A method and device for evaluating reliability of power system

Abstract

The present application discloses a method for evaluating the reliability of an electric power system in electric power system technology, comprising the following steps: obtaining the reliability parameters of each component of the electric power system, historical data of load and renewable energy power generation output, and constructing the original probability distribution of all random variables in the electric power system; obtaining the importance distribution and pre-sampling reliability index and variance of each random variable through the first stage pre-sampling iteration of the importance sampling method; obtaining the formal reliability index and variance through the second stage of the importance sampling method using the importance distribution for formal sampling; obtaining the final reliability index through weighted averaging of the pre-sampling reliability index and variance and the formal reliability index and variance. The present application solves the problem of waste of computing power of the pre-sampling samples in the first stage of importance sampling, and performs weighted summation on the index estimation values ​​obtained in the pre-sampling stage and the formal sampling stage, thereby improving the accuracy of the reliability index estimation.

Description

Technical Field

[0001] The present application relates to the technical field of power system reliability, and in particular to a power system reliability assessment method. Background Art

[0002] The proportion of renewable energy generation represented by wind and solar energy in new power systems continues to grow, which has led to the efficiency of existing power system reliability assessment methods, such as analytical methods and simulation methods, being reduced to varying degrees. The main reason for the decline in the efficiency of analytical methods is that after the large-scale access of renewable energy generation, the number of uncertain variables in the power system increases, resulting in a geometric increase in the number of states that need to be enumerated, which is prone to the curse of dimensionality, and it lacks a method to deal with the complex correlation structure between uncertain variables. The reason for the decline in the efficiency of simulation methods is that the increase in power generation resources in the system has significantly reduced the absolute value of the probability of power outage in the system, and the simulation method is extremely sensitive to this, resulting in a significant increase in the number of samples when estimating reliability indicators. Therefore, the application of both methods in modern power systems faces different bottlenecks.

[0003] In comparison, the simulation method based on the Monte Carlo sampling idea is more intuitive and convenient in dealing with the power flow constraints in the reliability index estimation process. In recent years, there have been many research results on improving the calculation accuracy and efficiency of this type of method, and the main ideas are focused on how to reduce its sample size. Among them, the method with more outstanding effects is the importance sampling method, but there are still problems such as insufficient sample uniformity and failure to fully utilize the sample status evaluation results in the pre-sampling stage, so its calculation efficiency still has room for improvement. Summary of the invention

[0004] The purpose of the present application is to provide a power system reliability assessment method to solve the problems in the prior art that Latin hypercube sampling and non-parametric importance sampling cannot be directly combined and that samples in the pre-sampling stage cannot be effectively utilized.

[0005] In order to solve the above technical problems, this application is implemented by adopting the following technical solutions:

[0006] In a first aspect, a method for evaluating the reliability of a power system comprises the following steps:

[0007] Obtain the reliability parameters of each component of the power system, historical data on load and renewable energy power generation output, and construct the original probability distribution of all random variables in the power system;

[0008] Through the first stage iteration of the importance sampling method, the sampling reliability index and variance of the importance distribution of each random variable are obtained;

[0009] The formal reliability index and variance are obtained by iterating the second stage of importance sampling method and using importance distribution;

[0010] The final reliability index is obtained by weighted averaging the sample reliability index, variance and the formal reliability index, variance.

[0011] A further solution of the present application is to fit the original probability distribution function of the discrete variables and the original probability density function of the continuous variables through the reliability parameters of the components of the power system, the historical data of the load and the output of the renewable energy power generation; and the original probability density function of the continuous variables;

[0012] The discrete variables include: vector x composed of the states of each conventional unit in the system gu ; The vector x composed of the states of each transmission line in the system ln ;

[0013] The continuous variables include: the vector P composed of the maximum available power of each wind farm in the system wf ; The net load vector L of each load node in the system net .

[0014] In a further embodiment, the discrete variables include functions under the conventional unit state and functions under the state of each transmission line;

[0015] The functions under normal unit status are as follows;

[0016]

[0017] Among them, x g is the state of the g-th conventional unit, n gu is the total number of conventional units, θ g is the failure outage rate of the g-th conventional unit;

[0018] The function is obtained under each transmission line state;

[0019]

[0020] Among them, x l is the state of the lth line, n ln is the total number of lines, θ l is the failure outage rate of the lth line;

[0021] The original probability density function is calculated by calculating the node net load L net , which is expressed as

[0022] L net,b =L b -P pv ,b (28)

[0023] Among them, b is the subscript of the node, L b is the load demand of the bth node, Ppv,b is the output of the photovoltaic power station connected to the bth node, and then obtained by using the GMM method;

[0024]

[0025] Among them, n GM Represents the number of components of GMM, ω k , μ k and Σ k Represent the weight, expected value vector and covariance matrix of the kth component respectively; Represents the multidimensional normal distribution function corresponding to the kth component.

