Optimal Production Planning for Small-Scale Hydropower
Transcript of Optimal Production Planning for Small-Scale Hydropower
IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS
, STOCKHOLM SWEDEN 2018
Optimal Production Planning for Small-Scale Hydropower
ANNA-LINNEA TOWLE
KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
OPTIMAL PRODUCTION
PLANNING FOR SMALL-
SCALE HYDROPOWER Anna-Linnea Towle
Master’s Thesis
KTH
2018
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Abstract
As more and more renewable energy sources like wind and solar power are added to the electric
grid, reliable sources of power like hydropower become more important. Hydropower is
abundant in Scandinavia, and helps to maintain a stable and reliable grid with added irregularities
from wind and solar power, as well as more fluctuations in demand. Aside from the reliability
aspect of hydropower, power producers want to maximize their profit from sold electricity. In
Sweden, power is bid to the spot market at Nord Pool every day, and a final spot price is decided
within the electricity market. There is a different electricity price each hour of the day, so it is
more profitable to generate power during some hours than others.
There are many other factors that can change when it is most profitable for a hydropower plant to
operate, like how much local inflow of water there is. Hydropower production is an ideal case for
using optimisation models, and they are widely used throughout industry already. Though the
optimisation calculations are done by a computer, there is a lot of manual work from the spot
traders that goes into specifying the inputs to the model, such as local inflow, price forecasts, and
perhaps most importantly, market strategy. Due to the large amount of work that needs to be done
for each hydropower plant, many of the smaller power plants are not optimised at all, but are left
to run on an automatic control that typically tries to maintain a constant water level. In Fortum,
this is called, VNR, or vattennivåreglering (water level regulation).
The purpose of this thesis is to develop an optimisation algorithm for a small hydropower plant,
using Fortum owned and operated Båthusströmmen as a test case. An optimisation model is built
in Fortum’s current modelling system and is tested for 2016. In addition, a mathematical model is
also built and tested using GAMS. It is found that by optimising the plant instead of running it on
VNR, an increase of about 15-16% in profit could be seen for the year 2016. This is a significant
improvement, and is a strong motivator to being optimising the small hydropower plants.
Since the main reason many small hydropower plants are not optimised is because it takes too
much of employees time, a second phase of this thesis was conducted in conjunction with two
other students, Jenny Möller and Johan Wiklund. The focus of this portion was to develop a
centralized controller to automatically optimise the production schedule and communicate with
the central database. This would completely remove the workload from the spot traders, as well
as increase the overall profit of the plant. This thesis describes the results from both the Fortum
model and the GAMS model, as well as the mathematical formulation of the GAMS model. The
basic structure of the automatic controller is also presented, and more can be read in the thesis by
Möller and Wiklund (Möller & Wiklund, 2018).
Keywords: Optimisation, optimization, hydropower planning, self-adaptive, automatic control,
optimal planning
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Sammanfattning
Tillförlitliga energikällor som vattenkraft blir allt viktigare vart eftersom elkraftsystemet utökas
med fler förnybara energikällor som vindkraft och solenergi. I Norden finns det rikligt med
vattenkraft, vilket bidrar till att upprätthålla ett stabilt och pålitligt elnät även med ökade
oregelbundenheter från vindkraft och solkraft samt större variationer i efterfrågan. Bortsett från
vattenkraftens tillförlitlighetsaspekter vill kraftproducenter maximera sin vinst från såld el. I
Sverige läggs dagligen bud på effektvolym till spotmarknaden Nord Pool och ett slutgiltigt
marknadspris bestäms därefter av elmarknaden. Varje timme under dygnet motsvarar ett enskilt
elpris, därmed är det mer lönsamt att generera effekt under de timmar där priset är som högst.
Det finns många andra faktorer som påverkar när det är mest lönsamt för ett vattenkraftverk att
producera el, exempelvis hur stort det lokala inflödet av vatten är. Vattenkraftproduktion är idealt
för tillämpning av optimeringsmodeller, vilka är vanligt förekommande inom verksamhetsområdet.
Även om optimeringsberäkningarna utförs av en dator innebär optimeringen mycket manuellt
arbete för Fortums elhandlare som specificerar indata till modellen. Exempel på indata är lokalt
inflöde, prisprognoser och kanske viktigast av allt marknadsstrategi. På grund av den stora
mängden arbete som fordras för varje vattenkraftverk, optimeras inte produktionen för många av
de småskaliga kraftverken utan de regleras automatiskt med mål att upprätthålla en konstant
vattennivå. Denna typ av reglering kallas vattennivåreglering, VNR.
Syftet med examensarbetet var att utveckla en optimeringsalgoritm för ett småskaligt
vattenkraftverk, där Fortumägda vattenkraftverket Båthusströmmen används som testobjekt. En
optimeringsmodell utvecklades i Fortums befintliga system och testades för 2016. Dessutom har
en matematisk modell utvecklats och testades med GAMS. Det konstaterades att genom att
optimera produktionen från vattenkraftverket istället för att reglera den via VNR kan en
vinstökning med cirka 15-16 % för noteras år 2016. Detta är en väsentlig förbättring och är ett
starkt argument för att optimera produktionen från småskaliga vattenkraftverk.
Eftersom den främsta orsaken till att många småskaliga vattenkraftverk inte optimeras är den
utökade arbetsbelastningen det skulle innebära för de anställda, genomfördes en andra fas i
examensarbetet i samverkan med två andra studenter, Jenny Möller och Johan Wiklund. Fokus för
denna del var att utveckla en centraliserad styrenhet för att automatiskt optimera produktionsplaner
och kommunicera med det befintliga centrala systemet. Detta innebär att utökad arbetsbelastningen
från elhandlarna undviks, samt öka vattenkraftverkets totala vinst. Denna rapport beskriver
resultaten från både Fortum-modellen och GAMS-modellen, liksom den matematiska
formuleringen av GAMS-modellen. Även grundstrukturen för det självreglerande
optimeringsverktyget presenteras, mer kan läsas i rapporten av Möller och Wiklund (Möller &
Wiklund, 2018).
Nyckelord: Optimering, vattenkraftplanering, självreglerande, automatisk styrning, optimal
planering
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Acknowledgements
There are many people who I wish to thank for their help with this thesis.
I want to sincerely thank my suprvisors at Fortum, Zahra Faridoon and Hans Bjerhag, as well as
Erik Byström, for their continuous help and guidance throughout this project. Thank you also to
my intructor, Mikael Amelin, and supervisor, Meng Song, from KTH for their valuable support
and assistance. I am deeply grateful to the staff at Fortum for their help and advice from the very
beginning, and their willingness to teach me as much as I could learn.
Lastly, thank you to Jenny Möller and Johan Wiklund, with whom I worked on the second
portion of this thesis. It was a great collaboration, and one that I think improved the quality of
both of our works.
Anna-Linnea Towle
Stockholm
2018-06-08
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TABLE OF CONTENTS
Table of Contents .......................................................................................................................................... 4
List of Figures ............................................................................................................................................... 6
List of Tables ................................................................................................................................................. 6
1 Introduction ........................................................................................................................................... 7
1.1 Background ................................................................................................................................... 7
1.2 Focus and Assumptions ................................................................................................................. 7
1.3 Research Objectives ...................................................................................................................... 8
2 Electricity Markets ................................................................................................................................ 9
2.1 Nordic Electricity Market .............................................................................................................. 9
2.2 Supply and Demand .................................................................................................................... 11
2.3 Spot Market ................................................................................................................................. 13
2.4 System Spot Price ........................................................................................................................ 14
2.5 Area Spot Price ............................................................................................................................ 15
3 Hydropower System Characteristics ................................................................................................... 16
3.1 Hydropower Operation ................................................................................................................ 16
3.2 Reservoir Characteristics ............................................................................................................. 16
3.3 Structure of a Hydropower System ............................................................................................. 17
4 Hydropower Production planning ....................................................................................................... 19
4.1 Planning Concepts ....................................................................................................................... 19
4.2 Steering from Mid-term Planning ............................................................................................... 19
4.3 Volume Coupling ........................................................................................................................ 19
4.4 Resource Cost Coupling .............................................................................................................. 20
4.5 Short-term Planning .................................................................................................................... 21
4.5.1 Pre-Spot Planning ................................................................................................................ 22
4.5.2 Post-Spot Planning .............................................................................................................. 22
4.6 Hydropower Modelling Theory ................................................................................................... 22
4.6.1 Linear Programming ............................................................................................................ 22
4.6.2 Non-linear Programming ..................................................................................................... 23
4.6.3 Dynamic Programming ....................................................................................................... 23
4.6.4 Stochastic Programming ...................................................................................................... 23
5 Hydropower Planning Model: Fortum System .................................................................................... 25
5.1 Båthusströmmen .......................................................................................................................... 25
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5.2 Optimal Planning vs VNR Control Results ................................................................................. 26
6 Hydropower Planning Model: Theory ................................................................................................. 32
6.1 Nomenclature .............................................................................................................................. 33
6.2 Explanation of Flexibility of Model ............................................................................................ 34
6.3 Static Model ................................................................................................................................ 34
6.4 Iterative Updates Based on New Head ........................................................................................ 39
7 Optimal Planning Algorithm Results .................................................................................................. 40
8 Central Automatic Control .................................................................................................................. 45
8.1 Description .................................................................................................................................. 45
8.2 Communication Flow .................................................................................................................. 45
