Method for statistically operating overvoltage based on kriging surrogate model

Abstract

The application relates to a method for statistically operating overvoltage based on a Kriging proxy model, and belongs to the technical field of electric power. The method comprises the following steps: 1) establishing a simulation model by using PSCAD software; 2) determining random variables, collecting training data, and constructing a Kriging proxy model according to sampling samples and overvoltage responses of each phase; and 3) predicting simulation response values corresponding to sample points and statistically processing and analyzing the simulation response values. The method provided by the application is convenient for electric workers to quickly statistically operate overvoltage, effectively reduces the simulation running times compared with a traditional Monte Carlo method, saves a large amount of working time, and has strong engineering practicability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electric power and relates to a method for statistically operating overvoltage based on a Kriging surrogate model. BACKGROUND

[0002] PSCAD / EMTDC is a kind of electromagnetic transient simulation software widely used in the field of power system fault analysis, and the calculation of operating overvoltage involves a transient process of microseconds. At present, the conventional method for statistically operating overvoltage caused by the dispersion of switch closing phase in PSCAD is as follows: usually, hundreds of different-period closing of main and auxiliary contacts of switches are carried out, the contact-on time (phase) is randomly sampled according to the specified distribution rule, and then hundreds of closing overvoltage calculations are carried out according to the electromagnetic transient calculation program to obtain the overvoltage amplitude and calculate the basic statistical data. This simulation operation mode is time-consuming, and the simulation model needs to be repeatedly run hundreds of times, which is a large amount of work.

[0003] Therefore, it is necessary to replace the part of work of obtaining hundreds of closing overvoltage data with a Kriging surrogate model to obtain a method for statistically operating overvoltage based on a Kriging surrogate model. SUMMARY

[0004] Therefore, the purpose of the application is to provide a method for statistically operating overvoltage based on a Kriging surrogate model.

[0005] To achieve the above purpose, the application provides the following technical scheme.

[0006] A method for statistically operating overvoltage based on a Kriging surrogate model, which comprises the following steps:

[0007] S1: establishing a simulation model by using PSCAD software;

[0008] S2: determining random variables, collecting training data, and constructing a Kriging surrogate model according to the sampling samples and the overvoltage response of each phase;

[0009] S3: predicting the simulation response value of the corresponding sample point and statistically processing and analyzing it.

[0010] Optionally, in the S2, the step of determining random variables, collecting training data, and constructing a Kriging surrogate model according to the sampling samples and the overvoltage response of each phase is as follows:

[0011] S21: taking the factors affecting the operating overvoltage as random variables, establishing them in the Multiple Run element, and specifying the value range of the random variables; the factors affecting the operating overvoltage include the dispersion of switch closing phase and the pre-breakdown of switch contacts;

[0012] S22: Random variables are sampled using a normal distribution within a specified range to obtain model phase overvoltage response values, forming a sample set of the objective function f(x);

[0013] S23: A second-order polynomial is used for the regression model, and a Gaussian function is used for the correlation function, and a Kriging surrogate model is established for the objective function f(x) That is:

[0014]

[0015] f(β,x)=[f1(x),…,f p (x)] T β=f(x) T β

[0016] Where x represents a set of factors affecting the operating overvoltage, f(x) represents a basis function, β is the corresponding regression coefficient, f(β,x) is a second-order polynomial regression model, z(x) represents a random error part with an expectation of 0 and a non-zero covariance;

[0017] The covariance between any two sample points ω and x in the sample set is calculated as:

[0018]

[0019] Where σ 2 is the process variance of z, is a Gaussian function with parameter θ, representing the spatial correlation between training sample points.

[0020] Optionally, in S3, the step of predicting the simulation response value of the corresponding sample point and performing statistical processing and analysis thereon is:

[0021] S31: Latin hyper-sampling is used to obtain n sets of factor sets affecting the operating overvoltage within a given range that have not been tested;

[0022] S32: Using the Kriging surrogate model that has been established, n sets of phase overvoltage response values are obtained by calling the Kriging prediction model with the n sets of factor sets affecting the operating overvoltage as input parameters;

[0023] S33: The output parameter three-phase overvoltage values are sorted and grouped, and the corresponding frequency histogram and cumulative frequency curve are drawn;

[0024] S34: The n sets of three-phase overvoltage responses are used as statistical samples for chi-square test to determine whether the statistical distribution assumption is credible;

[0025] S35: Overvoltage characteristic value calculation, including calculating overvoltage mean value and calculating the estimate of standard deviation, obtaining 2% overvoltage amplitude U 2％ .

