CN113361146B - Improved particle swarm optimization-based manganese-copper shunt structure parameter optimization method - Google Patents
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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
Technical Field
The invention relates to the technical field of electric energy metering, in particular to a method for optimally designing structural parameters of a manganin current divider 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 manganese-copper current divider is improved, so that the manganese-copper current divider can resist magnetic field interference from uncertain directions, and the metering accuracy of an electronic electric energy meter is ensured. 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 structure parameter optimization method based on an improved particle swarm optimization algorithm, which is used for optimizing the structure 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 induction current are determined by simulation analysis of the manganin shunt induction 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 key influence factors and an induced 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 fields in X and Y directions
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic field x Standard deviation sigma of induced current under interference of power frequency magnetic field in Y direction y And carrying out pairwise comparison of the importance degrees of the three indexes 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:
in the formula, λ max In 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, the judgment matrix needs to be reestablished, and when the consistency is reached, 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:
in the formula, an induced current I is taken x And an induced current I y Root mean square, induced current I of x Standard deviation of (a) x Induced current I y Standard deviation of (a) y As an objective function, a weight vector { alpha } 1 、α 2 、α 3 The ratio coefficient between multiple targets is determined by an analytic hierarchy process; x = [ X ] 1 ，x 2 ，…x n ]For the solution to be optimized for the objective function, g j (X) is the equality constraint to be solved, h i (X) is an inequality constraint condition to be solved, X U And X L Representing 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 via hole 1 Size X of the through hole 2 Length X of upper leading-out end 3 And lower lead-out length X 4 Calculating the velocity v of each particle of the population according to equation (3) i (t + 1) and position p i (t+1)：
In the formula, v i (t) is the vector velocity of the ith particle after the population is updated for t times; p is a radical of i (t) and p i (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. C 1 、c 2 And c 3 Is an acceleration factor; w (t) is inertia weight, and rand is random number between 0 and 1; p is best,i The local optimal position of the ith particle of the population; g best Is the global optimum position of the population;
the inertia weight w (t) of the population refers to a simulated annealing algorithm and is set by using the idea of random vibration, and the inertia weight formula is as follows:
where rands is a random number between-1 and t is the number of iterations.
Acceleration factor c of population 1 And c 2 Replacing the constant acceleration factor by a decreasing and increasing change factor, respectively, c 3 With reference to simulated annealing algorithms, i.e.
In the formula, c 1,s 、c 2,s Respectively correspond to the learning factors c 1 、c 2 Initial value of c 1,e 、c 2,e And c 3,e Respectively correspond to the learning factors c 1 、c 2 And c 3 T is the current iteration number, and T is the maximum iteration number. In general c 1,s >c 1,e ，c 2,s <c 2,e ，c 1 Decreasing with t, c 2 Increasing with t, c 3 Then gradually increases with the vibration and continuously approaches c 3,e 。
Substituting the formulae (4) and (5) for the formula (3) to obtain p i After (t + 1), correction is performed according to the boundary conditions:
in the formula, p max Is the upper limit of position, p min Is a lower limit of position, forThe position of the particles is normalized and undesirable dependent variables are removed.
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 of formula i (t) is the position of the ith particle after t population updates, F (p) i (t)) represents p i (t) fitness of particle position.
Step 4, the current fitness F (p) of each particle is calculated i (t)) and the fitness F (p) of the previous time i (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:
step 5, updating t = t +1, continuously repeating the step 3 and the step 4, and when the particle iteration is finished or reaches the optimal value, the last G best 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.
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 to be better, and compared with the original manganin shunt, the manganin shunt has the advantages that the power frequency magnetic field interference resistance of the manganin shunt is improved, and meanwhile, the stability 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 interference x Induced current I under interference of power frequency magnetic field in Y direction y And 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 quantities of four size parameters are positioned +/-0.1 by error factors corresponding to the four key size parameters according to the tolerance standard GB/T1804-2000 m. Respectively selecting 3 levels for each error factor, wherein the 3 levels respectively correspond to the 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 designing the manganese copper diverter experimental scheme for the 3 levels, if each level combination is calculated, calculating for 81 times is needed, and selecting L18 (2) according to four input three levels in the invention 1 ×3 7 ) The orthogonal method can obtain more accurate and reliable results only by calculating 18 times, finally obtain each induced current, and make standard deviation sigma of the induced current under the interference of the X-direction power frequency magnetic field x Standard deviation sigma of induced current under interference of power frequency magnetic field in Y direction y As two other optimization objectives.
