Power grid reliability evaluation method based on important sampling of source-load correlation generalized cross entropy method

Abstract

The invention relates to the field of large power grid reliability evaluation, in particular to a power grid reliability evaluation method based on important sampling of a source load correlation generalized cross entropy method. Comprising the following steps: step 1, establishing a sparse probability model (GCE model) about a source-load correlation variable, and initializing relevant parameters of important sampling; 2, a pre-sampling stage: extracting system state samples according to a current important sampling function, carrying out system state analysis on the samples extracted each time, and respectively carrying out updating iteration on probability density distribution functions of element state variables and source-load variables in the system state variables until a pre-sampling convergence condition is met; and step 3, in a main sampling stage, extracting a system state sample according to the finally obtained important sampling function, and calculating a power grid reliability index until a main sampling convergence condition is met. According to the method, the important sampling process is simpler, and the power grid reliability evaluation efficiency considering the source-load correlation is improved.

Description

Technical Field

[0001] The method relates to the field of large power grid reliability assessment, and specifically is a power grid reliability assessment method based on important sampling of source-load correlation generalized cross entropy method. Background Art

[0002] With the large-scale integration of renewable energy such as wind power and photovoltaics into the power grid, and the widespread access to power terminals such as electric vehicles, the power system is facing increasingly prominent energy and environmental problems. However, renewable energy has greater randomness and intermittency, and the concentration of electric vehicle charging may also lead to instability in power load, bringing greater challenges to the reliable operation of the current power system. In addition, there are complex correlation variation characteristics between renewable energy and load, such as there is often a positive correlation between wind farms in the same area and between adjacent node loads. If the complex correlations and uncertainties in these power grids are ignored, it will be difficult to accurately grasp the law of system reliability changes.

[0003] In order to accurately characterize the source-load correlation in the power system, it is necessary to establish a correlation probability model for the source-load correlation variables. The kernel density estimation (KDE) model is based on a data-driven approach and does not require any subjective assumptions. As long as the sample size is large enough, it can converge to the true probability distribution according to probability. Therefore, it is widely used in source-load uncertainty and correlation modeling. The cross-entropy importance sampling method (CEIS) is often introduced into the reliability assessment simulation process to reduce the variance as the criterion, thereby reducing the reliability assessment time. The CE-IS method aims to minimize the cross-entropy distance (i.e., Kullback-Leibler distance) between the importance sampling density function (IS-PDF) and the theoretical optimal IS-PDF. In the CE-IS method, the distribution form of the importance sampling function needs to be selected based on experience. When the importance sampling function adopts a parameter model, the above function optimization problem can be transformed into a parameter optimization problem, and the approximate optimal IS-PDF can be obtained by optimizing the parameters of the parameter model. When the importance sampling function adopts a KDE model, the approximate optimal IS-PDF can be obtained by optimally perturbing the weight parameters of the KDE model. IS-PDF sampling makes it easier to capture system fault states and reduce the variance of reliability indicators, thereby achieving rapid grid reliability assessment taking into account source-load correlation.

[0004] The CE-IS method requires that the distribution form of the important sampling function be selected based on experience. When the important sampling function adopts a parameter model, the important sampling function has the problem of being single in form and not flexible enough. When the important sampling function adopts the KDE model, the optimization of a large number of weight parameters with small values ​​based on a limited pre-simulation sample will result in accuracy degradation. Because the KDE model is a non-sparse probabilistic model, the large sample approximation characteristics make the model contain a large number of weight parameters with small values ​​to be optimized. The IS-PDF obtained by optimally perturbing the weight parameters of the KDE model through CEIS is still a non-sparse model, which results in the need to extract sufficient samples in the iterative process to ensure the full optimization of a large number of parameters of the KDE model, affecting the efficiency of the reliability assessment of the power grid taking into account the source-load correlation. In addition, the optimization of the weight parameters of the KDE model by CEIS is essentially still a parameter optimization process, and the derivation of its parameter iteration update formula is relatively complicated. Summary of the invention

[0005] In view of the deficiencies of the above-mentioned prior art, the present invention proposes a power grid reliability assessment method based on important sampling of the generalized cross entropy method of source-load correlation, and adopts the generalized cross entropy (GCE) method to replace the parameter optimization process of the traditional CEIS method to iteratively optimize the IS-PDF. The GCE method does not rely on large sample approximation, and can achieve the original probability density estimation taking into account the correlation based on a small number of samples, and the obtained density estimation has good sparsity. The GCE method is used to directly perform non-parametric probability density estimation on the fault domain samples, which jumps out of the scope of parameter optimization of the traditional CEIS method and can avoid the derivation of complex parameter optimization formulas in the traditional CEIS method. The sparsity of the GCE probability model also makes the important sampling process simpler, which improves the efficiency of power grid reliability assessment taking into account source-load correlation.

