Two-stage robust optimization scheduling method for microgrid based on data-driven uncertain sets

Abstract

The present invention discloses a two-stage robust optimization scheduling method for a microgrid based on a data-driven uncertainty set, including: obtaining historical data of wind power forecast values ​​and actual values, and constructing a conditional normal Copula model based on the historical data; inputting the wind power forecast value of the day before into the conditional normal Copula model to obtain the wind power sample of the next day; based on the wind power sample of the next day, constructing a data-driven uncertainty set that considers the time correlation of wind power through support vector clustering and dimensional decomposition; constructing a microgrid two-stage robust optimization scheduling model of a min-max-min structure based on the data-driven uncertainty set; optimizing scheduling through the microgrid two-stage robust optimization scheduling model and a column constraint generation algorithm to obtain an optimized scheduling result. The present invention can fully consider the time correlation of wind power in adjacent time periods through dimensional decomposition, further reduce the conservativeness of the uncertainty set, and reduce the scheduling cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of microgrid optimization scheduling, and in particular relates to a microgrid two-stage robust optimization scheduling method based on data-driven uncertainty sets. Background Art

[0002] In recent years, the environmental problems caused by the use of traditional fossil energy have become increasingly serious. Microgrids, as an important carrier for absorbing new energy such as wind power, have received widespread attention from various countries. With the increase in the penetration rate of wind power in microgrids, the problem of environmental pollution has been alleviated to a certain extent, but at the same time, the uncertainty of its power generation has also brought great challenges to the optimization and scheduling of microgrids.

[0003] At present, there are many types of optimization scheduling methods for wind power uncertainty, which can be mainly divided into two categories: robust optimization and stochastic optimization. Among them, stochastic optimization includes: (1) Assuming that the load probability distribution function is a normal distribution and the wind speed distribution function is a Rayleigh distribution, a multi-objective reactive power stochastic optimization scheduling model for the power system is established, and the ε-constrained optimization method is used to solve the model, thereby reducing the active power loss and improving the voltage stability of the system. (2) By establishing a two-stage stochastic optimization scheduling model for the AC and DC power grid two days in advance, a number of scenarios are randomly generated and then the scenarios are reduced. The retained scenarios are combined to obtain a typical scenario, thereby obtaining the corresponding scheduling strategy. However, the effect of stochastic optimization depends to a large extent on the accuracy of the probability distribution function. The distribution function estimated by historical data often has errors with the true distribution, resulting in the optimization result failing to meet expectations. Unlike stochastic optimization, robust optimization does not require knowing the exact probability distribution of random variables, but instead constructs an uncertain set to find the optimal solution under the worst conditions.

[0004] Robust optimization uncertainty sets describe the range of variation of uncertain parameters, so uncertainty sets directly affect the conservatism of scheduling schemes. In addition to containing possible uncertain scenarios, general uncertainty sets also contain many invalid areas, resulting in the resulting scheduling schemes being more conservative. Therefore, how to construct a compact uncertainty set has become the research focus of many experts and scholars. The prior art proposes a variety of uncertainty set construction methods, including box-type, polyhedron and ellipsoid, aiming to reduce the conservatism while ensuring the same robustness of the solution. Specifically, it includes: (1) By constructing a two-stage robust optimization model for microgrids, an uncertainty adjustment parameter is introduced on the basis of the box-type uncertainty set, and the conservatism of the scheduling scheme can be adjusted by adjusting the parameter. (2) By constructing a polyhedron uncertainty set and introducing a load correlation coefficient to describe flexible resources, a demand response decision model that actively responds to uncertainty is established, and the conservatism of the robust solution is reduced by constructing an uncertainty set that fits the data better. However, the assumption that the uncertain variables at each moment are independent of each other and the relatively simple structure make its conservatism need to be further reduced. (3) In addition, by establishing a Markov chain model based on the wind speed transfer probability matrix, the non-zero values ​​of the transfer probability matrix are basically concentrated near the diagonal, which proves that the wind speed has the characteristic of temporal correlation. In the traditional uncertainty set, both the polyhedron and the ellipsoid uncertainty set can consider the temporal correlation of the data. By constructing an ellipsoid uncertainty set to surround the historical wind power output data, the temporal correlation of the wind power output is considered. The simulation results show that the proposed uncertainty set reduces conservatism. (4) The temporal correlation of wind power prediction error and load prediction error is considered, avoiding the frequent fluctuations of wind power and load, thereby reducing the operating cost of the power system. Therefore, the existing technology considers the correlation of uncertain variables on the basis of the traditional uncertainty set, which reduces the conservatism of the robust solution to a certain extent.

[0005] In summary, most existing technologies only consider one aspect of constructing a compact uncertainty set and considering the correlation of uncertain variables, and it is urgent to consider comprehensively to minimize the conservatism of the scheduling scheme. In addition, the data used to construct the uncertainty set often contains some abnormal data in practice, and few literatures study the impact of abnormal data on the scheduling results, that is, the problem of the resistance of the uncertainty set to abnormal data. In practical applications, the geometric structure of the traditional uncertainty set is fixed, and it often cannot fit the data well when facing complex data distribution. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a two-stage robust optimization scheduling method for a microgrid based on a data-driven uncertainty set, comprising:

[0007] Acquire historical data of wind power forecast values ​​and actual values, and construct a conditional normal Copula model based on the historical data;

[0008] Input the day-ahead wind power forecast value into the conditional normal Copula model to obtain the next day's wind power sample;

[0009] Based on the next day wind power samples, a data-driven uncertainty set considering wind power time correlation is constructed by support vector clustering and dimensionality decomposition;

[0010] A two-stage robust optimization scheduling model for a microgrid with a min-max-min structure is constructed based on the data-driven uncertainty set;

[0011] The optimized scheduling is performed through the microgrid two-stage robust optimization scheduling model and the column constraint generation algorithm to obtain the optimized scheduling result.

