A fast evaluation method for static voltage stability considering wind power forecast error

Abstract

The present invention belongs to the technical field of power grid voltage stability, and specifically relates to a method for rapid assessment of static voltage stability taking into account wind power prediction errors. In view of the shortcomings of the existing system voltage stability analysis methods in terms of low computational accuracy and efficiency, the present invention adopts the following technical solutions: historical data of wind farms are obtained, and a historical data set containing wind power predictions and measured power is constructed; the wind power prediction power in the historical data set is divided using a fixed step size to obtain different data subsets, and the wind power measured power at the same moment is divided into corresponding data subsets; the wind power prediction error in each data subset is calculated, and a non-parametric kernel density estimation method is used to construct a probability distribution of the power prediction error; a radial basis function proxy model is constructed to obtain a load margin, and a rapid assessment of the system static voltage stability is achieved based on the load margin. The beneficial effects of the present invention are: rapid and accurate assessment of static voltage stability is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power grid voltage stability, and in particular relates to a method for rapid evaluation of static voltage stability taking into account wind power prediction errors. Background Art

[0002] Integration of a high proportion of wind power into power systems has become a trend in current energy development. However, wind power generation is affected by numerous meteorological factors, such as wind speed and direction, and its output is subject to significant fluctuation and randomness. Therefore, conducting voltage stability analysis under large-scale wind power integration is of practical significance for ensuring the safe operation of the system.

[0003] Generally, accurate assessment of power systems with a high proportion of wind power requires two key requirements: a reliable wind power output model and an accurate and rapid probabilistic assessment method. Regarding the first aspect, extensive research has been conducted on wind power forecasting methods, with predicted power used as input for system safety and stability analysis, unit commitment, and other issues. However, wind power is significantly affected by weather fluctuations, resulting in biased power forecasts. Therefore, in actual operation, it is necessary to model the probability distribution of errors under different wind power forecasts to develop a probabilistic model that describes short-timescale wind power output uncertainty. This model can be used to quantify the impact of wind power output uncertainty on system voltage stability. Regarding the second aspect, Monte Carlo simulation is the most direct probabilistic assessment method, but its computational efficiency is limited, making it difficult to apply to large-scale, real-world systems. While semi-invariant and point estimation methods can improve computational efficiency through certain simplifications, they often result in reduced accuracy.

[0004] Specifically, current system voltage stability analysis considering wind power output uncertainty primarily uses the Weibull distribution to describe wind speed fluctuations, and calculates load margins using Monte Carlo simulation, semi-invariant methods, and other methods. However, the Weibull distribution is suitable for describing wind speed fluctuations over long time scales, but it is difficult to accurately describe wind speed distribution over short time scales. Zhang Qian et al. published a paper [Evaluation Scheme for Static Voltage Stability of Power Systems Considering Electric Vehicle Charging and Load Fluctuation Calculations [J]. Power System Technology, 2017, 41(6): 1888-1895] that studies the impact of electric vehicle charging loads on system static voltage stability and uses quasi-Monte Carlo simulation to solve the problem. Compared to the Monte Carlo simulation method, this method can effectively improve computational efficiency. In the paper published by Zheng Xiaodian et al. [Probabilistic analysis of static voltage stability based on semi-invariant and maximum entropy principle [J]. Acta Energiae Solaris Sinica, 2022, 43(3):126-132], Weibull distribution is used to describe wind speed fluctuations and the load margin is calculated by semi-invariant method. However, due to the calculation accuracy of the semi-invariant method, there is a large error in the tail of the probability distribution of the obtained result. In the paper published by Y.Xu et al. [A Data-driven nonparametric approach for probabilistic load-margin assessment considering wind power penetration [J]. IEEE Transactions on Power Systems, 2020, 35(6):4756-4768], a data-driven method is used to construct a volatility and correlation model based on historical wind power output data. The results show that the correlation structure of wind power output has a great influence on the load margin assessment results. The paper published by C.Xia et al. [Probability analysis ofsteady-state voltage stability considering correlated stochastic variables[J].International Journal of Electrical Power and Energy Systems,2021,131:107105] uses the semi-invariant method to analyze the impact of wind power correlation on the static voltage stability of the system. The results show that the increase in wind power correlation will cause the load margin fluctuation range to increase.A. Mohammed et al. (Electric Power Systems Research, 2022, 206, 107807) analyzed the optimal wind speed probability distribution for different regions. The results showed that the Weibull distribution is suitable for describing high wind speed probability distributions, while the Gamma distribution is suitable for describing low wind speed probability distributions. Furthermore, the results of this study indicate that using different wind speed probability distributions significantly impacts the system voltage stability assessment results.

