Risk-averse stochastic model predictive control-based real-time operation method for a wind energy generation system supported by a pumped hydro storage unit
Introduction
The penetration of wind energy has increased rapidly in the last decades worldwide. Environmental concerns along with decreasing capital costs, low operation costs, and improvements in turbine efficiencies constitute the driving forces behind this growth. In addition, there are currently incentives in many countries for supporting renewable sources. Energy is bought at a constant tariff rate ignoring variations in production. However, such subsidies are valid for a limited period after which generation companies are expected to join deregulated markets. The intermittent nature of wind makes energy trading in the market environment a difficult task.
The problem faced by wind energy producers can be understood by investigating the operation principles of the market. Consider a company participating in a day-ahead market and compensating its deviations in a real-time balancing market. The associated timing diagram is depicted in Fig. 1. As can be observed from the figure, the market trading can be separated into two phases. In the first phase, which is day-ahead bidding, the company is required to submit its production offers for each hour of the next day (day D) at the gate closure time in day D-1. These contracts are to be made under uncertainty, as the wind production that will occur in the future cannot be predicted perfectly, and energy prices, which are determined after the market clearing, are not known. In the second phase, which is real-time operation, the company should decide on how much energy to supply at each hour. If there are discrepancies between the supplied energy and the production contracts determined during the day-ahead bidding stage, they are compensated in the balancing market. These deviations could lead to significant economic losses because in the balancing market, the buying price is higher and the selling price is lower than the day-ahead market price.
As can be inferred from the preceding discussion, appropriate bidding and real-time operation algorithms should be devised in order to maximize profits of wind producers by avoiding imbalances as much as possible. There are several studies in this direction, a review of which is given below.
The simplest approach to the day-ahead bidding problem is to compute point forecasts of wind generation and submit them as production contracts. The success of this method depends on the accuracy of the predictions. There is a rich literature on wind forecasting [1], [2]. The proposed methods range from primitive persistence forecasts to more advanced techniques such as autoregressive integrated moving average-based time-series methods [3], artificial neural networks [4], and numerical weather prediction models [5]. However, there is a limit on the accuracy of these tools [6]. Although improvements have been achieved over time, according to recent figures, the estimation errors of the state of art methods are no less than 10% for day-ahead timescales [1], [7].
Another idea is to make use of probabilistic methods [8]. Instead of point forecasts, the probability distribution of uncertainty, such as the Weibull distribution [9], can be employed to formulate the bidding as an expectation maximization problem. For simple systems only composed of wind farms, analytical solutions that provide optimal contracts can be found [10], [11], [12]. However, with the involvement of energy storage or some other aspects such as risk control, deriving explicit formulas becomes a challenging task if not impossible. Stochastic programming methods, which converts the bidding problem into a numerical optimization by approximating uncertainties with scenario trees, constitute a remedy to this difficulty [13]. This approach was used for bidding of price taker wind energy companies [14], [15], [16], [17], wind farms supported by Pumped Hydro Storage (PHS) plants or hydro reservoirs [18], [19], [20], [21], and standalone PHS systems [22]. Moreover, in [23], a system having multiple wind farms and battery storage units was investigated taking into account transmission network constraints. All these studies agree on the improvements that can be achieved using a stochastic approach instead of a deterministic method based on point forecasts. This gain is referred to as the value of the stochastic solution.
Although maximizing the expected profit is a desirable target, companies are usually sensitive to risks encountered due to contingencies. They want to avoid the worst-case low probability scenarios that can lead to significant losses in case such events occur. With this in mind, a stochastic programming-based risk-averse bidding strategy for a wind energy producer was developed in [15]. Conditional Value at Risk (CVaR) was chosen as the risk measure, which was optimized in conjunction with the expected profit. Later, this idea was applied to wind–hydro systems and virtual power plants [24], [25], [26], [27].
