A Probabilistic Transient Voltage Stability Assessment Method Considering Correlated Random Variables

Abstract

A probabilistic transient voltage stability assessment method considering relevant random variables is proposed, comprising the following steps: Step 1: Modeling key random variables in the system, including determining their probability distribution types; Step 2: Calculating the maximum load margin under the current system configuration using the interior-point method, and using this margin as an index for evaluating the system's transient voltage stability; Step 3: Based on considering the random variables and their interrelationships, rationally selecting the power increment direction for generators and loads; Step 4: Generating samples by combining Latin hypercube sampling and singular value decomposition quadratic permutation techniques; Step 5: Conducting multiple simulation experiments using the generated sample set, and evaluating the probabilistic transient voltage stability through iterative deterministic calculations. This invention proposes a probabilistic transient voltage stability assessment method considering relevant random variables, preserving the actual operating characteristics of the power system.

Description

Technical Field

[0001] This invention relates to the field of transient voltage stability assessment in power systems, and more specifically to a probabilistic transient voltage stability assessment method that considers relevant random variables. Background Technology

[0002] With the increasing use of new energy sources in the power system, and the growing number of random factors such as photovoltaic and wind power generation and load changes, the relationships between input random variables make the stochastic characteristics of the power system more complex. The large-scale grid connection of these sources makes grid stability and security a challenging task. Therefore, ensuring rapid and reliable transient voltage stability assessment results is crucial for guaranteeing the safe and stable operation of the power system.

[0003] Patent document CN115017735A discloses a multi-surrogate probabilistic voltage stability calculation method for high-dimensional systems. This method collects historical data of random variables in a power system, estimates the probability density function of these random variables, determines the power system's operating scenarios, and constructs surrogate models corresponding to deterministic voltage stability assessment models based on different operating scenarios within the operating cycle. The method then uses Monte Carlo simulation to sample inputs from the probability density function of the random variables into the surrogate models for probabilistic voltage stability assessment. However, this method does not consider the influence of random variables and their interrelationships, which may lead to a decrease in the accuracy of transient voltage stability assessment results, or even unreliable assessment results. Patent document CN116914852A discloses a distribution network carrying capacity estimation method based on probabilistic voltage sensitivity. It constructs a distribution network voltage sensitivity model to quantify the impact of node power fluctuations on observed node voltages. Simultaneously, it calculates the probability distribution function of observed node voltage changes and analyzes the impact of distributed renewable energy sources with different penetration rates on distribution network voltage volatility. By quantifying the random fluctuations in renewable energy output, it effectively assesses the probability distribution characterizing the distribution network voltage operating state, determining the probability of system node voltage exceeding limits and the maximum capacity of renewable energy sources that the distribution power source can accommodate. However, the quantitative analysis method in this approach is complex and may lead to unreliable evaluation results. None of the above methods provide a reasonable solution that considers random variables and their interrelationships while simplifying the transient voltage stability assessment process.

[0004] Therefore, the applicant proposes a probabilistic transient voltage stability assessment method that considers relevant random variables, conducts in-depth research on the impact of uncertainties in power systems, and fully ensures the safety of the system. Summary of the Invention

[0005] The purpose of this invention is to solve the technical problem of inaccurate voltage stability assessment caused by the uncertainty of new energy sources.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical methods:

[0007] A probabilistic transient voltage stability assessment method considering relevant random variables includes the following steps:

[0008] Step 1: Model the key random variables in the system, including determining their probability distribution types;

[0009] Step 2: Calculate the maximum load margin under the current system configuration using the interior point method, and use this margin as an indicator to evaluate the transient voltage stability of the system;

[0010] Step 3: Based on the random variables and their interrelationships, rationally select the direction of power increment for the generator and the load;

[0011] Step 4: Generate samples by combining Latin Hypercube Sampling (LHS) and Singular Value Decomposition (SVD) quadratic permutation techniques;

[0012] Step 5: Use the generated sample set to conduct multiple simulation experiments, and evaluate the probabilistic transient voltage stability through repeated deterministic calculations.

