Reliability analysis method for low-voltage urban rail power distribution system

Abstract

The invention discloses a low-voltage urban rail power distribution system reliability analysis method, which solves the problem of inaccurate failure probability estimation in the prior art through failure mode determination, Monte Carlo simulation, Kriging model construction and optimization, model weighted averaging and failure probability estimation based on an adaptive Bayesian average Kriging model. The method significantly improves the efficiency and precision of reliability analysis of the low-voltage power distribution system, and is suitable for reliability evaluation of subway power, environmental control and illumination power distribution systems.

Description

Technical Field

[0001] The present invention relates to the field of subway low-voltage power distribution systems, and in particular to a reliability analysis method for a low-voltage urban rail power distribution system. Background Art

[0002] With the development of my country's cities and the increase in urban population density, the development of urban rail transit systems has attracted increasing attention. At the same time, due to the relatively concentrated flow of people and the relatively closed environment of urban rail transit, when a power distribution failure occurs in an important circuit, it will directly endanger the normal operation of urban rail transit, not only easily causing casualties, but also causing huge negative social impacts. Since people began to study the reliability of power systems in the middle of the last century, they have often emphasized the reliability of the power generation system. However, system reliability analysis is highly dependent on accurate proxy models. Currently, a variety of Kriging methods (the core idea is to estimate the value of unknown points by establishing an optimal prediction model) have been used to calculate failure probabilities. For example, patent document CN202311245724.8 discloses a reliability analysis method that couples active Kriging algorithms with uniform importance sampling. This reliability analysis method uses a coupled active Kriging algorithm and uniform importance sampling to reduce the number of function calls and improve sampling efficiency by constructing a Kriging model and learning function, and calculates the structural failure probability through uniform importance sampling. However, this method still has problems with computational cost and efficiency. Power system reliability often emphasizes the reliability of the power generation system. However, system reliability analysis is highly dependent on accurate surrogate models; existing multiple kriging methods for reliability analysis generally do not incorporate model form selection into the modeling process, resulting in inaccurate failure probability estimates.

[0003] Therefore, there is an urgent need to improve the efficiency and accuracy of failure probability estimation of each structure in the low-voltage distribution system. Summary of the Invention

[0004] Based on the structural composition of subway low-voltage power distribution systems, this paper proposes a reliability analysis method for low-voltage urban rail power distribution systems based on an adaptive Bayesian average kriging model. This method uses Bayesian model averaging to integrate individual kriging models composed of different basis functions. The principle of effect genetics is employed to improve model search efficiency and eliminate models with poor predictive performance from the candidate set. For the final ensemble forecast, each individual model is weighted according to its corresponding posterior model probability. This significantly improves the efficiency and accuracy of failure probability estimation for individual structures in the low-voltage power distribution system.

[0005] To achieve the above object, the present invention provides a method for analyzing the reliability of a low-voltage urban rail power distribution system, which is characterized by comprising the following steps:

[0006] S1. Based on the composition, function, and operating conditions of the low-voltage urban rail power distribution system structure, determine the failure mode of each structure and the corresponding performance function G(X), and obtain the random variables X that affect the performance function of each structure and the joint probability density function of the random variables X;

[0007] S2. According to the joint probability density function, the sample size N is obtained by using the Monte Carlo simulation experiment method. MC The initial population S;

[0008] S3. Randomly select N from the initial population S D Calculate the output response G(x) at each point and define the initial experimental design DoE (Design of experiments);

[0009] S4. Use the initial experimental design DoE to build an ordinary kriging model and define the empirical Bayesian parameters Calculate the marginal likelihood value P(M0|X,Y) of model M0 and initialize the active model set M A ;

[0010] S5. Perform basis function expansion on the models in the active model set to generate a new model set, calculate the posterior probability and eliminate redundant models, and update the model set until convergence;

[0011] S6. Calculate weights for the Kriging models in the final model set and determine whether convergence conditions are met based on the learning function;

[0012] S7. Estimate the failure probability and calculate the coefficient of variation. If the target value is not met, expand the sample and repeat the prediction process.

