Distribution Robust Energy Storage Planning Method Considering the Spatial Correlation of Renewable Power Sources

Abstract

The present invention discloses a distributionally robust energy storage planning method considering the spatial correlation of renewable power sources. The method includes the following steps: establishing a spatial correlation model of renewable power sources by using the kernel density estimation method and the multivariate copula function according to historical data, and generating scenarios by using the Latin hypercube; establishing a deterministic two-stage energy storage planning model considering the node system and energy storage types; considering the characteristics of renewable energy data in the planning stage, transforming the above model into an uncertainty model by using the distributionally robust optimization method based on multiple discrete scenarios, solving the decision results in the operation stage according to the typical scenarios generated from historical data, and finally obtaining the energy storage planning decision results under the worst probability distribution of uncertain variables. The energy storage planning method provided by the present invention comprehensively considers the uncertainty of renewable energy during the planning period and the spatial correlation of actual operation, ensures the reliability and effectiveness of the planning, and can be well applied to the planning of power system energy systems.

Description

Technical Field

[0001] The present invention relates to the technical field of energy storage planning in power systems, and particularly to a distributionally robust energy storage planning method considering the spatial correlation of renewable power sources. Background Art

[0002] The output of renewable energy has strong uncertainties such as volatility and intermittency. With the increasing proportion of renewable energy connected to the power system, energy storage systems have become a key technology to cope with the uncertainties of renewable energy. Energy storage has flexible charge and discharge characteristics and is an effective tool to improve the operation stability and economy of the system. Therefore, for a power system with a high proportion of renewable energy, it is crucial to plan the installation location and capacity of energy storage.

[0003] Existing energy storage planning problems generally only consider the existence of a single renewable power source in the system. The modeling of the uncertainties of renewable power sources mainly focuses on the construction of stochastic scenarios or output uncertainty sets, thereby establishing an energy storage siting and sizing model considering the uncertainties of renewable energy.

[0004] However, most of the current models do not consider multiple renewable power sources and the correlation characteristics of the power sources in the spatial dimension. Ignoring this spatial correlation characteristic will reduce the accuracy of the model in the planning and solution stages. Moreover, in the uncertainty modeling, the construction of stochastic scenarios generally assumes a certain specific distribution, and the scale of the number of scenarios is also a major limitation. Secondly, although the construction of the output uncertainty set has strong robustness, the calculation results are too conservative. Therefore, the results of energy storage planning have limitations and are restricted in practical applications. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a distributionally robust energy storage planning method considering the spatial correlation of renewable power sources. For the spatial distribution of multiple renewable power sources, a spatial correlation characteristic model of multiple output scenarios is established, and a probability distribution fuzzy set is constructed to consider the influence of its uncertainties, thereby improving the feasibility and universality of the practical application of the energy storage planning results. To achieve the above object, the present invention adopts the following technical solutions:

[0006] The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources is carried out according to the following steps:

[0007] (1) Collect the historical output statistical data of multiple adjacent renewable energy power plants, and perform preprocessing normalization on the data;

[0008] (2) Introduce non-parametric kernel density estimation (KDE) to calculate the marginal distribution function (MDF) of the historical output data of each wind farm, and establish a spatial correlation model using the multivariate copula function;

[0009] (3) Adopt the Latin Hypercube Sampling (LHS) technique to generate scenarios with spatial correlation from the correlation model and perform scenario reduction to obtain typical scenarios;

[0010] (4) Add renewable energy power plants to the nodal system, select appropriate energy storage types and introduce them to form an improved nodal system, and fix the positions of renewable power sources;

[0011] (5) Set the positions of energy storage as binary variables, while the capacity and power of energy storage are set as continuous variables. The above three are used as decision variables, and a deterministic energy storage planning model is formed according to constraint conditions such as system power constraints, network constraints, charge and discharge constraints, etc.;

[0012] (6) According to the reduced typical discrete scenarios containing the spatial correlation of renewable energy, use the multi-discrete scenario method of distributionally robust optimization to construct a fuzzy set of uncertain variables, and introduce this uncertainty model into the above deterministic planning model to form an uncertain energy storage planning model;

[0013] (7) Initially solve the installation location, power and capacity of energy storage in the planning stage, and optimize the energy storage location and capacity using scenarios with spatial correlation in the operation stage.

