CN113468792A

CN113468792A - Parameter correction method and device of electromagnetic transient simulation model and electronic equipment

Info

Publication number: CN113468792A
Application number: CN202110831598.9A
Authority: CN
Inventors: 张迪; 杨慧彪; 郭艺谭; 李宏强; 张汉花; 顾雨嘉; 柴元德; 王克荣
Original assignee: Sichuan Energy Internet Research Institute EIRI Tsinghua University; State Grid Qinghai Electric Power Co Ltd; Electric Power Research Institute of State Grid Qinghai Electric Power Co Ltd; Electric Power Research Institute of State Grid Ningxia Electric Power Co Ltd
Current assignee: Sichuan Energy Internet Research Institute EIRI Tsinghua University; State Grid Qinghai Electric Power Co Ltd; Electric Power Research Institute of State Grid Qinghai Electric Power Co Ltd; Electric Power Research Institute of State Grid Ningxia Electric Power Co Ltd
Priority date: 2021-07-22
Filing date: 2021-07-22
Publication date: 2021-10-01
Anticipated expiration: 2041-07-22
Also published as: CN113468792B

Abstract

The invention provides a parameter correction method and device of an electromagnetic transient simulation model and electronic equipment, which relate to the technical field of power systems and comprise the following steps: acquiring multiple groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under preset working conditions; constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model; the target parameter set is determined using a maximum expectation algorithm and the akage information criterion. Based on the above, when the parameter space is large, the number of the Gaussian components and the covariance matrix dimension of each Gaussian component can be automatically adjusted so as to give consideration to the calculation efficiency and the fitting precision; in addition, the invention utilizes the particle swarm algorithm and the conditional probability density function of the simulation parameters during the characteristic quantity determination to invert the target model parameter set, thereby effectively controlling the dimension of the learning space and simplifying the problem search process. The electromagnetic transient simulation model corrected by the target model parameter set can accurately guide accident inversion and production practice.

Description

Parameter correction method and device of electromagnetic transient simulation model and electronic equipment

Technical Field

The invention relates to the technical field of power systems, in particular to a parameter correction method and device of an electromagnetic transient simulation model and electronic equipment.

Background

With the increasing large scale of the power grid and the construction of direct current transmission engineering, the dynamic behavior of the system is increasingly complex, and the establishment of a detailed and reliable power grid full electromagnetic transient simulation model can be used for guiding accident inversion and production practice. However, in the operation process of the power system equipment, the power system equipment is influenced by various factors such as the operation environment and equipment aging, the control parameters and the setting parameters have certain dispersibility, the parameters of the power grid equipment can also present similar variation characteristics, and the load model can also present richer dispersibility compared with a constant impedance model due to the fact that the number of power electronic equipment is continuously increased.

In the prior art, the parameter dispersibility is not considered too much, the nameplate data is taken as the standard, other parameters which are not easy to measure and do not have relevant reference data are verified by using empirical data and a trial and error method, and accordingly the parameters are modified as appropriate. For the working condition of large power grid parameter space, the model parameters obtained by the parameter determination method and the actual model parameters have larger deviation, so that the electromagnetic transient simulation model loses the practical guiding significance of the engineering.

Disclosure of Invention

The invention aims to provide a parameter correction method and device of an electromagnetic transient simulation model and electronic equipment, so as to relieve the technical problem that the electromagnetic transient simulation model cannot accurately guide accident inversion and production practice.

In a first aspect, the present invention provides a method for correcting parameters of an electromagnetic transient simulation model, including: acquiring multiple groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under preset working conditions; constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the multiple groups of simulation parameters and the reference waveform; wherein the characteristic quantity represents the deviation of the reference waveform and the simulation waveform of the electromagnetic transient simulation model to be corrected under the simulation parameters; determining a target parameter set of the joint probability density function by utilizing a maximum expectation algorithm and an akachi pool information criterion; inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function, and correcting the target model parameter set by utilizing the target model parameter set; wherein the target probability density function represents a conditional probability density function of the simulation parameter at the time of the feature quantity determination.

In an optional embodiment, constructing a joint probability density function between simulation parameters and feature quantities based on a gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the plurality of sets of simulation parameters, and the reference waveform, includes: determining a target simulation waveform based on the target group simulation parameters and the electromagnetic transient simulation model to be corrected; wherein the target set of simulation parameters represents any one of a plurality of sets of the simulation parameters; determining a target characteristic quantity corresponding to the target group simulation parameters based on the target simulation waveform and the reference waveform; and constructing the joint probability density function based on the multiple groups of simulation parameters and the characteristic quantities corresponding to each group of simulation parameters.

In an optional embodiment, constructing the joint probability density function based on the plurality of sets of simulation parameters and the feature quantities corresponding to each set of simulation parameters includes: respectively carrying out normalization processing on the target group simulation parameters and the target characteristic quantity to obtain normalized simulation parameters and normalized characteristic quantity; determining a target relation vector corresponding to the target group simulation parameters based on the normalized simulation parameters and the normalized characteristic quantity; and fitting a joint probability density function between the simulation parameters and the characteristic quantity by utilizing a Gaussian mixture model based on the corresponding relation vectors of the multiple groups of simulation parameters.

In an alternative embodiment, determining the set of target parameters for the joint probability density function using a maximum expectation algorithm and a Chi information criterion comprises: acquiring the quantity range of Gaussian components of the Gaussian mixture model; determining a set of parameters of an objective function using the maximum expectation algorithm; wherein the objective function represents a joint probability density function having a target number of Gaussian components; determining a composite score of the objective function based on the akachi information criterion; determining a set of target parameters for the joint probability density function based on the composite scores for all target functions within the quantity range.

