lower U-value and to use a higher solar area and therefore increase

the yearly solar hot water share factor to 70%. All other optimising results are the same as for

the reference calculation. The number of hours with over heating above 26° and 28°C are

about 2% more than for the reference data.

For the second comparison the influence of the expected lifetime of the whole building is

investigated. A lifetime of 20 instead of 30 years was assumed for this run. It can be seen that

the LCC are about 23% lower, but all other optimised results stay as they had been in the

reference run. This can be interpreted that changing the lifetime within a certain range does

not have such a big influence on the optimisation results but contributes in a great difference

on LCC.

For the third comparison the influence of the availability of district heating should be

investigated. It can be seen that on one side the LCC are about 9% lower than for the

reference and that on the other side the HHW consumption is about 10% more. This is

because the district system has lower running costs and a higher efficiency.

Therefore it is more economical to choose a lower insulation thickness for the outer wall and

floor. Therefore the outer wall is changed from pore concrete to the light concrete. The solar

hot water system will not be chosen. The mean temperature in the building is lower, due to

the lower insulation levels.

The following figures are a graphical comparison of the results discussed above:


Page: 87

Comparison LCC

2052504

1735776

2427288

2259984

1700000

1800000

1900000

2000000

2100000

2200000

2300000

2400000

2500000

Original Energy rise rate 2% Lifetime 20 years District Heat

Type

Cos

t [ D

KK

]

Figure 35: Comparing the LCC of the scenarios with different starting conditions

Comparison energy consumption

62470

56763

52176

56763

51000

53000

55000

57000

59000

61000

63000

65000


Type

Con

sum

ptio

n [ k

Wh

/ yea

r ]

Figure 36: Comparing the energy consumption of the scenarios with different starting conditions


Page: 88

Comparison of over heating hours

0

100

200

300

400

500

600


Type

[ hou

rs/y

ear ]

Mean temperature over28 degree Celsius

Mean temperature over26 degree Celsius

Figure 37: Comparing the over heating hours of the scenarios with different starting conditions

With this sensitivity analysis it was shown that the program works in the expected manner.

3.4 Discussion It would be useful to have more floor types and ceiling types to choose from, to allow further

comparisons between these parts. This can be easily added in the future.

The linear losses between the different building parts should be also given in a database,

because for example the losses between the same wall type, but different floor types will not

be the same. Such a database would have to be created once, but could be of considerable use

for such a survey. It would also be useful for the building part manufacturer to know which

connections produce high or low losses.

The introduction of a daylight factor would be beneficial for setting up requirements for the

aspect ratio of the building.


Page: 89

For the heating system it could be worth trying to find more realistic prices. For example the

heating system could and should be defined by the maximum consumption needed during the

yearly period. This number is given in the program but not enough data for the investment of

such systems was found. Therefore the method relating the prices to the area was chosen.

A closer look should be taken at the ventilation and especially the cooling system to obtain

more realistic figures. It is very hard to define the investment, maintenance or running costs

for such systems with this low number of fixed inputs. The input of the investment and energy

costs for the cooling system should at least be checked before future use.

The program needs a long time for the optimisation if it shall be done in a proper way. It was

shown that because of the huge amount of possibilities the program can choose from, a

stepwise optimisation was done. This can lead to mistakes, if the user is not familiar enough

with the background of the program. One suggestion is to change the free floating aspect ratio

and window percentage to fields with a fixed number of values. For example, the window

percentage resolution could be limited to whole integer percentage steps, and the aspect ratio

resolution could be limited to a step width of 0,05 between 0 and 20. These measures will still

give a large number of possibilities, but the program could probably handle this in one long

calculation, and the likelihood of an error is reduced.

These results give energy engineers and/or architects a basis for choosing optimal building

design and the most cost effective energy saving modifications. This means that if the costs

are optimised by the program but the desired energy saving aspects are not reached, the

program should be expanded to show automatically what further measures could do. This

would require an automatic comparison of all available options to reduce the energy

consumption with the remaining finances.

The best energy-cost ratios should be chosen and could be displayed in sequence to allow the

user to see and choose the best options to reach the design target. Currently this program will

need a further examination of the given results by an architect or energy engineer. However it

can show the user and the client how certain decisions would influence the results. This

requires an explanation of the different scenarios and integrates the client further into the

planning decisions.


Page: 90

The results of the different runs show that the influence and consideration of the temperature

in the building and the connected over heating periods are still underestimated. It would be

beneficial to include a function which would give an over temperature - cost relationship.

This could ensure that the program considers unwanted uncomfortable indoor conditions.

The comparison of the Life Cycle Costs and the energy consumption of a building could be

used to set up new building standard regulations. In this new regulation a certain limit for the

energy consumption should be required, the way to reach the energy saving requirements

should be left open.

It can be seen as a result of the sensitivity analysis of the different optimisation runs that the

biggest influences on the chosen energy saving level come from the type of heating used, and

what price has to be paid for the fuel. In addition to the actual price paid for energy, an energy

price rise will greatly influence the result. Therefore reliable data should be used for these

assumptions.

As mentioned before, it is difficult to give reliable assumptions for future energy prices. A

good example of this is that the price for one barrel of oil was about US$15 in spring 1999

and is about US$30 in summer 2000.56 These figures are enough to show the dilemma in

which energy engineers and architects will find themselves by trying to give good advises to

their clients.

Nevertheless, this is a point which the government could handle in such a way as to let people

know what they can expect in the future. To couple the interest rate for a building loan with

the change of the energy price could be an option to reduce the uncertainty of the investors.

This means that if the investors decide to invest more money, by incorporating energy saving

measures, they should not be excessively punished by a falling energy price rate.

If the energy price falls, the interest rate for the additional funds spent for energy saving

measures should also become lower to help to compensate.

On the other hand, if the energy price rises the interest rate could also rise. However the

investor shall still be able to save more money with the energy saving, by virtue of lower

energy costs, than a comparable but less energy efficient building.


Page: 91

Another aspect of the sensitivity analysis is that the influence of the expected lifetime for the

whole building does not have a big influence on the optimisation results, but contributes in a

great difference on LCC. This result appears to be due to the method used for the LCC

calculation, in which future costs do not have such a big influence on the result. However, a

method that considers a long lifetime of a building and the connected Life Cycle Costs is a

good way for future choice of energy saving possibilities, considering ecological aspects.

A lot of other things used by humans such as cars, machinery, computers and so on have a

very short lifetime compared to a building. For example, presuming the technology needed is

available, changing cars into a really environmentally friendly transport possibility would take

between 10 and 15 years. For the same improvement in the building sector it would still take

100 years or even longer to replace all these buildings.

This method of considering the Life Cycle Costs could also be used in politics, for example to

introduce an energy tax on non-renewable energy sources. If this tax was introduced as a

stepwise method, the general population could see how this would influence the total cost. If

such a policy was chosen people would know what to expect in the next decades and could

for example spend more money on insulation or renewable sources, such as the solar heating

system. This would make it easier for countries to reach the Kyoto goal and reduce their CO2

emissions.

56 Page 40,Energistatistik 98


Page: 92

4 Conclusion

In this thesis the aim was to develop an optimisation program which finds the optimum

building construction, concerning an efficient use of energy by minimising the total Life

Cycle Costs (LCC), by given design options of the building and the project specific boundary

conditions.

This optimisation program gives the energy conscious building designer suggestions

regarding which energy conservation methods to choose and shows the user how certain

decisions would influence the results.

The program uses a simplified dynamically heat load and consumption calculation, taking the

outdoor temperature and solar radiation variations under consideration. It optimises a building

regarding the LCC minimum by taking different heat insulation levels, the aspect ratio of the

building, window areas and types, solar shading systems, orientation possibilities, heating

systems, solar hot water production systems, ventilation and cooling systems under

consideration.

The most sensible parameters for the chosen energy saving level are the type of heating used

and the price paid for the energy. In addition a rise of the energy price will greatly influence

the result. Therefore reliable data must be used for these assumptions. This will require an

explanation of the different scenarios and will therefore integrate the designer’s client further

into the planning decisions.

On one hand it can be seen in the results of the program that varying the amount of insulation

does not influence the Life Cycle Costs to a high degree, but gives a noticeable change in the

heating and hot water demand. This can support the important decision whether to choose or

not to choose a higher insulation thickness and therefore to save heat energy and connected

energy costs.

On the other hand the comparison of the different building part types can support the decision

which wall type to choose to get the same heating and hot water demand, but maintain low

LCC.


Page: 93

The different types of windows also have a big influence on the costs and heat consumption

of a building. With this method it can be seen that it is worth using a more efficient window,

without paying more over the lifetime.

For the future use of this program a closer look should be taken at the ventilation, heating and

especially the cooling system to obtain more realistic figures. It is very hard to define the

investment, maintenance or running costs for such systems with this low number of fixed

inputs.

It would be beneficial to include a function which would give an over temperature - cost

relationship. This could ensure that the program considers the unwanted uncomfortable indoor

conditions.

The introduction of a daylight factor would be good to set up requirements for the aspect ratio

of the building.

It will be also very difficult to give reliable assumptions for future energy prices, which can

be used in the program.

The comparison of the Life Cycle Costs and the energy consumption of a building could be

used to set up new building standard regulations. In this new regulation a certain limit for the

energy consumption could be set up, but left open as to which energy saving measures should

be used.

This method of considering the Life Cycle Costs could also be used in politics, for example to

introduce an energy tax on non-renewable energy sources. If this tax was introduced as a

stepwise method, the general population could see how this would influence the total cost. If

such a policy was chosen people would know what to expect in the next decades and could

for example spend more money on insulation or renewable sources, such as the solar heating

system. This would make it easier for countries to reach the Kyoto goal and reduce their CO2

emissions.

In conclusion, this thesis has demonstrated the merit in using the developed program, which

considers the lifetime for a building and the connected Life Cycle Costs, for future choice of

energy saving methods. This program can be used to find a successful realisation strategy for

building design by detecting, evaluating and sorting the economical and ecological measures.


Page: 94

5 References Adalberth K.,1997: “Energy use during the Life Cycle of Single Unit

Dwellings, Examples”, Building and Environment, Vol. 32, No. 4, Great Britain

Bjorkman M., 1999: “Program „gclSolve“”, Optimisation Theory, Dep. Of

Mathematics and Physics, Malardalen University, Vasteras, Sweden

Boligministeriet,1995: “Bygningsreglement”, Danish building regulations,

Boligministeriet, Bygge og Boligstyrelsen, København, Denmark

Carmody J., 1996: “Residential Windows”, A guide to new to technology

and energy performance, New York, USA Energistyrelsen, 1999: “Energistatistik 1998”, Eneristyrelsen, Amaliegade 44,

1256 Copenhagen, Denmark Grim Ges. m. b. H. (1999): “Solar Preisliste 1999”, Solar & Heizungssysteme, 3390

Melk, Austria Gustafsson Stig -Inge,1986: “Optimal energy retrofits on existing multifamily

buildings”, Department of Mechanical Engineering, Energy Systems, Linköping Studies in Science and Technology, Thesis No. 91, Linköping, Sweden

Hansen et. al., 1992: “Varme og Klimateknik”, danvak Aps, Teknisk Forlag

A/S, København, Denmark Humm O., 1997: “Niedrig Energie Häuser”, Innovative Bauweisen und

neue Standards, 7. Auflage, Staufen bei Freiburg, Germany

International Energy Agency, 1997: “Solar Energy Houses”, Strategies, Technologies,

Examples, Published by James & James, London, Great Britain

Johnsen et. al, 1993: “TSBI 3 program”, Statens Byggeforskningsinstitut,

Postboks 119, 2970 Hørsholm, Denmark Københavns Energi, 2000: “http://www.kb.kk.dk”, Homepage of Copenhagens

energy producer Mc. Mullan Randall, 1992: “Environmental Science in Building”, Third edition, London, Great Britain


Page: 95

Nielsen Toke Rammer, 1994: “Forvarming af ventilationsluft”, Master Thesis at the Institute for Buildings and Energy, Technical University of Denmark, 2800 Lyngby, Denmark

Nørgård J., 1999: “Energy and Environment”, Note 1 from the course

64480 Energy End-Use Efficiency and Environment at the Institute of Building and Energy, Technical University of Denmark, 2800 Lyngby, Denmark

Paulsen Otto, 2000: Technical Institute for Energy, Taastrup, Denmark Pilkington, 1999: “Pilkington Brand Names”, glas-priser, September 1999,

Pilkington Floatglas A/S, Oslo Plads 14, København, Denmark

Pilkington,1998: “Glas 98 – program”, Pilkington Floatglas A/S, Oslo

Plads 14, København, Denmark Q8, 2000: “http://www.q8.dk”, Homepage of the Oil company Q8 Rafnsson Rafn Yngvi, 1997: “Vinsim program”, Master Thesis at the Institute for

Buildings and Energy, Technical University of Denmark, 2800 Lyngby, Denmark

Rafnsson Rafn Yngvi, 1998: “Soldia program”, Soldia for windows 95 version 2.0,

Institut for Bygninger og Energi, Danmarks Tekniske Universitet, 2800 Lyngby, Denmark

Rationel, 1999: “Vinduer & Døre”, Vejledende Salgsprisliste September

1999, Company Rationel, Denmark Rouvel L., 1978: “Raumkonditionierung”, Wege zum energetisch

optimierten Gebäude, Schriftenreihe der Forschungsstelle für Energiewirtschaft, Band 12 Springer Verlag, Heidelberg, Germany

Sakulin et. al., 1999: “Methods to compare the economic effectiveness of

energy savings of warm water supply systems”, Paper of the Institute for Electrical Power Systems, TU Graz, Inffeldgasse 18, 8010 Graz, Austria

Skov Morten, 2000: Københavns Energi, Copenhagen, Denmark Statens Byggeforskningsinst., 1996: ”Bygningers energibehov”, SBI Anvisning 184, Postboks 119, 2970 Hørsholm, Denmark Tommerup et. al.,2000: “Udvikling af Klimaskærmkonstruktioner”, Report R-

042, Institute for Buildings and Energy, Technical University of Denmark, 2800 Lyngby, Denmark


Page: 96

Türk J., 1996: “Kostenoptimaler Anlageneinsatz zur Energiebedarfsdeckung für die Bereiche Raumwärme und Warmwasser unter Berücksichtigung von Emissionsgrenzwerten-Optimierung mit dem Programmpaket SCICONIC”, Diplomarbeit am Intitut für Elektrische Anlagen der Technischen Universität Graz, Graz, Austria

V&S Byggedata A/S, 1997: “Renovering & Drift – BRUTTO 1997”,

Frederikssundsvej 194, 2700 Brønsby, Denmark V&S Byggedata A/S, 2000: “Husbygning – BRUTTO 2000”, Frederikssundsvej 194,

2700 Brønsby, Denmark


Page: 97

Appendix

Appendix A: Fixed variable database.........................................................Page 1

Building structure database...................................................Page 1

Appendix B: Start program........................................................................Page 1

Optimise program.................................................................Page 7

LCC program......................................................................Page 25

Appendix C: Simpleroom program............................................................Page 1

gclSolve program................................................................Page 11

Optimisation of Energy Efficiency Methods in Buildings regarding Life Cycle Costs Appendix A

Page: 1

Appendix A: In this Appendix the type and values used in the databases are stated. For a lot of data, different sources have been used. If the sources are not already mentioned in the report or in the section of the building parts, they will be stated directly at the given values. 1. Fixed variable:

totalLC_time: 30 [ years ] building_area: 612 [ m² ] height: 2.5000 [ m ] roomnumber: 10 [ 1 ] temperature_set: 20 [ °C ] temperature_cooling: 26 [ °C ] load: 1200 (8°° - 17°°) [ W ] floor_to_outerside_flag: 'Yes' ceiling_to_outerside_flag: 'Yes' linloss_tofloor: 0 [ W/(K m) ] linloss_toceiling: 0 [ W/(K m) ] temperatur_difference_water: 50 [ °C ] waterconsumption: 900 [ l/day ] solarradiation_air: 0.5000 [ 1 ] solarradiation_wall: 0.5000 [ 1 ] heatcap_air: 1213 [ J/(K m³) ] infilrate_with_ventilation: 0.2000 [ 1/h ] infilrate_without_ventilation: 1 [ 1/h ] mech_ventrate: 1 [ 1/h ] pressure_drop: 500 [ pa ] interest_rate: 5 [ % ] inflation_rate: 2 [ % ] energy_rise_rate: 0 [ % ] gas_fixprice: 340 [ DKK/year ] gas_price: 0.4800 [ DKK/kWh ] oil_fixprice: 0 [ DKK/year ] oil_price: 0.4536 [ DKK/kWh ] electricity_price: 1.2380 [ DKK/kWh ] electricity_fixprice_night: 504 [ DKK/year ] electricity_price_night: 0.9770 [ DKK/kWh ] districtheat_price: 0.3500 [ DKK/kWh ] districtheat_fixprice: 113 [ DKK/(kW year) ]