[0013] Step 1: Model the key random variables in the system, including determining their probability distribution types. Specifically, select appropriate probability distributions to describe the active power of wind power generation, photovoltaic power generation, and load, as follows:

[0014] Step 1-1: Identify key random variables and collect historical data;

[0015] Step 1-2: Select a suitable probability distribution for modeling, where the active power P of wind power generation... W The active power P of photovoltaic power generation is usually determined by the Weibull distribution modeled by wind speed. PV It is usually modeled as a Beta distribution, with the active power P of the load... L It is usually modeled as a normal distribution.

[0016] Step 2: Calculate the maximum load margin under the current system configuration using the interior-point method, and use this margin as an indicator to evaluate the transient voltage stability of the system. The optimization model is a nonlinear optimization problem, solved using the interior-point method, as detailed below:

[0017] Step 2-1: Construct the optimal power flow model for the system;

[0018] Step 2-2: Use the interior point method to solve the nonlinear optimization problem in the model to find the solution that maximizes the load margin λ;

[0019] Steps 2-3: Calculate the maximum load margin. Once the optimal solution is obtained, the maximum load margin λ that the system can withstand under the current configuration can be determined, and λ can be directly used as the index.

[0020] Step 3: Based on the random variables and their interrelationships, rationally select the power increment direction for the generator and load. When selecting the power increment direction, the actual operating characteristics of the system must be considered, especially the correlation between random variables. To ensure that these correlations are preserved during the evaluation process, the directions of the base generator and load power are used as the increment directions.

[0021] Step 3-1: First, identify the key random variables that affect generator output and load demand, and then model the probability distribution of these random variables;

[0022] Step 3-2: Analyze the dependencies and correlations between random variables, and use the correlation coefficient to quantify the linear correlation between variables;

[0023] Step 3-3: Select the direction of generator power increment based on probabilistic risk assessment and select the direction of load power increment based on demand response strategy.

[0024] Step 4: Generate samples by combining Latin hypercube sampling and singular value decomposition (SVD) with quadratic permutation techniques. The method employs a combination of power-based transformation, LHS, and SVD, with the specific steps as follows:

[0025] Step 4-1: Transformation based on the power method. Z i Let be a random variable with an arbitrary distribution. If we transform its expected value to 0, it can be expressed in standard form:

[0026]

[0027] In the formula: E(·) is the expected value function; Var(·) is the variance function; U i It is Z i The standard form of a standard random variable. A standard random variable can be approximated by an m-th order polynomial as follows:

[0028]

[0029] In the formula: S i It is a standard normal distribution; c ir The polynomial coefficients are obtained by solving for m U. i The equation for the correlation moments is obtained as follows:

[0030]

[0031] In the formula: Let U be a random variablei The m-order matrix can be calculated given the marginal distribution or sample of the random variable, and the correlation coefficient r in the correlation matrix R is established. ij and its corresponding R * Intermediate correlation coefficient The equation, the intermediate correlation coefficient matrix R * It can be represented as:

[0032]

[0033] Step 4-2: Latin hypercube sampling. LHS is a stratified sampling method. The sample generated using LHS is shown below:

[0034]

[0035] In the formula: row vector (x i1 ,…,x ik (θ) is a sample from a standard normal distribution; i1 ,…,θ in ) is a random permutation of (1,…,n); μ ij Given a uniform random variable, the sample matrix of size n×k is shown below:

[0036]

[0037] Step 4-3: Quadratic permutation method based on singular value decomposition. The purpose of the first permutation is to remove the samples generated by the LHS (Locally Hierarchically Relevant) algorithm. Then, the independent samples are permuted a second time to generate samples with a specified correlation. After generating samples through the LHS process, the correlation matrix R of the sample matrix X can be calculated. X Generally, the correlation matrix is ​​symmetric, and its SVD is shown below. The specific process of the second permutation is as follows:

[0038]

[0039] In the formula: Q is a lower triangular matrix; D is a real diagonal matrix with R X The singular values ​​of a matrix Y with n×k elements can be constructed as follows:

[0040]

[0041] It can be proven that y i The mean is 0. Given the required correlation coefficient matrix R, the intermediate correlation coefficient matrix R can be calculated. * Then R * The SVD is symmetric, as detailed below:

[0042]

[0043] In the formula: P is a lower triangular matrix; E is a real diagonal matrix with singular values ​​R. * A matrix Z containing n×k elements * It can be constructed as follows:

[0044]

[0045] Arrange each row of X according to matrix Z * The samples are arranged to obtain a sample matrix S, whose features are similar to those of matrix Z. * The rank correlation matrix is ​​the same.

