CN113361146A - Improved particle swarm optimization-based manganese-copper shunt structure parameter optimization method - Google Patents

Improved particle swarm optimization-based manganese-copper shunt structure parameter optimization method Download PDF

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CN113361146A
CN113361146A CN202110825223.1A CN202110825223A CN113361146A CN 113361146 A CN113361146 A CN 113361146A CN 202110825223 A CN202110825223 A CN 202110825223A CN 113361146 A CN113361146 A CN 113361146A
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manganin shunt
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CN113361146B (en
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赵燕
刘仕萍
郭雪薇
王珺
胡涛
朱亮
邓高峰
赵震宇
祝婧
熊紫腾
杨立行
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Power Supply Service Management Center Of State Grid Jiangxi Electric Power Co ltd
State Grid Corp of China SGCC
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Abstract

The invention provides a manganin shunt structure parameter optimization method based on an improved particle swarm optimization algorithm, which optimizes the design of each key size parameter of the manganin shunt by adopting the improved particle swarm optimization algorithm. Firstly, the robustness of the manganin shunt is referenced by combining the actual manufacturing process of the manganin shunt, a multi-target global optimization model of induced current is established, multi-targets are converted into single-target optimization by utilizing an analytic hierarchy process, global optimization is carried out based on the establishment of an improved particle swarm algorithm, and finally the global optimal structural design size of the manganin shunt is obtained. The invention can select the design parameters of the better manganin shunt, and compared with the original manganin shunt, the invention not only improves the power frequency magnetic field interference resistance of the manganin shunt, but also improves the robustness of the manganin shunt.

Description

Improved particle swarm optimization-based manganese-copper shunt structure parameter optimization method
Technical Field
The invention relates to the technical field of electric energy metering, in particular to an optimized design method for structural parameters of a manganin shunt in an intelligent electric meter.
Background
The manganin shunt is widely applied to the field of current sampling of intelligent electric meters due to the characteristics of good stability, small temperature coefficient and the like, and particularly occupies a leading position in current application of single-phase electric energy meters. In consideration of current heating and cost, the resistance value of the existing manganin shunt is generally designed to be between 100u omega and 300u omega, and the converted voltage signal is only in the level of microvolts to millivolts, so that the current signal acquired by the manganin shunt is easily interfered by a power frequency magnetic field, the current signal sampling is inaccurate, and particularly, the error can reach more than 6% when small current is sampled.
In order to improve the anti-interference capability of the existing intelligent electric meter, the structure of the manganin shunt is improved, so that the existing intelligent electric meter can resist magnetic field interference from uncertain directions, and the metering accuracy of an electronic electric energy meter is guaranteed. According to the structural characteristics of the existing manganin shunt, simulation analysis finds that the position of a through hole, the size of the through hole, the length of an upper leading-out end and the length of a lower leading-out end of the manganin shunt in the existing structure have great relation to induced current generated under the interference of a power frequency magnetic field. Therefore, the minimum induced current can be obtained by changing the position of the through hole, the size of the through hole, the length of the upper leading-out end and the length of the lower leading-out end, and the manganin shunt with stronger power frequency magnetic field interference resistance is formed. Conventional manganin shunts are designed using the Taguchi robust parameters, but the Taguchi method is not global to the optimization of the manganin shunt since the parameter levels are chosen discretely and the induced current is a nonlinear response.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a manganin shunt structural parameter optimization method based on an improved particle swarm optimization algorithm, which is used for optimizing the structural parameter design of a manganin shunt so that the manganin shunt has stronger power frequency magnetic field interference resistance, and the key influence factors of the manganin shunt induced current are determined by simulation analysis of the manganin shunt induced current under a power frequency magnetic field: the position of the through hole, the size of the through hole, the length of the upper leading-out end and the length of the lower leading-out end, and the establishment of a key influence factor and induction current approximate model is completed.