In an alternative embodiment, determining a composite score for the objective function based on the akage information criterion comprises: equation of utilization

Determining a composite score for the objective function; wherein AIC represents the composite score, k represents the number of the targets, n represents the total number of parameters of each set of the simulation parameters and the feature quantities, and L represents the maximum value of the likelihood function of the objective function。

In an optional embodiment, inverting the target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm, and the target probability density function includes: initializing a particle swarm with a random initial position in a preset search range; wherein, the central positions of all the particles in the initial state are 0; repeatedly executing the following steps until a preset termination condition is reached, and determining the target model parameter group based on the global optimal position of the particles under the preset termination condition: determining a target probability density function under a target characteristic quantity based on the target parameter set and the joint probability density function; wherein the target characteristic quantity represents a current position of any one particle in the particle swarm; determining a pre-estimation parameter set of the electromagnetic transient simulation model to be corrected based on the target probability density function; determining an adaptive function of each particle in the particle swarm algorithm based on the prediction parameter set, the electromagnetic transient simulation model to be corrected and the reference waveform; updating the velocity of each of the particles, the optimal position of each of the particles, and the current candidate position based on the fitness function; wherein the current candidate position represents a global best position of a particle; updating the current position of each particle based on the motion formula of the particles in the particle swarm optimization.

In an alternative embodiment, determining an adaptive function of each particle in the particle swarm algorithm based on the set of prediction parameters, the electromagnetic transient simulation model to be corrected, and the reference waveform includes: determining an actual simulation waveform based on the estimation parameter group and the electromagnetic transient simulation model to be corrected; and calculating the actual simulation waveform and the reference waveform to determine a simulation error, and taking the simulation error as the adaptive function.

In a second aspect, the present invention provides a parameter correction device for an electromagnetic transient simulation model, including: the acquisition module is used for acquiring a plurality of groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under a preset working condition; the construction module is used for constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the multiple groups of simulation parameters and the reference waveform; wherein the characteristic quantity represents the deviation of the reference waveform and the simulation waveform of the electromagnetic transient simulation model to be corrected under the simulation parameters; the determining module is used for determining a target parameter set of the joint probability density function by utilizing a maximum expectation algorithm and a Chichi information criterion; the inversion module is used for inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function and correcting the target model parameter set by utilizing the target model parameter set; wherein the target probability density function represents a conditional probability density function of the simulation parameter at the time of the feature quantity determination.

In a third aspect, the present invention provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program operable on the processor, and the processor executes the computer program to implement the steps of the method according to any of the foregoing embodiments.

In a fourth aspect, the invention provides a computer readable medium having non-volatile program code executable by a processor, the program code causing the processor to perform the method of any of the preceding embodiments.

The invention provides a parameter correction method of an electromagnetic transient simulation model, which comprises the following steps: acquiring multiple groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under preset working conditions; constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model according to the electromagnetic transient simulation model to be corrected, a plurality of groups of simulation parameters and a reference waveform; the characteristic quantity represents the deviation of a reference waveform and a simulation waveform of the electromagnetic transient simulation model to be corrected under simulation parameters; determining a target parameter set of a joint probability density function by utilizing a maximum expectation algorithm and a Chi information criterion; inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function, and correcting the target model parameter set by using the target model parameter set; the target probability density function represents a conditional probability density function of the simulation parameter when the feature quantity is determined.

The invention provides a parameter correction method of an electromagnetic transient simulation model, which comprises the steps of firstly constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model after acquiring a plurality of groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under preset working conditions, and then determining a target parameter set by utilizing a maximum expectation algorithm and a Chichi information criterion; in addition, the invention utilizes the particle swarm algorithm and the conditional probability density function of the simulation parameters during the characteristic quantity determination to invert the target model parameter set, thereby effectively controlling the dimension of the learning space and simplifying the searching process of the problem. The electromagnetic transient simulation model corrected by the target model parameter set can accurately guide accident inversion and production practice.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.

Fig. 1 is a flowchart of a parameter calibration method for an electromagnetic transient simulation model according to an embodiment of the present invention;

fig. 2 is a flowchart of constructing a joint probability density function based on a plurality of sets of simulation parameters and feature quantities corresponding to each set of simulation parameters according to an embodiment of the present invention;

FIG. 3 is a flowchart of a target parameter set for determining a joint probability density function using a maximum expectation algorithm and a Chi information criterion according to an embodiment of the present invention;

FIG. 4 is a functional block diagram of a parameter calibration apparatus for an electromagnetic transient simulation model according to an embodiment of the present invention;

fig. 5 is a schematic diagram of an electronic device according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.

Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Some embodiments of the invention are described in detail below with reference to the accompanying drawings. The embodiments described below and the features of the embodiments can be combined with each other without conflict.

As an important means for solving the energy crisis, new energy power generation technologies such as wind power and photovoltaic are rapidly developed, a large number of power electronic devices are included, and the reactive power regulation capability is obviously insufficient relative to a synchronous machine. The voltage and frequency stability problems of a power grid containing high-proportion renewable energy sources are obviously different from those of the traditional synchronous machine power grid, so that the power electronization characteristics of the power grid cannot be reproduced by using the traditional electromechanical transient simulation program.

In addition, in the operation process of the power system equipment, the power system equipment is influenced by various factors such as the operation environment, equipment aging and the like, the control parameters and the set parameters have certain dispersity, the parameters of the power grid equipment can also present similar change characteristics, and the load model can also present richer dispersity compared with a constant impedance model due to the fact that the number of power electronic equipment is continuously increased. In consideration of these factors affecting the parameters of the power grid simulation model, parameter correction of the simulation model is necessary.

In engineering, an efficient and reliable general parameter correction method does not exist at present, model parameters are determined by a conventional common experience method and a trial-and-error method of a small power grid system, but for a working condition with a large power grid parameter space, a large deviation is inevitably generated between the model parameters obtained by the parameter determination method and actual model parameters, and further an electromagnetic transient simulation model loses the practical guiding significance of the engineering. In view of the above, the present invention provides a method for correcting parameters of an electromagnetic transient simulation model, so as to alleviate the above-mentioned technical problems.

Example one

Fig. 1 is a flowchart of a parameter correction method for an electromagnetic transient simulation model according to an embodiment of the present invention, and as shown in fig. 1, the method specifically includes the following steps:

step S102, acquiring multiple groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under preset working conditions.

