An investigation of the Cost of Primary Regulation
Master of Science Thesis by
Susanne Franzén
XR-EE-ES 2007:003
Electric Power Systems Lab School of Electrical Engineering
Royal Institute of Technology Stockholm, Sweden 2007
Abstract
Primary regulation is essential to compensate for unplanned variations in production and consumption plans. The responsible for the availability of primary regulation is the system operator in each country. In Sweden contracted balance providers offer their accessible primary regulation weekly and hourly, to the system operator, to a price that will compensate the costs that derive from the primary regulation. This master thesis investigates the costs and the profitability of the primary regulation in a balance provider's perspective. The project was initiated by Fortum.
The production plan is the result of an optimization based on spot price forecasts where the income is maximized. Primary regulation implies further constraints for the optimization model which give a different result. The difference in the result is due to the primary regulation and thereby an obvious cost caused by the same. Given the costs the bid and profit could be calculated. The thesis is based on optimization results for some small hydropower systems. These results gave the costs that have been evaluated and compared with the model recommended by the Swedish system operator Svenska Kraftnät.
The results show the importance of the spot price, especially the difference in the spot price within the planning period. The inflow to the power plants is also an important parameter in a small reservoir, but it cannot be compared to the impact of the price. The optimal bid is hard to find, as the model does not count with the uncertainties in price and weather forecasts. It considers though the same parameters as the existing model, but with more exact values. To be sure that the primary regulation is profitable, using this model, a risk factor and investment costs need to be added.
Sammanfattning
Primärregleringen är nödvändig för att kompensera för oplanerade variationer i produktions- och förbrukningsplaner. Systemoperatören i varje land är ansvarig för att se till att det finns tillräckliga primärregleringsreserver. I Sverige är det balansansvariga producenter som tillhandahåller primärregleringen genom att bjuda in den reglerstyrka som de har tillgänglig. Detta sker på tim- och veckobasis till det pris de anser täcker kostnaderna som härrörs till primärregleringen. Rapporten undersöker det optimala budet för primärregleringen samt lönsamheten för att tillhandahålla den i en balansansvarigs perspektiv. Rapporten har gjorts på uppdrag av Fortum.
Produktionsplanen är resultatet av en optimering baserad på spotprisprognoser där inkomsten maximeras. Primärreglering innebär fler villkor för optimeringsmodellen vilket ger ett annat resultat. Skillnaden beror på primärregleringsvillkoren och är därmed en uppenbar kostnad orsakad av primärregleringen. Med hjälp av kostnaderna kan man beräkna lönsamheten då man jämför med buden som läggs idag. Rapporten bygger på optimeringsresultat för några mindre vattenkraftssystem. Resultaten har jämförts för att få fram kostnaderna och med det budet och lönsamheten. Resultaten jämfördes sedan med den befintliga modellen som rekommenderas av Svenska Kraftnät.
Resultaten visade på en stor påverkan från spotpriset och särskilt skillnaden i spotpris inom planeringsperioden påverkade. Tillrinningen visade sig också vara en viktig faktor i fallet med veckomagasin, men i jämförelse med priset är tillrinningen av mindre betydelse. Det optimala budet är svårt att hitta eftersom modellen inte tar hänsyn till osäkerheter i pris- och väderprognoser. Optimeringsmodellen tar dock hänsyn till samma parametrar som den rekommenderade modellen, men med mer exakta värden. Använder man optimeringsmodellen bör man lägga till en riskfaktor och investeringskostnader för att försäkra sig om att primärregleringen går med vinst.
Contents
Abstract ... iii
Sammanfattning ... v
Contents ... vii
List of Figures ... ix
List of Tables ... x
Nomenclature and abbreviations... xi
1 Introduction... 1
1.1 Background ... 1
1.2 Aim ... 1
1.3 Problem formulation ... 2
1.4 Delimitations... 2
1.5 Method ... 2
1.6 Fortum... 2
2 The Nordic Power System ... 4
2.1 Hydropower ... 4
2.1.1 Hydropower in Nordic countries ... 4
2.1.2 Principles... 4
2.1.3 Environmental effects ... 5
2.2 System planning... 5
2.3 Production planning ... 7
2.3.1 Planning horizons... 7
2.3.2 Expansion planning... 7
2.3.3 Long-term/Seasonal planning ... 7
2.3.4 Short-term planning ... 7
2.3.5 Regulation and balance management... 8
2.4 The power market ... 8
2.4.1 The Nordic deregulated power market ... 8
2.4.2 Participants on the Nordic power market... 8
2.4.3 Markets within the power market ... 9
2.4.4 Time span... 10
3 Frequency regulation ... 12
3.1 What is frequency regulation? ... 12
3.1.1 Different regulation systems ... 12
3.1.2 Primary regulation ... 12
3.1.3 Secondary regulation ... 13
3.2 Bidding and price setting of regulation capability ... 14
3.2.1 Primary regulation capacity ... 14
3.2.2 Primary regulation energy... 14
3.2.3 Secondary regulation - Upward and downward regulation price ... 15
3.2.4 Balance settlement ... 16
3.2.5 Differences in price setting between the Nordic countries ... 16
3.2.6 Calculation model by Svenska Kraftnät (SvK)... 17
4 Optimization and modeling... 21
4.1 Approach... 21
4.2 Model of regulation capability in hydroelectric power plants ... 21
4.2.1 Optimization ... 21
4.2.2 Uncertainties ... 22
4.2.3 Parameters and prerequisites... 22
4.2.4 Model ... 26
4.2.5 GAMS ... 29
5 Case studies... 30
5.1 Introduction... 30
5.1.1 Two scenarios and two cases ... 30
5.1.2 Parameter sets ... 30
5.1.3 Comments on the evaluation of the optimization results... 31
5.2 Case 1 – daily and weekly reservoirs... 32
5.2.1 Background ... 32
5.2.2 Results... 32
5.2.2.1 Production plans... 33
5.2.2.2 Primary regulation costs ... 35
5.2.3 Comparison with SvK-model ... 37
5.3 Case 2 – yearly reservoirs ... 38
5.3.1 Background ... 38
5.3.2 Results... 39
5.3.2.1 Production plans... 39
5.3.2.2 Primary regulation costs ... 40
6 Discussion ... 42
6.1 Problem formulation ... 42
6.1.1 Is it profitable to offer regulation capability? ... 42
6.1.2 Which are the influencing factors? ... 42
6.1.3 What is the optimal bid to make the regulation capability profitable? ... 42
6.1.4 How much of the total capacity should be reserved for primary regulation? .. 42