[0012] Preferably, the process of obtaining historical data of wind power forecast values ​​and actual values ​​and constructing a conditional normal Copula model based on the historical data includes:

[0013] Define y WT =[y 1 ,...,y n ] is the wind power forecast value for each dispatching period of the day, n is the wind power data dimension, and the conditional normal Copula model is constructed using the historical data of wind power forecast values ​​and actual values.

[0014] Preferably, the process of inputting the day-ahead wind power forecast value into the conditional normal Copula model to obtain the next day's wind power sample includes:

[0015] Considering the time correlation and conditional correlation of wind power forecast error, the input wind power forecast value y WT , N wind power actual value samples are obtained by sampling, among which the i-th wind power actual value sample is

[0016] Preferably, based on the next day wind power sample, the process of constructing a data-driven uncertainty set considering wind power time correlation by support vector clustering and dimensionality decomposition includes:

[0017] Based on the next-day wind power sample, an uncertainty set is constructed by a data-driven method of support vector clustering, and then the uncertainty set is represented as the intersection of multiple low-dimensional uncertainty sets through dimensionality decomposition to characterize the time correlation of wind power, thereby obtaining the final data-driven uncertainty set; the data-driven uncertainty set is used to capture the geometric shape of data distribution, flexibly adjust its own geometric structure to fit the data tightly, and exclude outliers in the sample data, thereby reducing the conservatism of robust optimization while having outlier resistance.

[0018] Preferably, the process of constructing the uncertainty set based on the next day wind power sample by a data-driven method of support vector clustering includes:

[0019] The actual value samples of wind power are transformed into the nonlinear mapping function Mapped to the high-dimensional feature space F, the minimum sphere that can surround the data is obtained by support vector clustering to describe the sample data set; the minimum sphere is obtained by the following optimization problem:

[0020]

[0021] In the formula, u (i) is the actual value sample of wind power, is a nonlinear mapping function, with the center of the sphere being p and the radius being R, ξ i is the slack variable, ν is the regularization parameter;

[0022] The minimum radius sphere surrounding the data sample is obtained through the minimum sphere optimization problem, and outliers are penalized at the same time. The trade-off between the two different objectives is achieved by adjusting the regularization parameter ν, and the explicit expression of the initial uncertainty set based on support vector clustering is obtained:

[0023]

[0024] Among them, u is the uncertain variable of wind power;

[0025] Define the intermediate variables as:

[0026]

[0027] Further introduce auxiliary variable V = [v 1 ,...,v N ], and substitute it into formula (9) to obtain the explicit expression of the target uncertainty set based on support vector clustering:

[0028]

[0029] Preferably, the process of expressing the uncertainty set as an intersection of multiple low-dimensional uncertainty sets by dimensional decomposition includes:

[0030] Assume that the decomposition dimension is T D , considering T D Wind power time correlation of time interval, N D =nT D +1 is the number of low-dimensional uncertain sets after decomposition, the i-th D The time interval considered by the low-dimensional uncertain set is [i D ,i D +T D -1], 1≤i D ≤ND , the corresponding expressions are as follows:

[0031]

[0032] In the formula, For the i D The wind power uncertain variables corresponding to the low-dimensional uncertainty set are: and The i D The low-dimensional uncertainty sets correspond to the lower and upper bounds of wind power data samples;

[0033] The uncertainty set obtained by dimensional decomposition is the intersection of all low-dimensional uncertainty sets, and the expression is shown in formula (13):

[0034]

[0035] Preferably, after obtaining the final data-driven uncertainty set, the method further includes:

[0036] Constructing a comprehensive performance index of the evaluation index to evaluate the performance of the data-driven uncertainty set, thereby obtaining an optimal decomposition dimension;

[0037] The evaluation indicators include coverage indicators and capacity indicators;

[0038] The coverage index expression is:

[0039]

[0040] In the formula, Θ is the coverage index, which is used to reflect the U DD-SVC Coverage of wind power outside the sample, N test is the number of days of data for evaluating the performance of the uncertainty set, N i is the U corresponding to the i-th day DD-SVC The maximum number of time periods of out-of-sample wind power that can be covered is generated by the conditional normal Copula model based on the day-ahead wind power forecast value on the ith day. DD-SVC The wind power data of N T is the number of wind power time periods;

[0041] The capacity index expression is:

[0042]

[0043] In the formula, η is the capacity index, which is used to reflect the DD-SVC The relative size relationship with the box uncertainty set, the larger η is, the smaller U DD-SVC The smaller the capacity of the relatively box-like uncertain set, the smaller the capacity of V i DD-SVC is the U corresponding to the i-th dayDD-SVC Capacity, V i BOX is the capacity of the box uncertainty set on the i-th day;

[0044] The comprehensive performance index is obtained based on the weighted definition of the coverage index and the capacity index, and the expression is:

[0045] ζ=ω·Θ+(1-ω)·η (17)

[0046] Among them, ω is the weight of the coverage index, and its value range is (0,1); the larger the comprehensive performance index ζ is, the better the comprehensive performance of the corresponding uncertain set is, and the decomposition dimension corresponding to the maximum comprehensive performance index value is called the optimal decomposition dimension.

[0047] Preferably, the process of constructing a two-stage robust optimization scheduling model of a microgrid with a min-max-min structure based on the data-driven uncertainty set includes:

[0048] Based on the data-driven uncertainty set, a two-stage day-ahead robust optimization model is established with the goal of minimizing the day-ahead scheduling cost:

[0049]

[0050] x and y are optimization variables, and the expression is

[0051]

[0052] Where: c is the coefficient column vector corresponding to the objective function; D, K, F, G, J are the coefficient matrices corresponding to the variables under the corresponding constraints; d and h are constant column vectors.