[0046] Due to matrix S and matrix Z * Since they have the same rank correlation matrix, the correlation matrix of S is close to that of R. * Finally, using (1) and (2), the sample Z with an approximate expected correlation coefficient matrix R is calculated. Each column in the sample matrix Z forms a set of samples, which are substituted into equation (1) as input for the deterministic maximum load margin λ.

[0047] Step 5: Conduct multiple simulation experiments using the generated sample set, and evaluate the probabilistic transient voltage stability through iterative deterministic calculations. Specifically, multiple simulation experiments are conducted using the generated sample set, and probabilistic transient voltage stability is evaluated through iterative deterministic calculations. Then, the probabilistic characteristics of the maximum load margin are obtained statistically, and the standard deviation of the average error is used as an indicator to evaluate the stability of the proposed method.

[0048] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0049] (1) By modeling the stochastic characteristics of the system and the correlation between new energy sources, this invention can more accurately reflect the actual operating status of the power system. Compared with traditional deterministic analysis, this method can capture the impact of more uncertainties on system stability, thereby improving the accuracy of the assessment;

[0050] (2) This invention uses Latin hypercube sampling and singular value decomposition secondary permutation technology for probability evaluation, which can reduce the number of simulation experiments required while ensuring sample diversity, improve computational efficiency and shorten simulation time. Attached Figure Description

[0051] Figure 1 This is a flowchart of the power system transient voltage stability assessment method proposed in this invention;

[0052] Figure 2 This is a flowchart of the probabilistic transient voltage stability evaluation method proposed in this invention;

[0053] Figure 3It is the average of the relative errors of the maximum load margin in 100 tests in the examples of this invention.

[0054] Figure 4 It is the average of the relative errors of the standard deviation of the maximum load margin in 100 tests in the examples of this invention.

[0055]

[0056] Figure 5 It is the standard deviation of the relative error of the mean of 100 tests for maximum load margin in the example of this invention.

[0057] Figure 6 It is the standard deviation of the relative error of the standard deviation of the maximum load margin in 100 tests in this invention example.

[0058] Detailed Implementation

[0059] like Figure 1 As shown, a probabilistic transient voltage stability assessment method considering relevant random variables is provided, the method comprising the following steps:

[0060] Step 1: Model the key random variables in the system, including determining their probability distribution types. Specifically, select appropriate probability distributions to describe the active power of wind power generation, photovoltaic power generation, and load, as follows:

[0061] Step 1-1: Identify key random variables and collect historical data;

[0062] Step 1-2: Select a suitable probability distribution for modeling, as follows:

[0063] The Weibull distribution is used to describe the statistical characteristics of wind speed, and its probability density function is:

[0064]

[0065] In the formula: v is the wind speed; m and d are the shape and scale parameters of the wind speed, respectively. The power output P of the wind turbine... W (v) can be determined from the velocity-power curve:

[0066]

[0067] In the formula: P r This refers to the rated power of the wind power; v ci v r and v co These are the cut-in wind speed, rated wind speed, and cut-out wind speed, respectively.

[0068] The beta distribution is used to describe the statistical characteristics of photovoltaics, and its probability density function is:

[0069]

[0070] In the formula: Γ(·) is the gamma function; α and β are the shape parameters of the Beta distribution; P max This refers to the capacity of a photovoltaic power station.

[0071] Using a normal distribution to describe load characteristics, its active power probability density function is:

[0072]

[0073] In the formula: P and Q are the active and reactive power of the load, respectively; σ P and σ Q These are the standard deviations of the active and reactive power of the load, respectively; μ P and μ Q These are the expected values ​​of the active and reactive power of the load, respectively.

