CN112528561A - PI parameter optimization method of MMC (Modular multilevel converter) based on ant colony simulated annealing algorithm - Google Patents

PI parameter optimization method of MMC (Modular multilevel converter) based on ant colony simulated annealing algorithm Download PDF

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CN112528561A
CN112528561A CN202011412725.3A CN202011412725A CN112528561A CN 112528561 A CN112528561 A CN 112528561A CN 202011412725 A CN202011412725 A CN 202011412725A CN 112528561 A CN112528561 A CN 112528561A
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陈波
朱坤
黄凯成
沈道贤
肖洒
储昭碧
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Hefei University of Technology
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Abstract

The invention discloses a PI parameter optimization method of a Modular Multilevel Converter (MMC) based on an ant colony simulated annealing algorithm, which comprises the following steps: determining a setting range of PI parameters according to the circulation waveform output of the MMC system, providing an improved ant colony algorithm, improving the pheromone updating rule of the traditional ant colony algorithm, introducing an annealing mechanism of a simulated annealing algorithm into the improved ant colony algorithm, establishing the ant colony simulated annealing algorithm, and finally optimizing the parameters of the MMC system by taking an absolute error integral criterion as a target function. The invention effectively fuses the ant colony algorithm and the simulated annealing algorithm, takes the searched optimal solution as the current solution of the simulated annealing algorithm by improving the pheromone updating rule of the ant colony algorithm, improves the optimization effect of PI parameters in the MMC, and effectively improves the bridge arm waveform quality and the inhibition of circulation.

Description

PI parameter optimization method of MMC (Modular multilevel converter) based on ant colony simulated annealing algorithm
Technical Field
The invention relates to the optimization category of PI parameters in an MMC system, in particular to an ant colony simulated annealing algorithm-based PI parameter optimization method in the MMC system.
Background
MMC (modular multilevel converter) topology mainly uses a half-bridge submodule as a basic power unit, and adopts a module cascading mode to form a three-phase six-bridge arm, and the MMC simplifies the capacity expansion and redundancy design of the converter due to the modular topology of the MMC, has the advantages of low harmonic frequency, no need of phase-change voltage, strong expansibility and the like, and is made to be valued by scholars at home and abroad. In the control of MMC, the most widely used controller is the PI controller, and its function is to make the error approach to the smaller and smaller direction required to achieve the control accuracy required by MMC control. It has the advantages of simple structure, convenient adjustment and the like. Where the ratio Kp is proportional to the deviation signal of the control system, the controller immediately generates a control action to reduce the deviation once it is generated. The integral element Ki is mainly used for eliminating static difference.
The ant colony algorithm is a bionic algorithm which is provided by simulating the foraging process of ants in the nature. It is the shortest distance that ants can finally find between the food source and the nest in the process of foraging. Compared with other heuristic algorithms, the ant colony algorithm has the advantages of better robustness and low requirement on the starting route. However, the traditional ant colony algorithm selects a path according to the concentration of pheromones, and due to the existence of a positive feedback effect in the algorithm, the algorithm is easy to sink into a local optimal solution, so that the premature phenomenon occurs.
The simulated annealing algorithm is a probability-based algorithm based on the solid annealing principle, and consists of a heating process, an isothermal process and a cooling process. The algorithm sets an initial temperature corresponding to the warming process, the Metropolis sampling process of the algorithm corresponds to the isothermal process, and the drop in the control parameter corresponds to the cooling process. The simulated annealing algorithm receives a poor solution with a certain probability, can effectively improve the premature phenomenon of the ant colony algorithm, but has a low convergence rate.
Disclosure of Invention
In order to solve the problems in the background art and overcome the technical defect that the PI parameter value of the MMC is easy to fall into a local optimal value by the conventional ant colony algorithm, the invention provides PI parameter optimization of the MMC based on the ant colony simulated annealing algorithm, so that the optimized parameter improves the interphase circulating current of the MMC.
The technical means adopted by the invention are as follows:
a PI parameter optimization method of MMC (modular multilevel converter) based on ant colony simulated annealing algorithm converts PI parameter optimization problem of MMC into a traveling salesman problem, wherein TSP (total suspended particulate), is as follows: the traveler looks for the shortest path to traverse the given c cities and does not repeat and eventually returns to the origin.
