Hyper-spherical sampling alternating direction method and system for power robust scheduling

Abstract

The invention relates to the technical field of power system scheduling, and discloses a hyperspherical sampling alternating direction method and system for power robust scheduling, and the method comprises the steps: building a condition probability model of wind power, and obtaining a wind power output sample for constructing an ellipsoid uncertainty set through the latest wind power prediction data; establishing a robust prospective power dispatching model considering the ellipsoid uncertainty set; camp is adopted; two-stage problems in a CG algorithm solving model are decomposed into a main problem and a sub-problem, the sub-problem is sampled on a unit hypersphere, points on the hypersphere are projected to an ellipsoid according to a special formula of an ellipsoid expression constructed by a conditional probability model, iterative solution of an alternating direction method is started, and the ellipsoid is obtained. When the robust look-ahead power dispatching model considering the ellipsoid uncertainty set is solved, the problem is difficult to solve by a general solving method due to the second-order cone expression form of the ellipsoid, and the robust look-ahead dispatching can be ensured to obtain an accurate solution in a short time.

Description

Technical Field

[0001] The present invention relates to the technical field of power system dispatching, and in particular to a hypersphere sampling alternating direction method and system for robust power dispatching. Background Art

[0002] In the forward-looking power dispatching stage, wind power uncertainty poses a threat to the safe and stable operation of the system. The deterministic dispatching method can no longer adapt to the current large-scale wind power access situation. Therefore, it is necessary to introduce a dispatching method that considers uncertainty. Robust optimization has been widely studied in the power field for its robustness, computational tractability and probability guarantee. The two-stage robust optimization reduces the conservatism of the optimization results due to its adjustable form. The two-stage robust optimization method can effectively take into account the uncertainty of wind power in the intraday stage in the forward-looking power dispatching stage. Uncertain sets are the key to robust optimization modeling. Reasonable modeling methods will affect the conservatism of the optimization results. The ellipsoid uncertainty set can effectively capture the correlation between data and reduce the conservatism of the solution, but its modeling will introduce second-order cone constraints into the original problem. For a two-stage robust optimization problem, this will make it difficult to solve the sub-problem using existing solution methods. Summary of the invention

[0003] In view of the above existing problems, the present invention is proposed. The present invention is aimed at the robust forward-looking power dispatching problem considering the ellipsoid uncertainty set, and can ensure that the robust forward-looking dispatching obtains an accurate solution in a relatively short time. It handles the problem that the bilinear terms of the sub-problem are difficult to handle after the dual transformation, and can make the solution process of the dual sub-problem accurate and efficient.

[0004] In order to solve the above technical problems, a hypersphere sampling alternating direction method for robust power dispatch is proposed, including:

[0005] A conditional probability model for wind power is established, and wind power output samples for constructing an ellipsoid uncertainty set are obtained through the latest wind power forecast data. A robust forward-looking power dispatch model considering the ellipsoid uncertainty set is established. The C&CG algorithm is used to solve the main problem and sub-problems in the robust forward-looking power dispatch model, sampling is performed on the unit hypersphere, and the points on the hypersphere are projected onto the ellipsoid surface according to the special formula of the constructed ellipsoid expression. The alternating direction method is started to solve the sub-problems, and the main problem and sub-problems are iteratively calculated to make a convergence judgment.

[0006] As a preferred solution of the hypersphere sampling alternating direction method for robust power dispatching described in the present invention, the conditional probability model includes calculating the wind power conditional probability density function according to historical data, calculating the corresponding covariance matrix according to the expression form of the covariance matrix in the Gaussian Copula function, calculating the conditional distribution of the multivariate Gaussian distribution, and collecting wind power samples:

[0007] For the actual wind power output X in historical data, 11 ,…,x NT ] T and predicted value Y = [y 11 ,…,y NT ] T , let the corresponding marginal distribution be (u,v), and calculate the basic conditional probability density function:

[0008]

[0009] Among them, f X|Y is the conditional probability density function of X with respect to Y, c is the Gaussian Copula probability density function, f xij (x ij ) is x ij The probability density function of is, N is the total number of wind farms, and T is the total number of window times.

[0010] Consider that there is:

[0011] c(u 11 ,…,u NT ,v 11 ,…,v NT |Σ)=Φ Gauss (φ -1 (u 11 ),…,φ -1 (v NT ))

[0012] c(v 11 ,…,v NT |Σ yy )=Φ Gauss (φ -1 (v 11 ),…,φ -1 (v NT ))

[0013] Among them, Φ Gauss is a multivariate Gaussian distribution, φ -1 (·) is the pseudo-inverse function of the standard Gaussian distribution, and Σ is the covariance.

[0014] make The covariance matrix of can be expressed as linear correlation coefficient:

[0015]

[0016] in:

[0017] Where ρ is the linear correlation coefficient.