[0006] A cross entropy method for power grid reliability assessment based on normal space vector optimization in the present invention comprises:

[0007] Step 1: Establish a sparse probability model (GCE model) for source-load correlation variables and initialize the relevant parameters of important sampling;

[0008] Step 2: Pre-sampling stage: extract system state samples according to the current important sampling function, perform system state analysis on each sample, and update and iterate the probability density distribution functions of the component state variables and source-load variables in the system state variables until the pre-sampling convergence conditions are met;

[0009] Step 3: In the main sampling stage, the system state samples are extracted according to the important sampling function finally obtained, and the power grid reliability index is calculated until the main sampling convergence condition is met.

[0010] The beneficial effects of the present invention are:

[0011] 1. In the present invention, the GCE probability model is used to perform probability modeling on the source-load correlation variables in the system variables, which ensures the sparsity of the probability model while considering the source-load correlation, and can effectively reduce the computational complexity of the power grid reliability assessment considering the source-load correlation.

[0012] 2. In some embodiments of the present invention, a generalized cross-entropy important sampling method is proposed, which performs sparse probability density estimation on the IS-PDF of correlation variables from the perspective of non-parametric density estimation. This is different from the traditional cross-entropy important sampling method which must perform parameter estimation (optimization disturbance), and breaks away from the limitation that the traditional CEIS method must perform parameter optimization. It can avoid the derivation of complex parameter optimization formulas in the traditional CEIS method. The obtained IS-PDF not only has good sparsity, making the extraction of fault samples more efficient, but also can further improve the convergence of the Monte Carlo simulation in the main simulation stage, thereby improving the efficiency of power grid reliability assessment considering source-load correlation. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The figure is an overall flow chart of power grid reliability assessment based on important sampling of generalized cross entropy method in an embodiment of the present invention.

[0014] Figure 2 Flow chart of the two-stage sampling method of the generalized cross entropy probability model in an embodiment of the present invention.

[0015] Figure 3 The figure is a flow chart of the generalized cross entropy importance sampling method in the pre-sampling stage of an embodiment of the present invention. DETAILED DESCRIPTION

[0016] The power grid reliability assessment method based on the source-load correlation generalized cross entropy method important sampling in this embodiment is basically as follows: Figure 1 As shown, the following steps are included:

[0017] S1. Establish a sparse probability model (GCE model) for source-load correlation variables and initialize relevant parameters of important sampling;

[0018] In S1, the parameters that need to be initialized are: the number of samples N for each pre-sampling, the quantile ρ, the smoothing coefficient α, the number of re-sampling samples Nr, the number of iterations k=0, and the main sampling convergence coefficient β. The number of samples N for each pre-sampling is related to the reliability level of the system and is generally set between 10,000 and 30,000; the quantile ρ is generally set to 0.01~0.1; the smoothing coefficient α is generally set to 0.01; the number of re-sampling samples Nr is generally set to 10,000, and the number of iterations k increases by k=k+1 as the number of iterations in the pre-sampling stage increases; the convergence coefficient β is generally set to 0.01~0.03; the important sampling function g(x) can be initialized using the probability density function f(x) of the actual system state variable, and the expression is as follows:

[0019]

[0020] In the formula, x d is the component state part of the system state variable x; c is the system state variable x c The source-load state part; u j is the original unavailability rate of the jth component; f(x c ) is the original GCE model for source-load correlation variables, M is the number of kernel functions in the GCE model, and p i is the weight of the i-th kernel function, X i is the mean vector of the i-th kernel function, and Σ is the covariance matrix of the i-th kernel function.