6.2 Result discussion... 43
6.3 Results compared to SvK model... 43
6.4 Neglected costs ... 43
6.5 Conclusions... 44
6.6 Future work ... 44
6.6.1 Develop the model ... 44
6.6.2 Simplify the managing of input data to the SvK-model ... 45
6.6.3 Implement the SvK-model in the optimizing process... 45
6.6.4 Investigate costs and uncertainties... 45
7 References... 46
7.1 Litterature... 46
7.2 Internet ... 46
7.3 Oral communication... 47
7.4 Figures... 47
Appendices... 48
Appendix 1 – Results Power plant A ... 48
Appendix 2 – Results Power plant C ... 50
Appendix 3 – Results Power plant D ... 53
Appendix 4 – Results Power plant F... 61
Appendix 5 – Results Power plant G ... 64
Appendix 6 – A fictive example of a weekly bid given to SvK ... 68
List of Figures
Figure 1 Hydropower plant ... 4
Figure 2 The power transmission network in northwestern Europe ... 6
Figure 3 Time table for trading and balance ... 11
Figure 4 Price ladder with the price for regulation capability ... 15
Figure 5 Four different settlement cases for regulation capability ... 16
Figure 6 Differences between the Nordic countries ... 16
Figure 7 Method flow chart ... 21
Figure 8 Model of one of Fortum's hydropower plants with two segments and a forbidden interval... 25
Figure 9 Positions of the power plants in the first reach of river used for modeling... 32
Figure 10 Positions of the power plants in the second reach of river used for modeling . 32 Figure 11 Optimization results of the two scenarios, low inflow ... 33
Figure 12 Optimization results of the two scenarios, yearly average inflow... 34
Figure 13 Optimization results of the two scenarios, high inflow ... 34
Figure 14 Change in primary regulation cost depending on statics... 35
Figure 15 Change in primary regulation cost depending on inflow. ... 36
Figure 17 Positions of the power plants in the model with yearly reservoirs... 38
Figure 18 Optimizations result of the two scenarios, all inflows ... 39
Figure 19 Change in primary regulation cost depending on water value. The water value is presented as a percentage of the weekly average spot price... 40
Figure 21 Change in primary regulation cost depending on regulation capability... 41
List of Tables
Table 1 The relation between statics and regulation capability ... 13
Table 2 Example of a frequency evaluation ... 31
Table 3 Comparison between SvK- and Optimization model ... 38
Table 4 Comparison between SvK- and the simple model... 38
Nomenclature and abbreviations
Sets Explanation
i power plants
j segments y levels of regulation capability t hours scen scenarios Parameters Explanation
H max installed i effect
M max i maximum reservoir content
MaxS maximum i spillage
Vtot min minimum i discharge
Vtot max maximum i discharge
j
Vmini, minimum discharge in segment j
j
Vmaxi, maximum discharge in segment j
j
µi, marginal production equivalent γi average production equivalent
scen
Qvaluesi, local inflow
Q i local inflow
scen
esi
Mstartvalu , reservoir content at the beginning of the planning period Mstart i reservoir content at the beginning of the planning period Mend i reservoir content at the end of the planning period
scen
est
Rtotalvalu , agreed regulation capability Rtotal t agreed regulation capability
y
regi, available regulation capability
scen fvalues
λ water value
λf water value
scen
valuest,
λ spot price forecasts (SEK)
λt spot price forecasts (SEK) Variables Explanation
t j
Vi, , discharge per power plant, segment and hour
t
Si, spillage per hour t in power plant i
t
Mi, reservoir content in the end of hour t
t
Vrni, minimum discharge at downward regulation
t
Vrui, maximum discharge at upward regulation
t
ui, commitment of power plant i during hour t
t y
ri, , commitment of power plant i to supply regulation capability level y during hour t
z income
Abbreviations
AGC Automatic Generation Control FADR Fast Active Disturbance Reserve
FCDR Frequency Controlled Disturbance Reserve FCNOR Frequency Controlled Normal Operation Reserve GAMS General Algebraic Modeling System
GDX GAMS Data Exchange
SEK Swedish Krona
SvK Svenska Kraftnät – Swedish transmission system operator
1 Introduction
1.1 Background
On the Nordic power market, electricity is sold per hour through the common market Nord Pool, which has consisted of Norway, Sweden, Finland and Denmark since the year 2000. Apart from selling the electricity on Nord Pool, there is also the possibility to do bilateral agreements. Based on production plans, together with forecasts of inflow and price development, every producer decides how to offer their output for sale on the market.
To secure the operation of the power network and the delivery of electric energy to the consumers, the power system must be in balance. Balance is reached when the supply (production and import) is equal to the demand (consumption and export). In an ideal market, supply and demand is in balance thanks to the market forces which implies that the power system is in balance as well. While the power market is not an ideal market due to information imperfections caused by uncertainties in input data, there are economic incentives that make the participants strive for balance.
Despite the ambition of keeping the balance there are variations that are impossible to anticipate. That is why there is a need of a system operator. A system operator's responsibility implies among other things assurance of the short-term (within the hour) balance in the power system. This balance is kept with automatic and ordered regulation capability and the system operator's task is to have the regulation capability available through contracts with balance providers that generally are producers. The regulation capability is traded on regulation markets which are parallel with the spot market.
Producers which are balance providers can choose which market they want to sell to. If capacity is reserved on regulation markets, it cannot be sold to the spot-market. If a producer has sold primary regulation, that is automatic regulation capability, it implies that they have committed to keep a certain capacity available for momentary up- /downward regulation. Keeping this capacity available means a restriction in the discharge of hydro power plants, the minimum discharge is increased and the maximum discharge is decreased. These restrictions lead to costs for the primary regulation, costs that have not been very clear. This thesis is trying to sort the costs out and to find the optimal bid that make sure that offering primary regulation will not cause decreasing profit.