[0014] Preferably, in step (1), the historical output statistical data of multiple adjacent renewable energy power plants are represented by a matrix:

[0015]

[0016] In the matrix, FarmN represents the Nth renewable energy power plant, and W N represents the column variable formed by this power plant; perform normalization preprocessing on the historical data, and use the maximum-minimum normalization method (mapminmax) to transform the historical data into the range of [0, 1]. The formula is as follows:

[0017]

[0018] Among them, x is the sample data, x max is the maximum value of the sample data, and x min is the minimum value of the sample data.

[0019] Preferably, the method for calculating the marginal distribution function of the output data of each wind farm using non-parametric kernel density estimation in step (2) is as follows:

[0020]

[0021] where x i is the sample point, K(·) is the Gaussian kernel function, h is the smoothing parameter or bandwidth, and the historical data generates the marginal distribution function [F(P w1 ) F(P w2 )…F(P wN )]; according to the multivariate copula function, the marginal distribution functions are fitted to establish a spatial correlation model:

[0022] F(x1, x2,..., x N ) = C(F(x1), F(x2),..., F(x N ))

[0023] For the correlation of multiple variables, generally, the Gaussian Copula or t-Copula function is used to model it.

[0024] Preferably, the method for sampling using the Latin hypercube technique in step (3) is as follows:

[0025] ① Assume that the cumulative distribution function of the random variable is [F(x1) F(x2) … F(x N )], and set the number of samplings to K;

[0026] ② Divide the value interval of the distribution function into K equally spaced non-overlapping subspaces, and the length of each subinterval is 1 / K;

[0027] ③ Sample randomly layer by layer, and select a sampling value of the distribution function from each subinterval through the Monte Carlo sampling method and shuffle the order;

[0028] ④ According to the inverse function F -1 (·) of the cumulative distribution function, the final sample value is deduced.

[0029] Preferably, the formation of the improved node system in step (4) is to fix the node positions of the renewable energy power plants in the system, and on this basis, introduce electrochemical energy storage as a unit of the system, and solve the energy storage position, power, and capacity suitable for the system.

[0030] Preferably, the method for forming a deterministic energy storage plan in step (5) is as follows:

[0031] ① The location, power, and capacity of energy storage are defined as decision variables [a, P, E], where the node location a of energy storage installation belongs to {0, 1}, and P, E > 0;

[0032] ② List the constraints, including: energy storage location capacity constraint, investment cost constraint, conventional unit constraint, power balance constraint, line transmission capacity constraint, energy storage charge and discharge constraint, and energy storage SOC constraint;

[0033] ③ The goal of deterministic energy storage planning is:

[0034] min F(a, P, E) + G(P g , P ch , P dc , SOC, P w )

[0035] In the formula, F(·) represents the investment cost function related to the energy storage decision variables, and G(·) represents the operating cost function related to the system operating variables. Among them, a represents the energy storage installation location, which is a 0 / 1 binary variable, P represents the energy storage installation power, and E represents the energy storage installation capacity; P g represents the power generation of conventional units, P ch , P dc respectively represent the energy storage charge and discharge power, SOC represents the energy storage state of charge variable, and P w represents the power generation of renewable energy sources.

[0036] Preferably, the method for constructing a multi-discrete scenario fuzzy set based on distributionally robust optimization in step (6) is as follows:

[0037] ① Cut the original renewable energy source scenarios with spatial correlation into some intervals, and form a reference distribution of sample probabilities according to the samples in each interval;

[0038] ② Construct a fuzzy set of uncertain variables by taking the initial probability distribution value, that is, the reference distribution of sample probabilities, as the center and using the comprehensive norm including the 1-norm and ∞-norm as the constraint conditions to constrain the probability distribution values of discrete scenarios;

[0039] ③ Set the confidence level so that the scenario probabilities satisfy the confidence level constraint;

[0040] ④ Introduce the above uncertainty fuzzy set into the deterministic model to obtain an uncertain energy storage planning model:

[0041]

[0042] In the formula, F(·) represents the investment cost function related to the energy storage decision variable, and G(·) represents the operating cost function related to the system operating variable. Among them, a represents the energy storage installation location, which is a 0 / 1 binary variable, P represents the energy storage installation power, and E represents the energy storage installation capacity; P g represents the power generation of the traditional unit, P ch and P dc respectively represent the charging and discharging power of the energy storage, SOC represents the state of charge variable of the energy storage, P w represents the power generation of the renewable power source (taking a wind farm as an example); p s represents the probability of each scenario.

