Energy Economics 33 (2011) 2–11

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Energy Economics

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Balancing energy strategies in electricity portfolio management

Christoph Möller a, Svetlozar T. Rachev a, Frank J. Fabozzi b,⁎a University of Karlsruhe and KIT, Schlossbezirk 12, D-76131, Karlsruhe, Germanyb Yale School of Management, 135 Prospect Street, New Haven, CT 06511, United States

⁎ Corresponding author. Tel.: +1 215 598 8924; fax:E-mail addresses: christoph.moeller@statistik.uni-ka

rachev@statistik.uni-karlsruhe.de (S.T. Rachev), frank.fa

0140-9883/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.eneco.2010.04.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 September 2009Received in revised form 11 March 2010Accepted 2 April 2010Available online 22 April 2010

JEL classification:Q41Q47

Keywords:Electricity market designBalancing energyStrategic behaviorInterchangeable marketplacesElectricity portfolio management

Traditional management of electricity portfolios is focused on the day-ahead market and futures of longermaturity.Within limits,market participants canhowever also resort to the balancing energymarket to close theirpositions. In this paper, we determine strategic positions in the balancing energy market and identifycorresponding economic incentives in an analysis of the German balancing energy demand. We find that thosestrategies allow an economically optimal starting point for real-time balancing and create a marketplace forflexible capacity that is more open than alternative marketplaces. The strategies we proffer in this paper webelieve will contribute to an effective functioning of the electricity market.

+1 215 598 8932.rlsruhe.de (C. Möller),bozzi@yale.edu (F.J. Fabozzi).

ll rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

In the late 20th century, electricity markets were liberalized acrossthe world. Since this restructuring, integrated companies haveseparated into specialized individual market participants. In addition,institutional investors such as banks and hedge funds have entered themarket not solely to exploit its opportunities but also for riskdiversification. All these players face not only the risk of a highlyvolatile energy market, but also the inner-market risk of the electricitymarket. Naturally, market participants want to actively trade and hedgethis risk.

Alongside with traditional bilateral over-the-counter (OTC) con-tracts, electricity exchange-traded contracts have emerged as instru-ments for these inner-market trades. Among these contracts, the day-ahead futures contract is the principal instrument. This futures contractoffers the shortest delivery period — often 1 h — and serves as thereference price for longer-dated futures contracts. For this reason, theday-ahead futures contract is sometimes referred to as the spot contract.The properties of the day-ahead market and the market for futureswritten on day-ahead contracts have been analyzed using variousmodeling approaches (see, for example, Geman and Roncoroni, 2006;Trück et al., 2007; Römisch andWegner-Specht, 2005). In addition, theinterdependence of the day-ahead market and the futures market has

been investigated (see, for example, Bessembinder and Lemmon, 2002;de Jong and Huisman, 2002).

The aggregate positions in the futures and day-aheadmarkets serveas a preliminary schedule for operating anelectricitynetwork.However,because electricity is practically non-storable, the market for electricityconsumption and delivery also requires a marketplace for ancillaryservices so that blackoutsmay be avoided. The capacity reservemarket isone suchmarketplace. Capacity reserve is provided by installations suchas the fraction of power stations or factories that are readily adjustableto counter deviations from the preliminary schedule. The capacity ofthese installations canbe tradedon the electricity exchange aswell asonthe capacity reserve market. Thus, the day-ahead market and thecapacity reserve market are interchangeable marketplaces for tradingthis capacity. It should be noted that ancillary services value theflexibility of electricity interchange, whereas the focus of the futuresmarket is energy content. Nonetheless, it is recognized that thecompetition between these two marketplaces should be taken intoaccount in formulating optimal bidding strategies in both tradingforums (see Weigt and Riedel, 2007; Simoglou and Bakirtzis, 2008). Inthis paper, we extend this notion of interchangeable marketplaces toanother ancillary services market, the balancing energy market whereelectricity transactions relative to the preliminary schedule are settled.

The market design of the balancing energy market is a crucialcomponent of electricitymarkets as it mediates between the liberalizedfutures and day-ahead markets, and the natural monopoly of the gridand its operation (see ETSO, 2007). In view of the stated objective ofincreasing renewable generation in the future (see EU, 2008 and U.S.

3C. Möller et al. / Energy Economics 33 (2011) 2–11

Congress, 2009), this importance is likely to become even morepronounced. Clearly the value of flexible electricity interchangeincreases with a higher market share of renewables such as windenergy (see EU, 2005). Therefore, a harmonization of the balancingenergy markets is being pursued in Europe.

Several studies compare and analyze the current European marketdesigns to identify potential approaches to achieve harmonization(see ETSO, 2007; Belmans et al., 2009). However, all these studies arefocused on the point of view of system security and disregard theimplications of strategic positions in the balancing energy market. Infact, such positions are controversial. It has been argued that any use ofthe balancing energy market, apart from the settlement of imbalancescaused by unpredictable events, might endanger the system operationby adding the uncertainty associated with market participants'strategic positions. As a consequence, the balancing energy marketis reduced to a marketplace with a single focus on secure systemoperation and blackout prevention (see Belmans et al., 2009; ERGEG,2006). In analyzing these positions, we add the perspective of marketequilibria with interchangeable marketplaces in our discussion ofEuropean market designs. Outside European markets, this notion isrecognized in the PJM electricitymarket, for example, that even allowspurely financial positions to enhance market price convergence (seeZhou et al., 2003 Longstaff and Wang, 2004).

