Probabilistic transient voltage stability evaluation method considering related random variables

Abstract

A probabilistic transient voltage stability evaluation method considering related random variables comprises the steps that 1, modeling is conducted on key random variables in a system, and the probability distribution type of the key random variables is determined; 2, calculating the maximum load margin under the current system configuration by using an interior point method, and taking the margin as an index for evaluating the transient voltage stability of the system; 3, reasonably selecting a power increment direction for a generator and a load on the basis of considering random variables and mutual relations thereof; 4, generating a sample in combination with Latin hypercube sampling and singular value decomposition secondary replacement technologies; and 5, performing multiple simulation experiments by using the generated sample set, and performing probabilistic transient voltage stability evaluation through repeated determinacy calculation. The invention provides a probability transient voltage stability evaluation method considering related random variables, and the actual operation characteristics of a power system are reserved.

Description

Technical Field

[0001] The present invention relates to the field of transient voltage stability assessment of power systems, and in particular to a probabilistic transient voltage stability assessment method taking into account relevant random variables. Background Art

[0002] With the increasing use of renewable energy in the power system, the increase in random factors such as photovoltaic, wind power generation and load changes, and the relationship between input random variables, the random characteristics of the power system have become more complex. Their large-scale grid connection makes the stability and security of the power grid a challenging task. Therefore, ensuring fast and reliable transient voltage stability assessment results is crucial to ensure the safe and stable operation of the power system.

[0003] The patent document with application publication number CN115017735A discloses a multi-agent probabilistic voltage stability calculation method for high-dimensional systems, which collects historical data of random variables in the power system, estimates the probability density function of random variables, determines the power system operation scenario, and constructs a proxy model of the deterministic voltage stability assessment model corresponding to the operation scenario based on different operation scenarios of the power system during the operation cycle. The random variable probability density function is sampled and input into the proxy model based on the Monte Carlo simulation method to perform probabilistic voltage stability assessment. However, this method does not take into account 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. The patent document with application publication number CN116914852A discloses a distribution network carrying capacity estimation method based on probabilistic voltage sensitivity, constructs a distribution network voltage sensitivity model, quantifies the impact of node power fluctuations on the observed node voltage, and calculates the probability distribution function of the observed node voltage change. The impact of distributed new energy with different penetration rates on the distribution network voltage volatility is analyzed. When quantitatively analyzing the random fluctuations in new energy output, the probability of system node voltage exceeding the limit and the maximum capacity of the distribution source to accept renewable new energy can effectively evaluate the probability distribution that characterizes the operating state of the distribution network voltage. However, the quantitative analysis method in this method is relatively complex and may lead to unreliable evaluation results. None of the above methods can provide a reasonable solution that can both consider random variables and their relationships and simplify the transient voltage stability evaluation process.

[0004] Therefore, the applicant proposed a probabilistic transient voltage stability assessment method considering relevant random variables, conducted an in-depth study on the impact of uncertainty in the power system, and fully guaranteed the safety of the system. Summary of the invention

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

[0006] In order to achieve the above-mentioned invention object, the present invention adopts the following technical methods:

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

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

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

[0010] Step 3: Based on the consideration of random variables and their interrelationships, reasonably select the power increment direction 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 perform probabilistic transient voltage stability evaluation through repeated deterministic calculations.

[0013] Step 1: Model the key random variables in the system, including determining their probability distribution type. Among them, select appropriate probability distribution 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 an appropriate probability distribution for modeling, where the active power P of wind power generation W Usually determined by the Weibull distribution of wind speed modeling, the active power P of photovoltaic power generation PV Usually modeled as a Beta distribution, the active power P of the load L Often modeled as a normal distribution.

[0016] Step 2: Use the interior point method to calculate the maximum load margin under the current system configuration, and use this margin as an indicator to evaluate the transient voltage stability of the system. Among them, the optimization model is a nonlinear optimization problem, which is solved by the interior point method, as follows:

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

[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] Step 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 an indicator.

[0020] Step 3: Based on the consideration of random variables and their interrelationships, the power increment direction is reasonably selected for the generator and load. The actual operating characteristics of the system, especially the correlation between random variables, need to be considered when selecting the power increment direction. In order to ensure that these correlations are preserved during the evaluation process, the direction of the basic generator and load power is used as the increment direction.