[0018] The probability density function of the final conditional probability is constructed based on the calculation results:

[0019]

[0020] in, The derivation formula based on the mean and covariance of the conditional probability density is:

[0021]

[0022] As a preferred solution of the hypersphere sampling alternating direction method for robust power dispatching described in the present invention, the collection of wind power samples includes obtaining the Gaussian distribution parameters of the actual value in the Gaussian domain at a given wind power forecast output value through the derivation formula of the mean and covariance of the conditional probability density, and directly sampling according to the current parameters: using the historical actual output value X and the forecast value Y of n wind farms, the marginal distribution (u, v) of each point is calculated, and the covariance matrix Σ of the joint distribution is calculated. When the wind power forecast value is updated, Convert the predicted value from the real value domain to the Gaussian domain and calculate the multivariate Gaussian conditional distribution z x |z y The mean vector of and the covariance matrix Perform multivariate normal distribution sampling to obtain z that follows the distribution x Sample, and through x = F -1 (φ(z x ))Convert the data from Gaussian domain to real-valued domain to obtain sampling samples of actual output.

[0023] As a preferred scheme of the hypersphere sampling alternating direction method for robust power dispatching described in the present invention, the robust forward-looking power dispatching model includes establishing a robust forward-looking power dispatching model that takes into account the ellipsoid uncertainty set, and establishing the ellipsoid uncertainty set based on the sampling samples for collecting wind power samples.

[0024] The robust forward-looking power dispatch framework consists of two stages. The first stage solves the unit commitment problem, and the second stage focuses on the worst-case economic dispatch. The abstract model of robust forward-looking power dispatch considering the ellipsoid uncertainty set is expressed as follows:

[0025]

[0026] In the first stage, x represents the decision variables of the first stage, including the unit status, c T x is the unit combination cost in the first stage, including no-load cost, startup cost and shutdown cost of the total unit. Ax≤b represents the unit logic constraint. In the second stage, y is the decision variable including unit output, δ is the external parameter for system load, and q Tu represents the penalty cost of reducing wind power, d T y is the second-stage dispatch cost in the worst case, Bx+Cu+Dy+Eδ-e≤0 is the constraint condition of power balance, ramping, spinning reserve, network transmission and wind farm output, u is an uncertain parameter, belonging to the uncertain set U. The present invention adopts an ellipsoidal uncertain set, where Q is the covariance matrix, u c is the center of the ellipsoid.

[0027] The covariance matrix Q is calculated based on the wind power output sampling samples, and the predicted value is the sphere center u c Construct the uncertain set U.

[0028] As a preferred solution of the hypersphere sampling alternating direction method for robust power dispatching of the present invention, wherein: the C&CG algorithm includes two stages of decomposing the robust forward-looking power dispatching framework by using the C&CG algorithm, decomposing it into a main problem and a sub-problem;

[0029] The two-stage decomposition of the robust forward-looking power dispatch framework includes the following main problems:

[0030]

[0031] The sub-problems are:

[0032]

[0033] As a preferred solution of the hypersphere sampling alternating direction method for robust power dispatching described in the present invention, wherein: the solving of the main problem includes directly solving the main problem using a solver, and solving the main problem to obtain a feasible solution And update the algorithm iteration lower bound accordingly

[0034] The dual problem of the sub-problems after the computational decomposition includes converting the inner min problem into a max problem through the strong duality theorem:

[0035]

[0036] Replace the indeterminate set expression in with the ellipsoid expression associated with the unit hypersphere:

[0037] U={u|u=u c +Rx,||x|| 2 ≤1}

[0038] Where x is a point in the unit hypersphere, R is a symmetric positive definite matrix, where R = Q -1 / 2 , sample the hypersphere and project it onto the ellipsoid according to U.

[0039] As a preferred solution of the hypersphere sampling alternating direction method for robust power dispatching described in the present invention, the alternating direction method includes uniformly taking points on the hypersphere, generating random points on the n-dimensional hypersphere uniformly by the Muller method, and assigning a coordinate vector (x 1 ,x 2 ,…,x n ), each coordinate is independently sampled from a standard Gaussian distribution and then normalized:

[0040]

[0041] Among them, the normalized coordinate vector Located on the unit hypersphere, the n-dimensional Gaussian probability density function is given by a constant:

[0042]

[0043] The alternating direction method based on hypersphere sampling is as follows: the ellipsoid sampling is used as the initial value of the algorithm's uncertain parameters. For the subproblem, the sampling initial value is used to fix the uncertain parameters. Assume the number of iterations k = 1, let Fixing the uncertain parameters, we obtain the linear programming with respect to the dual variables:

[0044]

[0045] The optimal solution of the dual variable is obtained by solving the linear programming of the dual variable Fix the dual variables with the current optimal solution and obtain the second-order cone constraint programming problem with uncertain parameter u:

[0046]

[0047] Determine whether the convergence criterion is met|Objval λ -Objval u |<ò: When the convergence criterion is met, the algorithm converges and outputs the optimal value of the subproblem and the optimal solution of the variable. When the convergence criterion is not met, the uncertain parameters continue to be fixed, and k=k+1.