[0005] In summary, the existing system voltage stability analysis methods considering wind power output uncertainty are all based on long-time scale wind power uncertainty, and short-time scale wind power output uncertainty is not modeled. The computational accuracy and efficiency of voltage stability probabilistic assessment methods need to be improved. Summary of the Invention

[0006] The present invention addresses the shortcomings of existing system voltage stability analysis methods that take into account wind power output uncertainty, such as low calculation accuracy and efficiency, and provides a rapid static voltage stability assessment method that takes into account wind power prediction errors, thereby achieving rapid and accurate assessment of static voltage stability on a short time scale.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for rapidly evaluating static voltage stability considering wind power prediction errors, the method comprising:

[0008] Step S1: Obtain historical data of the wind farm and construct a historical data set containing predicted wind power and measured wind power;

[0009] Step S2: using a fixed step size to divide the wind power forecast in the historical data set to obtain different data subsets, and dividing the wind power measured at the same time into corresponding data subsets;

[0010] Step S3: Calculate the wind power prediction error in each data subset, and construct the probability distribution of the power prediction error using a non-parametric kernel density estimation method;

[0011] Step S4: Based on the probability distribution of prediction errors under different wind power prediction powers, a system static voltage stability rapid assessment model is constructed to obtain a load margin, and a rapid assessment of the system static voltage stability is performed based on the load margin. The system static voltage stability rapid assessment model adopts a radial basis function proxy model.

[0012] The present invention provides a rapid static voltage stability assessment method that takes into account wind power prediction errors. The method uses a non-parametric kernel density estimation method to construct a probability distribution of prediction errors under different wind power prediction powers. A radial basis function proxy model is used to approximate the nonlinear relationship between system node injection power and load margin. The constructed radial basis function proxy model is used to achieve a rapid assessment of the static safety stability of the system that takes into account prediction errors on a short time scale when the wind power prediction value is known. The wind power prediction power is divided into different data subsets according to a fixed step size, and a probability distribution of power prediction errors is constructed for each data subset, which is more accurate.

[0013] As an improvement, step S4 includes:

[0014] Step S41: superimpose the power prediction error probability distribution on the corresponding predicted power to obtain a probability distribution describing the uncertainty of wind power output;

[0015] Step S42: sampling a small amount of the probability distribution of wind power output uncertainty to obtain a small sample set of wind power output, and substituting the wind power output sample into the continuous power flow model to obtain a load margin sample that can characterize the static voltage stability of the system;

[0016] Step S43: using wind power output and load margin samples as input and output variables respectively, and constructing a nonlinear relationship between input and output through a radial basis function proxy model, and solving to obtain a radial basis function proxy model;

[0017] Step S44: A large number of samples are taken from the probability distribution of wind power output, and the samples are substituted into the radial basis function proxy model to achieve rapid calculation of the load margin samples.

[0018] As an improvement, in step S1, in a wind farm equipped with electrical measurement equipment, a data set including predicted wind power and measured wind power is constructed:

[0019]

[0020] Wherein, the subscript i represents the historical data sequence number; P i f and P i r are respectively the predicted power and measured power data of the i-th wind farm at the same moment.

[0021] As an improvement, in step S2, a fixed step size ΔP is used to divide the wind power forecast into different data subsets. Assume that the boundary values ​​of the j-th data subset are P j and P j +ΔP, taking the wind farm i-th predicted power sample P i fFor example, if the sample satisfies P j <P i f ≤P j +ΔP, the sample is divided into the jth data subset, and the jth data subset is expressed as:

[0022]

[0023] in, The predicted power and measured power data of the wind farm at the same time in the j-th data subset.