8.3 Final Program .............................................................................................................................. 46
9 Conclusion ........................................................................................................................................... 48
9.1 Thesis........................................................................................................................................... 48
9.2 Further Analysis .......................................................................................................................... 49
10 References ....................................................................................................................................... 50
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LIST OF FIGURES
Figure 1 Nordel electricity consumption by sector, 2008, source: (ENTSO-E, 2018) ................................ 11
Figure 2 Nordel electricity generation, 2008, source: (ENTSO-E, 2018) ................................................... 12
Figure 3 Production cost curve, source: (Nord Pool, 2017) ........................................................................ 13
Figure 4 Nordic power flow, source: (Statnett, 2018) ................................................................................. 14
Figure 5 Area price curves in a two area market, source: (Kerola, 2006) ................................................... 15
Figure 6 Hydropower plant operation, source: (Vattenfall, 2017) .............................................................. 16
Figure 7 Example hydropower system, source: (Hassis, 2011) .................................................................. 18
Figure 8 Water value function, source: (Hassis, 2011) ............................................................................... 21
Figure 9 Båthusströmmen Location (Google Maps, 2018) ......................................................................... 25
Figure 10 Marginal Water Value Curves for Båthusströmmen ................................................................... 27
Figure 11 2016 Week 1 Båthusströmmen Reservoir Level ......................................................................... 28
Figure 12 2016 Week 23 Båthusströmmen Reservoir Level ....................................................................... 29
Figure 13 2016 Week 40 Båthusströmmen Reservoir Level ....................................................................... 30
Figure 14 Optimal Planning Algorithm ....................................................................................................... 32
Figure 15 Piece-wise linear power curve .................................................................................................... 35
Figure 16 PWL example curve .................................................................................................................... 36
Figure 17 Week 1 Reservoir level and flow rate ......................................................................................... 40
Figure 18 Week 1 Reservoir level and electricity price .............................................................................. 41
Figure 19 Week 23 Reservoir level and flow rate ....................................................................................... 41
Figure 20 Week 23 Reservoir level and electricity price ............................................................................ 42
Figure 21 Week 40 Reservoir level and flow rate ....................................................................................... 42
Figure 22 Week 40 Reservoir level and electricity price ............................................................................ 43
Figure 23 Inflow and spillage for 2016 ....................................................................................................... 43
Figure 24 Optimised and VNR discharge comparison ................................................................................ 44
Figure 25 Information Flow of Central Control Unit .................................................................................. 46
Figure 26 Visual Basic Main Program (Möller & Wiklund, 2018) ................................................................ 47
LIST OF TABLES
Table 1 Båthusströmmen Simulation Comparison ...................................................................................... 30
Table 2 Algorithm Nomenclature ................................................................................................................ 33
Table 3 Test Case Parameters...................................................................................................................... 40
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1 INTRODUCTION
1.1 BACKGROUND Hydropower has been an important source of power in Sweden for centuries. Starting as early as
the 12th century, water power was used in sawmills, to mill grains, and to transport logs along
rivers. The industrial revolution (1871-1914) saw hydropower being used to supply electricity for
the numerous factories that had sprung up across Sweden, and the electrification of the railroads
motivated the building of the first large scale hydropower plants (Flood, 2015). Now hydropower
makes up about 41% of Sweden’s total generation capacity of almost 40000MW (ENTSO-E,
2018). Smaller hydropower plants, under 10MW, are often run-of-the-river plants, and aren’t
controlled as much as the larger plants. They are usually left to run on their own based on the
inflow of the river and the height of their own reservoirs. However, about 1GW of capacity in
Sweden comes from these small hydropower plants, and control and optimisation of them could
have a significant influence on the total productivity of the system (ENTSO-E, 2018). As more
and more variable renewable power sources like wind and solar are installed, the more need there
is for stable and predictable power to balance the electricity supply. Hydropower, a renewable,
fossil-fuel free power source with stable production, is the ideal solution to this growing problem.
1.2 FOCUS AND ASSUMPTIONS This thesis focuses on the optimisation and control of small hydropower plants, done in
cooperation with Fortum Sverige AB. The test case used is Båthusströmmen, a 3.3MW plant in
the river Dalälven, in Dalarna county, Sweden, owned and operated by Fortum. The plant
typically operates at water level regulation, meaning that it controls the discharge and spillage in
order to maintain a constant set water level in the reservoir. There are no hydropower plants
upstream of Båthusströmmen, and the closest hydropower plant and reservoir on the downstream
side is Trängslet, one of the largest reservoirs in Sweden. Since Båthusströmmen is so much
smaller than Trängslet, it has little to no effect on the downstream plant. For this thesis, it is
assumed that any changes to the operation of Båthusströmmen will not have any effect on the
operation downstream, so the entire river system need not be considered. For the operation
planning of Båthusströmmen, the main electricity market considered is the spot market, including
the predicted spot prices and actual spot bids.
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Optimisation for hydropower dispatch is quite common, and is used for the larger plants that
Fortum owns. Today, running an optimization algorithm for small plants takes too much time and
effort from the employees, who could instead focus on larger, more profitable plants. To get the
best of both worlds, an optimization algorithm is developed for Båthusströmmen, and a control
scheme to automatically run the optimization and send the chosen schedule to the central
database. The automatic control of Båthusströmmen is investigated and simulated using
Microsoft Visual Basic. Communication with the central database is established, and a control
scheme is developed to automatically run the optimisation algorithm and update the database
with new optimal schedules. This portion of the project is done in conjunction with two
undergraduate thesis students, Jenny Möller and Johan Wiklund (Möller & Wiklund, 2018).
1.3 RESEARCH OBJECTIVES There are two main objectives for this thesis. The first is to develop an optimal planning
algorithm that can be continuously run to plan the production at Båthusströmmen. This algorithm
will be based on similar algorithms used for general hydropower modelling, and will be able to
run at any time taking in updated inputs like spot price and local water inflow. Different methods
for optimisation are analysed, and a final method is chosen based on accuracy, flexibility, and run
time.
The second objective is to develop a control scheme to automatically control the hydropower
plant based on the optimal planning. The control scheme will then be implemented and tested.
This phase of the project is done in cooperation with two other thesis students.
Though Båthusströmmen is the focus of this work, both the optimal planning algorithm and the
control mechanism should be flexible enough to be applied to similar hydropower plants in the
future. This means that a response to all possible scenarios should be built into the control
system, and that the optimal planning algorithm should be able to run for similar plants in
different locations.
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2 ELECTRICITY MARKETS
2.1 NORDIC ELECTRICITY MARKET In 1991 Norway deregulated its electricity market, causing the power providers to act more
competitively and be more profit driven. A deregulated market ensures that the cheaper
generation options are used first, and the more expensive ones used only when necessary. It also
allows consumers to choose who they buy electricity from, promoting competition and
encouraging profitable investments (Rothwell & Gomez, 2003). In 1996, Sweden joined this
deregulated market and formed Nord Pool. Today, 380 customers from 20 different countries
trade in Nord Pool markets, generating around 420 TWh every year from the Nordic and Baltic
countries (Nord Pool, 2017). Within a power system, there are several key players: producers,
consumers, retailers, system operators, grid owners, and balance responsible players. These will
be explained briefly (Söder & Amelin, 2011).
Producers and Consumers
Producers are the owners and operators of power plants and consumers are the end users of
electricity. While the large economies of scale of electricity generation has resulted in very few,
but large, producers, consumers operate all throughout the power system, and are much more
numerous (Söder & Amelin, 2011). Consumers can be large industry or individual households,
with variable and sometimes difficult to predict consumption patterns.
Retailers
It would be very complicated for each individual consumer to purchase their electricity directly
from the producers, so retailers are available to act as middle men between the two. Retailers can
sell electricity to consumers in many ways, including offering a simple fixed price rather than a
price that varies throughout the day. This simplifies consumer sales, and places the risk of a
dramatic price change on retailers. Having many retailers also increases competition, both
between retailers and between producers (Söder & Amelin, 2011).
Grid Owners
An electric grid has very high investment costs, making it hard for different companies to enter
the market. This makes grid ownership a natural monopoly, and it is convenient to give some
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companies or municipal authorities control over an area of the same grid instead of having
several competing grids. Grid owners must operate and maintain the grid with an agreed upon
power quality, as well as measure the transfer of electricity from producers to consumers. Grid
owners may have to buy power to make up for electric losses in the grid. To cover this cost as
well as maintenance costs, they are allowed to charge grid tariffs to all users (Söder & Amelin,
2011).
System Operators
With so many players already in the market, it is best to have one player that oversees the total
day to day operation. System operators, ISOs1 or TSOs2, are administrators of the power system
and electricity trading. TSOs have the ultimate responsibility for maintaining the power balance
of the grid at all time. This involves maintaining a constant frequency of 50Hz and also voltage
and MVAr properties (Byström, 2018).
This means that system operators are usually responsible for post trading (see section Error!
Reference source not found.), and they are often also transmission grid owners (Söder &
Amelin, 2011). An electricity market, like Nord Pool, can have multiple system operators, each
of which controls a certain area. The system operator for Sweden is Svenska Kraftnät.
Balance Responsible Players
Every watt of produced power must be consumed immediately. Though companies promise to
produce a certain amount of power in advance (see section 2.3), there will always be small
deviations from the plan due to unpredictable things such as changes in consumption or loss of
production in a plant. When such deviations occur, producers have to be compensated for
generating more power or charged for not producing enough. Balance responsible players make
sure that this balance is maintained, and that all energy is correctly paid for. Likewise, there are
balance responsible players on the demand side accounting for any changes from planed
consumption. Electricity retailers are commonly balance responsible players acting on behalf of
their customers (Söder & Amelin, 2011).
