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Strategies for combined operation of PV/storage systems integrated into electricity markets

2019; Institution of Engineering and Technology; Volume: 14; Issue: 1 Linguagem: Inglês

10.1049/iet-rpg.2019.0375

1752-1424

Thomas Carrière, Christophe Vernay, Sébastien Pitaval, François-Pascal Neirac, Georges Kariniotakis,

Electric Power System Optimization

IET Renewable Power GenerationVolume 14, Issue 1 p. 71-79 Special Section: Medpower 2018 Selected PapersFree Access Strategies for combined operation of PV/storage systems integrated into electricity markets Thomas Carriere, Corresponding Author Thomas Carriere thomas.carriere@mines-paristech.fr orcid.org/0000-0003-3529-6801 MINES ParisTech, PSL University, Centre PERSEE, CS 10207, rue Claude Daunesse, 06904 Sophia Antipolis Cedex, France Third Step Energy, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, FranceSearch for more papers by this authorChristophe Vernay, Christophe Vernay SOLAÏS, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, FranceSearch for more papers by this authorSebastien Pitaval, Sebastien Pitaval Third Step Energy, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, France SOLAÏS, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, FranceSearch for more papers by this authorFrancois-Pascal Neirac, Francois-Pascal Neirac MINES ParisTech, PSL University, Centre PERSEE, CS 10207, rue Claude Daunesse, 06904 Sophia Antipolis Cedex, FranceSearch for more papers by this authorGeorge Kariniotakis, George Kariniotakis MINES ParisTech, PSL University, Centre PERSEE, CS 10207, rue Claude Daunesse, 06904 Sophia Antipolis Cedex, FranceSearch for more papers by this author Thomas Carriere, Corresponding Author Thomas Carriere thomas.carriere@mines-paristech.fr orcid.org/0000-0003-3529-6801 MINES ParisTech, PSL University, Centre PERSEE, CS 10207, rue Claude Daunesse, 06904 Sophia Antipolis Cedex, France Third Step Energy, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, FranceSearch for more papers by this authorChristophe Vernay, Christophe Vernay SOLAÏS, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, FranceSearch for more papers by this authorSebastien Pitaval, Sebastien Pitaval Third Step Energy, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, France SOLAÏS, 55 allée Pierre Ziller, 06560 Sophia Antipolis Cedex, FranceSearch for more papers by this authorFrancois-Pascal Neirac, Francois-Pascal Neirac MINES ParisTech, PSL University, Centre PERSEE, CS 10207, rue Claude Daunesse, 06904 Sophia Antipolis Cedex, FranceSearch for more papers by this authorGeorge Kariniotakis, George Kariniotakis MINES ParisTech, PSL University, Centre PERSEE, CS 10207, rue Claude Daunesse, 06904 Sophia Antipolis Cedex, FranceSearch for more papers by this author First published: 31 May 2019 https://doi.org/10.1049/iet-rpg.2019.0375Citations: 9AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The increasing share of photovoltaic (PV) power in the global energy mix presents a great challenge to power grid operators. In particular, PV power's intermittency can lead to mismatches between energy production and expectation. Battery energy storage systems (BESSs) are often put forward as a good technological solution to these problems, as they can mitigate forecast errors. However, the investment cost of such systems is high, which questions the benefits of using these systems in operational contexts. In this work, we compare several strategies to manage a PV power plant coupled with a BESS in a market environment. They are obtained by stochastic optimisation using a model predictive control approach. This study proposes an approach that takes into account the aging of the BESS, both at the day-ahead level and in the real-time control of the BESS, by modelling the cost associated with BESS usage. As a result, the BESS arbitrates between compensating forecast errors and preserving its own life expectancy, based on both PV production and price scenarios derived from probabilistic forecasts. A sensitivity analysis is also carried out to provide guidelines on the optimal sizing of the BESS capacity, depending on market characteristics and BESS prospective costs. 