Research Article  Open Access
Yuwei Wang, Huiru Zhao, Peng Li, "Optimal Offering and Operating Strategies for WindStorage System Participating in Spot Electricity Markets with Progressive StochasticRobust Hybrid Optimization Model Series", Mathematical Problems in Engineering, vol. 2019, Article ID 2142050, 19 pages, 2019. https://doi.org/10.1155/2019/2142050
Optimal Offering and Operating Strategies for WindStorage System Participating in Spot Electricity Markets with Progressive StochasticRobust Hybrid Optimization Model Series
Abstract
With the increase of wind power installed capacity and the development of energy storage technologies, it is gradually accepted that integrating wind farms with energy storage devices to participate in spot electricity market (EM) is a promising way for improving wind power uncertainty accommodation and bringing considerable profit. Hence, research on reasonable offering and operating strategies for integrated wind farmenergy storage system (WFESS) under spot EM circumstances has important theoretical and practical significance. In this paper, a newly progressive stochasticrobust hybrid optimization model series is proposed for yielding such strategies. In the dayahead stage, dayahead and balancing prices uncertainties are formulated by applying joint stochastic scenarios, and realtime available wind power uncertainties are modeled by using the seasonal autoregression (AR) based dynamic uncertainty set. Then, the first model of this model series is established and utilized for cooptimizing both the dayahead offering and nominal realtime operating strategies. In the balancing stages, wind power uncertainty set and balancing prices stochastic scenarios are dynamically updated with the newly realized data. Then, each model from the remaining of this model series is established and utilized period by period for obtaining the optimal balancing/realtime offering/operating strategies adjusted from the nominal ones. Robust optimization (RO) in this progressive framework makes the operation of WFESS dynamically accommodate wind power uncertainties while maintaining relatively low computational complexity. Stochastic optimization (SO) in this progressive framework makes the WFESS avoid pursuing profit maximization strictly under the worstcase scenarios of prices uncertainties. Moreover, by adding a riskaversion term in form of conditional value at risk (CVaR) into the objective functions of this model series, the optimization models additionally provide flexibility in reaching a tradeoff between profit maximization and risk management. Simulation and profit comparisons with other existing methods validate the scientificity, feasibility, and effectiveness of applying our proposed model series.
1. Introduction
Nowadays, wind power has experienced a dramatic increase of installed capacity [1]. Participating in spot electricity markets (EMs) is considered by many researchers as a promising way for integrating wind power into power system [1, 2]. Owning to its unpredictable and stochastic natures, other controllable generators or flexible demand resources must be redispatched by system operator for balancing the deviations of wind farms’ (WFs) realtime power outputs from their aforehand scheduled ones, which causes substantial balancing costs [3]. Moreover, WFs should suffer financial loss for their power output deviations because they should buy or sell up/downregulations in balancing market. Fortunately, with the development of energy storage and newly energy conversion technologies such as batteries [4], flywheels [5], hydro pumped storage [6], and fuel cell facilities [7, 8], it is gradually accepted that WFs should be integrated into hybrid energy systems containing energy storage and/or newly energy conversion sources [9]. Taking the integrated wind farmenergy storage system (WFESS) as representative, due to the flexible charging and discharging capabilities of energy storage, WFESS has two potentials when participating in spot EMs. One is to internally accommodate wind power uncertainties (power compensation), and the other is to strategically offer its integrated power outputs according to forecasted price differences at different market stages and time units (arbitrage). However, exploiting the above potentials urgently requires reasonable offering and operating strategies. Therefore, studies on such strategies for an integrated WFESS participating in spot EMs have received more and more attentions from both the industry and academia.
It should be noted that spot EM clearing prices and realtime available wind power outputs are usually uncertain for a WFESS (or other hybrid energy systems integrated with WF, etc.) at the time to make its offering and/or operating decisions. Reference [10] proposed an optimal operation model for a fuel cellwind turbine hybrid system by applying a new extremum seeking control algorithm. Authors in [11] investigated the operation of a photovoltaicwindfuel cell hybrid system based on the simulated method performed in the HOMER software, in which the technical and economic feasibilities of this hybrid system have been numerically validated. However, uncertainties are not mathematically considered in [10, 11]. In [12], a twostage optimization approach was applied for dayahead and realtime scheduling of a hybrid power system consisting of WFs and batteries, etc. In the dayahead stage, genetic algorithm based scheduling strategy was proposed for obtaining the “bestfit” dayahead schedules. In the realtime stage, a probabilistic optimal power flow model was constructed for accommodating wind power uncertainties based on wind power stochastic scenarios. Authors in [13] established a mixed integer linear stochastic optimization (SO) model for cooptimizing offering strategies of windthermalpumped storage system in energy and regulation markets, where uncertainties include wind power, dayahead clearing prices, and regulation deployments. Reference [14] presented a multistage SO model to find the optimal offering and operating strategy of a WFESS in the dayahead, intraday, and secondary reserve markets while taking into account uncertainties in wind power generation and EM clearing prices. Reference [15] added a riskaversion term in form of conditional value at risk (CVaR) in SO based model to additionally provide flexibility in finding a tradeoff between profit maximization and risk management of WFESS operation under EM circumstances. In [16], machine learning was leveraged to define scenarios; then a twostage convex SO model was formulated for WFESS to participate in pool market. Reference [17] introduced the demand response (DR) for integration with WFESS, and a SO based dayahead offering decisionmaking model was proposed for this DRWFESS. Reference [18] integrated wind turbines, natural gas unit, energy storage, etc. as an energy hub (EH) and proposed a SO based dayahead bidding decisionmaking model for this EH considering clearing prices and wind power uncertainties. Reference [19] proposed a multiobjective SO based dispatch model for optimizing total system losses and operating cost for a wind, PV, and storage integrated hybrid energy system. Via using SO related approaches, joint energy and reserve market clearing mechanisms were presented in [20–22] with the consideration of renewable power uncertainties.
In addition to the SO based approaches, robust optimization (RO) methods are also applied by many researchers in obtaining the optimal offering and/or operating strategies for a WFESS (or other hybrid energy systems integrated with WF and ESS, etc.). Reference [23] proposed an adaptive robust selfscheduling model for a WF paired with a compressed air energy storage system to participate in the dayahead EM, given the inherent uncertainties in EM clearing prices and available wind power output. In [24], a robust securityconstrained unit commitment model is established for a wind–thermal–hydro system with energy storage, in which uncertainty sets are used to characterize the uncertainty of wind power outputs. Authors in [25] developed a RO based model predictive control (RMPC) scheme to determine the optimal offering and operating strategies of a WFESS participating in multistage spot EMs, given the uncertainty set in spot EM prices. Considering multiple uncertainties such as wind power, a multiintervaluncertainty constrained RO model was established in [26] to yield the optimal dayahead offering and dispatching strategy for an AC/DC microgrid containing wind turbines, energy storage devices, etc. Reference [27] aggregated the wind and photovoltaic generation, thermal and electrochemical storage devices at the residential level, and proposed a RO based model for this aggregator to participate in dayahead market. Reference [28] integrated wind turbines, electrical energy storage, etc. into a community energy system (ICES) and proposed a RO based dayahead scheduling model for this ICES in a joint energy and ancillary service market. Combined with an interval forecasting method for depicting wind power and clearing prices uncertainties, a RO based model was proposed in [29] to obtain the optimal offering and operating strategies of a WFESS participating in dayahead EM.