[0043] Preferably, the method for solving the uncertainty model described in step (7) is as follows:

[0044] ① Set the lower bound value LB = 0, the upper bound value UB = +∞, set the iteration number m = 1, and the initial scenario probability distribution is obtained according to the historical experience data distribution

[0045] ② Solve the master problem (MP): min F(a, P, E)+η, and obtain the optimal solution (a * , P * , E * , η * ), and update the lower bound value LB = max{LB, F(a * , P * , E * )+η *};

[0046] ③ Fix the first-stage variables [a * , P * , E * , and solve the sub-problem (SP): Obtain the probability distribution under the worst-case scenario and the optimal objective function value L * . Update the upper bound value UB = min{UB, F(a * , P * , E * )+L *};

[0047] ④ Judge the gap of the optimization value. If UB - LB ≤ ε, stop the iteration and return the optimal value x * ; otherwise, update the worst-case probability distribution in the master problem and add new variables in the master problem Add the constraint conditions related to the new variables;

[0048] ⑤ Update the number of iteration times, return to step 2, and finally solve to obtain the siting and sizing strategy of energy storage.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] 1. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources provided by the present invention takes into account the spatial correlation of historical data of multiple adjacent wind farms and establishes a correlation model, making the multi-wind farm model more in line with the actual situation and effectively improving the accuracy of the planning model.

[0051] 2. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources provided by the present invention proposes a scenario generation method for a multivariate joint distribution function, samples the joint distribution function using the Latin hypercube sampling technique, realizes the effect of achieving the same result as multiple random samplings with fewer times, and retains the spatial correlation characteristics of the sample results.

[0052] 3. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources provided by the present invention proposes an uncertainty energy storage planning model based on distributionally robust multi-discrete scenarios, constructs a fuzzy set according to the historical data of wind power output, comprehensively considers the impact of the uncertainty of wind power output on the system, and makes the planning result feasible and not overly conservative. Description of the Drawings

[0053] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0054] Figure 1 is the overall flowchart of the present invention;

[0055] Figure 2 is the improved IEEE 24-node system diagram with wind power for energy storage siting and sizing of the present invention;

[0056] Figure 3 is the spatial correlation structure diagram of the data of each wind farm generated after modeling by the multivariate Copula function;

[0057] Figure 4 is the implementation abstract diagram of the present invention. Detailed Embodiments

[0058] The following will further elaborate on the present invention in conjunction with the drawings, but the embodiments of the present invention are not limited thereto.

[0059] The case uses the distributionally robust energy storage planning method described in the present invention to plan the energy storage location and capacity of a node test system with renewable power sources.

[0060] The distributionally robust energy storage planning considering the spatial correlation of renewable power sources is as follows:

[0061] 1. Collect the historical output statistical data of multiple adjacent renewable energy power plants; the historical data of multiple adjacent renewable energy power plants are represented by P w The output data of 4 wind farms are selected and represented by {P W1 , P W2 , P W3 , P W4}. The historical output statistical data of the 4 wind farms in this embodiment are selected from the historical wind power output data of the Australian Energy Market Operator in 2013, with a data resolution of 5 minutes and a total of 105,120 groups of data.

[0062] Re-arrange the historical data according to each wind farm. For example, represents the t-th observation value of the N-th wind farm. The result of matrix arrangement is as follows:

[0063]

[0064] Preprocess the historical data by normalizing it column by column. Use the min-max normalization method (mapminmax) to transform the historical data into the range [0, 1]. The formula is as follows:

[0065]

[0066] In the formula, x is the sample data, x max is the maximum value of the sample data, and x min is the minimum value of the sample data.

[0067] Table 1 shows some of the historical output statistical data after normalization processing.