[0074] Step 2: Calculate the maximum load margin under the current system configuration using the interior-point method, and use this margin as an indicator to evaluate the transient voltage stability of the system. The optimization model is a nonlinear optimization problem, solved using the interior-point method, as detailed below:

[0075] Step 2-1: Construct the model, as follows:

[0076] (1) Objective function:

[0077] maxλ(15)

[0078] In the formula: λ is the load margin.

[0079] (2) Equality constraints:

[0080]

[0081] In the formula: P Li and Q Li P represents the active power and reactive power of the load at bus i, respectively; Ri and Q Ri These represent the active and reactive power of the new energy source at bus i, respectively; and These are the base power of the conventional generator and the bus i-load, respectively; V i and V j Let θ be the voltages at bus i and j, respectively; ij G represents the phase angle difference between bus i and bus j; ij and B ij The conductance and susceptance of the line connecting busbar i and busbar j are respectively; P ij and Qij The active and reactive power flows are from bus i to bus j; t ij The rate of change from bus i to bus j

[0082] (3) Inequality constraints:

[0083]

[0084] In the formula: P Gi and Q Gi These represent the active power and reactive power of the thermal power generating unit, respectively; P Gi,max P Gi,min These are the upper and lower limits of the generator's active power output, respectively; Q Gi,max Q Gi,min These are the upper and lower limits of the generator's reactive power output, respectively; V i,min and V i,max These are the upper and lower limits of bus i, respectively; S ij,max The apparent maximum power from bus i to bus j;

[0085] Step 2-2: Use the interior point method to solve the above nonlinear optimization problem to find the solution that maximizes the load margin λ, as follows:

[0086] (1) Initialization: Select a suitable initial point, ensure that it is within the feasible region, and set the obstacle parameters.

[0087] (2) Construct a barrier function: introduce a barrier term to penalize behaviors that approach the boundary, ensuring that the process remains within the feasible region during iteration.

[0088] (3) Iterative optimization: The decision variables are updated through a series of iterations, and the obstacle parameters are gradually reduced until the convergence criterion is met. At each step, a new search direction is calculated, and the decision variables are adjusted according to a certain step size rule;

[0089] Steps 2-3: Calculate the maximum load margin. Once the optimal solution is obtained, the maximum load margin λ that the system can withstand under the current configuration can be determined, and λ can be directly used as the index.

[0090] Step 3: Based on the random variables and their interrelationships, rationally select the power increment direction for the generator and load. When selecting the power increment direction, the actual operating characteristics of the system must be considered, especially the correlation between random variables. To ensure that these correlations are preserved during the evaluation process, the directions of the base generator and load power are used as the increment directions.

[0091] Step 3-1: First, identify the key random variables that affect generator output and load demand, and then model the probability distribution of these random variables;

[0092] Step 3-2: Analyze the dependencies and correlations among random variables, and use the correlation coefficient to quantify the linear correlation between variables. Specifically, for any two loadings P... Li and P Lj Its correlation coefficient r ij ((1+λ)P Li ,(1+λ)P Lj The load remains constant as the load increases. For any given load P... Li And any new energy P Rj The correlation coefficient r between them ij ((1+λ)P Li ,P Rj This also remains constant as the load increases. This choice maintains the correlation between random variables, thus better reflecting the actual operating characteristics of the system;

[0093] Step 3-3: Select the direction of generator power increment based on probabilistic risk assessment and select the direction of load power increment based on demand response strategy.

[0094] Step 4: Generate samples by combining Latin hypercube sampling and singular value decomposition (SVD) with quadratic permutation techniques. The method employs a combination of power-based transformation, LHS, and SVD, with the specific steps as follows:

[0095] Step 4-1: Transformation based on the power method. Z i Let be a random variable with an arbitrary distribution. If we transform its expected value to 0, it can be expressed in standard form:

[0096]

[0097] In the formula: E(·) is the expected value function; Var(·) is the variance function; U i It is Z i The standard form of a standard random variable. A standard random variable can be approximated by an m-th order polynomial as follows:

[0098]

[0099] In the formula: S i It is a standard normal distribution; c ir The polynomial coefficients are obtained by solving for m U. i The equation for the correlation moments is obtained as follows:

[0100]