In summary, SO and RO are popular approaches to address WFESS’s offering and operating decisionmaking problems nowadays. In those SO related methodologies ([13–22], etc.), uncertainties are forecasted and formulated by applying multiple stochastic scenarios. In those RO related methodologies ([23–29], etc.), uncertainties are forecasted and formulated by using interval based uncertainty set. WFESS’s potentials for power compensation and arbitrage can be exploited to some extent due to the market fluctuations and power intermittences reflected in corresponding scenarios and uncertainty sets. However, with regard to the SO models, the computational complexity increases significantly with the introduction of multiple stochastic scenarios which make the number of WFESS’s operational constraints increase accordingly. With regard to the RO models, although the computational complexity is relatively low due to the actual consideration of the “worst point” in uncertainty set affecting WFESS’s profit, it often results in over conservativeness (obtained offering and/or operating strategies with relatively low economic efficiency) because the “good opportunities” in uncertainty set for bringing higher profits are ignored. More intuitive and specific presentations for the urgent competitive characteristics of the above reviewed researches are reflected in Table 1.

Moreover, as mentioned in [30, 31], another critical factor impacting the performance of a general RO based model is the structure of the uncertainty set. According to the definition and classification standards in [31], uncertainty sets proposed in [23–29] can be regarded as static ones which usually result in the overly conservative solutions. That is because in a static uncertainty set, on one hand, value interval of every uncertain parameter within every time unit can hardly be dynamically updated as time goes by and, on the other hand, correlations among different time units and/or different uncertain parameters are not systematically represented [30].
Since both the SO and RO methods have their own disadvantages mentioned above, a natural idea is that it may be possible to combine SO with RO to make the hybrid method further improve the optimization effect. Moreover, authors in [30] have proposed that realtime available wind or solar power outputs present significant temporal correlations. Hence, uncertainties of realtime available wind power outputs forecasted by using newly updated information would gradually weaken as time approaching. That is to say progressively making WFESS’s offering and operating decisions in multistage spot EMs can dynamically take advantage of newly added data so as to make the WFESS pursue more profit.
Therefore, in this paper, by taking a “price taker” WFESS participating in dayahead and balancing EMs [15] as representative, a newly progressive stochasticrobust hybrid optimization model series is proposed to obtain the WFESS’s offering and operating strategies in multistage spot EMs. Different from most existed models, the main novelties of this paper can be summarized as follows.(1)Every model in our model series has the mathematical characteristics of stochasticrobust hybrid optimization structure. SO is mainly reflected in that the objective function (pursuing profit maximization) is constructed according to the joint stochastic scenarios of dayahead and/or balancing clearing prices; RO is mainly reflected in that all constraints must be satisfied when the “worst point” of wind power uncertainties affecting the operation of WFESS occurs.(2)In every model of our model series, since all operational constraints of WFESS are not directly affected by price scenarios, the computational complexity of our models is greatly reduced compared to the SO based models.(3)In every model of our model series, since all operational constraints of WFESS must be satisfied under the “worst point” of wind power uncertainties, the internal power compensation potential of WFESS is fully exploited.(4)In every model of our model series, since the objective function is not directly affected by wind power uncertainties, WFESS does not need to make offering and/or operating decisions when the “worst point” of wind power uncertainties affecting WFESS’s profit occurs, which greatly reduces the conservativeness of decisionmaking compared to the RO based models.(5)In every model of our model series, since the objective function only contains the price stochastic parameters, the arbitrage potential of WFESS to pursue profit maximization based on forecasted price signals from multistage spot EMs is fully reflected.(6)Our proposed model series can be divided into two progressive parts. The first part models the WFESS’s dayahead offering decisionmaking problem, and the second part consists of the balancing/realtime offering/operating decisionmaking models corresponding to balancing market stages throughout the whole delivery day. By progressively implementing our model series, both of the price stochastic scenarios and dynamic wind power uncertainty set are dynamically updated due to the new data, thus reducing the uncertainties of price and wind power and their impact on decisionmakings.(7)By adding a riskaversion term in form of conditional value at risk (CVaR) into the objective functions of this model series, the optimization models additionally provide flexibility in reaching a tradeoff between profit maximization and risk management.
Accordingly, in addition to directly provide an efficient and feasible decisionmaking tool for WFESS operating and participating in spot EM circumstances, the contributions of this paper are mainly reflected in those abovementioned novelties which further expand the operation optimization theories of hybrid energy systems.
The rest of this paper is organized as follows: in Section 2, WFESS’s offering and operating process based on our proposed progressive optimization frame work is concretely introduced. Section 3 formulates the dayahead offering decisionmaking model and balancing/realtime offering/operating decisionmaking models for WFESS through using our proposed progressive stochasticrobust hybrid optimization model series. Simulation and model comparisons are implemented in Section 4 for verifying the feasibility and rationality of our method, and Section 5 concludes the paper.
2. WFESS’s Offering and Operating Process Based on Progressive DecisionMaking Framework
2.1. Imbalance Management in Electricity Market
Generally speaking, due to the small trading amount in intraday markets, deregulated spot EMs can be typically assumed as consisting of dayahead and balancing market stages [15]. Participants are permitted to bid for their generation schedules of the whole time horizon of the next day (delivery day) in the dayahead EM which is cleared 10 to 12 hours prior to the start of the delivery day. If a stochastic generator is integrated in a participant, realtime deviations from this participant’s dayahead scheduled power outputs are often inevitable and must be settled in the balancing market. For example, the WFESS should buy or sell up/downregulation services for its negative or positive deviations, respectively, in balancing markets if the WF’s realtime power deviations cannot be fully compensated by ESS. In some EMs like Dutch APX, balancing prices for up and downregulations are the same, which are known as the oneprice balancing settlement. Furthermore, balancing settlements which consist of different up and downregulation prices are called twoprice ones such as that in Nord Pool and the Iberian markets. In our paper, we propose the dayahead offering and balancing/realtime offering/operating decisionmaking model series based on the oneprice balancing settlement for a “price taker” WFESS while the probabilities for WFESS to provide ancillary services are neglected. Moreover, our proposed model series can be easily extended to the case of twoprice balancing settlement.
