PRICE FORECASTING AND UNIT COMMITMENT IN ELECTRICITY MARKETS

Julian Bouchard, EDF R&D, Phone +33 1 47 65 37 85, E-mail: julianbouchard@edf.fr Audun Botterud, Argonne National Laboratory, Phone +1 630 234 8854, E-mail: abotterud@anl.gov

Prakash R. Thimmapuram, Argonne National Laboratory, Phone +1 630 252 9291, E-mail: prakash@anl.gov

Abstract

Traditionally, unit commitment in power systems was a centralized optimisation problem most often solved with classical mathematical programming techniques. In restructured electricity markets where multiple generating companies compete to supply demand, unit commitment is still a relevant issue but tends to take a different form since bidding into a market may require all companies to solve their individual unit commitment problem without having full knowledge of the system. In this paper, we present how agent-based modelling may be applied to analyze such a situation and how it may capture the impact on the system of the imperfect knowledge of all producers.

1 Introduction Traditionally, unit commitment (UC) in power systems was a centralized optimisation problem where the objective was to find the commitment schedule that minimized the cost of meeting the electricity load, taking the inter-temporal costs and constraints of the power plants into account. A centralized UC was typically performed by a utility company to optimize the commitment of its generating units for meeting the loads within its service region. In restructured electricity markets there are multiple generating companies (GenCos) competing to meet the demand for electricity. However, the UC problem is still relevant, although the underlying context has changed. In some markets, the system operator performs a centralized system-wide UC based on the bids from the market participants. In this case, the UC is part of the market clearing and determines which units will be committed and dispatched. This is currently the case in most US electricity markets, where an independent system operator (ISO/RTO) is in charge of operating the electricity market and the power system. The ISO/RTO typically uses security constrained UC, which is similar to the traditional UC formulation, to operate the system in a cost-efficient and reliable manner. In other regions, the UC is left to the individual market participants, who have to determine their commitment schedule based on their expectations about future prices. In this case, the GenCos may use price based UC to optimize their generation schedule with the objective of maximizing profits, and bid into the market accordingly. This is more common in European electricity markets, which tend to have a more decentralized structure. For GenCos that resort heavily to the day-ahead market to sell their electricity, it becomes very important to forecast the prices, and in turn, use this information to perform their UC. For a detailed discussion and formulation of cost-based and price-based UC we refer to Shahidehpour et al. (2002). In this paper we show how an agent-based model can be used to study the issue of price-based UC. We use the Electricity Market Complex Adaptive Systems (EMCAS) model to analyze GenCos’ price forecasting methods and UC decisions. GenCos are represented as individual agents interacting in the complex environment of an electricity market. By using an agent-based approach we can study the interactions between GenCos’ individual strategies for price forecasting and UC, and the resulting impact on other the overall market results. We first give a brief introduction to EMCAS and its methodologies for price forecasting and UC. We then present a case study of the UK electricity market, where we simulate different price forecasting and UC strategies. We discuss a number of interesting results, which follow from the simulations. Conclusions are provided in the end.

2 Methodology

2.1 The Electricity Market Complex Adaptive Systems Model (EMCAS) The EMCAS model is an advanced electricity market simulator, which is based on agent-based modelling and simulation (ABMS)1. EMCAS simulates the GenCos’ bidding into the day-ahead electricity market. Consumer agents are represented with fixed hourly loads or they can bid into the day-ahead market based on their price elasticity of demand. A system (and market) operator agent solves the day-ahead market and determines the generators’ scheduled generation for the next day along with the hourly prices. A real-time market clearing is also performed, and forced outages may cause the real-time dispatch to deviate from the day-ahead schedule. Finally, the system operator determines the financial settlement between the market participants. The settlement can be based on either locational marginal prices (LMPs), zonal prices, or the uncongested system marginal price (SMP), depending on the market rules. A number of different market designs for the day-ahead and real-time markets can be simulated, along with different business strategies for the market participants. EMCAS also has a generation expansion simulation module. For an overview of the EMCAS model we refer to Conzelmann et al. 2004, Botterud et al. 2006, and Wang et al. 2008. In this paper we focus on the relationship between price forecasting and unit commitment decisions for GenCos’ bidding in the day-ahead market. In EMCAS, the system operator solves the day-ahead market by running an economic dispatch algorithm (DC-OPF). The algorithm can take transmission constraints into account, but it does not consider the generators’ UC constraints. A GenCo has the option to use a price-based UC algorithm at the day-ahead stage in order to plan what generators to switch on the next day. It uses a price forecast for the next day as input and considers its generators’ start-up time, start-up cost, and minimum downtime to calculate the commitment schedule. The price projection methods and the price-based unit commitment algorithm are further described below.