[0026] A further solution is to select basic functions for the original probability distribution function of the importance of the discrete variables and the original importance probability density function of the continuous variables, and establish a method for updating the parameters of the importance probability function using the cross entropy concept.

[0027] In a further embodiment, the method for updating the importance probability function parameters comprises the following steps:

[0028] Select the basic form of the importance probability distribution function, for discrete variables x gu 、x ln , select the same function form as the original distribution, that is:

[0029]

[0030] Among them, η g and η l are the parameters that need to be optimized for the g-th thermal power unit and the l-th transmission line respectively;

[0031] For the continuous variable P wf and L net , GMM is selected as the basic form of the joint importance probability density function, that is:

[0032]

[0033] in, and is the unknown parameter of the kth normally distributed component of the joint importance probability density function, k = 1, ..., n GM ;

[0034] Define the system state evaluation function S(x) and the system power shortage index function I(x), where x is the vector synthesized by all discrete and continuous variables in the system, that is:

[0035] x=[x gu ,x ln ,P wf ,Lnet ] (33)

[0036] The definition of S(x) needs to rely on the objective function value of the minimum load shedding model. The minimum load shedding model based on DC power flow is often used. The objective function expression of this model is:

[0037]

[0038] Among them, L sh is the sum of the load shedding of all nodes in the system, L sh,b is the load shedding amount at node b, n bus is the total number of nodes in the system;

[0039] Using the objective function L sh S(x) can be defined as:

[0040]

[0041] Among them, P g,max is the installed capacity of the g-th unit, P w is the output of the w-th wind farm in sample x, L net,b is the load demand of the bth node in sample x;

[0042] Using the defined S(x), we can further define I(x);

[0043]

[0044] Among them, S th is the threshold value of power shortage;

[0045] Use the original distribution to sample N pre Samples are substituted into the following formula to obtain the estimated values ​​of the unknown parameters in equations (4)-(6); the parameter update formula of the discrete variable importance probability distribution function is as follows:

[0046]

[0047] Among them, x s is the sth sample obtained by sampling, x g,s is x s The state variable value of the g-th unit, x l,s is x s The value of the state variable of the lth line in ;

[0048] The parameter update formula of the importance probability density function of continuous variables is as follows:

[0049]

[0050] Among them, Pwf,s and L net,s The samples x are s The output vector P of the wind farm wf The value of and node net load vector L net The value of r k,s For sample x s , the calculation formula is as follows:

[0051]

[0052] A further solution also includes introducing a pre-sampling iterative process, using Latin hypercube sampling to obtain a sample set in each round of iteration, and iteratively optimizing and updating the parameters of the importance probability function based on this, using the sample set to estimate the system reliability index, and saving the index value and the corresponding index accuracy.

[0053] In a further solution, the sampling method for discrete variables and continuous variables is as follows:

[0054] In the i-th round of iterative sampling, the importance probability distribution function obtained in the i-1th round of iteration is used to generate samples; therefore, first, Separate the corresponding standard deviation parameter vector And the linear correlation coefficient matrix

[0055]

[0056] Where diag(·) is a vector expansion function that can expand a vector into a diagonal matrix with the vector elements as diagonal elements. -1 When acting on a matrix, it represents the inversion of the matrix;

[0057] According to the Latin hypercube sampling method, all discrete variables x gu and x ln Sample N pre Second, we get the sample matrix X of discrete variables. dv , a total of N pre Columns, each column is a sample, and the number of rows is (n gu +n ln );

[0058] According to the Latin hypercube sampling method, the continuous variable P wf and L net The joint distribution function sampling N pre times; where the joint distribution is a GMM function, and the number of samples sampled for each component is allocated according to the weight of each GMM component, that is, the kth component needs to be sampled Second-rate;

[0059] For the kth component, use The information contained in the construction (n wf +n bus ) continuous variables marginal importance probability density function, that is:

[0060]

[0061] In the formula, x e represents the e-th variable in the random variables of wind farm output and node net load, e=1,…,(n wf +n bus ), Represents x in the kth GMM component e The corresponding marginal one-dimensional normal importance probability density function;

[0062] Then, using the obtained marginal distribution Yes(n wf +n bus ) continuous variables are sampled separately samples; specifically, for the e-th variable, the sampling process is as follows:

[0063]

[0064] Among them, X ke The e-th variable is sampled using the k-th component of GMM samples, P is a row vector consisting of a sequence of consecutive positive integers. The order is shuffled, ε is a random number vector with the same dimension as P, each element of which is uniformly distributed on the interval (0,1) and independent of each other, Φ ke -1 (·)represent The corresponding inverse of the cumulative distribution function;

[0065] When (n wf +n bus After all continuous variables are sampled, all X ke Combined into sample matrix X k ,Right now:

[0066]

[0067] in,(·) T is the transposition operator;

[0068] Find X k The correlation coefficient matrix between rows ρ k0 , and for ρ k0 and Perform Cholesky decomposition to obtain the corresponding auxiliary matrices Z0 and Z k, as shown below;

[0069]

[0070] Use Z0 and Z k Construct the auxiliary sorting matrix Y:

[0071] Y=Z k Z0 -1 X k (49)

[0072] Adjust X k The order of the elements in each row of X is consistent with the order of the elements in the corresponding row of matrix Y, so that k Carry out correlation control, so that the correlation coefficient matrix becomes

[0073] Finally, when all components of GMM are sampled, X k Combined into a complete N pre The matrix X of samples cv :

[0074]

[0075] Among them, X cv P is a continuous variable wf and L net N pre A matrix consisting of samples;

[0076] X cv With X dv Combined into a complete sample matrix X, that is

[0077]

[0078] For each sample, calculate the corresponding S(x) value according to formula (35) and sort them from small to large to obtain {S[1],…,S[N pre ]}, extract the pre ) bit value S[α·N pre ]; where α is the proportion of samples in the power-off state, which can be 0.05 or 0.1;

[0079] Then, we judge S[α·N pre ]≤0; if so, then the proportion of samples that can put the system in a power-off state among the samples obtained by sampling the current importance probability density function has reached α, and let S in formula (36) th =0; if >0, let S in equation (36) th =S[α·N pre ]; then S thSubstitute into formula (36) and calculate I(x) for all samples;

[0080] According to the calculated I(x) and S(x) values, the reliability index of the system is estimated; the index includes the probability of power shortage and the expected value of power shortage, and the calculation formula is as follows:

[0081]

[0082] Among them, γ LOLP,i and γ EPNS,i are the LOLP and EPNS indicators estimated using the samples of the i-th iteration; Q i (x s ) is the sample x in the i-th iteration s The likelihood ratio function of is expressed as:

[0083]

[0084] From formula (15), we can see that when calculating the likelihood ratio at the i-th iteration, the importance probability distribution function in the i-1th round is used as the denominator;

[0085] The variance of LOLP and EPNS indicators estimated by formula (13) and formula (14) is used to reflect the indicator accuracy. The calculation formula is as follows:

[0086]

[0087] Among them, V LOLP,i and V EPNS,i They are γ LOLP,i and γ EPNS,i The corresponding variance;

[0088] Among them, if S th =0, the pre-sampling iteration is terminated and the next step is executed; otherwise, the parameters of the importance probability distribution function are updated according to formulas (57)-(59), and the sample is reprocessed when returning to the i-th round of iterative sampling, and the sample is resampled until the iteration termination condition is met;

[0089] The iterative update formula for the undetermined parameters of discrete variables is as follows:

[0090]

[0091] The iterative update formula for the undetermined parameters of continuous variables is as follows:

[0092]

[0093]

[0094] A further solution is to formally sample the importance probability function obtained after the pre-sampling is completed, and combine the index value and corresponding accuracy obtained in each round of pre-sampling iteration to comprehensively evaluate the system reliability index.

[0095] In a further embodiment, the Latin hypercube sampling method samples the importance probability distribution function N at the end of the pre-sampling iteration. main Next, use these samples to estimate the values ​​of LOLP and EPNS indicators:

[0096]

[0097] Among them, γ LOLP,main and γ EPNS,main They are the LOLP and EPNS index values ​​estimated using the formal sampling samples;

[0098] The variance of LOLP and EPNS indicators obtained according to formula (18) and formula (19) reflects the indicator accuracy. The calculation formula is as follows:

[0099]

[0100] Among them, V LOLP,main and V EPNS,main They are γ LOLP,main and γ EPNS,main The corresponding variance;

[0101] Then, the index value and variance estimated by the pre-sampling sample and the index value and variance estimated by the formal sampling sample are weighted averaged to obtain a high-precision reliability index. The formula is as follows:

[0102]

[0103] Among them, γ LOLP and γ EPNS is the high-precision LOLP and EPNS index value obtained by mixing the pre-sampling and formal sampling index estimates; β LOLP and β EPNS Respectively reflect γ LOLP and γ EPNS Coefficient of variance of precision.