1 Independent system operator 2 Transmission system operator
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2.2 SUPPLY AND DEMAND The driving force behind electricity production and electricity cost is the balance between supply
and demand. The instant a light bulb is turned on, the total production throughout the system
must increase slightly to accommodate it. Electricity consumption, or demand, is usually quite
independent of the price. Demand fluctuation does, however, follow several patterns, including
daily and seasonal patterns. Households and industry both consume more electricity during the
morning than during the middle of the night. Industry especially has a larger consumption during
the week than on the weekends, as well as reduced consumption on holidays (Hassis, 2011). The
consumption also changes with temperature, usually increasing during colder temperatures to
supply electric heating. The breakdown of consumption in the Nord Pool area on 2008 is shown
in Figure 1 (ENTSO-E, 2018). Industry makes up about half of the consumption, influencing the
weekday pattern for overall consumption. Household consumption makes up over one quarter of
total consumption, contributing to the daily consumption pattern.
Figure 1 Nordel electricity consumption by sector, 2008, source: (ENTSO-E, 2018)
Hydropower is the largest source of electricity in Nord Pool, accounting for 58% of production in
2008 (ENTSO-E, 2018), as shown in Figure 2. It is also the most flexible, as there are few start-
up or ramping costs for the plants. In addition, it is one of few power sources that can store
28%
47%
22%
3%
Housing Industry (incl. energy sector)
Trade and Services (incl. transport) Other (incl. agriculture)
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energy, in the form of reservoir water, for the future. There are many factors that affect
hydropower supply, including inflow, profit maximisation plans, reservoir levels, etc. Since the
fuel for hydropower is water, it is essentially free. This means that hydropower can make a profit
even at low electricity prices, and has a large influence on the spot price of the electricity market.
This will be explained further in section 2.3.
Figure 2 Nordel electricity generation, 2008, source: (ENTSO-E, 2018)
Hydropower has high seasonal variations due to what is called the “spring flood”. This is when
all the snow melts and fills the rivers and reservoirs during the spring. This is an annual, large
event, and is prepared for by having low reservoir levels going into the spring. This means that
production increases during the winter and autumn as the reservoirs are emptied.
Nuclear power is the second largest resource, making up 20% of generation in 2008. Nuclear
power has high investment costs, but low variable costs, so producers want to always operate at
high levels (Hassis, 2011). Since nuclear and hydropower have such low operating costs and are
very predictable sources of power, they usually supply most of the load, together making up
around 80% of total generation.
The “other thermal” section is mainly coal and oil condensing, which have much higher variable
costs. Thermal plants have start-up and sometimes shut-down costs to operate, and the fuel itself
58%
20%
19%
3%
Hydro Nuclear Other thermal Wind
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is not free like with hydropower. In addition, there are costs based on CO2 emissions, driving the
variable costs higher. Therefore, production is highly dependent on the spot price, and the spot
price is also highly dependent on how much thermal power is needed to meet the demand.
The electricity price is calculated based on how supply meets demand. An example of supply and
demand curves is shown in Figure 3 (Nord Pool, 2017), where the demand is the dashed line and
the supply curve is made up of the available generation blocks. Here it is clear that hydro power
makes up a majority of the production, and keeps the price low. This price calculation will be
explained further in the following sections.
Figure 3 Production cost curve, source: (Nord Pool, 2017)
2.3 SPOT MARKET The electricity market is broken into two main times frames: the spot market (Elspot) for day
ahead sales, and the intra-day market for trading and balancing up to an hour in advance. The
spot market determines the spot price for the following day. Producers in each area submit bids
for how much power they want to sell for which price during each hour of the following day
(Faridoon, 2018) (Rasmussen, 2018). Bids consist of a piece-wise linear curve for how much they
want to buy or sell based on what the spot price is. These bids must be submitted to the electricity
market, Nord Pool, by 12:00 CET each day, and the market operator will release the realized spot
price at 12:42 CET. The realised spot price is calculated for each hour based on the supply and
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demand curve shown in Figure 3, using predicted consumptions and demand bids for the demand
and the production bids for the supply.
2.4 SYSTEM SPOT PRICE Within the Nord Pool market there are different bidding areas. In Sweden there are four areas,
SE1-4, each of which submits its own spot bid to the spot market.
Figure 4 Nordic power flow, source: (Statnett, 2018)
Generally, power flows from low to high price areas. The system price is the price that would
occur if there were no physical limitations on transmission between areas. The total consumption
from all areas should be met at the lowest cost. Theoretically, if one area could supply all of Nord
Pool at the absolute lowest price, only power plants in that area would generate power. There are,
however, practical limitations to this based on the transmission capacity between areas. When the
transmission limits are reached, areas are separated from each other and must have different area
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prices. Figure 4 shows the different areas in Nord Pool and an example of power flow between
areas.
2.5 AREA SPOT PRICE When transmission limits are reached, individual areas need to adjust their production to match
the area consumption, which results in an adjusted supply and demand curve. Figure 5 shows the
price curves for a two-area market where the transmission limits between the areas A and B have
been reached. Area A has much more demand than it can supply at the system price, so it must
import as much as possible from area B according to transmission capacity. The area price is set
to be where the difference between supply and demand is equal to the transmission capacity from
area B, resulting in an area price higher than the system price. Similarly, area B now has excess
power capacity. The area price is set to be where the difference between supply and demand is
equal to the export to area A, resulting in an area price lower than the system price. Note that
power always flows from lower price areas to higher price areas in order to generate as much
power as possible at lower prices (Kerola, 2006).
Figure 5 Area price curves in a two area market, source: (Kerola, 2006)
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3 HYDROPOWER SYSTEM CHARACTERISTICS
3.1 HYDROPOWER OPERATION Hydropower plants use running water to generate electricity. Figure 6 shows how a basic
hydropower plant is set up. A dam holds back water in a reservoir, making the upstream, or head
water level, higher than the downstream, or tail water level. This difference in height is called
head. The larger the head, the larger the potential energy in the water due to gravity, and the more
energy can be extracted by the turbine. The water flows through the intake rack and penstock and
turns the turbine, then flows out through the draft tube. The turbine is connected to the electrical
generator, which generates power and injects it into the local grid system. The amount of water
flowing through the turbine, and the rate of electric power (MW) production is controlled by
adjusting the guide vanes (Byström, 2018). The intake gate is fully open during operation , and
only closed during emergency-stop or for maintenance reason (Bjerhag, 2018).
Figure 6 Hydropower plant operation, source: (Vattenfall, 2017)
3.2 RESERVOIR CHARACTERISTICS There are several practical and environmental limitations on reservoirs. Environmental agencies
provide minimum and maximum water levels for each reservoir in order to not damage the
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surrounding ecosystems, and these limits must be obeyed. Other limits include practical limits on
how much the reservoir can physically handle, and also must be obeyed so as not to damage the
reservoir or plant. Since these rules must be followed, these are often called hard limits. There
are other tactical limits, often called soft limits or good will limits, that further constrain the water
levels in order to build in a margin of safety. If an environmental limit is exceeded, there is a
penalty, so producers don’t want to risk being too close to these limits in case something like a
large unexpected inflow occurs.
There can also be environmental or tactical limits on flow rate and ramping rate. For example, a
plant may be required to have a minimum flow rate in order for fish to continue moving
throughout the river. A producer may set their own flow rate limits to operate the generators most
efficiently, or they may set ramping limits (how fast the flow rate can change) to protect different
components. All of these limits can change throughout a year.
3.3 STRUCTURE OF A HYDROPOWER SYSTEM Hydropower plants are based on river systems and reservoirs. Unlike most electricity production
types, hydropower is able to store energy by keeping water in reservoirs just upstream of the
plants. This water is available, with certain limitations, to be used by the plant when it will be
most profitable.
Hydropower plants are located along a river, and a plant upstream has an effect on the plants
further downstream, creating a coupling effect between plants throughout an entire river system.
Hydropower plants have three main factors to consider when deciding how much power to
generate: reservoir levels, local inflow, and electricity price. The amount of power a plant
generates is based on how much water it discharges through its turbines. The amount of water
available to discharge is based on the reservoir level and the local inflow of water from the river
system. If there is too much local inflow, or if a large amount of inflow is expected in the future,
a plant may have to discharge water through spillways, or side exits, that do not run the water
through the turbines. The plant does not generate any power from spilled water, so it usually not
desirable, but the water is still available to be used by plants further downstream. When an entire
river system is considered, it may be worth it to spill water in an upstream plant in order to
provide water to a larger, more profitable plant downstream.
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Figure 7 Example hydropower system, source: (Hassis, 2011)
Figure 7 shows an example river system with three reservoirs R1-3, plants P1-3, spillage s1-3, and
local inflow v1-3. The discharge is indicated by q1-3. The three plants are connected, and water
from plants and reservoirs 1 and 2 go to reservoir 3. The water level in R3 is increasing all the
time by v3, q1, s1, q2, and s2. It is decreasing by s3 and q3.
An important thing to consider is that water discharged from plant 1 does not immediately arrive
at reservoir 3, it takes some time to travel there through the river. This time delay is different
between each plant, and the time delays of spilled water and discharged water are often very
different. It is common for spilled water to take a much longer path, and thus take longer to reach
the next plant. Downstream plants will thus not be affected by changes in discharge or spillage
until sometime after the change occurs.
When planning hydropower production, local inflow is a very important parameter, but it can be
very difficult to predict. The inflow is affected by precipitation, melting snow, freezing ice, and
other weather related issues, meaning there are many sources of error. Throughout the river
system there are water flow measurement devices, or stream gauges, which report back the actual
inflow, but these devices can also report errors.
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4 HYDROPOWER PRODUCTION PLANNING
4.1 PLANNING CONCEPTS As has been mentioned, hydropower has the ability to store energy in the form of reservoir
waters. This allows a plant to save water for hours when the electricity price is highest. This
planning is on the short-term horizon, from the day ahead to about 2-3 weeks ahead. Not only are
the hours of the day considered, but also the inflow and price forecasts for the coming weeks.
