Incorporating energy storage into probabilistic security‐constrained unit commitment
2018; Institution of Engineering and Technology; Volume: 12; Issue: 18 Linguagem: Inglês
10.1049/iet-gtd.2018.5413
ISSN1751-8695
AutoresVictoria Guerrero‐Mestre, Yury Dvorkin, Ricardo Fernández‐Blanco, Miguel A. Ortega‐Vazquez, Javier Contreras,
Tópico(s)Optimal Power Flow Distribution
ResumoIET Generation, Transmission & DistributionVolume 12, Issue 18 p. 4206-4215 Research ArticleFree Access Incorporating energy storage into probabilistic security-constrained unit commitment Victoria Guerrero-Mestre, Corresponding Author Victoria Guerrero-Mestre victoria.guerrero@uclm.es E.T.S. de Ingenieros Industriales, University of Castilla–La Mancha, 13071 Ciudad Real, SpainSearch for more papers by this authorYury Dvorkin, Yury Dvorkin Electrical and Computer Engineering, Tandon School of Engineering, New York University, 11201 Brooklyn, New York, USASearch for more papers by this authorRicardo Fernández-Blanco, Ricardo Fernández-Blanco Department of Applied Mathematics, University of Malaga, 29010 Malaga, SpainSearch for more papers by this authorMiguel A. Ortega-Vazquez, Miguel A. Ortega-Vazquez Grid Operations and Planning, Electric Power Research Institute, 94304 Palo Alto, California, USASearch for more papers by this authorJavier Contreras, Javier Contreras E.T.S. de Ingenieros Industriales, University of Castilla–La Mancha, 13071 Ciudad Real, SpainSearch for more papers by this author Victoria Guerrero-Mestre, Corresponding Author Victoria Guerrero-Mestre victoria.guerrero@uclm.es E.T.S. de Ingenieros Industriales, University of Castilla–La Mancha, 13071 Ciudad Real, SpainSearch for more papers by this authorYury Dvorkin, Yury Dvorkin Electrical and Computer Engineering, Tandon School of Engineering, New York University, 11201 Brooklyn, New York, USASearch for more papers by this authorRicardo Fernández-Blanco, Ricardo Fernández-Blanco Department of Applied Mathematics, University of Malaga, 29010 Malaga, SpainSearch for more papers by this authorMiguel A. Ortega-Vazquez, Miguel A. Ortega-Vazquez Grid Operations and Planning, Electric Power Research Institute, 94304 Palo Alto, California, USASearch for more papers by this authorJavier Contreras, Javier Contreras E.T.S. de Ingenieros Industriales, University of Castilla–La Mancha, 13071 Ciudad Real, SpainSearch for more papers by this author First published: 05 September 2018 https://doi.org/10.1049/iet-gtd.2018.5413Citations: 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 System operators still rely on deterministic criteria such as the (i.e. the system would be able to withstand the outage of any single component without any load shedding) to hedge the system against contingencies. While simple and practical, this criterion miscalculates the actual amount of reserve required since it ignores the probability of contingency occurrence. Therefore, this criterion may lead to suboptimal reserve procurement and economic performance of the system. This study presents a multiperiod probabilistic security-constrained unit commitment (UC) model that includes the probabilities of generation and transmission contingencies for optimal reserve sizing, sourcing, allocation, and timing. The ability of energy storage systems (ESS) to provide contingency reserve is explicitly modelled. Benders' decomposition and linearisation techniques are applied to solve the proposed probabilistic UC, which would be intractable otherwise. The impact of ESS on the contingency reserve procurement and deployment in post-contingency states are analysed on a modified version of the IEEE One-Area Reliability Test System. Nomenclature Sets B Set of buses, indexed by b Set (subset) of generators (connected to bus b), indexed by i J Auxiliary set of generators, indexed by j Set of contingency states, indexed by k. Index denotes the pre-contingency state and indices denote the post-contingency states. Superscripts G and L denote post-contingency states caused by generator and line failures L Set of transmission lines, indexed by l T Set of time periods, indexed by t U Set of wind power scenarios, indexed by u. Indices and stand for the central forecast and min/max bounds Auxiliary indices , Index of sending and receiving buses of line l Index that relates generator i and state k Index that relates transmission line l and state k Binary variables Status of unit i at time t (1 if synchronised, 0 otherwise) Start-up status of unit i at time t (1 if started-up, 0 otherwise) Shutdown status of unit i at time t (1 if shut down, 0 otherwise) Variable that is equal to 1 if the energy storage system is in charging mode at time t, scenario u, and contingency state k, and 0 otherwise Continuous variables State of charge of energy storage