[0104] In a second aspect, a computer device comprises

[0105] Memory, for storing computer programs / instructions;

[0106] A processor is used to execute the computer program / instructions to implement the steps of the above-mentioned power system reliability assessment method.

[0107] Compared with the prior art, the present invention has the following beneficial effects:

[0108] This application solves the problem of difficulty in controlling sample correlation when Latin hypercube sampling is combined with the importance sampling method based on the GMM model, realizes the organic combination of the two methods, and solves the problem of waste of sample computing power in the pre-sampling stage of importance sampling. This method can concentrate system state samples in important areas that contribute greatly to reliability indicators, reduce sample duplication, and perform weighted summation of the indicator estimates obtained in the pre-sampling stage and the formal sampling stage, further improving the accuracy of reliability indicator estimation, and thus can significantly improve the efficiency of reliability assessment of modern power systems containing multiple renewable energy plants. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 This is a schematic diagram of the process of an embodiment of the present application;

[0110] Figure 2 This is a schematic diagram of an algorithm of an embodiment of the present application;

[0111] Figure 3 This is a schematic diagram of a new power system structure designed based on the IEEE RTS-79 test system;

[0112] Figure 4 The original marginal distribution fitting results of three wind farms based on the GMM model; DETAILED DESCRIPTION

[0113] It should be noted that: the technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0114] The term "and / or" is only a description of the association relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " generally indicates that the related objects are in an "or" relationship.

[0115] Embodiment 1

[0116] Reference Figure 1 , this embodiment discloses a method for evaluating the reliability of a power system, which includes the following steps:

[0117] Obtain the reliability parameters of each component of the power system, historical data on load and renewable energy power generation output, and construct the original probability distribution of all random variables in the power system;

[0118] Through the first stage iteration of the importance sampling method, the sampling reliability index and variance of the importance distribution of each random variable are obtained;

[0119] The formal reliability index and variance are obtained by iterating the second stage of importance sampling method and using importance distribution;

[0120] The final reliability index is obtained by weighted averaging the sample reliability index, variance and the formal reliability index, variance.

[0121] In some embodiments, Figures 1 to 4 As shown in FIG. 1 , a method for evaluating the reliability of a power system is provided, and an algorithm for evaluating the reliability of a power system containing renewable energy can be used to fully utilize the importance sampling pre-sampling samples. The basic implementation process is as follows

[0122] S1, input the reliability parameters of each component of the power system, historical data of load and renewable energy power generation output, fit the original probability distribution function of discrete variables, and the original probability density function of continuous variables;

[0123] S2, select basic functions for the importance probability distribution function of discrete variables and the importance probability density function of continuous variables, and use the cross entropy idea to establish a method for updating the parameters of the importance probability function;

[0124] S3, introduces the pre-sampling iteration process, uses Latin hypercube sampling to obtain a sample set in each iteration, and iteratively optimizes and updates the parameters of the importance probability function based on this, and uses the sample set to estimate the system reliability index, and saves the index value and the corresponding index accuracy;

[0125] S4, formally sample the importance probability function obtained after the pre-sampling is completed, and combine the index value and corresponding accuracy obtained in each round of pre-sampling iteration to comprehensively evaluate the system reliability index.

[0126] Reference Figure 2 ,

[0127] The discrete variables of the power system in step S1 include: the vector x composed of the states of each conventional unit in the system gu ; The vector x composed of the states of each transmission line in the system ln .

[0128] The continuous variables of the power system include: the vector P composed of the maximum available power of each wind farm in the system wf ; The net load vector L of each load node in the system net .

[0129] Step S11, fitting x with a two-state model gu The original probability distribution function of :

[0130]

[0131] Among them, x g is the state of the g-th conventional unit, n gu is the total number of conventional units, θ g is the failure outage rate of the g-th conventional unit. Because each conventional unit adopts a two-state model, namely normal operation and failure outage, corresponding to x g Take 1 and 0, so x g It is a 0-1 variable.

[0132] Step S12, fitting x using a two-state model ln The original probability distribution function of :

[0133]

[0134] Among them, x l is the state of the lth line. ln is the total number of lines, θ l is the failure outage rate of the lth line.

[0135] Step S13: Use historical data to fit the wind farm output vector P wf and node net load vector L net The original joint probability density function of the node net load L net The expression is as follows:

[0136] L net,b =L b -P pv ,b (3)

[0137] Where b is the subscript of the node. b is the load demand of the bth node, P pv,b is the output of the photovoltaic power station connected to the bth node.