Short-term planning allows the river system to optimise production in its plants during the
coming weeks.
Yearly inflow and price changes are important as well. Every year there is a spring flood, and the
reservoirs must be relatively empty going into spring to accommodate this. Mid-term planning
takes place between the end of the short-term planning until about 1-2 years out. When the mid-
term plans are optimised, a start value for the reservoirs is found. This value is the end point for
the short-term planning, and provides steering for the short-term planning.
Similarly, long-term planning provides steering for where the mid-term planning should end up at
the end of its planning horizon. Long-term planning considers the time from the end of the mid-
term planning to about 3-5 years out. The coupling between these different planning periods
allows the models to be very specific in the short-term while still following an overall plan for the
coming years. This thesis focuses on the short-term planning. More about the actual models will
be discussed in the following sections.
4.2 STEERING FROM MID-TERM PLANNING As mentioned above, the mid-term planning period begins at the end of the short-term planning
period, and determines the end point for the short-term planning. There are two main ways to
provide this steering, or coupling, for the short-term optimisation: volume coupling and resource
cost coupling (Hassis, 2011).
4.3 VOLUME COUPLING With the volume coupling method, mid-term planning passes on the end reservoir volumes to the
short-term optimisation. This method provides more flexibility to choose which mathematical
models to use, but does not always take end prices into account well enough. Downstream
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reservoirs depends highly on the flow of upstream reservoirs, not just their volume. This is
especially true because of the time delay between reservoirs. It is difficult to achieve consistent
coupling between models without taking this time delay into account in the final hours (Hassis,
2011). Volume coupling also does not consider the marginal value of water, which changes how
much the water is worth and may change the optimal plan.
4.4 RESOURCE COST COUPLING Water stored in a reservoir has the potential to create power in the future. When there is a lot of
water stored in a reservoir, adding a few more cubic meters does not increase the value of the
water significantly, so we say the marginal value of the water is low. When a reservoir is
approaching its lower limit, a few extra cubic meters of water makes much more of a difference,
so that water has a higher marginal value.
Resource cost coupling takes the marginal water value more into account. The mid-term planning
instead passes an end marginal cost value for each reservoir to the short-term planning. Figure 8
shows an example of a water value function. Each reservoir in a river system has its own water
value function. The future expected income increases with increased reservoir content, but the
slope decreases, meaning additional water is less valuable as the total reservoir content increases.
Note that the derivative of the water value function, or its slope, is the marginal water value
function. Points A, B, and C show the slope, or the marginal water value, at three different points.
At point A, the reservoir content is low, so adding more water increases the future income
significantly, shown here as a large slope. At point C, however, the reservoir content is high, so
the value of adding more water is not as significant, and the slope is lower. When the marginal
income in the short-term is larger than the future expected income, a marginal unit of water
should be used in the short-term.
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Figure 8 Water value function, source: (Hassis, 2011)
By requiring the water value function to be at a certain point at the end of the short-term planning
period, the models can take price dependency better into account. Also, this improves the
flexibility of the model to adapt the resources to the inflow conditions and reduce the amount of
start/stop cycles (Hassis, 2011).
Since different reservoirs have different volumes and flow rates, it is beneficial to use reservoir-
specific water values (Hassis, 2011). This means assuming that marginal water values in a river
system are independent of each other for each reservoir. A major drawback of this is that short-
term optimisation is very sensitive to the relative difference between marginal water values and
short-term spot price.
4.5 SHORT-TERM PLANNING Short-term planning makes an optimal production plan starting from the day ahead to 3-4 weeks
out, and is used every day to plan the spot bids. Though the plan is for about 3-4 weeks, the next
day is the most important and is what is sent in as a bid to the spot market by 12:00 CET. All
plans consider when the plants are unavailable, for example for maintenance.
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4.5.1 Pre-Spot Planning
Every morning the short-term model is used to plan the production for the next day. The inflow
and spot price forecasts, as well as the steering from the mid-term planning, are input into the
model, and the bid for the following day is formed. This optimisation considers several different
price scenarios and even different inflow scenarios, and the results are used to create a piece-wise
bid curve.
4.5.2 Post-Spot Planning
Once the actual spot prices have been determined and released at 12:42 CET, the short-term
model is run again. This time, the model has another constraint to generate exactly as much
power as was sold on the spot market per hour. It does not have to be generated by the same
plants as in the original optimisation in the pre-spot planning, so the plans can change in order to
be the most beneficial. The results of this optimisation are the production plans for the following
day, and are used by the dispatch center to actually run the plants and realize the production that
was promised. .
4.6 HYDROPOWER MODELLING THEORY There are many different methods for modelling hydropower systems, and the basic layouts have
been discussed thoroughly in literature, for example in (Söder & Amelin, 2011). The following
sections will introduce several mathematical methods for modelling.
4.6.1 Linear Programming
Linear programming is the simplest modelling method. The objective function and all constraints
are linear. It can efficiently solve large-scale problems, and will converge to global optimums
(Labadie, 2004). The most common linear programming method, simplex, is presented in (S.
Nash, 1996). When non-linear functions are required, separable programming is used to replace
them with piece-wise linear curves. Mixed Integer Linear Programming, MILP, allows the use of
both continuous and integer variables like binaries (Hassis, 2011). MILP is often used to
represent hydropower efficiency curves or unit commitment (deciding to have a unit, or a
generator and turbine pair, on). While linear programming is efficient, it often oversimplifies the
non-linearities of real life systems and is not the most accurate method.
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4.6.2 Non-linear Programming
Non-linear programming is able to more accurately represent real-life systems like the efficiency
curves of hydropower plants. The most robust methods are successive linear programming (SLP),
successive quadratic programming (SQP), and the method of multipliers (MOM) (Labadie,
2004). All equations must be differentiable, which can sometimes be problematic and require
creative solutions. SLP is the most efficient non-linear programming method (Hiew, 1987), but it
does not always converge to a global optimum (Bazaraa, 1993). With SLP, the objective function
is often quite flat near the optimum, and this point can change very slightly each iteration,
preventing the model from converging. A penalty can be applied to prevent the optimal value
from changing too much between iterations, forcing it to converge (Belsnes, Wolfgang, Follestad,
& Aasgård, 2015).
4.6.3 Dynamic Programming
Discrete dynamic programming breaks large problems down into sub-problems that can be
solved sequentially each time period. It is often used when there are dynamic features like system
control variables (discharges and spillages) and state variables (reservoir levels) (Hassis, 2011),
and is often used when the state of the system depends on the previous system state and the time
of occurrence. Dynamic programming is a flexible method and works with both convex and non-
convex problems. However, as the number of state-variables increases, the calculation time
grows exponentially as every discrete dimension is tested. This is known as the “curse of
dimensionality” (Labadie, 2004). A different method, differential dynamic programming, was
developed by (Jacobson & Mayne, 1970) to solve the dimensionality problems using analytical
instead of discretized methods. Differential dynamic programming was applied to the Mad River
System in northern California, and it was determined that the same problem would have taken 16
times longer in an LP formulation (Jones, Willis, & Finney, 1986).
4.6.4 Stochastic Programming
Stochastic programming assumes all future decisions and consequences are random, not fixed.
This is as opposed to a deterministic problem where all values are treated as the truth (Labadie,
2004). The problem is broken into multiple stages where the objective function includes the
maximum benefit from the first-stage decisions and the total expected future benefit from the
later stages. If all different future scenarios have a known probability, the problem can be
reformulated with a deterministic formulation, but it is difficult to definitively calculate these
24 | P a g e
problems. Stochastic programming allows uncertainties to be accounted for and recommends the
best decisions to make based on these uncertainties. In hydropower planning, the main
uncertainties come from the inflow and price forecasts.
Stochastic successive linear programming, SSLP, adds the stochastic programming capability to
the SLP discussed in section 4.6.2 (Belsnes, Wolfgang, Follestad, & Aasgård, 2015). SHOP, a
modelling tool used throughout much of Scandinavia, already implements SLP. This may be a
good choice for hydropower modelling because in reality, the efficiency of a hydropower plant
changes based on the available head. More head means more energy stored in the water. This
relationship could be made non-linear, or it could be modelled using a first-order variable that
estimates how much higher the production would be with higher efficiencies due to a higher
head. In each iteration, the efficiencies are updated based on the reservoir level in the previous
round. (Belsnes, Wolfgang, Follestad, & Aasgård, 2015) found that this method performs very
similarly to the non-linear formulation, so a linear approximation accurately represents the
system while being simpler and more efficient.
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5 HYDROPOWER PLANNING MODEL: FORTUM SYSTEM
5.1 BÅTHUSSTRÖMMEN Båthusströmmen is a small3 3.3 MW hydropower plant in Dalälven connected to the Hösthån
reservoir and is owned and operated by Fortum. It is the furthest upstream plant in its branch of
Dalälven, meaning there are no other plants upstream of Båthusströmmen. The next closest
downstream plant is Trängslet, one of the largest hydropower plants and reservoirs in Sweden.
Figure 9 Båthusströmmen Location (Google Maps, 2018)
Since Trängslet is so much larger than Båthusströmmen, 300 MW compared to 3.3 MW,
anything that Båthusströmmen does will not have any significant effect on Trängslet. This means
that Båthusströmmen can be modelled as an independent hydropower plant with no hydrological
coupling constraints (Bjerhag, 2018). This is an ideal case study since the impact of a single plant
can be analysed, and any results can be directly linked to changes in that specific plant instead of
some unknown factor throughout the river system.