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

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

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

[0024] Step 4: Generate samples by combining Latin hypercube sampling and singular value decomposition quadratic permutation technology. Among them, a method combining transformation based on power method, LHS and singular value decomposition is adopted. The specific steps are as follows:

[0025] Step 4-1: Transformation based on power method. i If a random variable with any distribution is transformed into 0, it can be expressed in standard form:

[0026]

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

[0028]

[0029] Where: S i is the standard normal distribution; c ir The coefficients of the polynomial are obtained by solving the equation with m U i The equation for the associated moment is obtained as follows:

[0030]

[0031] Where: is a random variable Ui The m-order matrix can be calculated when the marginal distribution or sample of the random variable is given, and the correlation coefficient r in the correlation matrix R is established. ij and its corresponding R * The intermediate correlation coefficient The equation of the intermediate correlation coefficient matrix R * It can be expressed as:

[0032]

[0033] Step 4-2: Latin Hypercube Sampling. LHS is a stratified sampling method. The sample generated by LHS is as follows:

[0034]

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

[0036]

[0037] Step 4-3: Quadratic permutation method based on singular value decomposition. The purpose of the first permutation is to decorrelate the samples generated by LHS, and then perform a second permutation on the independent samples to generate samples with specified correlation. After the samples are generated through the LHS process, the correlation matrix R of the sample matrix X can be calculated. X , in general, the correlation matrix is ​​symmetric, its SVD is below, and the quadratic permutation process is as follows:

[0038]

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

[0040]

[0041] It can be proved that i The mean value of is 0. When the required correlation coefficient matrix R is given, the intermediate correlation coefficient matrix R can be obtained. * , then R * The SVD of is symmetric and is as follows:

[0042]

[0043] Where: P is a lower triangular matrix; E is a real diagonal matrix with singular values ​​R * , a matrix Z with n×k elements * Can be constructed as:

[0044]

[0045] Transform each row of X into the matrix Z * Arrange them to get the sample matrix S, whose characteristics are the same as the matrix Z * The rank correlation matrix is ​​the same.

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

[0047] Step 5: Use the generated sample set to conduct multiple simulation experiments, and perform probabilistic transient voltage stability assessment through repeated deterministic calculations. Use the generated sample set to conduct multiple simulation experiments, and perform probabilistic transient voltage stability assessment through repeated deterministic calculations. Then, the probability characteristics of the maximum load margin are obtained through statistics, 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 present invention has the following beneficial effects:

[0049] (1) The present invention can more accurately reflect the operating conditions of the actual power system by modeling the random characteristics of the system and the correlation between the new energy sources. Compared with the traditional deterministic analysis, this method can capture the impact of more uncertain factors on the system stability, thereby improving the accuracy of the assessment;

[0050] (2) The present invention utilizes Latin hypercube sampling and singular value decomposition quadratic permutation technology for probability evaluation, which can reduce the number of simulation experiments required while ensuring sample diversity, thereby improving computational efficiency and shortening simulation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the transient voltage stability assessment method of the power system proposed by the present invention;

[0052] Figure 2 It is a flow chart of the probabilistic transient voltage stability assessment method proposed by the present invention;

[0053] Figure 3is the average value of the relative error of the mean value of 100 tests of the maximum load margin in the example of the present invention

[0054] Figure 4 is the average value of the relative error of the standard deviation of 100 tests of the maximum load margin in the present invention.

[0056] Figure 5 is the standard deviation of the relative error of the mean of 100 tests of the maximum load margin in the present invention

[0057] Figure 6 is the standard deviation of the relative error of the standard deviation of the maximum load margin 100 tests in the present invention DETAILED DESCRIPTION

[0059] like Figure 1 As shown, a probabilistic transient voltage stability assessment method considering correlated random variables comprises the following steps:

[0060] Step 1: Model the key random variables in the system, including determining their probability distribution types. Among them, 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 the appropriate probability distribution for modeling, as follows:

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

[0064]

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

[0066]

[0067] Where: P r is the rated power of wind power; v ci 、v r and v co They are cut-in wind speed, rated wind speed and cut-out wind speed respectively.

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

[0069]

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

[0071] Normal distribution is used to describe the load characteristics, and its load active power probability density function is:

[0072]

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

[0074] Step 2: Use the interior point method to calculate the maximum load margin under the current system configuration, and use this margin as an indicator to evaluate the transient voltage stability of the system. Among them, the optimization model is a nonlinear optimization problem, which is solved by the interior point method, as follows:

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

[0076] (1) Objective function:

[0077] maxλ(15)

[0078] Where: λ is the load margin.