at bus b, in period t, and scenario u in the pre-contingency state [MWh] Energy not served at bus b, in period t, scenario u, and state k [MW] Line flow at time t, line l, scenario u, and state k [MW] Power output of generator i at time t, scenario u, and state k [MW] Wind output at time t, bus b, scenario u, state k [MW] Storage charging/discharging power at bus b in period t, scenario u, and state k [MW] Up/down reserve provided by unit i at time t [MW] Up/down reserve deployed by unit i at time t, scenario u, and state k [MW] Up/down reserve provided by the energy storage at bus b and time t [MW] Phase angle difference between the buses connecting line l at time t, scenario u, and state k [radians] Probability of state k at time t [p.u.] Auxiliary continuous variables , , , , , , , Auxiliary variables used for linearisations Parameters Energy cost coefficient offered by generator i [$/MWh] Cost rate offered by generator i for up/down reserve [$/MWh] No-load cost coefficient offered by generator i [$] Start-up cost coefficient offered by generator i [$] Degradation cost of energy storage at bus b [$/MWh] Cost rate offered by the energy storage at bus b for reserve [$/MWh] Load at bus b and time t [MW] Min down/up-time of generator i [h] Max/min energy storage capacity at bus b [MWh] Power flow capacity of line l [MVA] Number of transmission lines connected to bus b Minimum number of periods during which generator i must remain initially synchronised/offline. If , then . If , then [h] Number of post-contingency states Number of time periods in the optimisation horizon Max/min power output of energy storage at bus b [MW] Max/min power output of generator i [MW] Wind power forecast at time t, bus b, scenario u [MW] Ramp-down/up rate of generator i [MWh] Initial commitment of generator i Value of lost load at bus b [$/MWh] Reactance of line l [p.u.] Availability of generator i/line l under state k (1 if available, 0 otherwise) Outage replacement rate of unit i/line l [p.u.] Reserve deployment time of generators/energy storage [h] Efficiency of the energy storage at bus b when charging/discharging [p.u.] 1 Introduction Contingency reserve is typically procured by generating units using deterministic rules such as the criterion. This criterion ensures that the system would be able to withstand the loss of any single generation or transmission element without curtailing load. A major drawback of the criterion is that it is insensitive to the failure rates of the individual elements and, thus, it miscalculates the contingency reserve requirements [1] and disregards its network allocation, which may hinder reserve deliverability in post-contingency states [2]. Several probabilistic approaches have been proposed, but they ignore either the transmission network or the dependence of probabilities of component failures to the commitment decisions (see [2] and references therein). Unlike ramp-constrained conventional generators, distributed energy storage systems (ESS) are flexible resources that are suitable for providing contingency reserve deliverability in post-contingency states [3]. Wen et al. [3, 4] study how ESS can provide contingency reserve, but the chosen contingency criterion is deterministic and does not reflect the probabilistic nature of generation and transmission failures. The model in [3] accounts for transmission failures only, while the model in [4] deals with generation failures only. The authors in [5, 6] account for both transmission line and generation failures within a stochastic security-constrained unit commitment (UC) with a large penetration of renewable energy and ESS. However, the failures of components in power systems are generated using Monte Carlo simulations (MCs). The short-term profitability of ESS is evaluated in [7] for different levels of renewable penetration, and the contingency analysis is tested after the UC is solved. Integrating renewable generation resources is a pressing societal demand. Grid-scale ESS, e.g. electrochemical batteries, have been deemed a solution for a variety of challenges such as to maintain system reliability or reduce the system-wide operating cost. For instance, ESS have been proven technically and economically feasible for providing spatiotemporal arbitrage [8], regulation and load following services [9, 10], congestion relief [11, 12], voltage and reactive power support [13] among other applications [14]. As quantified in [15], in order to justify its installation, grid-scale ESS will likely have to simultaneously provide multiple services. Therefore, the U.S. Department of Energy states that 'energy storage should be recognised for its value in providing multiple benefits simultaneously' and seeks to further explore potential storage applications [16]. This