Internal hydro- and wind portfolio optimisation in real-time market operations
Hans Ole Riddervold, Ellen Krohn Aasgård, Lisa Haukaas, Magnus Korpås
IInternal hydro- and wind portfolio optimisation in real-time marketoperations
Hans Ole Riddervold a,b, ∗ , Ellen Krohn Aasg˚ard c , Lisa Haukaas b , Magnus Korp˚as a a NTNU b Norsk Hydro c SINTEF
Abstract
In this paper aspects related to handling of intraday imbalances for hydro and wind powerare addressed. The definition of imbalance cost is established and used to describe thepotential benefits of shifting from plant-specific schedules to a common load requirementfor wind and hydropower units in the same price area. The Nordpool intraday pay-as-bidmarket has been the basis for evaluation of imbalances, and some main characteristics for thismarket has been described. We consider how internal handling of complementary imbalanceswithin the same river system with high inflow uncertainty and constrained reservoirs canreduce volatility in short-term marginal cost and risk compared to trading in the intradaymarket. We have also shown the the imbalance cost for a power producer with both windand hydropower assets can be reduced by internal balancing in combination with sales andpurchase in a pay-as-bid intraday market.
Keywords:
Wind power, Reservoir hydro, Marginal cost, Balancing, Intraday, Pay-as-bid
1. Introduction
With the increasing penetration of wind in the European market, power producers arein a larger extent managing combined portfolios of wind- and hydropower. In this contextit is interesting to evaluate the value of internal coordination for planning and balancing ofcombined portfolios owned or operated by the the same company.Basic economic theory suggest that as long as all market actors bid production atmarginal cost, the optimal balance of consumption and production will be established inthe market. This further implies that there should be no or limited need for internal bal-ancing of production within a company, and that all power plants should bid their marginal ∗ Corresponding author
Email addresses: [email protected] (Hans Ole Riddervold),
[email protected] (Ellen Krohn Aasg˚ard),
[email protected] (Lisa Haukaas), [email protected] (MagnusKorp˚as)
URL: (Hans Ole Riddervold)
Preprint submitted to Renewable Energy February 22, 2021 a r X i v : . [ q -f i n . GN ] F e b ost of production individually. The concept can be exemplified with a company owning twoplants. If one plant ends up with an expected imbalance caused by wind power productionbelow the original prediction, there is no need to compensate by changing production inanother plant as long as the expected imbalance volume can be bought or sold at lower cost.If it by chance should be the internal plant who provides the least costly solution, this wouldany how be found as long as this production is provided to the market place.However, there are several challenges that might hinder a company managing severalproduction units to find the optimal solution by only interacting with an external market.These challenges can be: • Limited liquidity and large spreads discouraging market participation • Interacting with a pay-as-bid versus a marginal cost market which has been a historicreference for many power producers • Real-time pricing and validity for hydropower based short term marginal cost • Establishing marginal- / opportunity cost for wind as basis for pricing in the intradaymarket • Time for placement of bids with continuously shifting market prices, volumes , inflowand wind. • Access to non-public information through observations and operational data within aportfolio • Emergence of autonomous trading systems and algorithmic trading • Trading- and imbalance fees associated with market interactionThe development and application of the virtual power plant (VPP) concept during thelast decade show that there has been a demand in the market for actors willing to take ona role as coordinator or aggregator between distributed energy production and the market.Several articles have addressed the topic of modelling VPP’s [1, 2], or related concepts ofbidding though an external agent [3].In section 2, a description of the market conditions forming the basis for this analysisare described together with some relevant market aspects that might influence the choiceof whether to handle imbalance internally or in the market. Further, operational challengesfrom the perspective of a power producer managing a combined portfolio of wind- andhydropower are addressed. In section 3, a method is proposed for evaluating the benefits ofinternal balancing in combination with the intraday market. This method is applied on acase study in section 4 before drawing a conclusion in section 5.The contribution of this paper is to asses if assets in a combined portfolio of wind and-hydropower only should rely on the market when clearing individual imbalances, or if there ispotential value obtained by internal coordination in addition to interaction with an intraday2ay-as-bid market. The topic is evaluated qualitatively with focus on some identified marketand operational challenges as well as quantitatively with case studies for an actor managingwind- and hydro assets.
2. Problem description
The topic of wind balancing using hydropower has been discussed in several papers. Thetheme has been evaluated from a system point of view where topics related to how largescale penetration of wind in Europe can be balanced by hydropower [4, 5, 6, 7], but hasalso been addressed from a portfolio perspective in [8]. Aspects related to bidding combinedhydro-generation and wind energy to the spot markets have been addressed in [9]. In [10, 11]optimal bidding- and operation strategies of wind-hydropower are suggested. Mathematicalformulations are presented for hourly optimization incorporating the stochastic characteris-tics for wind power.The additional contribution in this article is related to value creation obtained by in-ternal handling of complementary imbalances in a pay-as-bid market with shifting liquidityand bid-ask spreads. It is primarily addressing the real-time hourly optimization with lessuncertainty for wind and hydro production, but at the same time with more dynamic andcomprehensive marginal cost description for hydropower than presented in previous work.The proposed method with a common load commitment for a portfolio ensures optimalallocation of resources and is suited for real-time automatized load distribution within aportfolio.