[0053] Preferably, the process of optimizing scheduling by using the microgrid two-stage robust optimization scheduling model and the column constraint generation algorithm includes:

[0054] The two-stage robust optimization model is used to decompose the original problem into a main problem and sub-problems through a column constraint generation algorithm, and then it is solved iteratively;

[0055] Among them, the main problem form of decomposing the two-stage robust optimization model is as follows:

[0056]

[0057] The sub-problems are of the following form:

[0058]

[0059] In the formula, B u To consider binary variables related to wind power scenarios; is the day-ahead wind power forecast value; Γ is the wind power uncertainty adjustment parameter.

[0060] Preferably, the process of decomposing the original problem into sub-problems by using the column constraint generation algorithm of the two-stage robust optimization model includes:

[0061] The initial subproblem is transformed into a maximization problem using duality theory, and then combined with the outer maximization problem to obtain the dual problem;

[0062] The binary expansion method is adopted to introduce relevant constraints to linearize the bilinear terms in the dual problem, and then the final sub-problem formal expression is obtained.

[0063] Compared with the prior art, the present invention has the following advantages and technical effects:

[0064] The present invention constructs a data-driven uncertainty set through support vector clustering and dimensional decomposition, and establishes a two-stage robust optimization scheduling model based on this uncertainty set. The robust optimization based on traditional uncertainty sets performs optimization according to the worst scenario in the set, and the larger number of invalid areas leads to its strong conservatism.

[0065] The robust optimization based on data-driven uncertainty sets in the present invention can fit the data space compactly, has fewer invalid areas, and considers the worst scenario that is more in line with reality, thereby obtaining a more economical scheduling solution.

[0066] Based on the influence of wind power time correlation on the capacity of the uncertain set, the present invention can fully consider the time correlation of wind power in adjacent time periods through dimensional decomposition, further reduce the conservatism of the uncertain set, and reduce the scheduling cost.

[0067] The data-driven uncertainty set proposed in the present invention has excellent resistance to outliers. While adjusting the geometric structure of the uncertainty set according to the data, it can effectively exclude outliers in the uncertainty set, thereby eliminating the negative impact of outliers on the scheduling results. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0069] Figure 1 Schematic diagram of dimensional decomposition of an embodiment of the present invention, wherein (a) is a three-dimensional uncertainty set obtained by directly using SVC on the original data, and (b) is an uncertainty set constructed by using SVC when the decomposition dimension is 2;

[0070] Figure 2 A schematic diagram of a microgrid structure according to an embodiment of the present invention;

[0071] Figure 3 A scatter plot of wind power output according to an embodiment of the present invention;

[0072] Figure 4 It is a comprehensive performance indicator diagram under different decomposition dimensions of an embodiment of the present invention. DETAILED DESCRIPTION

[0073] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0074] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0075] Embodiment 1

[0076] like Figure 1-4 As shown, this embodiment provides a two-stage robust optimization scheduling method for a microgrid based on a data-driven uncertainty set, including:

[0077] Obtain historical data of wind power forecast and actual values, and build a conditional normal Copula model based on the historical data;

[0078] Input the day-ahead wind power forecast value into the conditional normal Copula model to obtain the next day's wind power sample;

[0079] Based on the next day wind power samples, a data-driven uncertainty set considering the time correlation of wind power is constructed by support vector clustering and dimensionality decomposition.

[0080] A two-stage robust optimization scheduling model for microgrids with a min-max-min structure is constructed based on data-driven uncertain sets.

[0081] The optimal scheduling is carried out through the microgrid two-stage robust optimization scheduling model and column constraint generation algorithm to obtain the optimal scheduling result.

[0082] Furthermore, the process of obtaining historical data of wind power forecast values ​​and actual values, constructing a conditional normal Copula model based on the historical data, and inputting the day-ahead wind power forecast value into the conditional normal Copula model to obtain a next-day wind power sample includes:

[0083] Remember WT =[y 1 ,...,y n] is the wind power forecast value for each dispatching period of the day, n is the wind power data dimension, and the present invention takes 24. The CNC model is constructed using the historical data of wind power forecast values ​​and actual values, thereby considering the time correlation and condition correlation of wind power forecast errors, and inputting the wind power forecast value y WT , N wind power actual value samples can be sampled, where the i-th wind power actual value sample is

[0084] Furthermore, based on the next day wind power samples, the process of constructing a data-driven uncertainty set considering the time correlation of wind power through support vector clustering and dimensionality decomposition includes:

[0085] Based on the next-day wind power sample, an uncertainty set is constructed through the data-driven method of support vector clustering, and then the uncertainty set is represented as the intersection of multiple low-dimensional uncertainty sets through dimensionality decomposition to characterize the time correlation of wind power, thereby obtaining the final data-driven uncertainty set; the data-driven uncertainty set is used to capture the geometric shape of data distribution, flexibly adjust its own geometric structure to fit the data tightly, and exclude outliers in the sample data, thereby reducing the conservatism of robust optimization while having outlier resistance.

[0086] Furthermore, based on the next day wind power samples, the process of constructing the uncertainty set through the data-driven method of support vector clustering includes:

[0087] For the actual value samples of wind power generated by the CNC model, a nonlinear mapping function is used Mapped to the high-dimensional feature space F, the minimum sphere that can surround the data is found through support vector clustering to describe the sample data set. The minimum sphere can be obtained through the following optimization problem:

[0088]

[0089] Where u (i) is the actual value sample of wind power, is a nonlinear mapping function, with the center of the sphere being p and the radius being R, ξ i is the slack variable and ν is the regularization parameter.

