CN111289937A - Optical current transformer error compensation method based on DE-SVM - Google Patents

Optical current transformer error compensation method based on DE-SVM Download PDF

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CN111289937A
CN111289937A CN202010149794.3A CN202010149794A CN111289937A CN 111289937 A CN111289937 A CN 111289937A CN 202010149794 A CN202010149794 A CN 202010149794A CN 111289937 A CN111289937 A CN 111289937A
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svm
error compensation
current transformer
parameter
model
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刘林
戴航
宋宇
韦景康
刘攸坚
严杰峰
包汉玲
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Guangdong Power Grid Co Ltd
Foshan Power Supply Bureau of Guangdong Power Grid Corp
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Guangdong Power Grid Co Ltd
Foshan Power Supply Bureau of Guangdong Power Grid Corp
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R35/00—Testing or calibrating of apparatus covered by the other groups of this subclass
    • G01R35/02—Testing or calibrating of apparatus covered by the other groups of this subclass of auxiliary devices, e.g. of instrument transformers according to prescribed transformation ratio, phase angle, or wattage rating

Abstract

The invention provides an error compensation method of an optical current transformer based on a DE-SVM, which comprises the steps of simultaneously injecting measured current into the optical current transformer and a traditional current transformer, constructing an input-output training sample, optimizing parameters of a support vector machine SVM by using a differential evolution algorithm DE, combining the input-output training sample with the optimized parameters of the support vector machine SVM to obtain a DE-SVM error compensation model, carrying out l-layer wavelet decomposition on the output current of the optical current transformer to obtain a wavelet decomposition signal, extracting a α -th layer high-frequency coefficient of the wavelet decomposition signal, drawing a wavelet waveform, and inputting the current of a transient time period in the wavelet waveform into the DE-SVM error compensation model to obtain compensated output current.

Description

Optical current transformer error compensation method based on DE-SVM
Technical Field
The invention relates to the technical field of optical current transformer error compensation, in particular to an optical current transformer error compensation method based on a DE-SVM.
Background
An intelligent transformer substation is an important component of an intelligent power grid, an electronic transformer is a key device of the intelligent transformer substation, and an all-fiber current transformer is one of main varieties of the electronic current transformers. Like the magneto-optical glass optical current transformer, the all-fiber current transformer has the advantages of no saturation, small volume, simple insulating structure, resistance to corrosion, aging resistance, wide measurement range and the like based on the Faraday magnetic gyrophoric effect, and is an important development direction of the electronic current transformer. However, because there is residual linear birefringence in the optical fiber material, and at the same time, various external factors such as temperature, vibration, pressure, etc. can cause linear birefringence, and the linear birefringence effect of the optical fiber can cause nonlinear errors of the optical current transformer, so that the stability and reliability of the optical current transformer can not be guaranteed, and the method for compensating the errors of the optical current transformer is limited in engineering application, and therefore, the method becomes a research hotspot of scholars at home and abroad.
At present, the following method is mainly adopted to compensate the error of the optical current transformer:
1) calculating the magnitude of the linear birefringence by establishing a complex linear birefringence mathematical model or compensating errors caused by the linear birefringence by a pure neural network and a Support Vector Machine (SVM); the method has the defects of complex model, low generalization capability, over-learning, easy falling into local optimization and the like, and has the consequences of large calculated amount and low precision in the compensation process.
2) The linear birefringence effect is suppressed by modifying the optical fiber current transformer body equipment; the method has the disadvantage of high cost and can only compensate the linear birefringence effect caused by temperature.
The differential evolution algorithm, called DE for short, is an efficient global optimization algorithm, belongs to one of evolution algorithms, and is widely applied to various fields of data mining, mode recognition, digital filter design, artificial neural networks, electromagnetism and the like due to the characteristics of simple structure, easy realization, rapid convergence, strong robustness and the like. In 1996, the differential evolution algorithm proved to be the fastest evolution algorithm in the first international evolutionary computing (ICEO) competition held in the famous ancient japan.
In summary, it is necessary to provide an optical current transformer error compensation method based on DE-SVM, which can more effectively compensate the optical current transformer error.
Disclosure of Invention
The invention provides an optical current transformer error compensation method based on a DE-SVM (Dee-support vector machine), aiming at overcoming the defects that the error compensation of the existing optical current transformer adopts a complex mathematical model or algorithm which is easy to fall into local optimization, and the direct modification of the optical current transformer body equipment has high cost.
