Probability transient stability assessment method considering wind power output randomness and correlation

Abstract

The invention discloses a probability transient stability evaluation method considering wind power output random and correlation. The method comprises the following steps: determining the optimal sampling point number of a wind power output random variable by adopting a practical dynamic security domain (PDSR) and an ant colony optimization algorithm; a multi-layer perceptron (MLP) is introduced to predict quantiles of future wind power generation output, so that the randomness of actual wind power generation output is described; according to the optimal sampling point and the quantile, Gaussian-Hermite integration is adopted to obtain wind power output uncorrelated original state variable distribution; adopting Nataf inverse transformation to process the correlation between the wind power plants; and performing calculation based on Cornish-Fisher expansion to obtain a transient stability probability. According to the method, the precision requirement of transient stability evaluation of the current wind power grid-connected power system can be met, and transient stable and safe operation of the wind power grid-connected system is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of transient stability assessment of power systems, and in particular to a probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output. Background Art

[0002] In recent years, wind power generation, as one of the representative renewable energy sources, has been widely integrated into power systems. Unlike traditional power generation methods, wind power generation is directly affected by wind speed and has obvious uncertainties and correlations. This uncertainty and the large-scale integration of wind power pose a major challenge to the transient stability of power systems. Therefore, it is particularly important to develop an effective transient stability assessment method that can take into account the uncertainty and correlation of wind farms for the planning and operation of power systems.

[0003] The Chinese patent application with publication number CN113435113A proposes a method and device for evaluating transient stability of power systems. This method establishes independent high-order feature extractors for different categories of power system features to extract high-order features from the measurement sequence, and finally obtains the transient stability evaluation result by performing feature crossover between different analogies through the classifier; the Chinese patent application with publication number CN113937762A proposes a method for evaluating transient stability of microgrids based on long short-term memory networks. This method constructs an evaluator based on a long short-term memory network, and burns it into the control unit of the virtual synchronous inverter for information interaction. When the microgrid is operating normally and the virtual power angle changes within the set range, the evaluator does not perform an evaluation, which simplifies the debugging of the neural network and realizes early judgment of transient stability. However, neither of the above two methods takes into account the impact of wind power access systems on transient stability.

[0004] Most of the current transient stability assessment methods do not consider the randomness and correlation of wind power output. The Chinese patent application publication number CN117937434A proposes a transient stability assessment method for the access of new energy equipment to the power system. A full-order model of the photovoltaic synchronous machine parallel power generation system is constructed, and it is decomposed into a slow system and a fast system based on the singular perturbation method. The stability of the fast system is analyzed by the preset eigenvalue method, and the stability of the slow system is analyzed based on the equal area rule, and finally the system is determined to be stable. This method improves the accuracy of transient stability assessment for the access of new energy equipment to the power system, and solves the problem that traditional technology does not fully consider the characteristics of photovoltaic synchronous machines and the poor processing effect of high-order systems. The Chinese patent application publication number CN116050867A proposes a data-driven transient stability assessment method for power systems with interpretability. The data-driven idea, feature dimensionality reduction and denoising, sample enhancement data preprocessing method, and interpretability principle are applied to study the transient stability assessment method of the power system and its interpretability analysis.

[0005] However, both of the above methods do not consider the randomness and correlation of wind power output. Summary of the invention

[0006] In order to more accurately evaluate the transient stability of wind power grid-connected systems, the impact of the randomness and correlation of wind power on the transient stability of the power system is considered. The present invention provides a probabilistic transient stability evaluation method that takes into account the randomness and correlation of wind power output. The method can meet the accuracy requirements of the current transient stability evaluation of wind power grid-connected power systems and ensure the transient stability and safe operation of wind power grid-connected systems.

[0007] The technical solution adopted by the present invention is:

[0008] A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output comprises the following steps:

[0009] Step 1: Use the practical dynamic security region (PDSR) and ant colony optimization algorithm to determine the optimal number of sampling points of the wind power output random variable;

[0010] Step 2: Introduce a multi-layer perceptron (MLP) to predict the quantiles of future wind power output, thereby describing the randomness of actual wind power output;

[0011] Step 3: Based on the optimal sampling points and quantiles, the Gauss-Hermite integration is used to obtain the uncorrelated original state variable distribution of wind power output;

[0012] Step 4: Use Nataf inverse transform to process the correlation between wind farms;

[0013] Step 5: Calculate the transient stability probability based on the Cornish-Fisher expansion.

[0014] The step 1 comprises the following steps:

[0015] S1.1: Set the transient stability probability index based on the practical dynamic safety region (PDSR):

[0016] Based on the practical dynamic security region (PDSR), the TSP of the power system under a given fault can be transformed from the complex n-degree integration in the n-dimensional power injection space to a simpler analytical calculation, as shown in Equation (1) and Equation (2):

[0017]

[0018] In formula (1), TSP is the transient stability probability; q is the vector of random variables of node injection power; Ω i is the dynamic safety region in the injection space, is the set of systems that maintain transient stability after a given fault, i = 1, 2, ..., n, n is the number of nodes; Pr(q∈Ωi ) is the transient stability probability of the power system under a given fault; j is the coefficient of the hyperplane associated with node j; P j is the critical active power injection at node j; A is a set of multiple random probability variables; D(A) is the cumulative distribution function of A.

[0019] In formula (2): C j is the active power injection of the i-th node. The probabilistic transient stability index based on practical dynamic security region (PDSR) is essentially to solve the cumulative distribution function of A.

[0020] S1.2: Determine the importance of different wind power access nodes based on the hyperplane coefficient of the practical dynamic security region (PDSR).

[0021] Considering that the hyperplane coefficient of the practical dynamic safety region (PDSR) can reflect the importance of different nodes, the weight of the power injection pair A of the wind farm node j is defined as shown in formula (3):

[0022]

[0023] In formula (3): is the weight of the power injection pair A of the wind farm node j, j = 1, 2, ..., k, k is the number of wind farm access nodes; is the expected value of active power injection of wind farm node j. Based on formula (3), the wind farms with overall weight contribution exceeding 90% are selected as the random variables to be optimized, and the sampling number of the random variables of the remaining wind farms is defined as 3.