[0079] (2) Equality constraints:

[0080]

[0081] Where: P Li and Q Li are the active power and reactive power of the load at bus i respectively; P Ri and Q Ri are the active power and reactive power of renewable energy at bus i respectively; and are the base powers of the traditional generator and bus load i respectively; V i and V j are the voltages of busbars i and j respectively; θ ij is the phase angle difference between busbar i and busbar j; G ij and B ij are the conductance and susceptance of the line connecting busbar i and busbar j respectively; P ij and Q ijis the active power flow and reactive power flow from bus i to bus j; t ij is the rate of change from bus i to bus j

[0082] (3) Inequality constraints:

[0083]

[0084] Where: P Gi and Q Gi are respectively the active power and reactive power of the thermal power generating set; P Gi,max , P Gi,min They are the upper and lower limits of the active output of the generator respectively; Q Gi,max , Q Gi,min are the upper and lower limits of the reactive power output of the generator respectively; V i,min and V i,max are the upper and lower limits of busbar i respectively; S ij,max is the maximum apparent 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 barrier parameters.

[0087] (2) Constructing a barrier function: Introducing a barrier term to penalize behavior close to the boundary, ensuring that the iteration process always remains within the feasible region.

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

[0089] Step 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 an indicator.

[0090] Step 3: Based on the consideration of random variables and their interrelationships, the power increment direction is reasonably selected for the generator and load. The actual operating characteristics of the system, especially the correlation between random variables, need to be considered when selecting the power increment direction. In order to ensure that these correlations are preserved during the evaluation process, the direction of the basic generator and load power is used as the increment direction.

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

[0092] Step 3-2: Analyze the dependence and correlation between random variables and use the correlation coefficient to quantify the linear correlation between variables. Specifically, for any two loads P Li and P Lj , and its correlation coefficient r ij ((1+λ)P Li ,(1+λ)P Lj ) remains unchanged when the load increases. Li and any new energy P Rj The correlation coefficient r ij ((1+λ)P Li ,P Rj ) also remains unchanged when the load increases. This choice can keep the correlation between random variables unchanged, thus better reflecting the actual operating characteristics of the system;

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

[0094] Step 4: Generate samples by combining Latin hypercube sampling and singular value decomposition quadratic permutation technology. Among them, a method combining transformation based on power method, LHS and singular value decomposition is adopted. The specific steps are as follows:

[0095] Step 4-1: Transformation based on power method. i If a random variable with any distribution is transformed into 0, it can be expressed in standard form:

[0096]

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

[0098]

[0099] Where: S i is the standard normal distribution; c ir The coefficients of the polynomial are obtained by solving the equation with m U i The equation for the associated moment is obtained as follows:

[0100]

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

[0102]

[0103] Step 4-2: Latin Hypercube Sampling. LHS is a stratified sampling method. The sample generated by LHS is as follows:

[0104]

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

[0106]

[0107] Step 4-3: Quadratic permutation method based on singular value decomposition. The purpose of the first permutation is to decorrelate the samples generated by LHS, and then perform a second permutation on the independent samples to generate samples with specified correlation. After the samples are generated through the LHS process, the correlation matrix R of the sample matrix X can be calculated. X , in general, the correlation matrix is ​​symmetric, its SVD is below, and the quadratic permutation process is as follows:

[0108]

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

[0110]

[0111] It can be proved that i The mean value of is 0. When the required correlation coefficient matrix R is given, the intermediate correlation coefficient matrix R can be obtained. * , then R * The SVD of is symmetric and is as follows:

[0112]

[0113] Where: P is a lower triangular matrix; E is a real diagonal matrix with singular values ​​R *, a matrix Z with n×k elements * Can be constructed as:

[0114]

[0115] Transform each row of X into the matrix Z * Arrange them to get the sample matrix S, whose characteristics are the same as the matrix Z * The rank correlation matrix is ​​the same.