1 Introduction The significant share of photovoltaic (PV) power employed in several countries poses challenges due to the discrepancies between expected and actual energy production. This is a major issue for transmission system operators (TSOs), which have to ensure that energy production and demand always match. Most countries apply policies whereby the risk is borne by the PV plant operators, which pay the TSO for any discrepancies between their day-ahead forecast production and actual production. Thus, the derivation of optimal bids on a day-ahead electricity market for intermittent energy production resources has been an active field of research in recent years. In [1, 2], the authors proposed different ways of deriving bids using probabilistic forecasts of the production. Bitar et al. [3] developed these ideas and proposed analytical solutions to the optimal bidding problem. However, the revenue of a given producer is still quite sensitive to the uncertainty of the power generation resource, and the financial penalties caused by forecast errors can represent a significant loss for the producer. Battery energy storage system (BESS) units are viewed as a good technical solution to deal with these problems, thanks to their ability to compensate for forecast errors. However, these systems are still costly and their actual financial benefit is difficult to quantify in the long term, which makes PV plant operators reluctant to install them. Thus, it is very important to define strategies that ensure the optimal operation of a PV/BESS system, so that the benefit of installing a storage system is maximised. Two strategies are required: one for the day-ahead level when bids are submitted to the electricity market, and one for the real-time control of the BESS. Several papers propose bidding strategies at the day-ahead level for standalone large-scale BESS [4, 5]. Although they report good performance, the optimal offering strategy is largely dependent on market design. Besides, these authors assume that a BESS can freely charge or discharge on the grid, which is not the case when considering combined PV/BESS. An interesting result from [5] is that maximising the BESS owner's profit results in reduced social welfare, which shows that the price signals do not necessarily work in favour of the grid's operation. In [6], the authors propose a bidding method for a combined wind/hydro plant, but they assume perfect wind forecasts at the operation stage. Bourry et al. [7] also propose a method for a wind/hydro plant for both the day-ahead and operational stages, but they do not attempt to model the market prices because of their high volatility. The standard method for real-time control of PV/BESS is model predictive control (MPC). This consists of optimising the control of the BESS on a receding horizon, of taking into account the forecast future state of the system when optimising the next time step. Different loss functions can be optimised on the receding horizon. In most cases, the optimised function is either the producer's profit [8, 9] or the energy imbalance [10], which is the deviation between the planned schedule and the actual outcome, without considering profit. Some authors also propose an MPC approach to bid on intra-day market sessions [11, 12]. The uncertainty of the upcoming PV production is sometimes included in both the day-ahead planning and the real-time control of the BESS, as in [13, 14] or [15]. Overall, several points are often neglected in the literature. The first is the aging cost of a BESS. This is mentioned in [9], where constraints are defined to improve the life expectancy of the BESS, and in [12] where the MPC loss function is penalised by the total amount of energy flowing in and out of the BESS. At the day-ahead level, He et al. [4] considers aging with a finer modelling. While few papers consider the uncertainty of renewable energy forecasts, the authors of [5, 16] model this uncertainty using production scenarios. We include all of these elements to propose and compare different strategies for controlling a PV/BESS system. These strategies include all of the elements that lacked in the previous approaches. Deterministic forecasts of both day-ahead and balancing prices are performed, along with probabilistic forecasts of the PV power production. In particular, we establish that it is very important to use a representation of the uncertainty based on production scenarios, derived from the forecasts. Using a sequence of forecast distributions fails to account for the temporal correlation of the forecast errors, which is critical to the good operation of a storage system. Also, a model of the cost associated with the BESS aging is implemented to take it into account at both day-ahead and real-time decision levels. Most of the strategies are obtained by stochastic optimisation using an MPC approach, but we also provide analytical solutions after simplifying the bidding problem. The key contributions of the paper are (i) the inclusion of the BESS usage cost as a penalisation of the revenue when proposing bids or managing the BESS in real time; (ii) the derivation of a closed-form analytic solution to the market penalty minimisation problem at the real-time level. This allows us to extend analytic solutions in the literature that provide the optimal bid for RES generation considering a hedging option based on a storage device; (iii) an additional contribution of this paper is the sensitivity analysis performed on the results to evaluate the