[0048] Solve the sub-problems to obtain feasible solutions and feasible scenarios And update the algorithm iteration upper bound is the objective function value of the subproblem based on the feasible solution.

[0049] The convergence judgment includes judging whether the upper bound UB and the lower bound LB can satisfy the convergence condition |UB-LB|≤ε: when the convergence condition is met, the optimal solution of robust forward scheduling considering the ellipsoid uncertainty set is output; when the convergence condition is not met, the optimization model of the main problem of robust forward scheduling considering the ellipsoid uncertainty set is updated, new constraints and variables are generated, and k=k+1 is set, and the solver is re-adopted to solve the main problem until |UB-LB|≤ε is satisfied, and the optimal solution of robust forward scheduling considering the ellipsoid uncertainty set is output.

[0050] Another object of the present invention is to provide a hypersphere sampling alternating direction system for robust power dispatching. The present invention solves the uncertainty problem in the dispatching of power systems containing wind power through the close interaction between the wind power scenario generation and ellipsoid uncertainty set construction module, the robust forward-looking power dispatching model establishment and optimization module, and the C&CG solution module based on the hypersphere sampling alternating direction method. The collaborative work of these modules significantly improves the adaptability of the power dispatching system to wind power uncertainty, enhances the robustness and economy of the dispatching scheme, and achieves the technical effect of improving the operating efficiency of the power system and reducing the operating cost.

[0051] As a preferred solution of the hypersphere sampling alternating direction system for robust power dispatching described in the present invention, it is characterized by including a wind power scenario generation and ellipsoid uncertainty set construction module, a robust forward-looking power dispatching model establishment and optimization module, and a C&CG solution module based on the hypersphere sampling alternating direction method.

[0052] The wind power scenario generation and ellipsoid uncertainty set construction module is responsible for establishing a conditional probability model for wind power, using the latest wind power forecast data to generate wind power output samples, expressing the conditional distribution of the multivariate Gaussian distribution through the Gaussian Copula function and the covariance matrix, analyzing historical data, and calculating the wind power conditional probability density function, so as to collect wind power samples and then construct an ellipsoid uncertainty set.

[0053] The robust forward-looking power dispatch model establishment and optimization module establishes a robust forward-looking power dispatch model considering the ellipsoid uncertainty set. The model includes two stages: the first stage solves the unit combination problem, and the second stage focuses on the economic dispatch in the worst case. The model includes constraints on power balance, ramping, rotating reserve, network transmission and wind farm output, and uses an ellipsoid uncertainty set to represent the uncertainty of wind power output. The covariance matrix is ​​calculated based on the wind power output sampling samples, and the uncertainty set is constructed with the current rolling window prediction value as the center of the sphere.

[0054] The C&CG solution module based on the alternating direction method of hypersphere sampling uses the C&CG algorithm to decompose the two-stage problem of the robust forward-looking power dispatching framework, and adopts the alternating direction method based on hypersphere sampling to solve the sub-problems; the hypersphere sampling includes uniformly taking points on the hypersphere, generating random points by the Muller method, and performing normalization processing to obtain coordinate vectors located on the unit hypersphere; the alternating direction method involves fixing uncertain parameters and dual variables to alternately solve sub-problems; the module solves the main problem and the sub-problems respectively, and updates the upper and lower bounds through an iterative process until the convergence conditions are met, thereby outputting the optimal solution of the robust forward-looking power dispatching.

[0055] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and is characterized in that when the processor executes the computer program, the steps of the method for alternating directions of hyperspherical sampling for robust power scheduling are implemented.

[0056] A computer-readable storage medium stores a computer program thereon, wherein when the computer program is executed by a processor, the steps of the method described in the hyperspherical sampling alternation for robust power scheduling are implemented.

[0057] Beneficial effects of the present invention: The method of the present invention takes into account the mapping relationship between the ellipsoid and the unit hypersphere, realizes the selection of initial values ​​of uncertain parameters in the ellipsoid uncertainty set, and can be applied to solving the robust forward-looking power dispatching problem that actually considers the ellipsoid uncertainty set. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0059] Figure 1 An overall flow chart of a hyperspherical sampling alternating direction method for robust power scheduling provided by an embodiment of the present invention.

[0060] Figure 2 A hyperspherical sampling alternating direction method for robust power scheduling provided in one embodiment of the present invention adopts a C&CG algorithm flow of an alternating direction method based on hyperspherical sampling.