[0026] The beneficial effects of the present application are:

[0027] (1) The method for statistically operating overvoltage based on the Kriging surrogate model provided by the present application reduces the time consumed by a large number of simulation running times;

[0028] (2) The method for statistically operating overvoltage based on the Kriging surrogate model provided by the present application has strong operability and high engineering practical value.

[0029] Other advantages, objects, and features of the present application will be apparent to those skilled in the art from the following specification, and it is intended to be covered by the following claims. The objects and other advantages of the present application can be realized and attained by the below specification. BRIEF DESCRIPTION OF DRAWINGS

[0030] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred detailed description of the present application will be combined with the drawings to make the objects, technical solutions and advantages of the present application clearer, wherein:

[0031] Figure 1 The flowchart of the present application.

[0032] Figure 2 The frequency histogram corresponding to the simulation of the present application;

[0033] Figure 3 The frequency histogram obtained by using the Monte Carlo method. DETAILED DESCRIPTION

[0034] The embodiments of the present application will be described below through specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in the specification. The present application can also be implemented or applied through other different specific embodiments, and each detail in the specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be noted that the diagrams provided in the following examples only illustrate the basic concept of the present application in a schematic manner, and the following examples and features in the examples can be combined with each other without conflict.

[0035] The drawings are only used for exemplary illustration, and the representation is only a schematic diagram, not a physical diagram, and cannot be understood as a limitation on the present application; in order to better illustrate the embodiments of the present application, some components of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0036] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that if the terms "upper", "lower", "left", "right", "front", "back" and the like indicate the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only used for exemplary illustration, and cannot be understood as a limitation on the present application, for those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0037] Since there are many factors affecting the probability distribution of overvoltage amplitude, including the dispersion of switch closing phase; pre-breakdown of switch contact; whether there is residual voltage on the line at the time of closing, etc., in this case, the dispersion of switch closing phase is taken as a random variable.

[0038] As shown in Figure 1 The method for statistically operating overvoltage based on Kriging surrogate model includes the following steps:

[0039] S1: determine the random variable, collect training data, and construct the Kriging surrogate model according to the sampling sample and the overvoltage response of each phase.

[0040] The sub-steps for determining the random variable, collecting training data, and constructing the Kriging surrogate model according to the sampling sample and the overvoltage response of each phase are:

[0041] S11: take the average time T0 of the three-phase switch contact of the circuit breaker and the deviation ΔT of the actual contact time T of each phase switch contact from T0 as a random variable;

[0042] S12: the four random variables are established in the Multiple Run element, and the value range and the number of runs are set;

[0043] S13: the average time T0 of the three-phase switch contact of the circuit breaker and the deviation ΔT of the actual contact time T of each phase switch contact from T0 are sampled using normal distribution within the specified range, the overvoltage response value of each phase of the model is obtained, and a sample set of the objective function f(x) is formed;

[0044] S14: A Kriging surrogate model is established for the objective function f(x) by using a second-order polynomial for the regression model and a Gaussian function for the correlation function That is,

[0045]

[0046] f(β, x) = [f1(x), …, f p (x)] T β = f(x) T β

[0047] where f(x) represents a basis function, β is a corresponding regression coefficient, z(x) represents a random error part, and the expectation is 0, and the covariance is not 0;

[0048] The covariance between any two sample points ω and x in the sample set is calculated as follows:

[0049]

[0050] where is a correlation function with a parameter θ, the correlation function is a Gaussian function, and the spatial correlation between the training sample points plays a decisive role in the accuracy of simulation;

[0051] S2: The simulation response value of the corresponding sample point is predicted, and statistical processing and analysis are performed.