[0021] S2 pre-sampling stage, such as Figure 2 As shown, in this stage, the system state samples are extracted according to the current important sampling function, the system state analysis is performed on each sample extracted, and the probability density distribution functions of the component state variables and the source-load variables in the system state variables are updated respectively until the pre-sampling convergence conditions are met;

[0022] In S2, the system state analysis uses the optimal load reduction model based on DC power flow to calculate the system performance measure under each system state sample. When the system state is in the load reduction state, the system performance measure is the negative value of the optimal load reduction amount of the system in this state; when the system state is in the normal state, the system performance measure is the power supply margin of the system in this state, that is, the remaining power generation capacity margin of the available generator compared to the system load.

[0023] Specifically, in the kth pre-sampling iteration process, according to the important sampling function g k-1 (x) Extract N system status samples and perform system status analysis to obtain the system performance measurement of each sample.

[0024] System state variables include independent variables and correlation variables. In power grid reliability assessment, it is generally assumed that each component is independent of each other, that is, the component state variables are independent variables. Power system components are described by two states: normal / faulty, that is, the component state variables are binary variables. The sampling method of component state is: for the jth component, a uniformly distributed random number between 0 and 1 is generated. If the random number is less than the unavailability rate v of the corresponding component, k-1,j , the component is considered to be in a faulty state. Otherwise it is in normal working condition.

[0025] The source-load state variable is a relevant variable, and its sample is obtained from the GCE probability model g k-1 (x c ) is used as Figure 1 The two-stage sampling method shown is used for extraction. The details of the two-stage sampling method are as follows:

[0026] The interval [0,1] is divided into M segments, and the length of each segment corresponds to the probability {p1,......p M}, corresponding to the weights of each kernel function. A random number r is drawn from a uniform distribution in the interval [0,1]. If the mth segment contains r, that is, p1+...+p m-1 ≤r≤p1+...+p m , then the mth kernel function is selected.

[0027] According to the mth kernel function, a source-load state sample x is randomly selected. c .

[0028] Then, the system performance measures of the N extracted system status samples are arranged in ascending order, and ρN elite samples with the smallest system performance measures are selected from the N samples according to the ratio of quantile ρ.

[0029] In the kth pre-sampling iteration, the unavailability rate of the component is updated according to the ρN elite samples. The specific expression is as follows:

[0030]

[0031] Where H(x) is the indicator function of the system state variable x. If the sample x i Belong to the elite sample, then H(x i )=1, otherwise H(x i )=0;v k,j is the unavailability rate of component j after the kth iteration update, including generators and transmission lines, and its initial value v 0,j =μ 0,j ; W k-1 (x i ) is the likelihood ratio of the i-th sample, and the specific expression is as follows:

[0032]

[0033] Among them, f(x i ) is the system state sample x i The original probability density function value of g k-1 (x i ) is the system state sample x i The probability density value of the importance sampling function.

[0034] In this example, a smoothing coefficient α is also substituted to smooth the update of the unavailability rate of the component to prevent the unavailability rate of the component from being 0 or 1. The specific expression of the smoothing process is as follows:

[0035] v k,j =(1-α)v k,j +αv k-1,j

[0036] In this embodiment, resampling is also performed based on the ρN elite samples to obtain Nr resampled samples. The resampling method is as follows:

[0037] The likelihood ratio W of ρN elite samples k-1 (x i ) as the weight of each sample, and normalize the weight so that the sum of the weights of all elite samples is 1.

[0038] The elite samples are resampled according to their weights to obtain Nr new samples.

[0039] Then, the GCE probability model is used to calculate the correlation variable x in Nr new samples. c Probability density estimation is performed, and the obtained GCE probability model g is used as the important sampling function g of the correlation variable obtained by the kth pre-sampling iteration k (x c ).

[0040] GCE probability density estimation can use uniform distribution as prior probability density p, Pearson-χ2 measure as cross entropy distance measure D, and generalized moment constraint as constraint set. Then the posterior probability g is optimized with the goal of minimizing the distance D(g,p). In the GCE algorithm, the posterior density function g to be estimated must satisfy the following m (m is a finite integer) linear integral constraint set:

[0041]

[0042] In the formula, A set of linearly independent smooth functions is selected, called kernel functions, which are usually based on the sample X i is the Gaussian function of the mean vector; It means to find the expectation under the probability density function g; Indicates that the true objective function π is K i (X i ) to find the mathematical expectation. However, since the true objective function π is unknown, κ i It is not possible to directly solve the expectation To calculate. Since {X1,...,X m} is a set of independent and identically distributed samples from the true target function π, then theoretically each sample X i should be independent of all other samples {X i}, j≠i, so the cross-validation principle can be used to i Make the following unbiased estimate:

[0043]

[0044] κ i It is called the sample empirical moment. It can be seen that in the GCE density estimation algorithm, the constraint set This realizes the connection between the estimated posterior density function g and the system information reflecting the true target function π. In practical applications, we set K0≡0, κ0=1 to simplify the above generalized moment constraint set That is, the normalization condition of the posterior probability density g is guaranteed by taking the zero-order constraint (i.e. the corresponding constraint when i=0) as a strict equation at all times.