In contrast to day-ahead bidding, real-time operation is a dynamic decision-making problem [28]. The company should make a decision on the amount of energy to supply to the grid at each hour based on new information available. If the only source is wind, not much can be done because the production is determined by weather conditions. On the other hand, if the system is supported by a storage unit, this unit can be used to adjust the energy injected into the grid by storing and supplying it when deemed necessary. At this stage, the decision maker has a certain advantage compared to the day-ahead bidding because new information on wind measurements is available. This leads to a substantial reduction in wind uncertainty as can be observed from Fig. 1. Moreover, the amount of stored energy can be measured in case there is a storage device and the spot market prices are known along with the accepted bids. All this information can be used to make more informed decisions.
Until recently, the real-time operation problem had not drawn enough attention. Most of the works concentrated on the bidding phase without considering this aspect rigorously. The underlying stochastic optimal control problem was either ignored completely or simple heuristics were employed. For example in [29], [30], [31], [32], a schedule, determined at the beginning of the operation, was applied without considering the actual realization of random data. This is an open-loop strategy, which is blind to available information and expectedly leads to suboptimal results. In [33], a ratio-based heuristic, which computes the ratios of certain variables before the start of operation, was developed. In real-time, decisions are made such that these ratios are preserved based on the wind energy realization. Finally, a popular heuristic employed in [34], [35], which will be referred to as bid-following heuristic in this work, tried to minimize the imbalances instantaneously with the help of a storage device without considering the economic benefits of using the available energy in the succeeding hours.
In recent years, a number of works that focus on the real-time operation more systematically have appeared. In most of them, Deterministic Model Predictive Control (DMPC)-based strategies are used to deal with imbalances [36], [37], [38], [39], [40], [41]. The underlying algorithm is a rolling horizon method in which an optimization problem depending on point forecasts of random variables is solved repeatedly. The real-time performance can be improved significantly as a result of the certainty gain arising from the repeated computation (recall Fig. 1). These studies mainly differ in the energy generation and storage technologies utilized. Apart from this, although real-time operation decisions and their consequences depend on the bidding strategy, this aspect was not elaborated in all of the works. In some of them, the bidding stage is ignored completely [40], [41] while in others, primitive approaches such as point forecast-based deterministic algorithms were utilized [36], [38], [42]. Another aspect, which was not treated well, is imbalance costs. Except for [37], in bidding and/or operation phases, either these losses were not taken into account or simply deviations from the contracts are penalized instead of incorporating the actual price paid in the balancing market into the objective.
The DMPC approach benefits from certainty gain with updated computations but it does not exploit probability distribution of uncertainties. Moreover, it is not amenable to incorporating a risk control because of the deterministic formulation. Similar to stochastic programming-based methods proposed for the bidding problem, one may naturally think about making use of the uncertainty information to compute better decisions and bring the risk control into the operation phase. To the best of our knowledge, there are just two works along these lines. In [43], a risk-neutral Stochastic Model Predictive Control (SMPC) method for the real-time operation of a system composed of a wind farm and a PHS unit was introduced. The other work used linear decision rules to obtain risk-averse bidding and operation strategies for a wind energy producer having a generic storage device [44].
We developed an integrated strategy for day-ahead market bidding and real-time operation of a wind energy producer supported by a PHS system. The real-time operation in the balancing market is based on an SMPC algorithm while the bidding is formulated as a Mixed-Integer Linear Programming (MILP)-based stochastic program. In both phases, random information is modeled as scenario trees, imbalance costs are considered realistically, and risk aversion based on CVaR measure is a part of the objective. Compared to previous works employing the DMPC approach, the distinguishing aspect of the proposed method is the incorporation of uncertainty information and risk control into real-time operation computations. The proposed algorithm differs from the other stochastic operation methods proposed in [43], [44] in that the former does not consider risk control while the latter is based on a completely different technique and uses a different type of storage unit. Moreover, the mathematical model utilized in this study involves several characteristics of a PHS plant, which were not taken into account completely in previous works.