2.2 Price projection methods The GenCos can choose from a number of different price forecasting methods in EMCAS. The default method is to look at the prices for the last few days, and project the next days’ hourly prices simply by taking the average of the previous days’ simulated hourly prices. As an alternative, GenCos can estimate the relationship between the price and the system reserve margin, and forecast the prices based on this relationship. Different methods can be used to estimate the price-reserve margin relationship, including linear regression, log linear regression, and neural network. Different GenCos can use different forecasting methods. The information used as input to the price projection is updated after each simulated day, so that most recent data is always taken into account. The different price projection methods are explained in more detail below.

2.2.1 5-Day Rolling Average This method is based on the idea that energy prices are related to recent historical prices, as they would have similar weather and loads. GenCos forecast next day hourly energy prices using a simple rolling or moving averages. The historical data used correspond to the same hour as the forecasted hour. For example, if 3 PM prices are being forecasted then the prices from the previous days that correspond to 3 PM is used. However, the historical days used for weekdays and weekend differ. For weekday forecast, the previous 5 weekday data are used where as for weekend forecast, the previous two weekend data is used. The formulas for calculating the projected prices2 for weekdays and weekend days are therefore as shown in equations (1) and (2):

∑=

−=5

1,,,,

51

iidhndhn LMPLMP , for weekdays (1)

1 For a detailed introduction to ABMS we refer to North and Macal (2007). 2 Note that in the notation for price projections we use LMP to refer to price, but the GenCos will forecast the LMP, zonal price, or SMP, depending on what price is being used in the market settlement.

3

∑=

−=2

1,,,,

21

iidhndhn LMPLMP , for weekends (2)

where n - node in the transmission network, h - hour of the day, d - day

2.2.2 Linear Regression Using System Reserve Margin It is well known that the system reserve margin has a profound impact on the marginal prices. Therefore, at the beginning of every day, each GenCo develops a linear regression model based on historical prices and system reserve margin. The ISO or the System Operator forecasts the next day system reserve margin based on the forecasted load and the available generation. Using these forecasted system reserve margins (which are assumed to be publicly available information) and the linear regression model developed, GenCos forecast the prices for the next day. The order of the linear regression can be specified by the user (modeller) and can vary across GenCos. The general regression equation is shown in equation (3).

mdhnmdhndhndhn SRaSRaSRaLMP ,,

2,,2,,1,, .... ⋅++⋅+⋅= (3)

where - mnma ,th order coefficient for the node n,

SRh,d - forecasted system reserve margin for the hour h and day d.

2.2.3 Log-Linear Regression Using System Reserve Margin Depending upon the system configuration and the range of reserve margin values, a log-linear regression model can better represent the relationship between the forecasted prices and the system reserve margin. This is similar to the above linear regression model except that this method uses a log-linear model, as shown in equation (4).

)log(....)log()log( ,,2

,,2,,1,,m

dhnmdhndhndhn SRaSRaSRaLMP ⋅++⋅+⋅= (4)

2.2.4 Neural Network Using System Reserve Margin In recent years, Artificial Neural Networks are increasingly being used for price forecasting. ANNs are simple and power tools with a capability to learn the complex input-output relationship when properly trained using historical data. System reserve margin and energy prices are used as input and output to the ANN and are trained using the last two weeks of historical data. EMCAS uses a three layer feed forward artificial neural network. The input layer uses a linear transfer function where the hidden and output layers use a sigmoid transfer function. The neural network is trained using a back propagation algorithm (steepest descent). The user can specify the learning rate, momentum and the number of epochs used during the training. EMCAS uses Joone, a free open source neural network framework (http://www.jooneworld.com/). The input to the ANN can be either the day-ahead forecast for system load or system reserve margin.

2.3 Price-based unit commitment algorithm A price-base UC algorithm can be applied for thermal power plants in EMCAS. The power plants that the UC is applied to are specified for each GenCo. For the purpose of UC, GenCos are assumed to be price takers. Hence, the UC is performed individually for each power plant. Of course, the resulting commitment schedule for the system may still influence the market-clearing price in the simulation. This will be further discussed in the case study. The GenCos’ price-based UC in EMCAS is based on a simplified heuristic algorithm, which compares the forecasted prices for the next day to operating costs, including fuel costs, maintenance costs and start-up costs. Note that a power plant can be

split into blocks, and that different heat rates can be specified for each block. Hence, the operating cost for the individual blocks of a power plant may vary. The algorithm also takes into account the minimum down-time of a plant, and the initial dispatch prior to the beginning of the 24-hour period. Other UC constraints, like ramping rates and minimum up-time are not considered. The following steps are performed in the UC algorithm, which is applied at the individual plant level:

1. For each hour of the next day, calculate the maximum operating profit based on the hourly price forecast and the fuel and maintenance cost. Start-up cost is not considered. For each hour, the optimal generation level is also calculated, based on the marginal costs for the unit’s blocks.