The market framework for this article is a day-ahead centrally cleared auction wherebids are made once a day, followed by intraday and balancing markets where imbalanceare cleared, and/or power producers seek to create additional profits. Focus has been onthe Nordic market, but resembles that of other liberalized power markets. We assume thatpower producers in this study act as price-takers when submitting bids.
Power producers in liberalized energy markets have a long tradition for pricing accord-ing to marginal cost (opportunity cost) in the spot and balancing markets. This follows therationale that price-takers will maximize their profits by bidding their marginal cost [12].These markets are defined as uniform or pay-as-clear auctions [13] They have been suc-cessfully applied in the Nordic market for decades together with strict rules against marketmanipulation and market surveillance from governmental institutions. With the introduc-tion of the Nordic intraday market around at the end of the millennium, power producerswhere gradually given the possibility to trade in a pay-as bid market. This market hasbeen running in parallel with the balancing market, with traded volumes rapidly increasingthe last few years (13 TWh 2018, 20 TWh 2019) [14]. Hydropower producers have beenable to choose whether to clear imbalances and trade available volumes in the intraday orbalancing market, and as such pricing signals to the two markets have been equal since any3rbitrage between the markets would have been captured by market actors. Interactionsand trade-offs between participation in the two markets have been investigated in [15].New requirements enforcing a stricter balancing responsibility can gradually force powercompanies and retailers to secure balance of the portfolio before entering into the hour orminute of operation. This might create an clearer distinction between the two marketsresulting in different pricing regimes. One given by the value of securing balance or incomeearly in the intraday market , opposed to a value associated with real time balancing in thebalancing market.
Nordpool defines a well-functioning and competitive day-ahead power market as a marketwhere electricity is produced at the lowest possible price for every hour of the day [14]. TheNordpool day-ahead market is divided into several price areas, but liquidity in the marketis still sufficient to ensure market clearing at all times. This is however not the case for theintraday market. This is a pay-as-bid market, and for several of the the price-areas, theliquidity had traditionally been low. This can either be caused by transmission constraints,volumes allocated to other markets, or simply because markets actors do not consider thevalue of providing volumes to the intraday market sufficiently high for participation. Asa result of limited liquidity, the bid-ask spread have in many cases historically been high.This is a general trend that can be observed for markets with low liquidity [16]. The resultis that there often is a large gap between the prices that someone is willing to buy for(BID), and the prices the seller is demanding (ASK). The large gaps might alone discourageparticipation from actors used to a pricing regime based on marginal cost(MC). As long asthere exist an alternative balancing market based on MC, this has to a large extent beenpreferred, especially by Norwegian hydropower producers. For companies with a traditionin pricing according to marginal cost, and strict rules against market manipulation, it mightbe more challenging to adjust to a market with a new pricing mechanism exposed to forinstant algorithmic based bidding [17].
Market structures and auctions in the electricity markets is a widely discussed topic inenergy politics and research [18]. It is not within the scope of this article to elaborate on thepros and cons with choice in relation to different market mechanisms. The objective is toillustrate how introduction of a pay-as-bid intraday market linked to a uniform price market(spot and balance) might create challenges and opportunities for a power company withimbalances, and how this might effect the choice of whether to clear these imbalances in amarket or through internal balancing. An important characteristic of a pay-as-bid market isthat volumes are cleared directly between two market actors. These actors can be located ina different price areas as long as there is available transmission capacity. As an example, aNorwegian hydropower producer can trade volumes directly with a German wind producer.4 .2. Wind- and hydro operations2.2.1. Managing imbalances in combined portfolios of wind and hydro
To evaluate the difference between internal or purely marked based balancing for a sin-gle operator in intraday market, it is first necessary to describe the cost associated withimbalances for wind- and hydro operations.
Imbalance cost.