1.2 Aim
The aim of this thesis is to find the costs and with that Fortum's bid for primary regulation and try to decide how much of their total capacity should be reserved for primary regulation, if any.
The optimal bid is the goal in this project. This bid makes reserving regulation capability profitable. The first task was to check if it is profitable to offer regulation capability. It was then desirable to localize the costs and which parameters that influenced the most.
Probable costs are lost income due to spillage, re-planning and efficiency losses, wear, maintenance and investment costs. The risk of variations from the forecasts also constitutes a cost. Some of these costs are used today for calculating the bid.
Several simulations of some reaches of rivers have been compared to a base scenario where no regulation capability is reserved. The difference between the incomes was seen as the optimal bid of the regulation capability. For the simulations the optimization software program GAMS has been used. An idea of the uncertainty in current production plan, price and inflow forecasts is illustrated in the results where different values of price and inflows have been utilized. Due to competition the power plants have been anonymized and specific characteristics of the power plants have been standardized.
1.3 Problem formulation The questions I will try to answer are:
• Is it profitable to offer regulation capability?
• Which are the influencing factors?
• What is the optimal bid to make regulation capability profitable?
• How much of the total capacity should be reserved for primary regulation?
1.4 Delimitations
Since the primary regulation is sold on a national level, I will primarily look at the Swedish system and only comment on the other systems briefly.
1.5 Method
The master thesis has been developed through literature studies, visits to power plants and related companies, interviews and the analysis of simulations.
To obtain the best background information the thesis began with literature studies, information searches on the internet, brief presentations from all teams concerned with the production planning process and visits to related companies such as Svenska Kraftnät.
Then a model was made to imitate the production planning and to make it possible compare different production planning scenarios and cases. The model was based on linear integer programming and the optimization program GAMS was used to develop it.
After running the model in GAMS there was a process to handle the output data. The most interesting output data is related to spillage, power production, discharges and income. The income values were compared and the results were then analyzed. Finally the conclusion was drawn from diagrams and discussions.
1.6 Fortum
Fortum is one of the leading energy companies in the Nordic countries. It is often
mentioned as one of the big three producers1 in the region. The company also has business interests in the Baltic countries. Fortum’s business activities are comprised of the production, distribution and sales of electricity and heat, operation; it is also involved in the maintenance of power plants and energy related services. The company’s main products are electricity, heat and steam. Fortum Corporation is divided in four corporate units and eight business units. One of these business units is Fortum Portfolio Management and Trading (PMT).
PMT is responsible among other things for planning, optimizing and delivery of Fortum's power capacity towards the physical spot- and balance market in the Nordic countries.
These tasks also require close cooperation with the business unit Fortum Generation, which implements the plans created by PMT. Production planning is a team that is a part of PMT and optimizes Fortum's production from the coming day to three years ahead.
They decide when and how much production that will be sold and it is also their responsibility to maintain the balance [10].
1 The other ones are Vattenfall and E.ON
2 The Nordic Power System
2.1 Hydropower
2.1.1 Hydropower in Nordic countries
Hydropower has played a significant role in the Nordic power generation for at least 100 years, but the first water wheel came to Sweden from China in the 13th century. It is not only important for the power generation, but also for its regulating capacity that is used in both primary and secondary regulation. Today the hydropower share of the generated power is around 50 percent in Sweden, in Norway it is almost 100 percent and in Finland it is about 17 percent [9]. The total production during a year varies with the weather conditions and it also depends of the time of the year, e.g. in springtime there is a greater inflow because of the spring flood. In a normal year the Nordic countries generate about 190 TWh [8], [15].
2.1.2 Principles
Figure 1 Hydropower plant
The hydropower plants harness the potential energy, from two different levels, of moving and falling water. There are hydropower plants with and without reservoirs, but to be able to regulate the power plant there has to be a reservoir. The reservoir is used for storage, to get an even flow through the turbine and for an increased head of the water.
Water flows from the reservoir through an intake and is led to the turbine and makes the turbine axis rotate. The turbine axis drives a generator that generates the electricity which then is passed to a transformer that increases the voltage to adjust it to the distribution network. The amount of power that is generated can be seen as a function of discharge, head and efficiency of the turbine [1].
2.1.3 Environmental effects
Hydropower is a renewable energy resource but expansion of hydropower implies great influence on the ecosystem in the flowing water as well as along the river shores and on the local population.
The expansions entail changes of landscapes due to different water levels which are a result of the flow through the hydropower plant. That is why water court permits exist, which set limits of minimum and maximum levels of the water. The great effects on the local environment have also resulted in a prohibition against further expansion of large scale hydropower plants and a total prohibition of exploitation of four rivers in northern Sweden.
Hydropower in the Nordic power system has an important role as a reserve of momentary power as the hydropower plants are the main resource of primary regulation. In the energy proposition from 2002 there is a demand of expansion of wind power and because of the uncertain production from wind power there will be an increased need of momentary power reserve. Then the hydropower needs an expansion of effect that will imply faster flow changes that will affect vegetation, animal and erosion [15].
2.2 System planning
The Nordic electricity grid is synchronously interconnected and thus the entire grid, except the Jutland in Denmark, has the same frequency. The nominal value of the frequency is 50 Hz and there is an allowance of variation between 49.9 and 50.1 Hz. The variations of the frequency describe the balance in the power system between electricity production and consumption. A good balance gives small frequency variations in the grid, which produces better quality electricity as a result [11].
To maintain the balance there is a need to plan and depending on the participants there are different approaches. The system operators are responsible for system planning and the producers are concentrated on production planning. The system operators in the Nordic countries are responsible for the momentary balance in their own area but they also cooperate to supervise the whole Nordic power system and restore the balance when it is needed. When possible, system operators exchange regulating power to activate the cheapest available resource. However, there is a limit to this exchange; two thirds of each area’s regulating power must be local, that is the regulating power must come from power plants in the specific area. Accessing the cheapest available resource can also become difficult when there are bottlenecks in the system [16].
Figure 2 The power transmission network in northwestern Europe
2.3 Production planning
2.3.1 Planning horizons
To run an efficient power production operation with the aim of maximizing the profit, a planning process is needed and it is not enough to have a settled plan a week before it is carried out. There is an uncertainty in most of the parameters that has to be considered to maximize the income and some of them are not certain until the exact moment of the process. For that reason there is an on-going planning process.