[0061] Figure 3 A schematic diagram of a 6-node power system using a hypersphere sampling alternating direction method for robust power scheduling provided by an embodiment of the present invention.

[0062] Figure 4A system solution design diagram of a hyperspherical sampling alternating direction system for robust power scheduling provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0064] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0065] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor is it an embodiment that is mutually exclusive with other embodiments, either individually or selectively.

[0066] The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0067] At the same time, in the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0068] In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0069] Example 1, reference Figure 1-Figure 2 , which is the first embodiment of the present invention, provides a hypersphere sampling alternating direction method for robust power scheduling, including:

[0070] S1: Establish a conditional probability model for wind power and obtain wind power output samples for constructing an ellipsoid uncertainty set through the latest wind power forecast data.

[0071] Furthermore, the wind power conditional probability density function is calculated based on historical data, and the corresponding covariance matrix is ​​calculated based on the covariance matrix expression in the Gaussian Copula function, and the conditional distribution of the multivariate Gaussian distribution is calculated to collect wind power samples:

[0072] For the actual wind power output X in historical data, 11 ,…,x NT ] T and predicted value Y = [y 11 ,…,y NT ] T , let the corresponding marginal distribution be (u,v), and calculate the basic conditional probability density function:

[0073]

[0074] Among them, f X|Y is the conditional probability density function of X with respect to Y, c is the Gaussian Copula probability density function, f xij (x ij ) is x ij The probability density function of is, N is the total number of wind farms, and T is the total number of window times.

[0075] Consider that there is:

[0076] c(u 11 ,…,u NT ,v 11 ,…,v NT |Σ)=Φ Gauss (φ -1 (u 11 ),…,φ -1 (v NT ))

[0077] c(v 11 ,…,v NT |Σ yy )=Φ Gauss (φ -1 (v 11 ),…,φ -1 (v NT ))

[0078] Among them, ΦGauss is a multivariate Gaussian distribution, φ -1 (·) is the pseudo-inverse function of the standard Gaussian distribution, and Σ is the covariance.

[0079] make The covariance matrix of can be expressed as linear correlation coefficient:

[0080]

[0081] in:

[0082]

[0083] Where ρ is the linear correlation coefficient.

[0084] The probability density function of the final conditional probability is constructed based on the calculation results:

[0085]

[0086] Where μ = [μ zx ,μ zy ] T , the derivation formula based on the mean and covariance of the conditional probability density is:

[0087]

[0088]

[0089] It should be noted that the Gaussian distribution parameters of the actual value in the Gaussian domain at a given wind power forecast output value are obtained through the derivation formula of the mean and covariance of the conditional probability density. Sampling is performed directly according to the current parameters: the historical actual output value X and the forecast value Y of n wind farms are used to calculate the marginal distribution (u, v) of each point, and the covariance matrix Σ of the joint distribution is calculated. When the wind power forecast value is updated, Convert the predicted value from the real value domain to the Gaussian domain and calculate the multivariate Gaussian conditional distribution z x |z y The mean vector of and the covariance matrix Perform multivariate normal distribution sampling to obtain z that follows the distribution x Sample, and through x = F -1 (φ(z x ))Convert the data from Gaussian domain to real-valued domain to obtain sampling samples of actual output.

[0090] S2: Establish a robust forward-looking power dispatch model considering the ellipsoidal uncertainty set.

[0091] Furthermore, a robust forward-looking power dispatching model considering the ellipsoid uncertainty set is established, and the ellipsoid uncertainty set is established according to the sampling samples collected for wind power samples.

[0092] The robust forward-looking power dispatch framework consists of two stages. The first stage solves the unit commitment problem, and the second stage focuses on the worst-case economic dispatch. The abstract model of robust forward-looking power dispatch considering the ellipsoid uncertainty set is expressed as follows:

[0093]

[0094] In the first stage, x represents the decision variables of the first stage, including the unit status, c T x is the unit combination cost in the first stage, including no-load cost, startup cost and shutdown cost of the total unit. Ax≤b represents the unit logic constraint. In the second stage, y is the decision variable including unit output, δ is the external parameter for system load, and q T u represents the penalty cost of reducing wind power, d T y is the second-stage dispatch cost in the worst case, Bx+Cu+Dy+Eδ-e≤0 is the constraint condition of power balance, ramping, spinning reserve, network transmission and wind farm output, u is an uncertain parameter, belonging to the uncertain set U. The present invention adopts an ellipsoidal uncertain set, where Q is the covariance matrix, u c is the center of the ellipsoid.

[0095] The covariance matrix Q is calculated based on the wind power output sampling samples, and the predicted value is the sphere center u c Construct the uncertain set U.