[0013] Furthermore, the low-voltage urban rail power distribution system includes a power distribution system, an environmental control distribution system and a lighting distribution system. The power distribution system uses power distribution boxes of different load levels as the minimum unit for reliability modeling. In the environmental control distribution system, the fire protection and environmental control systems and the non-fire protection and environmental control systems are distributed separately.

[0014] Furthermore, in step S2, let P f is the failure probability, x i (i=1,...,N MC ) represents random sample points, which are generated by the joint probability density function, n f represents the number of samples falling into the failure domain, I(G(x i )) represents an indicator function. When G(x)≤0, I=1, and when G(x)>0, I=0. The coefficient of variation COV can be used to evaluate the accuracy of the Monte Carlo simulation experiment and should be less than the target value COVtarget, as shown below

[0015]

[0016] Furthermore, in step S5, the specific steps of step S5 include:

[0017] S51, let M Ak is the kth model set, N MAk Indicates M Ak The number of models in M Ak Model M in i (i=1,...,N MAk ), through the principle of effect inheritance, its parent is included in M i Function in, get all the allowed basis functions addition, let n be the model M i The number of function additions;

[0018] S52, calculate the posterior probability of the model: by adding a basis function respectively, i Build a model ensemble of n models Calculate its posterior probability Where j = 1,…,n.

[0019] S53, for all larger models If the model If the posterior probability of is less than that of the simpler model, then eliminate the model

[0020] S54, for the k-th model set M Ak Each model in N MAk Repeat steps S51-S53 and add the remaining Kriging models to the set M Ak+1 middle;

[0021] S55, if the number of models in the k+1th set is greater than zero, then add M Ak+1 To enrich the model set M Ak , set k=k+1, and then return to S51; if not, apply the following formula to the candidate model set M A , we get the final model set:

[0022]

[0023] Furthermore, step S6 specifically calculates the weight ω for each Kriging model in MR i , update K to M R The number of models in S, calculate the response and prediction variance, calculate the learning function U(x) for all sample points in S, and determine whether the convergence condition is met

[0024] Furthermore, S1 analyzes the specifications, design standards, expert opinions and historical data of each structure of the low-voltage urban rail power distribution system to be evaluated, and obtains the composition, function and operating conditions of each structure of the low-voltage urban rail power distribution system to be evaluated.

[0025] Furthermore, step S7 specifically includes estimating the failure probability P f , calculate COV, if COV <COV target , then stop; otherwise, enrich S by adding a new Monte Carlo experimental population, predict the response of the new S based on the multiple Kriging method, and calculate the failure probability.

[0026] Furthermore, let y(x) represent the output prediction value, the i-th Kriging model M in S10 i The weight ω i Satisfy the following constraints:

[0027]

[0028] Furthermore, if the failure probability P is given f =10 -k , sample size N MCM Satisfy N MC ≈(P f (COV) 2 ) -1 =COV -2 10 k ; where P f is the failure probability; COV is the coefficient of variation, and COV should be less than the target value COV target .

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] 1. This invention utilizes the variance of multiple kriging to estimate local prediction errors and employs a ubiquitous learning function for adaptive learning. It introduces a new multiple kriging method for reliability analysis. By combining Bayesian averaging theory and the principle of genetic effects, this method significantly improves the accuracy of failure probability estimation.

[0031] 2. The present invention can obtain the failure probability of each structure of the subway low-voltage power distribution system, providing reliability prediction for the subsequent construction of other subways. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Attachment Figure 1 This is the overall structural division diagram of the subway low-voltage distribution system.

[0033] Attachment Figure 2 :Flowchart of reliability analysis method for low-voltage urban rail distribution system based on adaptive Bayesian average Kriging model. DETAILED DESCRIPTION

[0034] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0035] As attached Figure 1 As shown, the embodiment of the present invention divides the subway low-voltage power distribution system into three areas according to its different functions, namely, the power distribution system, the environmental control distribution system and the lighting distribution system. The power distribution system provides power to the remaining systems except the lighting system in the distribution boxes with different functions. According to the load level, it can be divided into the first-level load switching box, the second-level small power distribution box, the third-level small power distribution box on the station hall level, and the second and third-level small power distribution boxes on the platform level; in the environmental control distribution system, the fire protection and environmental control distribution system and the non-fire protection and environmental control distribution system are distributed separately, and each draws power from the 400V low-voltage switch cabinet; the lighting distribution system also draws power directly from the 400V low-voltage switch cabinet.