2. Building structure:

outerwall: [1x6 struct] innerwall: [1x3 struct] floor: [1x1 struct] ceiling: [1x1 struct] window: [1x5 struct] shading: [1x2 struct] orientation: [1x2 struct] heating_system: [1x12 struct] solar_system: [1x4 struct] vent_system: [1x3 struct] cooling_system: [1x2 struct]


Page: 2

Insulation building parts: The life times and maintenance costs were found in the Danish reference book “Renovering &Drift Brutto”1. Other values are either mentioned in the report “Udvikling af Klimaskaermkonstruktioner”2, or were directly given to me by one of the authors of the report (Henrik Monefeldt Tommerup). Some of the data were also found in the Danish reference book “Husbygning – BRUTTO”.3 Figures on the right side of the database values, show the numbers where the can be found in the two mentioned reference books. • Outer walls: It shall be mentioned again, that for the outer wall calculations 1 and 4 the inner part was made of pore concrete, for 2 and 5 made of light concrete and for 3 and 6 made of bricks. The corresponding values are used in the database. The life time and the maintenance costs are the same for all types and found in “Renovering & Drift Brutto” under [ 21.32.10.08 ]. The U-values, investment costs and linear losses can be found in the report “Udvikling af Klimaskaermkonstruktioner” or in the paper from Henrik Tommerup. Structure: 1x6 struct array with fields:

LC_time [ year ] name u_value [ W/(K m²) ] investmentcosts [ DKK/m² ] maintenancecosts [ DKK/(m² year) ] linloss_tofloor [ W/(K m) ] linloss_towindow [ W/(K m) ] linloss_toceiling [ W/(K m) ] linloss_tocorner [ W/(K m) ] insulation_thickness [ mm ] heattrans_wall [ W/(K m²) ] heatcap_wall [ J/(K m²) ]

T1a: building.outerwall(1)

LC_time: 100 name: 'Wall T1a' u_value: [0.2490 0.1680 0.1380 0.1180 0.1020 0.0900] investmentcosts: [1578 1663 1732 1803 1874 1944] maintenancecosts: 15.7800 linloss_tofloor: [0.2100 0.1380 0.1210 0.1120 0.1060 0.1020] linloss_towindow: [0.0590 0.0360 0.0360 0.0380 0.0400 0.0430] linloss_toceiling: [0.0390 0.0360 0.0340 0.0320 0.0310 0.0300] insulation_thickness: [125 200 250 300 350 400] linloss_tocorner: [0 0 0 0 0 0] heattrans_wall: 4 heatcap_wall: 64500

1 Renovering & Drift – BRUTTO 2 Report „Udvikling af Klimaskaermkonstruktioner“ 3 Husbygning - BRUTTO


Page: 3

T1b: building.outerwall(2) LC_time: 100 name: 'Wall T1b' u_value: [0.2680 0.1770 0.1440 0.1220 0.1050 0.0930] investmentcosts: [1623 1708 1777 1848 1919 1989] maintenancecosts: 16.2300 linloss_tofloor: [0.2190 0.1420 0.1240 0.1140 0.1070 0.1030] linloss_towindow: [0.0200 0.0270 0.0320 0.0350 0.0390 0.0420] linloss_toceiling: [0.0420 0.0370 0.0350 0.0330 0.0320 0.0310] insulation_thickness: [125 200 250 300 350 400] linloss_tocorner: [0 0 0 0 0 0] heattrans_wall: 8.2000 heatcap_wall: 120000

T1c: building.outerwall(3)

LC_time: 100 name: 'Wall T1c' u_value: [0.2720 0.1790 0.1450 0.1220 0.1060 0.0930] investmentcosts: [1612 1697 1766 1837 1908 1978] maintenancecosts: 16.1200 linloss_tofloor: [0.2240 0.1430 0.1250 0.1150 0.1080 0.1030] linloss_towindow: [0.1680 0.0460 0.0390 0.0390 0.0410 0.0430] linloss_toceiling: [0.0430 0.0390 0.0360 0.0340 0.0330 0.0310] insulation_thickness: [125 200 250 300 350 400] linloss_tocorner: [0 0 0 0 0 0] heattrans_wall: 14.2000 heatcap_wall: 174200

T2a: building.outerwall(4) LC_time: 100

name: 'Wall T2.1a' u_value: [0.2380 0.1630 0.1350 0.1150 0.1000 0.0890] investmentcosts: [1263 1326 1371 1416 1462 1508] maintenancecosts: 12.6300 linloss_tofloor: [0.1630 0.1430 0.1250 0.1150 0.1090 0.1050] linloss_towindow: [0.0100 0.0170 0.0210 0.0240 0.0270 0.0300] linloss_toceiling: [0.0440 0.0380 0.0350 0.0340 0.0320 0.0310] insulation_thickness: [125 200 250 300 350 400] linloss_tocorner: [0 0 0 0 0 0] heattrans_wall: 3.2000 heatcap_wall: 80625

T2b: building.outerwall(5)

LC_time: 100 name: 'Wall T2.1b' u_value: [0.2620 0.1740 0.1420 0.1200 0.1040 0.0920] investmentcosts: [1334 1397 1442 1487 1533 1579] maintenancecosts: 13.3400 linloss_tofloor: [0.1780 0.1500 0.1300 0.1190 0.1120 0.1080] linloss_towindow: [0.0700 0.0150 0.0190 0.0230 0.0260 0.0290] linloss_toceiling: [0.0490 0.0400 0.0370 0.0350 0.0330 0.0320] insulation_thickness: [125 200 250 300 350 400] linloss_tocorner: [0 0 0 0 0 0] heattrans_wall: 8.2000 heatcap_wall: 120000


Page: 4

T2c: building.outerwall(6) LC_time: 100 name: 'Wall T2.1c' u_value: [0.2620 0.1740 0.1420 0.1200 0.1040 0.0920] investmentcosts: [1459 1522 1567 1612 1658 1704] maintenancecosts: 14.5900 linloss_tofloor: [0.1650 0.1470 0.1290 0.1200 0.1140 0.1100] linloss_towindow: [0.0080 0.0150 0.0190 0.0230 0.0260 0.0290] linloss_toceiling: [0.0560 0.0470 0.0430 0.0400 0.0380 0.0360] insulation_thickness: [125 200 250 300 350 400] linloss_tocorner: [0 0 0 0 0 0] heattrans_wall: 10.4000 heatcap_wall: 237600

• Inner wall: The thickness of the inner wall is considered to be 0,1 meter. The gypsum wall is considered to have gypsum plates (10 mm) on each side of the insulation (80 mm). Structure: 1x3 struct array with fields:

name: LC_time: [ year ] Investmentcosts: [ DKK/m² ] Maintenancecosts: [ DKK/(m² year) ] heattrans_wall: [ W/(K m²)] heatcap_wall: [ J/(K m²)]

Plaster inner wall: building.innerwall(1)

name: 'Innerwall1' LC_time: 80 [ 22.24.10 ] investmentcosts: 302 [ 04.24.36.02 ]

[ 04.24.36.08 ] maintenancecosts: 3.0200 [ 22.24.10 ] heattrans_wall: 3.4000 heatcap_wall: 20000

Pore concrete Inner wall: building.innerwall(2)

name: 'Innerwall2' LC_time: 150 [ 22.21.25 ] investmentcosts: 309 [ 04.16.20.01 ] maintenancecosts: 6.1800 [ 22.21.25 ] heattrans_wall: 4 heatcap_wall: 64500

Brick inner wall: building.innerwall(3)

name: 'Innerwall3' LC_time: 150 [ 22.21.25 ] investmentcosts: 440 [ 04.16.15.02 ] maintenancecosts: 8.8000 [ 22.21.25 ] heattrans_wall: 15.6000 heatcap_wall: 158400


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• Floor: The U-values and corresponding insulation thickness can be found in the report “Udvikling af Klimaskaermkonstruktioner” on page 28 and the investment costs are calculated after data given from Henrik Tommerup. Structure: 1x1 struct array with field:

name LC_time [ year ] u_value [ W/(K m²) ] investmentcosts [ DKK/m² ] maintenancecosts [ DKK/(m² year)] insulation_thickness [ mm ] heattrans_floor [ W/(K m²) ] heatcap_floor [ J/(K m²) ]

Concrete 2300 floor: building.floor(1)

LC_time: 100 [ 13.28.10 ] u_value: [0.1990 0.1730 0.1420 0.1200 0.1040 0.0920] investmentcosts: [493 512 558 619 665 711] [ 03.15.20] [ 03.15.21.02 ] [ 03.15.44 ] [ 03.15.51.01 ] maintenancecosts: 9.8600 [ 13.28.10 ] insulation_thickness: [70 100 150 200 250 300] heattrans_floor: 32 heatcap_floor: 184000

• Ceiling: The U-values and corresponding insulation thickness can be found in the report “Udvikling af Klimaskaermkonstruktioner” on page 30 and the investment costs are calculated after data given from Henrik Tommerup. Structure: 1x1 struct array with field:

name LC_time [ year ] u_value [ W/(K m²) ] investmentcosts [ DKK/m² ] maintenancecosts [ DKK/(m² year) ] insulation_thickness [ mm ] heattrans_ceiling [ W/(K m²)] heatcap_ceiling [ J/(K m²) ]

Ceiling1: building.ceiling(1)

name: 'Ceiling1' LC_time: 50 [ 27.15.50.01 ] u_value: [0.1440 0.1220 0.1050 0.0930 0.0830 0.0750 0.0680 0.0630] investmentcosts: [569 600 652 682 712 765 817 1016]

[ 04.23.57.04 ] [ 04.24.63.01 ] [ 04.24.63.04 ] maintenancecosts: 5.6900 [ 27.15.50.01 ] insulation_thickness: [250 300 350 400 450 500 550 600 ] heatcap_ceiling: 20500 heattrans_ceiling: 0.8500


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• Window: As already mentioned in the report the calculation of the functions was quite difficult. The life cycle time and maintenance costs were again found in the Danish reference book “Renovering & Drift” [31.45.05]. All these values were assumed to be the same for the five different types. Structure: 1x5 struct array with fields:

name LC_time [ year ] frame_thickness [ m ] glas_u_value [ W/(K m²) ] frame_u_value [ W/(K m²) ] g_value [ 1 ] price.fix_costs: [ DKK ] price.var_costs: [ DKK/m² ] maintenancecosts [ % ] linear_losses [ W/(K m) ] description frame_factor [ 1 ]

Pilkington 1.3/77/66: building.window(1)

name: 'Pilkington 1.3/77/66' LC_time: 30 frame_thickness: 0.0115 glas_u_value: 1.2800 frame_u_value: 1.5000 g_value: 0.6600 price.fix_costs: 1257 price.var_costs: 712 maintenancecosts: 3 linear_losses: 0.0600 description: 'Klar float 4mm - Argon - Energi klar 4mm' frame_factor: []


name: 'Pilkington 1.1/65/54' LC_time: 30 frame_thickness: 0.0115 glas_u_value: 1.0920 frame_u_value: 1.5000 g_value: 0.5400 price.fix_costs: 1330 price.var_costs: 1.1866e+003 maintenancecosts: 3 linear_losses: 0.0600 description: 'Klar float 4mm - Argon - Optima klar 4mm' frame_factor: []


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name: 'Pilkington 1.3/56/61' LC_time: 30 frame_thickness: 0.0115 glas_u_value: 1.2800 frame_u_value: 1.5000 g_value: 0.6100 price.fix_costs: 1330 price.var_costs: 1.1866e+003 maintenancecosts: 3 linear_losses: 0.0600 description: 'Klar float 4mm - Argon - Optima neutral 4mm' frame_factor: []


name: 'Pilkington 2.8/82/76' LC_time: 30 frame_thickness: 0.0115 glas_u_value: 2.7550 frame_u_value: 1.5000 g_value: 0.7600 price.fix_costs: 1214 price.var_costs: 431.2 maintenancecosts: 3 linear_losses: 0.0600 description: 'Klar float 4mm - Air - Klar float 4mm' frame_factor: []


name: 'Pilkington 1.1/75/59' LC_time: 30 frame_thickness: 0.0115 glas_u_value: 1.0920 frame_u_value: 1.5000 g_value: 0.5900 price.fix_costs: 1262 price.var_costs: 748 maintenancecosts: 3 linear_losses: 0.0600 description: 'Klar float 4mm - Argon - Energi super 4mm' frame_factor: []

• Shading: As mentioned in the report for the shading database only the minimum shading factors are given, because no other values were found and it is assumed to have trees in front of the windows. Structure: 1x2 struct array with fields:

name LC_time [ year ] price.fix_costs [ DKK ] price.var_costs [ DKK/m² ] maintenancecosts [ % ] minimum_shading_factor [ 1 ]


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Shading1: building.shading(1) LC_time: 30 price.fix_costs: 0 price.var_costs: 0 maintenancecosts: 0 minimum_shading_factor: 0.7000 name: []

Shading2: building.shading(2)

LC_time: 30 price.fix_costs: 0 price.var_costs: 0 maintenancecosts: 0 minimum_shading_factor: 0.2000 name: []

• Orientation: The values of the direction vectors are not given in this database because the would be too big, but they can be found on the disk, containing the program data and come from the Danish program “Soldia”4. Structure: 1x2 struct array with fields:

direction1 direction2

Direction1 (south/north): building.orientation(1)

direction1: [8760x5 double] direction2: [8760x5 double]

Direction2 (east/west): building.orientation(2)

direction1: [8760x5 double] direction2: [8760x5 double]

• Heating system: The data used for the life time, maintenance costs and efficiency from gas and oil heating systems were given to me from the Technological Institute for Energy in Denmark.5 The data given for the maintenance costs, efficiency and life time for the district heating system were given to me from Københavns Energi (Copenhagens District heat producer).6 Structure: 1x12 struct array with fields:

name LC_time [ year ] fueltype price.fix_costs [ DKK/m² ] price.var_costs [ (DKK/m²)/m² ] maintenancecosts [ % ] efficiency [ % ]

4 Program Soldia, Technical University of Denmark 5 Otto Paulsen, TI – Energy Taastrup 6 Morten Skov, Københavns Energi


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Detached House Gas: building.heating_system(1) name: 'Detached House Gas' LC_time: 20 fueltype: 'gas' price.fix_costs: 626.5700 [ 05.29.43.01 ] price.var_costs: -0.6143 [ 05.29.43.01 ] maintenancecosts: 5 efficiency: 85

Detached House Oil: building.heating_system(2)

name: 'Detached House Oil' LC_time: 20 fueltype: 'oil' price.fix_costs: 626.5700 [ 05.29.43.01 ] price.var_costs: -0.6143 [ 05.29.43.01 ] maintenancecosts: 7 efficiency: 85

Detached House District H.: building.heating_system(3)

name: 'Detached House District heating' LC_time: 20 fueltype: 'dih' price.fix_costs: 547.4300 [ 05.29.46.01 ] price.var_costs: -0.5482 [ 05.29.46.01 ] maintenancecosts: 5 efficiency: 98

Terraced House Gas: building.heating_system(4)

name: 'Terraced House Gas' LC_time: 20 fueltype: 'gas' price.fix_costs: 539.4300 [ 05.29.43.02 ] price.var_costs: -0.5482 [ 05.29.43.02 ] maintenancecosts: 5 efficiency: 85

Terraced House Oil: building.heating_system(5)

name: 'Terraced House Oil' LC_time: 20 fueltype: 'oil' price.var_costs: -0.5482 [ 05.29.43.02 ] price.fix_costs: 539.4300 [ 05.29.43.02 ] maintenancecosts: 7 efficiency: 85