2. Split the hours of the next day into separate periods, differentiating the hours with positive and negative operating profit.

3. Adjust the periods based on the initial dispatch conditions and the minimum down-time constraint if necessary. 4. Calculate total profit for the next day for all feasible plant commitment (up/down) combinations over the identified

periods from step 2 and 3, taking start-up costs into account. 5. Compare the total profit for all feasible commitment combinations. 6. Identify the commitment schedule combination with the highest profit. Prepare bid based on optimal commitment

schedule and dispatch level for each hour. The procedure is illustrated in Figure 1. In this case, the price forecast results in a forecasted operating loss for the first 6 hours of the day (period 1), followed by periods of positive (period 2), negative (periode 3), and positive (period 4) profits. With four periods, the total number of commitment combinations becomes 2^4 = 16. By comparing the total daily profits for all 16 combinations, taking the start-up cost into account, the optimal commitment and dispatch schedule can be identified. For instance, if the start-up cost is $12,000 and the initial dispatch is on for the unit in this example, the optimal commitment schedule is to remain on throughout the operating day. This is because the cost of shutting down and starting up again is higher than the operating loss in period 1 and period 3. If the UC algorithm is used for a unit, the GenCo prepares bids into the day-ahead market (for the optimal dispatch level) for the hours the UC algorithm finds it profitable for the unit to be on. The unit is withheld from the market in other hours. In contrast, if the UC algorithm is not used, bids will be submitted for all hours of the next day for the same generator. In both cases, the final dispatch is based on the system operator’s economic dispatch routine, and the resulting dispatch is a function of the bids from all the GenCos in the market. Hence, the realized prices may deviate from the original price projections. Given the uncertainty in the realized market clearing price, a GenCo may risk missing out on potential profit by following the UC schedule if the realized price turns out to be higher than the forecasted one. It may therefore make sense to use a less stringent commitment schedule, although this would incur a risk of loosing money if the price turns out below the forecast. The optimal UC strategy is therefore a trade-off between risk and return. In order to model this trade-off, a parameter for minimum acceptable profit is used to model the required profitability to commit a unit. A less (more) risk-averse commitment strategy can be achieved by using a negative (positive) profit requirement. A GenCo’s UC schedule and its resulting profit in the market will clearly also depend on the quality of the price forecast. These issues are further discussed in the case study.

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Figure 1: Illustration of price forecast, hourly profits, and resulting periods used in UC algorithm.

3 Application to the UK electricity market

In this study, we model the UK electricity market. The generation fleet is taken from the Department for Business Enterprise & Regulatory Reform (BERR). The total thermal capacity is 72GW and the technology mix is described in Fig. 2. We used an exogenous hydro dispatch that does not vary between simulations and unit planned outages were randomly generated once for all simulations in order to keep consistency. Transmission constraints and interconnection exchanges were not modelled, and forced outages were not considered. The financial market settlement was therefore based on the simulated day-ahead SMP. The load is the historical January and February 2008 load as given by National Grid (national demand + imports/exports). The main seven GenCos in the market (EON, RWE, Scottish and Southern, EDF Energy, Scottish Power, Centrica and British Energy) and an aggregate of all other producers were modelled.

UK GENERATION FLEET

Nuclear

Coal

Gas

Peak

Renewable

Figure 2: UK generation fleet

We first run simulations where GenCos bid all units at operation costs, for all hours, without UC considerations. This gives a reference price level for the system and allows assessing the accuracy of different price forecasts. Then, we assume that all GenCos use the UC algorithm for their coal and gas plants and only bid them when they forecast they would be able to recover their start-up costs throughout the day. We vary the forecast methods across simulations as well as the minimum target profit for the UC algorithm. In a third part we consider the case where all the major GenCos are deemed to be vertically-integrated and do not perform price-based unit commitment for all of their plants, but where a small hypothetical GenCo, who owns only 3 plants, is the only GenCo using the price-based UC algorithm. We discuss the impact on that GenCo’s profits and costs of the accuracy of its price forecast and of its UC strategy (minimum target profit).

3.1 Price forecast Before tackling the issue of the impact of price forecast on unit commitment and system prices, we have to assess the accuracy of the price forecast methods used. In order to do so we consider, in this part, the situation where all GenCos systematically bid their plants at their production cost for all hours. This ensures that players’ price forecasts have no impact on the system dispatch.

3.1.1 System-Price distribution In Figure 3 we present the evolution of system marginal price with system reserve margin (i.e. the reserve margin at the day-ahead stage, without including forced outages occurring during the operating day) and system load across the simulation (From January 1st to February 7th). The lower group of points corresponds to the hours when coal plants are marginal; the above one corresponds to hours when the price is set by combined cycle gas turbines. For lower system reserve margins prices peak up as more expensive gas plants need to be called and the group around 55£/MWh corresponds to hours when oil fired peaking plants are marginal. The correlation between system marginal price and system reserve margin is better defined than the correlation between marginal price and total load. This is particularly true for the hours when the price is highest. This justifies our choice for players to forecast price from the expected system reserve margin rather than total load.