paper demonstrates the value of ESS as a contingency reserve provider in addition to its primary arbitrage duty. This paper proposes a multiperiod probabilistic security-constrained UC (PSCUC) model with ESS, which is a large-scale non-convex optimisation problem. Unlike other probabilistic approaches for addressing the security-constrained UC in the technical literature, this model includes the probabilities of component failures, their dependence to the commitment decisions, the effect of the transmission network, and distributed ESS as a contingency reserve provider. Therefore, it prevents attaining suboptimal solutions in terms of its costs and benefits and leads to an optimal reserve allocation, and thus their deployment in post-contingency states would be feasible. The UC problem is then solved by using Benders' decomposition (BD). The integration of ESS in the UC problem is improved by using BD [3, 17]. The inclusion of energy storage complicates the formulation of the problem due to the inter-temporal constraints related to the state-of-charge of the ESS. For the sake of simplicity, this paper considers a generic energy storage device, but the mathematical formulation of the proposed model could be applied to specific ESS technologies with small modifications. Moreover, the explicit modelling of the contingency states of thermal generators and transmission lines allows for reserve deliverability. Unlike MCS, where the outages are randomly generated in advance and then a probability of occurrence is set for each of them, the endogenous modelling of the contingency states takes into account the probability of all single-outage events in the optimisation problem (see Appendix for further information). The main contributions of this paper are as follows: The proposed PSCUC endogenously accounts for the following features: (i) the likelihood of pre- and post-contingency states and its dependence on the binary commitment variables, (ii) transmission network constraints, (iii) inter-temporal constraints on-ramp rates and minimum up and down times, (iv) wind power generation uncertainty via interval optimisation [18, 19], and (v) distributed ESS. This model optimally procures contingency reserve in a transmission network and the distributed ESS provides both arbitrage and contingency reserve. From a methodological perspective, the application of linearisation techniques and BD is proposed to solve the PSCUC model. The proposed method is capable of solving the PSCUC model for all time periods within a given day-ahead optimisation horizon while ensuring global optimality. The proposed PSCUC model and solution technique are tested on a modified One-Area IEEE Reliability Test System (RTS) [2, 8]. The proposed model and solution technique lead to significant computational advantages and operating cost savings when compared to a traditional deterministic benchmark with the security criterion and the model in [2]. The proposed PSCUC model also makes it possible to evaluate the value of ESS as a contingency reserve provider. To the best of the authors' knowledge, this is the first time that all the features enumerated in contribution i are jointly modelled in the security-constrained UC problem. Table 1 summarises the differences between the proposed model and other relevant works in literature. Table 1. Proposed approach against existing SCUC Reference [3] [4] [5] [6] [7] [9] Proposed model endogenous computation of probabilities ✗ ✗ ✗ ✗ ✗ ✗ ✓ reserve deliverability ✓ ✓ ✗ ✓ ✗ ✗ ✓ energy storage ✓ ✓ ✓ ✓ ✓ ✓ ✓ multiperiod ✓ ✓ ✓ ✓ ✓ ✓ ✓ 2 Probabilistic security-constrained UC model The objective function of the PSCUC is given as follows: (1) where and are, respectively, the probabilities of the pre- and post-contingency states computed as (2) (3) (4) The first term in (1) represents the expected pre-contingency operating cost of conventional generators, which includes their start-up, no-load, and production cost under the central load and wind generation forecast, as well as the cost of providing up/downward contingency reserve. The second term in (1) accounts for the charging and discharging costs of ESS, as in [20], that can be scheduled to provide arbitrage and up/downward reserve. ESS charging and discharging costs are only incurred by their electrochemical degradation which is modelled with the ESS cycle performance characteristic [21]. The third term in (1) computes the expected cost of energy not served in post-contingency states if the up/downward reserve procured in the pre-contingency state is not sufficient to meet the post-contingency demand for any wind power realisation. The expected post-contingency operating cost is included in the fourth term in (1), where and represent the deployment of up/down reserve in post-contingency