Specifically, for a certain circuit simulation model, the reference waveform is generally an actual waveform, that is, the circuit physical quantity is output under a certain preset working condition (known state), so that in order to ensure that the simulation model can guide accident inversion and production practice, if the simulation model is set to be under the same preset working condition, the deviation between the output waveform and the reference waveform should be smaller than a preset threshold, otherwise, the simulation model loses the guiding significance on engineering practice. Therefore, in the embodiment of the present invention, in order to perform parameter correction on the electromagnetic transient simulation model, first, a reference waveform of the electromagnetic transient simulation model to be corrected under a preset working condition is acquired.

Further, since the default parameters of the electromagnetic transient simulation model to be corrected (hereinafter referred to as the simulation model) deviate from the target parameters (parameters that make the deviation between the output waveform of the model and the reference waveform smaller than the preset threshold), even if the working condition same as the reference waveform is set, the output waveform does not completely conform to the reference waveform, although the parameters of the simulation model can be manually changed, when the parameters to be corrected are more, the output waveform of the simulation model is adjusted by manually changing the parameters, so that the output waveform of the simulation model can hardly conform to the reference waveform. Therefore, in the embodiment of the present invention, in addition to acquiring the reference waveform, it is also necessary to acquire a plurality of sets of simulation parameters of the electromagnetic transient simulation model to be corrected, and then, the parameter correction of the simulation model is gradually implemented through the following steps S104 to S108.

The embodiment of the invention does not specifically limit the number of the simulation parameters and the total number of the simulation parameters, and a user can set the simulation parameters according to actual requirements. After determining the simulation items in the simulation parameters, the multiple sets of simulation parameters may be obtained in a random generation manner, for example, if determining the simulation items in the set of simulation parameters includes: voltages, capacitances and inductances, then a set of voltage values, capacitance values and inductance values may be generated in a random manner. If the constraint conditions such as the correction range of the parameters, the power flow constraint and the like are preset, the simulation parameter group which does not meet the constraint conditions needs to be removed; or in the random parameter generation stage, constraint conditions are added, and the obtained multiple groups of simulation parameters can be used.

And step S104, constructing a joint probability density function between the simulation parameters and the characteristic quantity based on the Gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the multiple groups of simulation parameters and the reference waveform.

As can be seen from the above description, it is almost impossible to adjust the output waveform of the simulation model by manually modifying the parameters so that the output waveform matches the reference waveform, and therefore, in the embodiment of the present invention, the main task of parameter correction is to establish a relationship between the key parameters and the characteristic quantities of the dynamic behavior of the system, specifically, to perform batch simulation on the electromagnetic transient simulation model to be corrected by using multiple sets of simulation parameters, so as to obtain a statistical relationship between the input simulation parameters and the corresponding characteristic quantities, where the relationship is a high-dimensional correlation and can be represented by a probability density function. The characteristic quantity represents the deviation of the reference waveform and the simulation waveform of the electromagnetic transient simulation model to be corrected under the simulation parameters. That is, each set of simulation parameters corresponds to a simulation waveform, and the deviation obtained by comparing the simulation waveform with the reference waveform is the characteristic quantity of the set of simulation parameters.

In the embodiment of the present invention, the characteristic quantity is a deviation of the simulated waveform from the reference waveform, that is, a distance between the simulated waveform and the reference waveform in the combination of the parameters. The characteristic quantity can be selected from a plurality of typical steady-state quantities or transient-state quantities, such as node voltage estimation errors, rotor speed estimation errors, generator active output estimation errors and the like, the selection process can refer to the trajectory sensitivity of parameters to determine which parameters are key parameters for one characteristic quantity.

In addition, when the probability density function is used to represent the statistical relationship between the simulation parameters and the feature quantities, the embodiment of the present invention chooses to use a Gaussian Mixed Model (GMM) for fitting, that is, to construct a joint probability density function between the simulation parameters and the feature quantities based on the Gaussian Mixed Model. The joint probability density function can be expressed as

Where k represents the number of Gaussian components, π_cRepresents the weight of the c-th Gaussian component, and

μ_crepresents the mean of the c-th gaussian component,

the covariance matrix representing the c-th Gaussian component, θ represents the parameter set for GMM, i.e.

The reason for choosing the GMM to fit is: GMM can be expressed as linear summation of several Gaussian components, the probability density function analysis is easy to calculate, the cumulative distribution function is also easy to calculate, the degree of freedom of GMM is extremely high, the fitting precision can be improved along with the increase of the number of the Gaussian components, theoretically, the GMM can be used for accurately fitting any probability density function as long as the number of the Gaussian components is enough, and only the time efficiency can be reduced; furthermore, the GMM also has conditional probability invariance, and for a high-dimensional random variable, the conditional probability of the remaining part is still the GMM under the condition that several dimensions are determined, namely the conditional probability of the GMM is resolvable.

And S106, determining a target parameter set of the joint probability density function by using a maximum expectation algorithm and a Chichi information criterion.

After the combined probability density function based on the Gaussian mixture model is constructed, the fitting effect of the GMM is directly related to the number of Gaussian components of the GMM, although the more the Gaussian components are, the more accurate the fitting is, the problem of overfitting is inevitable, and the calculation efficiency is also reduced rapidly when the number of the Gaussian components is large, so that the number of the Gaussian components which can accurately express the relationship between the simulation parameters and the characteristic quantity, avoid overfitting and ensure the simulation efficiency is required to be found.

The Akaike Information Criterion (AIC) is a standard for measuring the fitting superiority of a statistical model, so that an AIC evaluation process is added in the process of fitting GMM parameters, namely, the rationality of the value of k is evaluated by solving AICs of different numbers of gaussian components, and k set when the problem is finally solved is determined.

The maximum likelihood estimation may be used when determining the parameter set of the GMM, and the embodiment of the present invention adopts the maximum-Expectation-algorithm (EM), which has the basic principle of finding the maximum of the likelihood function, i.e. ensuring that each step of the iterative process is toward the direction of increasing the likelihood function until convergence. Therefore, the embodiment of the invention can determine the value of the number k of the Gaussian components of the joint probability density function and the target parameter set corresponding to the value k by using the maximum expectation algorithm and the Chichi information criterion

And S108, inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function, and correcting the target model parameter set by using the target model parameter set.