Imbalance cost for wind normally reflect the cash flows from the clearing ofimbalances. If one assumes that the forecasted wind production is traded on the day-aheadmarket, [19] have shown that the average imbalance cost can be calculated according to eq.1 where c imb is the average specific imbalance cost per MWh wind power produced in theconsidered time period, Q act ( t ), Q forc ( t ) are actual and forecasted wind power generation inthe settlement period, while t and π imb ( t ) is the imbalance clearing price in t . c imb = − N (cid:80) t =1 ( Q act ( t ) − Q forc ( t )) · π imb ( t ) N (cid:80) t =1 Q act ( t ) (1)While eq. 1 can be applied directly in a one-price clearing system, for a two-priceclearing system one has to take into account the fact that the imbalance price depends onthe direction of the imbalance: where π imb,SB ( t ) is the system buy price and π imb,SS ( t ) is thesystem sell price in settlement period t . π imb ( t ) = π imb,SB ( t ) if Q act ( t ) < Q forc ( t ) π imb ( t ) = π imb,SS ( t ) if Q act ( t ) > Q forc ( t ) (2)The method for calculating imbalances can not be seen isolated from the revenues thatare generated in the spot market. Even though the calculation in eq. 1 generally give agood estimate for imbalance cost when considered over a long time period and assuming thataccumulated sum of imbalances are zero, it can give a misleading signal when consideringimbalances for a shorter time horizon and specifically hour by hour. If for instant the actualproduction is higher than the forecast for the majority of hours considered, the imbalancewould actually contribute to revenues rather than cost. This does not reflect the actual cashflows that are involved.A better performance measure for evaluating the real cost for a shorter time horizon isto apply the concept of ”cost of imperfect forecast” which also is proposed in [19]. Assumingthat the optimal revenue would be obtained by bidding the actual production to spot, thehourly cost compared to forecast can be calculated by eq. 3. c imp = − ( Q act ( t ) − Q forc ( t )) · ( π imb − π spot )( t ) (3)5nd the average cost can be calculated by: c imb = − N (cid:80) t =1 (( Q act ( t ) − Q forc ( t )) · ( π imb − π spot )( t ) N (cid:80) t =1 Q act ( t ) (4)Imbalances can now be calculated by comparing a scenario where the realised productionis sold to spot (best case), against the actual cost and incomes following from the originalsales to the DA market and sale and income from an intraday balancing market. Eq. 3and 4 will be the performance measures that will be used in the analysis, but since we areinvestigating cost in a two price clearing system eq. 2 also applies. Transmission System Operators (TSO) and regulators are increasingly imposing stricterresponsibilities on the market participants related to handling expected imbalances prior tothe hour of operation. The term ”balancing responsible” is often used [20], and suppliers ofpower are obliged to either become balance responsible or enter into an agreement with aparticipant with balance responsibility.
Balancing responsibility for wind power.
The power producer can either be the owner of theassets in a combined wind- and hydro portfolio, or they might have taken on a balancingresponsibility for parts of the portfolio. By balance responsible, we mean the actor who isresponsible for submitting daily production plans and balancing power for predefined groupsof power plants to the TSO [21]. In this article, it is not separated between fully owned assetsand assets that are commercially operated by a power producer even though there might bereasons given in either contracts and/or legislation that require assets within a portfolio tobe managed individually. An example of the latter could be that a wind farm is owned bytwo parties, but operated by one of the owners. If there exists an agreement between theowners to share imbalance cost, allocation of internal coordination benefits between the twoparties must be taken into consideration.
Imbalance cost for wind.
Fig. 1 represents 4 hours in a day where the power producerhas sold 100 MW for all hours at spot prices indicated by the blue line. The actual windproduction is according to the dashed blue line. The intraday prices are required to calculatethe imbalance cost, and the bid-ask prices in this simplified example is assumed to be -+15%of the spot price. Eq.4 can further be used to calculate the average imbalance cost to 0.5EUR/MWh.
Calculations related to imbalances cost for hydropower resembles those used for windpower, especially when it is related to run-of river hydro. For reservoir hydro there are someclear distinctions. The first relates to the possibility to store water, introducing regulating6 our 1 hour 2 hour 3 hour 44020020406080100120 P r o g n o s i s / P r o d u c t i o n / D e v i a t i o n [ M W h ] PrognosisProductionDeviation 1416182022242628 P r i c e [ E U R / M W h ] Time period
Spot priceBid priceAsk price
Figure 1: Wind production(dashed blue line) versus volume bid to the spot market (blue line). Spot-, bid-and ask prices (green lines) and difference between sold- and actual production (blue bar) capacity but also an additional complexity related to valuation of the stored energy, e.g.using the water value method [22, 23]When bidding hydro production into a market, which could be either a day-ahead orintraday market, an established economic principle is to bid the marginal cost of your pro-duction. Marginal cost for hydropower plant can be calculated by short-term optimisationmodels using successive linear optimisation (LP) such as in the commercial software SHOP[24, 25]. The marginal cost is then represented by the opportunity cost extracted from theLP-problem. Marginal cost can also be calculated from use of heuristics as presented in [26].Hydropower plants will in most cases have the possibility to regulate discharge throughthe power plant, and there could be significant variation in efficiency and marginal costassociated with different level of operation.For hydrological systems where there are common shared physical constraints betweenpower plants, the value of coordination seems obvious. The simplest case is when an up-stream plant produces, and water is lead directly to a downstream plant without reservoircapacity. The downstream plant can then either produce, or let the water by-pass withoutany income. The example illustrated in fig. 2 is such a system, but in this case with somelimited capacity in the downstream reservoir. This cascade will represent the system usedfurther in the analysis for evaluating the benefits of coordination.
