An Artificial Intelligence Solution for Electricity Procurement in Forward Markets
AAn Artificial Intelligence Solution for Electricity Procurement in Forward Markets
Thibaut Th´eate a, ∗ , S´ebastien Mathieu a , Damien Ernst a a Montefiore Institute, University of Li`ege (All´ee de la d´ecouverte 10, 4000 Li`ege, Belgium)
Abstract
Retailers and major consumers of electricity generally purchase a critical percentage of their estimated electricityneeds years ahead on the forward markets. This long-term electricity procurement task consists of determining when tobuy electricity so that the resulting energy cost is minimised, and the forecast consumption is covered. In this scientificarticle, the focus is set on a yearly base load product, named calendar (CAL), which is tradable up to three yearsahead of the delivery period. This research paper introduces a novel algorithm providing recommendations to either buyelectricity now or wait for a future opportunity based on the history of CAL prices. This algorithm relies on deep learningforecasting techniques and on an indicator quantifying the deviation from a perfectly uniform reference procurementstrategy. Basically, a new purchase operation is advised when this mathematical indicator hits the trigger associated withthe market direction predicted by the forecaster. On average, the proposed approach surpasses benchmark procurementstrategies and achieves a reduction in costs of 1.65% with respect to the perfectly uniform reference procurement strategyachieving the mean electricity price. Moreover, in addition to automating the electricity procurement task, this algorithmdemonstrates more consistent results throughout the years compared to the benchmark strategies.
Keywords:
Artificial intelligence, deep learning, electricity procurement, forward markets.
1. Introduction
Electricity retailers generally buy a critical share oftheir consumption years ahead on the forward markets.They have to accurately estimate their clients’ consump-tion and purchase the appropriate quantity of electricity.This challenging task also applies to major electricity con-sumers which sign flexible bilateral contracts with theirenergy retailer. Typically, they have to decide when topurchase blocks of energy at a price generally indexedon the forward prices. Each block corresponds to a cer-tain percentage of their total electricity consumption, thisquantity being formerly predicted by the retailer. Even-tually, the potential discrepancy between electricity pur-chased and forecast consumption is covered by the retailerat the end of the procurement horizon. The long-term elec-tricity procurement problem consists in determining whento purchase electricity on the forward markets, so that thepredicted consumption is secured and the energy cost isminimised. This decision-making problem is particularlychallenging because of its sequential and highly stochasticnature, coupled with a poorly observable and potentiallyadversarial environment.Nowadays, the long-term electricity procurement taskis generally performed by experienced consultants, based ∗ Corresponding author
Email addresses: [email protected] (ThibautTh´eate), [email protected] (S´ebastien Mathieu), [email protected] (Damien Ernst) on customised rules and their expectations regarding thefuture energy market direction. This research paper pro-poses an alternative approach: an algorithm providing rec-ommendations to either buy electricity now or to wait for afuture opportunity, based on the history of forward prices.This solution may interest these consultants, but also re-tailers who are willing to deploy more advanced procure-ment techniques and major consumers choosing not to relyon consultants for buying their electricity.The algorithm presented in this scientific article is basedon the idea that the purchase decisions should be split overthe procurement horizon to spread the trading risk, with anominal anticipation or delay depending on the market di-rection. This algorithm relies on a forecasting mechanismto predict the dominant market trend, and on an indicatorquantifying the deviation from a perfectly uniform refer-ence procurement strategy to trigger purchase decisions.In addition to classical approaches, Deep learning (DL)techniques are considered for the forecasting task becausedeep neural networks (DNNs) are able to efficiently handletemporal dependence and structures like trends.The present scientific research paper is structured asfollows. To begin with, a concise review of the scientific lit-erature referring to the long-term electricity procurementproblem is proposed in Section 2. Then, a formalisation ofthis decision-making problem is presented in Section 3. Analgorithm is proposed in Section 4 to solve this long-termelectricity procurement problem. Section 5 describes the
Preprint submitted to Elsevier June 11, 2020 a r X i v : . [ q -f i n . T R ] J un erformance assessment methodology and discusses the re-sults achieved by this algorithm. Finally, Section 6 con-cludes and suggests several leads for future work.