The majority of studies on renewable generation supported with energy storage systems are just based on the stochastic programming solutions of the bidding phase [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]. However, the actual performance achieved is determined by the outcomes of the real-time operation. With this in mind, we investigated the gap between the profits given by bidding and operation-based analyses in order to demonstrate how important the latter is for a realistic evaluation of the actual performance. As far as we know, this analysis has not been previously performed.
Different real-time operation methods from the literature were implemented along with the proposed SMPC algorithm and their performances were compared. To be more specific, first, daily operation schedules of the algorithms were analyzed. Second, because the problem studied has two conflicting objectives of expectation maximization and risk aversion, Pareto optimality of the methods relative to each other was investigated. Finally, long-term simulations were performed to compare the economic benefits of the strategies considered in a more general setting under changing imbalance market conditions.
All analyses were carried out for a realistic case study, which consists of a wind energy generation system and a PHS unit. The former is an existing collection of wind farms located in İzmir, Turkey. The latter, on the other hand, is a closed-loop plant near the wind farms, which does not exist yet but a feasibility analysis was carried out by the government and it can be constructed in the near future.
The paper is organized as follows. The wind–PHS system considered is introduced in Section 2. The proposed approach for day-ahead bidding and real-time operation is explained in Section 3. The compared algorithms are briefly described in Section 4. In Section 5, the case study is described and the simulation results are presented and analyzed. Possible applications of the proposed method to other real-world scenarios are discussed in Section 6. Finally, the main outcomes of this work are summarized in Section 7.
Section snippets
System description
In general, the system investigated is composed of a number of Wind Power Plants (WPPs) and a PHS plant as illustrated in Fig. 2. The payment received from () or made to () the day-ahead market at time is . The deviation of the supply from the contract, , is compensated in the balancing market at the cost of
In the imbalance cost equation above, we used a penalty formulation similar to the one presented in [45]
Proposed approach
An overall block diagram of the proposed approach is depicted in Fig. 3. It can be observed that at day D-1, energy contracts for the next day are computed based on the wind power () and day-ahead price () forecast scenarios. Throughout the day D, the SMPC algorithm controls the system by producing pumping ( and generation () decisions. The decisions are computed at each hour making use of the day-ahead bids determined (), announced market prices (), balancing market price ratios,
Algorithm comparison
The methods that are compared to the proposed SMPC approach are bid-following heuristic, open-loop algorithm, ratio-based heuristic, and DMPC method, which were discussed in Section 1.2. In addition, another alternative, i.e., perfect information solution, is also considered. This is the solution of the open-loop algorithm in which the actual wind realization is used as the forecast. It cannot be implemented in practice because the future wind production cannot be predicted perfectly but it
Case study
The system investigated is located in Turkey and comprises two wind farms and a PHS plant as depicted in Fig. 6. WPPs, namely Soma and Sayalar, are operated by the same company, and approximately 20 km apart. Due to the close proximity, they experience very similar weather conditions. Soma WPP has a total installed capacity of 240.1 MW provided by 169 Enercon turbines while Sayalar WPP has 48 Enercon turbines with a total capacity of 57.2 MW, the combined capacity being 297.3 MW.
Currently,
Extensions to real-world cases and other applications
The approach proposed in this work is not limited to the case study considered. In a similar manner, it can be adapted to systems composed of other storage and renewable generation technologies as well. This requires changing the associated equations employed in the bidding and operation models. We believe that as long as the optimization problem is tractable, the algorithm will exhibit a similar behavior and perform better compared to the alternative operation strategies investigated.
In the
Conclusion
In this paper, a new method is proposed for risk-averse day-ahead bidding and real-time operation of a wind energy generation system equipped with a PHS plant. The performances of the proposed approach and a number of real-time operation methods from the literature were compared. In addition, the validity of performance estimates provided by bidding computations was investigated. The conclusions are as follows:
- (1)
The proposed SMPC approach exhibited the best performance, followed by DMPC,
Acknowledgments
We would like to thank the editors and referees for their comments and suggestions, which helped us to improve the manuscript.
Funding
This work was supported by The Scientific and Technological Research Council of Turkey [BIDEB-2211].
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