[0024] S1.3: Using the ant colony optimization algorithm to determine the optimal number of sampling points for the wind power output random variable, including the following steps:

[0025] S1.3.1: The objective function is to minimize the number of sampling points of active power injection variables at each wind farm node, while satisfying constraints such as transient stability probability accuracy;

[0026] The objective function is shown in formula (4):

[0027]

[0028] In formula (4): F1 is the objective function; is the total number of variable sampling points; n WF is the number of wind farm installation nodes in the power system; t i is the number of sampling points of the wind farm active power injection variable with non-normal distribution, i=1,2,…n WF ;

[0029] In order to ensure that the calculation results of the multi-point estimation method meet the accuracy, the constraint conditions are established as shown in formula (5):

[0030]

[0031] In formula (5), abs is the absolute value symbol; f T The calculation process of solving the transient stability probability using the multi-point estimation method based on Gauss-Hermite integration combined with Nataf inverse transformation;

[0032] err is the value that satisfies the accuracy setting; is the percentage change of transient stability probability when the sampling point changes. When the values ​​of each variable satisfy equation (5), it can be considered that the transient stability probability calculated based on the sampling number meets the accuracy.

[0033] Based on the rule of the number of sampling points of non-normal distribution variables as shown in formula (6), the number of variable sampling points must satisfy formula (7):

[0034]

[0035] Formula (7) is the condition that the variable sampling number must meet.

[0036] S1.3.2: Initialize and set the number of ants, evaporation coefficient, pheromone intensity and other parameters;

[0037] The number of ants is set to about 1.5 times the target number; the evaporation coefficient is between 0.2 and 0.5; and the pheromone intensity is initialized according to the number of paths.

[0038] S1.3.3: During the walking process of the ants, local pheromones are updated on the paths they have walked, and their performance is evaluated according to the objective function. The pheromone update strategy is shown in Equations (8) and (9);

[0039] τ ij (t+n)=(1-ρ)τ ij (t)+△τ ij (8);

[0040]

[0041] In formula (8): ρ is the pheromone volatilization rate; τ ij (t+n) is the updated pheromone value; τ ij (t) is the local pheromone value; △τ ij is the pheromone iteration value.

[0042] In formula (9): is the optimal iteration value of pheromone; Q is a constant; F minis the total number of minimum variable sampling points; s i It is the optimal path corresponding to the minimum total number of variable sampling points in the i-th iterative search process.

[0043] S1.3.4: Obtain the optimal number of sampling points for the wind farm node active power injection variable through iterative updating.

[0044] Based on step 1.3.3, a local optimal solution that satisfies the calculation accuracy is obtained through iteration, as shown in formula (10):

[0045]

[0046] In formula (10): P' is the local optimal solution; t i ' is the number of sampling points of the wind farm active power injection variable with non-normal distribution, i = 1, 2, ... n WF ;n WF The number of wind farm installation nodes in the power system.

[0047] Finally, through normalization, the sampling point number vector of each wind farm active power injection variable with non-normal distribution is obtained:

[0048] In step 2, based on the quantile regression theory, the quantile regression model based on the multi-layer perceptron (MLP) is expressed as:

[0049]

[0050] In formula (11): is the loss function for quantile regression, specifically for different quantiles α b Customized to handle prediction errors at this quantile; c m is the actual output value of the mth observation point; x m is the input of the mth observation point; κ b is the weight of the b-th quantile from the hidden layer to the output layer; ψ ω (x m κ b ) is about the input x m and weight κ b The prediction function of the multi-layer perceptron MLP model; ψ ω (x m κ b+1 ) is about the input x m and weight κ b+1 The prediction function of the multi-layer perceptron MLP model. In formula (12), ω is the weight from the input layer to the hidden layer; B is the total number of quantiles; M is the number of samples in the training data set; κ b+1is the weight of the b+1th quantile from the hidden layer to the output layer; b is the function confidence.

[0051] Based on equations (12) and (13), the probability distribution of wind power output c can be obtained, as shown in equation (13):

[0052]

[0053] In formula (13): D(c) is the cumulative distribution function of output c under given input; is at quantile α b The predicted value under is calculated by the MLP model; is at quantile α b The predicted minimum value under ; is at quantile α b The predicted maximum value under .

[0054] The step 3 comprises the following steps:

[0055] S3.1: According to step 1 and step 2, the number of sampling points required for each node in statistical analysis is determined, and the sampling point number vector is:

[0056]

[0057] In formula (14), N is the number of sampling points vector; t i ' is the number of sampling points, i = 1, 2, ... n WF ;n WF The number of wind farm installation nodes in the power system.

[0058] S3.2: Use Gauss-Hermite integration to calculate the sampling points of each wind farm node and obtain its weight, which is:

[0059]

[0060] In formula (15): i,k is the sampling value, k=1,2,…,t i ;μ i is the i-th integration point; ω i,k is the weight corresponding to the sample value, k = 1, 2, ..., t i ;q k is the weight coefficient corresponding to the i-th integral point, as shown in formula (16):

[0061]

[0062] In formula (16): q k is the weight coefficient corresponding to the i-th integration point; n is the order of Gauss-Hermite integration; Hn-1 (μ i ) is the n-1th order Hermite polynomial in μ i The value at .

[0063] S3.3: Based on the sampling points of each wind farm node, the sampling vector in the independent standard normal space is constructed as:

[0064] X i,k =[0,…,0,χ i,k ,0,…,0] (17);

[0065] In formula (17): X i,k is the sampling vector; i,k is the sampling value, k=1,2,…,t i .

[0066] In step 4, the sampling vectors of the original space of the wind farm nodes and their corresponding weight vectors are obtained from the standard normal distribution space through the Nataf inverse transformation, including the following steps:

[0067] S4.1: Calculate the correlation matrix between the active power injection P of the wind farm node and the corresponding standard normal variable h.