System Price Vs System Reserve Margin

0

10

20

30

40

50

60

0 50 100 150

System Reserve Margin (%)

Syst

em P

rice

(£/M

Wh)

System Price Vs System Load

0

10

20

30

40

50

60

25000350004500055000

System Load (kWh, inverted scale)

Syst

em P

rice

(£/M

Wh)

Figure 3: Evolution of price with system reserve margin / System Load-6 weeks of simulation

When the system reserve margin lies between 60% and 90%, two discontinuous groups of prices can be observed. This is the result of the evolution of plants outages throughout the simulation. Indeed, for a same system reserve margin or system load, when the set of plants on outage varies significantly, the marginal plant, and hence the system marginal price, may vary. This phenomenon is the most significant when the marginal plant moves from one technology to another (say from coal to gas). It is because of such changes in the available generation fleet on very short notice (as well as evolution in players’ behaviour) that GenCos constantly need to update the forecast of prices.

3.1.2 Accuracy of price forecast We present here price forecasts using different regression methods, and compare the results to the simulated price in the day-ahead market. Note that the day-ahead price is not influenced by the various forecasts since no unit commitment is performed in these simulations. We present the results over one week exhibiting price “spikes” as peaking assets have to be dispatched

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to supply demand. We present results in 3 different graphs (Figures 4 to 6) for clarity purposes and to emphasize the impact of increasing the polynomial degree of the regression. The forecasts method used regress the system marginal price (or its logarithm) on the system reserve margin. We present here the accuracy of the following methods: • linear regression with an X-order polynom (LDX): SMP=P(SRM) • log-linear regression of X-order (LLDX): Log(SMP)=P(SRM) • historical average (H. Av.) • neural network forecast (NN) We use here the Mean Absolute Percentage Error (MAPE, see equation (5)) error indicator to classify the different forecast methods, since relative errors are more meaningful as unbiased indicators of the forecast error. A more detailed classification using other error indicators is given in Appendix A.

11

*100

Ni

i i

ForecastObservation

M APEN

=

−=

∑

(5)

where N is the number of observations.

Figure 4: Comparison of actual price (black) and price forecasted with different methods

Figure 5: Comparison of actual price (black) and price forecasted with linear regression of different order

Figure 6: Comparison of actual price (black) and price forecasted with log-linear regression of different order

As indicated in Table 1, all methods yield a relative error smaller than 6% which we consider satisfactory considering the price variations observed. The results presented in Table 1 take into consideration all hours throughout the simulation; in particular they present an average of errors for the peak hours and base-load hours. The figures above and the analysis of the regression polynoms presented in Appendix B reveal that the different forecast methods have significantly different accuracies during base-load and peak hours and that it is necessary to consider them separately to their overall efficiency.

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Hist Av L D1 L D2 L D3 L D4 L D5 L D6 L D7 LL D1 LL D2 LL D3 LL D4 NNMAPE 4.3% 5.0% 4.7% 5.5% 4.8% 3.8% 3.7% 3.7% 4.7% 5.2% 3.8% 3.6% 5.1% Table 1: Mean Average Percentage Error for each forecast method

In Table 2 we present the same results but we distinguish between peak hours (5pm-8pm) and base-load (the rest).

Hist Av L D1 L D2 L D3 L D4 L D5 L D6 L D7 LL D1 LL D2 LL D3 LL D4 NNMAPE 10.9% 7.6% 7.3% 7.3% 5.9% 5.1% 4.5% 3.9% 6.9% 6.2% 4.1% 4.1% 7.7%Ranking 13 11 10 9 6 5 4 1 8 7 3 2 12MAPE 3.3% 4.7% 4.3% 5.2% 4.6% 3.6% 3.6% 3.6% 4.3% 5.0% 3.7% 3.5% 4.8%Ranking 1 10 7 13 9 3 4 5 8 12 6 2 11

Peak

Base-load

Table 2: Classification of the different forecast methods

During peak hours the link between higher order regression and better forecast appears obviously. The SMP-SRM distribution, as seen in Figure 3 peaks off sharply for low SRM, and such a phenomenon can hardly be captured with low order polynoms. It also appears that the log linear regression is more powerful than the linear regression on straight price since it gives better accuracy at the same polynomial orders (and thus same calculus time). The historical average method performs poorly during peak hours, since that period is the least regular from one day to another. During base-load periods, however, the historical average method is the only one capturing accurately the smallest price variations between hours. This is due to the forecasting polynom being essentially linear for SRM values between 30% and 120% (see Appendix B). An important thing to notice here is that when performing linear regression, after a certain point, increasing the regression order stops improving the forecast accuracy. This is due to abnormal forecasts for the highest SRM values. Above a SRM of 120% the forecast polynoms deviate from the “flat” trend and yield forecasts that drop sharply or on the contrary increase. This phenomenon is increased for higher order polynoms but is not observed for log linear regressions.