In the context of interchangeable marketplaces, we focus on twoaspects of the balancing energy market. We first look at the balancingenergy market as an alternative marketplace for reserve capacity. Bycomparison, it offers market access to a wider and technically lessdemanding range of installations such as power stations or factories.Second,we investigate the balancing energymarket's interplaywith themarketplace for electricity consumption and delivery. Because the priceformation of the balancing energy market and the day-ahead marketdiffer, this alternative marketplace potentially dampens the effects ofelectricity price spikes on the electricity portfolio ofmarket participants.

In this paper, we provide evidence of the balancing energy marketbeing utilized as an alternative market for both the electricity exchangeand reserve capacity in Germany. The Germanmarket is chosen for thisanalysis due to the combination of its market design and generationstock. More specifically, among European markets, the German marketis the onlymajormarket that does not impose implicit transaction costsor even penalties on electricity transactions in the balancing energymarket. In fact, Boogert and Dupont, 2005 show that the level ofpenalties effectively prohibits strategic positions in the Netherlands.Therefore, it is only in theGermanmarket that strategic positions can beobserved undistorted. Moreover, the German market features athermal-based generation stock, allowing transferring results to similarmarkets. In this respect, a renewable power market share of 15% alsoreflects the importance of the balancing energy market for theintegration of renewables (see BMU, 2009). The share of inflexiblethermal and renewable generation translates into a high value of loadflexibility as reflected in a high spread between balancing energy pricesduring periods of positive and negative net deviation. This spreadenhances the economic incentive for strategic positions. Finally,different fundamental periods of the balancing energy market and theday-ahead market allow analyzing the interaction with the capacityreserve market and the day-ahead market separately. Therefore,Germany provides a suitable setting to observe the interaction withinterchangeable marketplaces described earlier.

The paper is organized as follows. Section 2 provides a brief reviewof balancing energy settlement schemes, followed by a description ofthe German market design and the motivation for the chosen settingin Section 3. Section 4 describes the data and introduces the proposedmodeling approach. A quarter–hourly pattern is analyzed in Section 5.Section 6 focuses on an hourly pattern, and the interdependence withthe day-ahead market. At the same time, we look at the incentivestructure leading to the observed patterns at these two timeframes.Additionally, we look at incentives for positions in the balancing

energy market persistent over longer periods of time in Section 7.Section 8 summarizes our results and their implications.

2. Balancing energy review

In the electricity market, supply and demand have to be in exactequilibrium at all times due to the practically non-storable characterof electricity. The equilibrium is monitored and maintained by thetransmission system operator (TSO) in a specific control area. Allparties connected to the grid within this control area are required toprovide the TSOwith a balanced forecast of feed-ins and withdrawals.Several market participants may pool this responsibility and form abalancing responsible party (BRP). The sum over all forecasts of all BRPsprovides a preliminary schedule that the TSO can use for balancing.However, a BRP can take a strategic position by concealing part of itselectricity portfolio. Along with any unforeseen changes to a BRP'sportfolio, these positions are settled with the TSO as so-calledbalancing energy. Therefore, every BRP's deviation from its providedforecast is calculated for a given settlement period.

Some of the costs of balancing — mainly the cost of short-liveddisturbances and capacity procurement— are socialized in grid tariffs.The cost of lasting disturbances — disturbances implying energytransactions— are attributed to the originator, however. That is, a BRPconsuming electricity in excess of its forecast pays the balancingenergy price, while a BRP providing the network with electricityrelative to its forecast is compensated.

In this paper, the deviation is defined as the difference between theactual load and the forecasted load. Accordingly, we will use thefollowing sign convention throughout this paper: a positive signmeans an undersupply and a negative sign means an oversupply. It isimportant to note that an individual BRP might deviate with theopposite sign to the control area's net deviation. In effect suchdeviations reduce the net deviation. Therefore, BRP's deviations donot incur cost per se, but might enhance system security in a givenperiod in the same way the TSO's active balancing does.

The design of balancing energy markets is diverse, reflecting localspecifics as generation stock and customary operation policies. Manyelectricity markets rely on a real-time market to organize thesettlement of balancing energy (California, New York, and Pennsyl-vania–New Jersey–Maryland). In contrast, balancing energy is settledat prices set after the real-time balancing in European electricitymarkets. There are two general settlement schemes in Europe: single-price and dual-price settlement. These settlement schemes reflect adifferent view on the stabilizing effect of deviations countering thecontrol area's net deviation (see ETSO, 2003, 2007).

In a single-price scheme the TSOwill set one price for both chargingpositive and compensating negative deviations in each settlementperiod. Naturally, this price is high during periods with a positive netdeviation as on thewhole there is a shortage of electricity. Equivalently,the price is low during periods with a negative net deviation and anoversupply of electricity. Thus, the single-price approach sets anincentive to deviate in the opposite direction to the net deviation inthe control area (i.e., receive payments during high price periods andmake payments during periods of low prices). If feasible, a strategicposition following this incentive will reduce the net deviation in muchthe same way as the deployment of capacity reserve.