states. The expected post-contingency operating costs could be omitted from the formulation due to two main reasons: (i) the corrective costs are negligible [18], and (ii) it is assumed that the system will be rescheduled following the deployment of contingency reserve using the intra-day planning framework. However, as explained in Section 4.4, considering second-stage costs improves the performance of the BD. Equations (2)–(4) compute the probabilities of the pre- and post-contingency states as a function of binary decision variables assuming that individual contingencies are independent and stationary [2], i.e. a failure of one system component does not trigger subsequent equipment failures and the likelihood of any failure does not change over time. The relation between the random outage events and the decision variables of the UC is demonstrated in Appendix. Non-linear constraints (2)–(4) are linearised as explained in Section 3.1. The optimisation problem is subject to the following constraints: (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) Constraints (5) and (6) model the binary logic on the commitment, start-up, and shutdown status of conventional generators. The minimum up and down time constraints on conventional generators are enforced in (7) and (8). Constraint (9) ensures that the minimum up and down time of generators are met during the first periods of the optimisation horizon. The minimum and maximum power output limits are set in (10) and (11). Constraint (12) sets the up/downward ramp rate limits. Constraints (13)–(16) limit the inter-hour ramping of conventional generators for the different wind power scenarios using interval optimisation [2, 18, 19, 22]. Interval optimisation ensures feasibility of any realisation of the uncertainty source (i.e. wind power) within the upper and lower bounds of the uncertainty interval. Thus, the schedule provided by this optimisation is feasible for any scenario that remains within the pre-defined bounds. The output of wind power generators is bounded by and in (17). The ESS state of charge is computed in (18) and is constrained by the power and energy capacity ratings (19)–(21). The power flow is computed in (22) while its bounds are enforced in (23). The nodal power balance is defined in (24) and (25) for the pre- and post-contingency states, respectively. While no load shedding is allowed in the pre-contingency state (), post-contingency load shedding () is bounded according to (26). The up- and downward reserve provision by generator i is bounded as in (27) and (28) while the upward and downward reserve deployments in post-contingency state limits are defined in (29) and (30). Constraint (31) ensures reserve deliverability in the post-contingency states. The reserve provided by the ESS is limited by its arbitrage schedule and minimum and maximum allowable state of charge (32) and (33). Note that the limits in (32) and (33) can be set to reflect battery health limits. Constraint (34) limits the ESS state of charge during the last period of the optimisation horizon to ensure its availability during the first periods of the next optimisation horizon. 3 Benders' decomposition approach Available off-the-shelf solvers fail to solve the proposed PSCUC model in (1)–(34) due to its highly non-linear and non-convex nature. This section proposes a tractable solution technique based on BD [23] to deal with the PSCUC problem without relying on simplifications, as proposed in [2] that lead to suboptimal decisions. The PSCUC can be split up into a master problem (MP) for the pre-contingency state, and as many independent subproblems (SP) as contingencies are modelled. Sections 3.1 and 3.2 present the MP and SP of Benders' algorithm described in Section 3.3. 3.1 Master problem The MP is formulated for the pre-contingency state and accounts for the total expected cost of load shedding in the post-contingency states via the auxiliary variable . The objective function (35) is subject to the following constraints: (36) (37) (38) (39) (40) (41) Superscript defines the current iteration. Equations (38) and (39) are the optimality and feasibility cuts, where are the dual variables of the SP constraints (66)–(76). Constraint (40) imposes the lower bound on . Constraint (41) is added to the MP to reduce the number of infeasible SPs during the first iterations. This constraint limits the production of the generators in the pre-contingency state at nodes which are connected to the network through one single line (i.e. ), and thus, would be isolated when that line is under contingency. Unlike conventional implementations of BD with single cuts (i.e. one cut per iteration), optimality cuts (38) are generated per iteration and per contingency. Adding multi-cuts (i.e. individual