The present invention aims to solve the above technical problem at least to some extent.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
an optical current transformer error compensation method based on a DE-SVM comprises the following steps:
s1, injecting a measured current into an optical current transformer and a traditional current transformer simultaneously;
s2, outputting the steady-state output current x of the optical current transformeriAs an input training sample for error compensation, the output current y of the traditional current transformer at the same time is usediForming input-output training sample set as output training sample for error compensation
Figure BDA0002402031460000021
i denotes the ith training sample, n denotes the training sampleThe number of the chips;
s3, selecting a Support Vector Machine (SVM), and optimizing a punishment parameter C, an insensitive loss parameter epsilon and a kernel parameter sigma of the SVM by using a differential evolution algorithm DE;
s4, combining input-output training samples with optimized SVM parameters by utilizing a Lagrange multiplier method to obtain a DE-SVM error compensation model;
s5, performing l-layer wavelet decomposition on the output current of the optical current transformer to obtain a wavelet decomposition signal of the output current;
s6, extracting α th-layer high-frequency coefficients of the wavelet decomposition signals, and drawing wavelet waveforms according to α th-layer high-frequency coefficients;
and S7, inputting the current in the transient state period in the wavelet waveform into a DE-SVM error compensation model to obtain the output current after linear birefringence compensation.
The support vector machine is a binary model, aims to find a hyperplane to segment a sample, maximizes an interval, and finally converts the hyperplane into a convex quadratic programming problem to solve.
Preferably, in step S3, the process of optimizing the penalty parameter C, the insensitive loss parameter epsilon, and the kernel parameter sigma of the support vector machine SVM is as follows:
s301, initialization: setting the initial population size N of a punishment parameter C, an insensitive loss parameter epsilon and a nuclear parameter sigmaPInitial variation parameter F0Maximum number of iterations GmaxMaximum cross probability CRmaxAnd minimum crossover probability CRmin；
S302, mutation: for each body s of G generation with punishment parameter c, insensitive loss parameter epsilon and nuclear parameter sigmaj GPerforming mutation operation to obtain the j th variant individual v of the G +1 th generationj G+1The formula for performing the mutation operation is as follows:
vj G+1＝sr3 G+F(sr1 G-sr2 G)
wherein r1, r2, r3 belongs to Np, r1, r2 and r3 are random numbers, and r1 ≠ r2 ≠ r3 ≠ j; sr3 GR3 individuals of G generation in the initial population, F the variation rate, which is real number, sr1 G-sr2 GRepresenting a difference variable, and determining the enlargement or reduction of the difference variable by F;
s303, crossing: variant individuals v of the G +1 generationj G+1With the current individual xj GPerforming two-term distribution cross operation to generate test individual uj G+1(ii) a The formula of the binomial distribution cross operation is as follows:
Figure BDA0002402031460000031
wherein u isj G+1For the resulting test subjects, rand (k) epsilon [0,1]Is a uniformly distributed random number; k represents a random number; cR∈[0,1]Representing the cross probability; m (j) is a random number between {1,2, …, D }, D representing the dimension of the solution space.
S304, selecting: calculating test individuals uj G+1Value h (u) corresponding to the objective function h(s)j G+1) Calculating the current individual sj GValue h(s) corresponding to the objective function h(s)j G) Taking h (u)j G+1) And h(s)j G) One corresponding individual with a small median value is taken as a new population individual sj G+1；
S305, judging whether the maximum iteration frequency is reached, if so, stopping iteration and outputting the optimal model parameters of the DE-SVM; otherwise, return to step S302.
Here, the mutation operation is to generate an intermediate individual vj G+1And the crossover operation is to ensure an intermediate individual vj G+1At least one "gene" per chromosome is inherited by the next generation, the first gene to cross-operate randomly from vj G+1The m (j) th gene is taken out as the crossed individual uj G+1All kinds of diseases "Gene ", the subsequent process is selection by cross probability CR
Figure BDA0002402031460000032
Or
Figure BDA0002402031460000033
As an allele.
Preferably, the penalty parameter c, the insensitive loss parameter epsilon and the kernel parameter sigma of the support vector machine SVM are optimized simultaneously by a differential evolution algorithm DE.
New population individuals S described in step S304j G+1The generation expression of (a) is:
Figure BDA0002402031460000034
wherein the content of the first and second substances,
Figure BDA0002402031460000041
h(s) is the average absolute percentage error of the output value of the training sample, and the independent variable s represents the population individual; y isiRepresenting the actual output value of the ith training sample; y isiRepresenting the actual output value of the ith training sample;
Figure BDA0002402031460000042
the output value of the DE-SVM model of the ith training sample is shown, and n represents the total number of the training samples.