After obtaining a reasonable number of gaussian components and solving a target parameter set, the expression of GMM is determined. In an embodiment of the present invention, the feature quantity represents a deviation (distance) between the simulated waveform and the reference waveform, and then, based on GMM conditional probability invariance, the feature quantity Y is made to be 0 (because the distance between the simulated waveform and the reference waveform is made to be zero as the correction target), and the conditional probability density function p (X | Y is made to be 0; θ) under the condition is solved to obtain the ideal model parameters, that is, the target model parameter set.

However, for practical engineering problems, a simulation model which can completely reflect a real scene accurately does not exist, and because some approximations and assumptions are always made in the model building process, a situation that a simulation waveform and a reference waveform cannot be completely matched occurs more likely, that is, the simulation model has limitations. The purpose of the parameter correction is to minimize the distance between the simulated waveform and the reference waveform, but it is not known in advance what the distance is in the process of solving the problem.

Therefore, in the embodiment of the present invention, a Particle Swarm Optimization (PSO) is introduced to search the value of the feature quantity Y, a corresponding target probability density function is determined according to different Y values and target parameter sets in the search process, a model parameter combination is inverted according to the target probability density function, and after the model parameter combination is substituted into the simulation model again, the solved feature quantity (simulation error) is used as an adaptation function, so as to complete the closed-loop verification. The target probability density function represents a conditional probability density function of the simulation parameter when the feature quantity is determined.

After the characteristic quantity Y which can enable the distance between the simulation waveform and the reference waveform to be minimum is determined by utilizing a particle swarm algorithm, a target model parameter set can be inverted according to a conditional probability density function corresponding to the Y, and finally, the target model parameter set is utilized to correct the electromagnetic transient simulation model to be corrected.

The parameter calibration method provided by the embodiment of the present invention is briefly described above, and the related method steps involved therein are described in detail below.

In an optional embodiment, in step S104, constructing a joint probability density function between the simulation parameters and the feature quantities based on the gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the plurality of sets of simulation parameters, and the reference waveform, specifically includes the following steps:

step S1041, determining a target simulation waveform based on the target group simulation parameters and the electromagnetic transient simulation model to be corrected.

Specifically, when batch simulation is performed on the electromagnetic transient simulation model to be corrected, specifically, target group simulation parameters are input into the electromagnetic transient simulation model to be corrected, and then a target simulation waveform output by the simulation model is obtained, wherein the target group simulation parameters represent any one group of parameters in a plurality of groups of simulation parameters; that is, the simulation waveforms corresponding to each set of simulation parameters can be obtained through batch simulation.

Step S1042, determining a target feature quantity corresponding to the target set of simulation parameters based on the target simulation waveform and the reference waveform.

Next, after the obtained target simulation waveform, a deviation (distance) between the target simulation waveform and the reference waveform is calculated to obtain a target feature amount corresponding to the target set of simulation parameters.

Step S1043, constructing a joint probability density function based on the plurality of sets of simulation parameters and the feature quantities corresponding to each set of simulation parameters.

As can be seen from the above description, in the embodiments of the present invention, the statistical relationship between the simulation parameters and the corresponding feature quantities is represented by using the joint probability density function based on the GMM, so that the joint probability density function can be constructed by combining all the simulation data after the feature quantities corresponding to each set of simulation parameters are obtained.

In an optional embodiment, as shown in fig. 2, the constructing a joint probability density function based on a plurality of sets of simulation parameters and feature quantities corresponding to each set of simulation parameters specifically includes the following steps:

step S10431, respectively performing normalization processing on the target group simulation parameters and the target feature quantities to obtain normalized simulation parameters and normalized feature quantities.

In order to reduce each simulation parameter and physical quantity to a solution space with the same dimension, the precision of the covariance matrix of the gaussian component in the iteration process is ensured, and therefore, after obtaining the target group simulation parameters and the target characteristic quantity, normalization processing needs to be performed respectively.

In the embodiment of the invention, during normalization processing, simulation parameters are reduced by referring to a preset optimization range, and characteristic quantities are reduced by referring to the maximum value and the minimum value in all simulation results.

The normalization equation is expressed as:

wherein y represents normalizedCharacteristic quantity before conversion, y_corRepresenting the characteristic quantity after normalization, y_minRepresents the minimum value of y in the simulation results, y_maxRepresenting the maximum value of y in the simulation result; x denotes the simulation parameters before normalization, x_corRepresenting the simulation parameter, x, after normalization_minRepresents the lower limit of the correction range of the simulation parameter x, x_maxRepresents the upper limit of the correction range of the simulation parameter x.

Step S10432, determining a target relation vector corresponding to the target group simulation parameter based on the normalized simulation parameter and the normalized feature quantity.

After the simulation parameters and the characteristics are normalized, the simulation parameters and the characteristics are combined and put into the same vector to obtain a target relation vector which can be recorded as [ X ]^T，Y^T]^TWherein X represents a combination of simulation parameters, and Y represents a combination of feature quantities. In the present embodiment, X and Y are both column vectors, so [ X ]^T，Y^T]^TIs the column vector with X and Y vertically pieced together. For ease of understanding, the following examples illustrate where X is [0, 1, 2 ]]^T，Y＝[3，4，5]^TThen [ X ]^T，Y^T]^T＝[0，1，2，3，4，5]^T。

And processing each group of simulation parameters and the corresponding characteristic quantity by utilizing the normalization and relation vector determination method to obtain a plurality of relation vectors.

Step S10433, fitting a joint probability density function between the simulation parameters and the feature quantities by using a gaussian mixture model based on the relationship vectors corresponding to the plurality of sets of simulation parameters.

Specifically, will [ X^T，Y^T]^TAnd each relation vector can be regarded as a scatter point in a high-dimensional space, and the probability density is higher at a place with high scatter point density, so that a joint probability density function between the simulation parameters and the characteristic quantity can be fitted by using a Gaussian mixture model according to all relation vectors obtained by the processing of the steps.

After determining the joint probability density function, in an alternative embodiment, as shown in fig. 3, in step S106, determining the target parameter set of the joint probability density function by using the maximum expectation algorithm and the akachi-pool information criterion specifically includes the following steps:

step S1061, obtaining a range of the number of gaussian components of the gaussian mixture model.