[0068] The linear correlation coefficient matrices of h and P are ρ0 and ρ respectively, where ρ is known. To simplify the calculation, the correlation coefficient matrix ρ0 of h can be obtained according to the semi-empirical formula; the semi-empirical formula is as follows:

[0069]

[0070] In formula (18): The active power injection P is a semi-empirical formula under Weibull distribution; ρ0 and ρ are as follows:

[0071]

[0072] In formula (19): 0i,j is the element in the linear correlation coefficient matrix of h, i=1,2,…,n WF ; j = 1, 2, ..., n WF ;

[0073] In formula (20): i,j is the element in the linear correlation coefficient matrix of P, i=1,2,…,n WF ; j = 1, 2, ..., n WF ;

[0074] n WF The number of wind farm installation nodes in the power system.

[0075] S4.2: Decompose the correlation matrix into a lower triangular matrix B using Cholesky decomposition;

[0076] ρ0=BB T (twenty one);

[0077] In formula (21), ρ0 is the correlation coefficient matrix; B is the lower triangular matrix; B T is the transposed matrix of the lower triangular matrix.

[0078] S4.3: Use the cumulative distribution function of each node to transform the sampling vector in the standard normal space back to the original variable space;

[0079] The evaluation matrix X composed of sampling vectors is converted into the evaluation matrix Z by formula (22); the value of the element in each sampling vector in the original space is obtained by formula (23), so that the evaluation matrix Z composed of sampling vectors is converted into the sampling matrix P in the original space, as shown in formula (24).

[0080] Z = BX (22);

[0081] P i =F -1 (z i ) (twenty three);

[0082]

[0083] In formula (22), X is the evaluation matrix composed of sampling vectors; Z is the transformed evaluation matrix; and B is the lower triangular matrix.

[0084] In formula (23): F -1 (·) is the inverse cumulative distribution function of the active power injected into the corresponding node; z i is the value of the element in the sampling vector; P i is the value of the element in the sample vector in the original space.

[0085] In formula (24): P is the sampling matrix; is the value of the element in the sampling vector, n TF is the number of wind farm installation nodes in the power system. Z and B are shown as follows:

[0086]

[0087]

[0088] In formula (25): b ij x k is the element in the evaluation matrix, i=1,2,…,n WF ; j = 1, 2, ..., nWF ; k = 1, 2, ..., n WF ;

[0089] In formula (26): b ij are the elements in the lower triangular matrix; i=1,2,…,n WF ; j = 1, 2, ..., n WF ;

[0090] n WF The number of wind farm installation nodes in the power system.

[0091] The step 5 comprises the following steps:

[0092] S5.1: Based on the sampling vector in the original space, calculate the statistics of active power injection of wind farm nodes: mean μ si ,variance and the third-order central moment And apply it to the multivariable function A.

[0093]

[0094] In formula (27): represents the expected value of the active power of the wind farm node; H(·) is the mean function; n is the total number of nodes.

[0095] In formula (28): is the constant coefficient of the hyperplane equation at the corresponding node i, i = 1, 2, …, n; For variable P i The standard deviation of , i = 1, 2, …, n;

[0096] In formula (29): is the third-order central moment.

[0097] S5..2: Based on the Cornish-Fisher series expansion, the cumulative distribution function of A is obtained and the transient stability probability is calculated:

[0098] The Cornish-Fisher series expansion provides an approximation of the quantile and cumulative value of the distribution function D(A). Assume that the quantile of the standard normal distribution with quantile level α is μ(α), and μ(α)=φ -1 (α),φ -1 (α) is the inverse function of the cumulative distribution function of the standard normal distribution, then the D(A) quantile with quantile level α can be expressed as formula (30):

[0099]

[0100] In formula (30), c(α) is the quantile of the variable A to be determined.

[0101] p3 and p4 are normalized semi-invariants of various orders, which can be calculated by formula (31):

[0102]

[0103] In formula (31): pt is the t-order normalized cumulative moment of A, which is used to correct the quantile in the Cornish-Fisher expansion; is the t-order central moment of A; σ is the standard deviation of A; is the first-order moment of A; δ a is the mean value of A; is the second central moment of A; is the variance of A; is the third-order central moment of A, which is related to the skewness of the distribution.

[0104] Based on equations (31) and (32), we get the quantile c(α) of the variable A to be determined, and then we get A through equation (33):

[0105] c(α)=F -1 (α) (32);

[0106]

[0107] In formula (33): α i is the coefficient of the hyperplane associated with node j, i = 1, 2, ..., n, n is the number of nodes; P i is the active power injection at node i in the original input variable space, i = 1, 2, …, n;

[0108] The calculated transient stability probability is shown in formula (34).

[0109] TSP=D(A)| A＝0 (34);

[0110] In formula (34), TSP is the transient stability probability; A is the variable to be determined.

[0111] The present invention provides a probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output, and the technical effects are as follows:

[0112] 1) In step 1 of the present invention, it is proposed to use PDSR and ant colony optimization algorithm to determine the optimal sampling point, reduce the blindness and redundancy of the number of sampling points selected by the current point estimation method, and thus realize the rapid solution of the cumulative distribution function that meets the calculation accuracy requirements;

[0113] 2) In step 2 of the present invention, a multi-layer perceptron (MLP) model is used to predict the quantiles of future wind power output. This method can effectively capture the random characteristics of wind power generation. MLP has a strong nonlinear fitting ability and can learn complex nonlinear relationships from historical data, thereby improving the prediction accuracy. Compared with traditional linear models, MLP can better describe the random fluctuations and uncertainties of wind power output. In addition, the use of quantile prediction can not only estimate the central trend of the output, but also provide prediction results under different confidence intervals, thereby providing richer information for risk assessment and scheduling decisions.