2.2. Progressive DecisionMaking Framework for Offering and Operating Process
Taking one day for example, it is assumed that the whole time horizon for a delivery day can be discretized into time units (e.g., 24 time units with 1 hour for the duration of each time unit). As mentioned in [32], balancing markets are singleperiod markets as they take place just minutes before actual energy delivery. Accordingly, there are one dayahead market and balancing markets for one delivery day, with one balancing market for each imbalance management corresponding to one time unit. With time proceeding, information for clearing prices and available wind power outputs can be progressively updated period by period, which are helpful for dynamically improving the WFESS’s total profit obtained from participating in both the dayahead and balancing markets. Hence, in our paper, a progressive decisionmaking framework is proposed for WFESS to determine, dynamically, the optimal dayahead/balancing offering and realtime operating strategies in spot EMs. Correspondingly, a series of optimization models are progressively established and solved. By solving each optimization model, the solutions in an adjustable finite predictive horizon are codetermined. However, only part of these solutions is implemented and the remaining ones are discarded or delivered to the rest models for further adjustment. Figure 1 depicts the decision procedure for a “price taker” WFESS participating in both dayahead and balancing markets based on our proposed progressive decisionmaking framework.
From Figure 1, the following can be seen.(1)There are one decisionmaking model for dayahead stage and decisionmaking models for balancing stages. Uncertainties and , forecasted right before the dayahead stage are fed to the dayahead decisionmaking model for obtaining the optimal dayahead offering quantities (offering strategies, ) and the nominal realtime operating powers (). Dayahead decisionmaking model is established for the whole time horizon of the delivery day. Moreover, only are submitted in the dayahead market, and are delivered to the balancing/realtime decisionmaking models for power adjustments.(2)Each of these balancing/realtime decisionmaking models is implemented for participating in the corresponding balancing market in the delivery day. Taking the th () balancing/realtime model for example, input information for this model consists of , , realization of and the latest updated uncertainties . It is assumed that realtime available wind power output forecasted few minutes before its actual delivery can be deemed as accurate information [26]. Then, the outputs of the th balancing/realtime model contain and . However, among those outputs, what the WFESS actually implements in the th balancing stage are only and according to the basic rules of our proposed progressive decisionmaking framework. The relationship between the actual and nominal operating powers of the WFESS for time unit can be formulated as where represents the optimal power adjustment vector for time unit . Actually, in the th balancing/realtime model, determining the optimal actual realtime operating power vector is equivalent to determining the optimal power adjustment vector .(3)It should be noted that when the th balancing/realtime model is executed, there actually exists a stationary mathematical relationship among , and , which can be formulated as where . Eq. (2) means if ( is positive), WFESS should sell MW upregulations in the th balancing market; otherwise, WFESS should buy MW downregulations in the th balancing market.
3. WFESS’s Offering and Operating Models Based on Progressive StochasticRobust Hybrid Optimization Method
3.1. Formulations for Uncertainties
According to [13–16], parameters in all operational constraints of a WFESS are irrelevant to dayahead and balancing clearing prices, which means uncertainties of dayahead and balancing clearing prices would not cause violations of operational constraints for a specific combination of dayahead/balancing offering (/) and realtime operating () strategies. That is to say, if using a number of joint stochastic scenarios to only represent uncertainties of dayahead and balancing prices, there would be no increase in the number of WFESS’s operational constraints. Hence, with respect to prices uncertainties, it is more feasible to apply the SO based methods for WFESS’s offering and operating decisionmaking modeling than RObased ones. On one hand, limited and constant number of operational constraints irrelevant to prices scenarios ensures low computational complexity. On the other hand, it often brings lower conservativeness for the solutions obtained from the expectedcase optimization than those from the worstcase optimization. Contrarily, parameters in most operational constraints of a WFESS are actually related to realtime available wind power outputs. That is to say, if using a number of stochastic scenarios to represent uncertainties of realtime available wind power outputs, the number of WFESS’s operational constraints would increase significantly. Hence, with respect to wind power uncertainties, it is more feasible to apply the RObased methods for WFESS’s offering and operating decisionmaking modeling than SO based ones due to the shortcomings for SO based models as mentioned in Section 1.
Therefore, we propose a stochasticrobust hybrid optimization method to construct both the dayahead offering decisionmaking model and every balancing/realtime offering/operating one for WFESS. On one hand, joint stochastic scenarios are dynamically generated for formulating prices uncertainties, which make the expectedcase optimization feasible in every decisionmaking model within our progressive model series. On the other hand, available wind power uncertainties are formulated as dynamic uncertainty set which can be easily updated period by period for the purpose of reducing the conservativeness of obtained strategies.
According to WFESS’s decision procedure mentioned in Section 2.2, joint stochastic scenarios for dayahead and balancing clearing prices are needed in the dayahead model while joint stochastic scenarios for balancing clearing prices from time unit to are needed in the th balancing/realtime model. Method for prices scenarios generation applied in our paper is the same as that in [15], which make the generated scenarios easily be dynamically updated via using newly realized prices data. The procedures for dynamically generating joint prices scenarios can be easily found in [15].
Moreover, according to [30], dynamic uncertainty set of realtime available wind power outputs can be formulated as (taking uncertainty set for the th balancing stage for example)s.t.where and account for deterministic seasonal components and is equivalent to a budget parameter over periods. Eq. (3b) separates the residual component from through seasonal decomposition method [30]. Eq. (3c) is the key equation that represents a linear dynamic relationship involving the residual at time unit t, residuals in earlier periods tL to t1, and an error term [30]. L represents the relevant time lags. represents the autoregressive coefficient vector. represents the standard deviation of the white noise term , which means actually stands for a standard normal random variable. Hence, Eq. (3d) controls the size of the whole set via adjusting ’s value; e.g. if is set to 0, it means none of the uncertainties of () is taken into account; if is set to 1, it means all of the uncertainties of () within are taken into account. Moreover, (3e) determines an upper bound (e.g., installed capacity for the WF) on .
It should be noted that(1)if the uncertainty set is forecasted and formulated in the dayahead stage, then both () and () for the delivery day are unrealized; parameters (), (), and are estimated by using historical available wind power data realized up to the dayahead stage;(2)if the uncertainty set is forecasted and formulated in the balancing stage corresponding to time unit n, then both () and () for the delivery day are realized; parameters (), (), and can be estimated by using realized available wind power data up to the th balancing stage, which is the fundamental of the proposed dynamic uncertainty set to be updated period by period.
3.2. Formulations for DayAhead Offering DecisionMaking Model
As mentioned in Section 2.2, the optimal dayahead offerings and nominal realtime operating powers throughout the whole time horizon of the delivery day are determined in the dayahead stage for a “price taker” WFESS. Hence, under a given combination of , , , and , total profit for the WFESS participating in both the dayahead and balancing markets can be formulated aswhere () represents the nominal balancing offering decision for buying ()/selling () up/downregulations in the tth balancing market of the delivery day, and represent cost parameters of WF and ESS (the degradation costs for ESS is ignored here), respectively. It is easy to tell from (4) that uncertainty of is only related to prices uncertainties due to our introduction of nominal variables. Moreover, it should be noted that both and are byproducts of , , and ; their relationship can be formulated as where stands for the initial residual energy of the ESS and and are charging and discharging efficiencies of the ESS.