[0024] As an improvement, in step S3, taking the jth data subset as an example, the wind power prediction error sample is expressed as:

[0025]

[0026] in, is the i-th wind power prediction error sample;

[0027] The nonparametric kernel density estimation method is used to construct its probability distribution, which is expressed as:

[0028]

[0029] Where n is the number of wind power prediction error samples; K(·) is the kernel function, and the Gaussian kernel function is selected to construct the nonparametric kernel density estimation of the variable; h is the bandwidth, which has a great influence on the accuracy of the nonparametric kernel density estimation. The bandwidth value is determined by the empirical formula:

[0030]

[0031] in, is the standard deviation of the wind power forecast error sample.

[0032] As an improvement, in step S42, the Monte Carlo simulation method is used to sample the wind power output probability distribution f(P) to obtain a small number of wind power output samples:

[0033] ξ=[P1,...,P i ,...P Ned ]

[0034] Among them, P i is the i-th wind power output sample; N ed is the number of wind power output samples generated;

[0035] The continuous power flow calculation model is expressed as:

[0036]

[0037] Where x is the input variable of the continuous power flow algorithm, representing the power injected into the nodes in the system, including load demand and wind power output; y is the output variable, which uses the system load margin as the output variable to characterize the system's static voltage stability. When the load margin is high, the system's static voltage stability is high. When the load margin is low, the system faces the risk of static voltage instability caused by load fluctuations.

[0038] Using variable x=[x1,...,x i ,...,x Ned ] represents the wind power output sample. Through continuous power flow calculation, the load margin sample y=[y1,…,y i ,…,y Ned ].

[0039] As an improvement, in step S43, the radial basis function proxy model The relationship with the continuous power flow model is expressed as:

[0040]

[0041] Among them, α i is the coefficient to be solved in the radial basis function proxy model; φ(·) is the radial basis function, and Gaussian radial basis function is used:

[0042] φ(r(x,x i ))=exp(-(cr) 2 )

[0043] Among them, c is the shape parameter; r(x,x i )=||xx i || represents the relationship between any sample point x and the i-th sample x i The Euclidean distance between .

[0044] As an improvement, in step S43, to solve the proxy model parameter α i Substituting the wind power output and load margin samples obtained in step 4-b) into the radial basis function proxy model yields:

[0045]

[0046] The above formula can be further written into matrix form:

[0047] y=Φa

[0048] To ensure that the matrix Φ is invertible, when selecting samples for constructing the radial basis function proxy model, it is necessary to avoid collinearity between samples as much as possible;

[0049] When the matrix Φ is a non-singular matrix, the coefficients to be solved are calculated using the following formula:

[0050] a=Φ -1 y

[0051] Among them, Φ -1 is the inverse matrix of the matrix Φ.

[0052] As an improvement, in step S44, after obtaining the proxy model for calculating the load margin, a large number of wind power output samples x = [x1, ..., x i ,...,x N ], and through Calculate the load margin sample y=[y1,...,y i ,...,y N ].

[0053] As an improvement, step S4 further includes step S45, calculating statistical characteristics based on the obtained load margin samples and constructing a probability distribution, so as to evaluate the impact of wind power output uncertainty on the system voltage stability margin.

[0054] The beneficial effects of the static voltage stability rapid assessment method considering wind power prediction error of the present invention are: using non-parametric kernel density estimation method to construct the prediction error probability distribution under different wind power prediction powers; using radial basis function proxy model to approximate the nonlinear relationship between system node injection power and load margin; using the constructed radial basis function proxy model, when the wind power prediction value is known, realizing the rapid assessment of the static safety stability of the system considering the prediction error; dividing the wind power prediction power according to a fixed step size to obtain different data subsets, and constructing the probability distribution of power prediction error for each data subset respectively, which is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of a method for rapidly evaluating static voltage stability according to a first embodiment of the present invention.