cuts per contingency) reduces the required number of iterations and speeds up convergence [24]. Note that this strategy may slow the MP to attain the required solution. The MP (35)–(41) is a mixed-integer non-linear program due to (2) and the objective function (35). Equation (2) computes the probability in the pre-contingency state for each time period t as a function of the binary scheduling variables , and thus is a highly non-linear and non-convex term. Other works in the literature [25–27] account for such relationship at the expense of neglecting the higher order terms of the product expansions of those probabilities. However, as proposed in [2], the product terms in expression (2) can be linearly approximated as follows: (42) where represents the slope of the linear function and represents its vertical offset. The accuracy of the linear approximation increases as the outage replacement rates reduce, and when they are comparable to each other in magnitude, as is the case in power systems (e.g. see [28, 29]). The linear approximation (42) replaced in the objective function (35) renders it non-linear. The non-linear products can then be replaced by mixed-integer linear expressions using integer algebra [30], which result in the following set of linear expressions: (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57) (58) (59) (60) (61) here , , , , , , , and are equal to the products , , , , , , , and , respectively. The linearised variables are modeled through (44)–(46), (47)–(48), (49)–(50), (51)–(52), (53)–(55), (56)–(57), (58)–(59), and (60)–(61), respectively [30]. Finally, the original MP is recast as the following mixed-integer linear program: (62) s.t. (63) (64) 3.2 Subproblem The SP is formulated for every post-contingency state k at every time period t as a linear programming problem, thus resulting in SPs which are solved in parallel. The objective function (65) of each SP is subject to the following constraints: (66) (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) where complicating variables obtained from the MP, i.e. , , , , , , , and are fixed. Hence, (65) is a linear expression that, in turn, makes each SP a linear problem. The dual variables of constraints (66)–(76) are after a colon corresponding to each constraint and are used to construct the feasibility and optimality cuts in (38) and (39). 3.3 BD algorithm Benders' algorithm [23] iterates as follows: (1) Initialisation : Set , , , and fix complicating variables. (2) SP solution : Solve the SPs (65)–(76) in parallel and calculate . (3) Computation of lower (LB) and upper (UB) bounds: (4) Convergence check : If , the optimal solution with a given tolerance is achieved. Otherwise, build the Benders' cuts for the next iteration, . (5) MP solution : Solve the MP as in (62)–(64) and calculate . Update the complicating variables and go to step (2). 4 Case study The proposed PSCUC model is tested on a modified single-area IEEE RTS [2]. Following the siting and sizing procedure described in [8], one ESS is installed at bus 21 with , , . The degradation cost of ESS is computed as in [21] with the degradation rate of energy capacity set to 0.00547 per cycle and the ESS capital cost from [8]. It is assumed that conventional generators offer reserve at and ESS offer reserve at , where and . The nodal load at each bus is chosen for Wednesday of the spring/fall week with a weekly factor of 0.9 [28]. The wind power generation forecast and its bound for each wind farm is obtained from [2]. The central forecast and the min/max bounds on the wind power generation output at each wind farm are obtained as the expected value and the 5th/95th percentile of 1000 randomly generated samples [18]. The impact of wind power generation is assessed in case the wind power output is positively and negatively correlated with the load. The daily penetration level of wind power generation achieves 16.17% of the daily demand. For the sake of simplicity, it is assumed that the value of lost load is the same at all buses, i.e. . The PSCUC model is compared against two benchmarks: Benchmark 1 is the deterministic UC (DUC) with the security criterion [31] and the (3 + 5)% reserve policy [32]. The criterion ensures that there is sufficient reserve capacity to sustain a loss of any single synchronised conventional generator without optimal network allocation. This may limit post-contingency reserve deployability due to congestion. Benchmark 2 is the multiperiod probabilistic interval UC (MPIUC) model proposed in [2]. Unlike Benchmark 1, it optimises the reserve requirement in a probabilistic fashion and allocates it in the network to ensure deployability in post-contingency states. However, Benchmark 2 is solved using a two-stage, heuristic procedure that disregards inter-temporal couplings of the UC decisions, and thus cannot accommodate the required models for ESS. This benchmark is only used in Section 4.1 in order to assess the PSCUC performance without considering the effects of distributed ESS. All models are implemented in GAMS 24.1 and solved with CPLEX on a Windows 8-based Server 2012 R2 Standard with 256 GB of RAM and two processors Intel Xeon E5-2698 clocking at 2.3 GHz. The MIP gap is and the tolerance of Benders' algorithm is . 