In step S1062, a parameter set of the objective function is determined using a maximum expectation algorithm.

In order to obtain the target parameter set, the number range of gaussian components of the gaussian mixture model is determined first, and the range is not specifically limited in the embodiment of the present invention, and the range has a relationship with a specific problem dimension and a data size, and can be set by a user according to actual requirements. For example, if [ X ]^T，Y^T]^TFor 15-dimensional random variables and a total of 15000 sets of simulation data, the number of gaussian components can be set to be generally 40-60.

Assuming that the number of gaussian components ranges from 40 to 60, solving a set of parameters of an objective function by using an EM algorithm, wherein the objective function represents a joint probability density function having a target number of gaussian components; that is, it is necessary to determine 60-40+1, which is a set of 21 joint probability density functions, and the 21 joint probability density functions have different gaussian components.

And step S1063, determining the comprehensive score of the objective function based on the Chichi information criterion.

Step S1064, determining a target parameter set of the joint probability density function based on the composite scores of all target functions within the number range.

In order to determine the appropriate number of gaussian components, the embodiment of the present invention needs to calculate the composite score of the joint probability density functions with different numbers of gaussian components, and continues with the above steps, that is, the scores of 21 different joint probability density functions need to be calculated, and the gaussian mixture model with the minimum composite score can well interpret the data and has the least free parameters. Therefore, in the embodiment of the present invention, the target parameter set of the joint probability density function between the simulation parameter and the feature quantity is determined by the target function with the smallest composite score.

In an optional embodiment, the determining of the composite score of the objective function based on the akachi pool information criterion specifically includes the following steps:

equation of utilization

Determining a composite score of the objective function; wherein AIC represents the comprehensive score, k represents the target number, n represents the total number of parameters of each group of simulation parameters and characteristic quantities, and L represents the maximum value of the likelihood function of the target function. The likelihood function is the probability of the result on the premise of parameter determination, and represents the fitting degree of the Gaussian mixture model, and the greater the likelihood function is, the better the fitting effect is. Therefore, after k is determined, the parameter set of the joint probability density function (i.e., the parameter set of the GMM) can be determined, and the calculation method of L is to bring each simulation data into the determined joint probability density function, obtain the probability, and then sum the probabilities.

Specifically, the calculation formula of AIC is expressed as AIC 2M-2L, where M represents the number of free parameters of the objective function, and L represents the maximum value of the likelihood function of the objective function, and in the present application, the number of free parameters M is equal to [ X [, [ X ]^T，Y^T]^TN (each group of simulation parameters is related to the total quantity of parameters of the characteristic quantity) and the quantity k of Gaussian components in the objective function, a parameter pi in a parameter set of the Gaussian mixture model represents the weight of each Gaussian component, and the quantity of free parameters in the pi is equal to k-1 because the sum of all weights is 1; the parameter mu represents the expectation of each Gaussian component, the quantity of mu is equal to the number k of Gaussian components, and each mu is a vector with the dimension of n, so that the total quantity of free parameters in mu is nk; parameter sigma²The number of covariance matrices representing each gaussian component is k, each covariance matrix is an n × n matrix, and since the covariance matrices are symmetric square matrices, the number of free parameters is 0.5n × (n +1) (the part of the covariance matrices where symmetry is removed by free parameter calculation). In summary, for the gaussian mixture model studied in the embodiment of the present invention, the expression for determining the composite score of the objective function by using the akachi information criterion AIC is as follows:

in the above, a detailed description is given of how to determine the target parameter set of the joint probability density function between the simulation parameters and the feature quantities, and a specific description is given below of how to determine the target model parameter set of the electromagnetic transient simulation model to be corrected.

In an optional embodiment, in step S108, inverting the target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm, and the target probability density function specifically includes the following steps:

step S1081, initializing a particle swarm with random initial positions in a preset search range; wherein, in an initial state.

The PSO is a heuristic algorithm, which is a random optimization technique in which a group searches for a target in a cooperative manner, and each individual in the group learns own experience and other individual experiences to change a search pattern.

In the embodiment of the present invention, the position of the PSO particle is set as the feature quantity, the position search range of the particle should be larger than the feature quantity value interval obtained by simulation, and the value of the feature quantity is 0 in an ideal state, so that when initializing the particle swarm, the central positions of all the particles are set as 0.

After the particle swarm initialization is finished, entering an iterative search stage, specifically, repeatedly executing the following steps S1082-S1086 until a preset termination condition is reached, and determining a target model parameter set based on the global optimal position of the particles under the preset termination condition:

step S1082, determining a target probability density function under the target characteristic quantity based on the target parameter set and the joint probability density function; wherein the target feature quantity represents a current position of any one particle in the particle group.

In particular toThe multidimensional gaussian distribution has conditional probability invariance, i.e. the conditional probability distribution of the multidimensional gaussian distribution is still a gaussian distribution given the partial variables, i.e.,

it also has similar properties to GMM, i.e., if [ X ]^T，Y^T]^TCharacterized by GMM, given Y ═ Y₀Under the condition(s), the conditional probability distribution of X is still a GMM and has

Wherein,

representing a conditional probability distribution f_X|YThe weight of the c-th gaussian component in (x | y),

representing a conditional probability distribution f_X|YThe average value of (x | y),

representing a conditional probability distribution f_X|YA covariance matrix of (x | y),

representing the mean of the c-th gaussian component in the joint probability density function,

a covariance matrix representing the c-th Gaussian component in the joint probability density function, X represents a simulation parameter combination, and y represents a feature quantity combination, since [ X [ ]^T，Y^T]^TEquivalent to piecing together the simulation parameters and the feature quantities, the mean and covariance matrices have a part dependent on x and a part dependent on y, which is the origin of the superscript in the above expression.