[0036] As attached Figure 2 As shown, the purpose of the present invention is achieved by adopting the following steps:

[0037] Step 1: According to the composition, function, and operating conditions of the low-voltage urban rail power distribution system structure, determine the failure mode of each structure and the corresponding function function G(X), and obtain the random variables X that affect the function of each structure and the joint probability density function of the random variables X;

[0038] Step 2: Based on the joint probability density function of the random variable X, use the Monte Carlo simulation method to obtain a sample size of N. MC The initial population S; if the failure probability P is given f =10 -k , N MC ≈(P f (COV) 2 ) -1 =COV -2 10 k .

[0039] Let P f is the failure probability, x i (i=1,...,N MC ) represents random sample points, which are generated by the joint probability density function, n f represents the number of samples falling into the failure domain, I(G(x i)) represents an indicator function, I = 1 when G(x) ≤ 0, and I = 0 when G(x) > 0. The coefficient of variation COV can be used to evaluate the accuracy of the Monte Carlo simulation experiment and should be less than the target value COV target , as shown below

[0040]

[0041] Step 3. Define the initial experimental design DoE: Randomly select N from the initial population S D The output response G(x) is calculated at each point.

[0042] Step 4: Use the initial experimental design DoE to build the ordinary kriging model and define the empirical Bayes parameters Calculate the marginal likelihood value P(M0|X,Y) of model M0 and initialize the active model set M A , set k = 1. Among them, the set M A1 ={M0},M A1 ∈M A .

[0043] Step 5: Set M Ak is the kth model set, N MAk Indicates M Ak The number of models in M Ak Model M in i (i=1,...,N MAk ), through the principle of effect inheritance (whose parents are included in M i Function in) get all the allowed basis functions addition, let n be the model M i The number of function additions.

[0044] Step 6: Calculate the posterior probability of the model: by adding a basis function to each of the models M i Build a model ensemble of n models Calculate its posterior probability where j = 1,…,n.

[0045] Step 7: For all larger models If the model If the posterior probability of is less than that of the simpler model, then eliminate the model

[0046]

[0047] Step 8: For the k-th model set M Ak Each model in N MAk Repeat S5-S7 and add the remaining Kriging models to the set M Ak+1 middle.

[0048] Step 9: If the number of models in the k+1th set is greater than zero, add M Ak+1 To enrich the model set M Ak , set k = k + 1, and then return to S5. If not, apply the following formula to the candidate model set M A , we get the final model set:

[0049]

[0050] Step 10, M R Each Kriging model in calculates the weight ω i , update K to M R Calculate the response and prediction variance, and calculate the learning function U(x) for all sample points in S. Determine whether the convergence conditions are met.

[0051] S11. Estimated failure probability P f . Calculate COV, if COV <COV target , then stop, otherwise, enrich S by adding a new Monte Carlo experimental population, predict the response of the new S based on the multiple Kriging method, and calculate the failure probability.

[0052] The low-voltage urban rail power distribution system is divided into a power distribution system, an environmental control distribution system, and a lighting distribution system. The power distribution system provides power to all systems except the lighting system in distribution boxes with different functions, and reliability modeling is performed using power distribution boxes with different load levels as the minimum unit. Depending on the layout of environmental control equipment, subway stations generally have environmental control control rooms at both ends of the station. The environmental control equipment is centrally distributed in the environmental control rooms, and the fire protection and environmental control systems are separately distributed from the non-fire protection and environmental control systems.

[0053] In step 1, the specifications, design standards, expert opinions and historical data of each structure of the low-voltage urban rail power distribution system to be evaluated are analyzed to obtain the composition, function and operating conditions of each structure of the low-voltage urban rail power distribution system to be evaluated.

