1 Energy sustainability framed as a dynamical flow network optimisation problem Robbie Morrison...

1

Energy sustainability framed as a dynamical flow network optimisation problem

Robbie Morrison

Physics DepartmentUniversity of OtagoPO Box 56, DunedinNew Zealand

[email protected]

Based on the UNIX application deeco : dynamic energy, emissions, and cost optimization

Issue L Complete set 22 December 2000

2

Preliminary comments

• these slides have been extended to make them more understandable in the absence of a spoken commentary

• this material should be of interest to anyone working with energy systems from either a structural or policy perspective

• I intend to develop some demos using deeco in order to reinforce the material given

• further information can be found in the selected references listed on the final slide

*

3

Summary

• deeco is a generic energy system modelling environment used to define, guide, and evaluate sustainability improvements

• deeco is useful for both policy evaluation and scheme design

• model output is used to guide system redesign initiatives, such as:

– demand management– plant efficiency upgrades– renewable energy additions– waste recovery

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• model construction proceeds as follows:

first, an energy system simulation, based on the existing plant and connectivity, is built

second, the simulation is subject to the prevailing energy-services demand and supply availability patterns

third, assuming redundancy within the network, a set of plant utilisations is found which minimises some nominated usage-related sustainability cost, such as:

– depletable fuel consumption– net carbon emissions

• energy resources can be stored but forward-looking storage management is not supported

• monetary costs are generally tallied to allow financial trade-off to be investigated

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Introduction

• Overview

• About deeco

• My contribution

• Context

6

Overview

energy system decision support tool for improved sustainability

public or private policy

network-based optimisation modelling (quantitative)

part simulation

part optimisation

but not stochastic

certain restrictions for mathematical tractability — most relate to either intensive state resolution and maintenance or optimisation stability and speed

instructive (qualitative)

7

Development team — deeco

Dr Thomas Bruckner — programmed deecoTechnical University of Berlinex Postdam Institute for Climate Impact Research

Dr Helmuth Groscurth — supervised deecoHamburg Electricity Worksex Centre for European Economic Research

Dr Dietmar Lindenberger — current developmentInstitute of Theoretical Physics, University of Würzburg

Professor Reiner Kümmel — oversight roleInstitute of Theoretical Physics, University of Würzburg

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Program metrics — deeco

written by Dr Thomas Bruckner in 1996

18 000 lines of object-oriented C++

66 user-defined classes, 3 deep inheritance

graph support : USL Standard Components 3.0

linear optimisation : simplex algorithm from Numerical Recipes

input/output by suitably formatted ASCII files

runs on a PC but requires commercial UNIX :SVR4.2-based SCO UnixWare 2.1 or better

web-interfaced deployment is an option

abbreviations given in final section

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My contribution — deeco

ported deeco from a 1991 HP UNIX workstation to a PC

identified the 'convex approximations' for:

decreasing plant efficiency with duty (eg, transmission)

convex strictly-increasing cost on flow

extended and generalised certain constructs

investigated the application of deeco to national policy support

defined 'nergy' as a the first law analog of exergy

proposed an exergy quality mismatch heuristic for identifying network improvements

*

exergy is described shortly

10

Decision support — deeco

Financial cost increase

–50%

0%

50%

100%

150%

200%

0% 10% 20% 30% 40% 50%

Depletable fuel savings

Co-generation +short distance heat grid

Medium solarSmall solar

Gas heat-pumps +heat grid

Oil-fired boilers +electricity imports

Everything –large solar

Everything

Large solar + seasonal storage

Source: Bruckner et al (1997)

Würzburg study, south Germany

Trade-off line

Note:

1. Insulation not modified

2. Study details given later

Day

Ene

rgy

use

[MW

]

Central areaspace heatdemand

Totalelectricitydemand

Location-aggregated demand

11

Energy Link — market analysis tools (Emarket)

AuStral EA — residential network design (RiNO)

IRL — wind turbine placement in weak networks

EMRG — hydro-storage management

Transpower — nodal electricity pricing (SPD)

Outhred — nodal auction model (NAM)

Europe — policy models which embed infrastructure capacity limitations (EFOM, MODEST)

Related network-based optimisation initiatives

*

Dunedin

Christchurch

12

Context — the energy sector

Current policy focus is decentralised decision-making

But physical networks typically require:

collective-interest management (private re-regulation)

substantial and long-lived investment (pre-emptive)

impose limitations (network effects)

Emerging 'distributed resource' structural paradigm

'Energy sustainability' crisis:

depletable resource use

CO2-e (6 greenhouse gases weighted by GWP)

air pollution (SOx, PM10)

13

Some network structure omitted for clarity

National infrastructure with centralist focus

Industrialuse

Transport fuel

Commercialand domestic

Exergy demands

Exergy inputs

Liquid fuel import

Wind farm

Gas recovery

Hydro inflows

Note:

Representative of New Zealand

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Energy-services obligations

fuel oil

Gas extraction Transmission

water water electricity

all plant

Resistance heater

Heat pump

Cogeneration

In-flows Reservoir Hydro- Transmission generation

Wind-farm

Hydrology

Fuel oil import

Reserve information

Wind patterns

Cost information

Load profile

Production requirements

Temperature set point

+

+

+

+

Ambient conditions

Energy supply offers

Information channelTime-series (8760 intervals)Loss-free energy connectionFuel busPlant instance (often aggregated)Circles represent processes

electricity

space heat

gas

steam

Storage usage policy

gas

Indoor environment

Process heat

Electricity demand

Duel-fuel boiler

Gas and electricity model — deeco

Primary energy Consumer energy

15

Energy systems best interpreted:

as providing exergy-services not exergy per se

as comprising dynamical processes

as flow networks

using the second-law constructs of exergy and exergetic efficiency

network in the mathematical sense

16

Model constructs

decision jurisdiction implies a patchwork of systems

sustainability as (non-monetary) cost minimisation

network representation with logical exergy flow

plant performance by entry/store/exit relationships

system operation as a sequence of steady-flow regimes

plant behaviour described in state-space

heat exchange conditions set by mimicking controllers

exergy storage with stated management regime

rationing not supported (unlike nodal electricity pricing)

logical in the computer science sense

17

Network currency — a caution

flow networks carry some commodity (in this case, a fuel) which is accounted using some extensive currency

the model underpinning deeco is described using:

exergy — referenced (by definition) to the prevailing (possibly zone-wide) dead-state

but actually implemented using:

energy — referenced to some fuel-specific time-invariant arbitrary datum, typically based on laboratory testing protocols, eg

this latter compromise does not downgrade the validity of

deeco in any way

fuel is definedlater

natural gas on LHV at:T0 = 288 KP0 = 101 kPa0 = 0.80

18

Disciplines

open-system thermodynamics (physics)

energy conversion and exergy analysis (engineering)

graph theory and optimisation (mathematics)

mathematical programming (operational research)

object-oriented software design (computer science)

impact assessment (environmental science)

production theory and related topics (microeconomics)

discounted cash flow analysis (finance)

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Background

• Exergy

• Exergy-service

• 'Energy sustainability'

• Flow network optimisation

20

Exergy (several slides)

exergy is the potential of a flow or stock resource to produce work under the prevailing conditions

used to:

quantify stock and flow 'energy' resources

analyse 'energy' process performance

treatment assumes the environment itself is in internal chemical equilibrium — not true, so need to construct a suitable proxy environment or dead-state definition which does comply

the following diagram forms the basis for later schematics

if unfamiliar with exergy, substitute energy in its colloquial sense

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Control volume analysis of a real system

Environment• in internal equilibrium

0QVP

0

iN

Q

inm

outmSteady-flow open system

WE Heat reservoir

Work export• ideal process to dead-state yields resource assessment• actual process versus ideal process yields performance measure

Mass flow

System control volume

Cut point• forms its own infinitesimal control volume• also used for heat and work transfer

Source: Bejan (1997)

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take a problem-relevant, steady-flow, open system not in equilibrium with its environment

establish mass, energy, and entropy balances

rearrange to provide an exergy balance of the form:

exergy terms are specified using T, P, h, s, v, z etc for system and environment (subscripted 0)

out

gen0in

STEEEdt

dE QW

exergy destruction

mass-based flow exergy

heat-based flow exergynonflow exergy

work-based flow exergy

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nonflow exergy:

mass-based flow exergy:

heat-based flow exergy:

)()( 00000 SSTVVPUU

QT

TEQ

01

)()(

2

)()( 000

20

2

0 ssTzzgvv

hhmE

internal energy

indicates dead-state value

bulk velocity

mass-specific enthalpy

entropy

Typical 'closed circuit' definitions species,0 iN i

*

mechanical exergy terms

given later as x

24

Exergy-service versus outright exergy rate

demand is best specified in term of exergy-service:

warmth, process heat, or refrigeration (temperature T )

movement of people and goods (velocity v )

material environment (chemical potential i )

in some cases an outright exergy rate is acceptable:

electronic equipment (kW electricity)

mechanical equipment (motive power)

or an equivalent physical output rate:

materials processing (x kW = 1 kg aluminium / hour)

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'Energy sustainability'

no generic method for assessing environmental impact

flow-dependent costs are usually valid in our case

costs must be network-wide in the spatial sense — the model cannot deal with localised intensities

for energy systems, concensus centres on:

depletable fuel use

net CO2-e emissions

air pollution

multi-criteria optimisation problematic, take suite approach:

optimise each goal separately, see how the results align

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Generalised flow network

Capacitated directed edge • specific flow cost• lower flow bound• upper flow bound

Virtual sink

Virtual source

Vertex Directed edge

Commodity flow

Note:

The underlying entity is called a directed-graph or digraph

ixFlow in edge iSupply

offersDemand requirements

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If flow-linear cost and under-determined, solve as linear program:

Alternatively, use out-of-kilter (OOK) graph algorithm

informational structure

Minimum cost flow problem (MCFP)

integer

subject to

min

x

uxl

bAx

xc

cost vector

flow vector

vertex-edge incidence matrixsupply/demand vector

lower bound vectorupper bound vector physical

structure

selected goal

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Constrained optimisation

1x

2xDirection of improvement given by peformance index

Unconstrained minimumConstrained

minimum at

)(xJ

xx

subject to)(min J

State vector),( 21 xxx

Feasible solutions set

x̂

*

Isolines

29

Network elements

• Processes

• Balance points and exergy flow

• Network state

• Plant in more detail

• Flows and stores

• Resolution issues

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Processes

Process• inserted in directed edge• will be encapsulated within plant

1x 2x

)influences external,( 12 xfnx

arbitrary dependencelinear dependence

Logical exergy flow, eg• electrical power flow• net-heat transfer

Cut-point• contains bulk intensive variables associated with the flow at this point

Implied control volume

Balance point• was

Note:

The concept will be extended to include multiple flows and internal storage

entry flowexit flow

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Balance points

balance points interpose plant vertices (the digraph is bipartite)

balance points enforce:

fuel matching — physical considerations

intensive state equality — no exergy destruction

flow conservation — no energy (or exergy) accumulation

Simple interface Flow joining Flow splitting

Loss-free logical exergy flow

Balance point

abstractions

fuel in its most general sense including heat

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Logical exergy flow

logical means 'not-actual but relies on physical assets'

multiple actual flows replaced by single connection for MCFP:

logical exergy flow is also loss-free — exergy destruction can only take place within processes

exergy transport with costs and/or losses requires dedicated plant

in essence, balance points represent control volume interfaces and logical exergy flows represent cross-boundary transfers

Method Requires Logical form

forced convection flo and return streams logical heat flow

electricity 2–4 cables logical work flow

hydraulic transfer flo and return pipework logical work flow

if unfamiliar with logical, substitute net

33

Internal exergy demand requests

internal exergy demand requests propagate in a direction anti-parallel to logical exergy flow

in essence, MCFP seeks an optimal set of such demand requests

therefore plant duty becomes the decision variables set

OOK algorithm works upstream (but may 'recirculate')

Logical exergy flow connection

Inter-plant exergy demand requests

*

Represents underlying physical flows

Represents data transfer

34

Network state

Resolving the network thermodymic state requires values for:

the bulk intensive variables covering each flow

the bulk intensive variables covering each store

at least one extensive rate measure for each flow

at least one extensive measure for each store

And an engineering system also requires values for:

the intensive variables defining the prevailing dead-state

the specific costs arising from each flow

the accrued costs associated with each plant

thermodynamic includes notions from mechanics and electrical theory

more properly, part of the problem characterisation, not the state

35

Dynamical plant and plant types

plant are used to 'wrap' processes

plant possess embodied costs and generate usage-related costs

plant report embodied costs based on maximum requested duty

plant are classified by type as follows:Type Comments

Demand provides exergy-service

Conversion transforms or refines fuel

Network transport with loss and/or cost

Import/export acts as a gateway

Storage stores exergy

Collector renewable harvest and extraction

[Virtual suppy] not currently supported

36

Plant schematics (several slides)

Plant type(details will vary)

All exergy destruction occurs within the plant domain

All costs arise within the plant domain

Environmental data time-series

exit flow

entry flow

Data inputs• optional inputs shown dotted

Balance point

Logical exergy flow connection• the flow itself is assigned by the two flow-setting algorithms TLFO and SRE

Plant domain• essentially the same as the process control volume

Circle represents the mathematical description of the process and its cost generation

Plant parameters time-series

Note:

Plant parameters time-series normally omitted for clarity

Internal exergy flowInternal data transfer

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exit flowoffer

Demand time-series

entry flowrequire-ment

Collector plant

Demand plant(no waste-heat)



Exergy 'source' • eg, windfarm

Exergy-service• eg, space heating at T

Overlay balance points to create simple exergy-services supply network.

Exit flow offer must exceed entry flow requirement — otherwise the model fails

both are abstractions

+

Contains relevant data•eg, windspeeds

38

Often, but not necessarily, the one balance point (always in the case of import/export plant)

co-fuel A

Storage plant(recharge mode)

Conversion plant(multiple fuel/product)

entry flow

co-fuel B

co-product C

co-product D

store



Controlled by SRE algorithm

Inter-temporal storage losses supported

For example, cogeneration

Fuel domains change across conversion plant

Right-hand side connection temporarily disconnected (opposite applies in discharge mode)

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exit flow

Network plant(with quadratic losses)

entry flow


B

A

C

entryflow

exit flow

Efficiencies constant but A > B > C

exit flowoffer

Storage plant(discharge mode)


store A store B

Two stores enable differing sets of bulk intensive variables, eg• for thermal stratification

Performance curve

For example, electricity transmission

Uses convex approximation

Note:

More plant schematics given later

40

Concept evolution (review)

+

MCFP vertex Balance point

MCFP directed edge

Actual process with logical exergy flow

Mathematical process description in plant block

MCFP virtual source

Abstract exergy source

Development

Note:

1. A plant may need to contain two or more abstract processes to represent a single actual process

2. Plant also 'create' non-thermodynamic costs

41

Flow and store types

interpreted using exergy with (zone-specific) dead-state

Flow type Symbol Comments

Logical work flow EW typically electricity

Mass-flow fuel E typically oxidisable compounds

Logical heat flow EQ typically forced convection

Store type Symbol Comments

Mass-related storage use appropriate formula

Thermal x 'heat' at P0 is TME

Steam x 'heat' at P > P0 is TME

Chemical ch oxidisable compounds at T0, P0

Mechanical x included in TME

see Bejan (1997) for details on x, ch

Note: TME is thermomechanical exergy x

forexample

42

Fuel domains and network currency

fuel is taken to be any necessary plant input which is best quantified using exergy — in addition, fuels often possess sustainablity costs and/or financial opportunity cost

a fuel domain describes the extent of a particular fuel in terms of the network

fuel domains can only change across conversion plant

hence: fuel domain local network currency

deeco uses energy relative to some time-invariant arbitrary datum as the local network currency for a given fuel, with no requirement that the same datum be used across domains

some merit in adopting exergy for a future release of deeco

network plant alsoin deeco

43

Spatial resolution

the model can only resolve to plant level and not to component level

a plant is the least entity for which energetic efficiency (or productivity in the case of exergy-services supply equipment) is meaningful

a component is the least entity for which exergetic efficiency is meaningful

the model cannot optimise the internal workings of plant, but it can evaluate the potential gains from any such improvement

L,QE

WE

H,QEPlant

Component

Steam turbine cycle

44

Temporal resolution

default time-interval is 1 hour

default time-horizon is 1 year = 8760 hours

step through each interval carrying information forward as appropriate

upon completion, report plant-specific and network-wide usage and cost statistics

time-interval may be reduced but should remain substantially greater than the time-constant of the least responsive plant, particularly if cross-interval changes of state are marked

45

Scenario definition

• An exergy-services supply system

• Plant connectivity

• Structure within the problem

• Data requirements

46

An exergy-services supply system

CO2 emissions

Residential

Commercial

Electricity transmission

Thermal generation

Depletable fuel use

Gas extraction

Wind farm

Co-generation

Industrial

Underlying system

Flow networkrepresentation

Exergy-services demand by time and place

Exergy supplyoffers by timeand place

47

Generalised plant showing data interchange

Note:

Work flow includes electrical and mechanical exergy

Exergy flow connection

Waste-heat

Data-channel

Logical work flow e

Mass-flow fuel f

Logical heat flow h

Useable waste-heat flow

Generalised exergy

plantContains:

• mathematical description of process state and behaviour and plant cost creation

• record of state

Logical work flow e

Mass-flow fuel f

Logical heat flow h


Demand time-series

Flow-independent cost register

Flow-dependent cost register

time-series described shortly

48

Plant connectivity

P2

P1

C2

N1

C1

D1

D2

e1f2

f1

P3

h3h1h2

Exergy plant(with label)

Balance pointbus(with label)

Logical exergy flow connection

Directed data-channel

X0

y0

'Breadboard' representation

Note:

Inter-plant data-channels omitted for clarity

Environmental data time-series Demand time-series

Flow-independent cost registerFlow-dependent cost register

49

Physical structure — example

Plant Balance point Connection (with label) (with label) (with label)XXXX C0

B0

Note:

1. Problem lacks storage

2. Plant electricity requirements not shown

Municipal situation(preferred scenario from

Würzburg study)

C9

B4

C8

C6

C2 C1

C11

C7

C3C5

C4B1B2B3

C10 ELEDElectricity demand

HOHEDomestic space heating

GBKOCondensing boiler

GPIMGas import

NWNODistrict heating grid

ELIMElectricity import

Thermal sub-network

Rectangles indicate plant

BHKWOCo-generation unit

physical in the tangible sense

50

Informational structure — example

Required indoor temperature T

Non-heating electricity demand J

Ambient windspeed v0

Ambient temperature T0

Time

Variousmetrics

information is by time and — if nodal layout used — by location

aggregate demand spatially when appropriate, eg, use 'mega' houses

Note:

Plots are hypothetical24 hour snapshot

informational in the intangible sense

51 Read from data-set

Data requirements

data input/output is by suitably structured ASCII files

a scenario is a single model run

information hierarchy as follows:

informational structure

physical structure

Scenario

External conditions

Connectivity

Plant module from library

Defined using balance points


Demand Demand time-series


Plant specification

52

Time-series (part of the input data)

– interval-specific exergy-service obligation for each demand plant

– interval-specific outright exergy rate as a compromise

– interval-specific 'ambient' data for use by any plant

– contains appropriate physical and societal information

– interval-specific parameter set for each plant

– but typically parameters are constant (interval-invariant)