In fig. 3 different repre-sentation of plant efficiency is illustrated. The green line illustrates a plant with constantefficiency. In this case the marginal cost will also be constant for all levels of production.The blue line is illustrating a piece-wise linear efficiency curve. In this case there will be oneMC valid for production changes within the discharge segment from 20-25 m/s and anotherMC from 25-30 m/s and so on. 7 igure 2: Simple system with two linked power plants. The two illustrated plants can have different marginalcost of production, but how much they influence each other depend on all the factors illustrated in the figure,as well as the discharge capacity for each plant. P r o d u c t i o n ( P [ M W h ]) PQ curve, primary axis 0.8000.8250.8500.8750.9000.9250.9500.9751.000 E ff i c i e n c y ( E [ % ]) continuous efficiency curvepicewise linear efficiency curveconstant efficiency Figure 3: Dynamic marginal cost for a plant with capacity of 140 MW and 42 m3/s plotted in the workingrange from 68 to 140 MW. The light blue curve illustrates the relationship between plant production anddischarge, often referred to as the PQ-curve. The other curves show ways to represent plant efficiency.Marginal cost for the piece-wise linear representation of the efficiency is also shown with numbers hour 1 hour 2 hour 3 hour 4Time period020406080100120140 p r o d u c t i o n production Figure 4: MC breakdown representing how a hydropower producer is providing volumes to the intradaymarket. The prices illustrated in fig. 1 are used as input to a river system illustrated in fig. 2. The plantefficiency is represented by the piece-wise linear curve illustrated in blue in fig. 3. Green colours indicatebid volumes and prices, while red indicate ask volumes and prices
Fig. 4 illustrate how a hydropower producer provide bids to the intraday market. We usethe average price for the 4 segments in fig. 1 as water value for the hydropower plant whichin this case is 20 EUR/MWh. The production bid to the day-ahead market is indicated bythe grey dots in fig. 4. With this production as basis for providing bids to the intradaymarket, the power producer would be willing to increase production by 16 MWh in hour1 at a price of 24.2 EUR/MWh. The producer would also be willing to reduce productionin this segment. First 17 MWh at 21.5 EUR/MWh, further 20 MWh at 18.3 EUR/MWh,and finally reduce production by 19 MWh to minimum production of 68 MW at a priceof 17.1 EUR/MWh. With a piece-wise linear representation of the marginal cost, it makessense to bid the full segment volume to the market. With a continuous representation ofthe marginal cost, any point of operation could be selected with a corresponding volume.
Constrained systems might generate “extreme dynamics”.
In cascade hydro systems whereproduction units are placed between large and small reservoirs one can observe large vari-ations in marginal cost for situations where there is either too much or too little water inthe system. If for instance a small reservoir downstream in the cascade suddenly receivesmore inflow and risk flooding, the marginal cost for the downstream plants might change9apidly from a marginal cost represented by the water value in the upstream plant to zero.Similarly, the upstream plant will receive a clear signal to reduce production to avoid flooddownstream dramatically increasing this water-value. hour 1 hour 2 hour 3 hour 4020406080100 M a r g i n a l ( o pp o r t un i t y ) c o s t ( E U R / M W h ) Time period
MC plant 1 & 2 without floodrisk (fl.risk)MC plant 1, with fl.riskMC plant 2, with fl.riskMC plant 1 and 2, with fl.risk and common load
Figure 5: ”Extreme” dynamics for MC the cascade river system illustrated in fig. 2 when exposed to highinflow and risk of flooding
Fig. 5 illustrate an example where inflow to the a downstream plant is delivered abovethe predictions that formed the basis for the planned production. The upstream plant musteither decrease production, or the downstream plant must increase production to avoidflooding. The production and marginal cost in this case are based on the same assumptionsas shown in fig. 4. We assume that the efficiency curves and water values are the same forthe upstream and downstream plant. We further consider a case where additional inflowis delivered in hour 1 and would lead to flood if production plans remain unchanged. Inthis case the marginal cost of the downstream plant falls from 21.5 EUR/MWh to zero.This makes sense since the alternative to increasing production is to flood the water. Forthe upstream plant, the opposite can be observed. The marginal cost jumps from 21.5EUR/MWh to almost 90 EUR/MWh. The reason for this dramatic increase is that reducingproduction in this plant, ”saves” water for production to a later stage where it can be utilizedin both plants. Since the head associated with the upstream plant in this example is muchlower than for the downstream plant, this effect is reinforced.An interesting observation for the example illustrated above is that there in this caseare clearly complementary imbalances that can be resolved by internal balancing by movingproduction intraday for hour 1 from the upstream plant to the downstream plant. In section3.1 the mathematical formulation associated with moving from plant- to a portfolio loadrequirement is given. When applying the portfolio load requirement in eq. 17, the newmarginal (opportunity) cost can be found. The blue dotted line in fig. 5 illustrate how thiscan reduce the volatility in MC if the marginal cost are calculated on portfolio level ratherthan plant level. 10 .2.5. Pricing of wind imbalances
For a wind producer, the option of pricing according to marginal cost is less obvious.With the very low marginal cost for wind production resulting in wind farms mostly pro-ducing at maximum available capacity [28], has shown that it is more relevant to applyopportunity cost based on potential real-time market revenues, or rather the lost opportu-nity of obtaining these revenues if the capacity is sold or committed to the forward market.Even though there exists a wide range of alternatives and strategies related to biddingwind production to the day-ahead market [29, 30], production is often provided as a priceindependent bids to the market based on expected wind forecast. There are national differ-ences on how strict rules are enforced by TSO’s related to planning production in balancealready at the time when bids are placed, but in several markets these requirements willlimit the freedom operators have to deviate from the expected forecast when bidding to theday-ahead market [31].Various approaches have until now been applied to manage the imbalances that occurduring intraday operations. These vary from doing nothing, sit back and enjoy life whilesimply being settled against the balance prices, to more active approaches where intradaymarket is used to resolve imbalances. A solution applied by some actors is to only sendupdated production plans to the TSO based on the expected imbalance production. Withinthe existing Nordic settlement systems, this would result in limited imbalance cost andpotentially imbalance incomes since imbalances contributing in the direction of the systemneeds will be compensated with profit margins compared to spot [32]. This settlementsystem is currently under review, and one expects that there no longer will be potentialgains for any plant with deviation from plan during an hour of operation [33, 34]. Therequirements related to planning production in balance is also receiving increased attention,and new regulations and incentives will increasingly drive the producers mad.However, when imbalance in a wind portfolio occurs, what is the price you should sellor buy the expected imbalance for? The typical approach is to price the imbalance more inaccordance with the price observed or expected in the intraday or balancing markets, muchin line with the opportunity cost described in [28]. Trading algorithms are increasinglybeing applied to manage bidding which in these cases in larger extent resembles strategicbidding than marginal cost bidding. In [35, 36] optimal bidding strategies for wind powerproducers in pay-as-bid electricity market are proposed. Common for the two methods isthe use of prediction models for both short term wind power production and intraday prices.Optimisation could result in a strategy where bidding takes into account the uncertainty ofthe wind power predictions, which lead to an arbitrage between expected intraday pricesand expected imbalance costs.