Terraced House District H.: building.heating_system(6)

name: 'Terraced House District heating' LC_time: 20 fueltype: 'dih' price.fix_costs: 473.8600 [ 05.29.46.02 ] price.var_costs: -0.5090 [ 05.29.46.02 ] maintenancecosts: 5 efficiency: 98


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Apartment House Gas: building.heating_system(7) name: 'Apartment House Gas' LC_time: 20 fueltype: 'gas' price.fix_costs: 417.2900 [ 05.29.43.03 ] price.var_costs: -0.2190 [ 05.29.43.03 ] maintenancecosts: 5 efficiency: 85

Apartment House Oil: building.heating_system(8)

name: 'Apartment House Oil' LC_time: 20 fueltype: 'oil' price.var_costs: -0.2190 [ 05.29.43.03 ] price.fix_costs: 417.2900 [ 05.29.43.03 ] maintenancecosts: 7 efficiency: 85

Apartment House Dist. H.: building.heating_system(9)

name: 'Apartment House District heating' LC_time: 20 fueltype: 'dih' price.fix_costs: 396.7000 [ 05.29.46.03 ] price.var_costs: -0.4429 [ 05.29.46.03 ] maintenancecosts: 5 efficiency: 98

Office Building Gas: building.heating_system(10)

name: 'Office Building Gas' LC_time: 20 fueltype: 'gas' price.fix_costs: 405 [ 05.29.43.12 ] price.var_costs: -0.0546 [ 05.29.43.12 ] maintenancecosts: 5 efficiency: 85

Office Building Oil: building.heating_system(11)

name: 'Office Building Oil' LC_time: 20 fueltype: 'oil' price.fix_costs: 405 [ 05.29.43.12 ] price.var_costs: -0.0546 [ 05.29.43.12 ] maintenancecosts: 7 efficiency: 85

Office Building District H.: building.heating_system(12)

name: 'Office Building District heating' LC_time: 20 fueltype: 'dih' price.fix_costs: 344.5000 [ 05.29.46.12 ] price.var_costs: -0.0470 [ 05.29.46.12 ] maintenancecosts: 5 efficiency: 98


Page: 11

• Solar hot water heating system: The data used for these calculations is relied on experience of a solar hot water systems installing company7 and therefore less scientific but more practical. The investment costs, the solar share factor and the net area factor are calculated as mentioned in the report and the data came from the price book of this company. The data used for the life time and maintenance costs was received through a oral examination at the company and is assumed to be the same for all solar systems. Structure: 1x4 struct array with fields:

name LC_time [ year ] solarshare [ % ] price.fix_costs [ DKK ] price.var_costs [ DKK/m² ] maintenancecosts [ % ] areafactor [ (m² day)/l ]

SUN2: building.solar_system(1)

name: 'SUN2' LC_time: 20 solarshare: [30 40 50 60 70] price.fix_costs: 5531 price.var_costs: 1982 maintenancecosts: 1 areafactor: [0.0160 0.0200 0.0250 0.0310 0.0420]

SUN3: building.solar_system(2)

name: 'SUN3' LC_time: 20 solarshare: [30 40 50 60 70] price.fix_costs: 5892 price.var_costs: 2162 maintenancecosts: 1 areafactor: [0.0156 0.0195 0.0244 0.0303 0.0410]

SUN-GEO: building.solar_system(3)

name: 'SUN-GEO' LC_time: 20 solarshare: [30 40 50 60 70] price.fix_costs: 7333 price.var_costs: 2095 maintenancecosts: 1 areafactor: [0.0133 0.0167 0.0208 0.0258 0.0350]

SUN-VAC: building.solar_system(4)

name: 'SUN-VAC' LC_time: 20 solarshare: [30 40 50 60 70] price.var_costs: 3892 price.fix_costs: 6432 maintenancecosts: 1 areafactor: [0.0110 0.0138 0.0173 0.0214 0.0290]

7 Ernst Grim Ges. m. b. H; Melk, Austria


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• Ventilation system: Most of the data used for the ventilation system, e.g. investment costs, system efficiency, heat recovery efficiency or the pressure drop of the appliance comes from the master thesis of my supervisor Toke Rammer Nielsen.8 The data for the life time and maintenance costs are taken from the Danish reference book [ 57.11.15 ] and are used for all three types. Structure: 1x3 struct array with fields:

name LC_time [ year ] investmentcosts [ DKK/(m³/s) ] maintenancecosts [ % ] system_efficiency [ % ] heat_recovery_efficiency [ % ] pressure_drop [ pa ]

Exhausto Vex: building.vent_system(1)

name: 'Exhausto VEX 1.5' LC_time: 30 investmentcosts: 981480 maintenancecosts: 5 system_efficiency: 41.7000 heat_recovery_efficiency: 66 pressure_drop: 100

Genvex: building.vent_system(2)

name: 'Genvex GE250' LC_time: 30 investmentcosts: 832000 maintenancecosts: 5 system_efficiency: 20.9000 heat_recovery_efficiency: 63 pressure_drop: 100

Temo Vex: building.vent_system(3)

name: 'Temo Vex' LC_time: 30 investmentcosts: 976800 maintenancecosts: 5 system_efficiency: 25.7000 heat_recovery_efficiency: 83 pressure_drop: 100

8 Pages 44 – 90, Master Thesis Toke Rammer Nielsen


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• Cooling system: As mentioned in the report the data used for the cooling systems is related to the ventilation system and on free assumed values, because it was not possible to receive realistic data. Structure: 1x2 struct array with fields:

name LC_time [ year ] investmentcosts [ DKK/(m³/s) ] maintenancecosts [ % ] COP_factor [ % ]

Cooling 1: building.cooling_system(1)

name: 'Cooling1' LC_time: 30 investmentcosts: 1000000 maintenancecosts: 5 COP_factor: 400

Cooling 2: building.cooling_system(2)

name: 'Cooling2' LC_time: 30 investmentcosts: 1000000 maintenancecosts: 4 COP_factor: 380

3. References: Grim Ges. m. b. H. (1999): “Solar Preisliste 1999”, Solar &

Heizungssysteme, 3390 Melk, Austria Nielsen Toke Rammer, 1994: “Forvarming af ventilationsluft”, Master Thesis at

the Institute for Buildings and Energy, Technical University of Denmark

Paulsen Otto, 2000: Technical Institute for Energy, Taastrup,

Denmark Rafnsson Rafn Yngvi, 1997: “Vinsim program”, Master Thesis at the Institute

for Buildings and Energy, Technical University of Denmark

Skov Morten, 2000: Københavns Energi, Copenhagen, Denmark Tommerup et. al.,2000: “Udvikling af Klimaskærmkonstruktioner”,

Report R-042, Institute for Buildings and Energy, Technical University of Denmark

V&S Byggedata A/S, 1997: “Renovering & Drift - BRUTTO 1997”, Denmark V&S Byggedata A/S, 2000: “Husbygning – BRUTTO 2000”, Denmark

Optimisation of Energy Efficiency Methods in Buildings regarding Life Cycle Costs Appendix B

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Appendix B: In this Appendix the start program and the variables and script files of the self written programs “Optimise.m” and “LCC.m” will be given. The tables with the variables include the name of variable used in the program, the unit, the dimension, function and a short description. Startprog.m: Purpose: The purpose of the ’startprog.m’ script is to check the important input data, to load the outdoor temperature file, to start the optimisation program, to prepare and display the output data and finally check the output data. Description: In the beginning the solar radiation factors are checked whether the sum is equal to 1. Then the interest, inflation and energy price rising rate are checked whether the numbers are given in the right percentage area; otherwise a warning will appear on the screen. Next the number of rooms will be checked whether they are an equal number and at least 6. The next step is to load the climate data with the outdoor temperatures of the country in which the calculation should take place. Then the optimisation program is started with the term:

LCCcostroom = gclSolve(‘Optimise’,’dummi’,[ minimum variables (X) ], [ maximum variables (X) ],0,0,0,0,0,[1 2 3 4 5 6 7 8 9 10 11 12 13 14 17])

Wherein the LCCcostroom returns the values for the optimisation, the “Optimise.m” program includes the database and its calculations, the “dummi.m” is only needed for the syntax of the gclSolve program. Then the wanted minimum and maximum values of the 17 variables are given as an input. The following five zeroes are also needed from the gclSolve program. Finally all variables which can only choose between integer variables have to be mentioned. Because of the high number of possibilities which can be combined together, it is wise to choose a way of stepwise optimisation. This means that during the first run, when the direction can be seen from the output data, a new run should be done where the borders are smaller. After the results from the optimisation program are returned in the LCCcostroom data file, the graphical indoor temperature simulation takes place. This was done to satisfy the requirement of checking the indoor climate (by measuring the temperature) and therefore making it visible to the user. The different room temperatures are given in different colours as follow:

Yellow: Temperature of the outer room with direction 1 Green: Temperature of the outer room with direction 2 Red: Temperature of the inner room with direction 1 Blue: Temperature of the inner room with direction 2 Black: Mean temperature of the building Magenta: Outdoor temperature


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The number of hours where the temperatures in the rooms are over 26, 28 and 30°C are also stated in numbers for the 4 different rooms and for the whole building. At the end a check is done and a warning will be given, if the cooling system was chosen but did not have any consumption. Another check tells the user that if the solar heating is not chosen, the solar area will be 0, even if another value will be given in the optimised result. Call to script: The script ’startprog.m’ is called by: • startprog Sub functions: • ’gclSolve.m’ • ’Optimise.m’ • ’Simpleroom.m’ • ’LCC.m’ List of the script: global fixed_var building Cooling Tout midtemp tempout1 global tempout2 tempin1 tempin2 Sin1 Sin2 Sout1 Sout2 load fixed_var_database load building_database % % % CHECKING % % % % Solarradiaton to air note [0-1] (wa+ww =1 !!) wa = fixed_var.solarradiation_air; % Solarradiaton to wall note [0-1] (wa+ww =1 !!) ww = fixed_var.solarradiation_wall; wtot = ww + wa; if wtot ~= 1 error ('Sum of solarradiation to air (wa) and wall (ww) must be 1!') end % Interest rate [%] iint = fixed_var.interest_rate; % Inflation rate [%] iinf = fixed_var.inflation_rate; % Energy price rise rate [%] iene = fixed_var.energy_rise_rate; if iint ~= 0 if iint < 0.5 if iint > -0.5 warning ('Is the interest rate given in integers between 0 and +/-100%?')


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end end end if iinf ~= 0 if iinf < 0.2 if iinf > -0.2 warning ('Is the inflation rate given in integers between 0 and +/-100%?') end end end if iene ~= 0 if iene < 0.2 if iene > -0.2 warning ('Is the energy price rising rate given in integers between 0 and +/-100%?') end end end % Check if the number of rooms is even and >= 6 rooms = fixed_var.roomnumber; rz = rooms/2; checkroom = rooms - floor(rz) * 2; if checkroom ~= 0 error('Number of rooms has to be even!') end if rooms < 6 error('Number of rooms has to be >= 6 !') end % % % Preperation of Data % % % load climate3600 Tout = CLIMATE(:,2)/10; clear CLIMATE % % % Optimization Parameters % % % LCCcostroom = gclSolve('Optimise','sinnlos',[1,1,1,1,1,1,1,1,10,0,0,0,1,2,1.75,30,1],... [6,6,3,1,6,1,8,5,11,0,3,4,5,2,4,50,2],0,0,0,0,0,[1 2 3 4 5 6 7 8 9 10 11 12 13 14 17]) % % % Graphical Indoor Temperature Simulation % % % save LCCcostroomrun LCCcostroom LCCcostroom = gclSolve('optimize','sinnlos',[LCCcostroom.x_k],... [LCCcostroom.x_k],0,0,0,0,0,[1 2 3 4 5 6 7 8 9 10 11 12 13 14 17]) % Yellow: Temperature of the outerroom with direction1. % Green: Temperature of the outerroom with direction2. % Red: Temperature of the innerroom with direction1. % Blue: Temperature of the innerroom with direction2.


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% Black: Average temperature of the building. % Magenta: Out door temperature t=linspace(1,8760,8760); plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([-inf 744 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in January') print -dmfile january january plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([744 1416 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in February') print -dmfile february february plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([1416 2160 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in March') print -dmfile march march plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([2160 2880 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in April') print -dmfile april april plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([2880 3624 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in Mai') print -dmfile mai mai plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([3624 4344 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in June') print -dmfile june june plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([4344 5088 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in July') print -dmfile july july plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([5088 5832 20 inf]) xlabel('Hours in the month [ h ]')


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ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in August') print -dmfile august august plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([5832 6552 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in September') print -dmfile september september plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([6552 7296 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in October') print -dmfile october october plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([7296 8016 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in November') print -dmfile november november plot(t,tempout1,'y',t,(tempout2),'g',t,tempin1,'r',t,(tempin2),'b',t,midtemp,'k',t,Tout,'m') axis([8016 8760 20 inf]) xlabel('Hours in the month [ h ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building in December') print -dmfile december december tday = linspace(0.04166,365,8760); plot(tday,tempout1,'y',tday,tempout2,'g',tday,tempin1,'r',tday,tempin2,'b',tday,midtemp,'k',tday,Tout,'m') axis([0.04166 365 -inf inf]) xlabel('Days of the year [ d ]') ylabel('Temperatures [ °C ]') title('Temperature distribution of the building') print -dmfile year year plot(tday,midtemp,'k',tday,Tout,'m') axis([0.04166 365 -inf inf]) xlabel('Days of the year [ d ]') ylabel('Temperatures [ °C ]') title('Mean and outdoor temperature distribution of the building') print -dmfile year_midtemp year_midtemp Hour_tempout1_over_26 = sum(tempout1 > 26) Hour_tempout1_over_28 = sum(tempout1 > 28) Hour_tempout1_over_30 = sum(tempout1 > 30) Hour_tempout2_over_26 = sum(tempout2 > 26) Hour_tempout2_over_28 = sum(tempout2 > 28) Hour_tempout2_over_30 = sum(tempout2 > 30) Hour_tempin1_over_26 = sum(tempin1 > 26) Hour_tempin1_over_28 = sum(tempin1 > 28) Hour_tempin1_over_30 = sum(tempin1 > 30) Hour_tempin2_over_26 = sum(tempin2 > 26)


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Hour_tempin2_over_28 = sum(tempin2 > 28) Hour_tempin2_over_30 = sum(tempin2 > 30) Hour_midtemp_over_26 = sum(midtemp > 26) Hour_midtemp_over_28 = sum(midtemp > 28) Hour_midtemp_over_30 = sum(midtemp > 30) % Information about the cooling system if LCCcostroom.x_k(10) ~= 0 if Cooling == 0 warning('The cooling system has no consumption') end end if LCCcostroom.x_k(12) == 0 warning('No solar hot water heating system is chosen! Solar Area is 0!') end Optimise.m: Purpose: The purpose of the function ’Optimise.m’ is to optimise the overall Life Cycle Costs (LCC) of a building by choosing different energy conservation options and technologies. Description: The program ’Optimise.m’ is used for optimising the life cycle costs of a building by first loading input data of the building from the database, then calculating the used building dimensions, followed by simple room model calculations and at last calculating the LCC with the defined inputs. Call to function: Function ’Optimise.m’ is called by: • Optimise(x) Sub functions: • ’Simpleroom.m’ • ’LCC.m’


Page: 7

Variables:


Page: 8

Variable: Unit: Dimension: Function: Description:AB [ m² ] 1x1 Help variable Area of the buildingAframe [ m² ] 1x1 Help variable Area of the frameAglas [ m² ] 1x1 Help variable Area of the glassAspectRB [ m/m ] 1x1 Help variable Aspect ratio of the buildingAspectRR [ m/m ] 1x1 Help variable Aspect ratio of the roomAwin [ m² ] 1x1 Help variable Area of the window

Database: Including the outer wall type,outer wall insulation thickness, inner wall type,floor type, floor insulation thickness, ceiling type,

building [ ] nx11 Global variable ceiling insulation thickness, window type,heating system type, cooling system type,ventilation system type, solar hot water system type,solarshare and orientation