According to the invention, the optimization method of the manganese-copper shunt structure parameters based on the improved particle swarm optimization algorithm comprises the following steps:
step 1, determining a global optimization target of the manganin shunt, and integrating a plurality of optimization targets into a single optimization target by utilizing an analytic hierarchy process. In the optimizing process, the improvement of one target performance can cause the reduction of the other target performance, so that multiple targets need to be planned, the invention utilizes an analytic hierarchy process to convert the multiple-target optimization into single-target optimization with weight, and the root mean square of induced current under the interference of power frequency magnetic field in direction X, Y
Figure BDA0003173342550000011
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic fieldxStandard deviation sigma of induced current under interference of power frequency magnetic field in Y directionyOf importance degree by three big indicatorsAnd comparing every two models to establish a judgment matrix of the model.
And after the judgment matrix is determined, consistency check is carried out on the established judgment matrix by utilizing the consistency ratio CR. The calculation mode of the consistency index CR is as follows:
Figure BDA0003173342550000012
in the formula, λmaxIn order to judge the maximum eigenvalue of the matrix, n is the order of the matrix, CI is a defined consistency index, and RI is a consistency index constant, corresponding to the order n of the comparison matrix one to one.
And when CR is less than or equal to 0.1, the consistency is passed, otherwise, a judgment matrix needs to be reestablished, and when the consistency is passed, the normalization processing is carried out on the eigenvector corresponding to the maximum eigenvalue, namely the weight corresponding to each factor.
An objective function is obtained by using an analytic hierarchy process and constraint conditions are given, and the general mathematical expression is as follows:
Figure BDA0003173342550000013
in the formula, an induced current I is takenxAnd an induced current IyRoot mean square, induced current I ofxStandard deviation of (a)xInduced current IyStandard deviation of (a)yAs an objective function, a weight vector { alpha }1、α2、α3The ratio coefficient between multiple targets is determined by an analytic hierarchy process; x ═ X1，x2，…xn]For the solution to be optimized for the objective function, gj(X) is the equality constraint to be solved, hi(X) is an inequality constraint condition to be solved, XUAnd XLRepresenting the upper and lower boundary values of the design variable, respectively.
Step 2, initializing the particle swarm: the number of key influence factors of the induced current of the manganin shunt is used as the dimension of the population, the size of the population is determined, and the initial speed, the initial position, the local optimal position and the global optimal position of each particle swarm are set.
And 3, starting training key influence factors of the induced current of the manganin shunt: position X of the through-hole1Size X of the through hole2Length X of upper leading-out end3And lower lead-out length X4Calculating the velocity v of each particle of the population according to equation (3)i(t +1) and position pi(t+1)：
Figure BDA0003173342550000026
In the formula, vi(t) is the vector velocity of the ith particle after the population is updated for t times; p is a radical ofi(t) and pi(t-1) the positions of the ith particles after the population is updated for t times and after the population is updated for t-1 times respectively; c. C1、c2And c3Is an acceleration factor; w (t) is an inertial weight, and rand is a random number between 0 and 1; pbest,iThe local optimal position of the ith particle of the population; gbestIs the global optimum position of the population;
the inertia weight w (t) of the population is set by referring to a simulated annealing algorithm and utilizing the idea of random vibration, and the inertia weight formula is as follows:
Figure BDA0003173342550000021
where rands is a random number between-1 and t is the number of iterations.
Acceleration factor c of population1And c2Replacing the constant acceleration factor by a decreasing and increasing change factor, respectively, c3With reference to simulated annealing algorithms, i.e.
Figure BDA0003173342550000022
In the formula, c1,s、c2,sRespectively correspond to the learning factors c1、c2Initial value of c1,e、c2,eAnd c3,eRespectively correspond to the learning factors c1、c2And c3T is the current iteration number, and T is the maximum iteration number. In general c1,s>c1,e，c2,s<c2,e，c1Decreasing with t, c2Increasing with t, c3Then gradually increases with the vibration and continuously approaches c3,e。
Substituting the formulae (4) and (5) for the formula (3) to obtain piAfter (t +1), correction is performed according to the boundary conditions:
Figure BDA0003173342550000023
in the formula, pmaxIs the upper limit of position, pminIs the lower limit of the position for specifying the position of the particles, removing undesirable dependent variables.