In the optimizing process, the performance of one target is improved to cause the performance of the other target to be reduced, so that multiple targets need to be plannedSingle target optimization with weight, root mean square of induced current under X and Y direction power frequency magnetic field interference
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic field x Standard deviation sigma of induced current under interference of power frequency magnetic field in Y direction y The 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 | a 11 | a 12 | …… | a 1n |
| A2 | a 21 | a 22 | …… | a 2n |
| …… | …… | …… | …… | …… |
| An | a n1 | a n2 | …… | a nn |
In Table 1, A2, \8230;, an denotes An influence factor, a ij Indicating how important Ai is relative to Aj. Wherein a is ij The nine point scale method is used and is shown in table 2.
TABLE 2 Scale values and their meanings
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:
in the formula, λ max In 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:
in the formula I x Is an induced current in the x direction, I y Is an induced current in the y direction, σ x Is the standard deviation, σ, of the induced current set in the x-direction with a fluctuation of ± 0.1 y Weight vector { alpha ] for the standard deviation of the induced current set in the y-direction with a fluctuation of + -0.1 1 、α 2 、α 3 The ratio coefficient between multiple targets is determined by an analytic hierarchy process; x 1 ，X 2 ，X 3 ，X 4 And 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: x 1 、X 2 、X 3 、X 4 Respectively showing 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. With X 1 、X 2 、X 3 And X 4 And 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 manganese copper current divider to start training key influence factors of the induction current of the manganese copper current divider: position X of the through-hole 1 Size X of the through hole 2 Length X of upper leading-out end 3 And lower lead-out length X 4 . Calculating the velocity v of each particle of the population according to equation (3) i (t + 1) and position p i (t+1)：
In the formula, v i (t) is the vector velocity of the ith particle after the population is updated for t times; p is a radical of i (t) and p i (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. C 1 、c 2 And c 3 Is an acceleration factor; w (t) is inertia weight, and rand is random number between 0 and 1; p is best,i The local optimal position of the ith particle of the population; g best Is the global optimal position of the population;
the inertia weight w (t) of the population refers to a simulated annealing algorithm and is set by using the idea of random vibration, and the inertia weight formula is as follows:
where rands is a random number between-1 and t is the number of iterations.
Acceleration factor c of population 1 And c 2 Using decreasing and increasing change factors instead of constant acceleration factors, respectively, c 3 With reference to simulated annealing algorithms, i.e.
In the formula, c 1,s ＝2、c 2,s =1.5 each corresponding to a learning factor c 1 、c 2 Initial value of (c) 1,e ＝1.5、c 2,e =2 and c 3,e =2 corresponding to the learning factors c, respectively 1 、c 2 And c 3 T is the current iteration number, and T =500 is the maximum iteration number. c. C 1,s >c 1,e ，c 2,s <c 2,e ，c 1 Decreasing with t, c 2 Increasing with t, c 3 Then gradually increases with the vibration and continuously approaches c 3,e 。
Substituting the formulae (4) and (5) for the formula (3) to obtain p i After (t + 1), corrections need to be made according to boundary conditions:
in the formula, p max Is the upper limit of position, p min Is 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 also the fitness of the function. p is a radical of i (t) is the position of the ith particle after t population updates, F (p) i (t)) represents p i (t) fitness of particle position.