[0138] Then, the GMM method is used to fit the joint probability density function expression of all wind farm outputs and all node net loads:

[0139]

[0140] Among them, n GM Represents the number of components of GMM. k , μ k and Σ k Represent the weight, expected value vector and covariance matrix of the kth component respectively. These three parameters can be estimated using historical data samples, Akaike Information Criterion and EM algorithm. Represents the multidimensional normal distribution function corresponding to the kth component.

[0141] Further, the step S2 comprises:

[0142] Step S21, select the basic form of the importance probability distribution function, for the discrete variable x gu 、x ln , select the same function form as the original distribution, that is:

[0143]

[0144]

[0145] Among them, η g and η l are the parameters that need to be optimized for the g-th thermal power unit and the l-th transmission line respectively.

[0146] For the continuous variable P wf and L net , GMM is selected as the basic form of the joint importance probability density function, that is:

[0147]

[0148] in, and is the unknown parameter of the kth normally distributed component of the joint importance probability density function, k = 1, ..., n GM .

[0149] Step S22, define the system state evaluation function S(x) and the system power shortage index function I(x), where x is a vector synthesized by all discrete and continuous variables in the system, that is:

[0150] x=[x gu ,x ln ,P wf ,L net ] (8)

[0151] The definition of S(x) needs to rely on the objective function value of the minimum load shedding model, and its constraints include power flow constraints, node voltage constraints, transmission line transmission power constraints, etc. In power system planning and reliability analysis, the minimum load shedding model based on DC power flow is often used. The objective function expression of this model is:

[0152]

[0153] Among them, L sh is the sum of the load shedding of all nodes in the system, L sh,b is the load shedding amount at node b, n bus is the total number of nodes in the system.

[0154] Using the objective function L sh S(x) can be defined as:

[0155]

[0156] Among them, P g,max is the installed capacity of the g-th unit, P w is the output of the w-th wind farm in sample x, L net,b is the load demand of the bth node in sample x.

[0157] Using the defined S(x), we can further define I(x).

[0158]

[0159] Among them, S th It is the threshold value of power shortage, which is usually 0.

[0160] Step S23, sampling N using the original distribution pre Substitute samples into the following formula to obtain the estimated values ​​of the unknown parameters in equations (4)-(6).

[0161] The parameter update formula of the discrete variable importance probability distribution function is as follows:

[0162]

[0163] Among them, x s is the sth sample obtained by sampling, x g,s is x s The state variable value of the g-th unit, x l,s is x s The value of the state variable of the lth line in .

[0164] The parameter update formula of the importance probability density function of continuous variables is as follows:

[0165]

[0166] Among them, P wf,s and L net,s The samples x are s The output vector P of the wind farm wf The value of and node net load vector L net The value of r k,s For sample x s The probability of the kth normal distribution component from the original probability density function is calculated as follows:

[0167]

[0168] Further, the step S3 comprises:

[0169] Step S31, the calculation formula for the pending parameters of the importance probability distribution established in step S2 is estimated directly using the samples obtained by sampling the original distribution. Among these samples, the number of system power outage samples is extremely small and the proportion is unstable, which leads to unsatisfactory estimation of the pending parameters. Therefore, a pre-sampling process for iteratively updating the pending parameters is designed to ensure the optimization effect of the pending parameters.

[0170] The sampling method in each round of pre-sampling iteration uses the Latin hypercube sampling method. The sampling process of this method for discrete variables and continuous variables is as follows.

[0171] In the i-th round of iterative sampling, the importance probability distribution function obtained in the i-1th round of iteration is used to generate samples. Separate the corresponding standard deviation parameter vector And the linear correlation coefficient matrix

[0172]

[0173] Where diag(·) is a vector expansion function that can expand a vector into a diagonal matrix with the vector elements as diagonal elements. (·) -1 When acting on a matrix, it represents the inversion of the matrix.

[0174] Secondly, Latin hypercube sampling is used to sample all discrete variables x gu and x ln Sample N pre Second, we get the sample matrix X of discrete variables. dv , a total of N pre Columns, each column is a sample, and the number of rows is (n gu +n ln ).

[0175] Then, Latin hypercube sampling was used to sample the continuous variable P wf and L net The joint distribution function sampling N pre times. Among them, the joint distribution is the GMM function. According to the weight distribution of each component of GMM, the number of samples sampled for each component is, that is, the kth component needs to be sampled Initialize k=1.