3.2 Impact of price-based unit commitment on the whole system In the previous section, we have assumed that GenCos always bid all their plants at their variable cost. In theory, if the whole generation fleet were equivalent to the long-term pure-and-perfect competition equilibrium3, all costs, including start-up costs, would be recovered by the short-term market price. However this is an idealised view and the actual generation fleet is never perfectly adapted to the long-term equilibrium. It is therefore a real concern for generators to ensure that they recover their costs. Start-up costs are a particularly risky element of costs since a GenCo who bids its production into the market is never sure ex-ante for how long it will be dispatched and when it will have to start-up and shut-down. Indeed, as price fluctuates during the day it is sometimes more profitable for a plant to remain online even when the market price goes below its operational cost rather than shut down and start-up again a few hours later. This can be done by bidding the minimum capacity of a plant below its cost during a few hours to ensure dispatch. On the contrary, when facing a very short period of demand, it might be a better solution to resort to plants with higher variable costs but lower start-up costs. When bidding their plants in a day-ahead market, players therefore have to somehow try to anticipate the state of the market for the day to come and adapt their bids accordingly. In this section, we assume that all players will forecast the price for the next day and will perform the price-based unit commitment described in the methodology above. At first, we will have the

3 The perfect competition long term equilibrium fleet is the generation fleet where all technologies have the same long-term total cost. In particular, this means that if all things remained constant it would be the same from an investor’s point of view to invest in any of the existing types of plants in the generation fleet. For more details, see Stoft (2002).

players use different price forecast methods4 to reflect the fact that players do not have exactly the same anticipations. All coal and gas plants will be submitted to the unit commitment algorithm. We will assume players are slightly risk-prone by setting the UC threshold to –5%. This means that as soon as the forecasted gains from the sale of the electricity represent 95% of its total costs, a plant will be bid into the market. This threshold represents the trade-off a GenCo makes between the risk of losing a little money in case of an optimistic forecast and the risk of missing a whole day of profit in case of a pessimistic forecast. We will first discuss the impact of the unit commitment on prices and system costs. We will than discuss the impact of the risk-aversion profile, through the use of the threshold. Finally, we will discuss the link between the accuracy of the forecast and the resulting market price.

3.2.1 Impact on unit commitment and system costs Figure 7 presents the evolution of system day ahead marginal price throughout the simulation. The impact of having all GenCos resort to price-based UC for their coal and gas plants has three main characteristics.

Figure 7: System Marginal Price throughout the simulation with and without UC

First of all, the number of price spikes at peak time is largely increased compared to the “base” case where units are systematically bid at marginal production cost without UC. This phenomenon occurs when the supply-demand balance in the system is relatively tight, but GenCos for some reasons do not anticipate the situation properly and much more expensive peaking assets have to be dispatched than in the base case. In our simulations, price even goes up to a “curtailment” level in

4 Unless specifically stated otherwise we have used Historical-Average forecast for EDF Energy and EON, LD1 for RWE, LLD1 for Scottish & Southern, LD6 for Scottish Power, LD6 for Centrica, LLD4 for British Energy and LLD5 for the rest of the market.

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some hours. This does not mean that there will actually be curtailment in the system, but this can be seen as a situation where the system operator has to call exceptional and expensive peaking assets, which depending on electricity markets’ specificities are not submitted to the same bidding rules. It may be more meaningful to consider the average increase in price. This increase represents the impact of risk and uncertainty born by GenCos who have to submit all their plants individually. Yet, even if we think it is more meaningful to consider the average increase in prices, such high spikes caused by GenCos failure to anticipate properly a tight market do occur in real markets. This is what happened in France on November 12th, 2007, when prices rose above 2000€/MWh 5. A second feature is that price may fall below its base level at night since it is more profitable for some coal plants, that would otherwise shut down for only a few hours at night (e.g. between 2 and 5), to keep operating at a loss rather than shut down and starting-up again soon afterwards. This can be observed regularly in Figure 7. Finally, by careful examination one can observe some price spikes at 1 a.m. in Figure 7. This is a result of the modelling of the markets, information, and unit commitment. UC is performed from midnight to midnight, therefore, if a plant were to close between 2a.m. and 5a.m. the algorithm would analyse, with the help of the forecasts, if it would not be profitable to keep the plant online during those hours. If the plant were to shut down between 11p.m an 6a.m. however, since the two hours belong to different days, the algorithm would always have the plant shut down at 23 a.m. This is the case of many coal plants. Because of the minimum down-time constraints all these plants are unable to produce before a period of 2 to 4 hours and this is why there can be a price increase during the first hours of the day. This problem would be rectified by extending the planning horizon for the UC algorithm beyond 24 hours. If we consider the average price increase per hour over one week6 we can see a quantification of the features mentioned above. This is shown in Figure 8 below.