3 Small hydropower plants here can be considered to be less than 10 MW
26 | P a g e
Båthusströmmen, as well as many other small hydropower plants, is run on VNR
(vattennivåreglering), or water level regulation (Faridoon, 2018). There is a simple controller
located in the plant that measures the water level of the reservoir and controls the amount of
discharge and spillage in order to maintain a constant water level. This type of control is used in
many small plants to simplify the operation. The central dispatch table is in charge of the
operation of every Fortum hydropower plant in Sweden, and there are many factors that have to
be monitored. Though an optimal schedule is created for each plant every day (see section 4.5),
the operators still must monitor the plants and adjust the schedule to account for any unexpected
changes, such as a larger inflow than expected. In order to be sure that the larger plants like
Trängslet are operating in the best way possible, the smaller, more “insignificant” plants are put
on automatic VNR control. This allows the operators to focus on the larger, more profitable
plants.
When on VNR control, plants like Båthusströmmen are not following an optimal dispatch
schedule and thus are not making as much profit as they could. The following sections show what
the operation of Båthusströmmen in 2016 would have looked like if an optimal dispatch schedule
were utilized instead of VNR control. The optimal schedule was made for January 1 to December
5 of 2016 using price forecasts made by Fortum and realized inflow values. The price forecasts
for the rest of December were not available. It is worth noting that 2016 was a leap year. The
optimisation was done as if a real spot trader were doing them, so a plan was created every day
for the following day, but considering up to 4 weeks ahead. The price forecasts are updated every
day, and the plans are assumed to have been followed exactly, with no unforeseen changes in, for
example, local inflow.
5.2 OPTIMAL PLANNING VS VNR CONTROL RESULTS A simple model was built in Fortum modelling system to model only Båthusströmmen and its
reservoir, Hösthån. The model uses the same constraints and efficiency curves as the current
model that Fortum uses for the other plants in Dalälven, but a marginal water value curve had to
be generated for Hösthån. Recall from section 4.4 that the water value curve can be used to give
the expected future value of the remaining water in a reservoir. The marginal water curve is
simply the derivative of a water value curve, and is used to estimate how much the water value
would increase by increasing the reservoir height. This curve is used in the model to create an
optimal schedule. The available curve was designed to simulate a VNR operation of
Båthusströmmen, and needed to be adapted to a more realistic curve. The new marginal water
value curve was created based on the existing curve as well as marginal water value curves of
similar plants. Two different curves were tested, and the difference in results was deemed to be
insignificant enough that a more accurate curve did not have to be generated, and the curves used
are just for calculation purposes.
In the original Fortum optimisation model, a model of Båthusströmmen is used more as a
placeholder for the rest of the model, and the reservoir level is only allowed to vary within a
20cm range. This means that the reservoir, Hösthån, had a capacity of 0.1Mm3. In the new model,
the reservoir is able to vary within a 2 meter range. This value was chosen based on the allowed
limits of similar sized plants. There are no known regulations for Båthusströmmen that would
27 | P a g e
limit the reservoir levels further (Faridoon, 2018). The original marginal water value curve and
two newly generated curves (V2 and V3) are shown below. The new curves represent the
reservoir having a 2 meter range, giving it a total usable capacity of 1Mm3. These curves were
generated based on the existing water value curves for similar sized Fortum plants, as well as
looking at water value curves for larger plants. The exact formulation of these curves is not the
focus of this thesis, and is a good candidate for further research.
Figure 10 Marginal Water Value Curves for Båthusströmmen
In total, 4 cases were simulated for Båthusströmmen:
1. VNR: Using the current model in the Fortum system with a 20cm range for reservoir
height and original marginal water value curve
2. V2: Using the model of Båthusströmmen with V2 of the marginal water value curve and a
2m range for the reservoir level
3. V3: Using the model of Båthusströmmen with V3 of the marginal water value curve and a
2m range for the reservoir level
4. Minimum Discharge (Min Q): Using the model of Båthusströmmen with V3 of the
marginal water value curve and 2m range for the reservoir level. There is also a lower
limit for the discharge to avoid many start/stops of the generator. Q here represents the
water discharged through the turbine.
Case 4 was added after the results from cases 2-3 showed that the generator should start more
than once a day. This adds a lot of wear and tear on the generator and turbine, and would require
a lot of extra maintenance. In addition, the maintenance cost is very high for Båthusströmmen
because it takes a worker about 2 hours to travel from Trängslet to perform the maintenance, plus
2 hours to return to Trängslet. Not only does the maintenance require a lot of time just in travel,
0
10000
20000
30000
40000
50000
60000
70000
0 0,2 0,4 0,6 0,8 1 1,2
Mar
gin
al W
ater
Val
ue
(EU
R/M
m3
)
Reservoir Filling (Mm3)
Marginal Water Value
Original
V2
V3
28 | P a g e
but it takes a worker away from Trängslet, a much more significant plant. Thus, case 4 was
simulated to prevent the generator from stopping unnecessarily.
Figure 11Figure 13 show the reservoir level for weeks 1, 20, and 40 respectively and for each of
the 4 cases. The realized reservoir level is also shown for comparison. The reservoir level is
measured in meters above sea level (masl). Case 1, the VNR case, forces the reservoir level to
vary only within a 20cm range. In reality, the VNR control kept the level nearly constant
throughout the year, only varying by a few centimeters. Case 2 and 3 utilize the full 2 meters of
reservoir level range, often causing the generator to turn off when the lower limit is reached. In
case 4, with a minimum discharge limit, the reservoir level does not dip as low because the
optimisation algorithm plans ahead to have enough water to satisfy the minimum discharge
constraint.
Figure 11 2016 Week 1 Båthusströmmen Reservoir Level
During June, the spring flood is still occurring, meaning that there is a lot of water running
through all of the rivers from ice and snow melt. This is why the reservoir level remains near the
upper limit during the spring and summertime.
493
493,5
494
494,5
495
495,5
496
16.1.4 0:00 16.1.5 0:00 16.1.6 0:00 16.1.7 0:00 16.1.8 0:00 16.1.9 0:00 16.1.10 0:00 16.1.11 0:00
Res
ervo
ir L
evel
(m
asl)
January 4-10, 2016
VNR V2 V3 MinQ Real
29 | P a g e
Figure 12 2016 Week 23 Båthusströmmen Reservoir Level
493
493,5
494
494,5
495
495,5
496
16.6.6 0:00 16.6.7 0:00 16.6.8 0:00 16.6.9 0:00 16.6.10 0:00 16.6.11 0:00 16.6.12 0:00 16.6.13 0:00
Res
ervo
ir L
evel
(m
asl)
June 6-12, 2016
VNR V2 V3 MinQ Real
30 | P a g e
Figure 13 2016 Week 40 Båthusströmmen Reservoir Level
Table 1 Båthusströmmen Simulation Comparison
% Increase
Profit
Total
Production
(MWh)
% Increase
Production
Total start-
ups
Realized
11192
40
Case 1: VNR -1.79 13215 18.08 615
Case 2: V2 2.89 11236 0.39 406
Case 3: V3 2.61 11224 0.29 421
Case 4: Min Q 15.05 9574 -14.46 0
Table 1 shows the increase in profit and production for the 4 cases as compared to the realized
operation. The profit here is calculated as the power sold at the predicted electricity price minus
the start-up cost of the generator. Every day there were new electricity predictions for the
493
493,5
494
494,5
495
495,5
496
16.10.3 0:00 16.10.4 0:00 16.10.5 0:00 16.10.6 0:00 16.10.7 0:00 16.10.8 0:00 16.10.9 0:00 16.10.10 0:00
Res
ervo
ir L
evel
(m
asl)
October 3-9, 2016
VNR V2 V3 MinQ Real
31 | P a g e
optimisation period, and the first day of predictions from each set was saved as the final predicted
price. The predicted electricity cost is used in the profit calculations, including the realized
version, to eliminate the influence of forecast error and focus solely on the optimisation. Cases 1-
3 have a lot of generator starts (and stops), at least one per day. This causes a high maintenance
cost, and thus not a very high increase in profit. The VNR case actually has a lower profit than
the realized operation. This discrepancy is most likely due to the fact that the optimised VNR
model was always considering the future value of water, not just the immediate spot sales. Case
4, however, has a 15.05% increase in profit as compared to the realized profit.
32 | P a g e
6 HYDROPOWER PLANNING MODEL: THEORY
When using the model at Fortum, the exact model formulation is not known. In addition, the
model cannot update the efficiency curve in between iterations, which would improve the
accuracy of the optimisation. The following chapter describes an optimisation model developed
to resemble, and improve, the Fortum model. First the theory is presented, then a case study is
presented in Chapter 7. This fictitious plant is comparable to Båthusströmmen and is also not
hydrologically coupled to other plants.
In addition to the reservoir upper level and minimum discharge constraints, a variable minimum
reservoir level constraint has been added. During the winter, the surface of the reservoirs freeze.
If the surface ice is cracked, which happens if the reservoir level varies too much, small cracks
can appear in the ice. These cracks allow cold air to flow through them into the running water
below, causing ice to form in the water and clog the intake grates of the power plant. This
phenomena is called frazil ice. To prevent this, the range for the reservoir level is restricted to just
20 centimeters during the winter time. This will limit the power production, but is a practical
limitation to prevent costly maintenance.
The second main difference between this model and the Fortum model is that the power-
discharge (PQ) curve is updated each iteration based on the reservoir level. When the reservoir is
completely full, there is more potential energy stored in the water because it has a larger head.
This means that the power that will result from the generator is greater than if the reservoir was at
its minimum level. In (Belsnes, Wolfgang, Follestad, & Aasgård, 2015), an iterative method for
updating the efficiency curve based on a new head is demonstrated. The following algorithm
implements this method on the PQ curve instead of the efficiency curve directly, since this is
what is practically available in many hydropower plants. A black box diagram of the described
algorithm is shown below.