Step 5, the current fitness F (p) of each particle is calculated i (t)) and the fitness F (p) of the previous time i (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:
step 6, updating t = t +1, continuously repeating the step 4 and the step 5, and when the particle iteration is finished or reaches the optimal value, the last G best It 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 (1)
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 manganese copperThe global optimization target of the splitter is used for 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 of induced current under the interference of power frequency magnetic fields in X and Y directions
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic field x Standard deviation sigma of induced current under interference of power frequency magnetic field in Y direction y Comparing the importance degrees of the three indexes to construct a comprehensive single-target planning model, wherein the mathematical expression of the model is as follows:
in the formula, an induced current I is taken x And an induced current I y Root mean square, induced current I of x Standard deviation of (a) x Induced current I y Standard deviation of (a) y As an objective function, a weight vector { alpha } 1 、α 2 、α 3 The ratio coefficient between multiple targets is determined by an analytic hierarchy process; x = [ X ] 1 ，x 2 ，...x n ]For the solution to be optimized for the objective function, g j (X) is the equality constraint to be solved, h i (X) is an inequality constraint condition to be solved, X U And X L Respectively 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 step 3, training key influence factors of the induced current of the manganin shunt: position X of the through-hole 1 Size X of the through hole 2 And lead out from the upper partEnd length X 3 And lower lead-out length X 4 The velocity v of each particle of the population is calculated according to equation (2) i (t + 1) and position p i (t+1)：
v i (t+1)＝w(t)·v i (t)+c 1 ·rand·(P best，i (t)-p i (t))+c 2 ·rand·(G best (t)-p i (t))+c 3 ·rand·(p i (t)-pi(t-1))
p i (t+1)＝p i (t)+w(t)·v i (t+1) (2)
In the formula, v i (t) is the vector velocity of the ith particle after the population is updated for t times; p is a radical of i (t) and p i (t-1) the positions of the ith particle after the population is updated for t times and after the population is updated for t-1 times respectively; c. C 1 、c 2 And c 3 Is an acceleration factor; w (t) is inertia weight, and rand is random number between 0 and 1; p best，i The local optimal position of the ith particle of the population is obtained; g best Is the global optimum position of the population;
the inertia weight w (t) of the population refers to a simulated annealing algorithm and is set by using the idea of random vibration, and the inertia weight formula is as follows:
in the formula, rands is a random number between-1 and 1, and t is the iteration frequency;
acceleration factor c of population 1 And c 2 Replacing the constant acceleration factor by a decreasing and increasing change factor, respectively, c 3 With reference to simulated annealing algorithms, i.e.
In the formula, c 1，s 、c 2，s Respectively correspond to the learning factors c 1 、c 2 Initial value of c 1，e 、c 2，e And c 3，e Respectively corresponding studyTraining factor c 1 、c 2 And c 3 T is the current iteration number, and T is the maximum iteration number; c. C 1，s ＞c 1，e ，c 2，s ＜c 2，e ，c 1 Decreasing with t, c 2 Increasing with t, c 3 Then gradually increases with the vibration and continuously approaches c 3，e ；
Substituting the formulas (3) and (4) into the formula (2) to obtain p i After (t + 1), corrections need to be made according to the boundary conditions:
in the formula, p max Is the upper limit of position, p min The 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, is taken as the fitness of the function, and adopts the small-expected characteristic; p is a radical of i (t) is the position of the ith particle after t population updates, F (p) i (t)) represents p i (t) fitness of particle position;
step 4, the current fitness F (p) of each particle is calculated i (t)) and the fitness F (p) of the previous time i (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:
step 5, updating t = t +1, continuously repeating the step 3 and the step 4, and when the particle iteration is finished or reaches the optimal value, the last G best Then it is the optimal solution;
step 6, designing, processing and manufacturing the manganin shunt by taking the optimal position as the design parameter of the manganin shunt;
the analytic hierarchy process can make the mesh moreThe standard optimization is converted into single-target optimization with weight, and the root mean square of the induced current under the interference of the power frequency magnetic field in the X direction and the Y direction
Standard deviation sigma of induced current under interference of X-direction power frequency magnetic field x Standard deviation sigma of induced current under interference of power frequency magnetic field in Y direction y Comparing 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:
in the formula, λ max In 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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