[0056] Figure 2 This is a scatter plot of historical data of wind power prediction power and measured power according to the first embodiment of the present invention.

[0057] Figure 3 This is a probability distribution diagram of wind power prediction error according to the first embodiment of the present invention.

[0058] Figure 4 This is a probability distribution diagram of wind power prediction error when the wind power prediction value is 0.3 pu in the first embodiment of the present invention.

[0059] Figure 5 This is a probability distribution diagram of wind power prediction error when the wind power prediction value is 0.5 pu in the first embodiment of the present invention.

[0060] Figure 6This is a probability distribution diagram of wind power prediction error when the wind power prediction value is 0.7 pu in the first embodiment of the present invention.

[0061] Figure 7 This is a probability distribution diagram of the system load margin when the wind power prediction value is 0.3 pu in the first embodiment of the present invention.

[0062] Figure 8 This is a probability distribution diagram of the system load margin when the wind power prediction value is 0.5 pu in the first embodiment of the present invention.

[0063] Figure 9 This is a probability distribution diagram of the system load margin when the wind power prediction value is 0.7 pu in the first embodiment of the present invention. DETAILED DESCRIPTION

[0064] The following is an explanation and description of the technical solutions of the embodiments of the present invention in conjunction with the drawings of the embodiments of the present invention, but the following embodiments are only preferred embodiments of the present invention and are not exhaustive. Based on the embodiments in the implementation mode, other embodiments obtained by those skilled in the art without creative work are all within the scope of protection of the present invention.

[0065] Example 1

[0066] See also Figures 1 to 9 The first embodiment of the present invention provides a method for rapidly evaluating static voltage stability considering wind power prediction errors. The method comprises:

[0067] Step S1: Obtain historical data of the wind farm and construct a historical data set containing predicted wind power and measured wind power;

[0068] Step S2: using a fixed step size to divide the wind power forecast in the historical data set to obtain different data subsets, and dividing the wind power measured at the same time into corresponding data subsets;

[0069] Step S3: Calculate the wind power prediction error in each data subset, and construct the probability distribution of the power prediction error using a non-parametric kernel density estimation method;

[0070] Step S4: Based on the probability distribution of prediction errors under different wind power prediction powers, a system static voltage stability rapid assessment model is constructed to obtain a load margin, and a rapid assessment of the system static voltage stability is performed based on the load margin. The system static voltage stability rapid assessment model adopts a radial basis function proxy model.

[0071] In this embodiment, step S4 includes:

[0072] Step S41: superimpose the power prediction error probability distribution on the corresponding predicted power to obtain a probability distribution describing the uncertainty of wind power output;

[0073] Step S42: sampling a small amount of the probability distribution of wind power output uncertainty to obtain a small sample set of wind power output, and substituting the wind power output sample into the continuous power flow model to obtain a load margin sample that can characterize the static voltage stability of the system;

[0074] Step S43: using wind power output and load margin samples as input and output variables respectively, and constructing a nonlinear relationship between input and output through a radial basis function proxy model, and solving to obtain a radial basis function proxy model;

[0075] Step S44: A large number of samples are taken from the probability distribution of wind power output, and the samples are substituted into the radial basis function proxy model to achieve rapid calculation of the load margin samples.

[0076] In this embodiment, in step S1, a data set including predicted wind power and measured wind power is constructed in a wind farm equipped with an electrical measurement device:

[0077]

[0078] Wherein, the subscript i represents the historical data sequence number; P i f and P i r are the predicted power and measured power data of the i-th wind farm at the same moment respectively.

[0079] In this embodiment, in step S2, a fixed step size ΔP is used to divide the wind power forecast into different data subsets. Assume that the boundary values ​​of the j-th data subset are P j and P j +ΔP, taking the wind farm i-th predicted power sample P i f For example, if the sample satisfies P j <P i f ≤P j +ΔP, the sample is divided into the jth data subset, and the jth data subset is expressed as:

[0080]

[0081] in, The predicted power and measured power data of the wind farm at the same time in the j-th data subset.