Like the day-ahead market, the balancing energy market also is amarket for energy transactions. If the spread between the day-aheadand the expected balancing energy price is positive, it is beneficial forBRPs to be in undersupply on the day-aheadmarket with a counteringposition in the balancing energy market, and vice versa for a negativespread. Note that the balancing energy price is set by the TSO after thesettlement period. Consequently, the balancing energy market canonly offer statistical-arbitrage opportunities.

The dual-price system is designed to suppress such statistical-arbitrage activity. In the dual-price settlement scheme, the TSO will

4 C. Möller et al. / Energy Economics 33 (2011) 2–11

set two prices for each settlement period, one price for positivedeviation and one price for negative deviation. These prices can beunderstood as the single-price settlement scheme with an additionalgeneral fine imposed for deviation. Dual-prices are employed in mostEuropean electricity markets (England, France, the Netherlands,Scandinavia, and Spain) to motivate each BRP to omit strategicpositions in the balancing energy market. From a TSO's perspective,the individually balanced forecasts constitute a reasonable startingpoint for real-time operations, because there is no uncertainty aboutthe intentional positions that complicates the TSO's task of balancing.However, at the same time, the imposed fines hamper the approach ofmarket equilibria and can thereby lead to distortions in the market.We illustrate this point by the example of two countries under a dual-price balancing energy scheme.

Kirschen and Garcia (2004) state that balancing energy is tooexpensive in the market in England and Wales. As a result, marketparticipants keep their own reserve capacity rather than resorting tosystem reserves. Consequently, deviations will be actively managedeven if an offsetting deviation exists somewhere else in the controlarea. This results in an inefficiently high allocation of reserve capacity(i.e., the market is in oversupply of production capacity). In contrast,Mielczarski et al. (2005) have argued that in Poland balancing energyis too inexpensive. So market participants use the system reserve tosupply about 4% of the total electricity demand (i.e., the market is inundersupply). These two examples demonstrate that the dual-pricescheme does not guarantee the absence of intentional positions in thebalancing energy market.

3. German market design

The German balancing energy market is divided into four controlareas. The transmission system in these control areas is owned andoperated by one of the four major players in the electricity market: E.ON AG (e.on), Rheinisch-Westfälisches Elektrizitätswerk AG (RWE),EnBW Energie Baden-Württemberg (EnBW), and Vattenfall AB(Vattenfall). All four control areas share a single-price balancingenergy settlement scheme with quarter–hourly settlement periods.The control areas have in common a high spread between balancingprices during periodswith positive and negative net deviations, whichis four to five times the price of electricity in the day-ahead market.This spread results in a strong economic incentive for BRPs to takestrategic positions in the balancing energy market. We choose toanalyze these strategic positions in the aggregated balancing energydemand of all four German control areas. These aggregated valueseliminate the issue of control areas balancing against each other andtherefore best correspond to the single German day-ahead market.

The wholesale market is based on bilateral contracts. The centralelectricity marketplace in the German market is the European EnergyExchange (EEX). Most importantly, day-ahead contracts for all 24 hintervals of the following day are traded on the EEX. These contractsare used as the underlying in longer-dated futures at the EEX, andoften serve as a reference price in the OTC trades. The day-aheadmarket reflects the value of energy in the whole of Germany at oneday's notice and is open to basically all market participants. Thebalancing energy market reflects the value of electricity transferred atvery short notice and is also open to all market participants. However,prices are set by the TSO based on the prices in the capacity reservemarket that is only open to the small fraction of market participantscontrolling readily adjustable installations.

The reserve capacity is based on auctions the four TSOs use forcapacity procurement. These auctions split reserve capacity intoprimary, secondary, and tertiary reserve categories based on a gradingof availability, reliability, and response-time requirements. Onlyfacilities that meet these requirements are able to partake in therespective auctions. Importantly in the context of balancing energy,the energy prices of secondary and tertiary reserve form the basis for

the formation of balancing energy prices. Secondary reserve capacityis allocated in monthly auctions, and tertiary reserve capacity isallocated in day-ahead auctions for six four-hour periods. Conse-quently, balancing energy prices will be less responsive to short-termsupply shocks than the hourly day-ahead futures (i.e., balancingenergy involves products with monthly and four-hourly averaging,while the day-ahead market is adapted to hourly averaging). In fact,during some periods of price spikes in the day-ahead market it mightbe beneficial for a BRP to have a positive deviation, regardless of thecontrol area's net deviation.

The market design just described encourages two strategiesinvolving active positions in the balancing energy market. First, aBRP should control its deviation so as to have the smallest correlationto the net deviation of its control area possible. Second, a BRP mighttry to exploit less responsive balancing energy prices in times of highprices. We will analyze such strategic positions in the balancingenergy market in Sections 5, 6, and 7.

It is important to note that such strategic positions are limited bygrid-access contracts in Germany. In a sample contract of the Germanstate agency, fuzzy boundaries are set. The contract specifies that themean deviation should not be excessively positive or negative anddeviations must not show conspicuously arbitrage-like correlationwith day-ahead exchange prices. As our subsequent analysis shows,deviations are predictably positive and negative and further identify acorrelation with day-ahead exchange prices (i.e., a BRP has someflexibility in providing a balanced forecast).