F (X) is an objective optimization function, and can be used as the fitness of the function to adopt the foreshortening property. p is a radical ofi(t) is the position of the ith particle after t population updates, F (p)i(t)) represents pi(t) fitness of particle position.
Step 4, the current fitness F (p) of each particle is calculatedi(t)) and the fitness F (p) of the previous timei(t-1)) making a comparison, if the fitness at the moment is better than that of the previous position, replacing the position at the previous moment, and otherwise keeping the fitness unchanged; if the fitness at the moment is the optimal result, replacing the result with the result of the optimal position, wherein the definition formula is as follows:
Figure BDA0003173342550000024
and 5, updating t to t +1, continuously repeating the step 3 and the step 4, and when the particle iteration is finished or the optimal value is reached, the last GbestIt is the optimal solution.
And 6, designing, processing and manufacturing the manganin shunt by taking the optimal position as the design parameter of the manganin shunt.
Compared with the prior art, the invention has the beneficial effects that:
according to the improved particle swarm optimization-based manganin shunt structure parameter optimization method, the design parameters of the manganin shunt can be selected better, and compared with the original manganin shunt, the power frequency magnetic field interference resistance of the manganin shunt is improved, and meanwhile, the robustness of the manganin shunt is improved.
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FIG. 1 is a flow chart of the method of the present invention;
Detailed Description
For a further understanding of the present invention, reference will now be made in detail to the present invention, examples of which are illustrated in the accompanying drawings.
Firstly, selecting a through hole type manganin shunt, and analyzing the key influence factors of the magnitude of the induced current of the manganin shunt under a power frequency magnetic field by simulation as follows: the position of the through hole, the size of the through hole, the length of the upper leading-out end and the length of the lower leading-out end; then, building a key influence factor and induction current approximate model by utilizing flux simulation analysis; finally, obtaining influence factors: and the fast calculation formula of the position of the through hole, the size of the through hole, the length of the upper leading-out end, the length of the lower leading-out end and the induction current value. The invention utilizes a quick calculation formula to optimally select key influence factors of the manganese-copper current divider.
According to the invention, as shown in fig. 1, the optimization method of the structural parameters of the manganin shunt based on the improved particle swarm optimization comprises the following steps:
step 1, determining a global optimization target of the manganin shunt, and integrating a plurality of optimization targets into a single optimization target by utilizing an analytic hierarchy process: wherein, induced current I under X-direction power frequency magnetic field interferencexInduced current I under interference of power frequency magnetic field in Y directionyAnd is a fixed optimization goal. In order to improve the robustness of the manganin shunt and solve the problems of poor consistency and unstable quality output of the shunt in the production process, the fluctuation quantity of the four size parameters is positioned to be +/-0.1 by the error factors corresponding to the four key size parameters according to the tolerance standard GB/T1804-2000 m. Taking 3 levels for each error factor, wherein 3 levels correspond to 3 levelsThe central value of each size parameter, the central value of each size parameter is-0.1 and the central value of each size parameter is +0.1, then the 3 levels are subjected to manganese copper diverter experimental scheme design, if each level combination is calculated, 81 times of calculation are needed, and the method selects L18 (2) according to four input three levels1×37) The orthogonal method can obtain more accurate and reliable results only by calculating 18 times, finally, the induced current of each time is solved, and the standard deviation sigma of the induced current under the interference of the X-direction power frequency magnetic fieldxStandard deviation sigma of induced current under interference of power frequency magnetic field in Y directionyAs two other optimization objectives.