Here, the selection operation is performed in order to determine individuals entering the next generation population.
Preferably, the step of obtaining the DE-SVM error compensation model in step S4 is:
s401, utilizing a nonlinear mapping function
Figure BDA0002402031460000043
Input-output training sample set
Figure BDA0002402031460000044
Mapping the linear indifferent input space to the linear divisible high-dimensional feature space, and adopting a Support Vector Machine (SVM) regression estimation function f (x) by the mapped error compensation modeli) The formula is as follows:
Figure BDA0002402031460000045
wherein the content of the first and second substances,
Figure BDA0002402031460000046
the method is a nonlinear mapping function from an input space to a high-dimensional feature space, w represents a weight coefficient, and b represents a threshold value;
s402, converting the initial model of the DE-SVM error compensation into a nonlinear equivalent programming model according to a structural principle:
wherein the objective function is:
Figure BDA0002402031460000047
constraint conditions are as follows:
Figure BDA0002402031460000048
Figure BDA0002402031460000049
Figure BDA00024020314600000410
wherein n represents the number of training samples ξ and ξ*All represent relaxation factors; c and epsilon are learning parameters of the nonlinear equivalent programming model, C is a penalty parameter, and epsilon is an insensitive loss parameter, and the complexity of the model and the proportion of training errors in the objective function are determined.
S403, converting the nonlinear equivalent programming model into a dual model by using a Lagrange multiplier method:
an objective function:
Figure BDA0002402031460000051
constraint conditions are as follows:
Figure BDA0002402031460000052
Figure BDA0002402031460000053
wherein, K (x)i,xl)＝φ(xi)φ(xl)；αi，
Figure BDA0002402031460000054
All represent lagrangian multipliers;
s404, solving the dual model to obtain Lagrangian parameters, and obtaining a final DE-SVM error compensation model by using the Lagrangian parameters:
Figure BDA0002402031460000055
wherein, K (x)i,xl) Representing the kernel function satisfying the Mercer condition, and taking the radial basis kernel function as:
K(xi,xl)＝exp(-‖xi–xl‖2/σ2)
where σ is a kernel function parameter.
Here, when the support vector machine is linearly inseparable when training samples, a nonlinear support vector machine is learned by kernel skill and soft space maximization to map a linearly inseparable input space to a linearly separable high-dimensional feature space.
Preferably, the method for performing l-layer wavelet decomposition on the output current of the optical current transformer in step S5 is a maratt algorithm, the maratt algorithm is an algorithm that vividly describes the multi-resolution characteristics of wavelets in a spatial concept, and different characteristics of an observed image can be observed from coarse to fine in each scale as the scale changes from large to small, and the method for extracting the α -th-layer high-frequency coefficient of the wavelet decomposition signal in step S6 is a reconstruction method of wavelet coefficient, which is a relatively mature prior art.
Preferably, the transient period in step S7 is:
Δt＝t2-t1
wherein, t2Indicating the line fault recovery time; t is t1Indicating the occurrence time of the line fault; Δ t represents a transient period.
Preferably, the current output value of the traditional current transformer in a steady state does not need to be compensated by a DE-SVM error compensation model.
Here, because the output current precision of the conventional electromagnetic current transformer can reach more than 0.2%, the current output value of the conventional current transformer in a steady state does not need to be compensated by a DE-SVM error compensation model, and the output current of the conventional current transformer is directly taken as an output training sample for error compensation, which is beneficial to ensuring the compensation precision of a subsequent DE-SVM error compensation model.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention provides an error compensation method of an optical current transformer based on DE-SVM, which optimizes the parameters of a support vector machine SVM by using a differential evolution algorithm DE, forms an input-output sample by using the steady-state output current of the optical current transformer and the output current of a traditional current transformer, constructs a DE-SVM error compensation model by combining with the support vector machine SVM, the parameter optimization of the SVM is carried out by the differential evolution algorithm DE, the defect that a DE-SVM error compensation model is easy to fall into local optimum when error compensation is carried out is avoided, and the steady-state output current of the optical current transformer and the output current of the traditional current transformer form an input-output sample, so that the compensation precision of the DE-SVM error compensation model is improved.