For example, suppose X has 8 dimensions and Y has 4 dimensions, due to the meanIs a one-dimensional vector, so

A vector of the first 8 dimensions representing the mean of the c-th gaussian component,

representing a vector formed by 4 dimensions after the c-th Gaussian component; according to the expression of the covariance matrix, the covariance matrix utilizes the concept of blocking, so that when solving the conditional probability density function, the corresponding block is used, that is, if X has 8 dimensions and Y has 4 dimensions, then the corresponding block is used correspondingly

Is an 8 x 8 matrix and is characterized in that,

is an 8 x 4 matrix and is characterized in that,

is a 4 x 8 matrix and is characterized in that,

is a 4 x 4 matrix.

The current position of a certain particle is known and is taken as a target characteristic quantity to be brought into the conditional probability distribution, and a target probability density function under the target characteristic quantity can be determined by combining known parameter values in a target parameter set. By analogy, the conditional probability density functions corresponding to all the particle positions in the particle swarm can be obtained.

Step S1083, determining a set of prediction parameters of the electromagnetic transient simulation model to be corrected based on the target probability density function.

As can be seen from the above description, the random variable in the target probability density function is only X, and therefore, by substituting the specific value of the feature quantity into the correlation equation of the conditional probability distribution in the above step S1082, the parameter set of the probability density function containing only the random variable X can be obtained, and then, the mathematical expectation of the probability density function is used as the estimated value of X to invert X, specifically,

and then, the estimation parameter set can be solved, that is, the position of each particle corresponds to one set of estimation parameter set.

Different from the random optimization of the parameters by directly using the PSO, the embodiment of the invention models the statistical relationship between the simulation parameters and the characteristic quantity by using the GMM, and can realize the reverse reasoning from the characteristic quantity to the simulation parameters on the basis of the conditional probability, thereby having the advantage of reducing the dimensionality of a solution space. For the multi-parameter optimization problem, the PSO is directly used to have insufficient searching capability on solution space, so that the situation of having no relation to most spaces easily occurs, after the characteristic quantity is introduced to the reverse mapping of simulation parameters, the particle coordinates (particle positions) become the manually selected characteristic quantity, the characteristic quantity selection is not too much, the dimension of the solution space is controlled, and the searching process of the problem is simplified.

And S1084, determining an adaptive function of each particle in the particle swarm algorithm based on the estimation parameter set, the electromagnetic transient simulation model to be corrected and the reference waveform.

In the embodiment of the invention, the adaptive function selected in the PSO execution process is the distance between a simulation waveform obtained after substituting the characteristic quantity and the estimation parameter set inverted by the GMM into the simulation model and a reference waveform, namely, the characteristic quantity is used for deducing the simulation parameter according to the simulation model, and then the simulation parameter is used for reversely deducing the actual characteristic quantity. Based on such closed-loop logic, the reliability of inverted parameter combinations is high, and the solution space range is easily determined after normalization processing is performed on the feature quantities.

Specifically, the method for determining the adaptive function of each particle in the particle swarm algorithm based on the estimation parameter set, the electromagnetic transient simulation model to be corrected and the reference waveform specifically comprises the following steps:

firstly, an actual simulation waveform is determined based on the prediction parameter set and the electromagnetic transient simulation model to be corrected. Then, the actual simulation waveform and the reference waveform are calculated to determine a simulation error, and the simulation error is used as an adaptive function. The method for calculating the adaptive function according to the embodiment of the present invention is the same as the data processing method in steps S1041 to S1042, and therefore, the description thereof is omitted here.

Step S1085, updating the velocity of each particle, the optimal position of each particle and the current candidate position based on the fitness function; wherein the current candidate position represents a global best position of the particle.

Step S1086, updating the current position of each particle based on the motion formula of the particles in the particle swarm optimization.

In the PSO algorithm, the update formula of the particle velocity is: v_ik+1＝V_ik+c₁rand1(pbest_i-x_ik)+c₂rand2(gbest-x_ik) Wherein i represents a particle number, k represents the number of iterations, V_ikRepresents the velocity, V, of the ith particle at the kth iteration_ik+1Represents the velocity, x, of the ith particle at the (k +1) th iteration_ikDenotes the position of the ith particle at the kth iteration, pbest_iDenotes the optimal position of the ith particle, gbest denotes the global optimal position of the particle, rand1 and rand2 represent random numbers between 0 and1, c₁，c₂All represent preset learning factors; the update formula of the particle position is: x is the number of_ik+1＝x_ik+V_ikWherein x is_ik+1Indicating the position of the ith particle at the (k +1) th iteration.

The steps S1082 to S1086 are repeatedly executed until a preset termination condition is reached, generally, the termination condition may be selected to reach the maximum iteration number, or reach a preset convergence condition, which is not specifically limited in the embodiment of the present invention. After iteration is terminated, a global optimum position of the particle can be obtained, then a corresponding conditional probability density function is determined according to the characteristic quantity corresponding to the position, and finally, the mathematical expectation of the conditional probability density function is used as a target model parameter group of the electromagnetic transient simulation model to be corrected.

In summary, when the parameter space is large, the method provided by the invention can automatically adjust the number of gaussian components and the covariance matrix dimension of each gaussian component to give consideration to both calculation efficiency and fitting accuracy, and compared with the prior art, the complexity of the empirical method is increased exponentially under the condition, which is very unfavorable for solving the problem; in addition, for the problem that constraint conditions are complex for parameters, if the solution space irregularity degree is extremely large and particles cannot escape from a hypercube, the search range of the particle swarm algorithm is further limited, but the reverse PSO based on the characteristic quantity in the method is not constrained, and the generalization performance is guaranteed to a certain extent, so that the parameter correction method provided by the invention has high operability and reliability.

Example two

The embodiment of the present invention further provides a parameter correction device for an electromagnetic transient simulation model, which is mainly used for executing the parameter correction method for the electromagnetic transient simulation model provided in the first embodiment of the present invention, and the following provides a detailed description of the parameter correction device for the electromagnetic transient simulation model provided in the first embodiment of the present invention.

Fig. 4 is a functional block diagram of a parameter calibration apparatus for an electromagnetic transient simulation model according to an embodiment of the present invention, as shown in fig. 4, the apparatus mainly includes: the method comprises an acquisition module 10, a construction module 20, a determination module 30 and an inversion module 40, wherein:

the acquiring module 10 is configured to acquire multiple sets of simulation parameters of the electromagnetic transient simulation model to be corrected, and a reference waveform under a preset working condition.