[0176] For the kth component, use The information contained in the construction (n wf +n bus ) continuous variables marginal importance probability density function (all are one-dimensional normal distribution functions), that is:

[0177]

[0178] In the formula, x e represents the e-th variable in the random variables of wind farm output and node net load, e=1,…,(n wf +n bus ). Represents x in the kth GMM component e The corresponding marginal one-dimensional normal importance probability density function.

[0179] Then, using the obtained marginal distribution Yes(n wf +n bus ) continuous variables are sampled separately Specifically, for the e-th variable, the sampling process is as follows:

[0180]

[0181] Among them, X ke The e-th variable is sampled using the k-th component of GMM P is a row vector consisting of a sequence of consecutive positive integers. ε is a random number vector with the same dimension as P, each element of which is uniformly distributed in the interval (0,1) and independent of each other. Φ ke -1 (·)represent The corresponding inverse of the cumulative distribution function.

[0182] When (n wf +n bus After all continuous variables are sampled, all X ke Combined into sample matrix X k ,Right now:

[0183]

[0184] in,(·) T is the transposition operator

[0185] Find X k The correlation coefficient matrix between rows ρ k0 , and for ρ k0 and Perform Cholesky decomposition to obtain the corresponding auxiliary matrices Z0 and Z k , as shown below.

[0186]

[0187] Use Z0 and Z k Construct the auxiliary sorting matrix Y:

[0188] Y=Z k Z0 -1 X k (twenty four)

[0189] Adjust X k The order of the elements in each row of X is consistent with the order of the elements in the corresponding row of matrix Y, so that k Carry out correlation control, so that the correlation coefficient matrix becomes

[0190] Finally, when all components of GMM are sampled, X k Combined into a complete N pre The matrix X of samples cv :

[0191]

[0192] Among them, X cv P is a continuous variable wf and L net N pre A matrix consisting of samples.

[0193] X cv With X dv Combined into a complete sample matrix X, that is

[0194]

[0195] Step S32: For each sample, calculate the corresponding S(x) value according to formula (10), and sort them from small to large to obtain {S[1],…,S[N pre ]}, extract the pre ) bit value S[α·N pre ]. Where α is the proportion of samples in power-off state, which can be 0.05 or 0.1.

[0196] Then, we judge S[α·N pre ] is less than or equal to 0. If it is less than or equal to 0, it means that the proportion of samples that can put the system in a power-off state among the samples obtained by sampling with the current importance probability density function has reached α, and let S in formula (11) th = 0. If it is greater than 0, let S in formula (11) th =S[α·N pre ]. Then the determined S th Substitute into formula (11) and calculate I(x) for all samples.

[0197] According to the calculated I(x) and S(x) values, the reliability index of the system is estimated. Commonly used indexes include the system power failure probability (loss of load probability, LOLP) and the expected power not supplied (expected power notsupplied, EPNS), and the calculation formula is as follows:

[0198]

[0199] Among them, γ LOLP,i and γ EPNS,i are the LOLP and EPNS indicators estimated using the samples of the i-th iteration. i (x s ) is the sample x in the i-th iteration s The likelihood ratio function of is expressed as:

[0200]

[0201] It can be seen from formula (15) that to calculate the likelihood ratio in the i-th iteration, it is necessary to use the importance probability distribution function in the i-1th round as the denominator.

[0202] The variance of the LOLP and EPNS indicators estimated by formula (13) and formula (14) is used to reflect the indicator accuracy. The calculation formula is as follows.

[0203]

[0204] Among them, V LOLP,i and V EPNS,i They are γ LOLP,i and γ EPNS,i The corresponding variance.

[0205] Step S33, if S th =0, the pre-sampling iteration is terminated and the process goes to step S4. Otherwise, the parameters of the importance probability distribution function are updated according to equations (32)-(37), and the process goes back to step S31 to resample samples until the iteration termination condition is met. In the first iteration, i=0, and the original distribution is used to obtain samples; when i>0, the importance probability distribution function obtained by the update in the i-1th round is used to obtain samples.

[0206] The iterative update formula for the undetermined parameters of discrete variables is as follows:

[0207]

[0208] The iterative update formula for the undetermined parameters of continuous variables is as follows:

[0209]

[0210] Further, the step S4 comprises:

[0211] Step S41, using the Latin hypercube sampling method described in step S31 to sample N importance probability distribution functions at the end of the pre-sampling iteration main Next, use these samples to estimate the values ​​of LOLP and EPNS indicators:

[0212]

[0213] Among them, γ LOLP,main and γ EPNS,main They are the LOLP and EPNS indicator values ​​estimated using the formal sampling samples.