[0096] S3: The C&CG algorithm is used to solve the main problem and sub-problems in the robust forward-looking power dispatching model. Samples are taken on the unit hypersphere, and the points on the hypersphere are projected onto the ellipsoid according to the special formula of the constructed ellipsoid expression. The alternating direction method is started to solve the sub-problems. The main problem and sub-problems are iteratively calculated to make a convergence judgment.

[0097] Furthermore, the C&CG algorithm based on the alternating direction method of hypersphere sampling is used to decompose the two stages of the robust forward-looking power dispatching framework, solve the main problem, calculate the dual problem of the decomposed subproblem, replace the original uncertain set expression with the ellipsoid expression related to the unit hypersphere, uniformly select points on the hypersphere and project them onto the ellipsoid surface, and solve the subproblem using the alternating direction method based on hypersphere sampling. The main problem and subproblems are iteratively calculated to make a convergence judgment.

[0098] The two-stage decomposition of the robust forward-looking power dispatch framework includes the following main problems:

[0099]

[0100] The sub-problems are:

[0101]

[0102] It should be noted that the main problem is solved directly by the solver, and the feasible solution is obtained by solving the main problem. And update the algorithm iteration lower bound accordingly

[0103] The dual problem of the sub-problems after the computational decomposition includes converting the inner min problem into a max problem through the strong duality theorem:

[0104]

[0105] Replace the indeterminate set expression in with the ellipsoid expression associated with the unit hypersphere:

[0106] U={u|u=u c +Rx,||x|| 2 ≤1}

[0107] Where x is a point in the unit hypersphere, R is a symmetric positive definite matrix, where R = Q -1 / 2 , sample the hypersphere and project it onto the ellipsoid according to U.

[0108] It should also be noted that points are uniformly taken on the hypersphere, and random points on the n-dimensional hypersphere are uniformly generated by the Muller method, and a coordinate vector (x 1 ,x 2 ,…,x n ), each coordinate is independently sampled from a standard Gaussian distribution and then normalized:

[0109]

[0110] Among them, the normalized coordinate vector Located on the unit hypersphere, the n-dimensional Gaussian probability density function is given by a constant:

[0111]

[0112] The alternating direction method based on hypersphere sampling is as follows: the ellipsoid sampling is used as the initial value of the algorithm's uncertain parameters. For the subproblem, the sampling initial value is used to fix the uncertain parameters. Assume the number of iterations k = 1, let Fixing the uncertain parameters, we obtain the linear programming with respect to the dual variables:

[0113]

[0114] The optimal solution of the dual variable is obtained by solving the linear programming of the dual variable Fix the dual variables with the current optimal solution and obtain the second-order cone constraint programming problem with uncertain parameter u:

[0115]

[0116] Determine whether the convergence criterion is met|Objval λ -Objval u |<ò: When the convergence criterion is met, the algorithm converges and outputs the optimal value of the subproblem and the optimal solution of the variable. When the convergence criterion is not met, the uncertain parameters continue to be fixed, and k=k+1.

[0117] Solve the sub-problems to obtain feasible solutions and feasible scenarios And update the algorithm iteration upper bound is the objective function value of the subproblem based on the feasible solution.

[0118] The convergence judgment includes judging whether the upper bound UB and the lower bound LB can satisfy the convergence condition |UB-LB|≤ε: when the convergence condition is met, the optimal solution of robust forward scheduling considering the ellipsoid uncertainty set is output; when the convergence condition is not met, the optimization model of the main problem of robust forward scheduling considering the ellipsoid uncertainty set is updated, new constraints and variables are generated, and k=k+1 is set, and the solver is re-adopted to solve the main problem until |UB-LB|≤ε is satisfied, and the optimal solution of robust forward scheduling considering the ellipsoid uncertainty set is output.

[0119] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

[0120] Example 2, reference Figure 3 , which is the second embodiment of the present invention, provides a hypersphere sampling alternating direction method for robust power scheduling. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through experiments.

[0121] The present invention employs a 6-node power system. Figure 3 The improved system is shown, with conventional generators located at nodes 1 and 2, wind farms connected at nodes 4 and 6, and loads at nodes 3-5.

[0122] The comparative method uses the Karush-Kuhn-Tucker (KKT) conditional method (hereinafter referred to as the "KKT method") to transform the subproblem. The transformed subproblem is an exact mixed integer second-order cone programming problem:

[0123]

[0124] The present invention sets four different rolling window ranges: 1, 4, 8 and 12, and the time granularity is 15 minutes. The solution methods are the method proposed by the present invention and the KKT method respectively. In terms of Gurobi solver parameters, MIPGap is set to 0.5%, Presolve parameter is set to 2, and MIPFocus parameter is set to 1 to improve the solution efficiency of mixed integer second-order cone programming. Table 1 records the total number of variables and constraints after pre-solution in all cases. The method proposed by the present invention avoids the introduction of integer variables, making the integer variables zero and the overall problem scale smaller.