A building module 20, configured to build a joint probability density function between the simulation parameters and the feature quantities based on the gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the multiple sets of simulation parameters, and the reference waveform; the characteristic quantity represents the deviation of the reference waveform and the simulation waveform of the electromagnetic transient simulation model to be corrected under the simulation parameters.

A determining module 30, configured to determine a target parameter set of the joint probability density function using a maximum expectation algorithm and an akabane information criterion.

The inversion module 40 is used for inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function and correcting the target model parameter set by utilizing the target model parameter set; the target probability density function represents a conditional probability density function of the simulation parameter when the feature quantity is determined.

According to the parameter correction device of the electromagnetic transient simulation model, provided by the embodiment of the invention, after a plurality of groups of simulation parameters of the electromagnetic transient simulation model to be corrected and a reference waveform under a preset working condition are obtained, a joint probability density function between the simulation parameters and characteristic quantities based on a Gaussian mixture model is firstly established, and then a target parameter set is determined by utilizing a maximum expectation algorithm and a Chichi-chi information criterion; in addition, the invention utilizes the particle swarm algorithm and the conditional probability density function of the simulation parameters during the characteristic quantity determination to invert the target model parameter set, thereby effectively controlling the dimension of the learning space and simplifying the searching process of the problem. The electromagnetic transient simulation model corrected by the target model parameter set can accurately guide accident inversion and production practice.

Optionally, the building block 20 includes:

the first determining unit is used for determining a target simulation waveform based on the target group simulation parameters and the electromagnetic transient simulation model to be corrected; wherein the target set of simulation parameters represents any one of the plurality of sets of simulation parameters.

And the second determining unit is used for determining the target characteristic quantity corresponding to the target group simulation parameters based on the target simulation waveform and the reference waveform.

And the construction unit is used for constructing a joint probability density function based on the multiple groups of simulation parameters and the characteristic quantities corresponding to each group of simulation parameters.

Optionally, the construction unit is specifically configured to:

and respectively carrying out normalization processing on the target group simulation parameters and the target characteristic quantity to obtain normalized simulation parameters and normalized characteristic quantity.

And determining a target relation vector corresponding to the simulation parameters of the target group based on the normalized simulation parameters and the normalized characteristic quantity.

And fitting a joint probability density function between the simulation parameters and the characteristic quantity by utilizing a Gaussian mixture model based on the corresponding relation vectors of the multiple groups of simulation parameters.

Optionally, the determining module 30 includes:

and the acquiring unit is used for acquiring the number range of the Gaussian components of the Gaussian mixture model.

A third determining unit for determining a parameter set of the objective function using a maximum expectation algorithm; wherein the objective function represents a joint probability density function having a target number of gaussian components.

And the fourth determination unit is used for determining the comprehensive score of the objective function based on the akachi pool information criterion.

And the fifth determining unit is used for determining the target parameter set of the joint probability density function based on the comprehensive scores of all the target functions in the quantity range.

Optionally, the fourth determining unit is specifically configured to:

equation of utilization

Determining a composite score of the objective function; wherein AIC represents the comprehensive score, k represents the target number, n represents the total number of parameters of each group of simulation parameters and characteristic quantities, and L represents the maximum value of the likelihood function of the target function.

Optionally, the inversion module 40 includes:

the device comprises an initial unit, a searching unit and a control unit, wherein the initial unit is used for initializing a particle swarm with a random initial position in a preset searching range; wherein, the central position of all the particles in the initial state is 0.

The repeated execution unit is used for repeatedly executing the following steps until a preset termination condition is reached, and determining the target model parameter group based on the global optimal position of the particle under the preset termination condition:

determining a target probability density function under the target characteristic quantity based on the target parameter set and the joint probability density function; wherein the target feature quantity represents a current position of any one particle in the particle group.

And determining a prediction parameter set of the electromagnetic transient simulation model to be corrected based on the target probability density function.

And determining an adaptive function of each particle in the particle swarm algorithm based on the estimation parameter set, the electromagnetic transient simulation model to be corrected and the reference waveform.

Updating the speed of each particle, the optimal position of each particle and the current candidate position based on the adaptive function; wherein the current candidate position represents a global best position of the particle.

And updating the current position of each particle based on the motion formula of the particles in the particle swarm optimization.

Optionally, the inversion module 40 is further configured to:

and determining an actual simulation waveform based on the estimation parameter group and the electromagnetic transient simulation model to be corrected.

And calculating an actual simulation waveform and a reference waveform to determine a simulation error, and taking the simulation error as an adaptive function.

EXAMPLE III

Referring to fig. 5, an embodiment of the present invention provides an electronic device, including: a processor 60, a memory 61, a bus 62 and a communication interface 63, wherein the processor 60, the communication interface 63 and the memory 61 are connected through the bus 62; the processor 60 is arranged to execute executable modules, such as computer programs, stored in the memory 61.

The Memory 61 may include a high-speed Random Access Memory (RAM) and may also include a non-volatile Memory (non-volatile Memory), such as at least one disk Memory. The communication connection between the network element of the system and at least one other network element is realized through at least one communication interface 63 (which may be wired or wireless), and the internet, a wide area network, a local network, a metropolitan area network, and the like can be used.

The bus 62 may be an ISA bus, PCI bus, EISA bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one double-headed arrow is shown in FIG. 5, but this does not indicate only one bus or one type of bus.

The memory 61 is used for storing a program, the processor 60 executes the program after receiving an execution instruction, and the method executed by the apparatus defined by the flow process disclosed in any of the foregoing embodiments of the present invention may be applied to the processor 60, or implemented by the processor 60.

The processor 60 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware or instructions in the form of software in the processor 60. The processor 60 may be a general-purpose processor, and includes a Central Processing Unit (CPU), a Network Processor (NP), and the like; the device can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA) or other Programmable logic device, a discrete Gate or transistor logic device, or a discrete hardware component. The various methods, steps and logic blocks disclosed in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in a memory 61, and the processor 60 reads the information in the memory 61 and, in combination with its hardware, performs the steps of the above method.