[0082] In this embodiment, in step S3, taking the jth data subset as an example, the wind power prediction error sample is expressed as:

[0083]

[0084] in, is the i-th wind power prediction error sample;

[0085] The nonparametric kernel density estimation method is used to construct its probability distribution, which is expressed as:

[0086]

[0087] Where n is the number of wind power prediction error samples; K(·) is the kernel function, and the Gaussian kernel function is selected to construct the nonparametric kernel density estimation of the variable; h is the bandwidth, which has a great influence on the accuracy of the nonparametric kernel density estimation. The bandwidth value is determined by the empirical formula:

[0088]

[0089] in, is the standard deviation of the wind power forecast error sample.

[0090] In this embodiment, in step S42, the Monte Carlo simulation method is used to sample the wind power output probability distribution f(P) to obtain a small number of wind power output samples:

[0091] ξ=[P1,...,P i ,...P Ned ]

[0092] Among them, P i is the i-th wind power output sample; N ed is the number of wind power output samples generated;

[0093] The continuous power flow calculation model is expressed as:

[0094]

[0095] Where x is the input variable of the continuous power flow algorithm, representing the power injected into the nodes in the system, including load demand and wind power output; y is the output variable, which uses the system load margin as the output variable to characterize the system's static voltage stability. When the load margin is high, the system's static voltage stability is high. When the load margin is low, the system faces the risk of static voltage instability caused by load fluctuations.

[0096] Using variable x=[x1,...,x i ,...,x Ned ] represents the wind power output sample. Through continuous power flow calculation, the load margin sample y=[y1,...,y i ,...,y Ned ].

[0097] In this embodiment, in step S43, the radial basis function proxy model The relationship with the continuous power flow model is expressed as:

[0098]

[0099] Among them, α i is the coefficient to be solved in the radial basis function proxy model; φ(·) is the radial basis function, and Gaussian radial basis function is used:

[0100] φ(r(x,x i ))=exp(-(cr) 2 )

[0101] Among them, c is the shape parameter; r(x,x i )=||xx i || represents the relationship between any sample point x and the i-th sample x i The Euclidean distance between .

[0102] In this embodiment, in step S43, to solve the proxy model parameter α i Substituting the wind power output and load margin samples obtained in step 4-b) into the radial basis function proxy model yields:

[0103]

[0104] The above formula can be further written into matrix form:

[0105] y=Φa

[0106] To ensure that the matrix Φ is invertible, when selecting samples for constructing the radial basis function proxy model, it is necessary to avoid collinearity between samples as much as possible;

[0107] When the matrix Φ is a non-singular matrix, the coefficients to be solved are calculated using the following formula:

[0108] a=Φ -1 y

[0109] Among them, Φ -1 is the inverse matrix of the matrix Φ.

[0110] In this embodiment, in step S44, after obtaining the proxy model for calculating the load margin, a large number of wind power output samples x = [x1, ..., x i ,...,x N ], and through Calculate the load margin sample y=[y1,...,y i ,...,y N ].

[0111] In this embodiment, step S4 further includes step S45 , calculating statistical characteristics based on the obtained load margin samples and constructing a probability distribution, thereby evaluating the impact of wind power output uncertainty on the system voltage stability margin.

[0112] Specific application examples

[0113] This paper takes the historical data of a wind farm in East China and the IEEE 30-bus system as an example to illustrate.

[0114] The method for rapidly evaluating static voltage stability considering wind power prediction error of the present invention comprises the following steps:

[0115] Step S1: construct a historical data set including wind power forecast and measured power based on historical statistical data of wind farms connected to the system. Figure 2 This is a scatter plot of the predicted and measured power for a wind farm in East my country. Based on the time series data recorded by the power plant's wind power prediction system and electrical measurement devices, a historical dataset of predicted and measured power can be constructed:

[0116]

[0117] Among them, the subscript i represents the historical data sequence number; The predicted power and measured power data of the wind farm at the same time in the j-th data subset.