Drawings
FIG. 1 is a flow chart of the error compensation method of the optical current transformer based on the DE-SVM provided by the invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The flow chart of the error compensation method of the optical current transformer based on the DE-SVM shown in figure 1 comprises the following steps:
s1, injecting a measured current into an optical current transformer and a traditional current transformer simultaneously;
s2, outputting the steady-state output current x of the optical current transformeriAs an input training sample for error compensation, the output current y of the traditional current transformer at the same time is usediForming input-output training sample set as output training sample for error compensation
Figure BDA0002402031460000061
i represents the ith training sample, and n represents the number of the training samples;
s3, selecting a Support Vector Machine (SVM), and optimizing a punishment parameter C, an insensitive loss parameter epsilon and a kernel parameter sigma of the SVM by using a differential evolution algorithm DE; the punishment parameter c, the insensitive loss parameter epsilon and the kernel parameter sigma of the support vector machine SVM are simultaneously optimized by a differential evolution algorithm DE, and the process is as follows:
s301, initialization: setting the initial population size N of a punishment parameter C, an insensitive loss parameter epsilon and a nuclear parameter sigmaPInitial variation parameter F0Maximum number of iterations GmaxMaximum cross probability CRmaxAnd minimum crossover probability CRmin；
S302, mutation: for each body s of G generation with punishment parameter c, insensitive loss parameter epsilon and nuclear parameter sigmaj GPerforming mutation operation to obtain the jth of the G +1 th generationVariant individuals vj G+1The formula for performing the mutation operation is as follows:
vj G+1＝sr3 G+F(sr1 G-sr2 G)
wherein r1, r2, r3 belongs to Np, r1, r2 and r3 are random numbers, and r1 ≠ r2 ≠ r3 ≠ j; sr3 GR3 individuals of G generation in the initial population, F the variation rate, which is real number, sr1 G-sr2 GRepresenting a difference variable, and determining the enlargement or reduction of the difference variable by F;
s303, crossing: variant individuals v of the G +1 generationj G+1With the current individual xj GPerforming two-term distribution cross operation to generate test individual uj G+1(ii) a The formula of the binomial distribution cross operation is as follows:
Figure BDA0002402031460000071
wherein u isj G+1For the resulting test subjects, rand (k) epsilon [0,1]Is a uniformly distributed random number; k represents a random number; cR∈[0,1]Representing the cross probability; m (j) is a random number between {1,2, …, D }, D representing the dimension of the solution space.
S304, selecting: calculating test individuals uj G+1Value h (u) corresponding to the objective function h(s)j G+1) Calculating the current individual sj GValue h(s) corresponding to the objective function h(s)j G) Taking h (u)j G+1) And h(s)j G) One corresponding individual with a small median value is taken as a new population individual sj G+1(ii) a New population individuals S described in step S304j G+1The generation expression of (a) is:
Figure BDA0002402031460000072
wherein the content of the first and second substances,
Figure BDA0002402031460000073
h(s) is the average absolute percentage error of the output value of the training sample, and the independent variable s represents the population individual; y isiRepresenting the actual output value of the ith training sample;
Figure BDA0002402031460000074
the output value of the DE-SVM model of the ith training sample is shown, and n represents the total number of the training samples.
S305, judging whether the maximum iteration frequency is reached, if so, stopping iteration and outputting the optimal model parameters of the DE-SVM; otherwise, return to step S302.
S4, combining the input-output training samples with the optimized SVM parameters by using a Lagrange multiplier method to obtain a DE-SVM error compensation model, wherein the process is as follows:
s401, utilizing a nonlinear mapping function
Figure BDA0002402031460000081
Input-output training sample set
Figure BDA0002402031460000082
Mapping the linear indifferent input space to the linear divisible high-dimensional feature space, and adopting a Support Vector Machine (SVM) regression estimation function f (x) by the mapped error compensation modeli) The formula is as follows:
Figure BDA0002402031460000083
wherein the content of the first and second substances,
Figure BDA0002402031460000084
the method is a nonlinear mapping function from an input space to a high-dimensional feature space, w represents a weight coefficient, and b represents a threshold value;
s402, converting the initial model of the DE-SVM error compensation into a nonlinear equivalent programming model according to a structural principle:
wherein the objective function is:
Figure BDA0002402031460000085
constraint conditions are as follows:
Figure BDA0002402031460000086
Figure BDA0002402031460000087
Figure BDA0002402031460000088
wherein n represents the number of training samples ξ and ξ*All represent relaxation factors; c and epsilon are learning parameters of the nonlinear equivalent programming model, C is a penalty parameter, and epsilon is an insensitive loss parameter, and the complexity of the model and the proportion of training errors in the objective function are determined.