2. Literature review
Scientific literature proposes multiple strategies for elec-tricity producers willing to sell their energy on the forwardmarkets. On the other hand, the sides of the retailers andconsumers lack proper scientific coverage, with only a fewarticles currently available. The solutions presented aretypically based on stochastic programming and optimisa-tion techniques. Article (Carrion et al., 2007) proposes asolution to the electricity procurement problem faced bya major consumer whose supply sources include bilateralcontracts, self-production and the day-ahead market. Astochastic programming approach is considered, with riskaversion being modelled using the conditional value at risk(CVaR) methodology. The proposed solution is assessedthrough a realistic case study which highlights the trade-offbetween cost minimisation and risk mitigation. One chap-ter of the book (Conejo et al., 2010) is dedicated to theelectricity procurement problem from a major consumerperspective, while another chapter discusses the case of aretailer in a medium-term horizon. In both cases, the elec-tricity procurement problem is mathematically formulatedas a multi-stage stochastic programming problem, wherethe evolution of the price is modelled as a stochastic pro-cess using a set of scenarios and the risk aversion is mod-elled through the CVaR. The work concludes that multi-stage stochastic programming appears to be an appropri-ate modelling framework to make electricity procurementdecisions under uncertainty, with the complex multi-stagestochastic model being translated into a tractable mixed-integer linear programming problem. Article (Zare et al.,2010) introduces a technique based on information gapdecision theory to assess different procurement strategiesfor major consumers. The objective is not to minimisethe procurement cost but rather to assess the risk aver-sion of some procurement strategies with respect to theminimum achievable cost. The results suggest that strate-gies related to a higher procurement cost are more robustand risk averse. Article (Nojavan et al., 2015) proposes arobust optimisation approach to solve the electricity pro-curement problem from a retailer perspective. A collec-tion of robust mixed-integer linear programming problemsis formulated, with the electricity price uncertainty beingmodelled by considering upper and lower limits for the en-ergy prices rather than the forecast prices. Articles (Be-raldi et al., 2017a) and (Beraldi et al., 2017b) present astochastic optimisation approach relying on the integra-tion of the paradigm of joint chance constraints and theCVaR risk measure to solve the electricity procurementproblem from a consumer perspective. The results for areal case study highlight the trade-off between risk andreliability by considering different levels of risk aversion.Article (Zhang et al., 2018) proposes another multi-stage - - - - - - - - - - Time . . . . . . . . C A L p r i ce [ E U R / M W h ] Figure 1: Illustration of the CAL 2018 product stochastic programming model for the long-term electricityprocurement problem faced by a major consumer, wherethe complexity of the task is reduced by dividing a one-year planning into seasons. In this model, a season is rep-resented by characteristic weeks and the seasonal demandis revealed at the beginning of each season.