[0118] Step S2: normalize the data and set the reference value to 1. Use a fixed step size ΔP = 0.05 pu to divide the wind power forecast into different data subsets, thereby obtaining data subsets at different power forecast levels. The jth data subset can be expressed as:

[0119]

[0120] Step S3: Calculate the wind power prediction error based on the data set under different wind power prediction powers in step S2, and construct the probability distribution of the wind power prediction error using a non-parametric kernel density estimation method;

[0121] Taking the jth data subset as an example, the wind power prediction error sample can be expressed as:

[0122]

[0123] in, is the i-th wind power prediction error sample.

[0124] For the jth data subset, the wind power prediction error probability density function can be constructed by non-parametric kernel density estimation. Figure 3The probability distribution of wind power forecast errors is shown in the graph. It can be seen that the overall probability distribution of wind power errors exhibits peaked and thick-tailed characteristics. Nonparametric kernel density estimation can accurately fit its probability distribution. In comparison, the commonly used Gaussian distribution performs poorly for wind power forecasts. Figures 4 to 6 Figure 2 shows the probability distribution of the prediction error for wind power forecasts of 0.3 pu, 0.5 pu, and 0.7 pu. It can be seen that the nonparametric kernel density estimation fits the prediction error probability distribution well, while the Gaussian distribution differs significantly from the true distribution. Furthermore, the probability distribution of the prediction error varies significantly at different wind power forecast levels. When the wind power forecast is 0.3 pu, the probability distribution is unimodal, while when the forecast is 0.5 pu and 0.7 pu, the probability distribution exhibits a multimodal distribution. Different forecast powers significantly influence the probability distribution of the error, so it is necessary to model the wind power forecast error separately in practical applications.

[0125] Step S4: Based on the probability distribution of prediction errors under different wind power prediction powers obtained in step S3, a system static voltage stability rapid assessment model is constructed. The specific process is as follows:

[0126] Step S41: superimpose the predicted power on the predicted error probability distribution to obtain a probability distribution describing the uncertainty of wind power output;

[0127] By using the wind power forecast value and the probability distribution of prediction error f(P e ) can be superimposed to obtain the probability distribution f(P) describing wind power output uncertainty. Taking a wind power forecast value of 0.3 pu as an example, superimposing it with the forecast error probability distribution yields a wind power fluctuation range of 0.06 pu to 0.60 pu. In comparison, when a wind power forecast value of 0.7 pu is superimposed with the corresponding forecast error probability distribution, the resulting wind power fluctuation range is 0.6 pu to 0.8 pu. This shows that different wind power forecast powers also have a significant impact on the range of wind power output fluctuation.

[0128] Step S42: perform a small amount of sampling on the probability distribution of wind power output in step S41. In the embodiment, the number of sampling is set to 300, and obtain a small sample set of wind power output x = [x1, ..., x i ,...,x Ned ], substituting the wind power output sample into the continuous power flow model The load margin sample y=[y1,…,y i ,…,y Ned ];

[0129] Step S43: wind power output x in step S43 = [x1, ..., xi ,...,x Ned ] and load margin samples y=[y1,…,y i ,…,y Ned ] are respectively regarded as the input and output variables of the rapid evaluation model, and the radial basis function proxy model is used Construct nonlinear relationships between input and output;

[0130] Step S44: perform a large amount of sampling on the probability distribution of wind power output to obtain its sample set x=[x1,…,x i ,...,x N ], the load margin sample y=[y1,...,y i ,...,y N ] fast calculation;

[0131] Step S45: Calculate the expected value, standard deviation and other statistical characteristics of the load margin samples obtained, and construct their probability distribution, so as to evaluate the impact of wind power output uncertainty on the system voltage stability margin.

[0132] Figures 7 to 9 The probability distribution of system load margin when wind power forecast is 0.3pu, 0.5pu and 0.7pu. Figures 7 to 9 It can be seen that the probability distribution obtained by the proxy model is close to that of the Monte Carlo simulation method, which shows that the proxy model can approximate the load margin calculation model with high accuracy. 4 The Monte Carlo simulation method takes 1385.6 seconds to calculate. In comparison, the proxy model method only takes 41.5 seconds. This comparison demonstrates that the constructed proxy model can quickly and accurately calculate the system load margin given the known wind power forecast value and the probability distribution of the forecast error, providing support for ensuring safe and stable system operation.