The planning process helps making technical and economical decisions that depend on each other. The decisions depend on among other things installed effect, available power plants, production costs and expected spot price.
It is difficult if not impossible to do correct predictions. The more short-term a plan is the more certain it is. Hence new plans have to be made over and over again to make them more certain the closer the operation period it gets. Due to different needs over time there are several planning processes on-going in parallel, each with its iteration time. There are different ways to group these processes and each producer does it its own way. A common way to group them though is in 4 different periods of time, which are [2]:
• Expansion planning
• Long-term/Seasonal planning
• Short-term planning
• Regulation and balance management 2.3.2 Expansion planning
Expansion planning or strategic planning has a time perspective of years or even decades.
The uncertainty is obvious and the planning typically determines whether to invest in new or existing power plants considering an increased demand and environmental effects. The uncertainty of spot prices and with that the profitability of an investment in the distant future makes these decisions quite difficult.
2.3.3 Long-term/Seasonal planning
Often long-term planning is seasonal planning because of the size of the reservoirs that normally hold water reserves for a year. In larger reservoirs the long-term planning can be for two or three years. The season begins with the spring flood and ends one year later just before the next spring flood. During this time the production should be optimized and it is about planning the weekly volumes that should be used, considering deficit of ground water, size of spring flood, water court permits etc. Forecasts of spot market prices, hydrological conditions and availability in the power plants are important parameters so that long-term planners are able to optimize the timing of hydro usage and of maintenance [19].
2.3.4 Short-term planning
From the seasonal planning the short-term planning receives data of planned volumes per week for some weeks in the near future. It is the short-term planners' task to specify these
plans day by day and hour by hour in accordance with information about inflow, weather forecasts, price forecasts and other physical behaviors. The planning is still about volumes but more in detail. They decide the discharges in m3/s and in the end of the planning process bids are given in MWh/h. The weather forecasts are at the most for a 16 day period, if it is desirable to make plans for more weeks, reference values can be used, e.g. historical averages [19].
2.3.5 Regulation and balance management
During the operational process the imbalance ought to be minimized in order to minimize the costs. Producers are often balance providers. That implies responsibility for the company's hourly balance according to the balance agreement [6]. Costs are minimized if the producers keep the balance, since the system favors this. A producer can also work actively to help the system when there is a breakdown by having power plants ready to start or to increase production in already operative power plants.
2.4 The power market
2.4.1 The Nordic deregulated power market
The first steps to a deregulated common Nordic power market were taken in the beginning of the 1990s. The production and sale of electricity was then separated from the network operation on a national level. The main objective was to increase the competition on the electricity market and subsequently lower the prices. System operators were established and made responsible for the national grids in order to secure the reliability of the transmission and to promote an open and competitive national, Nordic and European electricity market. The first open market was started in Norway in 1991 [14].
The Nordic countries were pioneers when they deregulated their power markets. It has resulted in the Nordic countries having a world leading position in deregulating the electric power sector and, in particular, in organizing international trade in electricity.
The beginning of the Nordic common power market was in 1993 when Statnett Marked AS, now known as Nord Pool ASA was funded in Norway.
In 1996, Nord Pool became the world's first multinational exchange for trading electric power. It was the start-up of the joint Norwegian-Swedish power exchange and it was created when the power exchange was renamed Nord Pool ASA [14].
2.4.2 Participants on the Nordic power market System Operator2
The system operator has the responsibility for the momentary system balance and the power reserve. That implies an overall control of the electrical power plants so that they
2 In the Nordic countries there is a system operator that is responsible for what e.g. in the USA is divided between a transmission system operator, TSO, and an independent system operator, ISO. I have chosen to name this participant a system operator.
are working in a reliable way. The system operator is also owner of the national grid. The balance responsibility makes the system operator the only buyer of regulation capability, power that is bought from contracted producers or in case of secondary regulation it can also be bought from industries. In the Nordic power system each country has its own system operator for its area, but since the system is the same there is cooperation between them [16].
Producers
The producers are the companies that generate the electricity and feed it into the network.
They sell it to the power exchange Nord Pool, either the physical or the financial part, or to big consumers like industries. Contracted producers sell regulation capability to the system operators.
Network owners
The network owners are responsible for some regional and local networks and their function is to transmit the electricity from the producer to the consumer. They also have to buy energy to cover the transmission losses.
Power trading companies
Power trading companies buy the electricity mainly from the power exchange and sell it to small and medium size consumers. They are also trading on financial markets.
Consumers
Consumers are all the ones that in one way or the other use the electricity; they are industries or households and everyone in between. The small consumer must have an agreement with an electricity trader to be able to buy electricity. The consumer also has an agreement with the network owner in order to be connected to his network.
2.4.3 Markets within the power market Primary power market
On the Nordic power market the main part of the produced energy is traded on Nord Pool. Not all power is traded on Nord Pool though, there are also trades with bilateral contracts, but it is mainly bigger industries that trade with these contracts [7].
Spot market
The spot market or Elspot is the core of the Nordic power market and it is organized by Nord Pool. Power is auctioned daily per hour for physical delivery in the next day's 24- hour period and it is possible to place bids until 12.00 the day before. There is always a system price but due to transmission restrictions in the various areas there can be price differences between them. There are seven different price areas: Sweden, Finland, two in Norway, two in Denmark and then the connection to the continent. Price calculation is based on the balance between bids and offers from all market participants. This trading method is referred to as equilibrium point trading or simultaneous price setting [14].
Adjustment market for physical trading
The Electricity Balance Adjustment Service (Elbas) is the organized balance adjustment market for Sweden, Finland and one of the areas in Denmark. On Elbas, continuous
adjustment trading can be performed until one hour before the delivery hour. The trading horizon is at the longest to the end of the next day. Contracts for the following day are opened for trading daily after the day-ahead Elspot prices have been set [14].
Regulation power market
Primary and secondary regulation is bought by Svenska Kraftnät on the regulation power market. If a company wants to participate on the regulation power market it has to be a balance provider. Only the one who has entered into a contract with a system operator can be a balance provider and they are either producers or, in case of secondary regulation, consumers such as big industries [7].