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

[0117] Step 5: Use the generated sample set to conduct multiple simulation experiments and perform probabilistic transient voltage stability assessment through repeated deterministic calculations. The specific calculation steps of the probabilistic voltage stability assessment method are as follows:

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

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

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

[0121] Step 5-4: Transform each row of X into the matrix Z * Arrange and obtain the sample matrix S;

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

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

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

[0125] The mean square error index of the correlation matrix is ​​used to measure the statistical accuracy of the sample, as follows:

[0126]

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

[0128] Since the sampling process is random, the mean of the average error of n tests 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 the present invention are based on two improved IEEE node systems. In order to verify the performance of the proposed probabilistic transient voltage stability assessment method, this test includes all the steps described in the method of the present invention. The test is performed on a computer equipped with an Intel Core i7 CPU and 4GB RAM, and the test results are obtained.

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

[0132] For the improved test system, two PV power stations are connected to busbars 6 and 7 respectively, and two wind farms are connected to busbars 11 and 12 respectively. The power factor of each PV power station is set to 1.0, the power factor of each wind farm is set to 0.96, the thermal limit of the line is set to 100MVA, and the lower and upper limits of the bus voltage are set to 0.7pu and 1.3pu respectively. The detailed parameters of the PV power station and wind farm 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 buses are correlated, the probability results using simple random sampling are accurate, and the correlation coefficients between different types of variables are taken into account, the errors of the solutions obtained by calculating the quadratic permutation PLT, the power transformation and Nataf transformation combining simple random sampling and quadratic permutation PST are studied to study different sample sizes.

[0136] (2) Improved IEEE 118 node system

[0137] The test system is divided into four areas, covering busbars 1-31, 32-58, 59-92, and 94-118 respectively. In the improved test system, four wind farms and four photovoltaic power plants are connected to each area. Among them, the capacity of the photovoltaic power plant is 30 MW, the capacity of the wind farm is 20 MW, the photovoltaic power plant is connected to busbars 1, 4, 6, 8, 32, 34, 36, 38, 60, 68, 72, 73, 99, 104, 105, and 107, and the wind farm is connected to busbars 16, 17, 19, 23, 40, 41, 52, 53, 74, 75, 76, 87, 110, 112, 113, and 116. The other parameters of the photovoltaic power plant and wind farm are the same as those of the 14-bus system study case.

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

[0139] The error indicators of 100 trials for different types of output random variables are as follows: Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown, in Figure 3 and Figure 4 The average value of the relative error of the mean value of the maximum load margin of PLT is The mean and standard deviation of the relative error The results of PLT are the smallest, indicating that under 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 is The standard deviation of the relative error and the standard deviation 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 method transformation combined with Latin hypercube sampling and quadratic permutation techniques can stably handle the correlation between input random variables and provide more accurate results even when the correlation matrix is ​​not positive definite. In addition, the time consumption for two permutations of the 14-node system and the 118-node system is 0.034 seconds and 0.165 seconds respectively, and the time consumption for one permutation of the 14-node system and the 118-node system is 0.032 seconds and 0.163 seconds respectively, so the two-permutation technique is effective.

Claims

1. A probabilistic transient voltage stability assessment method considering correlated random variables, characterized in that: The following steps are involved: Step 1: Model the key random variables in the system, including determining their probability distribution type; Step 2: Use the interior point method to calculate the maximum load margin under the current system configuration, and use this margin as an indicator to evaluate the transient voltage stability of the system; Step 3: Based on the consideration of random variables and their interrelationships, reasonably select the power increment direction for the generator and the load; Step 4: Generate samples by combining Latin hypercube sampling LHS and singular value decomposition SVD quadratic permutation technology; Step 5: Use the generated sample set to conduct multiple simulation experiments and perform probabilistic transient voltage stability assessment through repeated deterministic calculations.

2. The method for evaluating transient voltage stability with probability considering related random variables according to claim 1, characterized in that: In step 1, the key random variables in the system are modeled, including determining their probability distribution types; wherein, appropriate probability distributions are selected to describe the active power of wind power generation, photovoltaic power generation, and loads, as follows: Step 1-1: Identify key random variables and collect historical data; Step 1-2: Select an appropriate probability distribution for modeling, where the active power P of wind power generation W Usually determined by the Weibull distribution of wind speed modeling, the active power P of photovoltaic power generation PV Usually modeled as a Beta distribution, the active power P of the load L Often modeled as a normal distribution.

3. The method for evaluating transient voltage stability with probability considering related random variables according to claim 1, characterized in that: 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 indicator for evaluating the transient voltage stability of the system; the optimization model is a nonlinear optimization problem, which is solved using the interior point method, as follows: Step 2-1: Construct the system optimal power flow model; 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; Step 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 an indicator.