3. Problem formalisation
In this section, the long-term electricity procurementproblem considered is thoroughly presented and formalised.It is assumed that the only supply source at the disposal ofthe agent, whether a retailer or a consumer, is the calendarproduct (CAL). This yearly base load product is tradableup to three years ahead of the delivery period. For in-stance, the CAL 2018 product corresponds to the deliveryof electricity for the entire year 2018, this energy beingtradable between 2015 and 2017 included, as depicted inFigure 1. The long-term electricity procurement probleminvolves the forecast of the electric energy consumptionfor the future period considered. In this research paper,the total quantity of electricity to be purchased over theprocurement horizon is denoted Q . For the CAL product,this procurement horizon corresponds to a period of threeyears and the quantity Q represents the consumption forone future year. It should be mentioned that this prob-lem statement could be easily adapted to the case of amajor electricity consumer signing a flexible bilateral con-tract with its retailer. In such a context, the energy priceis generally set by another signal, defined in this contract,which is generally indexed on the CAL product prices.In this research paper, the continuous trading timelineis discretised into a number of discrete time steps t of con-stant duration ∆ t . In this case, the agent is assumed tobe able to make only one decision per trading day, mean-ing that ∆ t is equal to one day. In the context of thelong-term electricity procurement task, a trading or pro-curement strategy represents the set of rules considered to2ake a decision. Mathematically, a procurement strategyis defined as a programmed policy π : X → Y which, basedon some input information x t ∈ X at time step t , outputsa trading decision y t ∈ Y so as to maximise an objec-tive criterion. The input, output and objective criterionconsidered in this research paper for the electricity pro-curement problem are presented in the next subsections. Ideally, the procurement strategy input x t at time step t should encompass every single piece of information ca-pable of affecting future electricity prices. Nevertheless,a major difficulty of the electricity procurement problemis the unavailability of such information, which can beboth quantitative and qualitative, and can take variousforms. This situation leads to significant uncertainty, withchanges in price being impossible to accurately explainand/or predict. In this research paper, the input x t attime step t is modelled as follows: x t = { P t , S t } (1)where: • P t = { p t − τ | τ = 1 , ..., K } is the series of K previousCAL prices, K being a parameter. • S t is the trading agent state information, which ismathematically expressed as follows: S t = { t, T, q t , Q } (2)with: • t being the current trading time step. • T being the total number of trading time stepsover the procurement horizon. • q t being the quantity of electricity already pur-chased by the agent at time step t . • Q being the total quantity of electricity to bepurchased over the procurement horizon. At each trading time step, the agent has to decidewhether to purchase electricity right now or to wait for afuture opportunity. Consequently, the procurement strat-egy output y t at time step t is binary and can be mathe-matically expressed as the following: y t ∈ { , } (3)with y t = 0 corresponding to the advice of waiting, and y t = 1 to the advice of buying electricity.Whenever purchasing electricity, the agent is requiredto specify the quantity traded. In this research paper, the volume contracted is assumed to be fixed. The total quan-tity of electricity Q is simply split into N ∈ N purchaseoperations of a fixed amount of electricity A = Q/N . Con-sequently, the quantity of energy purchased at each tradingtime step t would either be equal to 0 or A depending onthe algorithm output y t . However, this approach does nottake into account the resolution of the market dQ , corre-sponding to the smallest block of electricity tradable. Toaddress this issue, the quantity of energy Q is constrainedto be a multiple of this market resolution dQ . Moreover,the procurement strategy parameter N is constrained tobe such that the amount of electricity A = Q/N is a mul-tiple of the market resolution dQ .An important constraint is assumed regarding the pro-curement strategy output y t . The agent is required to havepurchased the exact quantity of electricity Q by the end ofthe trading activity. Because no selling operations are per-mitted, the agent is not allowed to buy electricity in excessof its consumption. Moreover, anticipation is necessary asthe agent is only able to buy the amount of electricity A ata time. Let n t = ( Q − q t ) /A be the number of remainingpurchase operations to be performed by the agent at timestep t , this quantity should never exceed the number ofremaining time steps T − t in practice. Eventually, thisconstraint is mathematically expressed as follows: T (cid:88) t =0 y t A = Q (4)In order to realistically simulate the trading activity as-sociated