[0045] The above implements the prior density function p, the cross entropy distance D(g,p) and the constraint set After the selection of , the GCE optimization model of the posterior density function g can be written as follows:

[0046]

[0047] ∫g(x)dx=1

[0048] Based on the Lagrangian dual theory, the dual problem of the above functional extreme value problem is constructed to solve the posterior density function g. For this purpose, the following Lagrangian function is defined:

[0049]

[0050] At this point, the dual problem can be written as follows:

[0051]

[0052] s.tλ≥0

[0053] Solving inf L(g;λ,λ0) using the Euler-Lagrange formula yields:

[0054]

[0055] because The second derivative of but There is a unique inverse in the sample space. Therefore, the expression of the solution to the GCE optimization problem is as follows:

[0056] Ψ'=φ' -1

[0057] Substituting the above formula into the dual problem, we can get:

[0058]

[0059] stλ≥0

[0060] where λ=[λ1,...,λ m ] T .

[0061] The Lagrange multiplier λ in the above equation is [λ1,...,λ m ] T and λ0 can be obtained by the following quadratic programming problem (QPP):

[0062]

[0063] subject to:λ≥0

[0064] The elements of matrix C are:

[0065]

[0066] κ=[κ1,...,κ m ] T

[0067] However, the above QPP problem does not constrain λ0. When λ0<0, the obtained g(x) will be an invalid mixed density model. In fact, λ0≥0 can be obtained by using the kernel function {K i (X i )} Select a suitable bandwidth σ to achieve:

[0068]

[0069] λ0=0 is a necessary condition for the QPP problem to have an optimal solution. The gradient of the QPP problem with respect to λ0 is 0, so λ0=1-cT λ, when λ0=0, then c T λ=1, then the QPP problem evolves into the following equation with respect to the bandwidth σ and the Lagrange multiplier λ=[λ1,...,λ m ]'s implicit root-finding problem:

[0070]

[0071] By solving the above optimization problem, we can finally get the posterior density function g(x), which realizes the correlation variable x in Nr resampled samples. c Perform probability density estimation and obtain the important sampling function g of the correlation variable k (x c ).

[0072] Then, the important sampling functions of the independent variables and the correlation variables are combined to obtain the updated important sampling function, which is expressed as follows:

[0073]

[0074] When the load reduction of the elite samples with the smallest system performance measure ρN is greater than 0, that is, when the system is in a fault state under the elite sample state, it is considered that the pre-sampling stage has reached the convergence condition, and the final important sampling function g is output K (x); otherwise, continue the pre-sampling iteration, the number of iterations k=k+1, update the important sampling functions of the independent variables and the correlation variables, so that the important sampling functions continue to approach the fault domain.

[0075] In the S3 main sampling stage, system state samples are extracted according to the finally obtained important sampling function, and the power grid reliability index is calculated until the main sampling convergence condition is met.

[0076] In S3, the important sampling function g finally obtained in the pre-sampling stage is K (x) Extract system status samples. The sampling method of component status is as follows: for the jth component, generate a random number uniformly distributed between 0 and 1. If the random number is less than the unavailability rate v of the corresponding component, k-1,j , the component is considered to be in a faulty state. Otherwise it is in normal working condition.

[0077] The sample of correlated variables is obtained from the importance sampling function g K (x c ) is extracted using a two-stage sampling method, and each system state sample is analyzed and the reliability indicators LOLP and EENS are calculated. The calculation expression of the reliability index is as follows:

[0078]

[0079] In the formula, C s (x i ) is the system state x i The load reduction under the system state x i In normal state, the load reduction is 0; N s The number of samples drawn in the main sampling phase; W(x i )=f(x i ) / g K (x i ) is the likelihood ratio of the ith sample.