Demand time-series



53

Model building

• Concept development

• Program structure

• Plant and processes

• Algorithms and digraphs

• Plant details

• Model assumptions

54

Concept development

Concept Extension

inter-temporal variability

discrete steady-flow regimes

Single time-interval (1 hour)

Multiple time-intervals (8760)• storage• demand shifting

Linear program (LP) for flow cost optimisation• convex approximations

Abutting networks• import/export

Dynamic program (DP) for inter-temporal optimisation

limited authority

perfect or imperfectfuture knowledge

Mixed 0–1 program for fixed and flow cost optimisation

embodied costs

55

Program flow chart

Define scenario

Update plant characterisations

Identify least-cost flow routing

Inform plant

Replenish storage then export

Update network registers

Report plant and network statistics

TLFO

SRE

Fully specified problem

Fully resolved intensive state

Loop for each time-interval

Resolve heat exchangeflow attributes TSN

Algorithms explained shortly

56

Plant life cycle

Generic mathematical representation

Compile time

C++ code

Plant library module

from data-set

Run time

Fully characterised plant

Iteration begins

Fully specified plant

remainder of iteration

TSN

TLFOSRE

Fully resolved intensive state

*

Engineering info

Scenario data-set

External conditions

Neighbours' data

57

Plant versus process

a plant maps to a real world entity and has financial and physical attributes

a process represents a single distinct thermodynamic procedure (but may be further abstracted)

processes request and/or offer exergy flow

the key algorithms operate on digraphs containing processes (see next slide)

however system connectivity is described in terms of plant relationships

a digraph is a directed graph

Actual processEquivalent plant representation

Mathematical process description

Plant domain

important distinction

58

Abstract processes

the following plant types require abstract processes: storage, import/export, those offering waste-heat

in these cases, the actual process is split into two abstract processes, joined by data transfer in the case of waste-heat (within the TLFO digraph) and storage plant (across algorithms)

this arrangement means the same plant can both originate and be supplied with exergy flow, either sequentially or simultaneously — which allows the process digraph to be treated as static

Actual process with waste-heat co-product

Equivalent plant encapsulating two abstract processes

Data transfer:internal offer signal

Waste-heat co-product

59

uses simplified state-space representation:

equations used to receive, process, send, and log data

individual equation sets are algorithm-specific

the entire model can be viewed as a data abstraction

Mathematical representation of processes/plant

),,,(

),,,(1

tg

tf

tttt

tttt

azxy

azxx

output

state input

equation parameters

state equation

output equation

Note:

differs from earlier usagex

*

60

Key algorithms

Thermal sub-network algorithm

– resolves the conditions covering heat exchange between neighbouring plant prior to TLFO

Time-local flow optimisation algorithm

– solves the MCFP problem for each time-interval

Storage replenishment and export algorithm

– replenishes storage then exports if at zero optimisation cost

TSN

SRE

TLFO

intensive state resolution

flow setting

61

Heat exchange — algorithm

need to fully resolve the network intensive state prior to TLFO

TSN based on deterministic two-pass algorithm (not iterative)

mimics authority relationships within process controllers

thermal sub-network must possess a spanning out-tree structure and be subject to other limitations for tractability

thermal sub-network

Replacement logical heat flow connection with resolved intensive states (aka flow attributes) for flo and return streams

flo stream

return stream

Two plant thermal sub-network

Neighbouring plant exchanging heat via forced convection

TSN

Actual schematic

Model representation

62

Static optimisation — algorithm

sequential static optimisation comprises the core of the model

TLFO is based on MCFP (discussed earlier)

network intensive state assumed independent of flow regime

operates on TLFO sub-digraph (depicted shortly)

network can be nonplanar

deeco uses the simplex method

fixed as well as variable costs may be supported in a future release of deeco

time-local flow optimisation

cannot be drawn without crossing lines

TLFO

63

Use of storage — algorithm

deeco uses non-anticipatory storage policy:

replenish storage then export when zero optimisation cost — undertaken by SRE

renewable sourcing often a candidate

discharge storage when least-cost optimisation option — undertaken by TLFO

inter-temporal storage loss supported

create store and forward chains with episodic network plant

possibility for inter-temporal dynamic optimisation:

would need equivalent facility in underlying system

storage replenishment and export

SRE

64

Process Balance Loss-free logical Supply/demandpoint exergy flow information

Process digraphExergy originating processes:• collector – depletables• collector – renewables• storage – discharge• import• waste-heat

Exergy terminating processes:• demand• storage – replenishment• export

Exergy flow

structure

Group of plant exchanging heat

Abstract process plant:• storage • import/export• any plant offering waste-heat (not to itself though)

Intermediary processes:• conversion• network

65


sub-digraph

Exergy originating processes

Exergy terminating processes

Exergy flow

thermal sub-network

TSN

intensive state

Thermal sub-networkwith spanning out-tree structure (shown bold)