[0052] The sub-step of predicting the simulation response value of the corresponding sample point and performing statistical processing and analysis is as follows:

[0053] S21: Latin hyper-sampling is used to obtain a set of n groups of average time T0 of the influence of the overvoltage three-phase switch contact on the contact and the deviation ΔT of the actual contact time T of each phase switch contact from T0 in a given range, which has not been tested;

[0054] S22: The Kriging surrogate model is called by using the n groups of sets as input parameters, and the Kriging prediction model is used to obtain n groups of overvoltage response values of each phase;

[0055] S23: The output parameter three-phase overvoltage value is sorted and grouped, and the corresponding frequency histogram and cumulative frequency curve are drawn, as shown in Figure 2

[0056] S24: The n groups of three-phase overvoltage responses are used as statistical samples for chi-square test to determine whether the statistical distribution assumption is credible, and the correlation coefficient between the three phases is calculated as shown in Table 1;

[0057] Table 1 Correlation coefficient between three phases ​

[0058] between the two phases correlation coefficient r phase A and phase B 0.3126 phase A and phase C 0.1462 phase B and phase C 0.1730

[0059] Generally, the significance level β = 0.05 is taken when the overvoltage is analyzed, and from the table it can be seen that the correlation coefficient r of phase A and phase B exceeds the critical value r β = 0.195, the assumption of mutual independence cannot be accepted, and thus the maximum value of the overvoltage amplitude in the three phases is selected for statistical analysis;

[0060] S25: overvoltage characteristic value calculation, mainly calculating the estimation value of the overvoltage mean and standard deviation, and obtaining the statistical overvoltage U 2％ , and the calculation result is shown in Table 2.

[0061] Table 2 calculation result

[0062]

[0063] In Table 2, χ 2 , σ0, U 2％ indicate the chi-square test value, the overvoltage mean, the standard deviation and the 2% statistical overvoltage value, respectively. Compared with the calculation results of the two methods, the chi-square test is reliable, and the overvoltage mean, the 2% statistical overvoltage value and the standard deviation are not much different.

[0064] Figure 3 is the frequency histogram obtained by using the Monte Carlo method.

[0065] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the purpose and scope of the technical solutions, and all of them should be covered in the scope of the claims of the present application.

Claims

1. A method for statistically analyzing operational overvoltages based on the Kriging surrogate model, characterized in that: The method includes the following steps: S1: Use PSCAD software to create a simulation model; S2: Determine the random variables, collect training data, and construct a Kriging surrogate model based on the sampled data and the overvoltage response of each phase; the specific steps are as follows: S21: The factors affecting the switching overvoltage are established as random variables in the Multiple Run element, and the range of values ​​for the random variables is specified; the factors affecting the switching overvoltage include the dispersion of the switch closing phase and the pre-breakdown of the switch contacts; S22: Random variables are sampled using a normal distribution within a specified range to obtain the overvoltage response values ​​of each phase of the model, forming the objective function. The sample set; S23: The regression model uses a second-order polynomial, the correlation function uses a Gaussian function, and the objective function... Establishing the Kriging proxy model ,Right now: in, This represents the set of factors that affect operational overvoltage. Represented as basis functions, For the corresponding regression coefficients, It is a regression model of second-order polynomial. This represents the random error component, with an expected value of 0 and a non-zero covariance. Any two sample points in the sample set , The formula for calculating the covariance between them is: In the formula for Process variance For parameters The Gaussian function represents the spatial correlation between training sample points; S3: Predict the simulation response values ​​of the corresponding sample points and perform statistical processing and analysis; the specific steps are as follows: S31: Using Latin oversampling, obtain the untested data within a given range. n A set of factors that affect operating overvoltage; S32: Utilizing the established Kriging proxy model, n Using a set of factors influencing switching overvoltage as input parameters, the Kriging prediction model is called to obtain... n Overvoltage response values ​​for each phase of the group; S33: Organize and group the three-phase overvoltage values ​​of the output parameters, and draw the corresponding frequency histogram and cumulative frequency curve; S34: Will n The overvoltage response in the three-phase group was used as a statistical sample for a chi-square test to determine whether the statistical distribution assumption was reliable. S35: Overvoltage characteristic value calculation, including calculating the estimated overvoltage mean and standard deviation, to obtain the 2% overvoltage amplitude. U 2% .

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