In the optimizing process, the improvement of one target performance often causes the reduction of the other target performance, so that multi-target planning is needed, the invention utilizes a analytic hierarchy process to convert multi-target optimization into weighted single-target optimization, and the root mean square of induced current under the interference of power frequency magnetic field in the direction of X, Y is subjected to
Figure BDA0003173342550000031
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic fieldxStandard deviation sigma of induced current under interference of power frequency magnetic field in Y directionyThe three indexes are compared pairwise in importance degree, a comprehensive single-target planning model is constructed, a judgment matrix of the model is established, and the form of the judgment matrix is shown in table 1.
TABLE 1 general form of decision matrix
A1 A2 …… An
A1 a11 a12 …… a1n
A2 a21 a22 …… a2n
…… …… …… …… ……
An an1 an2 …… ann
In Table 1, A1, A2, … …, An represent influencing factors, aijIndicating how important Ai is relative to Aj. Wherein a isijThe nine point scale method is used and is shown in table 2.
TABLE 2 Scale values and their meanings
Figure BDA0003173342550000032
Figure BDA0003173342550000041
And after the judgment matrix is determined, consistency check is carried out on the established judgment matrix by utilizing the consistency ratio CR. The calculation mode of the consistency index CR is as follows:
Figure BDA0003173342550000042
in the formula, λmaxIn order to determine the maximum eigenvalue of the matrix, n is the order of the matrix, CI is a defined consistency index, RI is a consistency index constant, and corresponds to the order n of the comparison matrix one by one, and the corresponding values are shown in table 3.
TABLE 3 consistency index constant RI
n 1 2 3 4 5 6 7 8 9
RI 0 0 0.52 0.89 1.12 1.26 1.36 1.41 1.46
And when CR is less than or equal to 0.1, the consistency is passed, otherwise, a judgment matrix needs to be reestablished, and when the consistency is passed, the normalization processing is carried out on the eigenvector corresponding to the maximum eigenvalue, namely the weight corresponding to each factor.
According to the limiting conditions of the parameters of the manganin shunt and the calculation through an analytic hierarchy process, the target optimization function of the manganin shunt is as follows:
Figure BDA0003173342550000043
in the formula IxIs an induced current in the x direction, IyIs the induced current in the y direction, σxIs the standard deviation, σ, of the induced current set in the x-direction with a fluctuation of ± 0.1yWeight vector { alpha ] for the standard deviation of the induced current set in the y-direction with a fluctuation of + -0.11、α2、α3The ratio coefficient between multiple targets is determined by an analytic hierarchy process; x1，X2，X3，X4And solving the optimization of the objective function to be solved.
Step 3, initializing the particle swarm: key influencing factors of the induced current of the manganin shunt: x1、X2、X3、X4Respectively indicate the position and the through of the through holeHole size, upper terminal length, lower terminal length. With X1、X2、X3And X4And as the characteristics of each member in the population, determining the size of the population, and setting the initial speed, the initial position, the local optimal position and the global optimal position of each particle swarm.
And 4, substituting the initialized population into the training of key influence factors of the induced current of the manganin shunt: position X of the through-hole1Size X of the through hole2Length X of upper leading-out end3And lower lead-out length X4. Calculating the velocity v of each particle of the population according to equation (3)i(t +1) and position pi(t+1)：
Figure BDA0003173342550000045
In the formula, vi(t) is the vector velocity of the ith particle after the population is updated for t times; p is a radical ofi(t) and pi(t-1) the positions of the ith particles after the population is updated for t times and after the population is updated for t-1 times respectively; c. C1、c2And c3Is an acceleration factor; w (t) is inertia weight, and rand is random number between 0 and 1; pbest,iThe local optimal position of the ith particle of the population; gbestIs the global optimum position of the population;
the inertia weight w (t) of the population is set by referring to a simulated annealing algorithm and utilizing the idea of random vibration, and the inertia weight formula is as follows:
Figure BDA0003173342550000044
where rands is a random number between-1 and t is the number of iterations.