[0214] The variance of the LOLP and EPNS indicators estimated by equations (18) and (19) is used to reflect the indicator accuracy. The calculation formula is as follows:

[0215]

[0216] Among them, V LOLP,main and V EPNS,main They are γ LOLP,main and γ EPNS,main The corresponding variance.

[0217] Step S42, using the index value and variance estimated by the pre-sampling sample and the index value and variance estimated by the formal sampling sample, perform weighted averaging to obtain a reliability index with higher accuracy, the formula is as follows.

[0218]

[0219] Among them, γ LOLP and γ EPNS The LOLP and EPNS index values ​​with higher accuracy are obtained by mixing the pre-sampling and formal sampling index estimates. LOLP and β EPNS Respectively reflect γ LOLP and γ EPNS Coefficient of variance of precision.

[0220] Reference Figure 3 ,by Figure 3 Taking the test system shown in the figure as an example, the total installed capacity of the three wind farms in the test system is 150MW, and their respective historical output probability density curves are as follows Figure 4 Other parameters of the test system are consistent with the standard IEEE RTS-79 system.

[0221] In order to verify the correctness of the calculation results of the proposed new power system reliability assessment method based on the coordination of two-stage samples of importance sampling, it is necessary to compare it with the calculation results of other methods. In this section, the reliability assessment method based on simple random sampling is recorded as method 1, the reliability assessment method based on Latin hypercube sampling is recorded as method 2, and the reliability assessment method based on cross entropy importance sampling is recorded as method 3.

[0222] The method of this application and the above methods are used to calculate the reliability indicators such as LOLP and EPNS of the test system. For method 3, the sample size of the first stage is set to 30,000, which is consistent with the proposed method; the convergence conditions of all methods are set to the variance coefficient of the calculated reliability index ≤ 0.02. The average values ​​of the calculation results after 50 repetitions of each method are shown in Table 1:

[0223] Table 1 Comparison of reliability results of four methods for evaluating the improved IEEE-RTS 79 system

[0224]

[0225] The method of this application and the above methods are used to calculate the reliability indicators such as LOLP and EPNS of the test system. For method 3, the sample size of the first stage is set to 30,000, which is consistent with the proposed method; the convergence conditions of all methods are set to the variance coefficient of the calculated reliability index ≤ 0.02. The average values ​​of the calculation results after 50 repetitions of each method are shown in Table 1:

[0226] It can be seen that under the same convergence conditions, the reliability indicators of the test system calculated by the proposed method and the other three methods are basically consistent, which further proves the correctness of the proposed method.

[0227] Table 2 Samples and calculation time consumed by four methods to evaluate the reliability index of the test system

[0228]

[0229] As shown in Table 2, under the same accuracy requirement, the number of samples and the calculation time consumed by the proposed method are much smaller than those of Method 1 and Method 2. Due to the combination of Latin hypercube sampling, when calculating the reliability index, the proposed method shortens the calculation time of LOLP and EPNS by 22.5% and 30.4% respectively compared with the simple cross entropy importance sampling method (Method 3), which significantly improves the calculation efficiency.

[0230] Embodiment 2

[0231] A computer device in this embodiment includes a memory for storing computer programs / instructions; and a processor for executing the computer programs / instructions to implement the steps of the power system reliability assessment method in the above-mentioned embodiment 1.

[0232] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0233] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0234] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0235] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0236] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. A method for evaluating the reliability of a power system, characterized in that: The following steps are involved: According to the historical data of the power system, an original probability distribution function is constructed; wherein the historical data includes the state of conventional units, the state of transmission lines, the node load demand and the output of the photovoltaic power station connected to the node; the original probability distribution function includes the original probability distribution function of the state vector of the conventional unit, the original probability distribution function of the state vector of the transmission line, and the original probability density function of the wind farm output vector and the node net load vector; Perform importance sampling iteration on the original probability distribution function to obtain the importance probability distribution function of the last iteration and the reliability index and variance of the power system; Importance sampling is performed on the importance probability distribution function of the last iteration to obtain the reliability index and variance of the power system; The final reliability index of the power system is calculated based on the reliability index and variance obtained by importance sampling iteration and the reliability index and variance obtained by importance sampling; the reliability of the power system is evaluated based on the final reliability index of the power system.