[0114] 3) In step 3 of the present invention, the Gauss-Hermite integration method is used to efficiently solve the distribution of uncorrelated original state variables of wind power output by utilizing the optimal sampling points and quantiles. This method can effectively process random variables with normal or approximately normal distribution, reduce the consumption of computing resources in the integration process, and ensure fast calculation under the premise of high precision. At the same time, it avoids the error accumulation problem in traditional numerical integration, is particularly suitable for processing high-dimensional random variables, and ensures the accuracy of the cumulative distribution function (CDF). In addition, the Gauss-Hermite integration simplifies the processing of complex correlations, greatly improves the calculation efficiency, and provides strong technical support for wind power output prediction and optimization.

[0115] 4) In step 4 of the present invention, by using the Nataf inverse transform to process the correlation between wind farms, the correlation problem between the outputs of multiple wind farms can be effectively addressed. The Nataf inverse transform can convert correlated random variables with arbitrary distribution into uncorrelated variables under the standard normal distribution, thereby simplifying the modeling process of the correlation between wind farm outputs. This method can more accurately capture the correlation structure between wind farms and avoid the errors that may be caused by simply assuming no correlation. Compared with traditional correlation processing methods, the Nataf inverse transform has higher adaptability and flexibility, improves the accuracy and reliability of calculations, and helps to more accurately reflect the cluster output characteristics of wind farms, thereby improving the overall efficiency of wind power forecasting and scheduling;

[0116] 5) In step 5 of the present invention, by calculating the transient stability probability based on the Cornish-Fisher expansion, the accuracy of evaluating the transient stability of the power system under the influence of the randomness of wind power output can be effectively improved. The Cornish-Fisher expansion can map random variables under non-normal distribution back to the standard normal distribution, and then conveniently calculate the probability value. This method avoids the limitation of assuming that wind power output is a standard normal distribution, and more flexibly handles the asymmetry and heavy-tail characteristics of wind power output. Compared with traditional numerical integration methods, the Cornish-Fisher expansion method has higher computational efficiency, can quickly estimate the transient stability probability, and ensure the accuracy of the calculation results. Through this method, the impact of wind power access on the transient stability of the power system can be more accurately evaluated, providing a reliable basis for the safe operation of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] Figure 1 is a flow chart of the method of the present invention;

[0118] Figure 2 is a schematic diagram of an improved IEEE 39-node system in an example of the present invention;

[0119] Figure 3 is a comparison chart of the maximum error percentages of different methods under faults in the examples of the present invention;

[0120] Figure 4 It is a comparison chart of the calculation time of different methods under fault in the example of the present invention. DETAILED DESCRIPTION

[0121] A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output, a probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output, based on the practical dynamic safety domain boundary hyperplane expression to determine the weight contribution of non-normal distribution random variables of wind power output, further based on the ant colony optimization algorithm to obtain the optimal number of sampling points of each non-normal distribution random variable that meets the accuracy of transient stability probability solution in multi-point estimation; secondly, the multi-layer perceptron MLP is introduced to predict the quantile of future wind power output, from describing the randomness of actual wind power output; then, the cumulative distribution function of A is solved by the multi-point estimation method based on Gauss-Hermite integral, and the correlation between variables is processed based on the Nataf inverse transformation; finally, the transient stability probability is calculated by Cornish-Fisher expansion. The present invention can ensure the effectiveness of transient stability assessment of power system after large-scale wind power generation is connected to the grid.

[0122] The specific process of the present invention is as follows Figure 1 As shown, the method comprises the following steps:

[0123] Step 1: Use the practical dynamic security region (PDSR) and ant colony optimization algorithm to determine the optimal number of sampling points of the wind power output random variable;

[0124] Step 2: Introduce a multi-layer perceptron (MLP) to predict the quantiles of future wind power output, thereby describing the randomness of actual wind power output;

[0125] Step 3: Based on the optimal sampling points and quantiles, the Gauss-Hermite integration is used to obtain the uncorrelated original state variable distribution of wind power output;

[0126] Step 4: Use Nataf inverse transform to process the correlation between wind farms;

[0127] Step 5: Calculate the transient stability probability based on the Cornish-Fisher expansion.

[0128] The step 1 comprises the following steps:

[0129] S1.1: Set the transient stability probability index based on the practical dynamic safety region (PDSR):

[0130] Based on the practical dynamic security region (PDSR), the TSP of the power system under a given fault can be transformed from the complex n-degree integration in the n-dimensional power injection space to a simpler analytical calculation, as shown in Equation (1) and Equation (2):

[0131]

[0132] In formula (1), TSP is the transient stability probability; q is the vector of random variables of node injection power; Ω i is the dynamic safety region in the injection space, is the set of systems that maintain transient stability after a given fault, i = 1, 2, ..., n, n is the number of nodes; Pr(q∈Ω i ) is the transient stability probability of the power system under a given fault; j is the coefficient of the hyperplane associated with node j; P j is the critical active power injection at node j; A is a set of multiple random probability variables; D(A) is the cumulative distribution function of A.

[0133] In formula (2): C j is the active power injection of the i-th node. The probabilistic transient stability index based on practical dynamic security region (PDSR) is essentially to solve the cumulative distribution function of A.

[0134] S1.2: Determine the importance of different wind power access nodes based on the hyperplane coefficient of the practical dynamic security region (PDSR).

[0135] Considering that the hyperplane coefficient of the practical dynamic safety region (PDSR) can reflect the importance of different nodes, the weight of the power injection pair A of the wind farm node j is defined as shown in formula (3):

[0136]

[0137] In formula (3): is the weight of the power injection pair A of the wind farm node j, j = 1, 2, ..., k, k is the number of wind farm access nodes; is the expected value of active power injection of wind farm node j. Based on formula (3), the wind farms with overall weight contribution exceeding 90% are selected as the random variables to be optimized, and the sampling number of the random variables of the remaining wind farms is defined as 3.

