A method for constructing a multi-attribute evaluation system to determine the installation location of a static VAR compensator

Abstract

The method of constructing a multi-attribute evaluation system to establish the installation position of a static VAR compensator includes: S1, real-time measurement of transient voltage stability index data based on different principles; S2, using power flow calculation to obtain the corresponding voltage stability margin in real time; S3, establishing a regression relationship between multiple transient voltage stability indicators and voltage stability margin, and verifying the fitting effect; S4, using the knowledge of mathematical statistics to mine the characteristics of voltage stability margin data, and calculate the bus outage risk rate, and construct a multi-attribute evaluation index system; S5, combining entropy weight method, hierarchical analysis method and coefficient of variation method to calculate the combined weight of each index; S6, using the cosine method to find the best and worst solutions among the limited solutions, calculate the distance between the bus voltage stability and the best and worst solutions, and obtain the relative proximity of each bus voltage stability to the best solution. The present invention achieves the purpose of comprehensively evaluating the bus voltage stability and provides guidance value for establishing the installation position of the static VAR compensator.

Description

Technical Field

[0001] The present invention relates to the technical field of transient voltage calculation of power systems, and in particular to a method for constructing a multi-attribute evaluation system to determine the installation position of a static VAR compensator. Background Art

[0002] The current power system is expanding in scale and becoming increasingly complex, gradually forming a new power system dominated by new energy. In order to optimize resource utilization, meet diverse electricity demand, and adapt to the growing renewable energy generation model, the power grid operates with a smaller stability margin. This leaves hidden dangers for voltage instability or even collapse, which is an important cause of power outages in recent years. Therefore, finding the key factors affecting transient voltage stability and establishing the weak links of system transient voltage stability is conducive to the reasonable installation of static VAR compensators, thereby improving the safety margin of power grid operation.

[0003] The methods currently used to determine the installation location of the static VAR compensator include modal analysis, PQ and QV curve analysis, time domain simulation method and continuous power flow calculation. Although the power flow calculation using local parameterized extension technology to reformulate the power flow equation can be used to track the PV curve beyond the voltage collapse point, it involves iterative calculations. When faced with an expanded system scale, complex operating mode and an increase in the number of expected accidents, the solution efficiency is low, and it is difficult to calculate the voltage stability margin in real time, and it is difficult to quantify the weak links of the system transient voltage stability.

[0004] Moreover, the above method can only solve the voltage stability margin at a certain moment. Considering the cost of installing a static VAR compensator, if the voltage stability margin status over a period of time cannot be comprehensively evaluated to identify the weak links in the system's transient voltage stability, the installation location of the static VAR compensator will be unreasonable, and the effect of improving the safety margin of power grid operation will not be significant. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for constructing a multi-attribute evaluation system to determine the installation location of a static VAR compensator, thereby achieving the purpose of comprehensively evaluating bus voltage stability and providing effective guidance value for determining the installation location of a static VAR compensator.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] The method for constructing a multi-attribute evaluation system to determine the installation location of a static VAR compensator includes the following steps:

[0008] Step 1: Real-time measurement of busbar transient voltage stability index data based on different principles and inputting it into the database;

[0009] Step 2: Use local parameterized extension technology to reformulate the power flow equation and obtain the corresponding bus voltage stability margin in real time;

[0010] Step 3: Use the principal component analysis method to reduce the dimension of transient voltage stability indicators based on different principles, then establish the regression relationship between the transient voltage stability indicators with contribution rate reaching the threshold and the voltage stability margin, and verify the fitting effect;

[0011] Step 4: Select the statistical characteristics of seven voltage stability margin data to analyze voltage safety and stability, and calculate the busbar outage risk rate, so as to construct the evaluation index of the multi-attribute evaluation system;

[0012] Step 5, calculate the combined weight of each indicator by combining the analytic hierarchy process, entropy weight method and coefficient of variation method;

[0013] Step 6. Based on the normalized data matrix, the cosine method is used to find the optimal and worst solutions in the evaluation system, and the difference between the bus voltage stability and the optimal and worst solutions is calculated to obtain the relative difference between the voltage stability of each bus and the optimal solution, that is, the stability evaluation score. The bus with the lowest stability evaluation score is selected as the best location for installing the static VAR compensator.

[0014] The transient voltage stability indicators considered by different principles in the above Step 1 include:

[0015] Considering that the bus transient voltage has a real solution, the transient voltage stability load index VSLI i Expressed as:

[0016]

[0017] Where V i is the voltage on the ith bus, E Th Thevenin equivalent supply voltage, δ i Yes V i With E Th The phase angle difference

[0018] Considering the maximum power transfer state of the circuit, the transient voltage collapse is close to the exponential VCPI i Expressed as:

[0019] VCPI i =V i cosδ i -0.5E Th ;

[0020] Considering the maximum power transfer that meets two different local measurements on the bus, the bus transient voltage stability index BVSI iExpressed as:

[0021]

[0022] In the formula, and is the transient voltage and current vector difference between n and n+1 different measurements, and α is an indicator of the linearization characteristic;

[0023] Considering the maximum power transfer between the busbar and the generator at the shortest electrical distance, the simplified transient voltage stability index SVSI i Expressed as:

[0024]

[0025] Where V s is the voltage source, V m and V i are the maximum and minimum values ​​of the system transient voltage;

[0026] Considering that at the transient voltage collapse point, the load impedance is equal to the impedance of the Thevenin equivalent circuit; the impedance matching stability index ISI i can be reformulated as a calculation using local measurements on the bus:

[0027]

[0028] The wide area loss index WALI takes into account the maximum power transfer achieved by continuous power measurement in the area of ​​interest. i Expressed as:

[0029]

[0030] In the formula, is the change in generation and power input in the region of interest on the ith bus, is the change in loss in the region of interest on the ith busbar;

[0031] Considering the maximum power transfer of the circuit, the transient voltage stability margin VSM i Expressed as:

[0032]

[0033] In the formula, φ i is the bus power factor angle, θ Thi is the impedance angle of the Thevenin equivalent circuit;

[0034] Taking into account the available reactive reserve of the total reactive capacity of the grid-connected generators, the reactive reserve index ERPR i Expressed as:

[0035]

[0036] In the formula, Q op is the injected reactive power, Q lim is the total reactive capacity, N G is the number of buses in the power system.