Primary regulation is available in power plants with installed automation. The compensation for keeping primary regulation available constitutes of a fixed and a flexible part. The fixed compensation is paid for measured power. The flexible compensation for regulation power is auctioned weekly and daily3 [7].
Secondary regulation, which maintains the power balance and restore the nominal frequency, is up-/downward regulation bidding per hour on production increase/decrease.
A surplus of production leads to a downward regulation which implies a decrease in a producer's production or an increase in a consumer's consumption. The producer decreases the production and buys power from the system operator instead. The system operator use, when required, the bids in order of price. In a surplus situation this implies that the system operator calls off the maximum bid. In the opposite situation with a deficit of production upward regulation is needed. This time a producer increases the production and sells it to the system operator and then of course the system operator calls off the minimum bid [1].
Financial market
Financial trade of power is managed on Nord Pool’s financial market do decrease financial risks. Settlement and delivery are carried out as financial price-hedging seetlements without any physical delivery of electricity.
2.4.4 Time span
For different markets there are different deadlines. Except for the stated deadlines in figure 3 there is a deadline for the regulation market bids. The weekly bids for primary regulation have to be handed over at latest on Thursday at 16.00 for the coming week. At 9.00 the following Friday the result from the bidding is given to the participants.
Secondary regulation bids can be offered until 30 minutes before the delivery hour begins.
3 Even though the system is interconnected the regulation markets today are national, though there is an exchange between the system operators. The regulation capability is traded differently on each market and this is the Swedish way to trade. Nordel suggests a common regulation market and there is a wish that the Swedish model will be used for this market.
Figure 3 Time table for trading and balance
3 Frequency regulation
3.1 What is frequency regulation?
3.1.1 Different regulation systems
System operators use regulation systems when handling the balance responsibility. The most important regulation system is primary regulation that automatically senses the imbalance when the frequency varies and is able to react within seconds to get the balance back. The other one is secondary regulation. The primary regulation stabilizes the frequency and the balance between production and consumption. The frequency is though still at the lower or higher frequency that it reached before the stabilization. The secondary regulation is used to raise the production or lower it to reach the nominal frequency [1].
3.1.2 Primary regulation
A power system has to be in balance at every moment due to physical laws, but there is no one that can predict exactly how large the consumption will be in every moment and the energy cannot be stored as electricity. The solution to the problem is, when the supply of electricity does not cover the demand, that rotation energy from the turbines and the generators is used. The use of the rotation energy slows down the rotation and since the rotation velocity is well connected to the electrical frequency the result is a frequency fall. In those power plants with primary regulation there is a turbine regulator sensitive to frequency changes installed. A frequency fall leads to an increased production in proportion to the frequency fall and contrary. The production continues to increase as long as the frequency is falling. When the frequency is stabilized the production stays on the same level and the balance in the system is restored [1].
Small frequency variations provide better quality of electricity. By means of primary regulation the variations can be kept small. Every synchronous system has its own regulation. These systems can be any kind of system, small or big it does not matter. If the frequency is not the same in all the system voltages in opposition arise in each end of the power line which leads to unacceptable currents which results in disturbances of the grid.
To increase the production quickly there has to be reserves that can be put into production within 30 seconds. There are two different kinds of reserves. Frequency Controlled Normal Operation Reserve (FCNOR) regulates the frequency between 49.9 and 50.1 Hz which is the regulation of variations in demand. Then there is Frequency Controlled Disturbance Reserve (FCDR) that automatically can increase production when there is a breakdown in a power plant. This reserve should be able to avoid a frequency fall that is greater than 0.5 Hz in a normal operation situation. Both reserves react to frequency changes, the only difference is when they are activated [11].
In the Nordic system it is decided that the FCNOR should be 6000 MW/Hz in a normal operation situation. Sweden's share is minimum 2500 MW/Hz or 250 MW. The shares
are settled annually in proportion to the annual power consumption, but most of the available primary regulation is situated in Norway and Sweden because of the hydropower which is the resource that is mainly used for primary regulation. The reason to that is that the hydropower is easy to regulate.
Unlike the FCNOR, the FCDR are defined weekly, depending on the volume of production in conjunction with the largest fault in the system. Normally the reserve ought to be approximately 1000 MW in the whole system and Sweden's share is about 250-400 MW. [16]
The primary regulation is sold in MW/Hz, which is called frequency response or regulation capability. The definition of frequency response is the change of production in a power plant when there is a change of frequency. If is the production at the nominal frequency Hz:
Pn 0 =50
f
) (f f0 R
P
P= n − ⋅ − [1] (3.1)
Sometimes you also speak about the statics meaning the frequency response. Statics is the inverse function of the frequency response. The result is a decreased frequency response when the statics is increased, see also table 1. The correct definition is the unit's frequency change in percent of the nominal frequency divided in the unit's power change in percent of the unit's power capacity, which simplified is expressed as:
0
1 f P
Ep = R⋅ P (3.2)
Ep = Statics
R = Frequency response/Regulation capability
P = Peak power output p
Table 1 The relation between statics and regulation capability
Ep [%]
R [MW/Hz]
Pp
[MW]
f0
[Hz]
10 8 40 50
5 16 40 50
2 40 40 50
3.1.3 Secondary regulation
The primary regulation only prevents the frequency to fall or to rise over the set limits, but it cannot restore it to the nominal value. For that there is a secondary regulation or Fast Active Disturbance Reserve (FADR). Within 10 minutes unused power plants should be started up if there is a frequency fall or be turned down if there is a frequency rise in order to restore the nominal frequency. Contracted industries can also decrease or increase their consumption in order to stabilise the frequency at the nominal value. This is made manually and it is the system operators that call off the bids in order of price. In the Nordic countries the secondary regulation is manually, but there are countries that use an
automatic system called Automatic Generation Control (AGC) [1].
3.2 Bidding and price setting of regulation capability
3.2.1 Primary regulation capacity4
Primary regulation is a service that the balance providers offer to the system operator.
The system operator gives the balance providers a fixed and a flexible compensation for keeping primary regulation available. The fixed compensation that is paid for measured regulation capability is 1 SEK per MW/Hz and hour. The measurement is done by the balance providers themselves. The flexible compensation is divided in weekly and hourly purchase.