Acceleration factor c of population1And c2Replacing the constant acceleration factor by a decreasing and increasing change factor, respectively, c3With reference to simulated annealing algorithms, i.e.
Figure BDA0003173342550000051
In the formula, c1,s＝2、c2,s1.5 corresponds to the learning factor c1、c2Initial value of c1,e＝1.5、c2,e2 and c3,e2 corresponds to the learning factor c1、c2And c3T is the current iteration number, and T is 500, which is the maximum iteration number. c. C1,s>c1,e，c2,s<c2,e，c1Decreasing with t, c2Increasing with t, c3Then gradually increases with the vibration and continuously approaches c3,e。
Substituting the formulae (4) and (5) for the formula (3) to obtain piAfter (t +1), corrections need to be made according to the boundary conditions:
Figure BDA0003173342550000052
in the formula, pmaxIs the upper limit of position, pminIs the lower limit of the position for specifying the position of the particles, removing undesirable dependent variables.
F (X) is an objective optimization function and is the fitness of the function. p is a radical ofi(t) is the position of the ith particle after t population updates, F (p)i(t)) represents pi(t) fitness of particle position.
Step 5, the current fitness F (p) of each particle is calculatedi(t)) and the fitness F (p) of the previous timei(t-1)) making a comparison, if the fitness at the moment is better than that of the previous position, replacing the position at the previous moment, and otherwise, keeping the fitness unchanged; if the fitness at the moment is the optimal result, replacing the result with the result of the optimal position, wherein the defined formula is as follows:
Figure BDA0003173342550000053
step 6, updating t to t +1, and continuously repeating the step 4 and the step 5 when the t is equal to t +1After the particle iteration is over or reaches the optimum, the last GbestIt is the optimal solution.
And 7, designing, processing and manufacturing the manganin shunt by taking the optimal position as the design parameter of the manganin shunt.
Although the above is a disclosed example of the present invention, the example is not intended to limit the present invention. Any equivalent changes or modifications made without departing from the spirit and scope of the present invention also belong to the protection scope of the present invention. The scope of the invention should therefore be determined with reference to the appended claims.

Claims (2)

1. A manganin shunt structure parameter optimization method based on an improved particle swarm optimization algorithm is characterized in that: the method comprises the following steps:
step 1, determining a global optimization target of a manganin shunt, and integrating a plurality of optimization targets into a single optimization target by utilizing an analytic hierarchy process; in the optimizing process, the improvement of one target performance can cause the reduction of the other target performance, multiple targets are planned, the multiple-target optimization is converted into single-target optimization with weight by utilizing an analytic hierarchy process, and the Root Mean Square (RMS) of induced current under the interference of power frequency magnetic field in direction X, Y is subjected to
Figure FDA0003173342540000011
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic fieldxStandard deviation sigma of induced current under interference of power frequency magnetic field in Y directionyComparing the importance degrees of the three indexes, and constructing a comprehensive single-target planning model, wherein the general mathematical expression of the model is as follows:
Figure FDA0003173342540000012
in the formula, an induced current I is takenxAnd an induced current IyRoot mean square, induced current I ofxStandard deviation of (a)xInduced current IyStandard deviation of (a)yAs an objective function, a weight vector { alpha }1、α2、α3The ratio coefficient between multiple targets is determined by an analytic hierarchy process; x ═ X1，x2，…xn]For the solution to be optimized for the objective function, gj(X) is the equality constraint to be solved, hi(X) is an inequality constraint condition to be solved, XUAnd XLRespectively representing the upper and lower boundary values of the design variable;
step 2, initializing the particle swarm: taking the number of key influence factors of the induced current of the manganin shunt as the dimension of the population, determining the scale of the population, and setting the initial speed, the initial position, the local optimal position and the global optimal position of each particle swarm;
and 3, starting training key influence factors of the induced current of the manganin shunt: position X of the through-hole1Size X of the through hole2Length X of upper leading-out end3And lower lead-out length X4The velocity v of each particle of the population is calculated according to equation (2)i(t +1) and position pi(t+1)：
Figure FDA0003173342540000013
In the formula, vi(t) is the vector velocity of the ith particle after the population is updated for t times; p is a radical ofi(t) and pi(t-1) the positions of the ith particles after the population is updated for t times and after the population is updated for t-1 times respectively; c. C1、c2And c3Is an acceleration factor; w (t) is inertia weight, and rand is random number between 0 and 1; pbest,iThe local optimal position of the ith particle of the population; gbestIs the global optimum position of the population;
the inertia weight w (t) of the population is set by referring to a simulated annealing algorithm and utilizing the idea of random vibration, and the inertia weight formula is as follows:
Figure FDA0003173342540000014
in the formula, rands is a random number between-1 and 1, and t is the iteration frequency;
acceleration factor c of population1And c2Replacing the constant acceleration factor by a decreasing and increasing change factor, respectively, c3With reference to simulated annealing algorithms, i.e.