Figure 14 Optimal Planning Algorithm
In reality, this model should also consider whether or not the plant or generator is available or if, for
example, it is down for maintenance.
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6.1 NOMENCLATURE The sets, indices, parameters, and variables are described below. Here, a unit is a generator-turbine pair.
PWL stands for piece-wise linear, used to represent nonlinear curves.
Table 2 Algorithm Nomenclature
Sets and Indices
Set T, index t Time
Set I, index i Unit, including generator and turbine
Set J, index j Spillage gates
Set A, index a Linear segments for PWL PQ curve
Set N, index n Indices for binary values in PQ PWL curve
Set W, index w Linear segment for PWL water value curve
Set H, index h Indices for binary values in water value PWL curve
Variables
pi,t Power produced by unit i at time t (MW)
Qi,t Discharge through unit i at time t (m3/s)
Sj,t Spillage through gate j at time t (m3/s)
Mt Reservoir level at time t (masl, meters above sea level)
qi,a,t Amount of discharge for segment a of power curve (m3/s)
yi,n,t Binary variables for PQ PWL curve
dt Binary variable for discharge lower limit
zj,t Binary variable for spillage lower limit
WVt Water value of the reservoir (€)
mw,t Width of segment, reservoir level (meters)
kh,t Binary variable for water value PWL curve
ui,t Unit commitment binary for generator i
𝑠𝑖,𝑡+ Start-up binary for generator i
𝑠𝑖,𝑡− Stop binary for generator i
Parameters
Pt Spot price (predicted or real) at time t (€/MW)
Vt Inflow to reservoir at time t (m3/s)
Δxi,a Initial power per segment for unit at defined head (MW)
Δqi,a Width of segment, discharge (m3/s)
M0 Initial reservoir height (masl)
𝑄 Minimum discharge (m3/s)
�̅� Maximum discharge (m3/s)
𝑆 Minimum spillage (m3/s)
𝑆̅ Maximum spillage (m3/s)
𝑀𝑡 Minimum reservoir level (masl)
�̅� Maximum reservoir level (masl)
𝑝 Minimum power (MW)
�̅� Maximum power (MW)
TE Time equivalent, converts water flow to reservoir height, unit is hour equivalents/m
𝑊𝑉𝑤𝑠𝑙𝑜𝑝𝑒
Slope of segment w of water value curve
Δmw Width of reservoir level segments (meters)
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Ci Start-up cost for generator I (€)
ui,0 Initial state of generator, on or off
6.2 EXPLANATION OF FLEXIBILITY OF MODEL For this simple test case, only one plant with one generator (i=1) and one spillway (j=1) is used.
However, the algorithm is written in such a way that a more complex system could be used as
well. If more plants are added to the model, the hydrological coupling between them must be
added as well. This is highly dependent on the river system, especially the connection and travel
time between plants. Only one plant was used for this thesis both as a proof of concept and also
to be able to clearly see the benefit of using optimal planning. By using just one plant, any
changes in production are trackable, and are not dependent on many factors caused by the
coupling with other plants.
The model is implemented in GAMS, a commercial optimisation program.
6.3 STATIC MODEL A basic hydropower model is presented below where all parameters remain the same between
time steps except the electricity price and local inflow.
Objective Function
The goal of the model is to maximise the profit from the sales to the spot market. Often in
hydropower optimisation the future value of water is also included in the objective function, as it
is here. The water value curve is found by integrating the marginal water value curve in Figure
10. Version 3 of the curve is used in this simulation. Mid-term steering, as described in section
4.2, is not utilized here. That function will be explored later on in this thesis. Thus, the objective
function is
𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 ∑ (𝑃𝑡𝑡∈𝑇,𝑖∈𝐼 𝑝𝑖,𝑡 − 𝐶𝑖𝑠𝑖,𝑡+ ) + 𝑊𝑉𝑒𝑛𝑑 ( 1 )
Hydrological Constraint
There are no plants connected up- or downstream, so there are no hydrological couplings to
consider. The plant is therefore only affected by the local inflow, discharge, and spillage, as well
as the local hour equivalent of the reservoir. This hour equivalent, TE, is based on the size and
shape of the reservoir, and converts m3/s to reservoir height in meters.
𝑀𝑡 = 𝑀𝑡−1 +𝑉𝑡 − ∑ 𝑄𝑖,𝑡 − ∑ 𝑆𝑗,𝑡𝑗∈𝐽𝑖∈𝐼
𝑇𝐸
∀𝑡 ∈ 𝑇 ( 2 )
Piece-wise Linear Power-Discharge Curve
The power generated by the plant is based on the discharge and is represented by a piece-wise
linear curve. Figure 15 shows an example of such a curve for a single unit during time-step t.
35 | P a g e
Figure 15 Piece-wise linear power curve
The above graph shows variables for one unit (i), which is omitted from the subscripts. The
following constraints describe the piece-wise linear curve (Almassalkhi & Towle, 2016).
𝑄𝑖,𝑡 = ∑ 𝑞𝑖,𝑎,𝑡
𝑎∈𝐴
∀𝑡 ∈ 𝑇 ( 3 )
𝑝𝑖,𝑡 = ∑ 𝑞𝑖,𝑎,𝑡
∆𝑥𝑖,𝑎
∆𝑞𝑖,𝑎𝑎∈𝐴
∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 4 )
𝑦𝑖,1,𝑡∆𝑞𝑖,1 ≤ 𝑞𝑖,1,𝑡 ≤ ∆𝑞𝑖,1 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 5 )
𝑦𝑖,2𝑎−2,𝑡∆𝑞𝑖,𝑎 ≤ 𝑞𝑖,𝑎,𝑡 ≤ 𝑦𝑖,2𝑎−1,𝑡∆𝑞𝑖,𝑎 𝑓𝑜𝑟 𝑎 ∈ 𝐴 − {1, 𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 6 )
0 ≤ 𝑞𝑖,𝑎,𝑡 ≤ 𝑦𝑖,2𝑎−2,𝑡∆𝑞𝑖,𝑎 𝑓𝑜𝑟 𝑎 ∈ 𝐴{𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 7 )
𝑦𝑖,2,𝑡 ≤ 𝑦𝑖,1,𝑡 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 8 )
𝑦𝑖,𝑛+2,𝑡 ≤ 𝑦𝑖,𝑛,𝑡 𝑓𝑜𝑟 𝑛 ∈ 1,2,4,6 … 𝑒𝑛𝑑 − 2, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 9 )
𝑦𝑖,𝑛+3,𝑡 ≤ 𝑦𝑖,𝑛,𝑡 𝑓𝑜𝑟 𝑛 ∈ 2,4,6 … 𝑒𝑛𝑑 − 4, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 10 )
Let’s break this down. Equations ( 3 )-( 4 ) show how the total power and discharge are
calculated as the sum of the segments that make up the curve. Equations ( 5 )-( 7 ) limit the size
36 | P a g e
of qi,a,t to the size of each segment ∆𝑞𝑖,𝑡. The use of the binary variable yi,n,t in equations ( 5 )-( 10
) makes sure that the curve is utilized in order, meaning that qi,3,t can only be non-zero if qi,1,t and
qi,2,t are at their maximum values. For example, Figure 16 shows the same curve as above but
with values filled in for ∆𝑞𝑖,𝑎 and ∆𝑥𝑖,𝑎 .
Figure 16 PWL example curve
Suppose we want to calculate the shown point, where the discharge is 7.5 m3/s and the power is
15MW. This means that qi,1,t=3, qi,2,t=3, and qi,3,t=1.5. Equations ( 5 ) and ( 6 ) become:
𝑦𝑖,1,𝑡 ∗ 3 ≤ 𝑞𝑖,1,𝑡 ≤ 3
𝑦𝑖,2,𝑡 ∗ 3 ≤ 𝑞𝑖,2,𝑡 ≤ 𝑦𝑖,3,𝑡 ∗ 3
𝑦𝑖,4,𝑡 ∗ 3 ≤ 𝑞𝑖,3,𝑡 ≤ 𝑦𝑖,5,𝑡 ∗ 3
And equation ( 7 ) becomes
0 ≤ 𝑞𝑖,4,𝑡 ≤ 𝑦𝑖,6,𝑡 ∗ 3
In order for qi,1,t=3 and qi,2,t=3, 𝑦𝑖,1,𝑡 , 𝑦𝑖,2,𝑡 , and 𝑦𝑖,3,𝑡 must be set to 1, making
37 | P a g e
3 ≤ 𝑞𝑖,1,𝑡 ≤ 3
3 ≤ 𝑞𝑖,2,𝑡 ≤ 3
The next segment variable, qi,3,t can be any value in its allowed range, so 𝑦𝑖,4,𝑡 must be 0, and
𝑦𝑖,5,𝑡 must be 1, resulting in
0 ≤ 𝑞𝑖,3,𝑡 ≤ 3
The last segment must be empty, since the desired point is to the left of the entire segment. To set
𝑞𝑖,4,𝑡 to 0, 𝑦𝑖,6,𝑡 must also be 0, making
0 ≤ 𝑞𝑖,4,𝑡 ≤ 0
These binary choices force a segment q to either be full, partially full, or empty. To ensure that
the segments are “filled up” in order from left to right, equations ( 8 )-( 10 ) are used. From this
example, equation ( 8 ) becomes
𝑦𝑖,2,𝑡(1) ≤ 𝑦𝑖,1,𝑡(1)
The values are shown in parenthesis, and the equation holds true. Equation ( 9 ) becomes
𝑦𝑖,3,𝑡(1) ≤ 𝑦𝑖,1,𝑡(1)
𝑦𝑖,4,𝑡(0) ≤ 𝑦𝑖,2,𝑡(1)
𝑦𝑖,6,𝑡(0) ≤ 𝑦𝑖,4,𝑡(0)
The above equations are all true. Lastly, equation ( 10 ) becomes
𝑦𝑖,5,𝑡(1) ≤ 𝑦𝑖,2,𝑡(1)
Once again, this constraint holds true. That the segments must fill up in order is called an
adjacency constraint in (Almassalkhi & Towle, 2016). Since the power in each linear segment,
xi,a,t is based on the discharge from each linear segment, qi,a,t, those too will fill up in order and
the total power will be the correct value, 15, from this example.