[0068] Table 1 Statistics of historical output data of 4 adjacent wind farms

[0069]

[0070]

[0071] 2. Calculate the marginal distribution function of the historical output data of 4 wind farms according to the non-parametric kernel density estimation method. The calculation formula is as follows:

[0072]

[0073] Among them, x iis a sample point, K(·) is the Gaussian kernel function, and h is the smoothing parameter or called the bandwidth. After the calculation, four marginal distribution functions [F1(x1) F2(x2) F3(x3) F4(x4)] are obtained.

[0074] According to the multivariate copula function to fit the marginal distribution functions, a spatial correlation model is established:

[0075] F(x1, x2, x3, x4) = C(F(x1), F(x2), F(x3), F(x4))

[0076] For this implementation case, due to the characteristics of the selected data, the t-Copula is selected as the model function:

[0077]

[0078] The above formula is in the form of a bivariate copula. Since the case is four wind farms, it needs to be extended to a four-variate according to the actual situation.

[0079] 3. According to the Latin hypercube sampling technique, samples are generated from the established four-variate t-Copula to form scenarios with spatial correlation. The specific steps are as follows:

[0080] ① The marginal distribution functions of the current wind power random variables are [F(x1) F(x2) F(x3) F(x4)], and the number of samplings is set to 10,000;

[0081] ② The value interval [0, 1] of the distribution function is divided into 10,000 equally spaced non-overlapping subspaces, and the length of each sub-interval is 1 / 10,000;

[0082] ③ Sampling is performed layer by layer. By the Monte Carlo sampling method, a sampling value of the distribution function is selected from each sub-interval and the order is shuffled;

[0083] ④ According to the inverse function of the cumulative distribution function The final sample values are deduced inversely. Thus, the initial 10,000 wind power scenarios are generated.

[0084] 4. The method for forming an improved node system: By fixing the node positions of the renewable energy power plants in the system, on this basis, an electrochemical energy storage is introduced as a unit of the system, and the energy storage position, power, and capacity suitable for the system are solved. In this embodiment, the 24-node test system is selected for improvement, and the positions of the four wind farms are fixed at nodes 11, 12, 17, and 24 respectively, thus forming an improved node system for determining the position and capacity of the energy storage system.

[0085] 5. The specific steps for forming a deterministic energy storage planning model are as follows:

[0086] ① The location, power, and capacity of energy storage are defined as decision variables [a, P, E]. The node location a of energy storage installation belongs to {0, 1}, and P, E > 0.

[0087] ② List the constraints, including: energy storage location capacity constraint, investment cost constraint, traditional unit constraint, power balance constraint, line transmission capacity constraint, energy storage charge-discharge constraint, energy storage SOC constraint, etc. The specific details are as follows:

[0088] Energy storage location capacity constraint:

[0089]

[0090]

[0091]

[0092] Investment cost constraint:

[0093]

[0094] Traditional unit output constraint:

[0095]

[0096] Power balance constraint:

[0097]

[0098] Transmission capacity constraint:

[0099]

[0100] Energy storage charge-discharge constraint:

[0101]

[0102]

[0103] Energy storage SOC constraint:

[0104]

[0105]

[0106] ③ The goal of deterministic energy storage planning is:

[0107] min F(a, P, E) + G(P g , P ch , P dc , SOC, P w )

[0108] The specific details are as follows:

[0109]

[0110] 6. The method for constructing a multi-discrete scenario fuzzy set based on the distributionally robust optimization method is as follows:

[0111] ① Reduce from the original 10,000 scenarios with spatial correlation to 6 intervals. The number of interval samples in each discrete scenario is N1, N2, N3, N4, N5, N6, and the reference distribution is composed of the sample probabilities in each interval.

[0112] ② Construct a fuzzy set Ω that constrains the probability distribution values of discrete scenarios with the initial probability distribution value as the center and a comprehensive norm including the 1-norm and ∞-norm as the constraint condition:

[0113]

[0114] Among them, is the initial probability value of the s-th discrete scenario, and Ω1, Ω η correspond to the allowable probability deviation values under the 1-norm and ∞-norm constraints respectively.