In the dayahead stage, WFESS pursues the maximization of expected total profit while considering potential risk. Similar to [15], the risk is formulated by CVaR and is cooptimized with the expected total profit through linear combination. Moreover, owing to the introduction of nominal variables, WFESS’s dayahead offering decisionmaking problem can be formulated as the following stochasticrobust hybrid optimization model, which is the first model in our proposed progressive stochasticrobust hybrid optimization model series:s.t.
Eq. (5)
Eq. (6)
such thatwhere , , , and are the technical maximum limits for WF’s power output, ESS’s charging and discharging powers, as well as ESS’s residual energy; , , and are the technical minimum limits for ESS’s charging and discharging powers, as well as ESS’s residual energy.
Eqs. (5)(6) and (7b)(7e) together represent the operational constraints of WFESS. The robust feasible region represented by (7f)(7l) restricts the WFESS’s decision made in the dayahead stage so as to satisfy all operational constraints under any potential realization within (uncertainty set forecasted in the dayahead stage) by implementing existent corresponding adjustment .
Eq. (7a) indicates the objective function of the WFESS in the dayahead stage, where stands for the expected value function of ; represents the CVaR value function of at confidence level of . The objective function controls the tradeoff between the expectation and CVaR with an exogenous parameter (), the increase of which makes the strategy more riskneutral. Moreover, based on method proposed in [15] for CVaR linearization and according to our introduction of nominal variables, (7a) can be linearized by using dayahead and balancing prices joint stochastic scenarios, and the linearized form of (7a) is presented as follows:where and are, respectively, the index and index set for dayahead and balancing prices joint stochastic scenarios which are forecasted in the dayahead stage; represents the probability of scenario ; and () are intermediate variables introduced in the linearization process of , which are codetermined with (). Therefore, our proposed stochasticrobust hybrid optimization model for dayahead offering decisionmaking can also be written as Eq. (8a), s.t. Eqs. (8b)(8c), Eqs. (5)(6) and Eqs. (7b)(7l).
3.3. Formulations for Balancing/RealTime Offering/Operating DecisionMaking Model
In the balancing stage, taking the th balancing/realtime offering/operating decisionmaking model, for example, profits from dayahead market and balancing markets before time unit have already been obtained by WFESS. The remaining profits from the rest balancing markets of the delivery day should be maximized for the WFESS. Hence, similar to method in Section 3.3, WFESS’s th balancing/realtime offering/operating decisionmaking problem can be formulated as the following stochasticrobust hybrid optimization model, which is the n+1 th model in our proposed progressive stochasticrobust hybrid optimization model series:
such thatwhere and are, respectively, the index and index set for balancing prices joint stochastic scenarios which are forecasted in the th balancing stage by using the latest updated prices information prior to time unit n; represents the probability of scenario ; and () are intermediate variables introduced in the linearization process of CVaR. and () are codetermined with (although are cogenerated in the th balancing/realtime offering/operating decisionmaking model, only are actually implemented in the th balancing stage).
In summary, no matter with respect to dayahead or balancing stage, the general theoretical flowchart of our proposed stochasticrobust optimization methodology can be demonstrated as follows.
3.4. Model Reformulation
The basic idea of the above model proposed in Section 3.2 or 3.3 is to find a stochasticrobust solution which, on one hand, is immunized against any available wind power uncertainties within or () and, on the other hand, maximizes a linear combination of expectation and CVaR of profit based on prices stochastic scenarios. However, both of those two models should be reformulated so as to facilitate model solving. Inspired by [33], column and constraint generation (C&CG) based method is used to reformulate and solve the above models. With respect to the dayahead offering decisionmaking model proposed in Section 3.2, by using C&CG method for reformulating, its master problem (namely, MP1) and subproblem (namely, SP1) are established as follows:
(MP1) Eq. (8a)
Eqs. (5)(6) and Eqs. (7b)(7e)
Eqs. (7l)where is the index set for worst uncertainty points which are dynamically generated in (SP1) during the solution procedure. According to [33], the objective function in (SP1) contains the summation of nonnegative slack variables (), which evaluates the violation associated with the solution from (MP1) and can be explained as unfollowed uncertainties due to operational limitations of WFWSS. Hence, to solve (SP1) is to find the worst point in given the dayahead offering solution.
With respect to the th balancing/realtime offering/operating decisionmaking model proposed in Section 3.3, by using C&CG method for reformulating, its master problem (namely, MP2) and subproblem (namely, SP2) are established in Appendix A.
Moreover, no matter with respect to or , the solution procedure can be summarized as follows [34]:(1), define feasibility tolerance ;(2)while do(3)Solve (MP), obtain optimal solution of (MP) ;(4)Solve (SP) with , get solution ;(5);(6)end while.
After the convergence of the abovementioned solution procedure, the optimal stochasticrobust dayahead offering solution can be obtained by solving (MP1) for the last time; similarly, the optimal stochasticrobust balancing/realtime offering/operating solution for time unit can be obtained by solving (MP2) for the last time. Moreover, it is obvious that if is set to a very small positive value, a very important function of (SP1) and (SP2) is to tell whether the available wind power uncertainties could be well accommodated or not.
4. Simulation and Comparisons
4.1. Case Design
In this subsection, for the purpose of demonstrating our simulation and comparisons more lucidly, we introduce an experimental case design concretely. In our case, an integrated WFESS, which contains one wind turbine and one general energy storage device, participates as a “price taker” in both the dayahead and oneprice balancing markets. In the studied WFESS, WF and ESS are considered as being connected on the same node (same location) in the power system, Figure 3 simply demonstrates the relationship between the studied WFESS and spot EM (main grid).
A delivery day is discretized into 24 time units with 1 hour for the duration of each time unit. The technical and economic parameters for this WFESS are listed in Table 2 [15].
 
All the dynamic uncertainty sets for available wind power outputs, joint stochastic scenarios for dayahead, and balancing prices (applied in dayahead stage), as well as joint stochastic scenarios for balancing prices (applied in balancing stages), are constructed and generated based on historical data. Specifically, the historical hourly available wind power data are generated by using the power curve function in [35] and the hourly mean wind speed data in a Chinese city from September 1st to November 30th, 2016 [35]. Due to the inexistence of spot electricity markets in China, it is applied as the historical dayahead and balancing prices data the ones from DKWest area in the Nord Pool market during the same date range. Because the Nord Pool market is of twoprice balancing market, up/downregulation prices are different and one or the other of them is equal to the dayahead one at any specific time unit. So we take the different one as the balancing price in the oneprice balancing market [15]. Our model series are solved for every delivery day over the last 30 days (30 test days) in that date range. Take one delivery day, for example, in the dayahead stage, historical available wind power and prices data before this delivery day are used to construct and generate the available wind power dynamic uncertainty set and joint stochastic scenarios for dayahead and balancing prices corresponding to all time units of this delivery day. Moreover, in the th balancing stage, available wind power dynamic uncertainty set and joint stochastic scenarios for balancing prices corresponding to the rest time units of this delivery day are dynamically updated from the ones constructed and forecasted in the dayahead stage based on newly added intraday historical data which are considered as being realized or accurately forecasted as time went on to the th balancing stage.