[0125] Table 1 Number of model variables and constraints under different rolling windows

[0126]

[0127] Table 2 records the cost and calculation time of two different methods in different rolling cycles. The data in the table show that for 12 periods, the relative error of the cost of the two methods is 0.14%, which verifies the accuracy of the method proposed in this invention. Regarding the calculation time of robust forward-looking power dispatching, the method proposed in this paper takes a slightly longer calculation time when the problem scale is small (such as 1 period and 4 periods), which is mainly because the alternating direction method needs to perform iterative calculations based on multiple sampling initial values. As the problem scale increases, the calculation time of the KKT method will increase sharply due to the significant increase in the number of integer variables. For the cases of 8 periods and 12 periods, the calculation speed of the method introduced in this invention is 4.56 times and 19.52 times faster than the KKT method, respectively, showing its higher computational efficiency. It should be noted that the above example only tests a 6-node system with a maximum span of 12 periods. This is mainly because when the period span is further increased, the KKT method cannot find the optimal solution even after several hours.

[0128] Table 2 Cost and calculation time under different rolling windows

[0129]

[0130] In addition, the present invention also generates scenarios by setting 1000 rolling instances and adding 10% Gaussian error to the wind power generation forecast value to verify the calculation effectiveness under various scenarios. The test rolling window is set to 8 periods. Table 3 compares the average relative error and average calculation time

[0131] Table 3 Computational effect verification in multiple scenarios

[0132]

[0133] The data in Table 3 show that the optimal solution of the proposed method is very close to that of the KKT method, with an average relative error of only 0.0834%, which further verifies the effectiveness and accuracy of the proposed method. In addition, the proposed method is more efficient than the KKT method, with an average time consumption of only 16.5 seconds, which is about 8.85 times faster than the average calculation time of the KKT method. However, due to the conversion of the KKT method into a nonlinear mixed integer two-stage planning, the difficulty is greatly increased, resulting in unstable performance in many cases, and it often fails to converge to the optimal solution after 15 minutes. This makes the KKT method unsuitable for larger-scale problems. In contrast, the alternating direction method based on hypersphere sampling proposed in the present invention not only ensures the accuracy of the solution, but also ensures the efficiency and stability of the algorithm.

[0134] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

[0135] Embodiment 3, the third embodiment of the present invention, is different from the first two embodiments in that:

[0136] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program codes.

[0137] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0138] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0139] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0140] Example 4, reference Figure 4 , which is the fourth embodiment of the present invention, provides a hypersphere sampling alternating direction system for robust power dispatching, including a wind power scenario generation and ellipsoid uncertainty set construction module, a robust forward-looking power dispatching model establishment and optimization module, and a C&CG solution module based on the hypersphere sampling alternating direction method.

[0141] The wind power scenario generation and ellipsoid uncertainty set construction module is responsible for establishing the conditional probability model of wind power, using the latest wind power forecast data to generate wind power output samples, expressing the conditional distribution of the multivariate Gaussian distribution through the Gaussian Copula function and the covariance matrix, analyzing historical data, and calculating the wind power conditional probability density function, so as to collect wind power samples and construct the ellipsoid uncertainty set.

[0142] The robust forward-looking power dispatch model establishment and optimization module establishes a robust forward-looking power dispatch model considering the ellipsoid uncertainty set. The model consists of two stages: the first stage solves the unit combination problem, and the second stage focuses on the economic dispatch in the worst case. The model includes constraints on power balance, ramping, spinning reserve, network transmission and wind farm output, and uses an ellipsoid uncertainty set to represent the uncertainty of wind power output. The covariance matrix is ​​calculated based on the wind power output sampling samples, and the uncertainty set is constructed with the current rolling window prediction value as the center of the sphere.

[0143] The C&CG solution module based on the alternating direction method of hypersphere sampling uses the C&CG algorithm to decompose the two-stage problem of the robust forward-looking power dispatching framework, and adopts the alternating direction method based on hypersphere sampling to solve the sub-problems; hypersphere sampling includes uniformly taking points on the hypersphere, generating random points through the Muller method, and normalizing them to obtain coordinate vectors located on the unit hypersphere; the alternating direction method involves fixing uncertain parameters and dual variables to alternately solve sub-problems; this module solves the main problem and sub-problems respectively, and updates the upper and lower bounds through an iterative process until the convergence conditions are met, thereby outputting the optimal solution for robust forward-looking power dispatching.

[0144] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. Hypersphere sampling alternating direction method for robust power dispatching, characterized by: include, Establish a conditional probability model for wind power and obtain wind power output samples for constructing an ellipsoid uncertainty set through the latest wind power forecast data; A robust forward-looking power dispatch model considering ellipsoidal uncertainty set is established; The C&CG algorithm is used to solve the main problem and sub-problems in the robust forward-looking power dispatching model. Samples are taken on the unit hypersphere, and the points on the hypersphere are projected onto the ellipsoid according to the special formula of the constructed ellipsoid expression. The alternating direction method is started to solve the sub-problems. The main problem and sub-problems are iteratively calculated, and convergence judgment is made.