4. Model and data

We identify four factors that influence balancing energy demand(DB) on different time scales. These factors are the gradient of load(∇L), a day-ahead market arbitrage incentive (I), a technical incentive(Itec), and a varying general market position (f). In addition, the modelincludes a non-predictable event risk (σ). Assuming independence ofthe four factors, these factors can be modeled separately, yieldingEq. (1) as a general model for balancing energy demand:

DB tð Þ = q ∇L tð Þð Þ + h I tð Þ; Itec tð Þð Þ + f tð Þ + σ tð Þ ð1Þ

There is a twofold separation in this model. First, the modelseparates strategic positions according to the time scale to which theyare applied. These time scales are the quarter–hour interval, the hourinterval, and positions taken over extended periods of time. Second,the model separates positions corresponding to the two alternativemarketplaces, the day-ahead market and the capacity reserve market.All the model components — except for the σ term — demonstratethat market participants are not using their best minimum-varianceforecast because predictable components remain.

The analysis is based on the balancing energy demand datapublished by the four German TSOs. Publication of these data startedon February 1, 2001 for RWE Transportnetz Strom, 2009, December 1,2001 for e.on Netz, 2009, January 1, 2002 for EnBW Transportnetze,2009, and September 1, 2002 for Vattenfall Europe Transmission,2009. The aggregation of these data covering the years 2003 to 2008 isthe principal data source of our analysis. Three additional data sourcesare used. First, we use the hourly electricity prices at the EEX as a pricereference. Second, the yearly consumption package provided by theUnion for the Co-ordination of Transmission of Electricity (UCTE)serves as a proxy for electricity load. These data are crucial becausethe gradient of load and the day-ahead market arbitrage incentive aredependent on the load. In the case of the day-ahead market, thisdependence is a result of the price-load-dependence of electricitymarkets. It is therefore possible to recover the general shape of theGerman load profile from the balancing energy data.

We use such a recovery of the load profile as an illustrativedemonstration of the model's fitness and the underlying dependence

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in Sections 5 and 6. Fig. 1 shows the load pattern of a typical summerand winter week obtained from the 2006 data. As can be seen, there isa change from a higher general level in the winter to a lower level inthe summer. Also the shape of the first 5 cycles representing theweekdays differs considerably from the last two, the Saturday and theSunday cycle. Within a day, the drastic increase from low night-timeto high day-time levels in the morning, and vice versa in the evening,dominates the shape. One can also differentiate summer and winterload shapes by an additional load peak present in winter eveninghours.

As a third data base we amend the publicly available hourly loaddata by a 2004 load measurement in a quarter–hourly resolution,provided by the University of Karlsuhe IIP, 2008.We use these data fora detailed analysis on the quarter–hour timeframe.

5. Quarter–hourly pattern

Balancing energy is set with quarter–hour settlement periods inGermany, whereas the smallest contractual period on the day-aheadmarket is 1 hour. This discrepancy gives rise to a distinct pattern,which we appropriately term the quarter–hourly pattern. Let'sconsider the situation during an hour with an increasing load. Theminimum-variance forecast for this hour that is tradable in the day-ahead market is the mean load during that hour. With this forecast,the deviation will be negative in the first and second quarter of thathour and positive during the third and fourth quarter of that hour.Obviously, the same argument with opposite signs holds for a loaddecline. The effect will be more pronounced the higher the load'sgradient is during an hour. Nailis and Ritzau (2006) also observe thiseffect. Consequently, the effect can be modeled by the average loadduring the four quarter–hour periods (L q̅(t)) and the average loadduring the corresponding hour (L ̅h(t)). We introduce the model inEq. (2):

q ∇L tð Þð Þ = q⋅ ̅Lq tð Þ− ̅Lh tð Þ� �

q∈ 0;1½ � ð2Þ

Here the parameter q represents the electricity producers' abilityto keep to their step function profile of hourly scheduled production.Should consumption and production change at the same rate, thefactor will be zero. A value of one indicates a perfect step function ofoutput, corresponding to an infinite ramping speed of power stations.

To test this model, we compare it to the empirical average patternretrieved from the balancing energy data. We define this average

Fig. 1. Weekly load pattern (Monday to Sunday) in summer and winter.

pattern by the mean-balancing energy demand relative to thecorresponding hour's mean value, conditional on the quarter–hourinterval of a day. Fig. 2 shows the resulting pattern using 2004 data.Here the four quarter–hour intervals of each hour are joined by linesto sort the 96 values. Note that by definition this pattern cannot beinfluenced by effects on hourly or even longer time scale, as each hoursegment is centered on zero.

An estimation of the parameter q using a 2004 load measurementyields q=0.424. Comparing the pattern retrieved from this model tothe empirical pattern results in an R2 equal to 0.8696, which issignificant at the 0.1% significance level. This demonstrates the highexplanatory power of the model for the quarter–hourly pattern.Additionally, fully exploiting the model's prediction reduced thesample variance by 12.03%. To improve the illustration, the segmentsin Fig. 2 are joined in Fig. 3. The missing information on the gradientbetween two consecutive hours is estimated as the average of theadjacent segments. Fig. 3 shows the joint pattern based on the loaddata scaled by our parameter estimate. Clearly, the empirical patternresembles the average German load profile. This is yet anotherindication of the model's fitness.