All simulation and comparisons are implemented by utilizing the Matlab R2014a software on a PC laptop with an Intel Core i7 at2.1 GHz and 8 GB memory.
4.2. Calculation Results Analysis
In this subsection, simulation of our proposed progressive stochasticrobust hybrid optimization model series is implemented to obtain the WFESS’s optimal dayahead/balancing offering and realtime operating strategies for the 30 test days mentioned in Section 4.1. Primary parameters are set as , , , , , . It should be noted that the numbers of joint stochastic scenarios of prices we used in dayahead and balancing market stages (, ) are obtained by method of scenario reduction. The specific approach is as follows, Firstly, before each decisionmaking, method in [15] is applied to generate or update the dayahead and balancing price probability density function, respectively, based on the updated prices historical data. Secondly, before each decisionmaking, Monte Carlo sampling method is used to generate 10,000 dayaheadbalancing prices joint stochastic scenarios or balancing prices joint stochastic scenarios based on the corresponding probability density function. Finally, using the method in [36], the similar scenarios are further reduced by comparing the probability distances between the scenarios, and finally 100 scenarios used in the simulation are formed. Since the main innovations in this paper do not involve the generation and reduction of stochastic scenarios, please refer to [15, 36] for specific scenario generation and reduction methods.
Moreover, because simultaneous charging and discharging is prohibited and it has not been defined in our models the binomial variables representing the state of charge, the realtime operating power of ESS in time unit t (namely, ) is actually the net value between and :Since (12) is introduced in our model series, the actual charge or discharge power of ESS is , not and ( and are auxiliary variables), which means ESS charges in time unit when and discharges in time unit when .
4.2.1. Available Wind Power Uncertainty Accommodation Test
As mentioned in Section 3.4, after the solution procedure is terminated (no matter with respect to or ), a very important function of (SP1) and (SP2) is to tell whether the available wind power uncertainties could be well accommodated or not. That is because, taking the dayahead stage, for example, if the realtime available wind power uncertainties from time unit 1 to 24 of a delivery day cannot be well accommodated based on reasonable adjustments from the obtained nominal balancing/realtime offering/operating strategies, there should be ; otherwise, there should be .
To confirm the available wind power uncertainty accommodation ability of our proposed progressive stochasticrobust hybrid optimization model series, Figure 4 depicts the final obtained (“Psi(SP1)” in Figure 2) and (“Psi(SP2)” in Figure 2) values of the 30 test days, respectively (where “Delta” represents ).
From Figure 4, the following can be seen.(1)In every day of these 30 test days, relationship is valid, which means solutions obtained in dayahead decisionmaking stages using the dayahead model in our proposed model series have left enough rooms for WFESS’s power adjustments so as to accommodate the realtime available wind power uncertainties.(2)In every time unit of these 30 test days, relationship is valid, which means solutions obtained in balancing decisionmaking stages using the progressive balancing/realtime models in our proposed model series have left enough rooms for WFESS’s power adjustments so as to accommodate the realtime available wind power uncertainties in the rest time units of the corresponding delivery day.
Therefore, it is validated that by implementing our proposed progressive stochasticrobust hybrid optimization model series, the internal power compensation potential of WFESS can be adequately utilized so as to guarantee the realizations of realtime available wind power uncertainties accommodations.
4.2.2. DayAhead and Balancing Offerings Analysis
By implementing our proposed progressive stochasticrobust hybrid optimization model series, WFESS’s dayahead and balancing offerings in the 30 test days can be finally obtained and demonstrated in Figure 5.
From Figure 5, the following can be concluded.
In the dayahead stages, WFESS usually offers larger joint power outputs when the dayahead prices are relatively high and offers smaller joint power outputs when the dayahead prices are relatively low. In the balancing stages, WFESS usually offers positive joint power outputs (provide upregulations) when balancing prices are higher than dayahead ones, and offers negative joint power outputs (provide downregulations) when balancing prices are lower than dayahead ones. According to [32], on one hand, the strategy of “selling more at relatively high prices” and “selling less at relatively low prices” in dayahead market helps in profit improvement. On the other hand, if the balancing price is higher than the dayahead one corresponding to the same time unit, it shows that there is a problem of “power shortage” in balancing market, and providing upregulation in this balancing stage can make the provider benefit further; conversely, it shows that there is a problem of “load shortage” in balancing market, and providing downregulation in this balancing stage can make the provider benefit further. Therefore, it is validated that by implementing our proposed progressive stochasticrobust hybrid optimization model series, the arbitrage potential of WFESS can be reasonably utilized so as to make itself strategically participate in multistage spot EMs for total profit improvement. However, uncertainties from spot EM prices and realtime available wind power outputs may sometimes interfere with WFESS’s offering and operating decisionmakings; that is why the dayahead offerings at the 14th and 530th time units etc. (corresponding to 13 to 14 p.m. in November 1st and 1 to 2 a.m. in November 22nd, respectively), as well as the balancing offerings at 275th and 369th time units etc. (corresponding to 10 to 11 a.m. in November 11th and 8 to 9 a.m. in November 15th, respectively), deviate from the behavior patterns summarized above.
In order to facilitate the description, offering, and operating strategies obtained by our proposed progressive stochasticrobust hybrid optimization model series are called strategy 1 in the rest of this paper. Hence, WFESS’s actual daily profits of these 30 test days obtained by strategy 1 are listed in Table 3. Although it is obvious from Table 3 that WFESS can earn considerable daily profits during these 30 test day by strategy 1, advantages of our proposed progressive stochasticrobust hybrid optimization model series still need to be further validated by profit comparisons with other existed decisionmaking methods.
 
Note: Take one test day for example, after implementing the proposed model series for this day, WFESS’s optimal offering and operating strategies can be obtained. Hence, WFESS’s actual daily profit means the daily profit calculated by using the obtained strategies and the realized (actual) available wind power outputs and prices data. 
Moreover, by implementing our simulation in this subsection, it takes an average of 11.7 seconds for each of our dayahead model to calculate and takes an average of 5.2 seconds for each of our balancing/realtime model to calculate. It is generally known that dayahead market starts at least 12 hours before the delivery day and balancing market begins few minutes to half an hour in advance [32]; that is to say, low computational time makes our proposed model series feasible for obtaining WFESS’s offering and operating strategies in dayahead and balancing stages.