S403, converting the nonlinear equivalent programming model into a dual model by using a Lagrange multiplier method:
an objective function:
Figure BDA0002402031460000089
constraint conditions are as follows:
Figure BDA00024020314600000810
Figure BDA00024020314600000811
wherein, K (x)i,xl)＝φ(xi)φ(xl)；αi，
Figure BDA0002402031460000091
All represent lagrangian multipliers;
s404, solving the dual model to obtain Lagrangian parameters, and obtaining a final DE-SVM error compensation model by using the Lagrangian parameters:
Figure BDA0002402031460000092
wherein, K (x)i,xl) Representing the kernel function satisfying the Mercer condition, and taking the radial basis kernel function as:
K(xi,xl)＝exp(-‖xi–xl‖2/σ2)
where σ is a kernel function parameter.
S5, performing l-layer wavelet decomposition on the output current of the optical current transformer by using a Marait algorithm to obtain a wavelet decomposition signal of the output current;
s6, extracting α th-layer high-frequency coefficients of the wavelet decomposition signals by using a wavelet coefficient reconstruction method, and drawing wavelet waveforms according to α th-layer high-frequency coefficients;
and S7, inputting the current in the transient state period in the wavelet waveform into a DE-SVM error compensation model to obtain the output current after linear birefringence compensation. The transient period is:
Δt＝t2-t1
wherein, t2Indicating the line fault recovery time; t is t1Indicating the occurrence time of the line fault; Δ t represents a transient period.
Because the output current precision of the traditional electromagnetic current transformer can reach more than 0.2%, the output current of the traditional current transformer is directly taken as an output training sample for error compensation, and the compensation precision of a subsequent DE-SVM error compensation model is favorably ensured.
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. An optical current transformer error compensation method based on a DE-SVM is characterized by comprising the following steps:
s1, injecting a measured current into an optical current transformer and a traditional current transformer simultaneously;
s2, outputting the steady-state output current x of the optical current transformeriAs an input training sample for error compensation, the output current y of the traditional current transformer at the same time is usediForming input-output training sample set as output training sample for error compensation
Figure FDA0002402031450000011
i represents the ith training sample, and n represents the total number of the training samples;
s3, selecting a Support Vector Machine (SVM), and optimizing a punishment parameter C, an insensitive loss parameter epsilon and a kernel parameter sigma of the SVM by using a differential evolution algorithm DE;
s4, combining input-output training samples with optimized SVM parameters by utilizing a Lagrange multiplier method to obtain a DE-SVM error compensation model;
s5, performing l-layer wavelet decomposition on the output current of the optical current transformer to obtain a wavelet decomposition signal of the output current;
s6, extracting α th-layer high-frequency coefficients of the wavelet decomposition signals, and drawing wavelet waveforms according to α th-layer high-frequency coefficients;
and S7, inputting the current in the transient state period in the wavelet waveform into a DE-SVM error compensation model to obtain the output current after linear birefringence compensation.
2. The error compensation method of the optical current transformer based on the DE-SVM as claimed in claim 1, wherein the step S3 is to optimize the penalty parameter C, the insensitive loss parameter e and the kernel parameter σ of the support vector machine SVM by:
s301, initialization: setting the initial population size N of a punishment parameter C, an insensitive loss parameter epsilon and a nuclear parameter sigmaPInitial variation parameter F0Maximum number of iterations GmaxMaximum cross probability CRmaxAnd minimum crossover probability CRmin；
S302, mutation: for each body s of G generation with punishment parameter c, insensitive loss parameter epsilon and nuclear parameter sigmaj GPerforming mutation operation to obtain the j th variant individual v of the G +1 th generationj G+1The formula for performing the mutation operation is as follows:
vj G+1＝sr3 G+F(sr1 G-sr2 G)
wherein r1, r2, r3 belongs to Np, r1, r2 and r3 are random numbers, and r1 ≠ r2 ≠ r3 ≠ j; sr3 GR3 individuals of G generation in the initial population, F the variation rate, which is real number, sr1 G-sr2 GRepresenting a difference variable, and determining the enlargement or reduction of the difference variable by F;
s303, crossing: variant individuals v of the G +1 generationj G+1With the current individual sj GPerforming two-term distribution cross operation to generate test individual uj G+1；
S304, selecting: calculating test individuals uj G+1Value h (u) corresponding to the objective function h(s)j G+1) Calculating the current individual sj GValue h(s) corresponding to the objective function h(s)j G) Taking h (u)j G+1) And h(s)j G) One corresponding individual with a small median value is taken as a new population individual sj G+1；
S305, judging whether the maximum iteration frequency is reached, if so, stopping iteration and outputting the optimal model parameters of the DE-SVM; otherwise, return to step S302.