To further investigate the quarter–hourly pattern, we retrieve thepatterns of all years in the interval 2003 to 2008. Thesepatterns are usedto predict the other patterns in this group in an out-of-sample analysisas shown in Table 1. The high R2 values indicate the consistency of thequarter–hourly pattern. Moreover, the explanatory power tends to behigher for subsequent years.When using the pattern of the total sampleand an additional scaling factor to predict the yearly patterns, weobservea diminishingamplitudeof thequarter–hourlypatternas canbeseen in Table 1. This finding is supported by Fig. 4 which displays thepatterns of hourly line segments joined into daily patterns forillustration.

It is important to note that the quarter–hourly pattern is driven bythe consumption side of themarket rather than the production side. Byand large, the production side follows the step function dictated byhourly contracts, while consumption changes gradually. This bringsabout the quarter–hourly pattern. As there is no liquid market to tradeelectricity with sub-hourly delivery periods, there is practically no wayto avoid the quarter–hourly pattern. For this reason, BRPs that arepositively correlated to the load pattern (consumers) will incuradditional cost, while BRPs that are negatively correlated to the loadpattern (producers) will have a financial gain. So there is an economicincentive for BRPs to redistribute part of their load within an hour andobtain a negative correlation to the quarter–hourly pattern for that partof their load. Such a strategy is equivalent to buying electricity duringperiodswith an expected lower net deviation and price, and selling it athigher prices during periodswith an expected higher net deviation. Thisstrategy thatwe have just described results in an intervention similar to

Fig. 2. Expected quarter–hourly deviation conditional on the interval during a day(quarter–hourly pattern). Intervals forming an hour are joined by lines.

Fig. 3. Comparison of model (light) and scaled data (dark) using 2004 data.

Fig. 4. Shape of the load curve as estimated from quarter–hourly balancing energy data.

6 C. Möller et al. / Energy Economics 33 (2011) 2–11

that of reserve capacity and aids network stability. So on a quarter–hourly timeframe, the balancing energy market is an alternativemarketplace to the capacity reserve market. However, in contrast tothe capacity reserve market, there are no pre-qualification standards.Therefore, the quarter–hourly pattern can be employed at arbitraryreliability and response times specifications, if deemed profitable. Alsothere is no fixed compensation, but rather a statistical-arbitrage return.Consequently, the balancing energy market will also attract additionalcapacity which is not tradable on the capacity reserve market. Thedeclining amplitude of the quarter–hourly pattern is an indication ofmarket participants recognizing and exploiting the balancing energymarket in this manner.

6. Hourly pattern

On an hourly timeframe, the balancing energy market is analternative marketplace for the electricity trades in the day-aheadmarket and contracts in the capacity reserve market (see Section 2). Toinvestigate the balancing energy data on this timeframe, we integratethe data to hourly values, which correspond to the hourly contractstraded in the day-aheadmarket. All subsequent analysis is based on thishourly balancing energy data.

As introduced in Section4, there is a fundamentalweekly seasonalityin the German electricity market as was shown in Fig. 1. To match thisseasonality we extract a weekly pattern from the balancing energy datausing the following approach. For each day of the year a symmetric timewindow of 7 weeks is applied, and the balancing energy data areaggregated over the years 2003–2008. The pattern is then estimated bythe average demand, conditional on the hour within aweek (see Fig. 5).When compared to the load (see Fig. 1), a similar seasonality is inherentin the balancing energy demand. The hourly balancing energy pattern is

Table 1R2 using yearly quarter–hourly pattern and scaled total quarter-hourly pattern forprognosis. R2 values significant at the 0.1% significance level.

Predictorpattern

Year

2003 2004 2005 2006 2007 2008

R2 2003 – 0.9853 0.9074 0.9413 0.8867 0.78302004 0.9865 – 0.9393 0.9520 0.9130 0.84272005 0.9396 0.9569 – 0.9738 0.9681 0.93292006 0.9538 0.9588 0.9683 – 0.9775 0.92602007 0.9243 0.9367 0.9673 0.9809 – 0.97032008 0.8746 0.9010 0.9405 0.9457 0.9743 –

Totalscaled 0.9820 0.9861 0.9896 0.9909 0.9866 0.9667Scalein− sample 1.1478 1.1025 0.9301 1.0229 0.9405 0.8657

capturing both the weekly peak and off-peak shape, and the summer–winter dependence, well characterized by the presence of an additionalpronounced demand peak during evening hours in the winter months.The presence of this pattern is clearly incompatible with all BRPsproviding a balanced minimum-variance forecast, as such forecastingshould result in a purely random pattern. In general, the observedhourly positions result either froma reluctance ofmarket participants toprovide balanced forecasts, or they indicate intentional strategicbehavior. An inadequate consideration of transmission losses and aload-dependent outage risk could be the reason behind the former. Thelatter is linked to arbitrage incentives between the balancing energymarket and the day-ahead market, as outlined in Section 3. While it isimpossible to disregard the reluctance of market participants, thefollowing analysis demonstrates that the detected positions are at leastpartially of strategic nature.

To test the continuity of the hourly pattern, yearly patterns arecalculated. In this the data are averaged over summer and winter

Fig. 5. Weekly balancing energy pattern (Monday to Sunday) in summer (light) andwinter (dark) (hourly pattern).

Fig. 6. Factor value (I(t)) and hourly balancing energy demand.