[0080] The variance coefficient of the reliability index EENS is used as the convergence criterion in the main sampling stage. When the variance coefficient of EENS is less than the convergence coefficient β, the reliability indexes LOLP and EENS are output; otherwise, the important sampling function g is continued. K (x i ) Extract system status samples and calculate reliability indicators.

[0081] The following is a further detailed description through specific implementation methods:

[0082] In order to effectively take into account the source-load correlation, nodes 12, 36 and 59 in the MRTS96 system containing five regional loads are connected to three wind farms with an installed capacity of 300MW each, increasing the system peak load level by 10% to facilitate simulation calculations.

[0083] The reliability evaluation results of the IEEE-MRTS96 system obtained by different methods are shown in the following table:

[0084] Table 1 IEEE-MRTS96 system reliability evaluation results obtained by different methods

[0085]

[0086] In the present invention, a power grid reliability assessment method based on the importance sampling of the generalized cross entropy method of source-load correlation is proposed, which adopts the GCE probability model to model the correlation probability of source-load variables, and takes into account the influence of the correlation and uncertainty of source-load variables on power grid reliability. In the context of vigorous grid connection of new energy and large-scale use of electric vehicles, the correlation and uncertainty of source-load variables in the power grid are factors that cannot be ignored in power grid reliability assessment. The present invention can ensure the sparsity of the probability model while considering the source-load correlation, and can effectively reduce the computational complexity of power grid reliability assessment considering the source-load correlation.

[0087] In addition, a generalized cross entropy important sampling method is proposed to estimate the sparse probability density of the IS-PDF of the correlation variable from the perspective of non-parametric density estimation. The obtained IS-PDF not only has good sparsity, but also can further improve the convergence of Monte Carlo simulation in the main simulation stage, thereby improving the efficiency of power grid reliability assessment considering source-load correlation. For the IEEE-MRTS96 system, the traditional CEIS method is not sufficiently optimized for the cross entropy of a large number of weight parameters in KDE, resulting in poor reliability assessment accuracy, and the EENS relative error reaches 10.1%. In contrast, thanks to the density estimation characteristics of the small sample approximation of the GCE method, the GCE important sampling method can achieve non-parametric estimation of the IS-PDF under good conditions, and thus can achieve accurate reliability index estimation. The relative errors of LOLP and EENS are only 3% and 2.1%, which further verifies the small sample advantage of the non-parametric estimation of the IS-PDF in the GCE-IS method. In addition, due to the good sparsity of IS-PDF under the GCE importance sampling method, the extraction of fault samples is more efficient. The GCE importance sampling method reduces 60.1% of sample extraction and 63.4% of computational time in the main simulation phase compared with the traditional CEIS method. This verifies that the GCE importance sampling method can accurately and efficiently perform important sampling of source-load correlation variables, achieving further acceleration of reliability assessment.

[0088] In summary, the advantages and contributions of the present invention are to provide an efficient, fast and accurate reliability assessment method for power systems with increasingly complex source-load correlation and uncertainty. Through the GCE model, the impact of the correlation and uncertainty of source-load variables on the reliability of the power grid is characterized, while ensuring the sparsity of the probability model. The generalized cross entropy important sampling method performs sparse probability density estimation on the IS-PDF of the correlation variable from the perspective of non-parametric density estimation, breaking away from the limitation that the traditional CEIS method must perform parameter optimization. The obtained IS-PDF not only has good sparsity, but also can further improve the convergence of the Monte Carlo simulation in the main simulation stage, thereby improving the efficiency of power grid reliability assessment considering source-load correlation.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A cross entropy method for power grid reliability assessment based on normal space vector optimization in the present invention comprises: Step 1: Establish a sparse probability model GCE for source-load correlation variables and initialize relevant parameters of important sampling; Step 2: Pre-sampling stage: extract system state samples according to the current important sampling function, perform system state analysis on each sample, and update and iterate the probability density distribution functions of the component state variables and source-load variables in the system state variables until the pre-sampling convergence conditions are met; Step 3: In the main sampling stage, the system state samples are extracted according to the important sampling function finally obtained, and the power grid reliability index is calculated until the main sampling convergence condition is met.