There are two main distinctions when interacting with the intraday market. An actorcould either have an infrequent assessment of the market and select/match bids that al-ready are issued. This is typically the case if an actor is in need of resolving an expectedimbalance. We can defined this as a reactive approach to intraday market participation.Another approach is to actively place bids in the market. This could for instant be done11y placing bids that represent available capacity in the portfolio. This approach requiresa more continuous follow-up. This is especially important for hydropower producers whichin case of a bid published in the market is matched, might need to update the productionplan. This might again require that new system information is sent to the TSO, and finallythere might be need to re-calculate marginal cost for the remaining portfolio.
The issue related to time for placement of bids can best bedescribed by a simple example. Imagine a company operating two wind power plants (W1and W2). W1 receives an updated forecast with more wind than expected and need toincrease production for the next hour by 15 MWh. Let us further assume that bids tothe intraday market are provided by an external hydropower producer with marginal costindicated in fig. 4. A typical presentation of the bid-ask spreads on an intraday platform isillustrated in fig. 6.
16 18 20 22 24 26 28 30Price [EUR/MWh]01020304050 A cc u m u m l a t e d V o l u m e [ M W h ] bidask Figure 6: Bid-ask curves. Bid(buyers) side illustrated in green,Ask(sellers) side in red. The bid-ask spreadis the gap between the bid and ask side
W1 place a sales bid for the next hour at a price lower than the current bid price and willimmediately be met by a buy side who will purchase at 21.5 EUR/MWh . Some minuteslater, we receive information that there will be too little wind to plant W2, and productionwill have to be reduced by 15 MW. We can buy this production from the market at thepublished asked price at EUR 24.2, or place a buy bid just slightly above the ask price whichwould give the same result. Instead of just switching these obligations internally betweenW1 and W2, we have lost the spread times the volume which in this case is 40.5 EUR.If the bids had been placed at the exact same time, this would have placed W1 andW2 as the best seller and buyer in the intraday market and the volumes would be tradedbetween the two plants. This would however require strict coordination on when bids areplaced in the market. 12
First mover” advantage.
Let us assume in this case that W1 and W2 are owned andoperated separately, and that both wind operators receive an updated wind forecast atthe same time showing that both producers will have imbalances with 15 MWh higherproduction for the investigated hour the next day. In this case, the first come, first servedprinciple applies in the intraday market, and the first mover is able to clear the imbalanceat the lowest cost, represented by the lower green box in fig. 6. Assuming W1 respond first,this plant can sell the excess power at 21.5 EUR/MWh, while W2 must clear the imbalanceat the middle green box at 18.3 EUR/MWh. The result using eq. 3 is that W2 end upwith higher imbalance cost that W1. If W2 had been owned and/or operated by the hydro-power producer providing the bids in this example, this could ensure that the first moveradvantage is secured internally, and that the externally operated plant would have to clearthe imbalance at the unfavorable price.
Gate closure of markets.
Another important aspect related to placement of bids are closingtimes for markets. Various gate closure times for the intraday market are being appliedthroughout national markets, typically ranging from 30 to 60 minutes before the beginningof physical delivery. If information about potential imbalances for the next hour is receivedlater than this, it is not possible to manage this imbalance in the intraday market. Thealternative to internal balancing is to enter into the hour with expected imbalances whichthen will be cleared towards the balancing market.
Fees for participation in intraday are typically in the range 0.1-0.2 EUR/MWh. (Nord-pool, EURONEXT). In addition, producers might pay fees to suppliers of trading softwarebased on traded volumes in the market. If margins obtained in the markets are put underpressure, the fees associated with trading in the intraday market might be more significant,encouraging increased use of internal balancing. Power producers also have agreement withTSO’s or companies providing settlement services. These might charge fees in connectionwith imbalances which typically can be in the range 0.15-0.5 EUR/MWh (eSett). Thisis favouring a strategy where imbalances are solved prior to the hour of operation if costassociated with clearing the imbalance in the intraday or balancing market otherwise areequal.