[0101] In the formula: Let U be a random variable iThe m-order matrix can be calculated given the marginal distribution or sample of the random variable, and the correlation coefficient r in the correlation matrix R is established. ij and its corresponding R * Intermediate correlation coefficient The equation, the intermediate correlation coefficient matrix R * It can be represented as:

[0102]

[0103] Step 4-2: Latin hypercube sampling. LHS is a stratified sampling method. The sample generated using LHS is shown below:

[0104]

[0105] In the formula: row vector (x i1 ,…,x ik (θ) is a sample from a standard normal distribution; i1 ,…,θ in ) is a random permutation of (1,…,n); μ ij Given a uniform random variable, the sample matrix of size n×k is shown below:

[0106]

[0107] Step 4-3: Quadratic permutation method based on singular value decomposition. The purpose of the first permutation is to remove the samples generated by the LHS (Locally Hierarchically Relevant) algorithm. Then, the independent samples are permuted a second time to generate samples with a specified correlation. After generating samples through the LHS process, the correlation matrix R of the sample matrix X can be calculated. X Generally, the correlation matrix is ​​symmetric, and its SVD is shown below. The specific process of the second permutation is as follows:

[0108]

[0109] In the formula: Q is a lower triangular matrix; D is a real diagonal matrix with R X The singular values ​​of a matrix Y with n×k elements can be constructed as follows:

[0110]

[0111] It can be proven that y i The mean is 0. Given the required correlation coefficient matrix R, the intermediate correlation coefficient matrix R can be calculated. * Then R * The SVD is symmetric, as detailed below:

[0112]

[0113] In the formula: P is a lower triangular matrix; E is a real diagonal matrix with singular values ​​R. * A matrix Z containing n×k elements * It can be constructed as follows:

[0114]

[0115] Arrange each row of X according to matrix Z * The samples are arranged to obtain a sample matrix S, whose features are similar to those of matrix Z. * The rank correlation matrix is ​​the same.

[0116] Due to matrix S and matrix Z * Since they have the same rank correlation matrix, the correlation matrix of S is close to that of R. * Finally, using (1) and (2), the sample Z with an approximate expected correlation coefficient matrix R is calculated. Each column in the sample matrix Z forms a set of samples, which are substituted into equation (1) as input for the deterministic maximum load margin λ.

[0117] Step 5: Conduct multiple simulation experiments using the generated sample set, and evaluate the probabilistic transient voltage stability through iterative deterministic calculations. The specific calculation steps of the probabilistic voltage stability evaluation method are as follows:

[0118] Step 5-1: Input the cumulative distribution function and expected correlation matrix R for each random variable;

[0119] Step 5-2: Generate an n×k sample matrix X using LHS;

[0120] Step 5-3: Calculate Z using equation (10) * ;

[0121] Step 5-4: Arrange each row of X according to matrix Z * Arrange the samples to obtain the sample matrix S;

[0122] Step 5-5: Calculate sample Z using equations (1) and (2);

[0123] Steps 5-6: Repeat the solution for the deterministic maximum load margin for all random samples Z;

[0124] Steps 5-7: Statistically calculate the probabilistic characteristics of the maximum load margin results.

[0125] The statistical precision of a sample is measured using the mean squared error exponent of the correlation matrix, as follows:

[0126]

[0127] In the formula: r ij The element in the i-th row and j-th column of the expected correlation matrix; is the element in the i-th row and j-th column of the sample correlation matrix; m is the total number of random variables.

[0128] Since the sampling process is random, the average of the average error of n trials and the standard deviation of the average error of n tests are used as indicators to evaluate the stability of the proposed method.

[0129] Example:

[0130] The embodiments used in this invention are based on two improved IEEE node systems. In order to verify the performance of the proposed probabilistic transient voltage stability evaluation method, this test included all the steps described in the method of this invention. The test was conducted on a computer equipped with an Intel Core i7 CPU and 4GB RAM, and the test results were obtained.

[0131] (1) Improved IEEE 14-node system

[0132] For the improved test system, two photovoltaic power stations were connected to busbars 6 and 7 respectively, and two wind farms were connected to busbars 11 and 12 respectively. The power factor of each photovoltaic power station was set to 1.0, the power factor of each wind farm was set to 0.96, the thermal limit of the line was set to 100MVA, and the lower and upper limits of the bus voltage were set to 0.7pu and 1.3pu respectively. The detailed parameters of the photovoltaic power stations and wind farms are shown in Table 1.