7C. Möller et al. / Energy Economics 33 (2011) 2–11

months, so the resulting patterns will not uncover the summer–winter dependence. However, we compare individual years by usingthe out-of-sample average pattern for each year as a prediction for thein-sample pattern (see Table 2). With the exception of 2004, thissimplemodel has reasonable predictive power. A further inspection ofthe prediction error in 2004 shows that the prediction captures thegeneral shape well. However, it overestimates the amplitude. Thisfinding is supported by an in-sample fit of a scale parameter to theout-of-sample pattern reported as R2*. The scale parameter of 2004 isalmost halved. Reluctance does not explain such sudden changes inthe observed pattern as it would change gradually if at all. So thisreduced scale indicates a change in strategic positions in the balancingenergy market. What is more, 2004 was a year with an exceptionallylow number of electricity price spikes in the day-ahead market. In thiscontext, the absence of spikes reduces the arbitrage incentivebetween the balancing energy market and the day-ahead market,and may explain the change in amplitude of the hourly pattern.

As introduced in Section 3, the balancing energy prices are lessresponsive to supply shocks than the day-ahead prices. Instead, thelikelihood of positive and negative net deviation is the main price-setting criterion determining the expected balancing energy price.

In practice, market participants have an economic incentive toconsume more of the risky, but evenly priced balancing energy, asdemand and prices on the day-aheadmarket rise. Therefore, an hourlypattern in balancing energy should resemble the load profile. That is,market participants will exercise their grid excess as a real optionwhen electricity prices are high, as long as balancing energy isexpected to have a favorable price (i.e., until the twomarkets reach anequilibrium by an increasing likelihood of a positive net deviation).We stress that exploiting this spread between day-ahead marketprices and expected balancing energy prices is a statistical-arbitrageopportunity, as balancing energy prices are uncertain at the time aposition is entered.

We introduce a factor (I(t)) to capture this incentive for strategicpositions in the balancing energy market. This factor is defined by thedifference of day-ahead prices from the current price level. As aspecification of the price level, we use the median price of thepreceding 4 weeks. The time span of 4 weeks is chosen in an effort tobalance stability and slackness considerations in the definition of aprice level. This is supported by testing other multiples of weekly timespans that did not change the substance of the results. However, themedianwas explicitly chosen to create a spike-insensitivemeasure forthe price level, so the defined factor will capture price spikes.

The marks in Fig. 6 show the mean-balancing energy demandconditional on our factor value. Here the balancing energy demand ismeasured relative to a long-termmean level of 4 weeks. This separatesthe effects of longer time duration, which we will discuss in Section 7.Each individual year in the dataset is displayed, demonstrating acontinuous structure. The dependence structure reaches from a centrallinear domain into a domain of saturation at higher factor values. Theeffect of saturation is to be expected in view of the limited reservecapacity the grid operator provides (i.e., constraints imposed bynetwork stability considerations and grid-access contracts). In principle,these findings apply as well to all four control areas individually (seeFig. 7). However, the data cannot account for balancing activity betweencontrol areas. Such effects are excluded by netting all four control areas,

Table 2R2 using out-of-sample average and scaled out-of-sample average for prediction of thehourly pattern. R2 values significant at the 0.1% significance level.

Year 2003 2004 2005 2006 2007 2008

R2 0.7857 0.2003 0.7435 0.7712 0.8316 0.8492R2* 0.7863 0.6229 0.8019 0.8286 0.8381 0.8536Scalein− sample 0.9733 0.5483 0.7874 1.3570 1.0961 1.0772

and we therefore restrict the further investigation to the hypotheticalcombined control area.

We propose a three-parameter factor model for the hourlybalancing energy deviation pattern (see first summand in Eq. (3)):

h I tð Þ; Itec tð Þð Þ = a⋅2

1 + b⋅e−c⋅I tð Þ −1� �

+ Itec tð Þ∀a∈Rb; c∈Rþ ð3Þ

Fig. 8 and Table 3 show parameter estimates from out-of-samplefits for each year and corresponding R2 values. Evidently, the depen-dence structure is constant over time. Moreover, this factor modelcaptures the change in amplitude, introduced by less volatile elec-tricity prices in 2004.

In view of the R2 values in Table 2, the factormodel does not seem toexplain the hourly pattern fully. A further inspection of the residualpattern shows the change in amplitude for the year 2004 to be capturedwell, but some pronounced seasonal effects remain. One such exampleis a highly negative balancing energy demand between five and six atweekday mornings. This coincides with units going online to cover thefollowing steep ramping hours. To include such very technical effectsthat will be constant over time, we use the out-of-sample weeklyaverage pattern as an additional factor (Itec(t)). The resulting combinedmodel in Eq. (3) can explain much of the detected seasonal variation(see Table 3). Also when compared to the R2* values in Table 2, thecombination of arbitrage incentive and technical incentive showssimilar predictive power. However, the latter model does not resort toin-sample information. Using this out-of-sample prediction, thevariance of the hourly balancing energy data is reduced by 19.2%.

The detected hourly pattern can be modeled by Eq. (3). While theItec component in thismodel is compatible with a reluctance of marketparticipants to provide a balanced forecast, the contribution of thearbitrage incentive is evidence of strategic balancing energy deploy-ment. Clearly, market participants recognize and implement thearbitrage opportunities between the day-ahead market and thebalancing energy market in their portfolio management. Suchstrategies result in a lower than average amplitude of the hourlybalancing energy pattern in years with less than average electricityprice spikes as 2004.