[0037] The power flow calculation in Step 2 above can generate data on voltage and current vectors as well as voltage stability margin before the voltage collapse point. When the reactive power of the generator reaches its limit, it is regarded as a load, and the reactive power injection of the generator is set to its limit value. When the transformer is equipped with an on-load tap changer, the secondary voltage is adjusted between two set points until the maximum tap position is reached.

[0038] In the power flow calculation, the loads of all load buses are increased uniformly, or a load change pattern is introduced randomly. When the power flow calculation is performed, the trajectory is resampled to obtain the data of the transient voltage stability index and the corresponding voltage stability margin at each sampling point and save them in the database.

[0039] In the above Step 3, the principal component analysis method is used to reduce the dimension of transient voltage stability indicators based on different principles, including: 1: Calculation of sample correlation coefficient matrix

[0040] Assuming that there are i measurement time points and n transient voltage stability indicators in a certain time period, a sample matrix X of size i×n can be constructed:

[0041]

[0042] The formula for converting the sample matrix into the correlation coefficient matrix is ​​as follows:

[0043]

[0044] Where R = (r jk ) n×n ,r jj =1,r jk =r kj ,r jk represents the correlation coefficient between the jth indicator and the kth indicator;

[0045] 2: Determination of principal component variables

[0046] (1) Calculation of eigenvalues ​​and eigenvectors:

[0047] (R-λ j E)·u j =0;

[0048] Among them, λ j is the eigenvalue and λ1≥λ2≥L≥λj ≥0, normalized feature vector u1,u2,L,u n and u j =[u 1j ,u 2j ,L,u nj ] T ;

[0049] (2) Principal component variables:

[0050]

[0051] Among them, y n is the nth principal component;

[0052] 3: Calculation of principal component contribution rate and cumulative contribution rate

[0053] (1) Eigenvalue λ j (j=1,2,L,n) Information contribution rate:

[0054]

[0055] The formula is the main component y j Information contribution rate;

[0056] (2) Eigenvalue λ j (j=1,2,L,n) Cumulative contribution rate:

[0057]

[0058] The formula is mainly composed of y1,y2,L,y p The cumulative contribution rate of When the threshold value exceeds 0.99, the first p indicator variables y1, y2, L, y p As p principal components, they replace the original n indicator variables, thereby obtaining the influence of each of the p principal components on the voltage stability margin data.

[0059] The regression relationship between the transient voltage stability index with a contribution rate reaching a threshold value and the voltage stability margin in the above Step 3 includes the following steps:

[0060] Step 3.1, use VSLI to represent i VCPI i 、BVSI i 、ISI i 、VSM i SVSI i , L i WALI i and ERPR iThe transient voltage stability index whose contribution rate reaches the threshold, y represents the load margin, i=1,2,L,p represents the data number, y,x1,x2,L,x p The corresponding values ​​are

[0061] Step 3.2, data standardization, eliminating the influence of different dimensions, the calculation formula is:

[0062]

[0063] Step 3.3, data normalization, in order to make the preprocessed data limited to [0,1], so as to reduce the adverse effects caused by singular sample data, the calculation formula is:

[0064]

[0065] Step 3.4, establish a multivariate regression model:

[0066]

[0067] In the formula, β0, β1, L, β9 are called regression coefficients;

[0068] Step 3.5, use the least squares method to find the estimated values ​​of β0, β1, L, β9, that is, the estimated values ​​should be taken So that when j=1,2,···,p, the error sum of squares is:

[0069]

[0070] To minimize Q, let

[0071]

[0072] Solving for β0, β1, L, β9 is as follows:

[0073] [β0,β1,L,β9]=(x T x) -1 (x T Y);

[0074] Will Substituting into the original model we get the estimated value of y:

[0075]

[0076] In the above Step 3, the fitting effect of the multivariate linear regression model on the data is tested, and the goodness of fit R of the model is calculated. 2 The root mean square error (RMSE) includes the following steps:

[0077] Total sum of squares Decomposed, we have:

[0078]

[0079] In the formula, SSE stands for the error sum of squares, reflecting the impact of random errors on y, and SSR stands for the regression sum of squares, reflecting the impact of independent variables on y;

[0080] The goodness of fit is determined by two parameters: the regression sum of squares SSR and the total sum of squares SST. The calculated goodness of fit R 2 The larger it is, the better the fitting effect is; the calculation formula is as follows:

[0081]

[0082] The root mean square error is also called the fitting standard deviation of the regression system. The smaller the calculated root mean square error RMSE is, the better the fitting effect is. The calculation formula is as follows:

[0083]

[0084] Only when the goodness of fit and the root mean square error are within the specified range can the subsequent steps be carried out.