2. The hyperspherical sampling alternating direction method for robust power dispatching according to claim 1, characterized in that: The conditional probability model includes calculating the wind power conditional probability density function according to historical data, calculating the corresponding covariance matrix according to the expression of the covariance matrix in the Gaussian Copula function, calculating the conditional distribution of the multivariate Gaussian distribution, and collecting wind power samples: For the actual wind power output X in historical data, 11 ,…,x NT ] T and predicted value Y = [y 11 ,…,y NT ] T , let the corresponding marginal distribution be (u,v), and calculate the basic conditional probability density function: Among them, f X|Y is the conditional probability density function of X with respect to Y, c is the Gaussian Copula probability density function, is x ij The probability density function of , N is the total number of wind farms, T is the total number of window time; Consider that there is: c(u 11 ,…,u NT ,v 11 ,…,v NT |S)=F Gauss (f -1 (u 11 ),…,φ -1 (v NT )) c(v 11 ,…,v NT |S yy )=Φ Gauss (f -1 (v 11 ),…,φ -1 (v NT )) Among them, Φ Gauss is a multivariate Gaussian distribution, φ -1 (·) is the pseudo-inverse function of the standard Gaussian distribution, Σ is the covariance; make The covariance matrix of can be expressed as linear correlation coefficient: in: Where: ρ is the linear correlation coefficient; The probability density function of the final conditional probability is constructed based on the calculation results: in, The derivation formula based on the mean and covariance of the conditional probability density is:

3. The hyperspherical sampling alternating direction method for robust power dispatching according to claim 2, characterized in that: The wind power sample collection includes obtaining the Gaussian distribution parameters of the actual value in the Gaussian domain at a given wind power forecast output value through the derivation formula of the mean and covariance of the conditional probability density, and directly sampling according to the current parameters: using the historical output actual value X and forecast value Y of n wind farms, calculating the marginal distribution (u, v) of each point, calculating the covariance matrix Σ of the joint distribution, and when the wind power forecast value is updated, Convert the predicted value from the real value domain to the Gaussian domain and calculate the multivariate Gaussian conditional distribution z x |z y The mean vector of and the covariance matrix Perform multivariate normal distribution sampling to obtain z that follows the distribution x Sample, and through x = F -1 (φ(z x ))Convert the data from Gaussian domain to real-valued domain to obtain sampling samples of actual output.

4. The hyperspherical sampling alternating direction method for robust power dispatching according to claim 3, characterized in that: The robust forward-looking power dispatch model includes establishing a robust forward-looking power dispatch model that takes into account an ellipsoid uncertainty set, and establishing an ellipsoid uncertainty set based on sampling samples for collecting wind power samples; The robust forward-looking power dispatch framework consists of two stages. The first stage solves the unit commitment problem, and the second stage focuses on the worst-case economic dispatch. The abstract model of robust forward-looking power dispatch considering the ellipsoid uncertainty set is expressed as follows: stAx≤b Bx+Cu+Dy+Eδ-e≤0 u∈U={(uu c ) T Q -1 (uu c )≤1} In the first stage, x represents the decision variables of the first stage, including the unit status, c T x is the unit combination cost in the first stage, including no-load cost, startup cost and shutdown cost of the total unit. Ax≤b represents the unit logic constraint. In the second stage, y is the decision variable including unit output, δ is the external parameter for system load, and q T u represents the penalty cost of reducing wind power, d T y is the second-stage dispatch cost in the worst case, Bx+Cu+Dy+Eδ-e≤0 is the constraint condition of power balance, ramping, spinning reserve, network transmission and wind farm output, u is an uncertain parameter, belonging to the uncertain set U; the present invention adopts the ellipsoidal uncertain set, where Q is the covariance matrix, u c is the center of the ellipsoid; The covariance matrix Q is calculated based on the wind power output sampling samples, and the predicted value is the sphere center u c Construct the uncertain set U.

5. The hyperspherical sampling alternating direction method for robust power dispatching according to claim 4, characterized in that: The C&CG algorithm includes two stages of decomposing a robust forward-looking power dispatch framework using the C&CG algorithm, decomposing it into a main problem and sub-problems; The two-stage decomposition of the robust forward-looking power dispatch framework includes the decomposition of the main problem as follows: stAx≤b Bx+Cu+Dy+Eδ-e≤0 l＝1,…,r The sub-problems are:

6. The hyperspherical sampling alternating direction method for robust power dispatching according to claim 5, characterized in that: Solving the main problem includes directly solving the main problem using a solver, and solving the main problem to obtain a feasible solution And update the algorithm iteration lower bound accordingly The dual problem of the sub-problems after the computational decomposition includes converting the inner min problem into a max problem through the strong duality theorem: stλ≥0 -D T λ=d u∈U Replace the indeterminate set expression in with the ellipsoid expression associated with the unit hypersphere: U={u|u=u c +Rx,||x||2≤1} Where x is a point in the unit hypersphere, R is a symmetric positive definite matrix, where R = Q -1 / 2 , sample the hypersphere and project it onto the ellipsoid according to U.