Ca [ J / K ] 1x1 Help variable Heat capacity of the airCam [ J / (K*m³) ] 1x1 Help variable Heat capacity of the air per m³celinloss [ W / (K*m) ] 1x1 Help variable Ceiling linear losses per mcolinloss [ W / (K*m) ] 1x1 Help variable Corner linear losses per mCooling [ kWh / year ] 1x1 Global variable Sum of the room cooling demands per year.Coolingin1 [ kWh ] 1x1 Global variable Maximum cooling demand inner room with direction 1Coolingin2 [ kWh ] 1x1 Global variable Maximum cooling demand inner room with direction 2Coolingout1 [ kWh ] 1x1 Global variable Maximum cooling demand outer room with direction 1Coolingout2 [ kWh ] 1x1 Global variable Maximum cooling demand outer room with direction 2Cw [ J / K ] 1x1 Global variable Heat capacity of the roomCwceiling [ J / (K*m²) ] 1x1 Help variable Heat capacity of the ceiling per m²Cwfloor [ J / (K*m²) ] 1x1 Help variable Heat capacity of the floor per m²Cwinnerwall [ J / (K*m²) ] 1x1 Help variable Heat capacity of the inner wall per m²Cwouterwall [ J / (K*m²) ] 1x1 Help variable Heat capacity of the outer wall per m²direction1 [ ] 5x8760 Help variable Solar data base in one directiondirection2 [ ] 5x8760 Help variable Solar data base in the opposite directiondistricth [ money / kWh ] 1x1 Help variable Variable price for district heatingdistricthfix [ money / (kW*year) ] 1x1 Help variable Fixed price for district heatingDp [ pa ] 1x1 Help variable Pressure drop of the ventilation systemDpduct [ pa ] 1x1 Help variable Pressure drop of the ductingDpsystem [ pa ] 1x1 Help variable Pressure drop of the ventilation applianceDT [ °C ] 1x1 Help variable Temperature difference between cold and hot watereconsum [ kWh / year ] 1x1 Global variable Amount of electricity consumption.econsumcool [ kWh / year ] 1x1 Help variable Electricity consumption of the coolingeconsumvent [ kWh / year ] 1x1 Help variable Electricity consumption of the ventilationecoolingsy [ % ] 1x1 Help variable Efficiency of the cooling systemeheatingsy [ % ] 1x1 Help variable Efficiency of the heating systemeheatrec [ % ] 1x1 Help variable Efficiency of the heat recoveryeprice [ money / kWh ] 1x1 Help variable Variable price for electricityepricefixnight [ money / year ] 1x1 Help variable Fixed price for electricity during nighttimeepricenight [ money / kWh ] 1x1 Help variable Variable price for electricity during nighttimeeventsy [ % ] 1x1 Help variable Efficiency of the ventilation system

Database: Including the load in one room,water consumption, solar raditation to air factor,solar radiation to wall factor, heat capacity of the air,mechanical ventilation rate, presure drop of the ducting,interest, inflation and energy price rising rate,

fixed_var [ ] 1xn Global variable fixed prices and variable prices for gas, oil, electricityand district heat, considered life cycle time,temperature difference between cold and hot water,seting and cooling temperature, infiltration rates withand without ventilation, linear losses to the floor and ceiling, floor and ceiling flags, area and height of the building


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Variable: Unit: Dimension: Function: Description:

flinloss [ W / (K*m) ] 1x1 Help variable Floor linear losses per mframet [ m ] 1x1 Help variable Thickness of the fram per mgas [ money / kWh ] 1x1 Help variable Variable price for gasgasfix [ money / year ] 1x1 Help variable Fixed price for gasglasslength [ m ] 1x1 Help variable Length between the glass and the framegvalue [ 1 / m² ] 1x1 Help variable G value of the window glass per m²gwlinloss [ W / (K*m) ] 1x1 Help variable Glas - Window linear losses per mhconsum [ kWh / year ] 1x1 Global variable Amount of heat consumption.Heating [ kWh / year ] 1x1 Global variable Sum of the room heating demands per year.Heatingin1 [ kWh / year ] 1x1 Global variable Heating demand inner room with direction 1Heatingin2 [ kWh / year ] 1x1 Global variable Heating demand inner room with direction 2Heatingout1 [ kWh / year ] 1x1 Global variable Heating demand outer room with direction 1Heatingout2 [ kWh / year ] 1x1 Global variable Heating demand outer room with direction 2heightR [ m ] 1x1 Help variable Height of a roomhprice [ money / kWh ] 1x1 Global variable Costs for one kWh of heathpricefix [ money / year ] 1x1 Global variable Fixed price of a heating systemhsyfuel [ ] String Help variable Fuel type of the heating systemhwconsum [ kWh / year ] 1x1 Global variable Amount of hot water consumption.hwprice [ money / kWh ] 1x1 Global variable Costs of one kWh hot wateriene [ % ] 1x1 Global variable Energy price rising rate.iinf [ % ] 1x1 Global variable Inflation rate.iint [ % ] 1x1 Global variable Interest rate. infil [ 1 / h ] 1x1 Help variable Infiltration rateInvceiling [ money ] 1x1 Global variable Investment costs of the ceiling.Invceilingm [ money / m² ] 1x1 Help variable Investment costs of the ceiling per m²InvceilingR [ money ] 1x1 Help variable Investment costs of the ceiling in a roomInvcool [ money ] 1x1 Global variable Investment costs of the cooling system.Invcoolsym [ money / (m³/s) ] 1x1 Help variable Investment costs of the cooling system per m³/sInvfloor [ money ] 1x1 Global variable Investment costs of the floor.Invfloorm [ money / m² ] 1x1 Help variable Investment costs of the floor per m²InvfloorR [ money ] 1x1 Help variable Investment costs of the floor in a roomInvheatsy [ money ] 1x1 Global variable Investment costs of the heating system.Invheatsyfix [ money ] 1x1 Help variable Fixed investment costs of the heating systemInvheatsym [ money / m² ] 1x1 Help variable Variable investment costs of the heating system per m²Invinwall [ money ] 1x1 Global variable Investment costs of the inner wall.Invinwallin [ money ] 1x1 Help variable Investment costs of the inner room inner wallInvinwallm [ money / m² ] 1x1 Help variable Investment costs of the inner wall per m²Invinwallout [ money ] 1x1 Help variable Investment costs of the outer room inner wallInvoutwall [ money ] 1x1 Global variable Investment costs of the outer wall.Invoutwallin [ money ] 1x1 Help variable Investment costs of the inner room outer wallInvoutwallm [ money / m² ] 1x1 Help variable Investment costs of the outer wal per m²Invoutwallout [ money ] 1x1 Help variable Investment costs of the outer room outer wallInvshading [ money ] 1x1 Global variable Investment costs of the shading device.Invshadingfix [ money ] 1x1 Help variable Fixed investment costs for shadingInvshadingin [ money ] 1x1 Help variable Investment costs of the inner room shadingInvshadingm [ money / m² ] 1x1 Help variable Variable investment costs of the shading per m²Invshadingout [ money ] 1x1 Help variable Investment costs of the outer room shadingInvsolsy [ money ] 1x1 Global variable Investment costs of the solar hot water system.Invsolsyfix [ money ] 1x1 Help variable Fixed investment costs of the solar hot water systemInvsolsym [ money / m² ] 1x1 Help variable Variable investment costs of the solar hot water systemInvvent [ money ] 1x1 Global variable Investment costs of the ventilation system.Invventm [ money / (m³/s) ] 1x1 Help variable Investment costs of the ventilation system per m³/sInvwindow [ money ] 1x1 Global variable Investment costs of the window.Invwindowfix [ money ] 1x1 Help variable Fixed investment costs per windowInvwindowm [ money / m² ] 1x1 Help variable Variable investment costs of the window per m²InvwindowR [ money ] 1x1 Help variable Investment costs of the window in a room


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Kw [ W / K ] 1x1 Global variable Heat transfer coefficient of the roomKwceiling [ W / (K*m²) ] 1x1 Help variable Heat transfer coefficient ceiling per m²Kwfloor [ W / (K*m²) ] 1x1 Help variable Heat transfer coefficient floor per m²Kwinnerwall [ W / (K*m²) ] 1x1 Help variable Heat transfer coefficient inner wall per m²Kwouterwall [ W / (K*m²) ] 1x1 Help variable Heat transfer coefficient outer wall per m²lengthB [ m ] 1x1 Help variable Length of the buildinglengthR [ m ] 1x1 Help variable Length of the roomLoad [ W ] 1x8760 Help variable Load in one roomMaintceiling [ money / year ] 1x1 Global variable Maintenance costs of the ceiling.Maintceilingm [ money / (year*m²) ] 1x1 Help variable Maintenance costs of the ceiling per m²MaintceilingR [ money / year ] 1x1 Help variable Maintenance costs of the ceiling in a roomMaintcool [ money / year ] 1x1 Global variable Maintenance costs of the cooling system.Maintcoolsym [ % investmentcosts / year ] 1x1 Help variable Maintenance costs of the cooling systemMaintfloor [ money / year ] 1x1 Global variable Maintenance costs of the floor.Maintfloorm [ money / (year*m²) ] 1x1 Help variable Maintenance costs of the floor per m²MaintfloorR [ money / year ] 1x1 Help variable Maintenance costs of the floor in a roomMaintheatsy [ money / year ] 1x1 Global variable Maintenance costs of the heating system.Maintheatsym [ % investmentcosts / year ] 1x1 Help variable Maintenance costs of the heating systemMaintinwall [ money / year ] 1x1 Global variable Maintenance costs of the inner wall.Maintinwallin [ money / year ] 1x1 Help variable Maintenance costs of the inner room inner wallMaintinwallm [ money / (year*m²) ] 1x1 Help variable Maintenance costs of the inner wall per m²Maintinwallout [ money / year ] 1x1 Help variable Maintenance costs of the outer room inner wallMaintoutwall [ money / year ] 1x1 Global variable Maintenance costs of the outer wall.Maintoutwallin [ money / year ] 1x1 Help variable Maintenance costs of the inner room outer wallMaintoutwallm [ money / (year*m²) ] 1x1 Help variable Maintenance costs of the outer wall per m²Maintoutwallout [ money / year ] 1x1 Help variable Maintenance costs of the outer room outer wallMaintshading [ money / year ] 1x1 Global variable Maintenance costs of the shading device.Maintshadingm [ % investmentcosts / year ] 1x1 Help variable Maintenance costs of the shadingMaintsolsy [ money / year ] 1x1 Global variable Maintenance costs of the solar hot water system.Maintsolsym [ % investmentcosts / year ] 1x1 Help variable Maintenance costs of the solar hot water systemMaintvent [ money / year ] 1x1 Global variable Maintenance costs of the ventilation system.Maintventm [ % investmentcosts / year ] 1x1 Help variable Maintenance costs of the ventilation systemMaintwindow [ money / year ] 1x1 Global variable Maintenance costs of the window.Maintwindowm [ % investmentcosts / year ] 1x1 Help variable Maintenance costs of the windowMaintwindowR [ money / year ] 1x1 Help variable Maintenance costs of the window in a roommaxcoolin1 [ kWh / year ] 1x1 Global variable Cooling demand inner room with direction 1maxcoolin2 [ kWh / year ] 1x1 Global variable Cooling demand inner room with direction 2maxcoolout1 [ kWh / year ] 1x1 Global variable Cooling demand outer room with direction 1maxcoolout2 [ kWh / year ] 1x1 Global variable Cooling demand outer room with direction 2maxheatin1 [ kW ] 1x1 Global variable Maximum heating demand inner room with direction 1maxheatin2 [ kW ] 1x1 Global variable Maximum heating demand inner room with direction 2maxheatout1 [ kW ] 1x1 Global variable Maximum heating demand outer room with direction 1maxheatout2 [ kW ] 1x1 Global variable Maximum heating demand outer room with direction 2midtemp [ °C ] 1x8760 Global variable Mean temperature of the buildingMinshadingin1 [ 1 ] 1x1 Global variable Minimum shading factor inner room with direction 1Minshadingin2 [ 1 ] 1x1 Global variable Minimum shading factor inner room with direction 2Minshadingout1 [ 1 ] 1x1 Global variable Minimum shading factor outer room with direction 1Minshadingout2 [ 1 ] 1x1 Global variable Minimum shading factor outer room with direction 2n [ 1 / h ] 1x1 Help variable Mechanical ventilation ratencool [ 1/h ] 1x1 Help variable Mechanical cooling ratenettoareafac [ m² ] 1x1 Help variable Net area factor of the solar hot water systemoil [ money / kWh ] 1x1 Help variable Variable price for oiloilfix [ money / year ] 1x1 Help variable Fixed price for oilOverallLCC [ money ] 1x1 Global variable Overall sum of the Life Cycle Costs.p [ 1 ] 1x1 Help variable Frame condition factorQsun [ W/h ] 1x8760 Global variable Solar radiation per hour.


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Qw [ kWh / year ] 1x1 Help variable Energy consumption for hot water per year.rooms [ 1 ] 1x1 Global variable Number of rooms inside the building.sglas [ m ] 1x1 Help variable Width of the glassSin1 [ 1 ] 1x8760 Global variable Shading factor inner room with direction 1Sin2 [ 1 ] 1x8760 Global variable Shading factor inner room with direction 2Smin [ 1 ] 1x1 Help variable Minimum shading coefficientsolarshare [ % ] 1x1 Help variable Yearly share of hot water produced by solar energySout1 [ 1 ] 1x8760 Global variable Shading factor outer room with direction 1Sout2 [ 1 ] 1x8760 Global variable Shading factor outer room with direction 2swin [ m ] 1x1 Help variable Width of the windowtceiling [ year ] 1x1 Global variable Life time of the ceilingtcool [ year ] 1x1 Global variable Life time of the cooling systemTempcool [ °C ] 1x1 Help variable Set temperature of the cooling systemtempin1 [ °C ] 1x8760 Global variable Temperature of an inner room facing direction1tempin2 [ °C ] 1x8760 Global variable Temperature of an inner room facing direction2tempout1 [ °C ] 1x8760 Global variable Temperature of an outer room facing direction1tempout2 [ °C ] 1x8760 Global variable Temperature of an outer room facing direction2tfloor [ year ] 1x1 Global variable Life time of the floortheatsy [ year ] 1x1 Global variable Life time of the heating systemtinwall [ year ] 1x1 Global variable Life time of the inner walltLC [ year ] 1x1 Help variable Considered life time of the calculationTout [ °C ] 1x8760 Global variable Temperature of the outside.toutwall [ year ] 1x1 Global variable Life time of the outer wallTset [ °C ] 1x1 Help variable Set point of the minimum room temperaturetshading [ year ] 1x1 Help variable Life time of the shading systemtsolsy [ year ] 1x1 Global variable Life time of the solar hot water systemtvent [ year ] 1x1 Global variable Life time of the ventilation systemtwindow [ year ] 1x1 Global variable Life time of the windowUAc [ W / K ] 1x1 Global variable Sum of the U valuesUAceiling [ W / K ] 1x1 Help variable U value of the ceilingUAfloor [ W / K ] 1x1 Help variable U value of the floorUAlinlossin [ W / K ] 1x1 Help variable Sum of the U values of inner room linear lossesUAlinlossout [ W / K ] 1x1 Help variable Sum of the U values of outer room linear lossesUAmceiling [ W / (K*m²) ] 1x1 Help variable U value of the ceiling per m²UAmfloor [ W / (K*m²) ] 1x1 Help variable U value of the floor per m²UAmoutwall [ W / (K*m²) ] 1x1 Help variable U value of the outer wall per m²UAoutwallin [ W / K ] 1x1 Help variable U value of the inner room outer wallUAoutwallout [ W / K ] 1x1 Help variable U value of the outer room outer wallUAwin [ W / K ] 1x1 Help variable U value of the windowUVframe [ W / (K*m²) ] 1x1 Help variable U value of the window frame per m²UVglas [ W / (K*m²) ] 1x1 Help variable U value of the window glass per m²VB [ m³ ] 1x1 Help variable Volume of the buildingVR [ m³ ] 1x1 Help variable Volume of the roomwa [ 1 ] 1x1 Help variable Solar radiation to air note factorWconsum [ l / day ] 1x1 Help variable Water consumption of the building per daywidthB [ m ] 1x1 Help variable Width of the buildingwidthR [ m ] 1x1 Help variable Width of the roomwindowperc [ % ] 1x1 Help variable Window area given as a percentage of the outer wall area.ww [ 1 ] 1x1 Help variable Solar radiation to wall factor wwlinloss [ W / (K*m) ] 1x1 Help variable Window - Wall linear losses per mx [ ] 1x17 Global variable Variable of optimizing parameters.