influence of BESS size and market prices on the relevance of using a PV/BESS. In particular, the optimal sizing of the BESS depending on the control strategy is discussed. We also determine the best strategy depending on market prices, e.g. whether it is better to use a BESS only to compensate the forecast errors, or whether production should also be shifted to times with higher day-ahead prices. The paper is structured as follows: in Section 2, the assumptions we make for modelling the market are presented. Then Sections 3 and 4 present the methods proposed for controlling the PV/BESS at the day-ahead and real-time stages, respectively. Section 5 describes the tools involved in these methods, and Section 6 describes the test case. Section 7 shows the results, while the sensitivity analysis is performed in Section 8. Finally, Section 9 concludes the paper. 2 Market structure In this paper, the market structure we consider comprises two parts: A day-ahead market where all actors can submit buying and selling orders up to 12 AM before the day of delivery. The orders are then aggregated to make supply and demand curves and ultimately derive a day-ahead price for each market time unit. A balancing market where all actors must financially compensate any deviation between the amount of energy sold on the day-ahead market and the actual energy they have produced, i.e. the imbalance. The compensation is derived after the day of delivery. The deviations are compensated with a balancing price which changes for each market time unit. We consider a dual-price market. This means that the balancing prices are different depending on the sign of the imbalance. We note the balancing price for positive imbalances (energy produced higher than energy sold), and the balancing prices for negative imbalances (energy produced lower than energy sold). In such a situation, for a given time step, the revenue R of a producer that sells an amount of energy B (for Bid) but actually produces E writes (1) It is useful to rewrite the revenue as (2) with (3) This formulation is useful because it clearly reflects the way the revenue is calculated. The first term of the equation is the revenue generated from selling the actual energy produced at the day-ahead price. The second term is a penalty term corresponding to the financial compensation of the imbalances. Usually, the balancing prices are defined such that , so that this second term is positive. Finally, to derive the control algorithms, we reformulate by differentiating the part of the production E that comes from the PV panels and the part that comes from the BESS . We also introduce a term , that reflects the costs due to the aging of the BESS when used to deliver the amount of energy . This is obtained with the rainflow counting algorithm [17]. The aging of the BESS can be divided into two components, i.e. cycling aging and calendar aging, which is the degradation caused by time. In the remainder of the paper, we will focus on the cycling aging of the BESS and consider its calendar aging as a given lifetime. The end-of-life of the BESS is thus defined as the minimum lifetime given by the cycling and calendar aging. As an example, if the calendar aging gives a lifetime of 20 years, and the cycling aging a lifetime of 50 years, we consider that the actual lifetime of the BESS is 20 years (as opposed to considering that the cycling aging adds up to the 20 years given as the calendar lifetime). We penalise the revenue with the cost associated with the life-loss of the BESS. Note that the penalised revenue is not an actual cash flow, and that the cost associated with the life-loss is only here to make the control of the BESS more conservative regarding the lifetime. The penalised revenue then writes (4) 3 Day-ahead offering strategy Different algorithms are required for day-ahead bidding of the PV/BESS, and for real-time control of the system. The aim of the first control algorithm is to provide the bids of the combined PV/BESS for the forthcoming day. We propose a first benchmark where the BESS is not used at the day-ahead level, and a second where the BESS is taken into account along with its usage cost. In all the proposed algorithms, the PV/BESS is considered a price-taker. This means that we assume that the PV/BESS bids do not influence the day-ahead price. This hypothesis seems reasonable since the generation of the PV/BESS is low compared to the typical volume of energy exchanged on electricity markets. However, the number of participants with uncertain production, usually having a price taker behaviour, increases in electricity markets. Thus, the influence they have on the day-ahead prices becomes more and more significant. For the sake of simplicity, we do not model this influence in this paper. 