For the weekly purchase, bids are given every Thursday by 16 o'clock at the latest and concern the coming period Saturday 0.00 to Friday 24.00. The agreement for the following period is divided in three periods a day or a total of 21 periods independent of each other.5 Price and bid should be given in MW/Hz. Expressed in MW 10 % of the bid should be FCNOR and 15 % FCDR6. That is giving a bid of 10 MW/Hz implies 1 MW in FCNOR and 1.5 MW in FCDR, in total 2.5 MW must be available for regulation. It is not necessary that the FCNOR and FCDR are from the same unit. The bids are based on costs and give a certain space for extra charge for profit and risks due to uncertainties in forecasts, extra charges that should be well motivated to be approved. Supplementary purchase occurs hourly during the operating day. Bids are given by 16 at the latest the day before the coming 24-hour period. The bids can be changed within 2 hours. The price is given in MW/Hz and the same share of FCNOR and FCDR are required as in the weekly purchase. Accepted bids imply a guaranteed availability for primary regulation.
The availability is paid according the bid [6] [17].
3.2.2 Primary regulation energy
If the primary regulation is used, the price for it is set to the upward regulation price in case of an upward regulation within the hour and to the downward regulation price in case of a downward regulation. The price setting of the regulating prices is explained in section 3.2.3. If there are neither an upward nor a downward regulation price the balance base price is used, which is equal to the spot price in the price area [6].
4 This is the Swedish model and is so far only usable in Sweden
5 A detailed fictive bid is illustrated in appendix 6
6 The percentage of FCNOR is easy to understand since the demand for it is expressed in MW/Hz. That is not the case when it comes to FCDR where the demand for it is expressed in MW and is not directly connected to the frequency changes. Since the FCDR is today a part of the regulation capability bid it has to be expressed in MW/Hz. Sweden's total FCDR reserve should be around 300-400 MW, which is mentioned in section 3.1.2. 15 % of 2500 MW/Hz, which is the total FCNOR reserve, is 375 MW. There is a wish to change the current situation and make the FCNOR and FCDR to two different products.
3.2.3 Secondary regulation - Upward and downward regulation price Balance providers can make a bid, change it or take it back continuously from 14 days before the beginning of the operating day. For the next 24 hours bids should be made consecutively and they can be changed until 30 minutes before the beginning of the delivery hour. In some cases they are even closer to the delivery hour. The bid should contain the available volume in MW that can be upward or downward regulated, the price in currency/MWh and the constraint area. The power should be available during the whole current delivery hour.
The volume must be at the least 10 MW and at the most 500 MW. The price cannot exceed 50 000 SEK/MW or twice the balance base price if it is higher. If the total volume does not fulfill the need the system operator can request extra bids [6].
Figure 4 Price ladder with the price for regulating power
All bids are then organized according to price from the lowest to the highest, forming a price ladder for every delivery hour (figure 4). This price ladder is common for the Nordic countries and when it is needed the system operator activates the most advantageous bid. It is not always the most advantageous bid that can be activated.
Sometimes there are bottle necks in the transmission network and it is then important that the secondary regulation is activated in the specific area where it is needed. The upward regulation price is then set to the price of the most expensive activated upward regulation if the system within the delivery hour is in negative imbalance. All balance providers that have agreed about upward regulation with the system operator, get paid with the upward regulation price for the agreed energy if it is used for regulation.
In the opposite case with a positive imbalance within the hour the downward regulation price is set to the price of the lowest activated downward regulation. The balance providers that have agreed about downward regulation pay the downward regulation price for the agreed energy if there is a need for downward regulation [6].
3.2.4 Balance settlement7
When the delivery hour is completed and the regulation price is set, the costs for regulation and possible imbalances are divided between the balance providers. This is done by the system operators. There are four different cases (figure 5) depending on what measures that had to be done during the delivery hour.
Figure 5 Four different settlement cases for regulating power
The players that did not have any imbalance are not affected in any of the cases. In case of only upward regulation (case a), players with a negative imbalance have to pay the upward regulation price while the ones with positive imbalance are paid according to the spot price. If there is no secondary regulation activated at all, all imbalances are paid or get paid with the spot price (case b). If there have been both upward and downward regulation, the price is set to either upward or downward regulation price depending on which has been the larger volume (case c). Finally in the case of downward regulation, participants with a positive imbalance pay the downward regulation price and the others are paid with the spot price [5].
3.2.5 Differences in price setting between the Nordic countries
Statnett Energinet.dk Fingrid Svenska Kraftnät
System One price
Marginal
Two price Average
Two price Marginal
Two price Marginal Balance
calculation
1 - Total balance
3 - Separate balances for consumption, production and trade
1 - Total balance
3 - Separate balances for consumption, production and trade
Figure 6 Differences between the Nordic countries
7 This is the case in the Nordic countries except Norway which is using a one-price model.
Denmark, Finland, Norway and Sweden all act on the Nordic power market, but like mentioned above there are differences between them. Figure 6 shows some of these differences. Norway is the only country that instead of using a two price system uses a one price model. The total imbalance decides if the upward regulation price or the downward regulation price should be used. All imbalances are then priced to this price.
This means that it is profitable having a positive imbalance and that you get paid more if you help the system to balance without using secondary regulation.
When a delivery hour starts the system operator is responsible for the physical balance.
With help of the primary and secondary regulation the system operator is able to keep the balance. With a two price system, unlike the Norwegian model, the system operator is helped of the price system. For all participants there are economical incentives to keep the balance. Irrespective if a participant has a positive or a negative imbalance they will not make money of it, which is explained in section 3.2.4.
Another difference between the countries is that all except Denmark use a marginal price setting that is the highest price activated. Denmark uses an average price setting, where the average of the up- or downward regulation price that has been accepted decides the price [1]. The balance calculation in Norway and Finland is calculated according to the total balance for consumption, production and trade while in Sweden and Denmark they are separated.
The contracts for primary regulation also vary between the countries. Sweden has a weekly and hourly purchase while Finland for example has contracts for various years.