[0090] The optimization problem of formula (1) aims to pursue the minimum radius sphere surrounding the data sample, while penalizing outliers, and the trade-off between these two different objectives is achieved by adjusting the regularization parameter ν. The following Lagrangian function is obtained by introducing Lagrangian multipliers α and β:

[0091]

[0092] According to the KKT (Karush-Kuhn-Tucker) condition:

[0093]

[0094]

[0095]

[0096] Substituting equations (3)-(5) into equation (2), we get the following quadratic programming problem:

[0097]

[0098] Where K(·,·) is the weighted generalized cross kernel function, Q is the weight matrix, and q m is the mth column element of the weight matrix, Σ is the covariance matrix of wind power data samples, l m is the width parameter to ensure the convexity of formula (6).

[0099] When u (i) The corresponding α i >0, u (i) is the support vector (SV); when 0<α i When u (i) is the boundary support vector (BSV). The index set of support vector and boundary support vector is defined as follows:

[0100]

[0101]

[0102] Thus, we can get the explicit expression of the uncertain set based on SVC:

[0103]

[0104] Among them, u is the uncertain variable of wind power.

[0105] Define the intermediate variables as follows:

[0106]

[0107] Further introduce auxiliary variable V = [v 1 ,...,v N ], equation (9) can be rewritten as follows:

[0108]

[0109] Formula (11) shows that the uncertainty set U constructed based on SVC SVC It is essentially a polyhedron, and the difference from the traditional uncertain set is that USVC With the help of non-parametric representation of data samples, it has a more flexible shape to fit the data space while ensuring convexity.

[0110] Furthermore, U SVC The essence of the model is a high-dimensional polyhedral uncertainty set. Although it covers more wind power output scenarios, it directly models the original 24-dimensional wind power data, which is equivalent to considering the time correlation of wind power in distant time periods, resulting in a large capacity and still relatively conservative. SVC It is decomposed into multiple low-dimensional uncertainty sets, that is, the correlation of wind power in adjacent time periods is considered. The low-dimensional uncertainty set is constructed by the wind power output in adjacent time periods, such as Figure 1 shown.

[0111] Generate 1000 three-dimensional data through Gaussian distribution. Figure 1 (a) is the three-dimensional uncertainty set obtained by directly applying SVC to the original data. Figure 1 (b) The uncertainty set constructed using SVC when the decomposition dimension is 2, that is, two two-dimensional uncertainty sets are obtained by using SVC on the data of the xy dimension and the yz dimension respectively. The final uncertainty set is the intersection of the two two-dimensional uncertainty sets.

[0112] The process of expressing the uncertainty set as the intersection of multiple low-dimensional uncertainty sets by dimensional decomposition includes:

[0113] Assume that the decomposition dimension is T D , considering T D Wind power time correlation of time interval, N D =nT D +1 is the number of low-dimensional uncertain sets after decomposition, the i-th D The time interval considered by the low-dimensional uncertain set is [i D ,i D +T D -1], 1≤i D ≤N D , the corresponding expression is as follows

[0114]

[0115] Because U SVC In some dimensions, it may exceed the range of historical data, so it is also necessary to limit the fluctuation range of each dimension of wind power uncertainty variables. In formula (12), For the i D The wind power uncertain variables corresponding to the low-dimensional uncertainty set are: and The i D The low-dimensional uncertainty sets correspond to the lower and upper bounds of wind power data samples.

[0116] The uncertainty set obtained by dimensional decomposition is the intersection of all low-dimensional uncertainty sets, and the expression is shown in formula (13):

[0117]

[0118] U DD-SVC in U SVC On this basis, the time correlation of wind power in adjacent time periods is further considered, which can further reduce the conservatism of the uncertainty set.

[0119] U DD-SVC The corresponding expressions and performances are also different under different decomposition dimensions. Therefore, it is necessary to propose corresponding indicators to evaluate the performance of uncertain sets and then determine the optimal decomposition dimension.

[0120] After obtaining the final data-driven uncertainty set, this embodiment further includes:

[0121] Construct a comprehensive performance index of the evaluation index to evaluate the performance of the data-driven uncertainty set, and then obtain the optimal decomposition dimension;

[0122] The evaluation indicators include coverage indicators and capacity indicators;

[0123] The coverage index expression is:

[0124]

[0125] In formula (14), Θ is the coverage index, which reflects the DD-SVC Coverage of wind power outside the sample. test is the number of days of data for evaluating the performance of the uncertainty set, N i is the U corresponding to the i-th day DD-SVC The maximum number of time periods of out-of-sample wind power that can be covered. It should be noted that the out-of-sample wind power is generated by the CNC model based on the day-ahead wind power forecast value on the i-th day, which is consistent with the construction of U DD-SVC The wind power data of N T is the number of wind power time periods, which is taken as 24.

[0126]

[0127] In formula (15), η is the capacity index, which reflects the DD-SVC The relative size relationship with the box uncertainty set, the larger η is, the smaller U DD-SVC The relatively box-like uncertain set has a smaller capacity. V i DD-SVC is the U corresponding to the i-th day DD-SVC Capacity, V i BOXis the capacity of the box uncertainty set on the i-th day.

[0128] In fact, the restrictions imposed on each dimension of wind power uncertain variables in formula (12) indicate that U DD-SVC must be included in the box uncertainty set. Since V cannot be directly calculated i DD-SVC , so the Monte Carlo method is used to randomly generate in the box uncertainty set on the i-th day A random point falls into the i-th day U DD-SVC The number of random points is The ratio of the number of random points falling into the two uncertain sets is approximately the ratio of the capacities, so the capacity index can be expressed as:

[0129]

[0130] The comprehensive performance index ζ is defined by the weighted sum of the above two indicators:

[0131] ζ=ω·Θ+(1-ω)·η (17)

[0132] Where ω is the weight of the coverage index, and its value range is (0,1). The larger the comprehensive performance index ζ is, the better the comprehensive performance of the corresponding uncertain set is. The decomposition dimension corresponding to the maximum comprehensive performance index value is called the optimal decomposition dimension.