[0085] In the above Step 4, the specific features of voltage stability margin data mined using the knowledge of mathematical statistics are: mode, mean, median, variance, range, skewness and kurtosis;

[0086] Among them, skewness is a measure of the degree to which the probability distribution of voltage stability margin data deviates from the normal distribution, and kurtosis is used to indicate the degree of deviation of statistical data. The calculation formulas of skewness s and kurtosis k are as follows:

[0087]

[0088]

[0089] In the formula, represents the mean, m represents the median, and σ represents the standard deviation.

[0090] The formula for calculating the busbar outage risk rate in Step 4 above is:

[0091]

[0092] In the formula, the failure rate of busbar emergency is This data can be obtained from the power supply department.

[0093] The entropy weight method in Step 5 above to determine the indicator weight includes the following steps:

[0094] Step 5.1, data positive; after analysis, the mode, mean, and median reflect voltage safety, which are extremely large indicators, while the variance, range, skewness, and kurtosis reflect voltage stability, which are extremely small indicators, so they are uniformly converted into extremely large indicators, and the calculation formula is:

[0095]

[0096] Standardize and normalize the data;

[0097] Step 5.2, Calculation of information entropy; Information entropy reflects the disorder and randomness of information. The more likely something is to happen, the smaller the change in data and the less information. The information entropy of each evaluation index is e j The calculation formula is:

[0098]

[0099] Among them, p(x ij ) represents the probability that the value of the jth evaluation index is the i-th data value;

[0100] Step 5.3, Calculation of information utility value; Information utility value reflects the contribution of information to decision-making. The larger the value of information utility value, the more corresponding information it has. Information utility value of each evaluation index d j The calculation formula is:

[0101] d j =1-e j ;

[0102] Step 5.4, Determination of entropy weight: Normalize the information utility value to obtain the entropy weight w of each evaluation index. j for:

[0103]

[0104] The step 5 of determining the index weight by the hierarchical analysis method includes the following steps:

[0105] Construct a judgment matrix A for each indicator = (a ij ) n×n , where a ij is x i Relative to x j The importance of n is the number of evaluation indicators; the weight of each indicator is calculated and the consistency check is performed. The weight of each indicator calculated by this method is recorded as w j2 ;

[0106] The coefficient of variation method in Step 5 for determining the indicator weights includes the following steps:

[0107] Normalize the original matrix, and find the mean and standard deviation of each indicator data to calculate the coefficient of variation as follows:

[0108]

[0109] Normalize the coefficient of variation and get the weight of each indicator as follows: j3 :

[0110]

[0111] Finally, three different weights are calculated for each indicator through the above three methods: entropy weight method, hierarchical analysis method and coefficient of variation method; the average of the three weights is selected as the final weight of each indicator:

[0112]

[0113] The calculation of the relative difference between the bus voltage stability and the optimal solution in the evaluation system in the above Step 6 includes the following steps:

[0114] Step 6.1, determine the distance between positive and negative ideal solutions. Assuming there are m evaluation indicators and n buses as evaluation objects, construct the decision matrix X = (x ij ) n×m as follows:

[0115]

[0116] Define the maximum value:

[0117]

[0118] Define the minimum value:

[0119]

[0120] Define the distance D between the evaluation object and the maximum and minimum values i + , D i - for:

[0121]

[0122]

[0123] Step 6.2, calculate the value score, that is, calculate the relative difference between the voltage stability of each busbar and the optimal solution. Select the busbar with the lowest stability value score as the best location to install the static VAR compensator; the calculation formula is:

[0124]

[0125] The present invention provides a method for constructing a multi-attribute evaluation system to determine the installation location of a static VAR compensator. Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0126] Since each transient voltage stability index shows different accuracy levels under different conditions and load models, the present invention selects a variety of transient voltage stability indicators based on different principles, which can improve the accuracy of calculating real-time voltage stability margin data and is adaptable to power grid system disturbances and changes in operating modes.

[0127] The present invention uses principal component analysis to reduce the dimension of transient voltage stability indicators based on different principles. Compared with the empirical regression equation proposed by direct linear regression of data, the former has a smaller mean square error and stronger stability, while all coefficients of the latter are difficult to pass the significance test.

[0128] The present invention establishes a multivariate linear regression equation to explore the correlation between various transient voltage stability indicators and voltage stability margins, and uses the gradient descent method to find the optimal fitting parameters. When real-time transient voltage stability indicator data is input, the model can quickly calculate the real-time voltage stability margin to meet the timeliness requirements of voltage stability assessment.

[0129] The present invention deeply mines the characteristics of voltage stability margin data and then analyzes the safety and stability of voltage, and considers the risk of bus outage to construct a multi-attribute evaluation index; it can effectively identify the impact of accidental factors and systematic factors on voltage instability, achieve the purpose of comprehensively evaluating bus voltage stability, make the selection of static VAR compensator installation location more reasonable, and help improve the safety of power grid operation.

[0130] The present invention adopts a combined weighting method to calculate the weight of each evaluation index. The proposed combined weighting method combines the hierarchical analysis method in the subjective weighting method with the entropy weight method and the coefficient of variation method in the objective weighting method. Since the judgment of the hierarchical analysis method is relatively subjective, it is easily changed by the subjective influence of the decision maker. And since the data has the characteristics of high sensitivity, errors may occur due to the reasons of the data itself. The combined weighting method combines these methods to reduce evaluation errors and improve accuracy.