Figure 8: Difference in System Marginal Price across the day when using UC

The average increase in price is of 2.6 £/MWh and is mainly located during peak hours. This increase in price at peak hours stems originally from the taking into consideration of start-up costs as more flexible and more expensive plants have to be

5 An Inquiry led by the CRE, the French regulator, led to the conclusion that no price manipulation had occurred but that due to inaccurate forecasts during a weekend period where the market conditions were not supposed to be the tightest, the supply offer was not adequate to meet the demand. The CRE conclusions can be found at www.cre.fr/fr/content/download/5495/120447/file/080422_CP_Pics%20de%20prix%20oct-nov2007.pdf 6 We choose here the 5th week of the simulation, assuming that this week is in a “steady state” part of the simulation without a low impact of initial conditions.

substituted for cheaper plants with more binding dynamic constraints. As we will see later this phenomenon is amplified when GenCos have poor anticipations of the state of the system. The two other factors mentioned above have opposite effects on the price, and it is therefore harder to analyse their relative impact at night. However, it can be seen from Figure 8 that the average price with UC is above the base case in all the 24 hours.

3.2.2 Impact of risk aversion and UC profit requirement In the previous section, we have studied the case when GenCos would bid their plants as soon as they forecast gains equal to at least 95% of their forecasted costs for the day to come. We have compared this situation to the base case when players always bid their units, which is to say that they bid them regardless of their forecasted revenues for the next day. The profit threshold in the UC can be seen as a measure of the risk aversion of a market participant. The extreme risk-prone situation for GenCos is what we have considered in our base case. All the risk is born there by the GenCos who are not sure to recover their costs for all their plants. In this section, we will consider what happens to price for different “risk” thresholds. We only consider a zero or negative threshold, as a positive one would be equivalent to a kind of economic withholding. The results are shown in Figure 9.

Difference in market price between the cases with and without UC

0

5

10

15

20

25

0 6 12 18

Hour of the day

Pric

e di

ffere

nce

(£/M

Wh)

0% Treshhold - Av. Diff = +4.9£/MWh

-5% Treshhold - Av. Diff = +2.6£/MWh

-10% Treshhold - Av. Diff = +2.1£/MWh

-20% Treshhold - Av. Diff = +1.7£/MWh

-40% Treshhold - Av. Diff = 0£/MWh

Figure 9: Difference in price with/without UC for different risk aversion thresholds (week 5)

The more certain the GenCos want to be to recover their fixed costs and start-up costs, the higher the prices get. We naturally observe that for low enough threshold values (here –40%), which is when GenCos offer their plants without much consideration for their costs, the system dispatch and system marginal price goes back to the base case. In order to analyse further the impact of the unit commitment threshold on the system, we present in Table 3 the average System Marginal Price, the total system cost and total Start-up cost for the 5th week of simulation7. 7 See Appendix C for a plot of the full simulation SMP at the different UC thresholds.

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No UC UC 0% UC -5% UC -10% UC -20% UC -40%

Average SMP (£/MWh) 24.4 29.3 27.0 26.5 25.4 24.4

Total System Costs 1.1E+08 1.8E+08 1.8E+08 1.7E+08 1.3E+08 1.1E+08

Total Start-up Costs 1.1E+06 3.1E+06 3.1E+06 2.3E+06 1.6E+06 1.1E+06 Table 3: Evolution of costs and SMP with UC threshold

The average SMPs correspond to the ones seen above in Figure 9. The cost analysis brings surprising results. First of all, we observe that the total system costs and start-up costs are always higher or equal to the ones in the base case. It is important to consider the total system cost, since, if we consider the system as a whole, producers plus consumers, it reflects the efficiency of the system. Indeed, since we have considered that consumers have an inelastic electricity demand and since what consumers pay-out is received by the producers, the system price can be interpreted as a social equilibrium indicator and the real efficiency of the system is measured by the whole system costs to supply demand8. The fact that the total system cost is above the reference case in all UC cases shows that, in the short-run, there is no overall gain, and even a loss, for the system seen as a whole (producers plus customers) from having all GenCos use a price-based UC for all their plants individually. Changing the dispatch so that producers recover all their costs was bound to increase system prices, however it could have induced a gain in system efficiency and a decrease in total system costs by ensuring that more flexible assets are used when needed. The increase in total-start-up costs and total system costs in Table 3 shows that, because of the imperfect forecasts and the necessity to optimise each plant’s dispatch individually against them, this expected gain in efficiency was not achieved here.9