[0133] Furthermore, if Figure 2 As shown, the microgrid structure studied in this embodiment is composed of a micro gas turbine, a wind turbine, electric energy storage, a large power grid and conventional power loads.

[0134] Two-stage robust optimization model for the day-ahead

[0135] Based on the data-driven uncertainty set constructed above, with the goal of minimizing the day-ahead scheduling cost, the following two-stage day-ahead robust optimization model is established:

[0136]

[0137] The constraints are satisfied as follows:

[0138]

[0139]

[0140]

[0141]

[0142] E ESS (1) = E ESS (N T )(twenty three)

[0143]

[0144]

[0145]

[0146]

[0147] Among them, C MT is the power generation cost of micro gas turbine, C ESS is the energy storage charging and discharging cost, C M is the cost of electricity purchase and sale from the power grid, Δt is the length of the unit time period;

[0148] a MT 、b MT is the cost coefficient of micro gas turbine power generation, k ESS is the energy storage charging and discharging cost coefficient, k M (t) is the day-ahead transaction price of the large power grid at time t;

[0149] P MT (t), P ch (t) / P dis (t) and P buy (t) / P sell (t) respectively represent the output power of the micro gas turbine at time t, the charging / discharging power of the energy storage at time t and the power purchased / sold by the large power grid at time t, η ESS It is the energy storage charging and discharging efficiency;

[0150] U ESS (t), U M (t) are binary variables, representing the energy storage charging and discharging status and the microgrid's electricity purchase and sale status from the large grid. The value of 1 indicates energy storage discharging / microgrid purchasing electricity from the large grid, and the value of 0 indicates energy storage charging / microgrid selling electricity to the large grid.

[0151] and are the minimum and maximum output power of the micro-turbine respectively. is the maximum charging and discharging power of energy storage, and They are the minimum and maximum capacities allowed in the energy storage dispatch process;

[0152] E ESS (1) is the capacity of energy storage at the initial time of dispatch, is the maximum interactive power between the microgrid and the large grid, is the load power prediction value vector;

[0153] Formula (19) is the output power constraint of the micro gas turbine;

[0154] Formulas (20) and (21) are the energy storage charging and discharging power constraints;

[0155] Formula (22) constrains the minimum and maximum remaining capacity of energy storage within the dispatch cycle;

[0156] Formula (23) indicates that the total energy storage charge during the entire dispatch cycle is equal to the total discharge;

[0157] Formula (24) indicates that the change in energy storage capacity is only caused by charging and discharging;

[0158] Formulas (25) and (26) are the power constraints of the microgrid purchasing and selling electricity to the large power grid;

[0159] Equation (27) is the power balance constraint.

[0160] The above model can be written in a compact form

[0161]

[0162] x and y are optimization variables, and the expression is

[0163]

[0164] Where: c is the coefficient column vector corresponding to the objective function; D, K, F, G, J are the coefficient matrices corresponding to the variables under the corresponding constraints; d and h are constant column vectors.

[0165] The above two-stage robust optimization model is a min-max-min problem, which cannot be solved directly by commercial solvers. The present invention solves it by using a column constraint generation algorithm. The basic idea of ​​the column constraint generation algorithm is to decompose the original problem into a main problem and sub-problems, and then solve them iteratively. The above two-stage robust optimization model is decomposed, and the main problem is as follows:

[0166]

[0167] The sub-problems are of the following form:

[0168]

[0169] Where γ, λ, φ, π correspond to the dual variables corresponding to the constraints of the sub-problems. Since the minimization problem is a linear problem, the duality theory can be used to transform it into a maximization problem. After merging it with the outer maximization problem, the following dual problem is obtained:

[0170]

[0171] Since there is a bilinear term u in equation (32) Tπ, which makes the problem difficult to solve. The present invention adopts a binary expansion method to linearize the bilinear term.

[0172]

[0173] where π(t) is the t-th dimension component of the dual variable π, i.e., π=[π(1),...,π(t),...,π(N T )] T , π min (t) is a constant, indicating the minimum value of π(t). Δπ is the step size, b t,k is the binary variable related to the kth exponential form of the binary expansion, k 1 and k n are integers, representing the minimum and maximum exponential levels respectively. T π can now be expressed as:

[0174]

[0175] in u(t) is the t-th dimension component of the uncertain variable u of wind power output, that is, u=[u(1),...,u(t),...,u(N T )] T . Further, let

[0176]

[0177]

[0178] z t,k =b t,k u(t) (37)

[0179] Introduce relevant constraints to linearize equation (34):

[0180]

[0181] Where M is a sufficiently large positive real number, and ρ and z are both (k n -k 1 +1)N T dimensional column vector. The dual variable π corresponds to the shadow price of the microgrid. The final subproblem is approximated as:

[0182]

[0183] In formula (39), B u To consider binary variables related to wind power scenarios; is the day-ahead wind power forecast value; Γ is the wind power uncertainty adjustment parameter.

[0184] After the above transformation, the constructed two-stage robust optimization model is finally transformed into the main problem and sub-problem shown in Equation (30) and Equation (39), and then solved by the C&CG algorithm.

[0185] In order to verify the effectiveness of the two-stage robust optimization model proposed in this invention, Yalmip was used to program in MATLAB R2016b and Gurobi 10.0.2 was called to solve the model. The computer hardware environment was Intel Core i5-13400 CPU, 2.50 GHz, 32 GB memory, and the operating system was Win10 64 bit.