The current contract reaches until 31 of December 2010. Finland's system operator Fingrid pay a fixed fee and an hourly fee for the primary regulation and it is also divided in FCNOR and FCDR. The fixed fee for the FCNOR is 7500 €/MW if the reserve has been available to the system for more than 3000 hours in a year. The hourly fee is paid for the period of time during which the reserves have been available to the system and is 3.5 €/MW per hour until 31 of December 2007 and then 3.8 €/MW per hour between 1 January 2008 and 31 December 2010. The fees for the FCDR are respectively 4000
€/MW per year, 0.8 €/MW per hour and 0.85 €/MW per hour [20].
3.2.6 Calculation model by Svenska Kraftnät (SvK)
SvK developed in 1999, together with representatives for the power business, a model [17] to make the bidding for the primary regulation more effective. It is recommended to use the model but it is not obligatory. It is presented here to get a deeper understanding of the parameters that influence the costs. These formulae will then be compared to the optimization model values in chapter 5.
Case 1
The first case is the base case without any changes in the production plan due to the primary regulation. The flexible costs are constituted of efficiency losses only. The efficiency losses are only a cost when the power plant is run at best efficiency. This formula is general, but it can be difficult to use it because of the necessary efficiencies.
P R
RcI λ
η η η − ⋅
⋅
=
2 2 1
1 (3.3)
Where:
I
Rc = Regulation capability cost, case 1 [SEK/MW/Hz]
P1 = Planned effect at 50 Hz [MW]
η1 = Efficiency at 50 Hz
η = Efficiency at the frequency deviation (the deviation is set to 0.042 8, which is the standard deviation for the frequency used in evaluations)
λ = Forecasted spot price [SEK/MWh]
R = The unit's regulation capability [MW/Hz]
Case 2
Sometimes when there is a need of primary regulation the effect has to be planned at a lower level to be able to regulate upwards. In this case the efficiency due to the frequency variations are not seen as a cost because when it regulates upwards it implies a higher efficiency which more or less corresponds to the lower efficiency when there is a downward regulation. But the power plant is run with a lower efficiency than the best efficiency and that implies a loss.
P R
RcII λ
η η η − ⋅
⋅
=
2 2 1
2 (3.4)
Where:
II
R = Regulation capability cost, case 2 [SEK/MW/Hz] c
P2 = Planned effect at a lower efficiency [MW]
η = Best efficiency 1
η = The lower efficiency 2
λ = Forecasted spot price [SEK/MWh]
R = The unit's regulation capability [MW/Hz]
Case 3
If the inflow is low, the need of primary regulation can force producers to change their plans from producing during high price hours to low price hours. The price losses are as follows. The same formula can be used for yearly reservoirs where the high price and low price hours are changed to high season prices to low season prices. 3.3 or 3.4 should be added to the formula, that is Rc =RcIII +RcI or Rc =RcIII +RcII.
P R
RcIII =∆ ⋅∆λ (3.5)
8 The deviation in used frequency series from SvK
Where:
III
Rc = Regulation capability cost, case 3 [SEK/MW/Hz]
∆ = Moved effect from high price hours/season to low price hours/season [MW] P λ
∆ = Difference between high price hours/season to low price hours/season [SEK/MWh]
R = The unit's regulation capability [MW/Hz]
Case 4
In cases of high inflows primary regulation implies more spillage since the maximum discharge level is decreased due to making space for the upward regulation. The cost is a function of the spilled effect, the current spot price and the regulation capability that causes or increases the spillage. 3.3 or 3.4 should be added to the formula, that is
or .
I c IV c
c R R
R = + Rc =RcIV +RcII
P R RcIV s
⋅∆
= λ
(3.6) Where:
IV
Rc = Regulation capability cost, case 4 [SEK/MW/Hz]
Ps = Spilled effect
λ = Forecasted spot price [SEK/MWh]
∆ = The unit's regulation capability [MW/Hz] R Case 5
When a unit is started and is run at the lowest level possible to create more primary regulation reserves costs arise, partly from losses due to decreased efficiency and partly from costs for moved power. Based on previous formulae you could calculate a unit on a minimal production level to generate primary regulation.
⎟⎟⎠
⎜⎜ ⎞
⎝
⎛ − ⋅ +∆
⋅
= λ λ
η η η
2 2 1 2
R
RcV P (3.7)
Where:
V
Rc = Regulation capability cost, case 5 [SEK/MW/Hz]
P2 = Planned effect at a lower efficiency R = The unit's regulation capability [MW/Hz]
η1 = Best efficiency η2 = The lower efficiency
λ = Forecasted spot price [SEK/MWh]
λ
∆ = Forecasted spot price [SEK/MWh]
Apart from these costs SvK also mention that costs for uncertainties, investment costs and wear costs should be added. The risks are such as forecasts failure, spillage and power plant failure. Investment costs include turbine regulator, mechanical and hydraulically equipment, necessary communication equipment and then there are costs
for maintenance and administration. Wear in mechanical and hydraulically components and in the turbine are costs that are thought to be caused by the primary regulation [17].
4 Optimization and modeling
4.1 Approach
The main purpose in the thesis is the primary regulation bid and to be able to decide the bid it is important to know the costs. Production planning is easily formulated as an optimization problem since its purpose is to use resources optimally. A possible way to find the costs is to use optimization as a tool. Finding the difference in the objective function between the usual plans and those that include regulation capability as a constraint gives the costs of primary regulation. As hydropower is the main resource for primary regulation in the Nordic system it is the only source of power included in the optimization problem. The difference that arises from the two scenarios can be seen as the minimum bid under those circumstances leaving out all costs for uncertainties, wear, maintenance and investment.
Figure 7 Method flow chart
• An optimization model of a reach of river was developed. The model was then used for various reaches of rivers, though each one of them had some specific constraints.
The objective function and the hydrological balance had to be changed due to different positions of the hydropower plants. There are those that are positioned in a row and others that starts from parallel positions to meet up downstream.
• The objective function, that is the total income for the reach of river, was maximized for two different scenarios, one that included the primary regulation and one that did not.
• The results from both scenarios were compared for each power plant included in the primary regulation and the difference in income constituted the cost for the primary regulation.
• By dividing the total cost for each power plant in the number of hours that the primary regulation had been active and with the power plant's contribution of regulation capability the cost expressed as the bid was given.