3.1 Benchmark: no BESS in the day-ahead planning For the benchmark, we do not use the BESS at the day-ahead level, and thus, all the terms related to the BESS are ignored. To derive the optimal bids , we must then solve (5) where N is the number of market time units in a day. In these conditions, it has been proven that the optimal bids that minimise the penalties for the producer are given by [1] (6) where is a forecast cumulative distribution function (CDF) of the energy production of the plant for the ith market time unit. The application of this strategy for a PV power plant thus requires a probabilistic PV power forecasting model, and a forecasting model of the day-ahead and regulation prices. This benchmark strategy is referred to as strategy DA0 in the remainder of the paper. 3.2 Optimal bidding using the BESS When the BESS is used at both the day-ahead and real-time levels, then the entire formulation of the revenue from (4) is optimised. Once again, we separate the bids into one part accompanied by uncertainty from the PV plant , and the output from the battery . Since the BESS is controllable, we assume that the actual output of the BESS is equal to the amount bid . With these assumptions, the optimisation problem that needs to be solved to derive the optimal bids is (7) However, to ensure that we can assume that , and to correctly simulate the operation of a BESS, we must add several constraints. To define the constraints, we note as SOC (for state of charge) the amount of energy in the battery at a given time step, relative to its full capacity Cap. (8) (9) (10) The first constraint ensures that the energy in the BESS is never lower than 0 or higher than the capacity of the battery, taking into account the charge and discharge rates of the BESS, respectively, and . The second constraint ensures that the BESS can only be charged from the PV plant, and not from the grid. Finally, the third constraint is a limitation on the power rating of the BESS, defined by the parameter K. This strategy again requires probabilistic forecasts of the upcoming PV power production and forecasts of the day-ahead and balancing prices. In the remainder of the paper, this is referred to as strategy DA1. 4 Real-time control In real-time control of the PV/BESS, the algorithms are different. Since we are now in real time, the day-ahead prices and energy sold on the electricity market are known, and the only sources of uncertainty come from the PV power generation and balancing prices. Along with the benchmark strategy, which is not to use the BESS at all, we define two additional real-time control strategies. The first one is purely analytical and tries to minimise the penalties for the next market time unit, without taking into account the BESS aging cost or the near future after the next market time unit. In contrast, the second strategy takes all of these factors into account. 4.1 First strategy The first algorithm minimises the term arising from imbalances between the bids and PV/BESS production. Since we are in real time, the bids have already been submitted and the market has been cleared. Thus, the day-ahead prices are known and the only design variable is the BESS output . The BESS is allowed to deviate from its planning to compensate deviations coming from the PV power forecast error. Thus we do not necessarily have anymore. At this stage, the only design variable is the amount of energy we charge or discharge from the BESS . In this case, we can write the real-time revenue as a function of only and get (11) For the first method, we focus on reducing the penalties, so we neglect the term and the BESS usage costs . The first neglected term represents a profit that can be obtained from the difference in day-ahead prices during the day. However, this profit was supposed to have already been realised at the day-ahead level. Besides, the profit alternates between positive and negative values depending on the charge or discharge of the BESS. Its impact should thus be reduced when summed over several time steps. On the other hand, the penalty term is always positive. Finally, neglecting the BESS usage costs allows us to propose a closed-form solution to the revenue maximisation problem. The expectation of the penalty term Pen for the next time step writes (12) where is the maximum amount of energy that the plant can produce on a given time step, and is the probability distribution function (PDF) of the PV power. Since is dependent on the sign of the imbalance, the expectation of the penalty term must be rewritten (13) Usually, the prices are defined so that imbalances that support the grid imbalance at the national level are not penalised. That is (14) (15) We assume that we have an estimation of the probability for the grid to fall short on the national level. We can then substitute the forecast regulation prices with random variables modelled by a sum of Dirac distributions (16) (17) which gives (18) Using the variable change , we get (19) Finally, using the Leibniz rule for differentiating under the integral sign, we obtain (20) The second derivative is (21) This second derivative is always positive by definition of the regulation prices. Thus, by making the first derivative equal to 0, we find the minimum (22) The first method is then to compute a forecast distribution of the PV power, deterministic forecasts of the regulation prices, and the probability that the system will fall short, and to inject them into this optimal solution. Although the solution is in a closed form, the BESS constraints prevent the use of this solution more than a one-time step ahead, and the BESS usage cost is neglected. This is referred to hereafter as the RT1 method. 