[0131] The present invention uses the entropy weight method to weight the multi-attribute evaluation indicators, determines the objective weights according to the variability of the indicator data, reduces the influence of subjective factors on the evaluation results, and makes the evaluation results objective. BRIEF DESCRIPTION OF THE DRAWINGS

[0132] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0133] Figure 1A flow chart of a method for constructing a multi-attribute evaluation system to determine the installation location of a static VAR compensator shown in an embodiment of the present invention;

[0134] Figure 2 The Thevenin equivalent circuit diagram on the power system bus shown in an embodiment of the present invention;

[0135] Figure 3 This is an indicator composition diagram of a multi-attribute evaluation system shown in an embodiment of the present invention;

[0136] Figure 4 1 is a numerical table of transient voltage stability margin in the embodiment. DETAILED DESCRIPTION

[0137] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and embodiments.

[0138] like Figure 1 As shown, the method of constructing a multi-attribute evaluation system to determine the installation location of a static VAR compensator includes the following steps:

[0139] Step 1: Real-time measurement of busbar transient voltage stability index data based on different principles and inputting it into the database;

[0140] Step 2: Use local parameterized extension technology to reformulate the power flow equation and obtain the corresponding bus voltage stability margin in real time;

[0141] Step 3: Use the principal component analysis method to reduce the dimension of transient voltage stability indicators based on different principles, then establish the regression relationship between the transient voltage stability indicators with contribution rate reaching the threshold and the voltage stability margin, and verify the fitting effect;

[0142] Step 4: Select the statistical characteristics of seven voltage stability margin data to analyze voltage safety and stability, and calculate the busbar outage risk rate, so as to construct the evaluation index of the multi-attribute evaluation system;

[0143] Step 5, calculate the combined weight of each indicator by combining the analytic hierarchy process, entropy weight method and coefficient of variation method;

[0144] Step 6. Based on the normalized data matrix, the cosine method is used to find the optimal and worst solutions in the evaluation system, and the difference between the bus voltage stability and the optimal and worst solutions is calculated to obtain the relative difference between the voltage stability of each bus and the optimal solution, that is, the stability evaluation score. The bus with the lowest stability evaluation score is selected as the best location for installing the static VAR compensator.

[0145] The transient voltage stability indicators considered by different principles in the above Step 1 include:

[0146] Considering that the bus transient voltage has a real solution, the transient voltage stability load index VSLI i Expressed as:

[0147]

[0148] Where V i is the voltage on the ith bus, E Th Thevenin equivalent supply voltage, δ i Yes V i With E Th The phase angle difference

[0149] Considering the maximum power transfer state of the circuit, the transient voltage collapse is close to the exponential VCPI i Expressed as:

[0150] VCPI i =V i cosδ i -0.5E Th ;

[0151] Considering the maximum power transfer that meets two different local measurements on the bus, the bus transient voltage stability index BVSI i Expressed as:

[0152]

[0153] In the formula, and is the transient voltage and current vector difference between n and n+1 different measurements, and α is an indicator of the linearization characteristic;

[0154] Considering the maximum power transfer between the busbar and the generator at the shortest electrical distance, the simplified transient voltage stability index SVSI i Expressed as:

[0155]

[0156] Where V s is the voltage source, V m and V i are the maximum and minimum values ​​of the system transient voltage;

[0157] Considering that at the transient voltage collapse point, the load impedance is equal to the impedance of the Thevenin equivalent circuit; the impedance matching stability index ISI i can be reformulated as a calculation using local measurements on the bus:

[0158]

[0159] The wide area loss index WALI takes into account the maximum power transfer achieved by continuous power measurement in the area of ​​interest. i Expressed as:

[0160]

[0161] In the formula, is the change in generation and power input in the region of interest on the ith bus, is the change in loss in the region of interest on the ith busbar;

[0162] Considering the maximum power transfer of the circuit, the transient voltage stability margin VSM i Expressed as:

[0163]

[0164] In the formula, φ i is the bus power factor angle, θ Thi is the impedance angle of the Thevenin equivalent circuit;

[0165] Taking into account the available reactive reserve of the total reactive capacity of the grid-connected generators, the reactive reserve index ERPR i Expressed as:

[0166]

[0167] In the formula, Q op is the injected reactive power, Q lim is the total reactive capacity, N G is the number of buses in the power system.

[0168] The power flow calculation in Step 2 above can generate data on voltage and current vectors as well as voltage stability margin before the voltage collapse point. When the reactive power of the generator reaches its limit, it is regarded as a load, and the reactive power injection of the generator is set to its limit value. When the transformer is equipped with an on-load tap changer, the secondary voltage is adjusted between two set points until the maximum tap position is reached.

[0169] In the power flow calculation, the loads of all load buses are increased uniformly, or a load change pattern is introduced randomly. When the power flow calculation is performed, the trajectory is resampled to obtain the data of the transient voltage stability index and the corresponding voltage stability margin at each sampling point and save them in the database.

[0170] In the above Step 3, the principal component analysis method is used to reduce the dimension of transient voltage stability indicators based on different principles, including:

[0171] 1: Calculation of sample correlation coefficient matrix

[0172] Assuming that there are i measurement time points and n transient voltage stability indicators in a certain time period, a sample matrix X of size i×n can be constructed:

[0173]

[0174] The formula for converting the sample matrix into the correlation coefficient matrix is ​​as follows:

[0175]

[0176] Where R = (r jk ) n×n ,r jj =1,r jk =r kj ,r jk represents the correlation coefficient between the jth indicator and the kth indicator;

[0177] 2: Determination of principal component variables

[0178] (1) Calculation of eigenvalues ​​and eigenvectors:

[0179] (R-λ j E)·u j =0;

[0180] Among them, λ j is the eigenvalue and λ1≥λ2≥L≥λ j ≥0, normalized feature vector u1,u2,L,u n and u j =[u 1j ,u 2j ,L,u nj ] T ;

[0181] (2) Principal component variables:

[0182]

[0183] Among them, y n is the nth principal component;

[0184] 3: Calculation of principal component contribution rate and cumulative contribution rate

[0185] (1) Eigenvalue λ j (j=1,2,L,n) Information contribution rate:

[0186]

[0187] The formula is the main component y j Information contribution rate;

[0188] (2) Eigenvalue λ j(j=1,2,L,n) Cumulative contribution rate:

[0189]

[0190] The formula is mainly composed of y1,y2,L,y p The cumulative contribution rate of When the threshold value exceeds 0.99, the first p indicator variables y1, y2, L, y p As p principal components, they replace the original n indicator variables, thereby obtaining the influence of each of the p principal components on the voltage stability margin data.