[0138] S1.3: Using the ant colony optimization algorithm to determine the optimal number of sampling points for the wind power output random variable, including the following steps:

[0139] S1.3.1: The objective function is to minimize the number of sampling points of active power injection variables at each wind farm node, while satisfying constraints such as transient stability probability accuracy;

[0140] The objective function is shown in formula (4):

[0141]

[0142] In formula (4): F1 is the objective function; is the total number of variable sampling points; n WF is the number of wind farm installation nodes in the power system; t i is the number of sampling points of the wind farm active power injection variable with non-normal distribution, i=1,2,…n WF ;

[0143] In order to ensure that the calculation results of the multi-point estimation method meet the accuracy, the constraint conditions are established as shown in formula (5):

[0144]

[0145] In formula (5), abs is the absolute value symbol; f T The calculation process of solving the transient stability probability using the multi-point estimation method based on Gauss-Hermite integration combined with Nataf inverse transformation;

[0146] err is the value that satisfies the accuracy setting; is the percentage change of transient stability probability when the sampling point changes. When the values ​​of each variable satisfy equation (5), it can be considered that the transient stability probability calculated based on the sampling number meets the accuracy.

[0147] Based on the rule of the number of sampling points of non-normal distribution variables as shown in formula (6), the number of variable sampling points must satisfy formula (7):

[0148]

[0149] Formula (7) is the condition that the variable sampling number must meet.

[0150] S1.3.2: Initialize and set the number of ants, evaporation coefficient, pheromone intensity and other parameters;

[0151] The number of ants is set to about 1.5 times the target number; the evaporation coefficient is between 0.2 and 0.5; and the pheromone intensity is initialized according to the number of paths.

[0152] S1.3.3: During the walking process of the ants, local pheromones are updated on the paths they have walked, and their performance is evaluated according to the objective function. The pheromone update strategy is shown in Equations (8) and (9);

[0153] τ ij (t+n)=(1-ρ)τ ij (t)+△τ ij (8);

[0154]

[0155] In formula (8): ρ is the pheromone volatilization rate; τ ij (t+n) is the updated pheromone value; τ ij (t) is the local pheromone value; △τ ij is the pheromone iteration value. In formula (9): is the optimal iteration value of pheromone; Q is a constant; F min is the total number of minimum variable sampling points; s i It is the optimal path corresponding to the minimum total number of variable sampling points in the i-th iterative search process.

[0156] S1.3.4: Obtain the optimal number of sampling points for the wind farm node active power injection variable through iterative updating.

[0157] Based on step 1.3.3, a local optimal solution that satisfies the calculation accuracy is obtained through iteration, as shown in formula (10):

[0158]

[0159] In formula (10): P' is the local optimal solution; t i ' is the number of sampling points of the wind farm active power injection variable with non-normal distribution, i = 1, 2, ... n WF ;n WFThe number of wind farm installation nodes in the power system.

[0160] Finally, through normalization, the sampling point number vector of each wind farm active power injection variable with non-normal distribution is obtained:

[0161] In step 2, based on the quantile regression theory, the quantile regression model based on the multi-layer perceptron (MLP) is expressed as:

[0162]

[0163] In formula (11): is the loss function for quantile regression, specifically for different quantiles α b Customized to handle prediction errors at this quantile; c m is the actual output value of the mth observation point; x m is the input of the mth observation point; κ b is the weight of the b-th quantile from the hidden layer to the output layer; ψ ω (x m κ b ) is about the input x m and weight κ b The prediction function of the multi-layer perceptron MLP model; ψ ω (x m κ b+1 ) is about the input x m and weight κ b+1 The prediction function of the multi-layer perceptron MLP model. In formula (12), ω is the weight from the input layer to the hidden layer; B is the total number of quantiles; M is the number of samples in the training data set; κ b+1 is the weight of the b+1th quantile from the hidden layer to the output layer; b is the function confidence.

[0164] Based on equations (12) and (13), the probability distribution of wind power output c can be obtained, as shown in equation (13):

[0165]

[0166] In formula (13): D(c) is the cumulative distribution function of output c under given input; is at quantile α b The predicted value under is calculated by the MLP model; is at quantile α b The predicted minimum value under ; is at quantile α b The predicted maximum value under .

[0167] The step 3 comprises the following steps:

[0168] S3.1: According to step 1 and step 2, the number of sampling points required for each node in statistical analysis is determined, and the sampling point number vector is:

[0169]

[0170] In formula (14), N is the number of sampling points vector; t i ' is the number of sampling points, i = 1, 2, ... n WF ;n WF The number of wind farm installation nodes in the power system.

[0171] S3.2: Use Gauss-Hermite integration to calculate the sampling points of each wind farm node and obtain its weight, which is:

[0172]

[0173] In formula (15): i,k is the sampling value, k=1,2,…,t i ;μ i is the i-th integration point; ω i,k is the weight corresponding to the sample value, k = 1, 2, ..., t i ;q k is the weight coefficient corresponding to the i-th integral point, as shown in formula (16):

[0174]

[0175] In formula (16): q k is the weight coefficient corresponding to the i-th integration point; n is the order of Gauss-Hermite integration; H n-1 (μ i ) is the n-1th order Hermite polynomial in μ i The value at .

[0176] S3.3: Based on the sampling points of each wind farm node, the sampling vector in the independent standard normal space is constructed as:

[0177] X i,k =[0,…,0,χ i,k ,0,…,0] (17);

[0178] In formula (17): X i,k is the sampling vector; i,k is the sampling value, k=1,2,…,t i .

[0179] In step 4, the sampling vectors of the original space of the wind farm nodes and their corresponding weight vectors are obtained from the standard normal distribution space through the Nataf inverse transformation, including the following steps:

[0180] S4.1: Calculate the correlation matrix between the active power injection P of the wind farm node and the corresponding standard normal variable h.

[0181] The linear correlation coefficient matrices of h and P are ρ0 and ρ respectively, where ρ is known. To simplify the calculation, the correlation coefficient matrix ρ0 of h can be obtained according to the semi-empirical formula; the semi-empirical formula is as follows:

[0182]

[0183] In formula (18), R is the active power injection, P is the semi-empirical formula under Weibull distribution, and ρ0 and ρ are as follows:

[0184]

[0185] In formula (19): 0i,j is the element in the linear correlation coefficient matrix of h, i=1,2,…,n WF ; j = 1, 2, ..., n WF ;

[0186] In formula (20): i,j is the element in the linear correlation coefficient matrix of P, i=1,2,…,n WF ; j = 1, 2, ..., n WF ;

[0187] n WF The number of wind farm installation nodes in the power system.