[0115] ③ The scenario probability satisfies the confidence level constraint:

[0116]

[0117] By setting the confidence levels α1, α ∞ , it can be inversely deduced that:

[0118]

[0119] If the set confidence levels are both 95%, then θ1 = 0.00164, θ ∞ = 0.000274.

[0120] ④ Introduce the above uncertainty fuzzy set into the deterministic model to obtain the uncertain energy storage planning model:

[0121]

[0122] Specifically expanded as follows:

[0123]

[0124] 7. The specific steps of the C&CG solution method for the uncertain energy storage planning model are as follows:

[0125] ① Set the lower bound value LB = 0, the upper bound value UB = +∞, set the iteration number m = 1, and the initial scenario probability distribution is obtained according to the historical experience data distribution.

[0126] ② Solve the master problem (MP): min F(a, P, E) + η, and obtain the optimal solution (a * , P * , E * , η * ), and update the lower bound value LB = max{LB, F(a * , P * , E * ) + η *}.

[0127] ③ Fix the first-stage variables [a * , P * , E * , and solve the subproblem (SP): Obtain the probability distribution under the worst-case scenario and the optimal objective function value L * . Update the upper bound value UB = min{UB, F(a * , P * , E * ) + L *}.

[0128] ④ Judge the gap of the optimized value. If UB - LB ≤ ε, stop the iteration and return the optimal value x * ; otherwise, update the worst-case probability distribution in the master problem and add new variables in the master problem Add the constraint conditions related to the new variables.

[0129] ⑤ Update the number of iterations and return to step 2. Finally, obtain the siting and sizing strategy of the energy storage.

[0130] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A distributionally robust energy storage planning method considering the spatial correlation of renewable power sources, characterized in that, Proceed as follows: (1) Collect historical output statistical data of multiple adjacent renewable energy power plants, and preprocess and normalize the data; (2) Introduce non-parametric kernel density estimation to calculate the marginal distribution function of the historical output data of each wind farm, and use the multivariate copula function to establish a spatial correlation model; (3) Adopt the Latin hypercube sampling technique to generate scenarios with spatial correlation from the correlation model and perform scenario reduction to obtain typical scenarios; (4) Add the renewable energy power plant to the nodal system, select a suitable energy storage type and introduce it to form an improved nodal system, and fix the position of the renewable power source; (5) Set the position of the energy storage as a binary variable, while the capacity and power of the energy storage are set as continuous variables. The above three are used as decision variables, and a deterministic energy storage planning model is formed according to constraints such as system power constraints, network constraints, charge and discharge constraints, etc.; (6) According to the reduced typical discrete scenarios containing the spatial correlation of renewable energy, use the multi-discrete scenario method of distributionally robust optimization to construct a fuzzy set of uncertain variables, and introduce this uncertainty model into the above deterministic planning model to form an uncertain energy storage planning model; (7) Initially solve the installation position, power and capacity of the energy storage in the planning stage, and optimize the energy storage location and sizing using scenarios with spatial correlation in the operation stage.

2. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, wherein In step (1), the historical output statistical data of multiple adjacent renewable energy power plants is represented by a matrix: In the matrix, FarmN represents the Nth renewable energy power plant, and W N represents the column variable formed by this power plant; the historical data is preprocessed by normalization, and the maximum-minimum normalization method is used to transform the historical data into the range of [0,1]. The formula is as follows: where x is the sample data, x max is the maximum value of the sample data, x min is the minimum value of the sample data.

3. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, characterized in that The method for calculating the marginal distribution function of the output data of each wind farm using non-parametric kernel density estimation described in step (2) is as follows: where x i is a sample point, K(·) is a Gaussian kernel function, h is a smoothing parameter or called bandwidth, and historical data generates a marginal distribution function [F(P w1 ) F(P w2 ) … F(P wN )]; fitting the marginal distribution function according to the multivariate copula function to establish a spatial correlation model: F(x1,x2,...,x N ) = C(F(x1),F(x2),...,F(x N )) For the correlation of multiple variables, the Gaussian Copula or t-Copula function is used to model it.

4. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, wherein The method for sampling using the Latin hypercube technique described in step (3) is as follows: ① Suppose the cumulative distribution function of the random variable is [F(x1) F(x2) … F(x N )], and set the number of sampling times as K; ② Divide the value interval of the distribution function into K equally spaced non-overlapping subspaces, and the length of each sub-interval is 1 / K; ③ Randomly sample layer by layer, and select a distribution function sampling value from each sub-interval by the Monte Carlo sampling method and shuffle the order; ④Back-calculate the final sample value according to the inverse function F -1 (·) of the cumulative distribution function.

5. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, characterized in that The formation of the improved nodal system described in step (4) is achieved by fixing the nodal position of the renewable energy power plant in the system. On this basis, introduce electrochemical energy storage as a unit of the system, and solve the energy storage position, power and capacity suitable for the system.

6. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, wherein The method for forming a deterministic energy storage planning described in step (5) is as follows: ① The position, power and capacity of the energy storage are defined as decision variables [a, P, E], the nodal position a where the energy storage is installed ∈ {0, 1}, and P, E > 0; ② List the constraints, including: energy storage position capacity constraint, investment cost constraint, traditional unit constraint, power balance constraint, line transmission capacity constraint, energy storage charge and discharge constraint, energy storage SOC constraint; ③ The goal of deterministic energy storage planning is: minF(a,P,E)+G(P g ,P ch ,P dc ,SOC,P w ) In the formula, F(·) represents the investment cost function related to the energy storage decision variable, and G(·) represents the operating cost function related to the system operating variable. Among them, a represents the energy storage installation location, which is a 0 / 1 binary variable, P represents the installed power of the energy storage, and E represents the installed capacity of the energy storage; P g represents the power generation of the traditional unit, P ch , P dc respectively represent the charging and discharging power of the energy storage, SOC represents the state of charge variable of the energy storage, and P w represents the power generation of the renewable power source.

7. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, characterized in that The method for constructing a fuzzy set of multi-discrete scenarios based on distributionally robust optimization described in step (6) is as follows: ① Reduce the original scenarios of renewable power sources with spatial correlation to some intervals, and form a reference distribution of sample probabilities according to the samples in each interval; ②Construct a fuzzy set of uncertain variables by taking the initial probability distribution value, i.e., the sample probability reference distribution, as the center and using a comprehensive norm containing the 1-norm and ∞-norm as the constraint condition to constrain the probability distribution value of the discrete scenario; ③Set the confidence level so that the scenario probability satisfies the confidence level constraint; ④Introduce the above uncertainty fuzzy set into the deterministic model to obtain an uncertain energy storage planning model: In the formula, F(·) represents the investment cost function related to the energy storage decision variable, and G(·) represents the operating cost function related to the system operating variable. Among them, a represents the energy storage installation location, which is a 0 / 1 binary variable, P represents the installed power of the energy storage, and E represents the installed capacity of the energy storage; P g represents the power generation of the traditional unit, P ch , P dc respectively represent the charging and discharging power of the energy storage, SOC represents the state of charge variable of the energy storage, P w represents the power generation of the renewable power source (taking a wind farm as an example); p s represents the probability of each scenario.

8. The distributionally robust energy storage planning method considering the spatial correlation of renewable power sources according to claim 1, characterized in that The method for solving the uncertainty model described in step (7) is as follows: ① Set the lower bound value LB = 0, the upper bound value UB = +∞, set the number of iterations m = 1, and the initial scenario probability distribution is obtained according to the historical experience data distribution ②Solve the master problem (MP): min F(a, P, E) + η, and obtain the optimal solution (a * , P * , E * , η * ), and update the lower bound value LB = max{LB, F(a * , P * , E * ) + η *}; ③ Fix the first-stage variables [a * , P * , E * , and solve the subproblem (SP): Obtain the probability distribution under the worst-case scenario and the optimal objective function value L * ; update the upper bound UB = min{UB, F(a * , P * , E * ) + L *}; ④ Judge the difference of the optimization values. If UB - LB ≤ ε, stop the iteration and return the optimal value x * ; Conversely, update the worst probability distribution in the master problem and add new variables to the master problem Add constraint conditions related to the new variables; ⑤Update the number of iterations, return to step 2, and finally solve to obtain the siting and sizing strategy of the energy storage.

Images