[0186] Time correlation verification:

[0187] First, the time correlation of wind power is verified. This embodiment uses the actual wind power output data of Austria from January 2019 to April 2019 for a total of 100 days provided by ENTSO-E, with a time resolution of 1h. The data from 10:00 to 14:00 are analyzed to verify the existence of wind power time correlation.

[0188] like Figure 3 The lower triangle scatter plot of wind power output at different time intervals is shown. The scatter plot represents the joint distribution of wind power output in different time periods. It can be seen that the joint distribution of wind power output between adjacent time periods is basically concentrated on the diagonal line, indicating a strong time correlation. As the time interval increases, the scatter points become dispersed, indicating that the time correlation weakens.

[0189] Determination of the optimal decomposition dimension:

[0190] The present invention uses the actual wind power output data of Austria from January 2019 to September 2020, totaling 639 days, provided by ENTSO-E to construct the CNC model. October 9, 2020 is selected as a typical day. Based on the wind power forecast value of the day, 100 days of wind power forecast value data are randomly generated within a 20% error band. The U under different decomposition dimensions is used to calculate the wind power forecast value of the day. DD-SVC Performance evaluation, that is, N test is 100. Since the actual value of wind power is equivalent to out-of-sample data for the uncertainty set, when the coverage of the out-of-sample data by the uncertainty set is poor, the scheduling scheme obtained after optimization based on the uncertainty set may not be feasible in practice. Therefore, it is necessary to make the capacity of the uncertainty set as small as possible while ensuring the out-of-sample performance. The weight ω of the coverage index is set to 0.8 in the present invention. When the decomposition dimension is 1, it is a box-type uncertainty set, so it is not considered.

[0191] The comprehensive performance index ζ in different decomposition dimensions N D The corresponding values ​​are as follows Figure 4As shown. It can be seen that when the decomposition dimension is 2, the corresponding comprehensive performance index takes the minimum value, because the uncertainty set capacity obtained by dimensional decomposition is larger at this time. When the decomposition dimension is less than 4, it is mainly affected by the capacity. When the decomposition dimension is 4, the comprehensive performance index reaches the maximum value, that is, the comprehensive optimality of the coverage index and the capacity index is achieved. When the decomposition dimension is greater than 4, the curve changes gently, which is mainly affected by the coverage. The U used below DD-SVC The corresponding decomposition dimensions are all set to 4.

[0192] Microgrid dispatch results:

[0193] According to the predicted power curve of wind turbines and loads in Austria on October 9, 2020, the wind power uncertainty adjustment parameter is 8, that is, there are 8 periods in which the wind power output fluctuates downward relative to the predicted value. The values ​​of the microgrid parameters and the day-ahead transaction electricity price are shown in Tables 1 and 2.

[0194] Table 1

[0195]

[0196] Table 2

[0197]

[0198] The results of the microgrid optimization dispatch show that when the microgrid sells electricity to the large power grid, the value is positive, and when it purchases electricity from the large power grid, the value is negative; when the energy storage is discharged, the value is positive, and when it is charged, the value is negative. In 1-7h and 24h, the micro-turbine operates at the minimum power. This is because the unit power generation cost of the micro-turbine is higher than the day-ahead transaction price at this time, and in 8-23h, the day-ahead transaction price is higher than the unit power generation cost of the micro-turbine, so the micro-turbine outputs the maximum power to reduce the operating cost. The energy storage is charged during the 6-7h and 24h valley electricity price period, and discharged during the 9-11h peak electricity price period to achieve peak shaving and valley filling. Due to the low wind power output level, the total power generation is less than the load demand, so all periods purchase electricity from the large power grid to meet the power balance.

[0199] Optimization model comparison:

[0200] The costs corresponding to four models under different prediction errors are studied, including deterministic optimization (DO), robust optimization based on box uncertainty set (BUS), robust optimization based on polyhedral uncertainty set (PUS), and robust optimization based on dimension decomposition-support vector clustering (DD-SVC). The costs include day-ahead dispatching cost, balancing cost, and total cost. The day-ahead dispatching cost corresponds to the day-ahead power generation and consumption plan. The cost of compensating the imbalance between the planned power generation and consumption and the actual power generation and consumption in the real-time market is the balancing cost. The total cost is the sum of the day-ahead dispatching cost and the balancing cost.

[0201] The research results show that under the same prediction error, BUS has the highest day-ahead scheduling cost, followed by PUS and DD-SVC, and DO has the lowest. This is because DO is equivalent to not considering uncertainty. The compactness of the uncertainty sets surrounding the data corresponding to BUS, PUS and DD-SVC increases successively, and the corresponding day-ahead scheduling costs decrease successively. In terms of balance cost, DO is the highest, followed by BUS, and PUS and DD-SVC are similar. In terms of total cost, DO is the highest, followed by BUS and PUS, and DD-SVC is the lowest. The fundamental reason for the above conclusions is that DD-SVC can automatically adjust the geometric structure according to the data distribution, and has more vertices and edges than BUS and PUS. Robust optimization is to find the optimal solution in the worst case based on the set boundary, so DD-SVC can obtain less conservative optimization results.

[0202] Impact of wind power time correlation on costs:

[0203] i-SVC means that SVC is used to construct an uncertainty set directly on the original wind power data without dimensional decomposition. The decomposition dimension of DD-SVC is 4, which is equivalent to considering the time correlation of four adjacent time periods. By comparing DD-SVC and i-SVC, the impact of wind power time correlation on cost is obtained. The research results show that under different prediction error conditions, the day-ahead scheduling cost and total cost corresponding to DD-SVC are lower than those of i-SVC. This is because i-SVC uses wind power output data with a longer time interval to construct an uncertainty set, and does not consider the time correlation of wind power, resulting in a larger capacity of the obtained uncertainty set, so the obtained scheduling plan is more conservative.