3. The error compensation method for the optical current transformer based on the DE-SVM as recited in claim 2, wherein the penalty parameter c, the insensitive loss parameter ε and the kernel parameter σ of the support vector machine SVM are optimized simultaneously by a differential evolution algorithm DE.
4. The error compensation method of an optical current transformer based on a DE-SVM as claimed in claim 2 or 3, wherein the formula of the binomial distribution crossover operation of step S303 is:
Figure FDA0002402031450000021
wherein u isj G+1For the resulting test subjects, rand (k) epsilon [0,1]Is a uniformly distributed random number; k represents a random number; cR∈[0,1]Representing the cross probability; m (j) is a random number between {1,2, …, D }, D representing the dimension of the solution space.
5. The error compensation method for optical current transformers based on DE-SVM according to claim 2 or 3, characterized in that the new population S of individuals of step S304j G+1The generation expression of (a) is:
Figure FDA0002402031450000022
wherein the content of the first and second substances,
Figure FDA0002402031450000023
h(s) is the average absolute percentage error of the output value of the training sample, and the independent variable s represents the population individual; y isiRepresenting the actual output value of the ith training sample;
Figure FDA0002402031450000024
the output value of the DE-SVM model of the ith training sample is shown, and n represents the total number of the training samples.
6. The error compensation method of the DE-SVM based optical current transformer according to claim 5, wherein the DE-SVM error compensation model of step S4 is obtained by the steps of:
s401, utilizing a nonlinear mapping function
Figure FDA0002402031450000025
Input-output training sample set
Figure FDA0002402031450000026
Mapping the linear indifferent input space to the linear divisible high-dimensional feature space, and adopting a Support Vector Machine (SVM) regression estimation function f (x) by the mapped error compensation modeli) The formula is as follows:
Figure FDA0002402031450000031
wherein the content of the first and second substances,
Figure FDA0002402031450000032
the method is a nonlinear mapping function from an input space to a high-dimensional feature space, w represents a weight coefficient, and b represents a threshold value;
s402, converting the initial model of the DE-SVM error compensation into a nonlinear equivalent programming model according to a structural principle:
wherein the objective function is:
Figure FDA0002402031450000033
constraint conditions are as follows:
Figure FDA0002402031450000034
Figure FDA0002402031450000035
Figure FDA0002402031450000036
wherein n represents the number of training samples ξ and ξ*All represent relaxation factors; c and epsilon are learning parameters of the nonlinear equivalent programming model, and determine the complexity of the model and the proportion of training errors in the objective function, wherein C is a penalty parameter, and epsilon is an insensitive loss parameter.
S403, converting the nonlinear equivalent programming model into a dual model by using a Lagrange multiplier method:
an objective function:
Figure FDA0002402031450000037
constraint conditions are as follows:
Figure FDA0002402031450000038
Figure FDA0002402031450000039
wherein, K (x)i,xl)＝φ(xi)φ(xl)；αi，
Figure FDA00024020314500000310
All represent lagrangian multipliers;
s404, solving the dual model to obtain Lagrangian parameters, and obtaining a final DE-SVM error compensation model by using the Lagrangian parameters:
Figure FDA0002402031450000041
wherein, K (x)i,xl) Representing the kernel function satisfying the Mercer condition, and taking the radial basis kernel function as:
K(xi,xl)＝exp(-‖xi-xl‖2/σ2)
where σ is a kernel function parameter.
7. The error compensation method for an optical current transformer based on a DE-SVM as claimed in claim 1, wherein the method for performing l-layer wavelet decomposition on the output current of the optical current transformer in step S5 is a maratt algorithm.
8. The error compensation method of the optical current transformer based on the DE-SVM as claimed in claim 1, wherein the method of extracting the α -th layer high frequency coefficient of the wavelet decomposition signal of step S6 is a reconstruction method of wavelet coefficient.
9. The error compensation method for an optical current transformer based on a DE-SVM as claimed in claim 1, wherein the transient period of step S7 is:
Δt＝t2-t1
wherein, t2Indicating the line fault recovery time; t is t1Indicating the occurrence time of the line fault; Δ t represents a transient period.
10. The error compensation method of the optical current transformer based on the DE-SVM as recited in claim 1, wherein the current output value of the conventional current transformer in a steady state is not compensated by a DE-SVM error compensation model.
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