3.2.3 Impact of forecast Accuracy We have shown in 3.2.2 that having all GenCos perform a separate price-based UC for all their plants induced a loss of efficiency in the system and tended to increase prices. We now want to confirm that this stems, at least partly, from the fact that players can only forecast prices approximately. In all the simulations presented so far, the GenCos have used the same set of forecasting methods described in footnote 4. Now we will consider how SMP varies when the GenCos’ forecast changes in accuracy. We use the same set-up as previously and have all players perform a unit commitment with threshold –20% but we will successively have all GenCos use the Historical Average forecast, the Linear 2nd Order polynomial regression and the Log-Linear 3rd Order polynomial regression forecasts. The results are presented in Table 4, where “Base case” refers to the mix of forecasts used until now. For each case we present the average forecast error across all hours for all GenCos and the average SMP.

Base Case Hist. Average LD 2 LL D3

Average forecast error (%) 5.3% 12.8% 6.0% 5.2%

Average SMP (£/MWh) 25.4 26.1 25.5 24.8 Table 4: SMP and Mean Average Percentage Error for simulations with different forecasts

8 This is a simplified short-term reasoning that does not take into consideration the fact that too-high prices might make consumers unable to afford their demand, or that too-low prices might prevent producers from properly developing their fleet in the long-run. 9 One additional consideration, which we do not analyze in this paper, is the feasibility of the system dispatch. The likelihood of dispatch results which violate UC constraints are more likely in the case where no UC is performed. This may also influence the simulated system price and costs, which may be somewhat underestimated in the case without UC.

It clearly appears that the higher the forecast error the more the SMP increases. This confirms that when planning power plant dispatch, the uncertainty over the state of the system for the day to come is a source of sub-optimal plant dispatch and price increase.

3.3 Impact of price-based unit commitment on a single GenCo In 3.2, we have considered the case when producers have to bid all their plants separately in the day-ahead market and therefore perform UC tests for all of them. This is usually not the case. Indeed, in many European countries, like the United Kingdom or France, most of the electricity is dealt with through bilateral contracts and not offered in the market. Furthermore, offers are not made for individual plants but GenCos make bids for their whole fleet without specifying which plants will actually generate the electricity offered. It is only after market closure that GenCos have to submit their plant-level dispatch and the system operator then performs a centralised real-time dispatch procedure. However, in such markets there exist small producers who only own a very small number of plants and who are often not fully vertically integrated. These players therefore have to resort to the markets to sell their electricity and have to plan the dispatch of their plants almost individually. In this part we represent such a situation where only 3 intermediate plants in the whole system are submitted to the unit-commitment algorithm. We will focus on the case of an independent player who owns one of those 3 plants (an 800MW Combined Cycle Gas Turbine, CCGT) and see how the accuracy of its forecast and its strategy might affect its profit. Since only 3 plants in the whole fleet are submitted to the unit commitment algorithm, the overall SMP and system costs will only marginally change from one simulation to the other and we therefore focus to the profits generated by one of the 3 UC-plants.

3.3.1 Impact of risk-aversion on profits For intermediate plants like CCGTs that are only dispatched a few hours a day, the unit-commitment dilemma is to know whether or not the next-day prices will be sufficient to recover the start-up costs of the plant. The Owner of the plant must make an arbitrage between the possibility to lose money if the plant bids are accepted for too few hours or if the settlement price is too low on the one hand, and the possibility not to be dispatched at all and miss profit opportunities if prices are higher than expected. The GenCo must therefore choose the minimum expected profit it finds acceptable to bid its plant. This profit can be positive or negative, where negative means that the producer still bids the plant on the market even when it forecasts a small loss for the day. In Table 5 we present the monthly profit generated by one CCGT for different values of the minimum target profit (all simulations performed with the Historical Average price forecast). Minimum Target Profit No UC 40% 10% 1% 0% -1% -3% -7% -20% -40%

Monthly Profit (£) 1.7E+04 1.0E+03 2.3E+04 2.6E+04 2.7E+04 2.7E+04 3.2E+04 2.9E+04 2.0E+04 1.7E+04 Table 5: Evolution of a single plant’s profits with its target minimum profit

We find that there is an optimal level for the minimum acceptable profit and that this value is negative and near –3%. This means that, on average, it is more penalising for a producer to be too conservative and lose profit opportunity rather than take the risk not to recover fully its costs. This asymmetry can be seen in the extreme case. Below a certain threshold of target profit, the GenCo simply always bids its plant on the market (which in this case is profitable). On the other hand, above a certain threshold of target profit, the GenCo simply never bids its plant and get a profit of 0.

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3.3.2 Impact of forecast accuracy on profits If a GenCo’s risk aversion has an impact on its profits, the accuracy of its market anticipation is even more important. We present in Table 6 the monthly profit generated by the 800MW CCGT described above depending on the accuracy of its owner’s price forecast. We have performed a series of simulation with different forecasts methods and recorded both profits and forecast errors. Since the CCGT is only dispatched during peak hours the error presented in Table 6 is the absolute average error during peak hours.