7. Long-term pattern

After a few of their respective cycles, the average of both thequarter–hourly pattern and the hourly pattern is zero. In order tocomplete the analysis, we look at positions in the balancing energymarket that are persistent over longer periods of time. We extract

Fig. 7. Conditional average hourly balancing energy demand versus factor value (I(t)) in the four German control areas.

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these positions from the residuals of the hourly factor model (seeEq. (3)), by application of a seasonal autoregressive integratedmoving average (SARIMA) model. For this model, we resort to theresults of Möller et al. (2009), which we briefly present. Möller et al.(2009) suggest the SARIMA-(1,0,0)×(1,0,1)24 model given byEq. (4).

yt = a1yt−1 + a24 yt−24−a1a24 yt−25 + b24σ�t−24 + σ�t ; �t∈t νð Þ ð4Þ

In a comparison of the parameter estimates using data of theindividual years, similar parameter sets are found over the entire timespan. We therefore use the total sample estimates in the remainder of

Fig. 8. Factor model (I(t)) prediction and data.

this analysis. Additionally, the innovation process shows heavy-tailedeffects, which are modeled by a classical tempered stable (CTS)distribution (see, for example Kim et al., 2008; Menn and Rachev,2009).

Finally, the forecasts of the model are tested on two relevant timehorizons, which reflect the information disclosure on the balancingenergy market in Germany. It is found that the variance is reduced byapplying a three-day lag in information disclosure as well as using aone-month time horizon in forecasting. Moreover, the yearly averagevalue of these forecasts deviates from zero (see Fig. 9).

Let's consider these results in the context of electricity portfolios.Market participants use the balancing energy market not only forshort-term adjustments to their portfolio, but also to take positionsover extended periods of time. This view is supported by Fig. 9, whichshows the timely evolution of the three-day forecast. It clearlydisplays the predictable long-term offset in balancing energy demand.Also the magnitude and the sign of this offset vary over the years. Itpersists even in the case of the long forecast horizon of a month. Sothis offset cannot be attributed to a lack of information, and thechange in amplitude and sign indicates intentional positions.

As in the case of the hourly pattern, a long-term position in thebalancing energy market coincides with a countering position in thefutures market. Specifically, we use the day-ahead futures market as areference. From this perspective, the price of the deviation is thedifference between the balancing energy price and day-ahead market

Table 3Hourly pattern: parameters and R2 fitting to out-of-sample data. R2 values significant atthe 0.1% significance level.

Year Parameters R2 factor model

a[MWh] b[E] c[1/€] I(t) only I(t) and Itec(t)

2003 940.045 1.053 0.035 0.6948 0.72522004 901.082 1.113 0.039 0.4448 0.61702005 918.633 1.089 0.039 0.6069 0.75182006 902.485 1.072 0.038 0.8424 0.84992007 928.798 1.081 0.037 0.7571 0.79982008 884.110 1.068 0.043 0.6530 0.7025

Fig. 9. Prediction values with a three-day lag in information disclosure.

9C. Möller et al. / Energy Economics 33 (2011) 2–11

price. Or, in other words, a positive deviation can be described as ashort position in a day-ahead contract combined with a long positionin the balancing energy market, and vice versa for a negativedeviation. In turn, the cost of deviation is obtained by multiplyingprice and volume, and the cost function can be approximated by theaverage cost for a given deviation.

Fig. 10 shows the estimated cost function in the different controlareas using 2003–2008 as the sample data. At a deviation close to zero,the cost increases linearly, indicating a constant price. However, thecost function levels for large negative deviations, whereas it increasesdrastically at large positive deviations. This asymmetry in the costfunction is an important point. Consider a strategic position in thebalancing energy market. It displaces the location parameter of theforecast error, while scale and higher moments will not be affected.

Fig. 10. Expected cost of deviation [€] versus devia

Under the described cost function, shifting the deviation towards thenegative (i.e., a surplus of day-ahead contracts) will continuouslyincur cost from additional negative deviation, while reducing the riskof “unbounded” cost at high positive deviation. So given anunavoidable forecast error, a negative net position is a rationalresponse to the observed asymmetric cost function.

For a further inspection, we concentrate on the largest controlarea, in terms of load, the RWE control area. Looking closer at the costfunction of individual years, the slopes of the cost function vary as canbe seen in Fig. 11. Particularly interesting is the difference in slope forpositive and negative deviations within individual years. A differencein slope provides an incentive to move deviation risk towards theflatter side of the cost function in order to reduce cost. In the exampleof the RWE control area, the cost functions for the years 2005 and2006 indicate an incentive towards positive deviation, while for theother 4 years investigated a negative net deviation would have beenprofitable. Finally, the opening angle between the linear domains atthe positive and the negative branch of the cost function varies. Here,a wider opening angle will incur less cost for a strategic deviation.

Using these arguments, the increasing long-term position in 2005,2006, and 2008 (see Fig. 9) is an adequate adaption to a cost functiontilting towards positive deviation. In the cases of 2003, 2004, and2007, a negative position coincides with a cost function tilted towardsnegative deviation. Additionally, the opening angle of the costfunction narrowed in 2008, providing an incentive to reduce strategicpositions.