[0204] Resistance to outliers:

[0205] Assume u=[u 1 ,u 2] is a two-dimensional random vector, and 1000 sample data are generated by mixed Gaussian distribution. Under 99% data coverage, the uncertainty set, box uncertainty set and polyhedron uncertainty set results based on SVC are:

[0206] Polyhedral uncertain set:

[0207] The uncertainty set based on SVC excludes four obvious outliers, and has fewer invalid areas while maintaining the convexity of the uncertainty set; the box uncertainty set has more invalid areas at the four corners due to its incompatibility with the data distribution due to its geometric structure; the polyhedron uncertainty set is similar to the box uncertainty set, and there are also more invalid areas at the four corners. SVC can exclude serious outliers and flexibly adjust the shape of the uncertainty set under the set data coverage, so that outliers have less impact on the uncertainty set, that is, it is resistant to outliers.

[0208] In order to verify that the data-driven uncertainty set constructed by the present invention is resistant to outliers, the typical day in 4.3 is still used as the research object, and 700 days of wind power samples are obtained through CNC model sampling. On this basis, the maximum / minimum wind power output at each moment is selected respectively, and the maximum / minimum wind power output data is obtained by combination. 150 days of data are randomly generated within a certain error range of the maximum / minimum wind power output data. Since wind power rarely reaches the maximum / minimum value at each moment in reality, the generated 300 days of data can be considered as outliers. Compare and analyze the following three situations:

[0209] Case 1: Construct an uncertainty set with 700 days of normal wind power data and 300 days of abnormal data, a total of 1000 days of data.

[0210] Case 2: 75 days of abnormal data are reduced from each of the 300 days of abnormal data, and the uncertainty set is constructed with 700 days of normal wind power data and 150 days of abnormal data, a total of 850 days of data.

[0211] Case 3: Construct an uncertainty set based on 700 days of normal wind power data.

[0212] When the uncertainty is 8, the wind power scenarios considered by the three models fluctuate downward relative to the predicted values ​​in 8-9h and 18-23h. In case 1, compared with the wind power scenarios considered by BUS and PUS, the wind power considered by DD-SVC at 9h is larger. In case 2, the wind power considered by DD-SVC at 8-9h is significantly higher than that of BUS and PUS. In case 3, the wind power considered by DD-SVC at 18h and 23h is higher. Accordingly, in the three cases, the day-ahead dispatch cost and total cost of DD-SVC are lower than those of BUS and PUS. In fact, the wind power scenarios considered by BUS and PUS are exactly the same. This is because PUS considers the fluctuation range of each dimension of wind power uncertainty variables, resulting in the same lower bound of wind power uncertainty variables fluctuation for BUS and PUS. The proportion of outliers in the three cases is different. The wind power scenarios considered by BUS and PUS have only slight changes and show obvious regularity. This is because BUS and PUS cannot effectively identify and exclude outliers, and the corresponding dispatch plan costs are higher under the influence of outliers. The wind power scenarios considered by DD-SVC in the three cases are significantly different. This is because DD-SVC can adjust its own geometric structure according to the data, excluding outliers while fitting the data tightly. The wind power scenarios considered by BUS and PUS are less conservative, resulting in a lower cost scheduling solution obtained by DD-SVC.

[0213] The present invention proposes a two-stage robust optimization scheduling method for a microgrid based on a data-driven uncertainty set. First, the historical data of wind power prediction and actual values ​​are obtained to construct a CNC model, and then the wind power prediction value of a certain day is input into the CNC model to obtain the wind power sample of the next day. Secondly, based on the wind power sample of the next day, an uncertainty set is constructed by a data-driven method of support vector clustering, and then the uncertainty set is represented as the intersection of multiple low-dimensional uncertainty sets by dimensional decomposition to characterize the time correlation of wind power, thereby obtaining the final uncertainty set. The uncertainty set can capture the geometric shape of data distribution and exclude outliers in the sample data, thereby reducing the conservatism of robust optimization while having outlier resistance. Then, a two-stage robust optimization scheduling model of a microgrid with a min-max-min structure is established based on the constructed uncertainty set, and the safe and stable operation of the microgrid is realized. Finally, it is proved by simulation that the uncertainty set constructed by the present invention is less conservative than the traditional uncertainty set, and the conservatism can be further reduced after comprehensive consideration of the time correlation, and at the same time, it has stronger resistance to abnormal wind power data.

[0214] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A two-stage robust optimization scheduling method for microgrids based on data-driven uncertainty sets, characterized in that: include: Acquire historical data of wind power forecast values ​​and actual values, and construct a conditional normal Copula model based on the historical data; Input the day-ahead wind power forecast value into the conditional normal Copula model to obtain the next day's wind power sample; Based on the next day wind power samples, a data-driven uncertainty set considering wind power time correlation is constructed by support vector clustering and dimensionality decomposition; A two-stage robust optimization scheduling model for a microgrid with a min-max-min structure is constructed based on the data-driven uncertainty set; The optimized scheduling is performed through the microgrid two-stage robust optimization scheduling model and the column constraint generation algorithm to obtain the optimized scheduling result.

2. The method according to claim 1, characterized in that The process of obtaining historical data of wind power forecast values ​​and actual values ​​and constructing a conditional normal Copula model based on the historical data includes: Define y WT =[y1,...,y n ] is the wind power forecast value for each dispatching period of the day, n is the wind power data dimension, and the conditional normal Copula model is constructed using the historical data of wind power forecast values ​​and actual values.