No UC Hist. Average LD 2 LLD 4

Average forecast error (%) N/A 11.40% 7.40% 3.57%

Monthly Profit (£) 1.7E+04 9.1E+03 2.4E+04 3.4E+04 Table 6: Evolution of a single plant’s profits with its owner’s forecast accuracy

The correlation between accurate forecast and high profit is obvious and even stronger than the one between risk aversion and profit. Indeed, it is the inaccuracy of the forecast that creates the need for risk-taking. If a player could forecast prices perfectly the optimum minimum target profit in the UC would be 0.

4 Conclusions For GenCos relying heavily on the day ahead market to sell their electricity, forecasting prices and ensuring optimal plant dispatch is a key issue. We have found that a strong correlation exists between the simulated market price and the log of the system reserve margins, allowing good price forecasts to be made. Price-based UC may result in sub-optimal dispatch schedules, due to discrepancies between projected and actual prices. The gain in profits will be directly linked to the accuracy of the price forecasts. Our results indicate that GenCos can benefit from using a slightly risk-prone UC strategy. Finally, the paper also illustrates how agent-based modelling can be used to analyze the complex interactions between price forecasting and unit commitment in electricity markets.. Acknowledgements The authors would like to acknowledge Thomas D. Veselka at Argonne National Laboratory, who developed the price-based unit commitment algorithm used in EMCAS. References Botterud A., Koritarov V., Thimmapuram P.R. (2006), “Multi-agent simulations of the electricity market in Central Europe,” in Proc. of the 26th USAEE/IAEE North American Conference, Ann Arbor, MI, USA.

Conzelmann G., North M.J., Boyd G., Koritarov V., Macal C.M., Thimmapuram P.R., Veselka T.D. (2004), “Simulating Strategic Market Behavior Using an Agent-Based Modeling Approach,” in Proc. of the 6th European IAEE Conference, Zurich, Switzerland.

North M.J. and Macal C.M. (2007), “Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation”, Oxford University Press.

Shahidehpour M., Yamin H., Li Z. (2002), “Market Operations in Electric Power Systems: Forecasting, Scheduling, and Risk Management,” Wiley-IEEE Press. Stoft S. (2002), “Power system Economics”, IEEE Press, Wiley-Interscience. Wang J., A. Botterud, G. Conzelmann, V. Koritarov (2008), “Multi-agent system for short and long-term power market simulations”, Proceedings 16th Power Systems Computation Conference, Glasgow, Scotland.

Appendix A: Forecasts classification with different error indicators In order to assess the accuracy of the forecasting methods, different error indicators are used in this survey: mean average percentage error (MAPE), average absolute error (AAE), root mean square error (RMSE), and higher order RMSE-type

indicators (RMSE4 is { }44 Mean Errors . Increasing the order in RMSEn puts more emphasis on the biggest errors since

RMSEn tends towards the Max indicator as n increases).

Hist Av L D1 L D2 L D3 L D4 L D5 L D6 L D7 LL D1 LL D2 LL D3 LL D4 NNMAPE 13 11 10 9 6 5 4 1 8 7 3 2 12AAE 13 12 10 9 7 5 4 1 8 6 2 3 11RMSE 12 13 10 9 7 5 3 1 8 6 2 4 11RMSE4 10 13 11 9 7 4 3 1 8 6 2 5 12

Peak

Hist Av L D1 L D2 L D3 L D4 L D5 L D6 L D7 LL D1 LL D2 LL D3 LL D4 NNMAPE 1 10 7 14 9 3 4 5 8 13 6 2 11AAE 1 10 8 14 9 3 4 5 7 13 6 2 11RMSE 2 9 6 13 14 7 4 10 5 8 3 1 11RMSE4 7 8 5 10 12 11 9 13 3 4 2 1 6

Base-load

Appendix B: Forecast polynoms As explained in 2.2.2 and 2.2.3, a forecast-polynom is calculated every-day by each producer. For a given polynomial order, this polynom is the best fit to the past 2 weeks data. As time advances through the simulation new simulated data is added to the “memory” and old data is deleted. This way, even for the same polynomial order, the forecast polynom changes from one day to another.For each forecast method we therefore have a collection of forecasting polynoms for every simulation day. We present here the average (across the whole simulation) forecast polynom for each order.

Average Price forecasts with different regression equations

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0 50 100 150

System Reserve Margin (%)

Pric

e (£

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h)

LD 1LD 2LD 3LD 4LD 5LD 6LD 7LLD 1LLD 2LLD 3LLD 4SMP

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Appendix C: System Marginal Price across the whole simulation We present here the evolution of System Marginal Price during the whole simulation for different values of the UC threshold.