In order to omit a tabu list, the problem is simplified: there are multiple routes between two cities, and the travelers traverse all c cities in a fixed one-way order to find the shortest route.
The method is further completed by writing m function codes and building a simulink model under a Matlab/simulink environment, and the method comprises the following steps:
and S1, initializing operation.
The following parameters were set:
PI parameter setting range, ant quantity A, pheromone constant coefficient Q, residual coefficient rho, inter-city path quantity path and initial temperature T0The cooling rate q, the termination temperature Tend, the univariate coding length M, the problem dimension of optimization N, and the city number c equals to MN.
S2, decoding the path of each city of the single traversal of the ant colony algorithm into a proportion KpAnd integral Ki。
And S3, operating a simulink model, selecting an absolute value of error multiplied by time square integral ITAE2 criterion as an objective function of the algorithm, calculating ITAE2 and recording a corresponding optimal path and an ITAE2 value W1.
And S4, randomly generating a disturbance on the optimal path in the S3 to generate a new path, recording and decoding the new path, and operating a simulink model to obtain an ITAE2 value W2 of the new path.
S5, calculating delta E as W2-W1, and if the delta E is less than 0, receiving W2 as the current solution of the solution; otherwise, calculating the acceptance probability P of the W2 and deciding whether to accept the W2.
And S6, updating the pheromone concentration and cooling.
And S7, if the termination condition Stop is met, outputting the current solution W1 as the optimal solution, and ending the program. Otherwise, S2 through S6 are repeated.
Further, the specific determination PI parameter variables of step S1 are as follows:
determining the PI parameter variable to be optimized of the PI controller as [ K ]P,Ki]Optimization of the upper limit of the parameter variable Hlimits＝[Kpmax,Kimax]Lower limit of optimization parameter variable Llimits＝[Kpmin,Kimin]，KpmaxIs the maximum value of the P parameter, KimaxIs the maximum value of the I parameter, KpminIs the minimum value of the P parameter, KiminIs the minimum value of the I parameter.
Further, the specific steps of step S2 are as follows:
s21, the state transition formula for the kth ant to select the jth path from the city i to the next city is as follows:
Figure BDA0002818732530000031
in the formula: tau isip(t) is the pheromone concentration of the p-th path from city i to the next city in the t-th iteration.
S22, the trace of ant k completing one traversal is labeled as { Dk1,Dk2,Dk3…Dkc}. The corresponding solution in this traversal:
Figure BDA0002818732530000032
Xi＝(XiH-XiL)Ei+XiL。
Dkithe path selected for ant k from city i to the next city is numbered, i ═ 1,2,3 … c. DkiThe value of (1) is 0-10. EiIs a variable XiNormalized value of (2), variable XiI.e. the decoded value of the PI parameter, X, of the MMCiHAnd XiLAre respectively variable XiThe upper and lower limits of the value range.
Further, the ITAE2 formula of the step S3 is:
Figure BDA0002818732530000033
wherein z is the summation term number, n is the term upper limit,sis a time variable, Δ s is the summation time interval, e(s) is the difference between the actual value and the reference value: i.e. the difference between the actual value of the MMC circulation and the reference value.
Further, in step S5, if the new solution is a poor solution, the new solution is not discarded immediately, and then probability judgment is performed: firstly, a uniformly distributed random number epsilon is generated in an interval [0,1], if epsilon is less than p, the transfer is accepted, otherwise, the transfer is abandoned, and the next step is carried out, wherein the receiving probability p is as follows:
Figure BDA0002818732530000041
in the formula: t is temperature, and T ═ T0q，
Further, the specific steps of step S6 are as follows:
s61, the pheromone in the path taken by the kth ant is updated according to the following formula:
Figure BDA0002818732530000042
in the formula:
Figure BDA0002818732530000043
for the t traversal, the pheromone concentration on the jth path for ant k from city i to the next city.
Figure BDA0002818732530000044
To updated pheromonesConcentration, i.e. pheromone concentration on the jth path of the ant k from the city i to the next city in the t +1 th traversal.
Figure BDA0002818732530000045
The pheromone concentration increment left by ant k on the jth path from city i to the next city during the t traversal is:
Figure BDA0002818732530000046
wherein L iskThe total path length of the ant k in the t-th traversal is shown.