Increasing digitization and integration towards market platforms might enable producersand consumers to reflect their true MC in their bids and submit these in real time to themarket in a larger extent than today. Arguments for internal balancing based on in-houseknowledge about physical status will be less prominent, and producers might experience thatthe benefits of internal balancing might be obtained anyhow since their own information ismirrored in the marketplace.On the other hand, with an increasing implementation of autonomous trading systems wewill most likely see an increase in the application of trading robots, algorithms and strategicbidding in the market. This could support the use of internal balancing where the real time13rue marginal cost in the hydro portfolio can be used for internal balancing without exposureto a more unclear market representation.Finally, the use of autonomous trading systems will require extensive monitoring andquality assurance of input- and output data. The market actor will still be responsible forall interaction with the market, and ensuring that all rules and regulations are followed.The power sector being defined as critical related to security of supply and national securityissues, also have limitations related to how tightly integrated market and supervisory controland data acquisition (SCADA) systems can be.
3. Proposed solution
The previous section has illustrated that solely relying on a strategy where externalmarkets are used to manage imbalances within a power portfolio could lead to sub-optimalsolutions for a power producer. The price signals to and from the market might simply notsufficiently represent the marginal cost that would give the most profitable outcome for theproducer. A better solution might be a strategy where the true marginal cost generated byinternal models are applied and complimented with opportunities that exists in an externalmarket.With this in mind, it is interesting to look further into methods for internal balancing.The process for evaluating the value of internal balancing opposed to individual balancingof each energy resource is illustrated in fig. 7.
Figure 7: A step-wise process and model to evaluate performance of internal imbalance handling comparedto individual balancing .1. Mathematical formulation The processes in fig. 7 starts with tasks that are performed in connection with dayahead bidding. Assuming that the wind producer is risk neutral, the producer would bidthe expected production to the day-ahead market. The optimization problem for a reservoirhydropower producer in a system with predicted market prices can be expressed by theobjective function and constraints in eq. 5-14. The problem is a mixed integer problem andthe solution can be found by using Pyomo/Cplex [37, 38].
M ax. (cid:88) i (cid:88) t ( g i,t ∗ λ t ) + (cid:88) m R m ∗ W V m (5)s.t. P min i ≤ g i,t ≤ P max i ∀ i, t (6) Rmin m ≤ R m,t ≤ Rmax m ∀ m, t (7) R m,t = Rinit m − g i,t + inf m,t − f l m,t ∀ m, i = 1 , t = 1 (8) R m,t = Rinit m + g i − ,t − g i,t + inf m,t − f l m,t ∀ m, i > , t = 1 (9) R m,t = R m,t − − g i,t + inf m,t − f l m,t ∀ m, i = 1 , t > R m,t = R m,t − + g i − ,t − g i,t + in m,t − f l m,t ∀ m, i > , t > q SEG,i,n,t < = Z i,n ∀ i, t, n < = 1 (12) q SEG,i,n,t < = Z i,n ∗ µ i,n − ,t ∀ i, t, n > q SEG,i,n,t > = Z i,n ∗ µ i,n,t ∀ i, t, n (14)The objective function in eq. 5 optimizes the profits related to selling power to theday-ahead market given by the hourly prediced prices λ t . Here, g i,t is generation from unit i in time-step t , R m is the end reservoir level for reservoir m, and W V m is the water valuefor reservoir m . µ is a binary variable used to control use of water from the different segments. One cannot use water from a higher segment before the lower segment is at maximum utilisation.Eq. 13 ensures that that segment n − n , while eq. 14 ensuresthat all previous segments are maximized before segment n is used. Z i,n is the ”capacity”of the segment n for plant i in m3/s.The optimisation conducted in process step 2a using eq. 5-14 will result in a spotcommitment for the hydropower. The next steps are steps associated with the intradayoptimisation (step 2c) where trading of imbalances in an intraday market are included inthe model formulation. M ax. (cid:88) i (cid:88) t ( L i,t ∗ λ t − g BUY,i,t ∗ P ASK,t + g SELL,i,t ∗ P BID,t ) + (cid:88) m R m ∗ W V m (15) g i,t = L i,t − g BUY,i,t + g SELL,i,t (16)15
BID,t and P ASK,t are intraday bid and ask prices in time step t . g BUY,i,t and g SELL,i,t are the optimal volumes to be bought and sold in the intraday market in for unit i , timestep t . L i,t is the load requirement unit i in timestep t .For the final step in the process (step 3) we modify the load commitment to represent acommon portfolio commitment. The generator production for wind is also added as a sourceof supply ( g wind ). g i,t = L t − (cid:88) i g BUY,i,t + (cid:88) i g SELL,i,t (17)The constraints in eq. 16 and eq. 17 might seem similar , but there is a fundamentaldifference in the requirement that potentially will have a large impact on the objectivefunction and marginal cost. Constraint eq. 16 is a plant schedule constraint, and requiresthat each plant has to meet the specific load requirement that was allocated to this plantduring the optimisation towards market prices. Constraint eq. 17, only requires that theload requirement is met in total, but that this can be met by the combined production fromall plants.