4.1 Optimal reserve sizing and allocation This section analyses the effects of probabilistic reserve sizing and allocation across the network relative to the proposed benchmarks. To isolate these effects from those of wind power generation and ESS, this section assumes there is no wind power generation nor ESS in the system. Figs. 1a and b show the optimal reserve requirement and its allocation in the network obtained with the PSCUC model for different and compares it to the DUC reserve procurement shown in Fig. 1c. As the increases, the total reserve capacity scheduled by the PSCUC also increases and is spread over a larger set of buses. Even if the capacity requirements are nearly the same for and , as it occurs during hour 23, their optimal allocation in the network is different. When compared against the DUC, it can be seen that the total capacity requirement obtained with the PSCUC is usually lower and varies on an hourly basis. Thus, the DUC solution tends to overestimate reserve in most of the periods and procures insufficient reserve capacity in the remaining periods. While the DUC model allocates reserve at the same buses for several hours (see for instance, hours 4–5, 10–12, 13–19, and 21–22 in Fig. 1c), the reserve allocation in the proposed PSCUC varies in terms of amount and location over the course of the optimisation horizon. Fig. 1Open in figure viewerPowerPoint Optimal up reserve allocation for the PSCUC model (a) , (b) , (c) DUC model Blue line in all subplots denotes the total capacity requirement of the security criterion enforced in the DUC Table 2 compares the commitment decisions made by the PSCUC with and the DUC computed as . This difference indicates that in order to provide a constant amount of reserve, an extra high capacity generator is synchronised at bus 13 during all periods. However, in the PSCUC model, the flexible generators are only synchronised during the periods of high demand. The difference in the commitment status between PSCUC and the MPIUC proposed in [2] for is shown in Table 3 (). The MPIUC commitment is similar to the one obtained with the DUC. This is because, even if the minimum amount of reserve is calculated in the single-period probabilistic UC (SPPUC) its allocation is not optimised (see Section III.4 in [2] for further details). Note that the MPIUC model proposed in [2] is made up of two stages. First, a single-period probabilistic UC (SPPUC) is run to compute the nodal reserve requirements, which are then enforced in the MPIUC problem to ensure multi-period feasibility of UC decisions. For the sake of clarity, those periods where the commitment variables are the same for both models are left in blank in the tables above mentioned. Table 2. Commitment status differences between PSCUC and DUC t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Bus 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 −1 −1 −1 −1 −1 −1 −1 −1 −1 15 Table 3. Commitment status differences between PSCUC and MPIUC t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Bus −1 −1 −1 −1 −1 −1 −1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 −1 −1 −1 −1 −1 −1 −1 −1 7 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 13 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 15 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 1 15 1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 1 15 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 15 1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 15 −1 −1 −1 15 4.2 Energy storage system as a contingency reserve provider This section analyses the results attained with the PSCUC model for cases with and without ESS for negative and positive correlation between wind power and load. Thus, the total operating cost, i.e. the expected production cost plus the cost of expected energy not served (EENS), in cases with ESS is lower than without ESS, as shown in Fig. 2. In case of positively correlated wind power and load profiles, the increase in the cost of EENS (Fig. 2a) is outweighed by the production cost savings (Fig. 2b) leading to a reduction in the total operating cost (Fig. 2c). Fig. 2Open in figure viewerPowerPoint Results for in cases with and without ESS (a) Expected cost of energy not served, (b) Production cost, (
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