[0191] The regression relationship between the transient voltage stability index with a contribution rate reaching a threshold value and the voltage stability margin in the above Step 3 includes the following steps:

[0192] Step 3.1, use VSLI to represent i VCPI i 、BVSI i 、ISI i 、VSM i SVSI i , L i WALI i and ERPR i The transient voltage stability index whose contribution rate reaches the threshold, y represents the load margin, i=1,2,L,p represents the data number, y,x1,x2,L,x p The corresponding values ​​are Step 3.2, data standardization, eliminating the influence of different dimensions, the calculation formula is:

[0193]

[0194] Step 3.3, data normalization, in order to make the preprocessed data limited to [0,1], so as to reduce the adverse effects caused by singular sample data, the calculation formula is:

[0195]

[0196] Step 3.4, establish a multivariate regression model:

[0197]

[0198] In the formula, β0, β1, L, β9 are called regression coefficients;

[0199] Step 3.5, use the least squares method to find the estimated values ​​of β0, β1, L, β9, that is, the estimated values ​​should be taken So that when j=1,2,···,p, the error sum of squares is:

[0200]

[0201] To minimize Q, let

[0202]

[0203] Solving for β0, β1, L, β9 is as follows:

[0204] [β0,β1,L,β9]=(x T x) -1 (x T Y);

[0205] Will Substituting into the original model we get the estimated value of y:

[0206]

[0207] In the above Step 3, the fitting effect of the multivariate linear regression model on the data is tested, and the goodness of fit R of the model is calculated. 2 The root mean square error (RMSE) includes the following steps:

[0208] Total sum of squares Decomposed, we have:

[0209]

[0210] In the formula, SSE stands for the error sum of squares, reflecting the impact of random errors on y, and SSR stands for the regression sum of squares, reflecting the impact of independent variables on y;

[0211] The goodness of fit is determined by two parameters: the regression sum of squares SSR and the total sum of squares SST. The calculated goodness of fit R 2 The larger it is, the better the fitting effect is; the calculation formula is as follows:

[0212]

[0213] The root mean square error is also called the fitting standard deviation of the regression system. The smaller the calculated root mean square error RMSE is, the better the fitting effect is. The calculation formula is as follows:

[0214]

[0215] Only when the goodness of fit and the root mean square error are within the specified range can the subsequent steps be carried out.

[0216] In the above Step 4, the specific features of voltage stability margin data mined using the knowledge of mathematical statistics are: mode, mean, median, variance, range, skewness and kurtosis;

[0217] Among them, skewness is a measure of the degree to which the probability distribution of voltage stability margin data deviates from the normal distribution, and kurtosis is used to indicate the degree of deviation of statistical data. The calculation formulas of skewness s and kurtosis k are as follows:

[0218]

[0219]

[0220] In the formula, represents the mean, m represents the median, and σ represents the standard deviation.

[0221] The formula for calculating the busbar outage risk rate in Step 4 above is:

[0222]

[0223] In the formula, the failure rate of busbar emergency is This data can be obtained from the power supply department.

[0224] The entropy weight method in Step 5 above to determine the indicator weight includes the following steps:

[0225] Step 5.1, data positive; after analysis, the mode, mean, and median reflect voltage safety, which are extremely large indicators, while the variance, range, skewness, and kurtosis reflect voltage stability, which are extremely small indicators, so they are uniformly converted into extremely large indicators, and the calculation formula is:

[0226]

[0227] Standardize and normalize the data;

[0228] Step 5.2, Calculation of information entropy; Information entropy reflects the disorder and randomness of information. The more likely something is to happen, the smaller the change in data and the less information. The information entropy of each evaluation index is e j The calculation formula is:

[0229]

[0230] Among them, p(x ij ) represents the probability that the value of the jth evaluation index is the i-th data value;

[0231] Step 5.3, Calculation of information utility value; Information utility value reflects the contribution of information to decision-making. The larger the value of information utility value, the more corresponding information it has. Information utility value of each evaluation index dj The calculation formula is:

[0232] d j =1-e j ;

[0233] Step 5.4, Determination of entropy weight: Normalize the information utility value to obtain the entropy weight w of each evaluation index. j for:

[0234]

[0235] The step 5 of determining the index weight by the hierarchical analysis method includes the following steps:

[0236] Construct a judgment matrix A for each indicator = (a ij ) n×n , where a ij is x i Relative to x j The importance of n is the number of evaluation indicators; the weight of each indicator is calculated and the consistency check is performed. The weight of each indicator calculated by this method is recorded as w j2 ;

[0237] The coefficient of variation method in Step 5 for determining the indicator weights includes the following steps:

[0238] Normalize the original matrix, and find the mean and standard deviation of each indicator data to calculate the coefficient of variation as follows:

[0239]

[0240] Normalize the coefficient of variation and get the weight of each indicator as follows: j3 :

[0241]