4. Case study
Analysis of one day operation of hydro and wind power with exogenous market description.
To investigate the effect of internal balancing for a portfolio consisting of both wind andhydropower, a realistic case has been investigated by applying the process described in fig.7. The objective behind applying this case study is primarily to illustrate the concept andinteractions in a portfolio with wind and water assets, and not to quantify the long termeffects of coordination. One day is therefore selected to illustrate the concept, a day wherethere is imbalances both in the wind and hydropower plant.Both plants have bid their production to the Nordpool day-ahead market. The windplant has sent bids based on the the forecast (expected) wind prognosis that is availablebefore the bidding deadline (12-noon), this often based on the EC00 [39] prognosis whichtypically is available at 8 am. The hydropower has sent bids based on an optimisation withpredicted prices and inflow.To replicate the bidding process for the hydropower unit, a simple optimisation modelhas been established based on the equations described in section 3. Given the expectedinflow and prices for the next day, the model seems to fit production for the next day wellas seen in fig. 8. The deviation is primarily due to the higher resolution in the descriptionof the efficiency curve in real life operations which will generate a ”smoother” productioncurve for the operational model.Both plants will after the DA market clearing receive a production commitment for thenext day. The EC12 model results are also available on a daily basis at approx. 8 pm. Forthis example we assume that the updated results that are available just before entering intothe day of operation represent the realised inflow and wind for the next day. No additionaluncertainty is considered. 16 P r o d u c t i o n [ M W h ] bidmodel 6.26.46.66.87.0 P r i c e [ E U R / M W h ] Figure 8: Modelling of next day’s hydropower production (Step 2a). ”Bid” is the actual production sold tothe power exchange (real-life data). ”Model” is the approximation made by a simplified optimisation modelwith expected inflow and prices for the next day I m b a l a n c e [ M W h ] Sum imbalanceImbalance windImbalance hydro
Figure 9: Imbalances for wind- and hydropower as result of updated forecast. Sum imbalance is the nethourly imbalance for a portfolio before re-optimisation towards an intraday market. B i d a n d m o d e l w i t h o r i g i n a l i n f l o w : P r o d u c t i o n [ M W h ] ActualModel 6080100120140160180 B i d a n d m o d e l w i t h n e w i n f l o w : P r o d u c t i o n [ M W h ] Figure 10: Modelling of next days hydropower production with updated inflow forecast (step 2b). Due to aforecast with less inflow, there is a considerable reduction in modelled production in hour 3 and 4 comparedto the optimisation conducted in step 2a.
The plant and reservoir considered in this case study is such a plant. If no additionalmarket information is provided to the optimisation model, the recalculated plan based ona new inflow forecast for such a reservoir will attempt to maximise the profits based spotprices for the next day and the updated inflow forecast. Fig. 10 illustrates how the historicproduction turned out to be for the investigated plant, compared to results from the sim-plified optimisation model. While the historic production follows the original plan until theplant at a certain stage have to reduce production due to lack of water, the optimisationbased on a updated forecast seem to more actively exploit the price differences to reduceproduction in periods with lower prices. The total production over the 24 hours is equal.The first approach to evaluate the benefit of coordination is to merge the commitments forthe hydro and wind producer. Further, the total cost for the the common realised productioncleared against intraday prices is compared to a scenario where the imbalances are clearedindividually for wind and hydro.Imbalance cost are calculated according to eq. 3 were the hourly imbalance cost are18ummed to give a total imbalance cost for one day. This approach to internal balancing isdefined as reactive since we are not conducting any re-optimisation for the common load,but only exploiting the value of any complimentary imbalances. Results from such a reactiveapproach to coordination is illustrated together with other approaches in table 1.
Introducing a market.
To be able to calculate imbalance cost, a market description forintraday trading is required. The historical bid-ask prices related to the intraday marketare not easily accessible. These are dynamic prices that change continuously, and getting a”snap-shot” of the market for instance just before entering into a new day requires access toorder books containing large amounts of information. Order books can typically be providedby the market operators at some fee. High-, low, and last prices are more accessible, butthese tend to deviate considerably from observations made in the market several hour aheadof the closing time for each hour. To represent the market conditions in our case study, asynthetic market description has been generated. We assume the the bid and ask spreads aregiven by a fixed margin of +-15 % of the spot price. It is also expected that bid-ask pricesare effected by the ”system” imbalances that are expected the next day. We therefore adda correction factor of +- 1 % for each MW of imbalance. This ”system”-imbalance is purelycalculated as the hourly delta of inflow and wind in MWh between the ECOO and EC12prognosis. These figures are not calibrated towards market observations, and the sensitivityfactor of bid- ask- prices would be very different in a market with considerably more volume.It still illustrates some of the variations that can be expected in the intraday market, andhelp to illustrate some of the dynamics that arise when bid-ask spreads change throughoutthe day. Fig. 11 illustrate the prices used further in the analysis. P r i c e [ E U R / M W h ] ID bid price ID ask pricespot price 35302520151050510 " S y s t e m " i m b a l a n c e [ M W h ] imbalance Figure 11: Synthetic intraday prices for Oct 7. 2020, with the realized NO2 spot price for the same day.Bid- ask prices are calculated with fixed margin of +-15 % of the spot price and a correction factor of+- 1 % for each MW of imbalance between E00 and E12 prognosis illustrated by the bars in the chart.The ”system”-imbalance in this graph should not be confused with the imbalance in fig. 9 which is the”producer”-imbalance after re-optimisation of the hydro-power production
Re-optimisation of hydropower.