Root vertex (not necessarily at a terminating process)

Note:

Bold elements are active under prevailing algorithm

66


sub-digraph

Exergy-services demand obligations

Exergy supply offers arising from:

• depletables • renewables • waste recovery• storage• import



Exergy flow

Intensive state at all balance points need resolution prior to TLFO

time-local flow optimisation

TLFO

flowsetting

Either storage or import/export plant (cross-algorithm type)

Uses MCFP type optimisation on flow network (shown bold)

67


sub-digraph

Exergy supply offers arising fromzero cost sources, typically:

• renewables



Exergy flow

storage replenishment and export

SRE

flowsetting

Storage replenishmentor export (as the case may be) given that the optimisation cost is zero

Replenishment supply chain (shown bold)

68

Storage

a storage plant requires two abstract processes

discharge by TLFO, replenishment by SRE

model does not enforce use of a common balance point

plant schematics given earlier

Exergyoriginating processes


Storage plant

Discharge mode — TLFO Replenishment mode — SRE

Storage information transfer

Toggles

69

Import/export (two slides)

an import/export plant requires two abstract processes

based on abutting network with suitable gateway

import by TLFO, export by SRE

import means flow-dependent flow costs added

export means flow-dependent flow costs deducted



Plant represents network gateway

Import mode — TLFO Export mode — SRE

Export opportunity

Import opportunity

Toggles

70

Import/export plant(import mode)

exit flowoffer


Controlled by SRE algorithm


Contains interval-specific flow-dependent costs• eg, for electricity, has costs (inc spot price) associated with marginal generator

Import/export plant(export mode)

entry flow Plant parameters

time-series

Exergy 'sink' representing gatewayed network


+

−

Flow-dependent flow costs deducted

Same balance point for both modes

Exergy 'source' representing gatewayed network

71

Waste-heat reuse (two slides)

waste-heat reuse requires two abstract processes

both processes active during TLFO

some restrictions on location of re-injection

example shows demand plant:



Specially constructed plant

Waste-heat supply offer — TLFO

Normal demand process — TLFO

Internal offer signal

Exergy-service demand obligation

72

Demand plant(with waste-heat reuse)

waste-heat flow offer


Internal offer signal

+

Demand time-series

entry flowrequirement

Exergy-service obligation

Optional interconnection

exergy termination

exergy origination

73

Plant modules library — deeco

Currently supported modules:

– electricity demand– domestic space heating– heat pumps– gas boilers– gas co-generation– district heating grids– electricity import/export– gas import– thermal storage– solar thermal collection

Planned additions:

– electricity transmission– gas transmission– hydro reservoirs– hydro generation– wind farms

deeco contains a library of plant modules (C++ classes)

74

Plant module specification (two slides)

statement of plant type

statement of fuel type(s) and associated details

information on energetic performance covering entry/store/exit relationships which are:

constant with duty or stepwise decreasing (convex approximation)

arbitrary on external influences arising from either:

– external conditions via environmental data time-series

– the heat exchange flow attributes (intensive states of flo and return streams) as negotiated by neighbouring plant during TSN

in compliance with the fuel datums defined earlier

75

details of controller behaviour for plant exchanging heat

maintenance (threshold) and maximum capacities

load-independent exergy demand

flow-dependent cost creation — optimisation requires:

linear on flow or piecewise convex strictly-increasing (convex approximation)

flow-independent cost creation

initial conditions

energetic performance can be established using representative test data, engineering design formula, and/or first principle arguments

specification can be nonstationary through use of plant parameters time-series

76

Convex approximations

Flow

Cost

Exitflow

Entry flow

Flow

Specific cost

Duty

Efficiency

Piecewise convex strictly-increasing cost on flow

Stepwise decreasing plant efficiency with duty

Note:

Duty equates with exit flow

Maximum plant capacity

77

Costs

costs 'created' inside plant, but arise from individual flows (and aggravated by inefficiencies and storage loss):

flow-dependent (variable) costs — generated by all flows

flow-independent (fixed) costs — provoked by peak flows

single flow-linear cost required for optimisation, but convex approximation can apply (see earlier)

any number of flow-dependent and flow-independent costs can be tallied for decision support

flow-independent financial costs are amortised — hence economic life, salvage value, and discount rate required for each plant

flow-independent physical costs reported per unit-time — hence physical life estimate required for each plant