Limit Constraints
𝑄 ≤ 𝑄𝑖,𝑡 ≤ �̅� ∀t ∈ T, i ∈ I ( 11 )
𝑆 ≤ 𝑆𝑗,𝑡 ≤ 𝑆̅ ∀t ∈ T, j ∈ J ( 12 )
𝑝𝑖 ≤ 𝑝𝑖,𝑡 ≤ 𝑝�̅� ∀t ∈ T, i ∈ I ( 13 )
𝑀𝑡 ≤ 𝑀𝑡 ≤ �̅� ∀t ∈ T ( 14 )
38 | P a g e
Note that the discharge has a minimum level, as was determined to be best from the simulation in
Chapter 5. The reservoir lower limit can also be different for different time steps. This is to
prevent frazil ice from forming, as explained previously.
Piece-wise Linear Water Value Curve
Similarly, the water value curve must also be represented as piece-wise linear. The marginal
water value curve in Figure 10 has reservoir filling volume on the x-axis, and so will the water
value curve that is derived from it. To more easily implement the water value curve, the x-axis is
converted from volume(Mm3) to reservoir height (masl). The reservoir, within the available
reservoir levels, is assumed to be rectangular, so the height increases linearly with the volume.
WVt = ∑ mw,tWVwslope
w∈W
∀𝑡 ∈ 𝑇 ( 15 )
Mt = ∑ mw,tw∈W
∀𝑡 ∈ 𝑇 ( 16 )
𝑘𝑖,1,𝑡∆𝑚1 ≤ 𝑚1,𝑡 ≤ ∆𝑚1 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 17 )
𝑘𝑖,2𝑤−2,𝑡∆𝑚𝑤 ≤ 𝑚𝑤,𝑡 ≤ 𝑘𝑖,2𝑤−1,𝑡∆𝑚𝑤 𝑓𝑜𝑟 𝑤 ∈ 𝑊 − {1, 𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 18 )
0 ≤ 𝑚𝑤,𝑡 ≤ 𝑘𝑖,2𝑤−2,𝑡∆𝑚𝑤 𝑓𝑜𝑟 𝑤 ∈ 𝑊{𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 19 )
𝑘𝑖,2,𝑡 ≤ 𝑘𝑖,1,𝑡 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 20 )
𝑘𝑖,ℎ+2,𝑡 ≤ 𝑘𝑖,ℎ,𝑡 𝑓𝑜𝑟 ℎ ∈ 1,2,4,6 … 𝑒𝑛𝑑 − 2, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 21 )
𝑘𝑖,ℎ+3,𝑡 ≤ 𝑘𝑖,ℎ,𝑡 𝑓𝑜𝑟 ℎ ∈ 2,4,6 … 𝑒𝑛𝑑 − 4, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 22 )
Start-up Costs
Lastly, the generator starts need to be kept track of and the start cost subtracted from the profit.
With a minimum discharge constraint the generator should not have to turn off, but the start cost
should be included just in case a constraint must be violated in order to reach a solution. For this,
the time when the generator is on (unit commitment) must be kept track of. If a minimum
discharge constraint larger than zero is set, the unit will never turn off, so these equations can be
omitted.
𝑢𝑖,𝑡 − 𝑢𝑖,𝑡−1 = 𝑠𝑖,𝑡+ − 𝑠𝑖,𝑡
− 𝑓𝑜𝑟 𝑡 = 2 … 𝑒𝑛𝑑, ∀𝑖 ∈ 𝐼 ( 23 )
𝑢𝑖,𝑡 − 𝑢𝑖,0 = 𝑠𝑖,𝑡+ − 𝑠𝑖,𝑡
− 𝑓𝑜𝑟 𝑡 = 1, ∀𝑖 ∈ 𝐼 ( 24 )
39 | P a g e
6.4 ITERATIVE UPDATES BASED ON NEW HEAD The above static model does not change between iterations. In reality, the efficiency of the
turbine/generator is greater when there is greater head since there is more potential energy stored
in the water. This change in efficiency can be represented by updating the power curve each time
step (Belsnes, Wolfgang, Follestad, & Aasgård, 2015). The entire power curve is scaled based on
the most efficient point. This update is shown below. Note that the index a=best refers to the
point on the curve with the best efficiency, and a=rest refers to the remaining points. Note also
that instead of using the segment variables, 𝑥𝑖,𝑎,𝑡, the points on the graph, or the y-coordinates,
are updated. The segments are then reformed from the new points. The points here are
represented as 𝑥𝑖,𝑎,𝑡𝑝
.
𝑥𝑖,best,𝑡𝑝 = 𝑥𝑖,min 𝑒𝑓𝑓,𝑡−1
𝑝 + (𝑥𝑖,best,𝑡−1𝑝 − 𝑥𝑖,min 𝑒𝑓𝑓,𝑡−1
𝑝 )𝑀𝑡−1
�̅�
∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 25 )
𝑥𝑖,𝑟𝑒𝑠𝑡,𝑡𝑝
= 𝑥𝑖,𝑟𝑒𝑠𝑡,𝑡−1𝑝 𝑥𝑖,𝑏𝑒𝑠𝑡,𝑡
𝑝
𝑥𝑖,𝑏𝑒𝑠𝑡,𝑡−1𝑝
∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 26 )
This update is done outside of the above model. For example, the optimisation is done every day
for the following day and considering the next several weeks. The optimisation will be done
using the original PQ curve, then the optimal schedule for the first hour is kept. The PQ curve is
updated as shown above, and the program iterates and runs the optimisation again starting from
the second hour. This continues until the full 24 hours are planned. It was decided that iterating
through each hour of the planning period (up to 4 weeks) was not necessary, and that just
iterating through the desired day was sufficient. This was decided because adding more iterations
greatly increased the calculation time, and the changes in the curve were very small between
hours. Since only the first 24 hours are kept, they are the only ones where the PQ curve is
updated. This could be a subject for further research.
40 | P a g e
7 OPTIMAL PLANNING ALGORITHM RESULTS
Once again, 2016 was chosen as the simulation year. For the electricity price predictions, the
realized spot price was used with an introduced random error of up to 4%. The inflow was
generated based on real measurements and with a random error of up to 6%. The results for the
optimal planning algorithm are shown below. The parameters used are shown below.
Table 3 Test Case Parameters
M0 495.4 masl
𝑄 3 m3/s
�̅� 24 m3/s
𝑆 0 m3/s
𝑆̅ 252 m3/s
𝑀𝑡 495.0 masl (December 1-February 29) , 493.5 masl (March 1-November 30)
�̅� 495.5 masl
𝑝 0 MW
�̅� 3.3 MW
TE 350 hour equivalents/m
C 151 €
u0 1, on
The following graphs show the reservoir level, discharge, spillage, and electricity price for week
1, 23, and 40 of 2016.
Figure 17 Week 1 Reservoir level and flow rate
0
5
10
15
20
25
30
495,44
495,45
495,46
495,47
495,48
495,49
495,5
495,51
01-04 01-05 01-06 01-07 01-08 01-09 01-10 01-11
Flo
w R
ate
(m^3
/s)
Res
ervo
ir L
evel
(m
asl)
January 4-10, 2016
M (masl) Discharge (m3/s) Spillage (m3/s)
41 | P a g e
Figure 18 Week 1 Reservoir level and electricity price
During the winter, the reservoir level is more tightly restricted to stay above 495.0 masl. There is
no spillage needed during week 1. There is a clear correlation between the electricity price and
the reservoir level in Figure 18 where the drops in reservoir level occur when there are spikes in
electricity price.
Figure 19 Week 23 Reservoir level and flow rate
0
20
40
60
80
100
120
495,44
495,45
495,46
495,47
495,48
495,49
495,5
495,51
01-04 01-05 01-06 01-07 01-08 01-09 01-10 01-11
Elec
tric
ity
Pri
ce (€
/MW
)
Res
ervo
ir L
evel
(m
asl)
January 4-10, 2016
M (masl) Price (Eur/MW)
0
5
10
15
20
25
30
495,48
495,485
495,49
495,495
495,5
495,505
06-06 06-07 06-08 06-09 06-10 06-11 06-12 06-13
Flo
w R
ate
(m^3
/s)
Res
ervo
ir L
evel
(m
asl)
June 6-12, 2016
M (masl) Discharge (m3/s) Spillage (m3/s)
42 | P a g e
Figure 20 Week 23 Reservoir level and electricity price
During the summer the reservoir level is allowed to decrease until 493.5 masl, but the spring
flood is in full effect. At this time there is a large amount of inflow, so the reservoir level does
not get too low. During the fall, shown in Figure 21 and Figure 22, the reservoir level changes
daily based on the price, but still does not go below approximately 495.47 masl, refilling during
the night when the electricity price is low.