List of the program:


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function [OverallLCC] = Optimise(x); global building fixed_var rooms Cooling Tout midtemp tempout1 global tempout2 tempin1 tempin2 Sin1 Sin2 Sout1 Sout2 % % % Building calculation inputs: % % % % Buildingarea [m²] AB = fixed_var.building_area; % AspectR: %Length / width of the Building [m/m] if x(15) == 0 error('Aspect Ratio is 0!!') else AspectRB = x(15); end % Roomnumber [m²] rooms = fixed_var.roomnumber; % % % Room calculation inputs: % % % % Roomheight [m] heightR = fixed_var.height; % Roomload [W] Load = fixed_var.load; % Solarradiaton to air note [0-1] (wa+ww =1 !!) wa = fixed_var.solarradiation_air; % Solarradiaton to wall note [0-1] (wa+ww =1 !!) ww = fixed_var.solarradiation_wall; % Heatcapacity of the air [J/(K*m³)] Cam = fixed_var.heatcap_air; % Setpoint for minimum roomtemperature [°C] Tset = fixed_var.temperature_set; % % % Outerwall calculation inputs: % % % if x(1) ~= 0 if x(2) ~= 0 % Lifetime of the outer wall [year] toutwall = building.outerwall(x(1)).LC_time; % U value of the outer wall [W/(K*m²)] UAmoutwall = building.outerwall(x(1)).u_value(x(2)); % Investmentcosts outer wall [DKK/m²] Invoutwallm = building.outerwall(x(1)).investmentcosts(x(2)); % Maintenance costs outerwall [DKK/m²] Maintoutwallm = building.outerwall(x(1)).maintenancecosts; % Corner linear losses [W/(K*m)] colinloss = building.outerwall(x(1)).linloss_tocorner(x(2)); % Heat transfer coeff. to outerwall node [W/(K*m²)] Kwouterwall = building.outerwall(x(1)).heattrans_wall; % Heat capacity of the outerwall [J/(K*m²)] Cwouterwall = building.outerwall(x(1)).heatcap_wall; else error('No outerwall insulation level choosen!')


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end else error('No input from outerwall database given!') end % % % Innerwall calculation inputs: % % % if x(3) ~= 0 % Lifetime of the inner wall [year] tinwall = building.innerwall(x(3)).LC_time; % Investmentcosts inner wall [DKK/m²] Invinwallm = building.innerwall(x(3)).investmentcosts; % Maintenance costs innerwall [DKK/m²] Maintinwallm = building.innerwall(x(3)).maintenancecosts; % Heat transfer coeff. to innerwall node [W/(K*m²)] Kwinnerwall = building.innerwall(x(3)).heattrans_wall; % Heat capacity of the innerwall [J/(K*m²)] Cwinnerwall = building.innerwall(x(3)).heatcap_wall; else error('No input from innerwall database given!') end % % % Floor calculation inputs: % % % if x(4) ~= 0 if x(5) ~= 0 % Floor flag [Yes or No] if fixed_var.floor_to_outerside_flag == 'Yes' % U value of the floor [W/(K*m²)] UAmfloor = building.floor(x(4)).u_value(x(5)); % Floor linear losses [W/(K*m)] flinloss = building.outerwall(x(1)).linloss_tofloor(x(2)); else UAmfloor = 0; flinloss = fixed_var.linloss_tofloor; end % Lifetime of the floor [year] tfloor = building.floor(x(4)).LC_time; % Investmentcosts floor [DKK/m²] Invfloorm = building.floor(x(4)).investmentcosts(x(5)); % Maintenance costs floor [DKK/m²] Maintfloorm = building.floor(x(4)).maintenancecosts; % Heat transfer coeff. to floor [W/(K*m²)] Kwfloor = building.floor(x(4)).heattrans_floor; % Heat capacity of the floor [J/(K*m²)] Cwfloor = building.floor(x(4)).heatcap_floor; else error('No floor insulation level choosen!') end else error('No input from floor database given!') end % % % Ceiling calculation inputs: %


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% % if x(6) ~= 0 if x(7) ~= 0 % Ceiling flag [Yes or No] if fixed_var.ceiling_to_outerside_flag == 'Yes' % U value of the ceiling [W/(K*m²)] UAmceiling = building.ceiling(x(6)).u_value(x(7)); % Ceiling linear losses [W/(K*m)] celinloss = building.outerwall(x(1)).linloss_toceiling(x(2)); else UAmceiling = 0; celinloss = fixed_var.linloss_toceiling; end % Lifetime of the ceiling [year] tceiling = building.ceiling(x(6)).LC_time; % Investmentcosts ceiling [DKK/m²] Invceilingm = building.ceiling(x(6)).investmentcosts(x(7)); % Maintenance costs ceiling [DKK/m²] Maintceilingm = building.ceiling(x(6)).maintenancecosts; % Heat transfer coeff. ceiling [W/(K*m²)] Kwceiling = building.ceiling(x(6)).heattrans_ceiling; % Heat capacity ceiling [J/(K*m²)] Cwceiling = building.ceiling(x(6)).heatcap_ceiling; else error('No ceiling insulation level choosen!') end else error('No input from ceiling database given!') end % % % Window calculation inputs: % % % % windowperc: % % of the outer wall for windowarea [%] if x(16) == 0 error('Window has no area!!') elseif x(16) > 100 error('Window area exceeds 100%!') else windowperc = x(16); end if x(8) ~= 0 % Lifetime of the window; [year] twindow = building.window(x(8)).LC_time; % U value of the window glas [W/(K*m²)] UVglas = building.window(x(8)).glas_u_value; % U value of the window frame [W/(K*m²)] UVframe = building.window(x(8)).frame_u_value; % G value of the window glas [1/m²] gvalue = building.window(x(8)).g_value; % Thickness of the window frame [m] framet = building.window(x(8)).frame_thickness; % Fix investmentcosts window [DKK] Invwindowfix= building.window(x(8)).price.fix_costs; % Var. investmentcosts window [DKK/m²] Invwindowm = building.window(x(8)).price.var_costs; % Maintenance costs window [DKK/m²] Maintwindowm= building.window(x(8)).maintenancecosts; % Frame condiditon factor if isempty (building.window(x(8)).frame_factor)


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p = 3; else p = building.window(x(8)).frame_factor; end % Glas - Window linear losses [W/(K*m)] gwlinloss = building.window(x(8)).linear_losses; % Window - Wall linear losses [W/(K*m)] wwlinloss = building.outerwall(x(1)).linloss_towindow(x(2)); else error('No Window choosen!') end % % % Shading system inputs: % % % if x(14) ~= 0 % Lifetime of the shading system [year] tshading = building.shading(x(14)).LC_time; % Fix investmentcosts window [DKK] Invshadingfix = building.shading(x(14)).price.fix_costs; % Var. investmentcosts window [DKK/m²] Invshadingm = building.shading(x(14)).price.var_costs; % Maintenance costs window [% Investmentcosts] Maintshadingm = building.shading(x(14)).maintenancecosts; % Minimal shading coefficient Smin = building.shading(x(14)).minimum_shading_factor; % Shading flag Sha_check = 1; else tshading = 0; Invshadingfix = 0; Invshadingm = 0; Maintshadingm = 0; Smin = 1; Sha_check = 0; end % % % Heating system calculation inputs: % % % if x(9) ~= 0 % Fuel type of the heating system [ele,gas,dih, or oil] hsyfuel = building.heating_system(x(9)).fueltype; % Lifetime of the heating system [year] theatsy = building.heating_system(x(9)).LC_time; % Fix investmentcost heating system [DKK/m²] Invheatsyfix = building.heating_system(x(9)).price.fix_costs; % Var. investmentcosts heating system [(DKK/m²)/m²] Invheatsym = building.heating_system(x(9)).price.var_costs; % Maintenance costs heating system [%Investmentcosts] Maintheatsym = building.heating_system(x(9)).maintenancecosts; % Efficiency of the heating system eheatingsy = building.heating_system(x(9)).efficiency; else error('No input from Heating system given!') end % % % Hot water calculation inputs: %


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% % % Daily waterconsumption: [l/(day)] Wconsum = fixed_var.waterconsumption; % Temperaturdifference Water [°C] DT = fixed_var.temperatur_difference_water; % % % Cooling system calculation inputs: % % % if x(10) ~= 0 if x(11) ~= 0 % Setpoint for cooling roomtemperature [°C] Tempcool = fixed_var.temperature_cooling; % Lifetime of the cooling system [year] tcool = building.cooling_system(x(10)).LC_time; % Investmentcosts cooling system [DKK/(m³/s)] Invcoolsym = building.cooling_system(x(10)).investmentcosts; % Maintenance costs cooling system [% Investmentcosts] Maintcoolsym = building.cooling_system(x(10)).maintenancecosts; % Coefficient of Performance [%] ecoolingsy = building.cooling_system(x(10)).COP_factor; % Mechanical cooling rate [1/h] ncool = fixed_var.mech_ventrate; % Cooling flag Cool_check = 1; else error('Cooling is not working without the ventilation system!') end else Tempcool = 26; tcool = 0; Invcoolsym = 0; Maintcoolsym = 0; ecoolingsy = 100; ncool = 0; Cool_check = 0; end % % % Ventilation system calculation inputs: % % % if x(11) ~= 0 % Lifetime of the ventilation system [year] tvent = building.vent_system(x(11)).LC_time; % Investmentcosts ventilation system [DKK/(m³/s)] Invventm = building.vent_system(x(11)).investmentcosts; % Maintenance costs ventilation system [% Investmentcosts] Maintventm = building.vent_system(x(11)).maintenancecosts; % Infiltrationrate [1/h] infil = fixed_var.infilrate_with_ventilation; % Mechanical ventilation rate [1/h] n = fixed_var.mech_ventrate; % Pressure drop ventilation system [pa] Dpsystem = building.vent_system(x(11)).pressure_drop; % Pressure drop of the ducting system [pa] Dpduct = fixed_var.pressure_drop; % Ventilation system efficiency [%] eventsy = building.vent_system(x(11)).system_efficiency; % Efficiency of the heat recovery [%] eheatrec = building.vent_system(x(11)).heat_recovery_efficiency;


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else tvent = 0; Invventm = 0; Maintventm = 0; infil = fixed_var.infilrate_without_ventilation; n = 0; Dpsystem = 0; Dpduct = 0; eventsy = 100; eheatrec = 100; end % % % Solar hot water system calculation inputs: % % % if x(12) ~= 0 % Lifetime of the solar hot water system [year] tsolsy = building.solar_system(x(12)).LC_time; % Fix investment costs solar hot water system [DKK] Invsolsyfix = building.solar_system(x(12)).price.fix_costs; % Var investment costs solar hot water system [DKK/m²] Invsolsym = building.solar_system(x(12)).price.var_costs; % Maintenance costs solar hot water system [% Investmentcosts] Maintsolsym = building.solar_system(x(12)).maintenancecosts; if x(13) ~= 0 % Net area factor for the solar hot water system[m²/(l*day)] nettoareafac= building.solar_system(x(12)).areafactor(x(13)); % Yearly share of hot water [%] solarshare = building.solar_system(x(12)).solarshare(x(13)); else error('No solar area choosen!') end else x(13) = 0; tsolsy = 0; Invsolsyfix = 0; Invsolsym = 0; Maintsolsym = 0; nettoareafac= 0; solarshare = 0; end % % % Orientation calculation inputs: % % % % Choosing the data for orientation if x(17) == 0 error('No Orientation choosen !!') else % Defining the solar input directions (orientation) direction1 = building.orientation(x(17)).direction1; direction2 = building.orientation(x(17)).direction2; end % % % Economical calculation inputs: %


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% % % Interest rate [%] iint = fixed_var.interest_rate; % Inflation rate [%] iinf = fixed_var.inflation_rate; % Energy price rise rate [%] iene = fixed_var.energy_rise_rate; % Fix price for gas [DKK/year] gasfix = fixed_var.gas_fixprice; % Variable price for gas [DKK/kWh] gas = fixed_var.gas_price; % Fix price for oil [DKK/year] oilfix = fixed_var.oil_fixprice; % Variable price for oil [DKK/kWh] oil = fixed_var.oil_price; % Variable price for electricity [DKK/kWh] eprice = fixed_var.electricity_price; % Fix price for electricity [DKK/year] epricefixnight = fixed_var.electricity_fixprice_night; % Variable price for electricity night [DKK/kWh] epricenight = fixed_var.electricity_price_night; % Fix price for district heating [DKK/(kW*year)] districthfix = fixed_var.districtheat_fixprice; % Variable price for district heating [DKK/kWh] districth = fixed_var.districtheat_price; % Time of the considered period [year] tLC = fixed_var.totalLC_time; % % % % % C A L C U L A T I O N S % % % % % % Basic calculations for the building: % % rooms: Number of rooms in the building % lengthB: Length of the building % widthB: Width of the building % VB: Volume of the building lengthB = sqrt(AspectRB * AB); widthB = sqrt(AB / AspectRB); AR = (AB / rooms); VB = heightR * AB; % Basic calculations for the rooms: % % AspectRR: Aspectratio of the room % lengtR: Length of the room % widthR: Width of the room % Awin: Windowarea of the room % VR: Volume of one outer room AspectRR = AspectRB * (4 / rooms); lengthR = sqrt(AspectRR * AR); widthR = sqrt(AR / AspectRR); Awin = heightR * lengthR * (windowperc/100); VR = heightR * AR; % % % ROOM CALCULATIONS %


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% % % % % UA values calculatitons % % % % Calculation of the UA value of the floor UAfloor = UAmfloor * AR * 0.6; % Calculation of the UA value of the ceiling UAceiling = UAmceiling * AR; % Calculation of the UA value of the window % % swin is the width of the window % sglas is the width of the glas in the window % glasslength is the length along the glass and the frame swin = sqrt (Awin); sglas = swin - (2*framet); glasslength = 4 * sglas; Aglas = sglas^2; Aframe = Awin - Aglas; UAwin = (Aglas * UVglas + Aframe * UVframe + glasslength * gwlinloss); % % % Inddoor model input calculation % % % % Calculation of the heat capacity value of the air: Ca Ca = Cam * VR; % % % Calculation of investment costs % % % % Calculation of the investment floor costs if fixed_var.floor_to_outerside_flag == 'Yes' InvfloorR = Invfloorm * AR; else InvfloorR = 0.5 * Invfloorm * AR; end % Calculation of the investment ceiling costs if fixed_var.ceiling_to_outerside_flag == 'Yes' InvceilingR = Invceilingm * AR; else InvceilingR = 0.5 * Invceilingm * AR; end % Calculation of the investment window costs InvwindowR = Invwindowfix + Invwindowm * Awin; % % % Calculation of maintenance costs % % % % Calculation of the maintenance floor costs if fixed_var.floor_to_outerside_flag == 'Yes' MaintfloorR = Maintfloorm * AR; else MaintfloorR = 0.5 * Maintfloorm * AR; end