[0133] Furthermore, the wind power forecast value and its prediction error have a significant impact on the system load margin. When the forecast value is 0.3 pu, the average load margin is 5.208, with a fluctuation range of [3.0, 7.5]. When the forecast value is 0.7 pu, the average load margin is 5.351, with a fluctuation range of [3.5, 6.5]. This result is due to the increase in wind power generation, which allows the wind farm to meet the adjacent load demand, resulting in a higher system load margin. The fluctuation range of the prediction error has a significant impact on the load margin change. These results indicate that it is necessary to consider the wind power forecast value and its prediction error when evaluating the system load margin to ensure the accuracy of the analysis results.

[0134] The beneficial effects of the method for rapid assessment of static voltage stability considering wind power prediction error of the first embodiment of the present invention are as follows: first, a fixed step size is used to divide the wind farm power history data set into different data subsets according to the size of the predicted power; then, a non-parametric kernel density estimation method is used to construct a probability distribution of the prediction error for each data subset; further, the wind power prediction value and its error probability distribution are regarded as input variables, and the load margin that can characterize the static voltage stability of the system is regarded as the output variable, and wind power output samples are substituted into a continuous power flow model to obtain load margin samples that can characterize the static voltage stability of the system. A radial basis function proxy model is constructed based on a small number of input and output variable samples to approximate their nonlinear relationship; finally, a large number of wind power output samples are generated according to the wind power prediction value and its error probability distribution, and are substituted into the constructed radial basis function proxy model to achieve rapid calculation of the system load margin samples, thereby quickly and accurately assessing the impact of short-time-scale wind power output uncertainty on the static voltage stability of the system; the wind power prediction power is divided into different data subsets according to the fixed step size, and the probability distribution of power prediction error is constructed for each data subset, which is more accurate.

[0135] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art will understand that the present invention includes, but is not limited to, the contents described in the above specific embodiments. Any modifications that do not deviate from the functional and structural principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A rapid static voltage stability assessment method considering wind power forecast error is characterized by: The method for rapid evaluation of static voltage stability considering wind power prediction error includes: Step S1: Obtain historical data of the wind farm and construct a historical data set containing predicted wind power and measured wind power; Step S2: using a fixed step size to divide the wind power forecast in the historical data set to obtain different data subsets, and dividing the wind power measured at the same time into corresponding data subsets; Step S3: Calculate the wind power prediction error in each data subset, and construct the probability distribution of the power prediction error using a non-parametric kernel density estimation method; Step S4: constructing a system static voltage stability rapid assessment model based on the probability distribution of prediction errors under different wind power prediction powers, obtaining a load margin, and implementing a rapid assessment of the system static voltage stability based on the load margin, wherein the system static voltage stability rapid assessment model adopts a radial basis function proxy model; Step S4 includes: Step S41: superimpose the power prediction error probability distribution on the corresponding predicted power to obtain a probability distribution describing the uncertainty of wind power output; Step S42: sampling a small amount of the probability distribution of wind power output uncertainty to obtain a small sample set of wind power output, and substituting the wind power output sample into the continuous power flow model to obtain a load margin sample that can characterize the static voltage stability of the system; Step S43: using wind power output and load margin samples as input and output variables respectively, and constructing a nonlinear relationship between input and output through a radial basis function proxy model, and solving to obtain a radial basis function proxy model; Step S44: A large number of samples are taken from the probability distribution of wind power output, and the samples are substituted into the radial basis function proxy model to achieve rapid calculation of the load margin samples.

2. The method for rapid evaluation of static voltage stability considering wind power prediction error according to claim 1 is characterized in that: In step S1, in a wind farm equipped with electrical measurement equipment, a data set including predicted wind power and measured wind power is constructed: Wherein, the subscript i represents the historical data sequence number; P i f and P i r are the predicted power and measured power data of the i-th wind farm at the same moment respectively.