[0242] Finally, three different weights are calculated for each indicator through the above three methods: entropy weight method, hierarchical analysis method and coefficient of variation method; in order to make the model more accurate, the average of the three weights is selected as the final weight of each indicator to minimize the error:

[0243]

[0244] The calculation of the relative difference between the bus voltage stability and the optimal solution in the evaluation system in the above Step 6 includes the following steps:

[0245] Step 6.1, determine the distance between positive and negative ideal solutions. Assuming there are m evaluation indicators and n buses as evaluation objects, construct the decision matrix X = (x ij ) n×mas follows:

[0246]

[0247] Define the maximum value:

[0248]

[0249] Define the minimum value:

[0250]

[0251] Define the distance D between the evaluation object and the maximum and minimum values i + , D i - for:

[0252]

[0253]

[0254] Step 6.2, calculate the value score, that is, calculate the relative difference between the voltage stability of each busbar and the optimal solution. Select the busbar with the lowest stability value score as the best location to install the static VAR compensator; the calculation formula is:

[0255]

[0256] Example:

[0257] So far, the task of real-time calculation of bus transient voltage stability margin has been successfully completed.

[0258] The following is an example. Taking the simulation of IEEE 14-node system and IEEE 118-node system as examples, 365×24×2=17520 samples are generated for each, which are divided into training set and test set at a ratio of 4:1; the multiple linear regression method based on principal component analysis proposed in the present invention is compared with the multiple linear regression method directly adopted, and the goodness of fit and mean root error of each regression method are compared, and then the accuracy of each regression method is judged.

[0259] Table 1: Goodness of fit and root mean square error data of each regression method in IEEE 14-bus system

[0260]

[0261]

[0262] Table 2: Goodness of fit and root mean square error data of each regression method in IEEE 118-node system

[0263]

[0264] It can be seen from the above table that, whether in the simulation of the IEEE 14-bus system or the IEEE 118-bus system, the multivariate linear regression method based on principal component analysis proposed in the present invention has a greater goodness of fit and a smaller root mean square error than the direct use of the multivariate linear regression method. Therefore, the regression method proposed in the present invention has a higher accuracy in calculating the bus transient voltage stability margin; it provides more accurate data for the subsequent construction of a multi-attribute evaluation system, making the evaluation score more convincing.

[0265] like Figure 3 As shown, as a possible implementation of this embodiment, in step S4, the specific features of the voltage stability margin data mined using the knowledge of mathematical statistics include: mode, mean, median, variance, range, skewness and kurtosis.

[0266] Among them, skewness is a measure of the degree to which the probability distribution of voltage stability margin data deviates from the normal distribution, and kurtosis is used to indicate the degree of deviation of statistical data. The calculation formulas of skewness s and kurtosis k are as follows:

[0267]

[0268]

[0269] In the formula, represents the mean, m represents the median, and σ represents the standard deviation;

[0270] As a possible implementation of this example, in step S4, the formula for calculating the bus outage risk rate is:

[0271]

[0272] In the formula, the failure rate of busbar emergency is This data can be obtained from the power supply department.

[0273] As a possible implementation of this example, in step S5, the step of determining the indicator weight using the entropy weight method includes:

[0274] The data is positively transformed; after analysis, the mode, mean, and median are extremely large indicators, while the variance, range, skewness, and kurtosis are extremely small indicators, so they are uniformly converted into extremely large indicators. The calculation formula is:

[0275]

[0276] Standardize and normalize the data;

[0277] Calculation of information entropy; Information entropy reflects the disorder and randomness of information. The more likely something is to happen, the smaller the change in data and the less information it contains. The information entropy of each evaluation index is j The calculation formula is:

[0278]

[0279] Among them, p(x ij ) represents the probability that the value of the jth evaluation index is the i-th data value;

[0280] Calculation of information utility value; information utility value reflects the contribution of information to decision-making. The larger the value of information utility value, the more corresponding information it has; the information utility value of each evaluation index d j The calculation formula is:

[0281] d j =1-e j ;

[0282] Determination of entropy weight; Normalizing the information utility value, we can get the entropy weight w of each evaluation index j for:

[0283]

[0284] As a possible implementation of this example, in step S6, the step of judging the bus voltage stability based on the positive and negative superiority solutions includes:

[0285] To determine the distance between positive and negative ideal solutions, assuming that there are m evaluation indicators and n buses as evaluation objects, a decision matrix X = (x ij ) n×m as follows:

[0286]

[0287] Define the maximum value:

[0288]

[0289] Define the minimum value:

[0290]

[0291] Define the distance D between the evaluation object and the maximum and minimum values i + , D i - for:

[0292]

[0293]

[0294] The value score is calculated to obtain the voltage stability evaluation score of each bus. If the score is high, it means that the bus voltage stability is strong; if the score is low, it means that the bus voltage stability is weak. The bus with the lowest score is regarded as the best location for installing the static VAR compensator in the power system. The calculation formula is:

[0295]

[0296] So far, a multi-attribute evaluation system has been successfully established, and the calculation of the voltage stability score of each bus has been completed.

[0297] The following example verifies the rationality and stability of the evaluation system in this invention; taking the IEEE 39-node system simulation as an example, a three-phase ground short circuit fault is set, the fault point is located at 5% of the bus common end line, and the continuous short circuit duration is t=0.1s; the fault occurs at t=2s, and the simulation duration is t=10s.

[0298] Table 3 shows the instability moments and stability evaluation scores of 10 key buses in the IEEE 39-bus system, where the order is from large to small. The instability moment is the moment when the bus voltage stability margin is less than zero. The later this moment is, the stronger the voltage stability is.