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% Calculation of the maintenance ceiling costs if fixed_var.ceiling_to_outerside_flag == 'Yes' MaintceilingR = Maintceilingm * AR; else MaintceilingR = 0.5 * Maintceilingm * AR; end % Calculation of the maintenance window costs MaintwindowR = InvwindowR * (Maintwindowm/100); % % % OUTER ROOM CALCULATIONS % % % % % % UA values calculatitons % % % % Calculation of the UA value of the wall UAoutwallout = UAmoutwall * (heightR * lengthR - Awin + heightR * widthR); % Calculation of the linear losses of the room UAlinlossout = colinloss * heightR * 3 + flinloss * (lengthR + widthR) + ... celinloss * (lengthR + widthR) + 4 * swin * wwlinloss; % Calculation of the UA value of the room construction UAc = UAfloor + UAceiling + UAoutwallout + UAlinlossout + UAwin; % % % Inddoor model input calculation % % % % Calculation of the heat capacity value of the room: Cw Cw = (Cwouterwall * ((heightR * (lengthR + widthR))- Awin)... + Cwinnerwall * (heightR * (lengthR + widthR)) + Cwfloor * AR + Cwceiling * AR); % Calculation of the heat transfer coefficient of the room: Kw Kw = (1/(0.13 + 1/Kwouterwall)) * ((heightR * (lengthR + widthR))- Awin)... + (1/(0.13 + 1/Kwinnerwall)) * (heightR * (lengthR + widthR)) + (1/(0.13 + 1/Kwfloor))... * AR + (1/(0.13 + 1/Kwceiling)) * AR; % Calculation of Qsun for the first direction Qsun = Aglas * gvalue * (direction1(:,4).*(1-tan(pi*direction1(:,5)./ (2*180)).^p)+(direction1(:,2)+direction1(:,3))*(1-tan(pi*60/(2*180)).^p)); % Simple room model, which calculates energy use for heating and cooling, % the indoor temperature, and shade. [Heatingout1,maxheatout1,Coolingout1,maxcoolout1,tempout1,Sout1]=... simpleroom(wa,ww,Qsun,Tout,UAc,Kw,(eheatrec/100),n,infil,VR,Load,Ca,Cw,Tset,Tempcool,Smin,Sha_check,Cool_check); % Calculation of Qsun for the second direction Qsun = Aglas * gvalue * (direction2(:,4).*(1-tan(pi*direction2(:,5)./ (2*180)).^p)+(direction2(:,2)+direction2(:,3))*(1-tan(pi*60/(2*180)).^p)); % Simple room model, which calculates energy use for heating and cooling, % the indoor temperature, and shade. [Heatingout2,maxheatout2,Coolingout2,maxcoolout2,tempout2,Sout2]=... simpleroom(wa,ww,Qsun,Tout,UAc,Kw,(eheatrec/100),n,infil,VR,Load,Ca,Cw,Tset,Tempcool,Smin,Sha_check,Cool_check);


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% % % Calculation of investment costs % % % % Calculation of the investment outer wall costs Invoutwallout = Invoutwallm * (heightR * (lengthR + widthR)- Awin); % Calculation of the investment inner wall costs Invinwallout = 0.5 * Invinwallm * (heightR * (lengthR + widthR)); % Calculation of the investment shading costs Invshadingout = Invshadingfix + Invshadingm * Awin; % % % Calculation of maintenance costs % % % % Calculation of the maintenance outer wall costs Maintoutwallout = Maintoutwallm * (heightR * (lengthR + widthR)- Awin); % Calculation of the maintenance inner wall costs Maintinwallout = 0.5 * Maintinwallm * (heightR * (lengthR + widthR)); % % % INNER ROOM CALCULATIONS % % % % % % UA values calculatitons % % % % Calculation of the UA value of the wall UAoutwallin = UAmoutwall * (heightR * lengthR - Awin); % Calculation of the linear losses of the room UAlinlossin = colinloss * heightR * 2 + flinloss * lengthR + celinloss * lengthR +4 * swin * wwlinloss; % Calculation of the UA value of the room construction UAc = UAfloor + UAceiling + UAoutwallin + UAlinlossin + UAwin; % % % Inddoor model input calculation % % % % Calculation of the heat capacity value of the room: Cw Cw = (Cwouterwall * (heightR * lengthR - Awin) ... + Cwinnerwall * (heightR * lengthR + 2 * heightR * widthR)... + Cwfloor * AR + Cwceiling * AR); % Calculation of the heat transfer coefficient of the room: Kw Kw = (1/(0.13 + 1/Kwouterwall)) * (heightR * lengthR - Awin)... + (1/(0.13 + 1/Kwinnerwall)) * (heightR * lengthR + 2 * heightR * widthR).+ (1/(0.13 + 1/Kwfloor)) * AR + (1/(0.13 + 1/Kwceiling)) * AR; % Calculation of Qsun of the first direction Qsun = Aglas * gvalue * (direction1(:,4).*(1-tan(pi*direction1(:,5)./ (2*180)).^p)+(direction1(:,2)+direction1(:,3))*(1-tan(pi*60/(2*180)).^p)); % Simple room model, which calculates energy use for heating and cooling, % the indoor temperature, and shade.


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[Heatingin1,maxheatin1,Coolingin1,maxcoolin1,tempin1,Sin1]=... simpleroom(wa,ww,Qsun,Tout,UAc,Kw,(eheatrec/100),n,infil,VR,Load,Ca,Cw,Tset,Tempcool,Smin,Sha_check,Cool_check); % Calculation of Qsun of the second direction Qsun = Aglas * gvalue * (direction2(:,4).*(1-tan(pi*direction2(:,5)./ (2*180)).^p)+(direction2(:,2)+direction2(:,3))*(1-tan(pi*60/(2*180)).^p)); % Simple room model, which calculates energy use for heating and cooling, % the indoor temperature, and shade. [Heatingin2,maxheatin2,Coolingin2,maxcoolin2,tempin2,Sin2]=... simpleroom(wa,ww,Qsun,Tout,UAc,Kw,(eheatrec/100),n,infil,VR,Load,Ca,Cw,Tset,Tempcool,Smin,Sha_check,Cool_check); % Calculation of the mean value temperature in the building midtemp = (tempout1 * 2 + tempout2 * 2 + (tempin1 + tempin2) * (( rooms - 4) / 2))... / rooms; % % % Calculation of investment costs % % % % Calculation of the investment outer wall costs Invoutwallin = Invoutwallm * (heightR * lengthR - Awin); % Calculation of the investment inner wall costs Invinwallin = 0.5 * Invinwallm * (heightR * lengthR + 2 * heightR * widthR); % Calculation of the investment shading costs Invshadingin = Invshadingfix + Invshadingm * Awin; % % % Calculation of maintenance costs % % % % Calculation of the maintenance outer wall costs Maintoutwallin = Maintoutwallm * (heightR * lengthR - Awin); % Calculation of the maintenance inner wall costs Maintinwallin = 0.5 * Maintinwallm * (heightR * lengthR + 2 * heightR * widthR); % % % BUILDING CALCULATIONS % % % % % % Calculation of investment costs % % % % Calculation of the investment outer wall costs Invoutwall = Invoutwallin * (rooms - 4) + 4 * Invoutwallout; % Calculation of the investment inner wall costs Invinwall = Invinwallin * (rooms - 4) + 4 * Invinwallout; % Calculation of the investment floor costs Invfloor = InvfloorR * rooms; % Calculation of the investment ceiling costs Invceiling = InvceilingR * rooms;


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% Calculation of the investment window costs Invwindow = InvwindowR * rooms; % Calculation of the investment shading costs Invshading = Invshadingin * (rooms - 4) + 4 * Invshadingout; % Calculation of the investment heating system costs Invheatsy = (Invheatsyfix + Invheatsym * AB) * AB; % Calculation of the investment ventilation system costs Invvent = ((n * VB)/3600) * Invventm; % Calculation of the investment cooling system costs Cooling = 2 * (Coolingout1 + Coolingout2) + (Coolingin1 + Coolingin2) * ((rooms - 4) / 2); if Cooling > 0 Invcool = ((ncool * VB)/3600) * Invcoolsym; else Invcool = 0; end % Calculation of the investment solar hot water system costs; % The nettoareafactor multiplied with the Waterconsumption gives % the needed solar collector area. Invsolsy = Invsolsyfix + nettoareafac * Wconsum * Invsolsym; % % % Calculation of maintenance costs % % % % Calculation of the maintenance outer wall costs Maintoutwall = Maintoutwallin * (rooms - 4) + 4 * Maintoutwallout; % Calculation of the maintenance inner wall costs Maintinwall = Maintinwallin * (rooms - 4) + 4 * Maintinwallout; % Calculation of the maintenance floor costs Maintfloor = MaintfloorR * rooms; % Calculation of the maintenance ceiling costs Maintceiling = MaintceilingR * rooms; % Calculation of the maintenance heating system costs Maintheatsy = (Maintheatsym/100) * Invheatsy; % Calculation of the maintenance ventilation system costs Maintvent = (Maintventm/100) * Invvent; % Calculation of the maintenance cooling system costs Maintcool = (Maintcoolsym/100) * Invcool; % Calculation of the maintenance solar hot water costs Maintsolsy = (Maintsolsym/100) * Invsolsy; % Calculation of the maintenance window costs Maintwindow = MaintwindowR * rooms; % Calculation of the maintenance shading costs Maintshading = (Maintshadingm/100) * Invshading; % % % Variable costs calculation %


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% % % Choosing the type of fuel for heating if hsyfuel == 'ele' hprice = eprice; hwprice = epricenight; hpricefix = epricefixnight; elseif hsyfuel == 'gas' hprice = gas; hwprice = gas; hpricefix = gasfix; elseif hsyfuel == 'oil' hprice = oil; hwprice = oil; hpricefix = oilfix; elseif hsyfuel == 'dih' hprice = districth; hwprice = districth; maxheat = 2 * (maxheatout1 + maxheatout2) + (maxheatin1 + maxheatin2) * ((rooms - 4) / 2); hpricefix = districthfix * maxheat; iene = 0; else error('No fuel for heating choosen!!') end % Calculation of the energyconsumption for hot water % Qw: Energy consumption for one year of hot water [ kWh/year ] Qw = 365 * Wconsum * (1.16/1000) * DT; % Calculation of the whole energy consumption for roomheating + water Heating = 2 * (Heatingout1 + Heatingout2) + (Heatingin1 + Heatingin2) * ((rooms - 4) / 2) hconsum = Heating/(eheatingsy/100); hwconsum = ((1 - solarshare/100) * Qw)/(eheatingsy/100); heatconsumption = hwconsum + hconsum; % Calculation of the electricity consumption of the ventilation Dp = Dpsystem + Dpduct; econsumvent = (((2 * (Dp * n * VB)/3600)/(eventsy/100))/1000) * 365 * 24; % Calculation of the electricity consumption of the Cooling econsumcool = Cooling/(ecoolingsy/100); % Sum of the electricity consumption for cooling and ventilation econsum = econsumvent + econsumcool; % Function LCC calculates the Life Cycle Costs for maintenances, the restvalues, and % maintainance costs of the building parts. [OverallLCC] = LCC(tLC,toutwall,Invoutwall,Maintoutwall,tinwall,Invinwall,Maintinwall,... tfloor,Invfloor,Maintfloor,tceiling,Invceiling,Maintceiling,... twindow,Invwindow,Maintwindow,theatsy,Invheatsy,Maintheatsy,... tvent,Invvent,Maintvent,tcool,Invcool,Maintcool,... tsolsy,Invsolsy,Maintsolsy,tshading,Invshading,Maintshading,... hprice,hwprice,hconsum,hwconsum,hpricefix,eprice,econsum,iint,iinf,iene) ; LCC.m:


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Purpose: The purpose of the function ’LCC.m’ is to calculate the Life Cycle Costs (LCC) of a building, including the investments, the scrap values, maintenance and operating costs. Description: The Life Cycle Costs are calculated as the sum of the Net Present Values (NPV) of the Investment Costs (IC), Periodical Costs (PC) and Operating Costs (OC) minus the Scrap Values (SV) over the life cycle time. Call to function: Function ’LCC.m’ is called by: • LCC(tLC,toutwall,Invoutwall,Maintoutwall,tinwall,Invinwall,Maintinwall,tfloor,Invfloor,

Maintfloor,tceiling,Invceiling,Maintceiling,twindow,Invwindow,Maintwindow,theatsy, Invheatsy,Maintheatsy,tvent,Invvent,Maintvent,tcool,Invcool,Maintcool,tsolsy,Invsolsy, Maintsolsy,tshading,Invshading,Maintshading,hprice,hwprice,hconsum,hwconsum, hpricefix,eprice,econsum,iint,iinf,iene);

Sub functions: • ’None’ Variables:


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AllLCC [ money ] 1x1 Global variable Sum of the Life Cycle Costs.econsum [ kWh / year ] 1x1 Global variable Amount of electricity consumption.eine [ % ] 1x1 Global variable Energy price rising rate.eprice [ money / kWh ] 1x1 Global variable Costs for one kWh of electricity consumption.hconsum [ kWh / year ] 1x1 Global variable Amount of heat consumption.hprice [ money / kWh ] 1x1 Global variable Costs for one kWh of heat consumption.hpricefix [ money / year ] 1x1 Global variable Yearly fix costs for the heating system.hwconsum [ kWh / year ] 1x1 Global variable Amount of hot water consumption.hwprice [ money / kWh ] 1x1 Global variable Costs for one kWh of hot water consumption.id [ % ] 1x1 Help variable Discount rate.ide [ % ] 1x1 Help variable Discount rate, including the energy price rising rate.iinf [ % ] 1x1 Global variable Inflation rate.iint [ % ] 1x1 Global variable Interest rate. Invceiling [ money ] 1x1 Global variable Investment costs of the ceiling.Invcool [ money ] 1x1 Global variable Investment costs of the cooling system.Invfloor [ money ] 1x1 Global variable Investment costs of the floor.Invheatsy [ money ] 1x1 Global variable Investment costs of the heating system.Invinwall [ money ] 1x1 Global variable Investment costs of the inner wall.Invoutwall [ money ] 1x1 Global variable Investment costs of the outer wall.Invshading [ money ] 1x1 Global variable Investment costs of the shading device.Invsolsy [ money ] 1x1 Global variable Investment costs of the solar hot water system.Invvent [ money ] 1x1 Global variable Investment costs of the ventilation system.Invwindow [ money ] 1x1 Global variable Investment costs of the window.LCCceiling [ money ] 1x1 Help variable Life Cycle Costs of the ceiling.LCCcool [ money ] 1x1 Help variable Life Cycle Costs ot the cooling system.LCCfix [ money ] 1x1 Help variable Sum of the fix Life Cycle Costs.LCCfloor [ money ] 1x1 Help variable Life Cycle Costs of the floor.LCCheatsy [ money ] 1x1 Help variable Life Cycle Costs of the heating system.LCCinwall [ money ] 1x1 Help variable Life Cycle Costs of the inner wall.LCCmaint [ money ] 1x1 Help variable Sum of the maintenance Life Cycle Costs.LCCoutwall [ money ] 1x1 Help variable Life Cycle Costs of the outer wall.LCCshading [ money ] 1x1 Help variable Life Cycle Costs of the shading device.LCCsolsy [ money ] 1x1 Help variable Life Cycle Costs of the solar hot water system.LCCvar [ money ] 1x1 Help variable Sum of the variable (operational) Life Cycle Costs.LCCvent [ money ] 1x1 Help variable Life Cycle Costs of the ventilation system.LCCwindow [ money ] 1x1 Help variable Life Cycle Costs of the window.LCCx [ money ] 1x1 Help variable Counter for investment costs per period.Maintceiling [ money / year ] 1x1 Global variable Maintenance costs of the ceiling.Maintcool [ money / year ] 1x1 Global variable Maintenance costs of the cooling system.Maintfloor [ money / year ] 1x1 Global variable Maintenance costs of the floor.Maintheatsy [ money / year ] 1x1 Global variable Maintenance costs of the heating system.Maintinwall [ money / year ] 1x1 Global variable Maintenance costs of the inner wall.Maintoutwall [ money / year ] 1x1 Global variable Maintenance costs of the outer wall.Maintshading [ money / year ] 1x1 Global variable Maintenance costs of the shading device.Maintsolsy [ money / year ] 1x1 Global variable Maintenance costs of the solar hot water system.Maintvent [ money / year ] 1x1 Global variable Maintenance costs of the ventilation system.Maintwindow [ money / year ] 1x1 Global variable Maintenance costs of the window.tceiling [ year ] 1x1 Global variable Lifetime of the ceiling.tcool [ year ] 1x1 Global variable Lifetime of the cooling system.tfloor [ year ] 1x1 Global variable Lifetime of the floor.theatsy [ year ] 1x1 Global variable Lifetime of the heating system.tinwall [ year ] 1x1 Global variable Lifetime of the inner wall.tLC [ year ] 1x1 Global variable Lifetime of the building.toutwall [ year ] 1x1 Global variable Lifetime of the outer wall.tshading [ year ] 1x1 Global variable Lifetime of the shading device.tsolsy [ year ] 1x1 Global variable Lifetime of the solar hot water system.tvent [ year ] 1x1 Global variable Lifetime of the ventilation system.twindow [ year ] 1x1 Global variable Lifetime of the window.z [ 1 ] 1x1 Help variable Counter for reinvestment of a part.