4.2 Second strategy The second method is very similar to the offering strategy including the BESS from Section 3.2. However it is performed using an MPC approach, to adapt it to the real time. This means that the whole revenue formulation is maximised over the next time steps, then the result of the optimisation from the first time step is used as the command for the BESS for the next market time unit. This allows us to take into account the future forecast state of the system in real-time control. Since we are in a real-time setting, the day-ahead prices and bids are known, as for the first real-time strategy. As a result, the only design variable is the BESS command. Therefore, the optimisation problem to solve for each time step is (23) (24) subject to the same constraints as in Section 3.2. We also add the constraint that the day-ahead BESS schedule must remain feasible over the next time steps after the operation of the BESS, which translates by (25) We change at each time step, depending on the time of day, so that all of the remaining days is included in the optimisation. This is especially important because day-ahead planning often results in full discharge of the BESS in the evening when day-ahead prices are usually high due to high demand. As such, the whole day must be included in the optimisation loop. If is too low, the BESS could discharge itself entirely during the day to compensate forecast errors, and thus be unable to provide the energy in the evening. This second method is referred to as RT2. 5 Forecasting and optimisation tools To implement these different algorithms, several supplementary models are required. They are presented in this section. 5.1 Probabilistic forecasts for PV production One of the most important models required is the PV power forecast model. All approaches require probabilistic forecasts of PV power production. The model we implemented is based on the Analog Ensemble (AnEn) proposed in [18]. We extended it in several ways to improve its performance and allow it to produce reliable forecasts for both short-term and long-term forecasts, and with different time resolutions. The main extensions are The inclusion of different data sources such as measurements and satellite data, in addition to Numerical Weather Predictions (NWPs) that are the only data source in the original model. A dynamic algorithm to compute the relevance of each source of data depends on the forecast start time and horizon, so that the weight of the different sources varies over time. For example, the forecasts rely much more on measurements for forecasts with horizons under 1 h, or on NWPs for day-ahead forecasts. This model is well suited to control algorithms, since it can provide forecasts with both high resolutions (up to 1 min) for real-time control strategies, and long horizons (up to 48 h) for day-ahead planning algorithms. 5.2 Market quantity forecasts Day-ahead planning algorithms require forecasts of both day-ahead and balancing prices. Real-time control algorithms also require forecasts of balancing prices. Day-ahead prices are obtained with a Support Vector Regression (SVR) model, which is commonly used for energy price forecasting [19]. The inputs of the regression are the forecasts of national demand and renewable energy generation for the next day, along with the month and day of the week. In the next step, the balancing price forecasts are obtained by applying the k-nearest neighbour (k-NN) methodology to the day-ahead price. In real time, since the day-ahead prices are known, the k-NN model is applied again using the actual day-ahead prices to update the balancing price forecasts. 