[0188] S4.2: Decompose the correlation matrix into a lower triangular matrix B using Cholesky decomposition;

[0189] ρ0=BB T (twenty one);

[0190] In formula (21), ρ0 is the correlation coefficient matrix; B is the lower triangular matrix; B T is the transposed matrix of the lower triangular matrix.

[0191] S4.3: Use the cumulative distribution function of each node to transform the sampling vector in the standard normal space back to the original variable space;

[0192] The evaluation matrix X composed of sampling vectors is converted into the evaluation matrix Z by formula (22); the value of the element in each sampling vector in the original space is obtained by formula (23), so that the evaluation matrix Z composed of sampling vectors is converted into the sampling matrix P in the original space, as shown in formula (24).

[0193] Z = BX (22);

[0194] P i =F -1 (z i ) (twenty three);

[0195]

[0196] In formula (22), X is the evaluation matrix composed of sampling vectors; Z is the transformed evaluation matrix; and B is the lower triangular matrix.

[0197] In formula (23): F -1 (·) is the inverse cumulative distribution function of the active power injected into the corresponding node; z i is the value of the element in the sampling vector; P i is the value of the element in the sample vector in the original space.

[0198] In formula (24): P is the sampling matrix; is the value of the element in the sampling vector, n TF is the number of wind farm installation nodes in the power system. Z and B are shown as follows:

[0199]

[0200] In formula (25): b ij x k is the element in the evaluation matrix, i=1,2,…,n WF ; j = 1, 2, ..., n WF ; k = 1, 2, ..., n WF ;

[0201] In formula (26): b ij are the elements in the lower triangular matrix; i=1,2,…,n WF ; j = 1, 2, ..., n WF ;

[0202] n WF The number of wind farm installation nodes in the power system.

[0203] The step 5 comprises the following steps:

[0204] S5.1: Based on the sampling vector in the original space, calculate the statistics of active power injection of wind farm nodes: mean μ si ,variance and the third-order central moment And apply it to the multivariable function A.

[0205]

[0206] In formula (27): represents the expected value of the active power of the wind farm node; H(·) is the mean function; n is the total number of nodes.

[0207] In formula (28): is the constant coefficient of the hyperplane equation at the corresponding node i, i = 1, 2, …, n; For variable P i The standard deviation of , i = 1, 2, …, n;

[0208] In formula (29): is the third-order central moment.

[0209] S5.2: Based on the Cornish-Fisher series expansion, the cumulative distribution function of A is obtained and the transient stability probability is calculated:

[0210] The Cornish-Fisher series expansion provides an approximation of the quantile and cumulative value of the distribution function D(A). Assume that the quantile of the standard normal distribution with quantile level α is μ(α), and μ(α)=φ -1 (α),φ -1 (α) is the inverse function of the cumulative distribution function of the standard normal distribution, then the D(A) quantile with quantile level α can be expressed as formula (30):

[0211]

[0212] In formula (30), c(α) is the quantile of the variable A to be determined.

[0213] p3 and p4 are normalized semi-invariants of various orders, which can be calculated by formula (31):

[0214]

[0215] In formula (31): pt is the t-order normalized cumulative moment of A, which is used to correct the quantile in the Cornish-Fisher expansion; is the t-order central moment of A; σ is the standard deviation of A; is the first-order moment of A; δ a is the mean value of A; is the second central moment of A; is the variance of A; is the third-order central moment of A, which is related to the skewness of the distribution.

[0216] Based on equations (31) and (32), we get the quantile c(α) of the variable A to be determined, and then we get A through equation (33):

[0217]

[0218] In formula (33): α i is the coefficient of the hyperplane associated with node j, i = 1, 2, ..., n, n is the number of nodes; P i is the active power injection at node i in the original input variable space, i = 1, 2, …, n;

[0219] The calculated transient stability probability is shown in formula (34).

[0220] TSP=D(A)| A＝0 (34);

[0221] In formula (34), TSP is the transient stability probability; A is the variable to be determined.

[0222] Example:

[0223] In order to verify the feasibility of the present invention, Figure 2 The simulation is performed on the improved IEEE 39-node system shown in the figure. The traditional generators at nodes 33 and 34 are replaced by two wind farms with capacities of 632 MW and 508 MW respectively. The cut-in, cut-off and rated wind speeds are set to 4m / s, 23m / s and 15m / s respectively. The N-1 three-phase short-circuit fault is considered and the fault clearing time is 0.1s. As shown in Table 1. Five cases of positive and negative correlation coefficients CC between wind farms are considered. The proposed method is compared with other point estimation methods, which are shown as follows:

[0224] Method 1: Three-point estimation method based on Taylor expansion and Nataf inverse transform;

[0225] Method 2: Three-point estimation method based on Gauss-Hermite integration and Nataf inverse transformation;

[0226] Method 3: Five-point estimation method based on Gauss-Hermite integration and Nataf inverse transformation.

[0227] Table 1 Correlation settings between wind farms

[0228]

[0229]

[0230] Table 2 shows the calculation results of TSP under different methods when the wind farm correlation coefficient is 0.8, and the fault lines with TSP = 1 and TSP = 0 are not shown. Compared with other methods, the method proposed in the present invention can be roughly consistent with other methods in terms of transient stability probability, and is effective.

[0231] Table 2 Calculation results of TSP under different methods

[0232]

[0233] Figure 3 and Figure 4 The maximum error percentage and computation time comparison of different methods under fault conditions are shown, where the error percentage is based on the method with 5000 samples based on Monte Carlo simulation. Figure 3 and Figure 4 It can be seen that the calculation accuracy and speed of the method of the present invention are relatively high. While meeting the probability accuracy of transient stability assessment of wind power grid-connected system, the calculation speed is also improved. This is due to the use of PDSR and ant colony optimization algorithm to select the best sampling points, thereby reducing the impact of redundant sampling points and improving the calculation rate.