3. The method for rapid evaluation of static voltage stability considering wind power prediction error according to claim 2 is characterized in that: In step S2, a fixed step size ΔP is used to divide the wind power forecast into different data subsets. Assume that the boundary values ​​of the jth data subset are P j and P j +ΔP, taking the wind farm i-th predicted power sample P i f For example, if the sample satisfies P j <P i f ≤P j +ΔP, the sample is divided into the jth data subset, and the jth data subset is expressed as: in, The predicted power and measured power data of the wind farm at the same time in the j-th data subset.

4. The method for rapid evaluation of static voltage stability considering wind power forecast error according to claim 3 is characterized in that: In step S3, taking the jth data subset as an example, the wind power prediction error sample is expressed as: in, is the i-th wind power prediction error sample; The nonparametric kernel density estimation method is used to construct its probability distribution, which is expressed as: Where n is the number of wind power prediction error samples; K(·) is the kernel function, and the Gaussian kernel function is selected to construct the nonparametric kernel density estimation of the variable; h is the bandwidth, which has a great influence on the accuracy of the nonparametric kernel density estimation. The bandwidth value is determined by the empirical formula: in, is the standard deviation of the wind power forecast error sample.

5. The method for rapid evaluation of static voltage stability considering wind power prediction error according to claim 4 is characterized in that: In step S42, the Monte Carlo simulation method is used to sample the wind power output probability distribution f(P) to obtain a small number of wind power output samples: ξ=[P1,...,P i ,...P Ned ] Among them, P i is the i-th wind power output sample; N ed is the number of wind power output samples generated; The continuous power flow calculation model is expressed as: Where x is the input variable of the continuous power flow algorithm, representing the power injected into the nodes in the system, including load demand and wind power output; y is the output variable, which uses the system load margin as the output variable to characterize the system's static voltage stability. When the load margin is high, the system's static voltage stability is high. When the load margin is low, the system faces the risk of static voltage instability caused by load fluctuations. Using variable x=[x1,...,x i ,...,x Ned ] represents the wind power output sample. Through continuous power flow calculation, the load margin sample y=[y1,...,y i ,...,y Ned ].

6. The method for rapid evaluation of static voltage stability considering wind power forecast error according to claim 5 is characterized in that: In step S43, the radial basis function proxy model The relationship with the continuous power flow model is expressed as: Among them, α i is the coefficient to be solved in the radial basis function proxy model; φ(·) is the radial basis function, and Gaussian radial basis function is used: φ(r(x,x i ))=exp(-(cr) 2 ) Among them, c is the shape parameter; r(x,x i )=||xx i || represents the relationship between any sample point x and the i-th sample x i The Euclidean distance between .

7. The method for rapid evaluation of static voltage stability considering wind power prediction error according to claim 6 is characterized in that: In step S43, to solve the proxy model parameter α i Substituting the wind power output and load margin samples obtained in step 4-b) into the radial basis function proxy model yields: The above formula can be further written into matrix form: y=Φa To ensure that the matrix Φ is invertible, when selecting samples for constructing the radial basis function proxy model, it is necessary to avoid collinearity between samples as much as possible; When the matrix Φ is a non-singular matrix, the coefficients to be solved are calculated using the following formula: a=Φ -1 y Among them, Φ -1 is the inverse matrix of the matrix Φ.

8. The method for rapid evaluation of static voltage stability considering wind power prediction error according to claim 7 is characterized in that: In step S44, after obtaining the proxy model for calculating the load margin, a large number of wind power output samples x = [x1, ..., x i ,...,x N ], and through Calculate the load margin sample y=[y1,...,y i ,...,y N ].

9. The method for rapid evaluation of static voltage stability considering wind power prediction error according to claim 1, characterized in that: Step S4 also includes step S45, calculating statistical characteristics based on the obtained load margin samples and constructing a probability distribution, so as to evaluate the impact of wind power output uncertainty on the system voltage stability margin.

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