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List of the program: function [AllLCC] = LCC(tLC,... toutwall,Invoutwall,Maintoutwall,tinwall,Invinwall,Maintinwall,... tfloor,Invfloor,Maintfloor,tceiling,Invceiling,Maintceiling,... twindow,Invwindow,Maintwindow,theatsy,Invheatsy,Maintheatsy,... tvent,Invvent,Maintvent,tcool,Invcool,Maintcool,... tsolsy,Invsolsy,Maintsolsy,tshading,Invshading,Maintshading,... hprice,hwprice,hconsum,hwconsum,hpricefix,eprice,econsum,iint,iinf,iene); % Function LCC calculates the Life Cycle Costs of investments, including % the scrap values,running and maintainance costs of the building. % tLC Life cycle time of the whole calculation % t.. Life cycle time of the part % Inv.. Investment cost of the part % LCC.. Life cycle cost of the part % Maint.. Maintainance cost of the part % LCCfix Total fixed costs % LCCvar Total variable costs % LCCmaint Total maintainance costs % iint interest rate % iinf inflation rate % iene energy price rising rate % id discount rate % ide discount rate including the energy price rising rate iint = iint/100; iinf = iinf/100; iene = iene/100; id = iint - iinf; ide = iint - iinf - iene; % LCCoutwall Life Cycle Cost calculation for the outer wall LCCoutwall = 0; if toutwall ~= 0 if toutwall <= tLC z = tLC/toutwall; for n = 0:z LCCx = Invoutwall * (1+id)^(-n*toutwall); LCCoutwall = LCCoutwall + LCCx; end LCCoutwall = LCCoutwall - Invoutwall * (toutwall-(tLC-floor(z) *toutwall))/toutwall * (1+id)^(-tLC); else LCCoutwall = Invoutwall - Invoutwall * ((toutwall-tLC)/toutwall) * (1+id)^(-tLC); end end % LCCinwall Life Cycle Cost calculation for the inner wall LCCinwall = 0; if tinwall ~= 0 if tinwall <= tLC z = tLC/tinwall; for n = 0:z LCCx = Invinwall * (1+id)^(-n*tinwall); LCCinwall = LCCinwall + LCCx; end LCCinwall = LCCinwall - Invinwall * (tinwall-(tLC-floor(z)*tinwall)) /tinwall * (1+id)^(-tLC); else LCCinwall = Invinwall - Invinwall * ((tinwall-tLC)/tinwall) * (1+id)^(-tLC); end end % LCCfloor Life Cycle Cost calculation for the floor LCCfloor = 0; if tfloor ~= 0


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if tfloor <= tLC z = tLC/tfloor; for n = 0:z LCCx = Invfloor * (1+id)^(-n*tfloor); LCCfloor = LCCfloor + LCCx; end LCCfloor = LCCfloor - Invfloor * (tfloor-(tLC-floor(z)*tfloor))... /tfloor * (1+id)^(-tLC); else LCCfloor = Invfloor - Invfloor * ((tfloor-tLC)/tfloor) * (1+id)^(-tLC); end end % LCCceiling Life Cycle Cost calculation for the ceiling LCCceiling = 0; if tceiling ~= 0 if tceiling <= tLC z = tLC/tceiling; for n = 0:z LCCx = Invceiling * (1+id)^(-n*tceiling); LCCceiling = LCCceiling + LCCx; end LCCceiling = LCCceiling - Invceiling * (tceiling-(tLC-floor(z) *tceiling))/tceiling * (1+id)^(-tLC); else LCCceiling = Invceiling - Invceiling * ((tceiling-tLC)/tceiling) * (1+id)^(-tLC); end end % LCCwindow Life Cycle Cost calculation for the window LCCwindow = 0; if twindow ~= 0 if twindow <= tLC z = tLC/twindow; for n = 0:z LCCx = Invwindow * (1+id)^(-n*twindow); LCCwindow = LCCwindow + LCCx; end LCCwindow = LCCwindow - Invwindow * (twindow-(tLC-floor(z) *twindow))/twindow * (1+id)^(-tLC); else LCCwindow = Invwindow - Invwindow * ((twindow-tLC)/twindow) * (1+id)^(-tLC); end end % LCCheatsy Life Cycle Cost calculation for the heatingsystem LCCheatsy = 0; if theatsy ~= 0 if theatsy <= tLC z = tLC/theatsy; for n = 0:z LCCx = Invheatsy * (1+id)^(-n*theatsy); LCCheatsy = LCCheatsy + LCCx; end LCCheatsy = LCCheatsy - Invheatsy * (theatsy-(tLC-floor(z) *theatsy))/theatsy * (1+id)^(-tLC); else LCCheatsy = Invheatsy - Invheatsy * ((theatsy-tLC)/theatsy) * (1+id)^(-tLC); end end % LCCvent Life Cycle Cost calculation for the ventilation system LCCvent = 0; if tvent ~= 0 if tvent <= tLC z = tLC/tvent; for n = 0:z LCCx = Invvent * (1+id)^(-n*tvent);


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LCCvent = LCCvent + LCCx; end LCCvent = LCCvent - Invvent * (tvent-(tLC-floor(z)*tvent))... /tvent * (1+id)^(-tLC); else LCCvent = Invvent - Invvent * ((tvent-tLC)/tvent) * (1+id)^(-tLC); end end % LCCcool Life Cycle Cost calculation for the cooling system LCCcool = 0; if tcool ~= 0 if tcool <= tLC z = tLC/tcool; for n = 0:z LCCx = Invcool * (1+id)^(-n*tcool); LCCcool = LCCcool + LCCx; end LCCcool = LCCcool - Invcool * (tcool-(tLC-floor(z)*tcool))... /tcool * (1+id)^(-tLC); else LCCcool = Invcool - Invcool * ((tcool-tLC)/tcool) * (1+id)^(-tLC); end end % LCCsolsy Life Cycle Cost calculation for the solar hot water system LCCsolsy = 0; if tsolsy ~= 0 if tsolsy <= tLC z = tLC/tsolsy; for n = 0:z LCCx = Invsolsy * (1+id)^(-n*tsolsy); LCCsolsy = LCCsolsy + LCCx; end LCCsolsy = LCCsolsy - Invsolsy * (tsolsy-(tLC-floor(z)*tsolsy))... /tsolsy * (1+id)^(-tLC); else LCCsolsy = Invsolsy - Invsolsy * ((tsolsy-tLC)/tsolsy) * (1+id)^(-tLC); end end % LCCshading Life Cycle Cost calculation for the shading system LCCshading = 0; if tshading ~= 0 if tshading <= tLC z = tLC/tshading; for n = 0:z LCCx = Invshading * (1+id)^(-n*tshading); LCCshading = LCCshading + LCCx; end LCCshading = LCCshading - Invshading * (tshading-(tLC-floor(z) *tshading))/tshading * (1+id)^(-tLC); else LCCshading = Invshading - Invshading * ((tshading-tLC)/tshading) * (1+id)^(-tLC); end end % Total fix costs calculation LCCfix = LCCoutwall + LCCinwall + LCCfloor + LCCceiling + LCCwindow... + LCCheatsy + LCCvent + LCCcool + LCCsolsy + LCCshading; % Maintainance Cost calculation if id == 0 LCCmaint = (Maintoutwall + Maintinwall + Maintfloor + Maintceiling... + Maintwindow + Maintheatsy + Maintvent + Maintcool + Maintsolsy + Maintshading) * tLC; else LCCmaint = (Maintoutwall + Maintinwall + Maintfloor + Maintceiling... + Maintwindow + Maintheatsy + Maintvent + Maintcool + Maintsolsy


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+ Maintshading)* (1-(1+id)^(-tLC))/id; end % Total variable energy costs if ide == 0 LCCvar = (hprice * hconsum + hwprice * hwconsum + hpricefix +... eprice * econsum) * tLC; else LCCvar = (hprice * hconsum + hwprice * hwconsum + hpricefix +... eprice * econsum) * (1-(1+ide)^(-tLC))/ide; end % Total Life Cycle Cost calculation AllLCC = LCCfix + LCCmaint + LCCvar;

Optimisation of Energy Efficiency Methods in Buildings regarding Life Cycle Costs Appendix C

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Appendix C: In this Appendix the used program ’Simpleroom.m’, written by the supervisor Toke Rammer Nielsen will be described in detail and for the optimisation program ’gclSolve.m’ a short description will be given. SimpleRoom.m Purpose This function is a simple thermal model of a room. It calculates the heating and cooling demand, hourly heating and cooling load, hourly indoor air temperatures, hourly shading factor, and maximum and cooling load. Simple information on the building is needed as well as climate data. Description The room is described using a simple model with two nodes. From the indoor air heat can be exchanged with the outdoor air and the internal constructions. Solar gain is distributed between the air and internal constructions. Internal load heats the indoor air. The model is used in the program VinSim (Rafnsson, 1997). In Figure 1 an electrical representation of the model is given.

Figure 1. The room model represented by electrical network. The differential equation The differential equations governing the model is given in Eq. (1)

⋅

⋅++⋅

+

−

−−

=

w

sunw

a

osuna

w

a

w

w

w

w

a

w

a

w

w

a

CQw

CTUALQw

TT

CK

CK

CK

CKUA

dtdTdt

dT

(1)

where Tw is the wall temperature [K] Ta is the indoor air temperature [K] To is the outdoor air temperature [K] Cw is the heat capacity of the internal surfaces [J/K] Ca is the indoor air heat capacity [J/K] UA is the thermal transmittance to the outdoor climate [W/K]

Tw

Cw Ca

Ta

To wa·Qsun ww·Qsun L

UA Kw


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Kw is the thermal transmittance between the indoor air and internal surfaces [W/K] L is the internal load [W] Qsun is the solar gain [W] wa is the part of the solar gain absorbed in the air [-] ww is the part of the solar gain absorbed in the internal surfaces [-] t is the time [s] It is assumed that the total heat capacity of the internal surfaces and the total thermal transmittance between the indoor air and the internal surfaces can be estimated by the sum of the values for the different surfaces. The thermal transmittance to the outdoor climate is found as the sum of the thermal transmittance for the different constructions facing the outdoor climate including infiltration and ventilation. The total heat capacity, Cw, of the internal surfaces is found by summing the heat capacity of the different sub surfaces (eg. floor, wall, ceiling). Eq. (2) states how to calculate the total internal heat capacity.

∑ ⋅=n

1jjw cAC (2)

where n is the number of different internal surfaces [-] A is the area of surface j [m2] c is the heat capacity of surface j [J/m2K] The total thermal transmittance, Kw, to the internal surfaces is found by summing the thermal transmittances of the different sub surfaces. Eq. (3) states how to calculate the total thermal transmittance.

∑ ⋅=n

1jjw kAK (3)

where n is the number of different internal surfaces [-] Aj is the area of surface j [m2] kj is the thermal transmittance of surface j [W/m2K] The calculation of the total heat capacity and the total thermal transmittance is an approximation as the internal walls are only represented by a single temperature. The thermal transmittance to the outdoor climate, UA, is given in Eq. (4)

Vn)1(Vn34.0fAUUA mechinf

m

1jj ⋅⋅ε−+⋅⋅+⋅⋅= ∑ (4)

where m is the number of surfaces facing the outdoor climate [-] Uj is the U-value of construction j [W/m2K] Aj is the area of construction j [m2]


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f is a factor which is 0.6 for floors to the ground and 1 for ceilings and walls [-] ninf is the infiltration air change rate [1/h] nmech is the mechanical ventilation rate [1/h] V is the indoor air volume [m2] ε is the efficiency of the heat recovery [-] The solution to Eq. 1 gives the air and wall temperature as

+⋅⋅λ⋅+⋅⋅λ⋅=

2

1222111 z

zV)texp(cV)texp(c

TwTa

(5)

where c1,c2 are constants depending on the initial conditions λ1, λ2 are the eigenvalues

21 V,V are the eigenvectors z1,z2 are solutions to inhomogeneous system Solution to inhomogeneous system is:

osunasunw

1 TUA

LQwQwz +

+⋅+⋅= (6)

osunasunw

w

sunw2 T

UALQwQw

KQw

z ++⋅+⋅

+⋅

= (7)

The values of c1 and c2 are found as the solution to the equation

[ ]

−−

=

⋅

20w

10a

2

121

zTzT

cc

VV (8)

where Ta0 is the initial condition for the air temperature Tw0 is the initial condition for the wall temperature The time steps are one hour for which the solar gain, load and outdoor temperature are known. Also the air and wall temperature from the previous time step is known and used as initial conditions in the next time step. When the calculated air temperature is below the heating set point the heat exchanger is active, but if the air temperature is above the heating set point the heat exchanger is by-passed and the UA value is found from eq. 4 with ε=0. This is done to avoid high indoor temperatures. Heating When the solar gain and load in the building is not sufficient to keep the air temperature above the heating set point, Tset, an extra heating power is needed. The extra heating power is calculated so that the air temperature is kept at the set point for heating. From Eq. 5 we want to find the new load which gives the wanted air temperature at the end of the time step.


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With

osunasunw

1 TUA

QwQwP +

⋅+⋅= (9)

osunasunw

w

w2 T

UAQwQw

Kw

P +⋅+⋅

+= (10)

1,2210a2,120w1,1

1,1120w1,210a2,21,22,12,21,1set1

V)texp())PT(V)PT(V(V)texp())PT(V)PT(V()VVVV()TP(a

⋅⋅λ⋅−⋅−−⋅+

⋅⋅λ⋅−⋅−−⋅+⋅−⋅⋅−=

(11)

UA)VVVV(V)texp()VV(V)texp()VV(

b 1,22,12,21,11,222,11,11,111,22,2 ⋅−⋅−⋅⋅λ⋅−+⋅⋅λ⋅−= (12)

The new load, NL, required is

NL=ba (13)

and the heat load, H, is found as H=NL -L (14) Shading and cooling When the air temperature exceeds the cooling set point, Tcool, shading and cooling is activated to limit the indoor temperature. It is possible to have no cooling and shading systems or only one of the systems. The new load that is needed for keeping the air temperature at the cooling set point is calculated as for the heating demand by With

osunasunw

1 TUA

QwQwP +

⋅+⋅= (15)

osunasunw

w

w2 T

UAQwQw

Kw

P +⋅+⋅

+= (16)

1,2210a2,120w1,1

1,1120w1,210a2,21,22,12,21,1cool1

V)texp())PT(V)PT(V(V)texp())PT(V)PT(V()VVVV()TP(a

⋅⋅λ⋅−⋅−−⋅+

⋅⋅λ⋅−⋅−−⋅+⋅−⋅⋅−=

(17)

UA)VVVV(V)texp()VV(V)texp()VV(

b 1,22,12,21,11,222,11,11,111,22,2 ⋅−⋅−⋅⋅λ⋅−+⋅⋅λ⋅−= (18)

The new load, NL, required is

NL=ba (19)

and the excess heat, EH, is


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EH=L-NL (20) If a shading system is present it is used before cooling. The shading factor, S, is defined as the part of the solar gain that is transmitted when solar shading is active and is found by

S=suna

suna

QwEHQw

⋅−⋅

(21)

if the shading factor found by the equation is lower than the minimum shading factor, the minimum shading factor is chosen. If a cooling system is present it removes the rest of the excess heat. The cooling load, C, is found by C=EH-(1-S)⋅wa⋅Qsun (22) If no cooling system is available the air temperature can rise above the cooling set point. Running The time step in the calculations is one hour and as initial condition at time zero the air and wall temperature are equal to the set point for heating. References Rafnsson, Rafn Yngvi (1997) Calculation of indoor climate and energy demand in buildings (in Danish: Beregninger af bygningers indeklima og energibehov). Master Thesis. Department of Buildings and Energy, Technical University of Denmark. (in Danish) Variables Variable Dimension Description

Heating 1×1 The yearly heating demand in kWh MaxHeat 1×1 The maximum heating load in kW Cooling 1×1 The yearly cooling demand in kWh