4.3. Profit Comparison
In this subsection, WFESS’s profit earned by strategy 1 is compared with that earned by implementing some other existed methods. Similar to this paper, it has been established a model series in [15]. By sequentially solving each model in the model series, the offering and/or operating solutions corresponding to each market stage will be obtained one by one. The introduction of the model series is conducive to the use of dynamically updated electricity prices and wind power data. Hence, it has already been verified the strategy obtained by implementing model series proposed in [15] can make WFESS earn more profit than many other methods such as the expected utility maximization (EUM) one and filter control (FC) one which do not involve the use of dynamically updated electricity prices and wind power data. However, different from our paper, in [15], the dayahead market decisionmaking model is a stochastic optimization model based on the joint stochastic scenarios of dayahead, balancing electricity prices, and wind power outputs. Each balancing market decisionmaking model is only a linear affine function and does not involve reoptimization problems. In this subsection, naming strategy obtained by method in [15] as strategy 2, comparison of our proposed strategy 1 with strategy 2 is mainly conducted.
With respect to strategy 2 bringing here for comparison, both the forecasted scenarios for clearing prices and realtime available wind power outputs which are applied to optimization are based on the same historical data mentioned in Section 4.1. Moreover, for methods for scenario generation and reduction refer to [15, 36].
Figure 6 demonstrates WEESS’s daily actual profits of these 30 test days obtained by strategy 1 and by strategy 2 respectively.
From Figure 6, it is obvious that in most test days, WFESS’s actual daily profits obtained by strategy 1 are more than those obtained by strategy 2, which validates that WFESS can earn more profit by implementing our proposed progressive stochasticrobust hybrid optimization model series than method proposed in [15]. The most important reasons are as follows.(1)The realtime operating linear decision rule proposed in [15], to a certain extent, limits the feasible range of realtime power adjustments because the affine matrix proposed in [15] for constructing the realtime linear decision rule, which is responsible for generating WFESS’s realtime power adjustments, is only optimized in dayahead stage and is not dynamically adjusted by using newly added data in the progressive balancing stages. However, realtime power adjustments obtained by our proposed methods are dynamically optimized in progressive balancing stages based on newly updated data, which does not limit the feasible range of realtime power adjustments so as to make our strategy less conservative in pursuing more profit.(2)Strategy 2 only optimizes powers of ESS in dayahead decisionmaking models while in realtime operating linear decision rules, powers of ESS are not reoptimized so as to make WFESS participate in balancing markets strategically for pursuing more total profits. However, strategy 1 optimizes powers of ESS not only in dayahead decisionmaking models but also in balancing/realtime models, which means powers of ESS are dynamically reoptimized in balancing stages so as to make WFESS participate in balancing markets strategically for pursuing more total profits.
Moreover, it takes an average of 138.9 seconds by implementing strategy 2 for each dayahead market stage and takes an average of 0.1 seconds by implementing strategy 2 for each balancing market stage. Due to the only SO based structure, the number of variables and constraints in dayahead model in [15] is much more than that in our dayahead model. This makes the computational time of dayahead model in [15] much higher than that of ours. Due to the linear structure, the computational complexity of balancing/realtime model in [15] is lower than that of ours. This makes our balancing/realtime model to be more timeconsuming.
In summary, by implementing strategies 1 and 2 on these 30 test days, the profit improvement of our proposed model series compared with other works can be numerically concluded (with totally DKK in profit improvement compared with strategy 2). In addition, although implementing our balancing/realtime model is more timeconsuming, it is still feasible for taking our model series in practice because balancing market begins few minutes to half an hour in advance [34].
4.4. Sensitivity Analysis
Parameters of our proposed model series will significantly influence the result of the formulations. In this subsection, two important parameters are taken into account, which are parameter of the dynamic uncertainty set and weighting parameter controlling the tradeoff between the expectation and CVaR. Figure 7 depicts a relation curve between the obtained average and CVaR values of WFESS’s daily profit of these 30 test days, which corresponds to different values. More concrete details about the influence of on the result of the formulations are listed in Table 4. Moreover, a Pareto efficient frontier between the obtained average and CVaR values of WFESS’s daily profit of these 30 test days is demonstrated in Figure 8, which corresponds to different values. More concrete details about the influence of on the result of the formulations are listed in Table 5.
 
Note: ADP is the abbreviation of the “WFESS’s average daily profit”. WFESS’s average daily profit mentioned here means the average value calculated by using WFESS’s actual daily profits of 30 test days. CVaR in Tables 4 and 5 is calculated based on the actual profits of 30 test days and the frequency of each profit (1/30). The specific approach is: Firstly, the actual profits of the 30 test days are arranged from small to large, and the cumulative frequency of less than each actual profit is calculated; Secondly, it is approximately considered as VaR_{α} the actual profit with the cumulative frequency closest to the α value; Finally, the conditional average value of all actual profits less than VaR_{α} is calculated, and considered as CVaR_{α}. 

From Figure 7 and Table 4, the following can be concluded.(1)When is less than an appropriate value (namely, ), WFESS’s average daily profit increases with the increase of . When is greater than that value, WFESS’s average daily profit decreases with the increase of . The main reason for this phenomenon is that, in our model series, a too small value corresponds to a series of too narrow available wind power dynamic uncertainty sets, which make our dayahead and balancing/realtime decisionmaking approaches too deterministic to cope with potential risks caused by realtime available wind power uncertainties. Hence, increasing from a too small value helps reduce chances of profit losses due to wind power uncertainty. Conversely, a too large value corresponds to a series of too wide available wind power dynamic uncertainty sets, which make our dayahead and balancing/realtime decisionmaking approaches too conservative to pursue more profit. Hence, increasing from a too large value would result in profit losses.(2)Although WFESS’s average daily profit fluctuates with the increase of , the CVaR of WFESS’s daily profit has the monotonic relationship with . Specifically, the CVaR increase with the increase of . That is mainly because, in our model series, the larger the value of is, the more riskaverse the result of the formulations is for the available wind power uncertainties, by which the influence of available wind power uncertainties on WFESS’s actual daily profit would be weakened effectively.
In conclusion, the right side of the curve depicted in Figure 7 is a Pareto efficient frontier, which means the best choices for values, and there does not exist any solutions making both expectation (average) and CVaR better off at the same time.
From Figure 8 and Table 5, it can be concluded that increasing the weighting parameter can better guarantee the average daily profit but sacrifices the CVaR, otherwise the opposite. That is mainly because, in our model series, a larger implies a more riskneutral strategy to the prices uncertainties, by which the influence of prices uncertainties on WFESS’s actual daily profit would be strengthen effectively. The value selection of depends on the attitude of the WFESS to prices uncertainties risks and each value of maps to one point of the Pareto efficient frontier in Figure 8, which means there does not exist any solution which can make both expectation (average) and CVaR better off at the same time.