Figure 21 Week 40 Reservoir level and flow rate
0
5
10
15
20
25
30
35
40
45
50
495,48
495,485
495,49
495,495
495,5
495,505
06-06 06-07 06-08 06-09 06-10 06-11 06-12 06-13
Elec
tric
ity
Pri
ce (€
/MW
)
Res
ervo
ir L
evel
(m
asl)
June 6-12, 2016
M (masl) Price (Eur/MW)
0
2
4
6
8
10
12
14
16
18
20
495,465
495,47
495,475
495,48
495,485
495,49
495,495
495,5
10-03 10-04 10-05 10-06 10-07 10-08 10-09 10-10
Flo
w R
ate
(m^3
/s)
Res
ervo
ir L
evel
(m
asl)
October 3-9, 2016
M (masl) Discharge (m3/s) Spillage (m3/s)
43 | P a g e
Figure 22 Week 40 Reservoir level and electricity price
During most of the year there is no need to spill any water. However, during the spring flood the
inflow is well over the upper discharge limit, so some water must be spilled.
Figure 23 Inflow and spillage for 2016
0
5
10
15
20
25
30
35
40
45
495,465
495,47
495,475
495,48
495,485
495,49
495,495
495,5
10-03 10-04 10-05 10-06 10-07 10-08 10-09 10-10
Elec
tric
ity
Pri
ce (€
/MW
)
Res
ervo
ir L
evel
(m
asl)
October 3-9, 2016
M (masl) Price (Eur/MW)
0
50
100
150
200
250
300
01-01 02-20 04-10 05-30 07-19 09-07 10-27 12-16
Flo
w r
ate
(m3
/s)
Inflow and Spillage
Spillage Inflow
44 | P a g e
Even when the reservoir level is allowed to go to the lower limit of 495.0 masl, it remains
relatively high. This is most likely due to the fact that mid-term steering was not used in this
model, so the end water value was always a part of the objective function. This causes the model
to want to maintain a high reservoir level at the end of the planning period (short term) to have a
high end water value, and high objective function. To see the effect of the optimised planning, a
simple VNR simulation was done where the discharge exactly equalled the inflow. When the
inflow was larger than the allowed discharged, the remaining inflow was spilled. Using this
‘VNR’ discharge schedule, the benefit of using an optimising algorithm can be seen. For
example, week 1 discharge from the VNR and optimised versions are shown below. While the
VNR discharge remains quite constant, the optimised discharge varies throughout each day,
following the price.
Figure 24 Optimised and VNR discharge comparison
The optimal discharge plan varies much more on an hourly basis than the VNR discharge in order
to optimise the profit. There is a 16% increase in profit during 2016 by using the optimisation
algorithm. This is comparable to the 15% increase from case 4 in section 5.2, so the discussed
algorithm is similar to that implemented in the Fortum model.
0
5
10
15
20
25
30
04-jan 05-jan 06-jan 07-jan 08-jan 09-jan 10-jan 11-jan
Dis
char
ge (
m3
/s)
VNR vs Optimised Discharge January 4-10, 2016
VNR Optimised
45 | P a g e
8 CENTRAL AUTOMATIC CONTROL
8.1 DESCRIPTION The algorithm described above is capable of planning the operation of a hydropower plant for
varying lengths of time. With this in mind, it can be used for the mid-term planning as well as
short-term planning. As described in section 4.2, steering from mid-term planning can ensure that
future factors are considered. The above algorithm can be used for mid-term planning, which
then passes the steering, in the form of a reservoir water value, to a short-term planning model.
This short-term planning model will have two main differences: the objective function will no
longer consider future value of stored water, and there will be an additional steering constraint.
Equation ( 1 ) becomes
𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 ∑ (𝑃𝑡𝑡∈𝑇,𝑖∈𝐼 𝑝𝑖,𝑡 − 𝐶𝑖𝑠𝑖,𝑡+ ) ( 27 )
The steering constraint will simply be
𝑊𝑉𝑒𝑛𝑑 = 𝑊𝑉𝑠𝑡𝑒𝑒𝑟𝑖𝑛𝑔 ( 28 )
where WVsteering is the water value at the end of the short-term optimisation as determined in the
mid-term optimisation. With the mid-term and short-term planning algorithms, a hydropower
plant can be optimised in real time.
The following section describes the implementation of the planning algorithms with Fortum’s
central control. This work was done in collaboration with Jenny Möller and Johan Wiklund for
their Undergraduate thesis, titled “Optimisation tool for automated planning and control of
production in small-scale hydropower plants ” (Möller & Wiklund, 2018). For more details on
the results of the implementation, please refer to their thesis. Note that this work is written in
Swedish.
8.2 COMMUNICATION FLOW There exists already a controller in Båthusströmmen that controls the turbine to maintain a set
value. Right now this set value is the reservoir level, since it is running on VNR. This controller
can also receive other set values, such as the optimal schedules from the algorithm, and can send
different measurements back to the central database. The controller and the central database are
connected via a SCADA system, which ensures the proper communication flow and sets
standards for communication within the network (A. Daneels, 1999). Figure 25 shows how
information flows through the system, including the central database (Time-series), the central
controller where the algorithm is executed, and the local controller at the plant.
46 | P a g e
Figure 25 Information Flow of Central Control Unit
At Fortum there are already tools built in Excel to communicate with the central database, so the
central controller was written in Microsoft Visual Basic to take advantage of these tools. The
central controller reads the input values it needs, executes the algorithm, then writes the optimal
schedules back to the database, which are then automatically sent to the local controller at the
plant. In practice, the central controller will be a program located on a central server.
8.3 FINAL PROGRAM Initially the algorithm was rewritten to run in Visual Basic using the Microsoft Solver
Foundation, but the model was too large to be solved. Finally, communication was set up
between the Visual Basic project and a model built in GAMS. Since the algorithm was already
tested in Chapter 6, the main focus here was establishing communication between the database,
the Visual Basic project, and the GAMS code, as well as utilizing both the mid-term and short-
term algorithms. The Visual Basic project acts as the central controller, so it is capable of running
the algorithms and communicating with the database in real time. The basic structure of the code
is shown in Figure 26. For a detailed axplanation, refer to (Möller & Wiklund, 2018).
Due to security and licensing reasons, the full GAMS code was not able to be implemented on
the Fortum system, so the optimisation could not be tested at the same time as the communication
with the database. Both parts have been proven and tested separately, but have yet to be fully
implemented in the system. There are also several functions that should be added as options in a
real system, such as considering the availability of the plants, allowing the operators to override
the optimisation schedule and even disable the automatic optimisation, and of course adding
more plants to the program. With more plants comes a more complicated algorithm, but the
principles behind it are the same.
47 | P a g e
Figure 26 Visual Basic Main Program (Möller & Wiklund, 2018)
48 | P a g e
9 CONCLUSION
9.1 THESIS Hydropower has been a staple in the Nordic power system since its creation, and has been an
important source of power for centuries. The fact that hydropower is so consistent and reliable
means that it’s role only gets more and more important as more variable power sources, like wind
and solar, are added to the grid. Hydropower is used to balance out the irregularities of wind and
solar power production, as well as total demand in the system. Today, spot and intraday traders at
Fortum work with hydropower dispatch and the system operator, Svenska Kraftnät, to optimally
run their hydropower plants every day. This requires complex optimisation models to be run and
checked every day, and a lot of manual work for the traders. Besides running the optimisation,
they must check important inputs like price and inflow forecasts, maintenance, desired power,
etc. Fortum owns many large hydropower plants throughout the Nordic system, and it is crucial
that these important plants are run efficiently and optimally. In order to allow the traders to focus
on these important plants, many smaller plants are left to run on their own, often just maintaining
a constant reservoir level (VNR). Though they are still producing power and contributing to the
total profit, they are not being optimally run based on the electricity price. The purpose of this
thesis has been to investigate the added benefit of optimising small hydropower plants, using
Båthusströmmen as a test case.
This thesis was broken into two parts: developing an optimisation algorithm and simulating
Båthusströmmen for a years’ time, and working with two other thesis student on implementing a
real time program to automatically optimise and plan the schedule for Båthusströmmen. The
development of the algorithm is the main focus of this thesis, and included two separate
simulations in itself. First, a simulation of 2016 was done using Fortum’s existing optimisation
program. A model was made both to run on VNR and to optimise with more flexible reservoir
level limits. The results showed that by optimising the schedule for Båthusströmmen for 2016,
approximately a 15% profit could be seen.
Next, a new model was developed in GAMS to optimally plan the operation of Båthusströmmen,
including an additional function to update the power-discharge (PQ) curve based on the changing
reservoir level. This model was also simulated for 2016, both as VNR and with more flexible
limits. It was found that by optimising the plant with flexible reservoir limits, an increase in profit
49 | P a g e
by 16% could be realized. These results are similar to the results from the existing Fortum model,
verifying its validity.
The next phase, implementation, was done using Microsoft Visual Basic as a centrally located
program to automatically run the optimisation throughout the day, taking the load off of the
traders and allowing smaller plants like Båthusströmmen to be operated optimally. The
communication with the database was successfully done, and a full program to automatically run
both a mid-term and short-term optimisation in real time was made. More on this phase can be
read in (Möller & Wiklund, 2018).
9.2 FURTHER ANALYSIS Båthusströmmen is a single small hydropower plant in Sweden, chosen as a test case because it is
not hydrologically coupled to other plants (see section 5.1). There are, however, dozens of other
small hydropower plants that are currently on VNR which could be made to run based on an
optimal planning algorithm, generating more profit for Fortum. It is difficult to estimate the
increase in profit for most plants since there are many hydrological couplings in a river system. A
change in production at one plant can affect several others, and the entire river system needs to be
modelled at once. However, it can safely be said that by implementing an optimisation algorithm
for these plants, more profit stands to be made.
Furthermore, more research could be done on the water value and marginal water value curves,
both for Båthusströmmen and other plants. The cost of starting a generator is also up for debate,
since there are many factors that affect it, and much more research can be done in this area.
Another potential source of error is from the original PQ curve. Input-output curves like this are
generally measured at installation, and can change over time. Without accurate measurements,
the generators may not perform as expected.
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