3. The method according to claim 1, characterized in that The process of inputting the day-ahead wind power forecast value into the conditional normal Copula model to obtain the next day's wind power sample includes: Considering the time correlation and conditional correlation of wind power forecast error, the input wind power forecast value y WT , N wind power actual value samples are obtained by sampling, among which the i-th wind power actual value sample is 4. The method according to claim 1, characterized in that: Based on the next-day wind power sample, the process of constructing a data-driven uncertainty set considering the time correlation of wind power through support vector clustering and dimensionality decomposition includes: Based on the next-day wind power sample, an uncertainty set is constructed by a data-driven method of support vector clustering, and then the uncertainty set is represented as the intersection of multiple low-dimensional uncertainty sets through dimensionality decomposition to characterize the time correlation of wind power, thereby obtaining the final data-driven uncertainty set; the data-driven uncertainty set is used to capture the geometric shape of data distribution, flexibly adjust its own geometric structure to fit the data tightly, and exclude outliers in the sample data, thereby reducing the conservatism of robust optimization while having outlier resistance.

5. The method according to claim 4, characterized in that Based on the next day wind power sample, the process of constructing the uncertainty set by the data-driven method of support vector clustering includes: The actual value samples of wind power are transformed into the nonlinear mapping function Mapping to high-dimensional feature space The sample data set is described by obtaining the minimum sphere that can enclose the data through support vector clustering; the minimum sphere is obtained through the following optimization problem: In the formula, u (i) is the actual value sample of wind power, is a nonlinear mapping function, with the center of the sphere being p and the radius being R, ξ i is the slack variable, ν is the regularization parameter; The minimum radius sphere surrounding the data sample is obtained through the minimum sphere optimization problem, and outliers are penalized at the same time. The trade-off between the two different objectives is achieved by adjusting the regularization parameter ν, and the explicit expression of the initial uncertainty set based on support vector clustering is obtained: Among them, u is the uncertain variable of wind power; Define the intermediate variables as: Further introduce auxiliary variables V = [v1, ..., v N ], and substitute it into formula (9) to obtain the explicit expression of the target uncertainty set based on support vector clustering:

6. The method according to claim 4, characterized in that The process of expressing the uncertainty set as the intersection of multiple low-dimensional uncertainty sets by dimensional decomposition includes: Assume that the decomposition dimension is T D , considering T D Wind power time correlation of time interval, N D =nT D +1 is the number of low-dimensional uncertain sets after decomposition, the i-th D The time interval considered by the low-dimensional uncertain set is [i D ,i D +T D -1], 1≤i D ≤N D , the corresponding expressions are as follows: In the formula, For the i D The wind power uncertain variables corresponding to the low-dimensional uncertainty set are: and The i D The low-dimensional uncertainty sets correspond to the lower and upper bounds of wind power data samples; The uncertainty set obtained by dimensional decomposition is the intersection of all low-dimensional uncertainty sets, and the expression is shown in formula (13):

7. The method according to claim 1, characterized in that After obtaining the final data-driven uncertainty set, it also includes: Constructing a comprehensive performance index of the evaluation index to evaluate the performance of the data-driven uncertainty set, thereby obtaining an optimal decomposition dimension; The evaluation indicators include coverage indicators and capacity indicators; The coverage index expression is: In the formula, Θ is the coverage index, which is used to reflect the DD-SVC Coverage of wind power outside the sample, N test is the number of days of data for evaluating the performance of the uncertainty set, N i is the U corresponding to the i-th day DD-SVC The maximum number of time periods of out-of-sample wind power that can be covered is generated by the conditional normal Copula model based on the day-ahead wind power forecast value on the ith day. DD-SVC The wind power data of N T is the number of wind power time periods; The capacity index expression is: In the formula, η is the capacity index, which is used to reflect the DD-SVC The relative size relationship with the box uncertainty set, the larger η is, the smaller U DD-SVC The relatively box-like uncertain set has a smaller capacity; is the U corresponding to the i-th day DD-SVC The capacity, is the capacity of the box uncertainty set on the i-th day; The comprehensive performance index is obtained based on the weighted definition of the coverage index and the capacity index, and the expression is: ζ=ω·Θ+(1-ω)·η (17) Among them, ω is the weight of the coverage index, and its value range is (0,1); the larger the comprehensive performance index ζ is, the better the comprehensive performance of the corresponding uncertain set is, and the decomposition dimension corresponding to the maximum comprehensive performance index value is called the optimal decomposition dimension.

8. The method according to claim 1, characterized in that The process of constructing a two-stage robust optimization scheduling model of a microgrid with a min-max-min structure based on the data-driven uncertainty set includes: Based on the data-driven uncertainty set, a two-stage day-ahead robust optimization model is established with the goal of minimizing the day-ahead scheduling cost: x and y are optimization variables, and the expression is Where: c is the coefficient column vector corresponding to the objective function; D, K, F, G, J are the coefficient matrices corresponding to the variables under the corresponding constraints; d and h are constant column vectors.

9. The method according to claim 1, characterized in that: The process of optimizing scheduling by using the microgrid two-stage robust optimization scheduling model and column constraint generation algorithm includes: The two-stage robust optimization model is used to decompose the original problem into a main problem and sub-problems through a column constraint generation algorithm, and then it is solved iteratively; Among them, the main problem form of decomposing the two-stage robust optimization model is as follows: The sub-problems are of the following form: In the formula, B u To consider binary variables related to wind power scenarios; is the day-ahead wind power forecast value; Γ is the wind power uncertainty adjustment parameter.

10. The method according to claim 9, characterized in that The process of decomposing the original problem into sub-problems through the column constraint generation algorithm of the two-stage robust optimization model includes: The initial subproblem is transformed into a maximization problem using duality theory, and then combined with the outer maximization problem to obtain the dual problem; The binary expansion method is adopted to introduce relevant constraints to linearize the bilinear terms in the dual problem, and then the final sub-problem formal expression is obtained.

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