A complete investigation should include all four control areas.However, these findings demonstrate that there are economicincentives behind the detected long-term balancing energy positions.With its asymmetric cost function for balancing energy, the Germanmarket design appears to be prone to pushingmarket participants to astrategic short position in the balancing energy market. Thesepositions have to be countered by a long position in the futuresmarkets. In other words, the German market design creates a virtualdemand in the day-ahead market.

tion [MWh] in the four German control areas.

Fig. 11. Empirical cost function of deviation [€] versus deviation [MWh] in RWE control area from 2003 to 2008.

10 C. Möller et al. / Energy Economics 33 (2011) 2–11

8. Summary and conclusion

In this paper we discuss the deployment of balancing energy in themanagement of electricity portfolios for the particular setting of theGerman market design. The German market was selected because (1)strategic positions benefit from the high spreadbetween up- anddown-regulation periods and the absence of penalties and transaction cost, (2)the different settlement periods of the day-ahead and balancing energymarket allow a separate analysis of the interaction with the capacityreserve market, and (3) the generation mix of thermal and renewablesallows transferring results to other European markets.

We identify and model three strategies that reflect the interactionof the balancing energy market with other electricity marketplacesand corresponding economic incentives. These strategies are wellcharacterized by the timeframe of their deployment.

Within the hour, different settlement periods in the day-ahead andbalancing energy market lead to a pronounced quarter–hourly pattern.A high spread between up- and down-regulation balancing energyprices in different periods translates into an economic incentive toobtain less correlation to this quarter–hourly pattern. This strategyreduces load fluctuation in the network, which is equivalent to thedeployment of reserve capacity. For the given timeframe, the strategysets free capacity reserve otherwise deployed to compensate forfluctuations.

On an hourly timeframe, a pattern resembling the load curve isidentified. This hourly pattern shows that market participants exploitstatistical-arbitrage opportunities between the balancing energymarket and the day-ahead market. In other words, the hourly patterncan be understood as the exercise of grid-access as a real option, inmany ways comparable to a swing option. Only through the hourlypattern may the electricity price in the day-ahead market and thebalancing energy market reach equilibrium.

Additionally, we identify positions taken in the balancing energymarket over extended periods of time. Changes in these positionscoincide with changes in the asymmetric cost function of balancingenergy. This observed asymmetry provides an economic incentive topresent a trimmed forecast in order to reduce deviation cost.

Historically, the asymmetry displays a tendency to drive the markettowards oversupply.

The existence of the three predictable patterns is clearly incompat-ible with a minimum-variance forecasting objective of all marketparticipants, as sizeable efficiency reserves remain on all timeframes.Instead, themarket appears to follow a best economic forecast objectiveand actively allocates part of the electricity portfolio in the balancingenergy market whenever its expected price is competitive.

These positions in the German market represent an importantdifference to the dual-price settlement scheme adopted by otherEuropean countries. In the case of the quarter–hourly pattern, thebalancing energy market adds a liquid and transparent marketplace totrade electricity on a sub-hourly timeframe. An adaption of portfolios tothis pattern results in a reduction of fluctuations, which is a valuableaddition to capacity reserve market because market access to thebalancing energy market is less restricted. This is especially advanta-geous to the demand side management capacity that cannot meet thetechnical requirements set by the TSO for capacity reserve. As a result,additional flexible capacity enters the market as indicated by thequarter–hourly pattern diminishing over the years.

In contrast, the hourly and long-term strategies increase loadfluctuations. However, these positions are in line with the price signalsset by the market. This mechanism effectively reduces the ability toexploit market power in scarcity situations of electricity supply ordemand and reduces the total cost of electricity supply under demanduncertainty. Moreover, the long-term positions tending towardsnegative balancing energy demand help to reduce the cost of inevitablefluctuations, as themore expensive regime of positive balancing energydemand is avoided. The resulting biased preliminary schedule takes intoaccount that upward regulation is more demanding than downwardregulation and is economically superior to an unbiased schedule.

This information is distorted by the dual-price settlement schemedriving BRPs to omit strategic positions. In fact, the dual-price systemwill even undermine system security with respect to the quarter–hourly pattern by also driving BRPs negatively correlated to the netdeviation to reduce their fluctuations. These effects have to be valuedagainst the additional variability that might be imposed on the system

11C. Möller et al. / Energy Economics 33 (2011) 2–11

by misguided (i.e., unprofitable) strategic positions. Also, there is noindication that the German system security was inferior to that ofneighboring markets with a dual-price settlement scheme.

Overall, the experience of the German balancing energy marketdemonstrates that the market responds to the incentives set by themarket design, and indicates balancing energy to be an integral com-ponent of electricity portfolio management. Consequently, the balanc-ing energy market helps to direct investment into the most economicalcapacity extensions and forecasting procedures to secure systemsecurity. These are key issues in adapting the electricity market for thechallenges of integrating a higher share of renewables.

Acknowledgments

Rachev gratefully acknowledges research support through grantsfrom the Division of Mathematical, Life and Physical Sciences, Collegeof Letters and Science, University of California, Santa Barbara, theDeutschen Forschungsgemeinschaft and the Deutscher AkademischerAustausch Dienst. We thank Dr. Dominik Möst from the Institute forIndustrial Production at the University of Karlsruhe for valuablediscussions and providing some of the data we use in this paper.

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