5. Conclusion
This paper proposed a progressive stochasticrobust hybrid optimization model series for WFESS, as a “price taker” participating in both the dayahead and balancing markets, to optimally cogenerate offering and operating strategies from the integrated and progressive point of views. Simulation and comparisons based on realistic data have presented some interesting conclusions.(1)It is validated that by implementing our proposed progressive stochasticrobust hybrid optimization model series, the internal power compensation potential of WFESS can be adequately utilized so as to guarantee the realizations of realtime available wind power uncertainties accommodations.(2)It is validated that by implementing our proposed progressive stochasticrobust hybrid optimization model series, the arbitrage potential of WFESS can be reasonably utilized so as to make itself strategically participate in multistage spot EMs for total profit improvement.(3)Low computational time makes our proposed model series feasible for obtaining WFESS’s offering and operating strategies in dayahead and balancing stages.(4)By implementing the comparison test, significant profit improvement effect of our proposed model series compared with other existing works was numerically concluded. In addition, although implementing our balancing/realtime model is more timeconsuming, it is still feasible for taking our model series in practice because balancing market begins few minutes to half an hour in advance.(5)Sensitivity analyses have reached two Pareto efficient frontiers between the obtained average and CVaR of WFESS’s daily profit which provides important references for selecting different risk attitudes towards wind power and prices uncertainties, respectively.
Our future work will release the “price taker” assumption and focus on the “price maker” strategies of WFESS. Moreover, extending the WFESS to other hybrid energy systems such as microgrid, virtual power plant, and integrated energy system will also be the topic that we will focus on in the future.
Appendix
A. Model Reformulation for the Balancing Stage
With respect to the th balancing/realtime offering/operating decisionmaking model proposed in Section 3.3, by using CCG method for reformulating, its master problem (namely, MP2) and subproblem (namely, SP2) are established as follows:
(MP2) Eq. (9a)
Eqs. (9q)
where is the index set for worst uncertainty points which are dynamically generated in (SP2) during the solution procedure. According to [28], the objective function in (SP2) contains the summation of nonnegative slack variables (), which evaluates the violation associated with the solution from (MP2) and can be explained as unfollowed uncertainties due to operational limitations of WFWSS. Hence, to solve (SP2) is to find the worst point in given the realtime operating solution for time unit .
Nomenclature
:  Indices for time unit 
:  Number of time unit for a delivery day 
, , :  Random variables of realtime available wind power output, dayahead, and balancing prices for time unit 
, , :  Uncertainties for realtime available wind power outputs, dayahead, and balancing prices estimated in the dayahead stage 
, :  Uncertainties for realtime available wind power outputs and balancing prices estimated (latest updated) in the th balancing stage 
, , :  Realized realtime available wind power output, dayahead, and balancing prices for time unit 
:  WFESS’s dayahead offering volume for time unit 
:  WFESS’s realtime decisions for buying/selling up/downregulations in balancing market for time unit 
, , :  Nominal operating solutions for WF’s dispatched power output, ESS’s dispatched power charge, and discharge for time unit 
, , :  Adjusted operating solutions for WF’s dispatched power output, ESS’s dispatched power charge, and discharge for time unit 
:  ESS’s state of charge for time unit 
:  ESS’s nominal residual energy at the end of time unit 
:  ESS’s nominal residual energy at the end of time unit . 
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare no conflict of interest.
Authors’ Contributions
Yuwei Wang established the model, implemented the simulation, and wrote this article; Huiru Zhao and Peng Li guided the research.
Acknowledgments
This study is supported by the Major State Research and Development Program of China under Grant No. 2016YFB0900500 and No. 2016YFB0900501 and the Fundamental Research Funds for the Central Universities (2019MS131).
References
 N. Pearre, K. Adye, and L. Swan, “Proportioning wind, solar, and instream tidal electricity generating capacity to cooptimize multiple grid integration metrics,” Applied Energy, vol. 242, pp. 69–77, 2019. View at: Publisher Site  Google Scholar
 K. Afshar, F. S. Ghiasvand, and N. Bigdeli, “Optimal bidding strategy of wind power producers in payasbid power markets,” Journal of Renewable Energy, vol. 127, pp. 575–586, 2018. View at: Publisher Site  Google Scholar
 S. Surender Reddy, P. R. Bijwe, and A. R. Abhyankar, “Realtime economic dispatch considering renewable power generation variability and uncertainty over scheduling period,” IEEE Systems Journal, vol. 9, no. 4, pp. 1440–1451, 2015. View at: Google Scholar
 M. Kazemi, H. Zareipour, N. Amjady, W. D. Rosehart, and M. Ehsan, “Operation scheduling of battery storage systems in joint energy and ancillary services markets,” IEEE Transactions on Sustainable Energy, vol. 8, no. 4, pp. 1726–1735, 2017. View at: Publisher Site  Google Scholar
 P. Yulong, A. Cavagnino, S. Vaschetto, C. Feng, and A. Tenconi, “Flywheel energy storage systems for power systems application,” in Proceedings of the 6th International Conference on Clean Electrical Power, ICCEP 2017, pp. 492–501, June 2017. View at: Google Scholar
 B. S. Pali and S. Vadhera, “A novel pumped hydroenergy storage scheme with wind energy for power generation at constant voltage in rural areas,” Journal of Renewable Energy, vol. 127, pp. 802–810, 2018. View at: Publisher Site  Google Scholar
 F. Arpino, M. Dell'Isola, D. Maugeri, N. Massarotti, and A. Mauro, “A new model for the analysis of operating conditions of microcogenerative SOFC units,” International Journal of Hydrogen Energy, vol. 38, no. 1, pp. 336–344, 2013. View at: Publisher Site  Google Scholar
 F. Arpino, N. Massarotti, A. Mauro, and L. Vanoli, “Metrological analysis of the measurement system for a microcogenerative SOFC module,” International Journal of Hydrogen Energy, vol. 36, no. 16, pp. 10228–10234, 2011. View at: Publisher Site  Google Scholar
 A. L. Bukar and C. W. Tan, “A review on standalone photovoltaicwind energy system with fuel cell: system optimization and energy management strategy,” Journal of Cleaner Production, vol. 221, pp. 73–88, 2019. View at: Publisher Site  Google Scholar