4. The method for evaluating transient voltage stability with probability considering correlated random variables according to claim 1, characterized in that: In step 3, the power increment direction is reasonably selected for the generator and the load based on the consideration of the random variables and their mutual relations. The actual operating characteristics of the system, especially the correlation between the random variables, need to be considered when selecting the power increment direction. In order to ensure that these correlations are preserved during the evaluation process, the direction of the basic generator and load power is used as the increment direction. Specifically: Step 3-1: First, identify the key random variables that affect generator output and load demand, and perform probability distribution modeling on these random variables; Step 3-2: Analyze the dependency and correlation between random variables and use the correlation coefficient to quantify the linear correlation between variables; Step 3-3: Select the generator power increment direction based on the probabilistic risk assessment and select the load power increment direction based on the demand response strategy.

5. The method for evaluating transient voltage stability with probability considering related random variables according to claim 1, characterized in that: In step 4, Latin hypercube sampling and singular value decomposition quadratic permutation techniques are combined to generate samples; wherein, a method combining transformation based on power method, LHS and singular value decomposition is adopted to perform probabilistic transient voltage stability assessment; wherein, a method combining transformation based on power method, LHS and singular value decomposition is adopted, and the specific steps are as follows: Step 4-1: Transformation based on power method; Z i If a random variable with any distribution is transformed into 0, it can be expressed in standard form: Where: E(·) is the expected value function; Var(·) is the variance function; U i It's Z i The standard form of a standard random variable can be approximated by an m-order polynomial as follows: Where: S i is the standard normal distribution; c ir The coefficients of the polynomial are obtained by solving the equation with m U i The equation for the associated moment is obtained as follows: Where: is a random variable U i The m-order matrix can be calculated when the marginal distribution or sample of the random variable is given, and the correlation coefficient r in the correlation matrix R is established. ij and its corresponding R * The intermediate correlation coefficient The equation of the intermediate correlation coefficient matrix R * It can be expressed as: Step 4-2: Latin Hypercube Sampling; LHS is a stratified sampling method. The sample generated by LHS is as follows: Where: row vector (x i1 ,…,x ik ) is a sample from a standard normal distribution; (θ i1 ,…,θ in ) is a random permutation of (1,…,n); μ ij is a uniform random variable, and the sample matrix of size n×k is as follows: Step 4-3: Quadratic permutation method based on singular value decomposition; the purpose of the first permutation is to decorrelate the samples generated by LHS, and then the independent samples are permuted for the second time to generate samples with specified correlation. After the samples are generated through the LHS process, the correlation matrix R of the sample matrix X can be calculated. X , in general, the correlation matrix is ​​symmetric, its SVD is below, and the quadratic permutation process is as follows: Where: Q is a lower triangular matrix; D is a real diagonal matrix with R X The singular values ​​of , a matrix Y containing n×k elements can be constructed as: It can be proved that i The mean value of is 0. When the required correlation coefficient matrix R is given, the intermediate correlation coefficient matrix R can be obtained. * , then R * The SVD of is symmetric and is as follows: Where: P is a lower triangular matrix; E is a real diagonal matrix with singular values ​​R * , a matrix Z with n×k elements * Can be constructed as: Transform each row of X into the matrix Z * Arrange it and get the sample matrix S, whose characteristics are the same as the matrix Z * The rank correlation matrix of is the same; Since the matrix S and the matrix Z * have the same rank correlation matrix, so the correlation matrix of S is close to that of R * Finally, the sample Z with the approximate expected correlation coefficient matrix R is calculated using equations (1) and (2). Each column in the sample matrix Z forms a set of samples, which are substituted into equation (1) as the input of the deterministic maximum load margin λ.

6. The method for evaluating transient voltage stability with probability considering correlated random variables according to claim 1, characterized in that: In step 5, multiple simulation experiments are performed using the generated sample set, and probabilistic transient voltage stability assessment is performed through repeated deterministic calculations, and then the probabilistic characteristics of the maximum load margin are obtained through statistics; wherein, multiple simulation experiments are performed using the generated sample set, and probabilistic transient voltage stability assessment is performed through repeated deterministic calculations, and then the probabilistic characteristics of the maximum load margin are obtained through statistics, and the standard deviation of the average error is used as an indicator to evaluate the stability of the proposed method.

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