As soon as a market description for the next day is available,it is possible to actively re-schedule the next day’s production. In the Nordic market, the19ntraday market for the next day opens at 2 PM . If we assume the the bid- ask pricesillustrated in fig. 11 represent the market at the point of time when an updated wind andinflow forecast is present, the actors can attempt to close their imbalances based on theprevailing prices.The wind operator has no possibility to move production from hour to hour, and willhave to close the forecasted gaps. The hydropower producer has some reservoir capacityand can move production in a way where imbalances are moved away from the hours withhigh expected imbalance cost, to hours where it is possible to buy cheap and sell expensive.According to step 2c in fig. 7, the new imbalance cost for hydropower is calculated. Thisis then defined as our base case. The reason for using the new optimisation as base casefor evaluation of the value for internal balancing, is because we wish to evaluate the valueof wind-hydro coordination, and not the value of improved optimisation of the hydro-powerplant alone.The optimised uncoordinated benchmark is the sum of this re-optimised imbalance andwind imbalance and is shown in table 1. The price input in this model is a synthetic andsimplified representation of the intraday market. In real life, the bid and ask prices are linkedto volumes. Gradually increasing supply/demand in the market is normally associated withgradually lower/higher prices. One should therefore expect that if the hydropower producerattempts to move production from high-imbalance-cost hours to hours with more favorableprices, the prices would actually respond in a way limiting the value of changing production.This secondary effect is not considered in the presented case study. P r o d u c t i o n [ M W h ] Optimized uncordinatedProactive coordination
Figure 12: Changes in hydropower production as result of internal balancing. Green illustrate where thehydropower plant increase production compared to base-case, while red illustrate reduced production. Thetotal production is equal and limited by the availability of water in the downstream reservoir.
The final step (step 3 in fig. 7) is to add the wind production , and optimize towardsthe common commitment using the load constraint given by eq. 17. The results are shownin table 1, and illustrates that the value of internal balancing for this day is 170 EUR, given20 able 1: Results from approaches with individual- versus internal balancing. Scenario 2represents the base case.
Scenario Scenario imbalance cost Average IBC and IBC as Savings comparednr. name (IBC) percent of total income to base-case1 Individual balancing, no optimisation 500 EUR 0.13 EUR/MWH, 2.0%2 Individual balancing, hydro optimized, base-case 390 EUR 0.10 EUR/MWH, 1.5%3 Common commitment, reactive, hydro optimized 335 EUR 0.09 EUR/MWH, 1.3% 55 EUR4 Common commitment, proactive, all optimized 220 EUR 0.06 EUR/MWH, 0.9% 170 EUR by the reduced imbalance cost for the coordinated scenario compared to the uncoordinatedalternative.Comparing with the reactive coordination approach the additional value of proactivebalancing is 115 EUR. While the reactive approach is able to create value by exploitingthe complementary imbalance in the wind and hydro production, the active re-optimisationcreates additional value by using the flexibility in the hydropower reservoir. Fig. 12 illustratehow hydro production is decreased in periods where wind compliment the hydro imbalance,and that the production can increase in hour 6 where there is a considerable imbalance costfor the hydropower plant. The imbalance cost in hour 4-6 follows from the re-optimisationin the intraday market (step 2c), and the hours are chosen by the model due to the relativelylow system-imbalance and favourable ask prices in this period.
5. Conclusion
In this article we have shown how the imbalance cost for a power producer with bothwind and hydro-power assets can be reduced by internal balancing in combination with salesand purchase in a pay-as-bid intraday market. Knowledge about the marginal cost pricingmethod for hydropower production is important to understand and optimize the interactionsin the balancing process. The potential rapid changes in marginal cost that can be observedfor hydropower, and need to select volume- and price pairs when bidding to a pay-as-bidmarket, might in some cases favour internal balancing rather than clearing imbalances in themarket. For a realistic case study from the Norwegian power market, we have demonstratedhow a step-wise process can be applied to quantify the value of internal balancing, opposedto an uncoordinated approach from the hydro- and wind production. We have not attemptedto answer if the same results could be obtained if the hydropower producer had issued theavailable balancing power to the intraday market. There are however many aspects in thatprocess that could lead to optimality for the system, but end up as sub-optimal for theproducers managing both assets. Quantifying the long term effects by simulating over alonger time horizon with historic intraday prices could be a topic for further research.An important question is what happens if an increasing amount of participants chooseto conduct a large share of balancing internally rather then using the market as the primarysource for clearing of imbalances. Who will then provide capacity to the intraday market?If liquidity in this market increases which further could lead to decrease in bid-ask spreads,the incentive for internal balancing will be reduced. Power producers should therefore have21n incentive to increase liquidity in this market, and internal balancing should therefore belimited to cases where interactions with the market are challenging due to time restrictionsor dynamics in the system where it is difficult to publish and follow-up true marginal costin the market.
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