with the electricity procurement task, the tradingcosts have to be considered. This research paper assumesthat the only trading costs incurred by the agent are thetransaction costs. As their name indicates, these costs oc-cur when a transaction is performed. Therefore, they aremodelled with a fixed fee F to be paid per MWh of elec-tricity purchased. For the electricity procurement task,this parameter F is realistically set to 0.1 e /MWh.Making the hypothesis that the electricity is alwayssuccessfully purchased by the agent, the state variable q t is updated in line with the following equations: q t +1 = q t + y t A (5) In the scope of the electricity procurement problem, thecore objective is the minimisation of the costs incurred forbuying energy. However, such an intuitive goal lacks theconsideration of the risk associated with the trading activ-ity, which should ideally be mitigated as well. In fact, thereexists a trade-off between cost minimisation and risk miti-gation, in accordance with the popular saying: with greatrisk comes great reward. However, this research paperonly considers electricity cost minimisation as the objec-tive. Therefore, the quantity to be minimised is the total3ost incurred by the agent at the end of the procurementhorizon c T , which is mathematically expressed as follows: c T = T (cid:88) t =0 y t A ( p t + F ) (6)
4. Algorithm description
This section thoroughly presents a novel algorithm,named
Uniformity-based Procurement of Electricity (UPE),to solve the long-term electricity procurement problem.The key idea behind this algorithm is the potential bene-fit to speed up or delay purchase operations with respectto a reference procurement strategy when the prices areexpected to go up or down in the future. At its core,this algorithm is based on the coupling of both the iden-tification of the dominant market direction and the es-timation of the procurement uniformity level quantifyingthe deviation from a perfectly uniform procurement pol-icy. The first important component of this procurementalgorithm is the forecaster F whose responsibility is to ac-curately predict the dominant market trend, either upwardor downward. In this context, the trend can be defined asthe general direction in which the electricity price is cur-rently going. The forecaster F takes as input a series of K previous CAL prices P t , which were formerly normalised,and outputs the predicted trend: f t = F ( P t ) (7)with f t = 1 and f t = − k , typi-cally several weeks. The resulting smoothed price at timestep t is mathematically expressed as follows:¯ p t = 12 k + 1 t + k (cid:88) τ = t − k p τ (8)As an illustration, the result of this low-pass filteringoperation with k = 25 is depicted in Figure 2 for the CAL2018 product. The market trend at time step t is definedas the difference between two consecutive smoothed prices¯ p t and ¯ p t − . More specifically, an upward trend ˆ f t = 1 isdesignated when ¯ p t ≥ ¯ p t − and a downward trend ˆ f t = − - - - - - - - - - - Time t . . . . . . . C A L p r i ce p t [ E U R / M W h ] Original signalFiltered signal
Figure 2: Illustration of the CAL 2018 product is specified when ¯ p t < ¯ p t − , with ˆ f t representing the mar-ket trend labels. This rigorous mathematical definitionof a market trend is intuitive and convenient, but not per-fect. As future work, more complex definitions of the mar-ket trend could be investigated. For instance, the markettrend could be defined as the slope of the straight lineproduced by a linear regression operation on price dataover a certain time period. Despite being subjective, hu-man annotations could alternatively be considered as well.The second important component of the UPE algo-rithm is the concept of procurement uniformity, which isbased on the comparison of the current situation with areference policy: the perfectly uniform procurement strat-egy. This reference policy implies buying the same amountof electricity A u = Q/T at each trading time step over theentire procurement horizon. Despite being generally notfeasible in practice due to the market resolution dQ , thisstrategy is an interesting candidate for comparison pur-poses as the average electricity price is achieved with arisk spread over the entire procurement horizon. In doingso, this research paper introduces the procurement unifor-mity level u t ∈ [ − ,
1] which quantifies the deviation fromsuch a perfectly uniform strategy: u t = T − tT − Q − q t Q (9)Three cases arise depending on the value of u t : • u t = 0: The agent has purchased a quantity of elec-tricity equal to the amount of energy that a perfectlyuniform procurement strategy would have alreadybought at time step t . • u t ∈ ]0 , • u t ∈ [ − , u t with two trigger values u − and u + . Whenthe agent waits with purchase operations still to be per-formed, the procurement uniformity u t decreases over time.The idea of the proposed algorithm is to issue a new pur-chase operation when this indicator hits the trigger valueassociated with the predicted trend, u + for upward and u − for downward. Consequently, the triggers values representhow long the agent is willing to wait