2. The method according to claim 1, characterized in that In step 1, a GCE model describing wind speed-load variables is established; The initialization parameters include: the number of samples N for each pre-sampling, the quantile ρ, the smoothing coefficient α, the number of iterations k, the number of re-sampling samples Nr, and the initial important sampling function g0(x) uses the probability density function f(x) of the actual system state variable, which is expressed as follows: In the formula, x d is the component state part of the system state variable x; c is the system state variable x c The source-load state part; u j is the original unavailability rate of the jth component; f(x c ) is the original GCE model for source-load correlation variables, M is the number of kernel functions in the GCE model, and p i is the weight of the i-th kernel function, X i is the mean vector of the i-th kernel function, and Σ is the covariance matrix of the i-th kernel function.

3. The method according to claim 2, characterized in that In step 2, the component status samples and the wind speed-load status samples are sampled independently; The power system component status samples are extracted according to the normal / faulty states, and the probability of extracting a component in a faulty state is equal to its unavailability rate; Wind speed-load state samples are drawn according to the two-stage sampling method of the GCE model, and the probability of drawing each wind speed-load state obeys the GCE probability model.

4. The method according to claim 2, characterized in that: In step 2, the optimal load reduction model based on DC power flow is used to analyze the system status of N samples and calculate the system performance measure; When the system is in the load shedding state, the system performance measure is the negative value of the optimal load shedding amount of the system in this state; When the system state is in normal condition, the system performance measure is the power supply margin of the system in this state, that is, the remaining power generation capacity margin of the available generators compared to the system load; Select the elite sample with the smallest system performance measure from N samples in proportion to the quantile ρ.

5. The method according to claim 4, characterized in that In the kth pre-sampling iteration, the unavailability rate of the component is updated according to the ρN elite samples. The specific expression is as follows: Where H(x) is the indicator function of the system state variable x. If the sample x i If it belongs to the elite sample, then H(x i )=1, otherwise H(x i )=0;v k,j is the unavailability rate of component j after the kth iteration update, and its initial value v 0,j =μ 0,j ; W k-1 (x i ) is the likelihood ratio of the i-th sample, and the specific expression is as follows: Among them, f(x i ) is the system state sample x i The original probability density function value; gk-1(xi) is the system state sample x i The probability density value of the importance sampling function.

6. The method according to claim 5, characterized in that The smoothing coefficient α is also substituted to smooth the update of the unavailability rate of the component as follows: v k,j =(1-α)v k,j +av k-1,j 。 7. The method according to claim 5, characterized in that Resample ρN elite samples to get N r resampled samples; Using the GCE probability model N r The probability density of the correlation variables in the resampled samples is estimated. The GCE probability density estimation uses the uniform distribution as the prior probability density p and the Pearson-χ 2 The measure is the cross entropy distance measure D, with generalized moment constraints as the constraint set Then the posterior probability g is optimized with the goal of minimizing the distance D(g,p).

8. The method according to claim 7, characterized in that In the kth pre-sampling iteration, the important sampling functions of the independent variables and the correlation variables are combined to obtain the updated important sampling function g k (x), the expression is as follows:

9. The method according to claim 7, characterized in that: In step 2, when the load reduction of the elite samples with the smallest system performance measure of ρN is greater than 0, that is, when the system is in a fault state under the elite sample state, it is considered that the pre-sampling stage has reached the convergence condition, and the final important sampling function g is output. K (x); otherwise, continue the pre-sampling iteration, the number of iterations k=k+1, update the important sampling functions of the independent variables and the correlation variables, so that the important sampling functions continue to approach the fault domain.

10. The method according to claim 2, characterized in that In step 3, the important sampling function g finally obtained in the pre-sampling stage is K (x) extracting system status samples; The sampling method of component status is as follows: for the jth component, a uniformly distributed random number between 0 and 1 is generated. If the random number is less than the unavailability rate v of the corresponding component k-1,j , the component is considered to be in a faulty state. Otherwise it is in normal working condition. The sample of correlated variables is obtained from the importance sampling function g K (x c ) is extracted using a two-stage sampling method, and each system state sample is analyzed and the reliability indicators LOLP and EENS are calculated. The calculation expression of the reliability index is as follows: In the formula, C s (x i ) is the system state x i The load reduction under the system state x i In normal state, the load reduction is 0; N s The number of samples drawn in the main sampling stage; W(xi) = f(xi) / g K (xi) is the likelihood ratio of the i-th sample; The variance coefficient of the reliability index EENS is used as the convergence criterion. When the variance coefficient of EENS is less than the set threshold, the reliability indexes LOLP and EENS are output. Otherwise, the important sampling function g is used to continue. K (x) Extract system status samples and calculate reliability indicators.

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