[0299]

[0300]

[0301] It can be seen from Table 3 that the bus with the shortest instability moment is the same as the bus with the lowest comprehensive evaluation score, and the instability moment is highly consistent with the comprehensive score ranking, which shows that the evaluation results obtained by the evaluation system constructed by the present invention are consistent with the actual situation, thereby proving the rationality of this model.

[0302] To further prove the stability of the evaluation system in this invention, a sensitivity analysis is conducted; the bus transient voltage stability margin values ​​calculated by multivariate linear regression based on principal component analysis are preset upward and downward by 2% and 5%; the three buses with the lowest evaluation scores are selected, their evaluation scores are calculated, and the fluctuation of the ranking is observed; the results are as follows Figure 4 shown.

[0303] Depend on Figure 4 As we know, the ranking of the evaluation scores of these three buses does not change with the transient voltage stability margin, which means that this model can accept errors within a certain range and proves its stability; therefore, the method of establishing the bus with the lowest stability evaluation score as the installation location of the static VAR compensator is feasible.

Claims

1. Construct a multi-attribute evaluation system to determine the installation location of the static VAR compensator. It is characterized in that The following steps are involved: Step 1: Real-time measurement of busbar transient voltage stability index data based on different principles and inputting it into the database; Step 2: Use local parameterized extension technology to reformulate the power flow equation to calculate the power flow and obtain the corresponding bus voltage stability margin in real time; Step 3: Use the principal component analysis method to reduce the dimension of transient voltage stability indicators based on different principles, then establish the regression relationship between the transient voltage stability indicators with contribution rate reaching the threshold and the voltage stability margin, and verify the fitting effect; Step 4: Select the statistical characteristics of seven voltage stability margin data to analyze voltage safety and stability, and calculate the busbar outage risk rate, so as to construct the evaluation index of the multi-attribute evaluation system; Step 5, calculate the combined weight of each indicator by combining the analytic hierarchy process, entropy weight method and coefficient of variation method; Step 6. Based on the normalized data matrix, the cosine method is used to find the optimal and worst solutions in the evaluation system, and the difference between the bus voltage stability and the optimal and worst solutions is calculated to obtain the relative difference between the voltage stability of each bus and the optimal solution, that is, the stability evaluation score; the bus with the lowest stability evaluation score is selected as the best location for installing the static VAR compensator; The transient voltage stability indicators considered by different principles in Step 1 include: Considering that the bus transient voltage has a real solution, the transient voltage stability load index Expressed as: ； In the formula, It is i The voltage on the bus, Thevenin equivalent supply voltage, yes and The phase angle difference Considering the maximum power transfer state of the circuit, the transient voltage collapse is close to exponential Expressed as: ； Considering the maximum power transfer that satisfies two different local measurements on the bus, the bus transient voltage stability index Expressed as: ； In the formula, and yes and The transient voltage and current vector differences between different measurements, is an indicator of linearization characteristics; Considering the maximum power transfer between the busbar and the generator at the shortest electrical distance, the simplified transient voltage stability index Expressed as: ； In the formula, is a voltage source, and are the maximum and minimum values ​​of the system transient voltage; Considering that at the transient voltage collapse point, the load impedance is equal to the impedance of the Thevenin equivalent circuit; the impedance matching stability index can be reformulated as a calculation using local measurements on the bus: ； Considering the maximum power transfer achieved by continuous power measurement in the area of ​​interest, the wide area loss index Expressed as: ； In the formula, It is in i Changes in generation and power input in the area of ​​interest on the bus, It is in i Changes in losses within the region of interest on a bus; Considering the maximum power transfer of the circuit, the transient voltage stability margin Expressed as: ； In the formula, is the bus power factor angle, is the impedance angle of the Thevenin equivalent circuit; Considering the available reactive reserve of the total reactive capacity of the grid-connected generators, the reactive reserve index Expressed as: ； In the formula, is the injected reactive power, is the total reactive capacity, is the number of buses in the power system.

2. The method for establishing the installation location of a static VAR compensator by constructing a multi-attribute evaluation system according to claim 1, It is characterized in that The power flow calculation in Step 2 can generate data of voltage and current vectors and voltage stability margin before the voltage collapse point. When the reactive power of the generator reaches its limit, it is regarded as a load, and the reactive power injection of the generator is set to its limit value. When the transformer is equipped with an on-load tap changer, the secondary voltage is adjusted between two set points until the maximum tap position is reached; In the power flow calculation, the loads of all load buses are increased uniformly, or a load change pattern is introduced randomly. When the power flow calculation is performed, the trajectory is resampled to obtain the data of the transient voltage stability index and the corresponding voltage stability margin at each sampling point and save them in the database.

3. The method for establishing the installation location of a static VAR compensator by constructing a multi-attribute evaluation system according to claim 2, It is characterized in that In the Step 3, the principal component analysis method is used to reduce the dimension of transient voltage stability indicators based on different principles, including: 1: Calculation of sample correlation coefficient matrix Assume that in a certain period of time i The measurement time points, n transient voltage stability index, then the size can be The sample matrix X : ； The formula for converting the sample matrix into the correlation coefficient matrix is ​​as follows: ； in, , Indicates j The indicator and k The correlation coefficient of the indicators; 2: Determination of principal component variables (1) Calculation of eigenvalues ​​and eigenvectors: ； in, is the eigenvalue and , the standardized feature vector and ; (2) Principal component variables: ； in, For the n principal components; 3: Calculation of principal component contribution rate and cumulative contribution rate (1) Eigenvalue Information contribution rate: ； The formula is the main component Information contribution rate; (2) Eigenvalue Cumulative contribution rate: ； The formula is the main component The cumulative contribution rate of When the threshold exceeds 0.99, the previous p indicator variables As p principal components, replacing the original n indicator variables, thus obtaining p The influence of each principal component on the voltage stability margin data.