[0054] Let y(x) represent the output prediction value, the i-th Kriging model M in S10 i The weight ω i Satisfy the following constraints:

[0055]

[0056] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A reliability analysis method for a low-voltage urban rail power distribution system, characterized in that: The following steps are involved: S1. Based on the composition, function, and operating conditions of the low-voltage urban rail power distribution system structure, determine the failure mode of each structure and the corresponding performance function G(X), and obtain the random variables X that affect the performance function of each structure and the joint probability density function of the random variables X; S2. According to the joint probability density function, the sample size N is obtained by using the Monte Carlo simulation experiment method. MC The initial population S; S3. Randomly select N from the initial population S D Calculate the output response G(x) at each point and define the initial experimental design DoE (Design of experiments); S4. Use the initial experimental design DoE to build an ordinary kriging model and define the empirical Bayesian parameters Calculate the marginal likelihood value P(M0|X,Y) of model M0 and initialize the active model set M A ; S5. Perform basis function expansion on the models in the active model set to generate a new model set, calculate the posterior probability and eliminate redundant models, and update the model set until convergence; S6. Calculate weights for the Kriging models in the final model set and determine whether convergence conditions are met based on the learning function; S7. Estimate the failure probability and calculate the coefficient of variation. If the target value is not met, expand the sample and repeat the prediction process.

2. The method according to claim 1, characterized in that The low-voltage urban rail power distribution system includes a power distribution system, an environmental control distribution system and a lighting distribution system. The power distribution system uses power distribution boxes of different load levels as the minimum unit for reliability modeling. In the environmental control distribution system, the fire protection and environmental control systems and non-fire protection and environmental control systems are distributed separately.

3. The method according to claim 1, characterized in that In step S2, let P f is the failure probability, x i (i=1,...,N MC ) represents random sample points, which are generated by the joint probability density function, n f represents the number of samples falling into the failure domain, I(G(x i )) represents an indicator function. When G(x)≤0, I=1, and when G(x)>0, I=0. The coefficient of variation COV can be used to evaluate the accuracy of the Monte Carlo simulation experiment and should be less than the target value COV target , as shown below 4. The method according to claim 1, wherein In the step S5, the step S5 specifically includes: S51, let M Ak is the kth model set, N MAk Indicates M Ak The number of models in M Ak Model M in i (i=1,...,N MAk ), through the principle of effect inheritance, its parent is included in M i Function in, get all the allowed basis functions addition, let n be the model M i The number of function additions; S52, calculate the posterior probability of the model: by adding a basis function respectively, i Build a model ensemble of n models Calculate its posterior probability Where j = 1,…,n. S53, for all larger models If the model If the posterior probability of is less than that of the simpler model, then eliminate the model S54, for the k-th model set M Ak Each model in N MAk Repeat steps S51-S53 and add the remaining Kriging models to the set M Ak+1 middle; S55, if the number of models in the k+1th set is greater than zero, then add M Ak+1 To enrich the model set M Ak , set k=k+1, and then return to S51; if not, apply the following formula to the candidate model set M A , we get the final model set:

5. The method according to claim 1, wherein Step S6 specifically includes: R Each Kriging model in calculates the weight ω i , update K to M R The number of models in S is calculated, the response and prediction variance are calculated, the learning function U(x) is calculated for all sample points in S, and whether the convergence condition is met is determined.

6. The method according to claim 1, characterized in that In S1, the specifications, design standards, expert opinions and historical data of each structure of the low-voltage urban rail power distribution system to be evaluated are analyzed to obtain the composition, function and operating conditions of each structure of the low-voltage urban rail power distribution system to be evaluated.

7. The method according to claim 1, characterized in that Step S7 specifically includes estimating the failure probability P f , calculate COV, if COV <COV target , then stop; otherwise, enrich S by adding a new Monte Carlo experimental population, predict the response of the new S based on the multiple Kriging method, and calculate the failure probability.

8. The method according to claim 5, characterized in that Let y(x) represent the output prediction value, the i-th Kriging model M in S10 i The weight ω i Satisfy the following constraints:

9. The method according to claim 3, characterized in that If the failure probability P is given f =10 -k , sample size N MCM Satisfy N MC ≈(P f (COV) 2 ) -1 =COV -2 10 k ; where P f is the failure probability; COV is the coefficient of variation, and COV should be less than the target value COV target .

Images