Figure BDA0002818732530000047
And (5) reserving pheromone concentration increment for the optimal ants in the t-th traversal of all ant searching processes.
S62, cooling T ═ T0q。
The invention has the advantages that
The invention effectively fuses the ant colony algorithm and the simulated annealing algorithm, takes the searched optimal solution as the current solution of the simulated annealing algorithm by improving the pheromone updating rule of the ant colony algorithm, improves the optimization effect of PI parameters in the MMC, and effectively improves the bridge arm waveform quality and the inhibition of circulation.
The PI parameter optimization method of the MMC overcomes the defects of a single ant colony algorithm, namely the technical defect that the ant colony algorithm is easy to fall into a local optimal value, realizes the advantage complementation of the ant colony and the simulated annealing algorithm, improves the searching efficiency of the optimal PI parameter value, avoids the falling into the local optimal value, and improves the interphase circulation of the MMC by the optimized parameter.
Drawings
Fig. 1 is a schematic diagram of the topology employed in the present embodiment.
FIG. 2 is a diagram illustrating MMC capacitor voltage equalization control according to the present invention.
Fig. 3 is a schematic flow chart of PI parameter optimization of MMC based on ant colony simulated annealing algorithm according to the present invention.
Fig. 4 is a circular current waveform of PI parameters optimized based on ant colony algorithm.
FIG. 5 is a circular current waveform of PI parameter optimized based on ant colony simulated annealing algorithm in the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
The topology structure adopted in this embodiment is shown in fig. 1, and the topology structure is composed of three-phase six-bridge arms, each bridge arm is cascaded with 4 sub-modules SM, L ═ 0.03H is bridge arm inductance, R ═ 20 Ω is load equivalent resistance, and L is equivalent to load equivalent resistanceR0.01H is the load equivalent inductance, 0.002F is the capacitance of the sub-module SM, D1 and D2 are anti-parallel diodes, and IGBT1 and IGBT2 are switching tubes.
Fig. 2 shows a PI controller in a conventional MMC capacitor voltage balance control system, where the PI controller (proportional-integral controller) is a common feedback loop component in MMC control applications.
As shown in fig. 3, an MMC parameter optimization method based on an ant colony simulated annealing algorithm includes: the method comprises the following steps:
the technical means adopted by the invention are as follows:
a PI parameter optimization method of MMC based on an ant colony simulated annealing algorithm is completed by compiling m function codes and building a simulink model under a Matlab/simulink environment and comprises the following steps:
and S1, initializing operation.
The following parameters were set:
XiH、XiLrespectively, a fractional order PI parameter, i.e. variable XiUpper and lower limits of (3). In this embodiment, the proportional gain KpHas an upper and lower limit of [1, 7]]. Integral constant KiHas an upper and lower limit of [130, 160 ]]. The ant number a is 40, the problem dimension N of N optimization is 2, the univariate coding length is M10, and the city number c is 20. Pheromone constant coefficient Q is 1000, residual coefficient ρ is 0.8, chengNumber of paths between cities, path 10, initial temperature T01000, cooling rate q 0.9, and end temperature Tend 0.001.
S2, decoding the path of each city of the single traversal of the ant colony algorithm into a proportion KpAnd integral Ki。
And S3, operating a simulink model, selecting an absolute value of error multiplied by time square integral ITAE2 criterion as an objective function of the algorithm, calculating ITAE2 and recording a corresponding optimal path and an ITAE2 value W1.
And S4, randomly generating a disturbance on the optimal path in the S3 to generate a new path, recording and decoding the new path, and operating a simulink model to obtain an ITAE2 value W2 of the new path.
S5, calculating delta E as W2-W1, and if the delta E is less than 0, receiving W2 as the current solution of the solution; otherwise, calculating the acceptance probability P of the W2 and deciding whether to accept the W2.
And S6, updating the pheromone concentration and cooling.
And S7, if the termination condition Stop is met, outputting the current solution W1 as the optimal solution, and ending the program. Otherwise, S2 through S6 are repeated.
Further, the specific steps of step S2 are as follows:
s21, the state transition formula for the kth ant to select the jth path from the city i to the next city is as follows:
Figure BDA0002818732530000061
in the formula: tau isip(t) is the pheromone concentration of the p-th path from city i to the next city in the t-th iteration.