The method and the apparatus for correcting parameters of an electromagnetic transient simulation model, and the computer program product of an electronic device provided in the embodiments of the present invention include a computer-readable storage medium storing a non-volatile program code executable by a processor, where instructions included in the program code may be used to execute the method described in the foregoing method embodiments, and specific implementation may refer to the method embodiments, and will not be described herein again.

In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.

The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer-readable storage medium executable by a processor. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.

It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.

In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings or the orientations or positional relationships that the products of the present invention are conventionally placed in use, and are only used for convenience in describing the present invention and simplifying the description, but do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," "third," and the like are used solely to distinguish one from another and are not to be construed as indicating or implying relative importance.

Furthermore, the terms "horizontal", "vertical", "overhang" and the like do not imply that the components are required to be absolutely horizontal or overhang, but may be slightly inclined. For example, "horizontal" merely means that the direction is more horizontal than "vertical" and does not mean that the structure must be perfectly horizontal, but may be slightly inclined.

In the description of the present invention, it should also be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly and may, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A parameter correction method for an electromagnetic transient simulation model is characterized by comprising the following steps:

acquiring multiple groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under preset working conditions;

constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the multiple groups of simulation parameters and the reference waveform; wherein the characteristic quantity represents the deviation of the reference waveform and the simulation waveform of the electromagnetic transient simulation model to be corrected under the simulation parameters;

determining a target parameter set of the joint probability density function by utilizing a maximum expectation algorithm and an akachi pool information criterion;

inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function, and correcting the target model parameter set by utilizing the target model parameter set; wherein the target probability density function represents a conditional probability density function of the simulation parameter at the time of the feature quantity determination.

2. The method according to claim 1, wherein constructing a joint probability density function between simulation parameters and feature quantities based on a gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the plurality of sets of simulation parameters and the reference waveform comprises:

determining a target simulation waveform based on the target group simulation parameters and the electromagnetic transient simulation model to be corrected; wherein the target set of simulation parameters represents any one of a plurality of sets of the simulation parameters;

determining a target characteristic quantity corresponding to the target group simulation parameters based on the target simulation waveform and the reference waveform;

and constructing the joint probability density function based on the multiple groups of simulation parameters and the characteristic quantities corresponding to each group of simulation parameters.

3. The method of claim 2, wherein constructing the joint probability density function based on the plurality of sets of simulation parameters and the feature quantities corresponding to each set of simulation parameters comprises:

respectively carrying out normalization processing on the target group simulation parameters and the target characteristic quantity to obtain normalized simulation parameters and normalized characteristic quantity;

determining a target relation vector corresponding to the target group simulation parameters based on the normalized simulation parameters and the normalized characteristic quantity;

4. The method of claim 1, wherein determining the set of target parameters for the joint probability density function using a maximum expectation algorithm and a Chi-chi information criterion comprises:

acquiring the quantity range of Gaussian components of the Gaussian mixture model;

determining a set of parameters of an objective function using the maximum expectation algorithm; wherein the objective function represents a joint probability density function having a target number of Gaussian components;

determining a composite score of the objective function based on the akachi information criterion;

determining a set of target parameters for the joint probability density function based on the composite scores for all target functions within the quantity range.

5. The method of claim 4, wherein determining a composite score for the objective function based on the akabane information criterion comprises:

equation of utilization

Determining a composite score for the objective function; wherein AIC represents the composite score, k represents the number of targets, n represents a total number of parameters of each set of the simulation parameters and the feature quantities, and L represents a maximum value of a likelihood function of the objective function.

6. The method of claim 1, wherein inverting the target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm, and a target probability density function comprises:

initializing a particle swarm with a random initial position in a preset search range; wherein, the central positions of all the particles in the initial state are 0;

repeatedly executing the following steps until a preset termination condition is reached, and determining the target model parameter group based on the global optimal position of the particles under the preset termination condition:

determining a target probability density function under a target characteristic quantity based on the target parameter set and the joint probability density function; wherein the target characteristic quantity represents a current position of any one particle in the particle swarm;

determining a pre-estimation parameter set of the electromagnetic transient simulation model to be corrected based on the target probability density function;

determining an adaptive function of each particle in the particle swarm algorithm based on the prediction parameter set, the electromagnetic transient simulation model to be corrected and the reference waveform;

updating the velocity of each of the particles, the optimal position of each of the particles, and the current candidate position based on the fitness function; wherein the current candidate position represents a global best position of a particle;

updating the current position of each particle based on the motion formula of the particles in the particle swarm optimization.

7. The method of claim 6, wherein determining an adaptation function for each of the particles in the particle swarm algorithm based on the set of prediction parameters, the electromagnetic transient simulation model to be corrected, and the reference waveform comprises:

determining an actual simulation waveform based on the estimation parameter group and the electromagnetic transient simulation model to be corrected;

and calculating the actual simulation waveform and the reference waveform to determine a simulation error, and taking the simulation error as the adaptive function.

8. A parameter correction apparatus for an electromagnetic transient simulation model, comprising:

the acquisition module is used for acquiring a plurality of groups of simulation parameters of the electromagnetic transient simulation model to be corrected and reference waveforms under a preset working condition;

the construction module is used for constructing a joint probability density function between simulation parameters and characteristic quantities based on a Gaussian mixture model according to the electromagnetic transient simulation model to be corrected, the multiple groups of simulation parameters and the reference waveform; wherein the characteristic quantity represents the deviation of the reference waveform and the simulation waveform of the electromagnetic transient simulation model to be corrected under the simulation parameters;

the determining module is used for determining a target parameter set of the joint probability density function by utilizing a maximum expectation algorithm and a Chichi information criterion;

the inversion module is used for inverting a target model parameter set of the electromagnetic transient simulation model to be corrected based on the target parameter set, the particle swarm algorithm and the target probability density function and correcting the target model parameter set by utilizing the target model parameter set; wherein the target probability density function represents a conditional probability density function of the simulation parameter at the time of the feature quantity determination.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method of any of claims 1 to 7 when executing the computer program.

10. A computer-readable medium having non-volatile program code executable by a processor, the program code causing the processor to perform the method of any of claims 1 to 7.