78

Upon-completion reporting

For each plant:

maximum duty requested

the flow-independent costs associated with that duty

% overall contribution to downstream balance point(s)

total consequent flow-dependent costs

For the network as a whole:

network-wide flow-dependent costs

network-wide flow-independent costs

79

Key assumptions

cost selected for optimisation is linear on flow

plant entry/store/exit relationships constant over a time-interval

can relax either of above using convex approximations

all demand requests must be met — method cannot ration services

plant response instantaneous cf time-interval

low inertia and signal lags (limited state delay)

rapid observation (limited output delay)

network intensive state independent of flow regime

directed cyclic structures in thermal sub-networks prohibited

abutting networks included in above via import/export plant

deeco extends restriction to all non-electricity flow connections

80

Plant concept review (two slides)

each plant maps to a real world entity

each plant contains some identifiable thermodynamic process

that process will need to be further abstracted — that is split in two and perhaps connected by data transfer — if the plant both:

requests and offers exergy flow

plant are joined by exergy flow connections

that exergy flow will need to be defined as logical in the case of:

heat transfer

work transfer

81

balance points interpose plant

in the first instance, a balance point represents a control volume interface

flow-splitting and flow-joining by balance points is introduced as a convenient abstraction

each plant possesses financial attributes, which facilitates discounted cash flow (DCF) analysis

each plant possesses physical attributes, which may require some prior lifecycle analysis (LCA) to establish the details

82

Plant-specific environmental constraints (proposed treatment)

plant-specific environmental constraints built into plant equations

alternatively, visualise assimilative capacity as resource input

natural gas electricity

river cooling resource

Impact entitlement (as per RMA consent)

upstreamriver C25 TcmQ P

Thermal generator

Assimilative capacity 'creation' block (proposed)

*



Cannot be included in TLFO optimisation

83

Inter-temporal optimisation

deeco contains an inter-temporal storage management policy

deeco does not support dynamic optimisation

dynamic optimisation (in this case) requires:

some inter-temporal variability

perfect or imperfect future knowledge

some appropriate resource storage capability

a resource may vary in nature:

real — eg, hydro reservoir management

abstract — eg, carbon permit management

use dynamic programming if serial decision-making appropriate

84

Overview

• Key concepts

• Model classification

85

Key concepts (1)

patchworked network viewpoint

integration as a flow network optimisation problem (TLFO)

sustainability as a goal, not a constraint

demand is for exergy-services

method of generalising and particularising plant in light of:

prevailing environmental and network conditions

prior plant state (dynamical behaviour)

method of resolving heat exchange conditions (TSN)

use of storage and export (SRE)

86

Key concepts (2)

Demand requests

• for service• by time and place

Dynamical plant

• in state-space• various restrictions

Storage management

• non-anticipatory• includes export

Static optimisation

• 'merit order'• fixed intensive state

Flow network representation

• logical flow (single line connections)• resolves intensive state

Computational model

• graph theory based

Output

Net

wor

k su

rrou

ndin

gs

N

etw

ork

unde

r in

vest

igat

ion

External conditions

• physical• societal

Cost information

Nominated goal

decision support

87

Mathematical model

Simulation part Optimisation part

Nonlinear Linear

Lumped system

Dynamic Static

Nonstationary

Deterministic

Discrete-time

Lag-free

• flow-linear costs• flow-independent process performance

• time-local flow optimisation• undertaken sequentially

• mimimise selected flow-dependent cost

• flow network interpretation • capacity bounds

Model class

88

Interpretation

• Guided searching

• Public policy

• SOLEG study

• Closure

89

Exergy-service

demandby: time place

revise demand profiles and retest

modify consumer preference and retest

Plant performance in terms of: plant efficiency consequential impact ability to source exergy (financial cost)

upgrade plant and retest

anticipate development trajectories and retest

Connectivity and operationcomprising: routing architecture

optimise routingie, test

add or subtract plant and/or interconnections and retest

Fixed cost trade-off — modify and test

Depth of intervention

Operational

Short-run

Long-run

Very-long-run

90

Network design drivers

Define an exergy quality factor (between 0 and 1 approximately):

Look for flow-significant exergy quality mismatch across plant:

reconfigure the network

boost plant performance

add heat-pumps, expanders, etc

shift demand — in time or location

potential'heat '

potential'work '

nergy

exergy

Z

exergy quality factor

*

91

Synergy and competition between technologies and demand patterns

groups of technologies facing a particular demand profile may:

compete

coexist

act synergistically

numerical modelling is required to determine the interaction

carefully sited storage can be used to evade competition

Würzburg study found that under the existing demand pattern:

heat-pumps and co-generation compete

co-generation and uprated insulation act synergistically

92

Public policy restatement

'Energy sustainability'

=Plant efficiency

+Renewable sourcing

+Demand management

+Storage management

+Waste recovery

+Optimal dispatch

Dynamical flow network optimisation modelling

• Depletable fuel use

• CO2-e emissions

Primary policy drivers

93

'Energy efficiency' defined in network terms

*

'Energy efficiency' is any network modification — with location-aggregate exergy-services demand held fixed — which results in an overall reduction in depletable fuel use

* compare with unoperationalisable definition in recent Parliamentary Commissioner for the Environment (PCE) report: "Getting more from less"

94

Conceptual analogies

Concept

Storage Virtual upstream infrastructure

Passive methods Virtual supply

Demand shifting Virtual storagein time

Demand shifting Virtual reticulationby location (given prior constraint)

Export/import Effective storage

Analogy

*

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Passive methods

take heat transfer across finite temperature difference:

augmentation — reduce

insulation — increase

buffering — add passive storage (eg, high mass architecture)