5.3 Optimiser To solve the different optimisation problems that appear in the control algorithms, we decide to employ stochastic optimisation, since we have already disposed of probabilistic forecasts of the PV power generation. A large number of PV production scenarios are generated following [20]. The scenarios are then reduced using a Partitioning Around Medoids (PAM) algorithm, and the median of the objective over the scenarios is optimised. The resulting non-linear optimisation problem is solved using the COBYLA algorithm [21]. The PAM algorithm reduces the scenarios by partitioning the whole set of scenarios in a fixed number of classes k. The algorithm can be summarised as follows: Compute the distance between each pair of scenarios. In this paper, we used the sum of the Euclidean distances between the realisations as the distance. In other words, given two scenarios and , the distance between the scenarios is given by . Find k scenarios that are representative of the whole scenarios, called medoids. To do so, the sum of the distances between each scenario and its closest medoid is minimised using a heuristic optimisation algorithm. Associate each scenario to its closest medoid. Then, the medoids are used as probable scenarios, and the probability of each medoid is estimated by the number of scenarios populating this medoid's class compared to the total number of scenarios. We considered it important to use scenarios to represent the uncertainty because of the temporal dimension of the PV/BESS management problem. This temporal dimension can be seen from the second constraint formulated in (9). One of the essential characteristics of PV power forecasts is the positive correlation between the forecast errors at consecutive time steps. In other words, if a forecast error is positive (resp. negative) for a given time step, the forecast error for the following time step is also likely to be positive (resp. negative). This is a problem for BESSs, because since a BESS can compensate forecast errors, a significant error present on several consecutive time steps would quickly either charge the BESS to its maximum or discharge it to its minimum, depending on the sign of the error. Due to the temporal correlation of the errors, this worst-case scenario is much more likely than the consecutive distributions might suggest if they were considered independent. During the simulation, the energy remaining in the BESS is tracked to ensure that the second constraint from (9) is respected. 6 Test case A simulation of the control of the PV/BESS has been performed for four months (January to May 2017) for a large PV plant located in France. The plant is situated at longitude −0.9223889, latitude 44.19025 with an elevation of 72 m above sea level, and has an installed power of 9828 kWp. The entire control is carried out taking an MPC approach. For each time step, the PV power and market quantity forecasts were updated based on the inputs known at the time. Then, if the day-ahead market closes for the considered time step, bids are submitted for the next day using one of the two methods from Section 3. The control set-point for the next time step is obtained using one of the two methods from Section 4. Then, the process goes to the next time step, updates the BESS SOC, the PV power, and market quantities forecast, and continues the algorithm until the final time step. A flowchart of the algorithm is represented in Fig. 1. Fig. 1Open in figure viewerPowerPoint Flowchart of the overall optimisation approach The NWPs required for the AnEn model are obtained from the European Center for Medium-range Weather Forecasting (ECMWF), along with measurements and satellite data to improve short-term forecasts. Forecasts of the national demand and renewable energy generation required for the day-ahead price forecasts are provided by RTE, the French Transmission System Operator (TSO). The BESS considered in the test case is a lithium-ion storage system. Aging parameters for the rainflow counting algorithm are taken from [22, 23]. Regarding costs, prospective values for the year 2030 from [23] are used in the base case, that is a 200 €/kWh investment cost. Besides, in all simulations, we set the parameter K, which controls the power rating of the BESS so that the BESS can fully charge or discharge in 2 h. This is to simulate a BESS with a power rating of 0.5 C, which is common in commercial lithium-ion storage systems. The simulation is performed on the software R, using the packages e1071 [24] for the SVR model and nloptr [25] for the implementation of the COBYLA algorithm. Different combinations of day-ahead and real-time methods are evaluated. The sensitivity of the results to the installed capacity of the BESS and its investment costs is studied, providing guidelines on the sizing of the BESS for such applications. The different method combinations tested are summarised in Table 1. Table 1. Evaluated strategies Strategy DA bidding RT control S0 (benchmark) DA0 RT0 S1 DA0 RT1 S2 DA0 RT2 S3 DA1 RT1 S4 DA1 RT2 An example of the typical output from the four strategies is represented in Fig. 2. We can see that strategies S1 and S2 focus only on reducing the imbalance. Strategy S3 tends to reduce the imbalance but also shifts the production to benefit from high prices in the evening. Finally, strategy S4 spends most of the day charging the BESS and then e