• The bid was evaluated and compared with the SvK-model bid and conclusions could be drawn.
4.2 Model of regulation capability in hydroelectric power plants
4.2.1 Optimization
Optimization is used in various situations to find the best way to act according to current conditions [3]. The solution helps to decide how a problem has to be handled to for example minimize costs or maximize gains. It is based on a mathematical model where
Model Optimization Comparison
of income Bid
Bid
comparison Conclusions
an objective function constitutes the problem to be maximized or minimized. The function contains variables that are chosen so that the best possible solution is reached.
The variable values can be limited so that infeasible values are avoided and limitations are considered, such as technical, economical and legal restrictions. This is done with help of constraints which are formed as equations.
An optimization of a production plan can be made using different models. All of them are slightly different from reality, because none of them can take into account all the factors that affect the production. The perfect model is a nonlinear mixed integer model. This model has not yet been fully developed and cannot guarantee an optimal solution which makes it quite difficult to handle [4] and is therefore not used in this thesis.
Depending on the constraints that has to be considered due to the primary regulation it is necessary with binary variables. The model to be used is therefore a linear integer model that also can take into account the efficiency in a simplified way. A factor that is missed in this model is the dependence of the turbine head, which can result in emptied reservoirs which is not very likely in reality.
The production planning model is made with the optimization program GAMS. The model should maximize gains of power production and the water value in the reservoirs, taking into account the hydrological balance and sold regulation capability.
4.2.2 Uncertainties
The difficult part in production planning is the uncertainties in input data. Parameters such as inflow, reservoir content, spot price, future water value and demand are always uncertain. But depending on the planning horizon they can be more or less certain and the spot price can even be certain the day before the operation day. These parameters are often set to historical data but also with help of forecasts. In this thesis the horizon is short but still the uncertainty should be considered. In the model the uncertainty is neglected, but interpreting the results an idea of the uncertainty in current production plan, price and inflow forecasts is illustrated. The uncertain parameters have been varied in each optimization run to demonstrate the importance of each parameter and the results of the optimization runs have been compared. The uncertainties ought to be further investigated to show the risk factor, but that it is not within the scope for this thesis.
4.2.3 Parameters and prerequisites
The model is a simplified model of some reaches of rivers that are representative for the river system. They have been chosen depending on the yearly average inflow to the reservoir and the size of the reservoir.
Assumptions
I have chosen a simple model and have therefore excluded some parameters that could influence the result. It is important to remember that the model is used for comparison and not for the absolute results and the excluded parameters should not have that much affect on the result. Parameters that could have made the model even better are among others:
• Water time delay. When optimizing a hydropower system it is sometimes necessary
consider the water time delay, that is the time it takes for the water to flow between two reservoirs. In my small systems the water time delay is less than half an hour and since the resolution is one hour it is not probable that the delay affects that much.
• Costs. Costs that can be added in the model are start and stop costs and the extra wear cost due to the primary regulation. These have been excluded, mostly because they are difficult to identify. It is probable that start and stop costs affect the result and it would be interesting to investigate if that is the case. The extra wear cost could be added to the result when it is settled. It is though an uncertain cost that may be negligible, see also section 6.4. Other costs that also can be added after optimizing the model are investment costs and a risk factor.
• Water courts. In some systems there are water courts that prevent from operating the power plants in the most optimal way. It can be forced minimal discharges, a certain spillage or a demand on keeping a certain level of the reservoirs which can be different over the year. I have only considered the normal minimum and maximum levels of the reservoirs and excluded all the others since they are difficult modeling.
• Turbine head. In a linear programming model the importance of the head is neglected.
To be able to include the head a non-linear programming model has to be used.
Taking into account the head would prevent unlikely results with empty reservoirs.
• Power exchange. In Sweden all power plants in a river do not necessarily belong to one power company. In this case there is a water regulation company that decides the discharges after taking into account the wishes from the concerned power companies.
The result is a compromise of the wishes and there is an exchange of power so that the power companies get the power that they have wished but the discharge is another. In the model this power exchange and inflow is not considered but Fortum is seen as the only owner.
• Discharge. In some of the power plants the minimum discharge level is set at a higher level than it really is avoiding various forbidden discharge intervals. When the production plans are evaluated in the end planned discharge is equal to real discharge which normally is not the case since there is always a variation in efficiency and head.
Inflow
The inflow decides how much water that can be discharged and is an important parameter for the result of the optimization. It is though an uncertain parameter and it is set according to forecasts which are highly dependent on meteorology. Since meteorological forecasts only are done for the coming 16 days, historical average values are also used for long-term forecasts and planning.
Reservoir content
The reservoir content is the water volume between the maximum water level and the minimum water level that are set by water courts. The reservoir is often filled to approximately 80 percent of the maximum level to have a high head. The content varies with the variations in inflow and prices. Usually the daily and weekly reservoirs have a low level in the end of the winter just to let the spring flood fill them.
Production equivalent and efficiency
Given efficiency, discharge and head it is possible to calculate the produced power
according to:
η ρ⋅ ⋅ ⋅ ⋅
= V g h
H (4.1)
where:
=
H Power [W]
ρ = Water density [1000 kg/m3]
=
V Discharge [m3/s]
=
g Gravity acceleration [9.81 m/s2]
=
h Head [m]
η = Total efficiency
This formula is a nonlinear function and cannot be used in the linear integer model. To simplify it to a linear function production equivalents are used. The production equivalent
γ is defined as the production divided with the discharge [1].
V V V H( )
) ( =
γ MWh/TE (4.2)
The production equivalent is even more simplified to decrease the input data and instead a marginal production equivalent µ is used that is the derivative of the production equivalent [1].
dV V dH( )
µ = MWh/TE (4.3)
There is also an average production equivalent which can be used to decide the water value. I have defined it as γ in the model [1].
max max V
= H
γ MWh/TE (4.4)
The production is then calculated according to [1]:
V
H =µ⋅ (4.5)
It is also possible to have various segments to try to equal the reality even more.9 The total production per hour is then:
∑
⋅= J
j
t j j
t V
H µ , (4.6)
9 A detailed description of the calculation of marginal production equivalents in a piecewise linear model can be found in [1].