when a certain markettrend is detected. These are parameters of the algorithm tobe set by the agent according to its expectations regardingthe market dynamics and its sensitivity to the trading risk.Algorithm 1 details the decision-making process of theUPE algorithm for on time step t . If a stable increase inthe electricity prices is predicted by the forecaster F , hap-pening when f t = 1, the agent is instructed to wait for aslong as the procurement uniformity u t remains above thetrigger value u + . Similarly, if a downward trend is likelyto happen according to the forecaster F , with f t = − u t exceeds the trigger value u − . With sucha decision-making policy, the two trigger values quantifyhow long the agent is willing to wait when a certain trendis forecast. Consequently, u − should normally be inferiorto u + as it is natural to wait longer when the prices areexpected to decrease in the future.In this research paper, two forecasters are consideredto approximate the true values of the market trend f t pre-viously defined based on past price data only. They arerespectively called Basic forecaster and
DL forecaster . In finance, a popular approach to acquire insights aboutthe market trend from past data consists in comparing twomoving averages of different window lengths. The idea isto assess how the more recent prices represented by theshorter moving average evolved with respect to the olderprices described by the longer moving average. Both win-dow lengths L short and L long are parameters to be tuned,with typical values being several weeks or even months.The moving average of window length L for time step t ismathematically expressed as follows: M t ( L ) = 1 L t (cid:88) τ = t − L +1 p τ (10)With such a definition, an upward trend f t = 1 is nat-urally expected when the shorter moving average is largerthan the longer one, i.e. if M t ( L short ) ≥ M t ( L long ). Onthe contrary, a downward trend f t = − M t ( L short ) < M t ( L long ). This relatively basic ap-proach is considered for the first forecasting model F MA of this research paper. The UPE algorithm employing this basic forecaster is named Uniformity-based Procurement ofElectricity with Moving Averages (UPE-MA).
A more advanced approach based on recent DL tech-niques is considered for the second forecasting model. Thisforecaster F DL consists of a feedforward DNN composed of N L hidden layers with N N neurons each. A basic illustra-tion of the forecasting DNN is provided in Figure 3. Leakyrectified linear unit activation functions are chosen for thehidden layers. Generally referred to as Leaky ReLU , thisactivation function is mathematically expressed as follows: f ( x ) = (cid:40) x if x > , . x otherwise. (11)Because the trend forecast is a classification problem, asoftmax activation function is selected for the output layerto return the probabilities associated with each trend. Theforecaster F DL naturally outputs the market trend asso-ciated with the greatest probability. The softmax acti-vation function takes as input a vector of real numbers x = ( x , ..., x J ) ∈ R J and outputs a vector of J real num-bers bounded between 0 and 1 representing probabilities: S ( x ) i = e x i (cid:80) Jj =1 e x j ∀ i ∈ { , ..., J } (12)The training of this DNN is performed with the ADAMoptimiser and a cross-entropy loss to be minimised. Widelyused for classification tasks and also referred to as logarith-mic loss, the cross-entropy loss is computed as follows: L ( θ ) = 1 B B (cid:88) b =1 − log( p ( y b = ˆ y b | x b , θ )) (13)where: • B is the batch size. • x is the DNN input. • y is the DNN output. • ˆ y is the classification label. • θ represents the parameters of the DNN.Additionally, both dropout and L2 regularisation tech-niques are adopted for generalisation purposes. All theDL techniques mentioned are covered in more details inthe scientific article (LeCun et al., 2015) and the book(Goodfellow et al., 2016). As previously suggested, thedataset used to train this DL forecasting model includesa series of previous CAL price histories P t for the inputsand a series of associated market trends f t for the out-puts. The UPE algorithm operating the forecaster F DL isnamed Uniformity-based Procurement of Electricity withDeep Learning (UPE-DL).5 lgorithm 1
UPE algorithm decision-making policy for one time step t Inputs:
Procurement strategy input x t , forecaster F (formerly trained if necessary), trigger values u − and u + . Execute the forecaster f t = F ( P t ). Compute the procurement uniformity u t = T − tT − Q − q t Q . if f t = 1 and u t < u + then Make the trading decision to buy electricity: y t = 1. else if f t = − and u t < u − then Make the trading decision to buy electricity: y t = 1. else Make the trading decision to wait: y t = 0. end if return y t Figure 3: Basic illustration of the forecasting DNN
5. Performance assessment and results
This section evaluates the performance realised by theproposed UPE algorithm for the two forecasters consid-ered. Section 5.1 presents the performance assessmentmethodology. The results achieved by the UPE-MA andUPE-DL algorithms are discussed in Section 5.2.