[0234] The present invention proposes a probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output, which can meet the analysis of transient stability safety issues of the power system after wind power is connected to the grid, and at the same time, ensure the effectiveness of probabilistic transient stability assessment under different wind power-related situations.

Claims

1. A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output, characterized in that The following steps are involved: Step 1: Use practical dynamic safety region and ant colony optimization algorithm to determine the optimal number of sampling points of wind power output random variables; Step 2: Introduce a multi-layer perceptron to predict the quantiles of future wind power output, thereby describing the randomness of actual wind power output; Step 3: Based on the optimal sampling points and quantiles, the Gauss-Hermite integration is used to obtain the uncorrelated original state variable distribution of wind power output; Step 4: Use Nataf inverse transform to process the correlation between wind farms; Step 5: Calculate the transient stability probability based on the Cornish-Fisher expansion.

2. A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output according to claim 1, characterized in that: The step 1 comprises the following steps: S1.1: Set transient stability probability index based on practical dynamic safety region: Based on the practical dynamic security region, the TSP of the power system under a given fault can be transformed from the complex n-degree integration in the n-dimensional power injection space to a simpler analytical calculation, as shown in Equation (1) and Equation (2): In formula (1), TSP is the transient stability probability; q is the vector of random variables of node injection power; Ω i is the dynamic safety region in the injection space, is the set of systems that maintain transient stability after a given fault, i = 1, 2, ..., n, n is the number of nodes; Pr(q∈Ω i ) is the transient stability probability of the power system under a given fault; j is the coefficient of the hyperplane associated with node j; P j is the critical active power injection at node j; A is a set of multiple random probability variables; D(A) is the cumulative distribution function of A; in formula (2), C j is the active power injection of the i-th node; S1.2: Determine the importance of different wind power access nodes based on the hyperplane coefficient of the practical dynamic safety domain; Considering that the hyperplane coefficient of the practical dynamic safety region can reflect the importance of different nodes, the weight of the power injection pair A of the wind farm node j is defined as shown in formula (3): In formula (3): is the weight of the power injection pair A of the wind farm node j, j = 1, 2, ..., k, k is the number of wind farm access nodes; is the expected value of active power injection into wind farm node j; S1.3: Use the ant colony optimization algorithm to determine the optimal number of sampling points for the wind power output random variable.

3. A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output according to claim 2, characterized in that: S1.3 includes the following steps: S1.3.1: The objective function is to minimize the number of sampling points of active power injection variables at each wind farm node, while satisfying constraints such as transient stability probability accuracy; The objective function is shown in formula (4): In formula (4): F1 is the objective function; is the total number of variable sampling points; n WF is the number of wind farm installation nodes in the power system; t i is the number of sampling points of the wind farm active power injection variable with non-normal distribution, i=1,2,…n WF ; In order to ensure that the calculation results of the multi-point estimation method meet the accuracy, the constraint conditions are established as shown in formula (5): In formula (5), abs is the absolute value symbol; f T The calculation process of solving the transient stability probability using the multi-point estimation method based on Gauss-Hermite integration combined with Nataf inverse transformation; err is the value that satisfies the accuracy setting; is the percentage change of transient stability probability when the sampling point changes; when the values ​​of each variable satisfy formula (5), it can be considered that the transient stability probability calculated based on the sampling number meets the accuracy; Based on the rule of the number of sampling points of non-normal distribution variables as shown in formula (6), the number of variable sampling points must satisfy formula (7): Formula (7) is the condition that the number of variable samples must meet; S1.3.2: Initialize and set the number of ants, evaporation coefficient, and pheromone intensity parameters; S1.3.3: During the walking process of the ants, local pheromones are updated on the paths they have walked, and their performance is evaluated based on the objective function. The pheromone update strategy is shown in Equations (8) and (9); t ij (t+n)=(1-ρ)τ ij (t)+△τ ij (8); In formula (8): ρ is the pheromone volatilization rate; τ ij (t+n) is the updated pheromone value; τ ij (t) is the local pheromone value; △τ ij is the pheromone iteration value; In formula (9): is the optimal iteration value of pheromone; Q is a constant; F min is the total number of minimum variable sampling points; s i The optimal path corresponding to the minimum total number of variable sampling points in the i-th iteration search process; S1.3.4: Obtain the optimal number of sampling points for the wind farm node active power injection variable through iterative updating; Based on step 1.3.3, a local optimal solution that satisfies the calculation accuracy is obtained through iteration, as shown in formula (10): In formula (10): P' is the local optimal solution; t i ' is the number of sampling points of the wind farm active power injection variable with non-normal distribution, i = 1, 2, ... n WF ;n WF The number of wind farm installation nodes in the power system; Finally, through normalization, the sampling point number vector of each wind farm active power injection variable with non-normal distribution is obtained:

4. A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output according to claim 1, characterized in that: In step 2, based on the quantile regression theory, the quantile regression model based on the multilayer perceptron is expressed as: In formula (11): b is the loss function for quantile regression, specifically for different quantiles α b Customized to handle prediction errors at this quantile; cm is the actual output value of the mth observation point; xm is the input of the mth observation point; κ b is the weight of the b-th quantile from the hidden layer to the output layer; ψ ω (x m κ b ) is about the input x m and weight κ b The prediction function of the multi-layer perceptron MLP model; ψ ω (x m κ b+1 ) is about the input x m and weight κ b+1 The prediction function of the multi-layer perceptron MLP model; in formula (12): ω is the weight from the input layer to the hidden layer; B is the total number of quantiles; M is the number of samples in the training data set; κ b+1 is the weight of the b+1th quantile from the hidden layer to the output layer; b is the function confidence; Based on equations (12) and (13), the probability distribution of wind power output c can be obtained, as shown in equation (13): In formula (13): D(c) is the cumulative distribution function of output c under given input; is at quantile α b The predicted minimum value under ; is at quantile α b The predicted maximum value under .