S22, the trace of ant k completing one traversal is labeled as { Dk1,Dk2,Dk3…Dkc}. The corresponding solution in this traversal is:
Figure BDA0002818732530000062
Xi＝(XiH-XiL)Ei+XiL。
Dkithe path selected for ant k from city i to the next city is numbered, i ═ 1,2,3 … c. DkiThe value of (1) is 0-10. EiIs a variable XiNormalized value of (2), variable XiI.e. the decoded value of the PI parameter, XiHAnd XiLAre respectively variable XiThe upper and lower limits of the value range.
The ITAE2 formula of the step S3 is as follows:
Figure BDA0002818732530000063
wherein z is the number of summation terms, n is the upper limit of the number of terms, s is a time variable, Δ s is a small interval of summation time, e(s) ═ icir-icir_ref。
In step S4, the optimal ant path in step S3 is interchanged, reversed, and translated to generate a new solution.
In step S5, if the new solution is a poor solution, the new solution is not discarded immediately, but probability determination is performed again: firstly, a uniformly distributed random number epsilon is generated in an interval [0,1], if epsilon is less than p, the transfer is accepted, otherwise, the transfer is abandoned, and the next step is carried out, wherein the receiving probability p is as follows:
Figure BDA0002818732530000071
in the formula: t is temperature, and T ═ T0q，
Further, the specific steps of step S6 are as follows:
s61, the pheromone in the path taken by the kth ant is updated according to the following formula:
Figure BDA0002818732530000072
in the formula:
Figure BDA0002818732530000073
for the t traversal, the pheromone concentration on the jth path for ant k from city i to the next city.
Figure BDA0002818732530000074
The updated pheromone concentration is the pheromone concentration on the jth path of the ant k from the city i to the next city in the t +1 th traversal.
Figure BDA0002818732530000075
The pheromone concentration increment left by ant k on the jth path from city i to the next city during the t traversal is:
Figure BDA0002818732530000076
wherein L iskThe total path length of the ant k in the t-th traversal is shown.
Figure BDA0002818732530000077
And (5) reserving pheromone concentration increment for the optimal ants in the t-th traversal of all ant searching processes.
S62, cooling T ═ T0q。
If T < Tend is satisfied in step S7, the current solution W1 is output as the optimal solution, and the routine is ended. Otherwise, S2 through S6 are repeated.
The bridge arm circulation waveforms after the PI parameters are optimized by the ant colony algorithm and the ant colony simulated annealing algorithm are shown in fig. 4 and 5. As can be seen from fig. 5 in fig. 4, the range of the bridge arm loop current after the parameters are optimized by the ant colony simulated annealing algorithm is changed from [0.95,7.3] to [1.25,7 ]. The PI parameter optimized by the algorithm of the invention enhances the effect of the controller on inhibiting the circulation.

Claims (10)

1. The PI parameter optimization method of the MMC based on the ant colony simulated annealing algorithm is characterized in that the PI parameter optimization problem of the MMC is converted into a traveling salesman problem, wherein the traveling salesman problem, namely TSP, is as follows: the traveler looks for the shortest path to traverse the given c cities and does not repeat and eventually returns to the origin, looking for the shortest path.
2. The PI parameter optimization method of the MMC based on the ant colony simulated annealing algorithm in the step 1 is characterized in that a plurality of paths are set between two cities, a traveler traverses all c total cities according to a fixed unidirectional sequence, taboo tables are omitted in sequence, and the shortest path is sought.
3. The PI parameter optimization method of the MMC based on the ant colony simulated annealing algorithm in the step 1 is characterized by comprising the following steps of:
step S1, initializing operation;
step S2, decoding the path of the single traversal of the ant colony algorithm into the proportion KpAnd integral Ki；
Step S3, setting an objective function, and obtaining a corresponding optimal path and a corresponding ITAE2 value W1; the ITAE2 criterion is the absolute value of the error multiplied by the time squared integral,
step S4, randomly generating a disturbance on the optimal path in the step S3 to generate a new path, recording and decoding the new path to obtain an ITAE2 value W2 of the new path;
step S5, calculating Δ E ═ W2-W1,
if Δ E <0, receive W2 as the current solution of the solution;
otherwise, calculating the acceptance probability P of the W2, and determining whether to accept the W2;
step S6, updating pheromone concentration and cooling;
step S7, if the termination condition Stop is met, outputting the current solution W1 as the optimal solution, and ending the program; otherwise, S2 through S6 are repeated.