In this research paper, the performance of a procure-ment strategy is evaluated on a testbench composed ofCAL products over a period of eight years, ranging fromCAL 2012 to CAL 2019. This enables one to confrontthe strategy with diverse market behaviours: dominantupward and downward trends, various levels of volatility.Moreover, a clear separation between the training and testsets is imposed in order to avoid any false results due tothe overfitting phenomenon. Both the tuning of the strat-egy parameters and the training of the DL model are per-formed on the CAL product three years prior to the oneactually tested, so that the training and test sets do notshare any data. For instance, the training of a procure-ment strategy for the CAL 2018 product, with electric-ity purchased between 2015 and 2017, is performed on theCAL 2015 one, with energy bought between 2012 and 2014. For comparison purposes, two basic benchmark pro-curement strategies are considered in this research paper.The first one is named
Naive Balanced Electricity Procure-ment (NBEP). This strategy simply consists in dividingthe procurement horizon into N intervals of identical dura-tions, and executing a purchase operation in the middle ofeach interval. The second benchmark procurement strat-egy is named Electricity Procurement with Moving Aver-ages (EPMA), and is an adaptation of the popular movingaverages trend following strategy to the electricity procure-ment task. More details about this specific trading strat-egy widely used in the stock markets can be found in thebook (Chan, 2009). The resulting algorithm is based onthe same principle as the basic forecaster presented in Sec-tion 4.1, with two moving averages of different durationsfor estimating the market trend. A purchase operationis triggered each time a new upward trend is predicted,occurring when the shorter moving average M t ( L short )crosses and becomes higher than the longer moving av-erage M t ( L long ). If the number of purchase operationsperformed with this policy is smaller than N by the end ofthe procurement horizon, the remaining ones are executedat the last trading time steps.As previously explained in Section 3.3, the procure-ment strategy objective is the minimisation of the totalcost c T . To improve the readability of the results, thequantitative performance indicator C = c T /Q , represent-ing the average price expressed in e /MWh at which theelectricity is purchased, is considered instead. Moreover,several reference procurement policies achieving benchmarkvalues for this quantitative performance indicator are con-sidered for comparison purposes. Firstly, the best andworst procurement strategies achieving respectively theminimum and maximum values for the indicator C areexamined. Secondly, the mean electricity price achievedby a perfectly uniform procurement strategy is computed,although this policy is generally not feasible in practicedue to the market resolution dQ . Lastly, the UPE algo-rithm equipped with an ideal forecaster achieving 100%accuracy, i.e. always correctly predicting the trend labelsˆ f t , is considered under the name UPE-F.6 able 1: Hyperparameters used in the simulations. Name Symbol Value
Number of days in input variable P t K k Q N − u − − . u + N L N N D p L − ADAM learning rate l r − Number of epochs n For the reproducibility of the results presented in thissection, Table 1 reveals the hyperparameters used in thesimulations. Additionally, the CAL data exploited are pro-vided by Elexys (Dataset, 2020). In accordance with theperformance assessment methodology, Table 2 presents theresults achieved by both the benchmark (NBEP, EPMA)and proposed (UPE-MA, UPE-DL) procurement strate-gies, together with the reference policies.