5. The probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output according to claim 1, characterized in that: The step 3 comprises the following steps: S3.1: According to step 1 and step 2, the number of sampling points required for each node in statistical analysis is determined, and the sampling point number vector is: In formula (14), N is the number of sampling points vector; t i ' is the number of sampling points, i = 1, 2, ... n WF ;n WF The number of wind farm installation nodes in the power system; S3.2: Use Gauss-Hermite integration to calculate the sampling points of each wind farm node and obtain its weight, which is: In formula (15): i,k is the sampling value, k=1,2,…,t i ;μ i is the i-th integration point; ω i,k is the weight corresponding to the sample value, k = 1, 2, ..., t i ;q k is the weight coefficient corresponding to the i-th integral point, as shown in formula (16): In formula (16): q k is the weight coefficient corresponding to the i-th integration point; n is the order of Gauss-Hermite integration; H n-1 (μ i ) is the n-1th order Hermite polynomial in μ i The value at S3.3: Based on the sampling points of each wind farm node, the sampling vector in the independent standard normal space is constructed as: X i,k =[0,…,0,x i,k ,0,…,0] (17); In formula (17): X i,k is the sampling vector; i,k is the sampling value, k=1,2,…,t i .

6. A probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output according to claim 1, characterized in that: In step 4, the sampling vectors of the original space of the wind farm nodes and their corresponding weight vectors are obtained from the standard normal distribution space through the Nataf inverse transformation, including the following steps: S4.1: Calculate the correlation matrix between the active power injection P of the wind farm node and the corresponding standard normal variable h: The linear correlation coefficient matrices of h and P are ρ0 and ρ respectively, where ρ is known. To simplify the calculation, the correlation coefficient matrix ρ0 of h can be obtained according to the semi-empirical formula. The semi-empirical formula is as follows: In formula (18): The active power injection P is a semi-empirical formula under Weibull distribution; ρ0 and ρ are as follows: In formula (19): 0i,j is the element in the linear correlation coefficient matrix of h, i=1,2,…,n WF ; j = 1, 2, ..., n WF ; In formula (20): i,j is the element in the linear correlation coefficient matrix of P, i=1,2,…,n WF ; j = 1, 2, ..., n WF ; n WF The number of wind farm installation nodes in the power system; S4.2: Decompose the correlation matrix into a lower triangular matrix B using Cholesky decomposition; ρ0=BB T (21); In formula (21), ρ0 is the correlation coefficient matrix; B is the lower triangular matrix; B T is the transposed matrix of the lower triangular matrix; S4.3: Use the cumulative distribution function of each node to transform the sampling vector in the standard normal space back to the original variable space; The evaluation matrix X composed of sampling vectors is converted into the evaluation matrix Z by formula (22); the value of the element in each sampling vector in the original space is obtained by formula (23), so that the evaluation matrix Z composed of sampling vectors is converted into the sampling matrix P in the original space, as shown in formula (24); Z = BX (22); P i =F -1 (z i ) (23); In formula (22), X is the evaluation matrix composed of sampling vectors; Z is the transformed evaluation matrix; B is the lower triangular matrix; In formula (23): F -1 (·) is the inverse cumulative distribution function of the active power injected into the corresponding node; z i is the value of the element in the sampling vector; P i is the value of the element in the sampling vector in the original space; In formula (24): P is the sampling matrix; is the value of the element in the sampling vector, n TF is the number of wind farm installation nodes in the power system; Z and B are as follows: In formula (25): b ij x k is the element in the evaluation matrix, i=1,2,…,n WF ; j = 1, 2, ..., n WF ; k = 1, 2, ..., n WF ; In formula (26): b ij are the elements in the lower triangular matrix; i=1,2,…,n WF ; j = 1, 2, ..., n WF ;n WF The number of wind farm installation nodes in the power system.

7. The probabilistic transient stability assessment method taking into account the randomness and correlation of wind power output according to claim 1, characterized in that: The step 5 comprises the following steps: S5.1: Based on the sampling vector in the original space, calculate the statistics of active power injection of wind farm nodes: mean μ si ,variance and the third-order central moment and apply it to a multivariable function A; In formula (27): represents the expected value of the active power of the wind farm node; H(·) is the mean function; n is the total number of nodes; In formula (28): is the constant coefficient of the hyperplane equation at the corresponding node i, i = 1, 2, …, n; is the variable P i The standard deviation of , i = 1, 2, ..., n; in formula (29), is the third-order central moment; S5.2: Based on the Cornish-Fisher series expansion, the cumulative distribution function of A is obtained and the transient stability probability is calculated: The Cornish-Fisher series expansion provides an approximation of the quantiles and cumulants of the distribution function D(A); assuming that the quantile level of the standard normal distribution is α, the quantile is μ(α), and μ(α)=φ -1 (α),φ -1 (α) is the inverse function of the cumulative distribution function of the standard normal distribution, then the D(A) quantile with quantile level α can be expressed as formula (30): In formula (30): c(α) is the quantile of the variable A to be determined; p3 and p4 are normalized semi-invariants of various orders, which can be calculated by formula (31): In formula (31): pt is the t-order normalized cumulative moment of A, which is used to correct the quantile in the Cornish-Fisher expansion; is the t-order central moment of A; σ is the standard deviation of A; is the first-order moment of A; δ a is the mean value of A; is the second central moment of A; is the variance of A; is the third-order central moment of A; Based on equations (31) and (32), we get the quantile c(α) of the variable A to be determined, and then we get A through equation (33): c(a)=F -1 (a) (32); In formula (33): α i is the coefficient of the hyperplane associated with node j, i = 1, 2, ..., n, n is the number of nodes; P i is the active power injection at node i in the original input variable space, i = 1, 2, …, n; The transient stability probability is calculated as shown in formula (34); TSP=D(A)| A＝0 (34); In formula (34), TSP is the transient stability probability; A is the variable to be determined.

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