4. The PI parameter optimization method for MMC based on ant colony simulated annealing algorithm as claimed in claim 3, wherein in step S3, the objective function ITAE2 of the algorithm is:
Figure FDA0002818732520000011
wherein z is the summation term number, n is the term upper limit, s is a time variable, and Δ s is a summation time cell interval; e(s) is the difference between the actual value of the MMC loop and the reference value.
5. The PI parameter optimization method for MMC based on ant colony simulated annealing algorithm as claimed in claim 3, wherein in step S6, the pheromone update rule is as follows:
pheromones in the path taken by the kth ant are updated according to the following formula:
Figure FDA0002818732520000021
in the formula:
Figure FDA0002818732520000022
in the t traversal, the pheromone concentration of the ant k on the jth path from the city i to the next city;
Figure FDA0002818732520000023
the updated pheromone concentration is the pheromone concentration on the jth path of the ant k from the city i to the next city in the t +1 th traversal;
Figure FDA0002818732520000024
the pheromone concentration increment left by ant k on the jth path from city i to the next city during the t traversal is:
Figure FDA0002818732520000025
wherein L iskThe total length of the path traversed by the ant k at the t-th time, and Q is an information constant coefficient;
Figure FDA0002818732520000026
and (5) reserving pheromone concentration increment for the optimal ants in the t-th traversal of all ant searching processes.
6. The PI parameter optimization method for the MMC based on the ant colony simulated annealing algorithm according to claim 3, wherein the PI parameter optimization method is completed by writing m function codes and building a simulink model in a Matlab/simulink environment by means of a computer.
7. The PI parameter optimization method for MMC based on ant colony simulated annealing algorithm as claimed in claim 6, wherein in S3, a simulink model is run, the absolute value of error multiplied by time square integral ITAE2 criterion is selected as an objective function of the algorithm, ITAE2 is calculated and the corresponding optimal path and ITAE2 value W1 are recorded;
in S4, a perturbation is randomly generated from the optimal path in S3 to generate a new path, the new path is recorded and decoded, and the simulink model is run to obtain the ITAE2 value W2 of the new path.
8. The PI parameter optimization method for MMC based on ant colony simulated annealing algorithm as claimed in claim 3, wherein the specific determined PI parameter variables of step S1 are as follows:
determining the PI parameter variable to be optimized of the PI controller as [ K ]P,Ki]Optimization of upper limits of parametric variables
Figure FDA0002818732520000027
Lower limit L of optimization parameter variablelimits＝[Kpmin,Kimin]，KpmaxIs the maximum value of the P parameter, KimaxIs the maximum value of the I parameter, KpminIs the minimum value of the P parameter, KiminIs the minimum value of the I parameter.
9. The PI parameter optimization method for MMC based on ant colony simulated annealing algorithm as claimed in claim 3, wherein the specific steps of step S2 are as follows:
s21, the state transition formula for the kth ant to select the jth path from the city i to the next city is as follows:
Figure FDA0002818732520000031
in the formula: tau isip(t) is the pheromone concentration of the p-th path from city i to the next city during the t-th iteration;
s22, the trace of ant k completing one traversal is labeled as { Dk1,Dk2,Dk3…Dkc}; the corresponding solution in this traversal:
Figure FDA0002818732520000032
Xi＝(XiH-XiL)Ei+XiL；
Dkithe path selected by ant k from city i to the next city is numbered, i is 1,2,3 … c; dkiThe value of (1) is 0-10. EiIs a variable XiNormalized value of (2), variable XiI.e. the decoded value of the PI parameter, X, of the MMCiHAnd XiLAre respectively variable XiThe upper and lower limits of the value range.
10. The PI parameter optimization method for MMC based on ant colony simulated annealing algorithm as claimed in claim 3, wherein the ITAE2 formula of step S3 is as follows:
Figure FDA0002818732520000033
wherein z is the summation term number, n is the term upper limit,sis a time variable, Δ s is the summation time interval, e(s) is the difference between the actual value and the reference value: i.e. the difference between the actual value of the MMC circulation and the reference value.
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