[0133] Table 1

[0134]

[0135] There are a total of 15 random variables in the example. Assuming that the random variables on the directly connected bus are correlated, the probability results using simple random sampling are accurate. Furthermore, considering the correlation coefficients between different types of variables, the errors of the solutions obtained by power transformation and Nataf transformation of the quadratic permutation PLT, combined with simple random sampling and quadratic permutation PST are used to study different sample sizes.

[0136] (2) Improved IEEE 118-node system

[0137] The test system is divided into four zones, covering buses 1-31, 32-58, 59-92, and 94-118 respectively. In the improved test system, each zone connects four wind farms and four photovoltaic power plants. The photovoltaic power plants each have a capacity of 30 MW, and the wind farms each have a capacity of 20 MW. The photovoltaic power plants are connected to buses 1, 4, 6, 8, 32, 34, 36, 38, 60, 68, 72, 73, 99, 104, 105, and 107, while the wind farms are connected to buses 16, 17, 19, 23, 40, 41, 52, 53, 74, 75, 76, 87, 110, 112, 113, and 116. Other parameters for the photovoltaic power plants and wind farms are the same as in the 14-node system study case.

[0138] The average active power of the load is set as the deterministic active power of the load in the standard test system, and the standard rate of change is set to 6%. Similar to the 14-node system study case, the reactive power of the load is determined by a fixed power factor, and the correlation coefficients between different variables are taken into account.

[0139] Error indices for 100 trials of different types of output random variables, such as Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown, in Figure 3 and Figure 4 In the mean, the average relative error of the mean of the maximum load margin of the PLT The average of the relative errors of the standard deviation The fact that all values ​​are the smallest indicates that, with the same sample size, the results of PLT are more accurate than those of PST and Nataf. Figure 5 and Figure 6 The standard deviation of the relative error of the mean of the maximum load margin under PLT operation. The standard deviation of the relative error of the standard deviation The values ​​are also the smallest, indicating that the results under the action of PLT are more stable than those under the action of PST and Nataf.

[0140] The results show that the power-law transformation combining Latin hypercube sampling and quadratic permutation can stably handle the correlation between input random variables, providing more accurate results even when the correlation matrix is ​​not positive definite. Furthermore, the time taken for two permutations is 0.034 seconds and 0.165 seconds for the 14-node and 118-node systems, respectively, while the time taken for one permutation is 0.032 seconds and 0.163 seconds for the 14-node and 118-node systems, respectively, indicating that the two-permutation technique is effective.

Claims

1. A probabilistic transient voltage stability assessment method considering relevant random variables, characterized in that, Includes the following steps: Step 1: Model the key random variables in the system, including determining their probability distribution types; Step 2: Calculate the maximum load margin under the current system configuration using the interior point method, and use this margin as an indicator to evaluate the transient voltage stability of the system; Step 3: Based on the random variables and their interrelationships, rationally select the direction of power increment for the generator and the load; Step 4: Generate samples by combining Latin Hypercube Sampling (LHS) and Singular Value Decomposition (SVD) with secondary permutation techniques; Step 5: Use the generated sample set to conduct multiple simulation experiments, and evaluate the probabilistic transient voltage stability through repeated deterministic calculations; In step 1, the key random variables in the system are modeled, including determining their probability distribution types; specifically, an appropriate probability distribution is selected to describe the active power of wind power generation, photovoltaic power generation, and load, as follows: Step 1-1: Identify key random variables and collect historical data; Step 1-2: Select a suitable probability distribution for modeling, where the active power of wind power generation... The active power of photovoltaic power generation is typically determined by the Weibull distribution modeled for wind speed. It is usually modeled as a Beta distribution, with the active power of the load... It is usually modeled as a normal distribution; In step 2, the maximum load margin under the current system configuration is calculated using the interior-point method, and this margin is used as an index to evaluate the transient voltage stability of the system. The optimization model is a nonlinear optimization problem, solved using the interior-point method, as detailed below: Step 2-1: Construct the optimal power flow model for the system; Step 2-2: Use the interior point method to solve the nonlinear optimization problem in the model to find the load margin. The largest solution; Steps 2-3: Calculate the maximum load margin. Once the optimal solution is found, the maximum load margin that the system can withstand under the current configuration can be determined. and directly adopt As an indicator; In step 3, based on the random variables and their interrelationships, the power increment direction is reasonably selected for the generator and load. When selecting the power increment direction, the actual operating characteristics of the system, especially the correlation between random variables, need to be considered. To ensure that these correlations are preserved during the evaluation process, the directions of the base generator and load power are used as the increment directions. Specifically: Step 3-1: First, identify the key random variables that affect generator output and load demand, and then model the probability distribution of these random variables; Step 3-2: Analyze the dependencies and correlations between random variables, and use the correlation coefficient to quantify the linear correlation between variables; Step 3-3: Select the direction of generator power increment based on probabilistic risk assessment and select the direction of load power increment based on demand response strategy.