Figure FDA0003173342540000015
In the formula, c1,s、c2,sRespectively correspond to the learning factors c1、c2Initial value of c1,e、c2,eAnd c3,eRespectively correspond to the learning factors c1、c2And c3T is the current iteration number, and T is the maximum iteration number; in general c1,s>c1,e，c2,s<c2,e，c1Decreasing with t, c2Increasing with t, c3Then gradually increases with the vibration and continuously approaches c3,e；
Substituting the formulae (3) and (4) for the formula (2) to obtain piAfter (t +1), corrections need to be made according to the boundary conditions:
Figure FDA0003173342540000016
in the formula, pmaxIs the upper limit of position, pminThe lower limit of the position is used for regulating the position of the particles and removing the undesirable dependent variable;
f (X) is an objective optimization function, can be used as the fitness of the function, and adopts the small-expected characteristic; p is a radical ofi(t) is the position of the ith particle after t population updates, F (p)i(t)) represents pi(t) fitness of particle position;
step 4, the current fitness F (p) of each particle is calculatedi(t)) and the fitness F (p) of the previous timei(t-1)) making a comparison, if the fitness at the moment is better than that of the previous position, replacing the position at the previous moment, and otherwise, keeping the fitness unchanged; if the fitness at the moment is optimalAs a result, this result is replaced with the result of the optimal position, which is defined by the formula:
Figure FDA0003173342540000021
and 5, updating t to t +1, continuously repeating the step 3 and the step 4, and when the particle iteration is finished or the optimal value is reached, the last GbestThen it is the optimal solution;
and 6, designing, processing and manufacturing the manganin shunt by taking the optimal position as the design parameter of the manganin shunt.
2. The improved particle swarm optimization-based manganin shunt structure parameter optimization method according to claim 1, characterized in that: the analytic hierarchy process can convert multi-target optimization into weighted single-target optimization, and the root mean square of induced current under X, Y-direction power frequency magnetic field interference
Figure FDA0003173342540000022
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic fieldxStandard deviation sigma of induced current under interference of power frequency magnetic field in Y directionyComparing the importance degrees of the three indexes pairwise to establish a judgment matrix of the model;
after the judgment matrix is determined, consistency check is carried out on the established judgment matrix by utilizing a consistency ratio CR, wherein a calculation formula of a consistency index CR is as follows:
Figure FDA0003173342540000023
in the formula, λmaxIn order to judge the maximum eigenvalue of the matrix, n is the order of the matrix, CI is a defined consistency index, and RI is a consistency index constant which is in one-to-one correspondence with the order n of the comparison matrix;
and when CR is less than or equal to 0.1, the consistency is passed, otherwise, a judgment matrix is reestablished, and when the consistency is passed, the normalization processing is carried out on the eigenvector corresponding to the maximum eigenvalue, namely the weight corresponding to each factor.
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