Average performance:
Considering only the last line ofTable 2, the two variants of the UPE algorithm outperformboth benchmark procurement strategies on average. More-over, the UPE-MA and UPE-DL algorithms respectivelyperform 0.6% and 1.65% better than a perfectly uniformprocurement strategy (reference policy
Mean ). This indi-cates that the UPE algorithm is able to correctly identifyand exploit certain market phenomena. This also suggeststhat the forecaster F DL outputs more accurate markettrend predictions compared to the more basic forecaster F MA , the accuracy of the forecaster F being defined asthe number of correct predictions f t = ˆ f t over the to-tal number of predictions. This interpretation is backedup by the UPE-F policy which achieves a 100% accuracyand realises even better performance. Although the im-provement in performance achieved by the proposed al-gorithm may appear to be quite limited at first glance,it corresponds to a comfortable annual saving of tens oreven hundreds of thousands of euros for major electricityconsumers/retailers. For instance, the UPE-DL strategyachieves a yearly saving of e Results variance:
As indicated in Table 2, the meanelectricity price significantly varies over the years. There-fore, the variance of the procurement strategy performanceshould be assessed after subtracting this mean electricityprice from the achieved electricity cost C . The resultsvariance substantially differs depending on the procure- ment policy considered. On the one hand, the EPMAstrategy achieves the best results for half of the years in-cluded in the testbench, but totally fails the CAL 2019product due to a flaw in its design. On the other hand,the NBEP strategy is never the best procurement policybut achieves a lower variance without any unforgiving fail-ure. Concerning the UPE algorithm, both variants deliverconsistent results which are at least comparable and gener-ally better than the reference mean electricity price. Thisconsistency throughout the years demonstrates the stabil-ity of the UPE algorithm, this property being defined asthe ability to generate positive results whatever the pricedynamics. The stability of a procurement strategy is par-ticularly important for the electricity procurement prob-lem owing to considerable uncertainty. The non-negligiblevariance observed in Table 2 also highlights the intendeddiversity of the testbench, with multiple market phenom-ena handled better or worse by each procurement policy. Typical execution of the UPE-DL algorithm:
Fig-ures 4 and 5 illustrate the execution of the top-performingUPE-DL procurement strategy for the CAL 2012 product.Firstly, Figure 4 presents the predictions f t outputted bythe forecaster F DL together with the electricity price p t inthe upper plot, and the forecasting errors f t (cid:54) = ˆ f t in thebottom plot. For this particular year, the DL forecastingmodel achieves an encouraging accuracy of approximately80%. Moreover, the predictions do not incorrectly oscil-late between the two market trends during periods of pro-nounced volatility, a behaviour which could significantlyharm the performance of the UPE-DL algorithm. For in-stance, if an important downward trend occurs and if anupward trend is wrongly predicted several times during ashort temporary rebound in prices, some purchase opera-tions may be triggered too early at a higher price. Sec-ondly, Figure 5 depicts the electricity price p t evolutiontogether with the purchase decisions y t = 1 in the up-per plot, and the associated procurement uniformity level u t in the bottom plot. This figure illustrates the abilityof the UPE-DL procurement strategy to delay purchaseoperations when the prices are expected to decrease inthe future, so that they are executed close to local min-ima. Figures 4 and 5 also demonstrate the interpretabilityof the procurement decisions outputted by the UPE-DLalgorithm. This eases the reliability of the procurementstrategy as well as its monitoring by a human supervisor. Sensitivity analysis:
The long-term electricity procure-ment problem depends on the number of purchase oper-ations N to be performed over the procurement horizon,which is constrained due to the market resolution dQ . Fig-ure 6 depicts the sensitivity of the average electricity cost C achieved by each procurement strategy with respect tothis parameter N . Firstly, it can be observed that theUPE-DL algorithm is the leading strategy by a reason-able margin when N >