2. The power system reliability assessment method according to claim 1, characterized in that: The original probability distribution function of the conventional unit state vector is: Among them, x g is the state of the g-th conventional unit, n gu is the total number of conventional units, θ g is the failure outage rate of the g-th conventional unit, p(x gu ) is the original probability of the conventional machine group vector; The original probability distribution function of the transmission line state vector is: Among them, x l is the state of the lth line, n ln is the total number of lines, θ l is the failure outage rate of the lth line; p(x ln ) is the original probability of the transmission line state vector; The original probability density function of the wind farm output vector and the node net load vector is: Among them, n GM Represents the number of components of the mixed Gaussian distribution GMM, ω k , μ k and Σ k Represent the weight, expected value vector and covariance matrix of the kth component respectively; represents the multidimensional normal distribution function corresponding to the kth component; P wf is the wind farm output vector; L net is the node net load vector; f(P wf , L net ) is the original probability density of the wind farm output vector and the node net load vector.

3. The power system reliability assessment method according to claim 1, characterized in that: The process of the i-th iteration in the importance sampling iteration process includes; Step 1: Sample N according to the important probability distribution function updated after the i-1th iteration pre power system state samples, where when i=1, the power system state samples are sampled using the original probability distribution; Step 2: Calculate S(x) of each power system state sample and arrange them in order from small to large {S[1],…,S[N pre ]}, extract the arrangement in (α·N pre ) position value S[α·N pre ]; where S(x) is the evaluation function value corresponding to the power system state sample, and α is defined as the sample ratio of power shortage state; Step 3: If S[α·N pre ]≤0, let S th =0, calculate I(x) of all samples, and calculate the reliability index and variance of the power system based on I(x) and S(x) of all samples, and end the iteration; If S[[α·N pre ]>0, then S th =S[α·N pre ], calculate I(x) of all samples, and update the important probability distribution function according to I(x) and S(x) of all samples, where I(x) is the system power shortage indicator.

4. The power system reliability assessment method according to claim 3, characterized in that: The importance probability distribution function; The importance probability distribution function formula of the conventional unit state vector is: The importance probability distribution function formula of the transmission line state vector is: where η g and η l are the parameters that need to be optimized for the g-th thermal power unit and the l-th transmission line, respectively. gu is the state vector of the conventional unit, x ln is the state vector of the transmission line, x g is the status of the g-th conventional unit; x l is the state of the lth line, The probability density function formula of the combined importance of the wind farm output vector and the node net load vector is: in and is the unknown parameter of the kth normally distributed component of the joint importance probability density function, k = 1, ..., n GM ;P wf is the wind farm output vector; L net is the node net load vector, g(P wf , L net ) is the probability density of the joint importance of the wind farm output vector and the node net load vector; Represents the multidimensional normal distribution function corresponding to the kth component; The importance probability distribution function parameter update formula includes: The parameter update formula of the importance probability distribution function of the conventional unit state vector and the transmission line state vector is as follows; Among them, x s is the sth sample obtained by sampling, x g,s is x s The state variable value of the g-th unit, x l,s is x s The value of the state variable of the lth line in ; The parameter update formula of the importance probability density function of the wind farm output vector and the node net load vector is as follows: Among them, P wf,s and L net,s The samples x are s Wind farm output vector P wf The value of and node net load vector L net The value of r k,s For sample x s The probability of the kth normal distribution component from the original probability density function is calculated as follows:

5. The power system reliability assessment method according to claim 3, characterized in that: The reliability index and variance formula obtained by the importance sampling iteration; Among them, γ LOLP,i and γ EPNS,i are the system power outage probability LOLP and power shortage expected value EPNS indicators estimated using the samples of the i-th iteration; Q i (x s ) is the sample x in the i-th iteration s The likelihood ratio function of is expressed as: Among them, V LOLP,i and V EPNS,i They are γ LOLP,i and γ EPNS,i The corresponding variance.

6. The power system reliability assessment method according to claim 5, characterized in that: The reliability index and variance formula obtained by the importance sampling; Among them, γ LOLP,main and γ EPNS,main They are the LOLP and EPNS index values ​​estimated using importance sampling; Among them, V LOLP,main and V EPNS,main They are γ LOLP,main and γ EPNS,main The corresponding variance.

7. The power system reliability assessment method according to claim 6, characterized in that: The final reliability index formula of the power system; Among them, γ LOLP and γ EPNS The LOLP and EPNS index values ​​with higher accuracy are obtained by mixing the pre-sampling and formal sampling index estimates; β LOLP and β EPNS Respectively reflect γ LOLP and γ EPNS Coefficient of variance of precision.

8. A computer device, characterized in that: include Memory, for storing computer programs / instructions; A processor, configured to execute the computer program / instructions to implement the steps of the power system reliability assessment method according to any one of claims 1 to 7.

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