20destroy T

TQTE

mean transfer temperature

flow exergy destruction rate

heat transfer rate

transfer temperature difference

TT

Note:

holds forTT

Source: Bejan (1997)

*

96

Potential applications

individual facilities

rural energy schemes

industrial sites — opportunity for carbon management

municipalities

national policy studies

in the case of specific projects (as opposed to policy investigations) the output from deeco should be confirmed with further engineering/financial analysis

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Published studies

• Würzburg study

• SOLEG study

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Würzburg study — overview

investigates municipal energy system investment options

south German city of Würzburg, population 130 000

a proof-of-concept study

trade-off graph based on status quo insulation given earlier

published as Bruckner et al (1997)

99

Würzburg study — some details

Demand profiles (aka informational structure)

location-aggregated

space heat is for central area only

1993 data

Physical structure

'best' solution depicted:

this scheme was one of many tested

ELED

HOHE

GBKO

GPIM NWNO

ELIM

BHKWO

Note:

Detailed graphic was shown in an earlier slide

Day

Ene

rgy

use

[MW

]

Central areaspace heatdemand

Totalelectricitydemand

100

Würzburg study — recommendations

medium-scale co-generation and uprated domestic insulation reinforce

results indicate that, when compared with the status quo :

48% saving in depletable fuel use

15% financial cost penalty

requires willingness by homeowners to further insulate

your choice!

101

SOLEG study — overview

part of a state government-funded demonstration project

100 new well-insulated houses in south Germany

will be built and monitored shortly

up to 95% of space heating demand (first law accounting) can be supplied by the sun

published as Lindenberger et al (2000)

Note:

SOLEG is a German acronym for solar-supported energy supply for buildings

102

SOLEG study — schematic

Solar-supported district heating with seasonal storage

Solar collector(130 W/m2)

Seasonal storage

Gas-fired condensing boiler

Gas-fired co-generation plant orheat-pump

Heat distribution grid supplying 100 houses(2.2 TJ/year)

Heat exchanger Feed pump Water

Note: Plant electricity requirements not shown

Flowtemperature65°C

103

SOLEG study — recommendations

Reference case:

individual gas-fired boilers

Recommended solution:

central gas-fired co-generation (without export)

central gas-fired boiler for peak demand

Trade-off:

financial cost increase 120% (levelized)

solar contribution to heat 80% (first law accounting)

greenhouse gas reduction 33%

depletable fuel use reduction 34%Source: Lindenberger et al (2000)

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Closure

• Closure

• Abbreviations

• Network optimisation reading

• References

105

Closure

Regarding energy systems:

their purpose is to meet exergy-services needs

system design includes demand modification

a patchwork of networks implies 'distributed planning'

And regarding energy system integration modelling:

it is a decision support tool

it requires a high resolution of both informational and physical detail for the problem under investigation

it can provide a cogent qualitative explanation as well as numerical results

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Abbreviations

aka also known asCO2-e carbon dioxide equivalent

DCF discounted cash flow analysisdeeco dynamic energy, emissions, and cost optimisationGWP global warming potentialHP Hewlett-PackardLCA life cycle analysisLHV lower heating valueMCFP minimum cost flow problemOOK out-of-kilter algorithmPC personal computerPM10 particulate matter under 10 m diameter

RMA Resource Management Act 1991 (New Zealand)SCO Santa Cruz OperationSPD scheduling, pricing, and dispatchSRE storage replenishment and export algorithmSVR4.2 System Five release 4.2, a UNIX lineageTLFO time-local flow optimisation algorithmTSN thermal sub-network algorithmUSL UNIX Systems Laboratories

*

107

Flow network optimisation reading

Chapter 5 : The simplex method (optimization theory).

Casti, John L. 1996. Five golden rules : great theories of 20th-century mathematics — and why they matter. New York : John Wiley and Son. ISBN 0 471 19337 2.

108

Selected references

Bejan, Adrian. 1997. Advanced engineering thermodynamics. Second edition. New York: John Wiley and Sons. [ISBN 0-471-09438-2]

Bruckner, Thomas. 1997. Dynamische Energie- und Emissionsoptimierung regionaler Energiesysteme. PhD thesis. Institut für Theoretische Physik, Universität Würzburg, Germany. [In German, part translation available ]

Bruckner, Thomas, Helmuth Groscurth, and Reiner Kümmel. 1997. Competition and synergy between energy technologies in municipal energy systems. Energy. 22 (10):1005–1014.

Lindenberger, Dietmar, Thomas Bruckner, Helmuth Groscurth, and Reiner Kümmel. 2000. Optimization of solar district heating schemes : seasonal storage, heat pumps, and cogeneration. Energy. 25 (7):591–608.

Morrison, Robbie. 2000. Optimizing exergy-services supply systems for sustainability. MSc thesis. Physics Department, University of Otago, Dunedin, New Zealand. [Under examination ]

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