4. The method for establishing a multi-attribute evaluation system to determine the installation location of a static VAR compensator according to claim 3, It is characterized in that The regression relationship between the transient voltage stability index with a contribution rate reaching a threshold value and the voltage stability margin in Step 3 includes the following steps: Step 3.1, respectively express , , , , , , , and The transient voltage stability index with the contribution rate reaching the threshold value, Indicates the load margin, Indicates the data number, y, The corresponding values ​​are ; Step 3.2, data standardization, eliminating the influence of different dimensions, the calculation formula is: ； Step 3.3, data normalization, in order to make the preprocessed data limited to [0,1], so as to reduce the adverse effects caused by singular sample data, the calculation formula is: ； Step 3.4, establish a multivariate regression model: ； In the formula, is called the regression coefficient; Step 3.5, use the least squares method to find The estimated value should be taken , so that when , j =1,2,···,p, the error sum of squares is: ； To minimize Q, let ； Solved as follows: ； Will Substituting into the original model we get the estimated value of y: 。 5. The method for establishing the installation location of a static VAR compensator by constructing a multi-attribute evaluation system according to claim 4, It is characterized in that In Step 3, the fitting effect of the multivariate linear regression model on the data is tested and the goodness of fit of the model is calculated. and RMS error The following steps are involved: Total sum of squares Decomposed, we have: ； In the formula, , SSE represents the error sum of squares, reflecting the impact of random error on y, SSR represents the regression sum of squares, reflecting the impact of independent variables on y; The goodness of fit is determined by two parameters: the regression sum of squares SSR and the total sum of squares SST. The calculated goodness of fit is The larger it is, the better the fitting effect is; the calculation formula is as follows: ； The root mean square error is also called the fitted standard deviation of the regression system. The calculated root mean square error is The smaller it is, the better the fitting effect is; the calculation formula is as follows: Only when the goodness of fit and the root mean square error are within the specified range can the subsequent steps be carried out.

6. The method for establishing the installation location of a static VAR compensator by constructing a multi-attribute evaluation system according to claim 5, It is characterized in that In the Step 4, the specific features of the voltage stability margin data mined using the knowledge of mathematical statistics are: mode, mean, median, variance, range, skewness and kurtosis; Among them, skewness is a measure of the degree to which the probability distribution of voltage stability margin data deviates from the normal distribution, and kurtosis is used to indicate the degree of deviation of statistical data. The calculation formulas of skewness s and kurtosis k are as follows: ； ； In the formula, represents the mean, m represents the median, Represents standard deviation.

7. The method for establishing a multi-attribute evaluation system to determine the installation location of a static VAR compensator according to claim 6, It is characterized in that The formula for calculating the busbar outage risk rate in Step 4 is: ； In the formula, the failure rate of busbar emergency is , this data can be obtained from the power supply department.

8. The method for establishing a multi-attribute evaluation system to determine the installation location of a static VAR compensator according to claim 6, It is characterized in that The entropy weight method in Step 5 to determine the indicator weights includes the following steps: Step 5.1, data positive; after analysis, the mode, mean, and median reflect voltage safety, which are extremely large indicators, while the variance, range, skewness, and kurtosis reflect voltage stability, which are extremely small indicators, so they are uniformly converted into extremely large indicators, and the calculation formula is: ； Standardize and normalize the data; Step 5.2, Calculation of information entropy; Information entropy reflects the disorder and randomness of information. The more likely something is to happen, the smaller the change in data and the less information. The information entropy of each evaluation index is The calculation formula is: ； in, It represents the probability that the value of the jth evaluation index is the i-th data value; Step 5.3, calculation of information utility value; information utility value reflects the contribution of information to decision-making. The larger the value of information utility value, the more corresponding information; information utility value of each evaluation index The calculation formula is: ； Step 5.4, Determination of entropy weight: Normalize the information utility value to obtain the entropy weight of each evaluation index for: ； The step 5 of determining the index weight by the hierarchical analysis method includes the following steps: Construct a judgment matrix for each indicator ,in yes Relative to The importance of n is the number of evaluation indicators; the weight of each indicator is calculated and the consistency check is performed. The weight of each indicator calculated by this method is recorded as ; Determining the indicator weights by the coefficient of variation method in Step 5 includes the following steps: Normalize the original matrix, and find the mean and standard deviation of each indicator data to calculate the coefficient of variation as follows: Normalize the coefficient of variation and get the weights of each indicator as follows : Finally, three different weights are calculated for each indicator through the above three methods: entropy weight method, hierarchical analysis method and coefficient of variation method; the average of the three weights is selected as the final weight of each indicator: 。 9. The method for establishing a multi-attribute evaluation system to determine the installation location of a static VAR compensator according to claim 8, It is characterized in that The calculation of the relative difference between the bus voltage stability and the optimal solution in the evaluation system in Step 6 includes the following steps: Step 6.1, determine the distance between positive and negative ideal solutions. Assuming there are m evaluation indicators and n buses as evaluation objects, construct a decision matrix as follows: ； Define the maximum value: ； Define the minimum value: ； Define the distance between the evaluation object and the maximum and minimum values , for: ； ； Step 6.2, calculate the value score, that is, calculate the relative difference between the voltage stability of each bus and the optimal solution; select the bus with the lowest stability value score as the best location for installing the static VAR compensator; the calculation formula is: 。

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