4. When the number of purchaseoperations is too limited, this is a completely different situ-7 able 2: Comparison of the electricity cost C achieved by the procurement strategies. CAL product Procurement strategies ReferencesNBEP EPMA UPE-MA UPE-DL Min Mean Max UPE-F
Average - - - - - - - - - . . . . . . . C A L p r i ce p t [ E U R / M W h ] CAL price p t Forecast downward trendForecast upward trend - - - - - - - - - Time t . . . . . . . C A L p r i ce p t [ E U R / M W h ] CAL price p t Forecaster F DL error Figure 4: Forecasting model F DL output (top) and forecasting errors (bottom) for the CAL 2012 product. - - - - - - - - - . . . . . . . C A L p r i ce p t [ E U R / M W h ] CAL price p t Purchase action - - - - - - - - - Time t − . − . − . . . T r a d i n g un i f o r m i t y u t Figure 5: Purchase operations executed by the UPE-DL algorithm (top) and procurement uniformity u t (bottom) for the CAL 2012 product. Number of purchase operations N E l ec t r i c i t y c o s t C [ E U R / M W h ] NBEPEPMAUPE-MAUPE-DLMean
Figure 6: Effect of the number of purchase operations N on theelectricity cost C achieved by the procurement strategies on average. ation which should be avoided because the performance ofeach procurement strategy is generally the result of luck.Secondly, the UPE-DL curve is roughly shifted down com-pared to the UPE-MA one, which is once more an indica-tion that the DL forecasting model improves the markettrend predictions. Thirdly, larger values for the parame-ter N may be favoured as both the UPE-MA and UPE-DL algorithms performances stabilise when the numberof purchase operations increases. Regarding the bench-mark procurement strategies, the NBEP one is resilient toa change in the parameter N by design, and its perfor-mance tends toward the mean electricity price when thisparameter increases. On the contrary, the EPMA strategydoes not monitor the number of remaining purchase oper-ations. The policy executes a fixed number of purchaseoperations which is dependent on the number of markettrend inversions, and it executes the remaining purchaseoperations at the end of the procurement horizon. Thismay lead to an unacceptable behaviour for large values ofthe parameter N , especially when the last prices are highcompared to the average energy price.
6. Conclusions
The present scientific research paper proposes a novelalgorithm, named
Uniformity-based Procurement of Elec-tricity (UPE), advising a retailer or a major consumer ofelectricity for its procurement task in forward markets, es-pecially for the CAL product. This algorithm relies ona forecasting mechanism to predict the market trend andon the concept of procurement uniformity, which quanti-fies the deviation from a perfectly uniform reference policypurchasing a tiny amount of energy at each time step overthe entire procurement horizon. Two variants of this algo-rithm were developed depending on the forecasting modelconsidered, respectively UPE-MA for moving averages and UPE-DL for deep learning. On average, both variantssurpass the benchmark procurement strategies, and thetop-performing UPE-DL algorithm achieves a reductionin costs of 1.65% with respect to a perfectly uniform pol-icy achieving the mean price. This represents an averageyearly saving of e x t is not sufficient to accurately explain allthe market phenomena observed in the testbench. Otherinformation such as macroeconomic data, correlated com-modities prices, or news should be factored into the input x t to improve the accuracy of the DL forecaster. Thirdly,the trading risk associated with the long-term electricityprocurement problem should be mathematically defined.Once properly quantified, this risk should be considered inthe objective of the procurement strategies together withcost minimisation. Lastly, novel deep reinforcement learn-ing techniques could be well-suited to solve the complexdecision-making problem behind the long-term electricityprocurement task. This approach should be considered inthe future, drawing on what the article (Th´eate and Ernst,2020) realised for another algorithmic trading problem. Acknowledgments
Thibaut Th´eate is a Research Fellow of the F.R.S.-FNRS, of which he acknowledges its financial support.
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