MaxCool 1×1 The maximum cooling load in kW temp 1×8760 The hourly indoor temperatures in oC

S 1×8760 The hourly shading factor of the shading system MinShading 1×1 The minimum shading factor

heat 1×8760 The hourly heat load in W cool 1×8760 The hourly cooling load in W wa 1×1 Share of solar gain to air ww 1×1 Share of solar gain to wall

Qsun 1×8760 Hourly solar gain in W Tout 1×8760 Hourly outdoor temperature in oC UAc 1×1 The UA-value of constructions in W/K Kw 1×1 The thermal transmittance to the wall node in W/K e 1×1 The efficiency of heat exchanger n 1×1 The air change from mechanical ventilation in 1/h

infil 1×1 The infiltration air change in 1/h V 1×1 The volume of the room in m3

Load 1×1 or 1×8760 The internal load in W. One constant value for all hours or a


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profile with hourly values Ca 1×1 The heat capacity of the indoor air in J/K Cw 1×1 The heat capacity in the internal walls in J/K Tset 1×1 The set point for heating in oC

Tcool 1×1 The set point for shading and cooling in oC Smin 1×1 The minimal shading factor of the shading system

Sha_check 1×1 If shading system is present equal to one Cool_check 1×1 If cooling system is present equal to one

heatingseason 1×8760 Not used UA 1×1 The UA-value including air change when heat exchanger is active UA2 1×1 The UA-value including air change when heat exchanger is by-

passed dt 1×1 Time step is 3600s

Ta0 1×1 Initial indoor air temperature in oC Tw0 1×1 Initial wall temperature in oC

A 2×2 Matrix defining homogenious system when heat exchanger is active

vect 2×2 Eigenvectors when heat exchanger is active diag 2×2 Eigenvalues when heat exchanger is active

lambda1 1×1 Eigenvalue when heat exchanger is active lambda2 1×1 Eigenvalue when heat exchanger is active

V1 2×1 Eigenvector when heat exchanger is active V2 2×1 Eigenvector when heat exchanger is active A2 2×2 Matrix defining homogenious system when heat exchanger is by-

passed vect2 2×2 Eigenvectors when heat exchanger is by-passed diag2 2×2 Eigenvalues when heat exchanger is by-passed

lambda12 1×1 Eigenvalue when heat exchanger is by-passed lambda22 1×1 Eigenvalue when heat exchanger is by-passed

V12 2×1 Eigenvector when heat exchanger is by-passed V22 2×1 Eigenvector when heat exchanger is by-passed

i 1×1 counter z1 1×1 Inhomogenious solution z2 1×1 Inhomogenious solution c Factors in solution

P1 1×1 Helping variable P2 1×1 Helping variable

newload 1×1 Load needed when heating is required in W E 1×1 Excess heat load when cooling is needed in W

Function call The function is executed as shown below. [Heating,MaxHeat,Cooling,MaxCool,temp,S,MinShading,heat,cool]= simpleroom2(wa,ww,Qsun,Tout,UAc,Kw,e,n,infil,V,Load,Ca,Cw,Tset,Tcool,Smin, Sha_check,Cool_check); The output variables and input variables are described in the table of variables.


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Subfunctions Uses only standard MATLAB functions. Program list function [Heating,MaxHeat,Cooling,MaxCool,temp,S,MinShading,heat,cool]= simpleroom2(wa,ww,Qsun,Tout,UAc,Kw,e,n,infil,V,Load,Ca,Cw,Tset,Tcool,Smin, Sha_check,Cool_check); %[Heating,MaxHeat,Cooling,MaxCool,temp,S,MinShading,heat,cool]= %simpleroom2(wa,ww,Qsun,Tout,UAc,Kw,e,n,infil,V,Load,Ca,Cw,Tset,Tcool,Smin,Sha_check,Cool_check) % %Simple room model, which calculates energy use for heating and cooling, %the indoor temperature, and shading. The heating system always keep the %air temperature equal to or above the setpoint temperature, Tset. %If the shading system is active it tries to keep the air temperature %equal to or below the cooling setpoint, Tcool, but the shading factor %can never be lower than the minimal shading factor, Smin. If the cooling %system is active the air temperature is kept equal to or lower than the %cooling setpoint, Tcool. If both shading and cooling is active the shading %is used before the cooling. % %wa is the part of the solar gain to air node [-] %ww is the part of solar gain to wall node [-] %Qsun is the solar gain pr. hour. Vector of length 8760 [W] %UAc is the heat loss koefficient for constructions [W/K] %Kw is the heat transfer coefficient to wall node [W/K] %Tout is the outdoor temperature pr. hour. Vector of length 8760 [°C] %e is the efficiency of heat recovery [-] %n is the mechanical ventilation rate [1/h] %infil is the infiltration rate [1/h] %V is the volume [m³] %Load is the internal load. Either a constant value or vector of length 8760 [W] %Ca is the heat capacity of the air [J/K] %Cw is the heat capacity of the wall [J/K] %Smin is the minimal shading factor [-] %Sha_check must be 1 if shading is active otherwise not active %Cool_check must be 1 if cooling is active otherwise not active % %S is the shading factor pr. hour [-] %heat is the heating load pr hour [W] %cool is the cooling load pr. hour [W] %Heating is the yearly heating demand [kWh] %Cooling is the yearly cooling demand [kWh] %heat is the hourly heating load [W] %cool is the hourly cooling load [W] %Checking internal load if length(Load)==1 Load=ones(8760,1)*Load; elseif length(Load)~=8760 error('The internal load is not defined') end %Initializing variables E=zeros(8760,1); heat=zeros(8760,1); cool=zeros(8760,1); S=ones(8760,1);


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%Defintion of heating season heatingseason=[ones(1,3192) zeros(1,3191) ones(1,2377)]; %Total heat loss coefficient UA=UAc+(infil+(1-e)*n)*V*0.34; UA2=UAc+(infil+n)*V*0.34; %Timestep and initial values dt=3600; Ta0=Tset; Tw0=Tset; %Eigen values and eigen vectors A=[-(UA+Kw)/Ca Kw/Ca;Kw/Cw -Kw/Cw]; [vect,diag]=eig(A); lambda1=diag(1,1); lambda2=diag(2,2); V1=vect(:,1); V2=vect(:,2); A2=[-(UA2+Kw)/Ca Kw/Ca;Kw/Cw -Kw/Cw]; [vect2,diag2]=eig(A); lambda12=diag2(1,1); lambda22=diag2(2,2); V12=vect2(:,1); V22=vect2(:,2); for i=1:8760 z1=(ww*Qsun(i)+wa*Qsun(i)+Load(i))/UA+Tout(i); z2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i)+Load(i))/UA+Tout(i); c=[V1 V2]\[Ta0-z1; Tw0-z2]; %Reference temperatures Ta=c(1)*exp(lambda1*dt)*V1(1)+c(2)*exp(lambda2*dt)*V2(1)+z1; Tw=c(1)*exp(lambda1*dt)*V1(2)+c(2)*exp(lambda2*dt)*V2(2)+z2; %When Ta is lower than Tset heating is needed %Here the heating demand is calculated using heat recovery if (Ta<Tset) %& (heatingseason(i)==1) P1=(ww*Qsun(i)+wa*Qsun(i))/UA+Tout(i); P2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i))/UA+Tout(i); a=(P1-Tset)*(V1(1)*V2(2)-V1(2)*V2(1))+(V2(2)*(Ta0-P1)-V2(1)*(Tw0-P2))*... exp(lambda1*dt)*V1(1)+(V1(1)*(Tw0-P2)-V1(2)*(Ta0-P1))*exp(lambda2*dt)*V2(1); b=((V2(2)-V2(1))*exp(lambda1*dt)*V1(1)+(V1(1)-V1(2))*exp(lambda2*dt)*V2(1)... -(V1(1)*V2(2)-V1(2)*V2(1)))/UA; newload=a/b; heat(i)=newload-Load(i); z1=(ww*Qsun(i)+wa*Qsun(i)+newload)/UA+Tout(i); z2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i)+newload)/UA+Tout(i); c=[V1 V2]\[Ta0-z1; Tw0-z2]; Ta=c(1)*exp(lambda1*dt)*V1(1)+c(2)*exp(lambda2*dt)*V2(1)+z1; Tw=c(1)*exp(lambda1*dt)*V1(2)+c(2)*exp(lambda2*dt)*V2(2)+z2;


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%When Ta is larger than Tset heat recovery is bypassed to avoid to high temperatures %Heating, shading and coling is calculated without heat recovery elseif Ta>Tset z1=(ww*Qsun(i)+wa*Qsun(i)+Load(i))/UA+Tout(i); z2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i)+Load(i))/UA+Tout(i); c=[V12 V22]\[Ta0-z1; Tw0-z2]; Ta=c(1)*exp(lambda12*dt)*V12(1)+c(2)*exp(lambda22*dt)*V22(1)+z1; Tw=c(1)*exp(lambda12*dt)*V12(2)+c(2)*exp(lambda22*dt)*V22(2)+z2; if (Ta<Tset) %& (heatingseason(i)==1) P1=(ww*Qsun(i)+wa*Qsun(i))/UA+Tout(i); P2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i))/UA+Tout(i); a=(P1-Tset)*(V12(1)*V22(2)-V12(2)*V22(1))+(V22(2)*(Ta0-P1)-V22(1)*(Tw0-P2))*... exp(lambda12*dt)*V12(1)+(V12(1)*(Tw0-P2)-V12(2)*(Ta0-P1))*exp(lambda22*dt)*V22(1); b=((V22(2)-V22(1))*exp(lambda12*dt)*V12(1)+(V12(1)-V12(2))*exp(lambda22*dt)*V22(1)... -(V12(1)*V22(2)-V12(2)*V22(1)))/UA2; newload=a/b; heat(i)=newload-Load(i); z1=(ww*Qsun(i)+wa*Qsun(i)+newload)/UA+Tout(i); z2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i)+newload)/UA+Tout(i); c=[V12 V22]\[Ta0-z1; Tw0-z2]; Ta=c(1)*exp(lambda12*dt)*V12(1)+c(2)*exp(lambda22*dt)*V22(1)+z1; Tw=c(1)*exp(lambda12*dt)*V12(2)+c(2)*exp(lambda22*dt)*V22(2)+z2; end if Ta>Tcool P1=(ww*Qsun(i)+wa*Qsun(i))/UA+Tout(i); P2=ww*Qsun(i)/Kw+(ww*Qsun(i)+wa*Qsun(i))/UA+Tout(i); a=(P1-Tcool)*(V12(1)*V22(2)-V12(2)*V22(1))+(V22(2)*(Ta0-P1)-V22(1)*(Tw0-P2))*... exp(lambda12*dt)*V12(1)+(V12(1)*(Tw0-P2)-V12(2)*(Ta0-P1))*exp(lambda22*dt)*V22(1); b=((V22(2)-V22(1))*exp(lambda12*dt)*V12(1)+(V12(1)-V12(2))*exp(lambda22*dt)*V22(1)... -(V12(1)*V22(2)-V12(2)*V22(1)))/UA2; newload=a/b; E=-(newload-Load(i)); if Sha_check==1 if Qsun(i)>0 S(i)=(wa*Qsun(i)-E)/(wa*Qsun(i)); end if S(i)<Smin S(i)=Smin; elseif S(i)>1 warning('Large solar shading factor'); S(i)=1;


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end end if Cool_check==1 cool(i)=E-(1-S(i))*wa*Qsun(i); end z1=(ww*S(i)*Qsun(i)+wa*S(i)*Qsun(i)+Load(i)-cool(i))/UA+Tout(i); z2=ww*S(i)*Qsun(i)/Kw+(ww*S(i)*Qsun(i)+wa*S(i)*Qsun(i)+Load(i)-cool(i))/UA+Tout(i); c=[V12 V22]\[Ta0-z1; Tw0-z2]; Ta=c(1)*exp(lambda12*dt)*V12(1)+c(2)*exp(lambda22*dt)*V22(1)+z1; Tw=c(1)*exp(lambda12*dt)*V12(2)+c(2)*exp(lambda22*dt)*V22(2)+z2; end end temp(i)=Ta; Ta0=Ta; Tw0=Tw; end MaxHeat=max(heat)/1000; %In kW MaxCool=max(cool)/1000; %In kW Heating=sum(heat)/1000; %In kWh Cooling=sum(cool)/1000; %In kWh MinShading=min(S);


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Description of the optimising program gcl.Solve: % gclSolve.m % % This is a standalone version of glcSolve.m which is a part of the % optimization environment TOMLAB, see http://www.ima.mdh.se/tom/ % % Solves general constrained mixed integer global optimizaion problems. % % gclSolve.m implements the algorithm DIRECT by Donald R. Jones presented % in the paper "DIRECT", Encyclopedia of Optimization, Kluwer Academic % Publishers 1999. % % gclSolve solves problems of the form: % % min f(x) % x % s/t x_L <= x <= x_U % b_L <= A x <= b_U % c_L <= c(x) <= c_U % x(i) integer, for i in I % % % Calling syntax: % % function Result = gclSolve(p_f,p_c,x_L,x_U,A,b_L,b_U,c_L,c_U,I,GLOBAL,PriLev) % % INPUT PARAMETERS % % p_f Name of m-file computing the function value. % p_c Name of m-file computing the nonlinear constraints. % x_L Lower bounds for x % x_U Upper bounds for x % A Linear constraint matrix. % b_L Lower bounds for linear constraints. % b_U Upper bounds for linear constraints. % c_L Lower bounds for nonlinear constraints. % c_U Upper bounds for nonlinear constraints. % I Set of integer variables, default I=[]. % % GLOBAL.MaxEval Number of function evaluations to run, default 200. % GLOBAL.epsilon Global/local search weight parameter, default 1E-4. % % If restart is wanted, the following fields in GLOBAL should be defined % and equal the corresonding fields in the Result structure from the % previous run: % % GLOBAL.C Matrix with all rectangle centerpoints. % GLOBAL.D Vector with distances from centerpoint to the vertices. % GLOBAL.F Vector with function values. % GLOBAL.Split Split(i,j) = # splits along dimension i of rectangle j % GLOBAL.T T(i) is the number of times rectangle i has been

trisected. % GLOBAL.G Matrix with constraint values for each point. % GLOBAL.ignoreidx Rectangles to be ignored in the rect. Selection

proceedure. % GLOBAL.I_L I_L(i,j) is the lower bound for rect. j in integer

dim. I(i) % GLOBAL.I_U I_U(i,j) is the upper bound for rect. j in integer

dim. I(i) % GLOBAL.feasible Flag indicating if a feasible point has been found. % GLOBAL.f_min Best function value found at a feasible point. % GLOBAL.s_0 s_0 is used as s(0) % GLOBAL.s s(j) is the sum of observed rates of change for constraint j. % GLOBAL.t t(i) is the total # splits along dimension i. % % PriLev Printing level:


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% PriLev >= 0 Warnings % PriLev > 0 Each iteration info % % OUTPUT PARAMETERS % % Result Structure with results from optimization: % x_k Matrix with optimal points as columns. % f_k Function value at optimum. % c_k Nonlinear constraints values at x_k % Iter Number of iterations. % FuncEv Number of function evaluations. % GLOBAL, special structure field (to make restart possible) containing: % C Matrix with all rectangle centerpoints. % D Vector with distances from centerpoint to the vertices. % F Vector with function values. % Split Split(i,j) = # splits along dimension i of rectangle j % T T(i) is the number of times rectangle i has been trisected. % G Matrix with constraint values for each point. % ignoreidx Rectangles to be ignored in the rect. Selection

proceedure. % I_L I_L(i,j) is the lower bound for rect. j in integer

dim. I(i) % I_U I_U(i,j) is the upper bound for rect. j in integer

dim. I(i) % feasible Flag indicating if a feasible point has been found. % f_min Best function value found at a feasible point. % s_0 s_0 is used as s(0) % s s(j) is the sum of observed rates of change

for constraint j. % t t(i) is the total # splits along dimension i. % % % Mattias Bjorkman, Optimization Theory, Dep of Mathematics and Physics, % Malardalen University, Box 883, S-721 23 Vasteras, Sweden. % E-mail: [email protected] % Written Apr 8, 1999. Last modified Apr 16, 1999.

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