2. The probabilistic transient voltage stability assessment method considering relevant random variables according to claim 1, characterized in that: In step 4, samples are generated by combining Latin hypercube sampling and singular value decomposition (SVD) with secondary permutation techniques. Specifically, a power-based transformation, LHS, and SVD approach is used to assess probabilistic transient voltage stability. The specific steps of this power-based transformation, LHS, and SVD approach are as follows: Step 4-1: Transformation based on the power method; Let be a random variable with an arbitrary distribution. If we transform its expected value to 0, it can be expressed in standard form: (1)； In the formula: It is the expected value function; It is a variance function; yes The standard form; standard random variables can be used The approximation of the order polynomial is as follows: (2)； In the formula: It follows a standard normal distribution; The polynomial coefficients are obtained by solving for... indivual The equation for the correlation moments is obtained as follows: (3)； In the formula: For random variables of The order matrix can be calculated given the marginal distribution or sample of a random variable, and a correlation matrix can be established. correlation coefficient and its corresponding Intermediate correlation coefficient The equation, the intermediate correlation coefficient matrix It can be represented as: (4)； Step 4-2: Latin hypercube sampling; LHS is a stratified sampling method. The sample generated using LHS is shown below: (5)； Where: row vector It is a sample that follows a standard normal distribution; yes Random arrangement; It is a uniform random variable with a size of The sample matrix is ​​shown below: (6)； Step 4-3: Quadratic permutation method based on singular value decomposition; the purpose of the first permutation is to remove the samples generated by the LHS (Locally Hierarchically Relevant) algorithm, and then the independent samples are permuted a second time to generate samples with a specified correlation. After generating samples through the LHS process, the sample matrix can be calculated. X Correlation matrix Generally, the correlation matrix is ​​symmetric, and its SVD is shown below. The specific process of the second permutation is as follows: (7)； In the formula: It is a lower triangular matrix; It is a real diagonal matrix with The singular value, a value containing A matrix of elements It can be constructed as follows: (8)； It can be proven The mean is 0, given the required correlation coefficient matrix. At that time, the intermediate correlation coefficient matrix can be obtained. ,but The SVD is symmetric, as detailed below: (9)； In the formula: It is a lower triangular matrix; It is a real diagonal matrix with singular values. A containing A matrix of elements It can be constructed as follows: (10)； Will X Each row according to the matrix Arrange the samples to obtain the sample matrix. S Its characteristics and matrix The rank correlation matrices are the same; Due to the matrix S With matrix They have the same rank correlation matrix, therefore S The correlation matrix is ​​close to Finally, the correlation coefficient matrix with approximate expectation is calculated using equations (1) and (2). samples Z Sample matrix Z Each column in the equation forms a sample, which is substituted into equation (1) as the deterministic maximum load margin. Input.

3. The probabilistic transient voltage stability assessment method considering relevant random variables according to claim 1, characterized in that: In step 5, multiple simulation experiments are conducted using the generated sample set. Probabilistic transient voltage stability is evaluated through iterative deterministic calculations, and then the probabilistic characteristics of the maximum load margin are obtained through statistics. The standard deviation of the mean error is used as an indicator to evaluate the stability of the proposed method.

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