7. The hyperspherical sampling alternating direction method for robust power dispatching according to claim 6, characterized in that: The alternating direction method includes uniformly selecting points on the hypersphere, generating random points on the n-dimensional hypersphere uniformly by the Muller method, and assigning a coordinate vector (x1, x2, ..., x n ), each coordinate is independently sampled from a standard Gaussian distribution and then normalized: Among them, the normalized coordinate vector Located on the unit hypersphere, the n-dimensional Gaussian probability density function is given by a constant: The alternating direction method based on hypersphere sampling is as follows: the ellipsoid sampling is used as the initial value of the algorithm's uncertain parameters. For the subproblem, the sampling initial value is used to fix the uncertain parameters. Assume the number of iterations k = 1, let Fixing the uncertain parameters, we obtain the linear programming with respect to the dual variables: stλ k+1 ≥0,-D T l k+1 =d The optimal solution of the dual variable is obtained by solving the linear programming of the dual variable Fix the dual variables with the current optimal solution and obtain the second-order cone constraint programming problem with uncertain parameter u: s.t.u k+1 ∈U Determine whether the convergence criterion is met|Objval λ -Objval u |<ò: When the convergence criterion is met, the algorithm converges and outputs the optimal value of the subproblem and the optimal solution of the variable. When the convergence criterion is not met, the uncertain parameters continue to be fixed, and k=k+1; Solve the sub-problems to obtain feasible solutions and feasible scenarios And update the algorithm iteration upper bound is the objective function value of the subproblem based on the feasible solution; The convergence judgment includes judging whether the upper bound UB and the lower bound LB can satisfy the convergence condition UB-LB|≤ε: when the convergence condition is met, the optimal solution of robust forward scheduling considering the ellipsoid uncertainty set is output; when the convergence condition is not met, the optimization model of the main problem of robust forward scheduling considering the ellipsoid uncertainty set is updated, new constraints and variables are generated, and k=k+1 is set, and the solver is re-adopted to solve the main problem until |UB-LB|≤ε is satisfied, and the optimal solution of robust forward scheduling considering the ellipsoid uncertainty set is output.

8. A hyperspherical sampling alternating direction method for robust power dispatching according to any one of claims 1 to 7, characterized in that: It includes wind power scenario generation and ellipsoid uncertainty set construction module, robust forward-looking power dispatch model establishment and optimization module, and C&CG solution module based on hypersphere sampling alternating direction method; The wind power scenario generation and ellipsoid uncertainty set construction module is responsible for establishing a conditional probability model for wind power, using the latest wind power forecast data to generate wind power output samples, expressing the conditional distribution of the multivariate Gaussian distribution through the Gaussian Copula function and the covariance matrix, analyzing historical data, and calculating the wind power conditional probability density function, thereby collecting wind power samples and constructing an ellipsoid uncertainty set; The robust forward-looking power dispatch model establishment and optimization module establishes a robust forward-looking power dispatch model considering the ellipsoid uncertainty set. The model includes two stages: the first stage solves the unit combination problem, and the second stage focuses on the economic dispatch under the worst case. The model contains constraints on power balance, ramping, spinning reserve, network transmission and wind farm output, and uses an ellipsoid uncertainty set to represent the uncertainty of wind power output. The covariance matrix is ​​calculated based on the wind power output sampling samples, and the uncertainty set is constructed with the current rolling window prediction value as the sphere center; The C&CG solution module based on the alternating direction method of hypersphere sampling uses the C&CG algorithm to decompose the two-stage problem of the robust forward-looking power dispatching framework, and adopts the alternating direction method based on hypersphere sampling to solve the sub-problems; the hypersphere sampling includes uniformly taking points on the hypersphere, generating random points by the Muller method, and performing normalization processing to obtain coordinate vectors located on the unit hypersphere; the alternating direction method involves fixing uncertain parameters and dual variables to alternately solve sub-problems; the module solves the main problem and the sub-problems respectively, and updates the upper and lower bounds through an iterative process until the convergence conditions are met, thereby outputting the optimal solution of the robust forward-looking power dispatching.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the hyperspherical sampling alternating direction method for robust power scheduling according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the hyperspherical sampling alternating direction method for robust power scheduling according to any one of claims 1 to 7 are implemented.

Images