 N. Bizon, “Optimal operation of fuel cell/wind turbine hybrid power system under turbulent wind and variable load,” Applied Energy, vol. 212, pp. 196–209, 2018. View at: Publisher Site  Google Scholar
 A. C. Duman and Ö. Güler, “Technoeconomic analysis of offgrid PV/wind/fuel cell hybrid system combinations with a comparison of regularly and seasonally occupied households,” Sustainable Cities and Society, vol. 42, pp. 107–126, 2018. View at: Publisher Site  Google Scholar
 S. S. Reddy and J. A. Momoh, “Realistic and transparent optimum scheduling strategy for hybrid power system,” IEEE Transactions on Smart Grid, vol. 6, no. 6, pp. 3114–3125, 2015. View at: Publisher Site  Google Scholar
 M. S. AlSwaiti, A. T. AlAwami, and M. W. Khalid, “Cooptimized trading of windthermalpumped storage system in energy and regulation markets,” Energy, vol. 138, pp. 991–1005, 2017. View at: Publisher Site  Google Scholar
 F.J. Heredia, M. D. Cuadrado, and C. Corchero, “On optimal participation in the electricity markets of wind power plants with battery energy storage systems,” Computers & Operations Research, vol. 96, pp. 316–329, 2018. View at: Publisher Site  Google Scholar
 H. Ding, P. Pinson, Z. Hu, and Y. Song, “Optimal offering and operating strategies for windstorage systems with linear decision rules,” IEEE Transactions on Power Systems, vol. 31, no. 6, pp. 4755–4764, 2016. View at: Publisher Site  Google Scholar
 J. L. CrespoVazquez, C. Carrillo, E. DiazDorado, J. A. MartinezLorenzo, and M. NoorEAlam, “A machine learning based stochastic optimization framework for a wind and storage power plant participating in energy pool market,” Applied Energy, vol. 232, pp. 341–357, 2018. View at: Publisher Site  Google Scholar
 F. Kalavani, B. MohammadiIvatloo, and K. Zare, “Optimal stochastic scheduling of cryogenic energy storage with wind power in the presence of a demand response program,” Journal of Renewable Energy, vol. 130, pp. 268–280, 2019. View at: Publisher Site  Google Scholar
 V. Davatgaran, M. Saniei, and S. S. Mortazavi, “Optimal bidding strategy for an energy hub in energy market,” Energy, vol. 148, pp. 482–493, 2018. View at: Publisher Site  Google Scholar
 S. S. Reddy, “Optimization of renewable energy resources in hybrid energy systems,” Journal of Green Engineering, vol. 7, no. 1, pp. 43–60, 2017. View at: Publisher Site  Google Scholar
 S. S. Reddy, P. R. Bijwe, and A. R. Abhyankar, “Multiobjective market clearing of electrical energy, spinning reserves and emission for windthermal power system,” International Journal of Electrical Power & Energy Systems, vol. 53, pp. 782–794, 2013. View at: Publisher Site  Google Scholar
 S. S. Reddy, P. R. Bijwe, and A. R. Abhyankar, “Joint energy and spinning reserve market clearing incorporating wind power and load forecast uncertainties,” IEEE Systems Journal, vol. 9, no. 1, pp. 152–164, 2015. View at: Publisher Site  Google Scholar
 S. S. Reddy, P. R. Bijwe, and A. R. Abhyankar, “Optimum dayahead clearing of energy and reserve markets with wind power generation using anticipated realtime adjustment costs,” International Journal of Electrical Power & Energy Systems, vol. 71, pp. 242–253, 2015. View at: Publisher Site  Google Scholar
 A. Attarha, N. Amjady, S. Dehghan, and B. Vatani, “Adaptive robust selfscheduling for a wind producer with compressed air energy storage,” IEEE Transactions on Sustainable Energy, vol. 9, no. 4, pp. 1659–1671, 2018. View at: Publisher Site  Google Scholar
 P. Xia, C. Deng, Y. Chen, and W. Yao, “MILP based robust shortterm scheduling for wind–thermal–hydro power system with pumped hydro energy storage,” IEEE Access, vol. 7, pp. 30261–30275, 2019. View at: Publisher Site  Google Scholar
 A. A. Thatte and L. Xie, “A robust model predictive control approach to coordinating wind and storage for joint energy balancing and frequency regulation services,” in Proceedings of the IEEE Power and Energy Society General Meeting, PESGM 2015, pp. 1–5, IEEE, July 2015. View at: Google Scholar
 H. Qiu, W. Gu, J. Pan et al., “Multiintervaluncertainty constrained robust dispatch for AC/DC hybrid microgrids with dynamic energy storage degradation,” Applied Energy, vol. 228, pp. 205–214, 2018. View at: Publisher Site  Google Scholar
 C. A. CorreaFlorez, A. Michiorri, and G. Kariniotakis, “Robust optimization for dayahead market participation of smarthome aggregators,” Applied Energy, vol. 229, pp. 433–445, 2018. View at: Publisher Site  Google Scholar
 Y. Zhou, Z. Wei, G. Sun, K. W. Cheung, H. Zang, and S. Chen, “A robust optimization approach for integrated community energy system in energy and ancillary service markets,” Energy, vol. 148, pp. 1–15, 2018. View at: Publisher Site  Google Scholar
 Z. Zhang, Y. Zhang, Q. Huang, and W. Lee, “Marketoriented optimal dispatching strategy for a wind farm with a multiple stage hybrid energy storage system,” CSEE Journal of Power and Energy Systems, vol. 4, no. 4, pp. 417–424, 2018. View at: Publisher Site  Google Scholar
 A. Lorca and X. A. Sun, “Multistage robust unit commitment with dynamic uncertainty sets and energy storage,” IEEE Transactions on Power Systems, vol. 32, no. 3, pp. 1678–1688, 2017. View at: Publisher Site  Google Scholar
 C. Ning and F. You, “Adaptive robust optimization with minimax regret criterion: Multiobjective optimization framework and computational algorithm for planning and scheduling under uncertainty,” Computers & Chemical Engineering, vol. 108, pp. 425–447, 2018. View at: Publisher Site  Google Scholar
 J. Morales M, A. Conejo J, H. Madsen et al., Integrating Renewables in Electricity Markets: Operational Problems, Springer Science & Business Media, 2013.
 A. Lorca and X. A. Sun, “Adaptive robust optimization with dynamic uncertainty sets for multiperiod economic dispatch under significant wind,” IEEE Transactions on Power Systems, vol. 30, no. 4, pp. 1702–1713, 2015. View at: Publisher Site  Google Scholar
 H. Ye, Y. Ge, M. Shahidehpour, and Z. Li, “Uncertainty marginal price, transmission reserve, and dayahead market clearing with robust unit commitment,” IEEE Transactions on Power Systems, vol. 32, no. 3, pp. 1782–1795, 2017. View at: Publisher Site  Google Scholar
 Hourly mean wind speed data: https://wenku.baidu.com/view/dc8cc130c8d376eeafaa3183.html.
 Y. Gao, R. Li, H. Liang et al., “Two step optimal dispatch based on multiple scenarios technique considering uncertainties of intermittent distributed generations and loads in the active distribution system,” Proceedings of the CSEE, vol. 35, no. 7, pp. 1657–1665, 2015. View at: Google Scholar
Copyright
Copyright © 2019 Yuwei Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.