A Control Method for Three-Phase Rectifier System Based on Multi-Objective Hybrid Elite Particle Swarm Optimization

Abstract

The present invention provides a control method for a three-phase rectifier system based on multi-objective hybrid elite particle swarm optimization, including: Step 1, select the objective function; Step 2, perform minimization optimization on the objective function; Step 3, obtain circuit values through simulation operation of the circuit; Step 4, calculate the dominance relationship of the objective values of all particles to find all non-dominated solutions; Step 5, use entropy-minimized particles and particles with higher quality to form hybrid elite particles to represent the global optimal particles; Step 6, dynamically adjust the flight coefficient of the hybrid elite particles; Step 7, update the particle velocity and position; Step 8, repeat Steps 3 to 7 until the set conditions are reached; Step 9, when the number of archived particles exceeds the maximum capacity, delete the particles in the archive; Step 10, output the particles in the final archive. The present invention maintains objective independence, avoids weight allocation, and better handles objective conflicts.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent control optimization of three-phase rectification, and particularly relates to a control method for a three-phase rectification system based on multi-objective hybrid elite particle swarm optimization. Background Art

[0002] In an electronic power system, as an important device in the field of power electronics, a three-phase rectification system has the advantages of low harmonic content in the grid-side current, high power factor, bidirectional energy flow, and fast dynamic response. With the continuous development of power electronics technology, the requirements for the control performance of three-phase rectifiers are also getting higher and higher. Therefore, it is of great practical significance to study high-performance control strategies for three-phase rectifiers. In recent years, in order to achieve efficient and fast DC output, in the modulation technology of three-phase rectification circuits, many studies have chosen space vector pulse width modulation (SVPWM) as an advanced control strategy. In SVPWM control, the adjustment mainly relies on three groups of PI (Proportional-Integral) controllers adjusted by experience. The setting of these controller parameters often requires the debugger to adjust according to personal experience and understanding of the system. This method has several main problems:

[0003] Subjectivity: The debugging process highly depends on the personal experience and professional knowledge of the debugger, which may lead to different control effects obtained by different debuggers under the same conditions. This dependence limits the repeatability and generality of the control strategy and makes it difficult to maintain consistency between different scenarios or different debuggers.

[0004] Difficulty in optimization: The parameter adjustment of PI controllers usually relies on the trial-and-error method, gradually approaching the optimal solution through multiple experiments. This process is not only time-consuming but also inefficient, and it is difficult to ensure finding the true global optimal solution. In addition, due to the complexity of parameter adjustment, even after multiple adjustments, the ideal control effect may not be achieved.

[0005] Different environmental performance requirements: In the process of optimizing traditional optimization algorithms in combination with specific performance, only a set of solutions based on the fitness function is obtained, and this set of solutions may not be able to adapt to different environmental requirements, such as better requirements for ST or OV, SSE, etc.

[0006] To solve these problems, researchers have begun to explore the use of algorithms to optimize PI control parameters. Among them, evolutionary algorithms have been widely studied due to their advantages in solving complex optimization problems. Evolutionary algorithms can find approximate optimal solutions in multi-objective optimization problems by simulating natural selection and genetic mechanisms. However, there are also some challenges when evolutionary algorithms are applied to the control optimization of three-phase rectification:

[0007] Weight relationship of multi-objective performance parameters: If multiple performances need to be considered during the design of the overall system, then when designing the fitness function, weight coefficients need to be used to linearly combine different objectives. During this process, the setting of the weight coefficient values may cause the optimization result to be biased towards certain specific objectives while ignoring other equally important objectives.

[0008] Poor adaptability of a single solution: Using ordinary particle swarm optimization algorithms or other genetic algorithms, a set of solutions based on the fitness function is finally obtained. This solution is found based on the fitness function, but with the change of the external environment, it may not be able to achieve better adaptability to different performance requirements. For example, it cannot adapt to external conditions with higher requirements for OV performance.

[0009] Poor effect of traditional multi-objective particle swarm optimization: In traditional multi-objective particle swarm optimization algorithms, since different from ordinary particle swarm optimization algorithms that can directly calculate the global optimal particle, selecting poor particles during the update process may not be able to better find a better Pareto solution set. Summary of the Invention

[0010] Object of the Invention: The technical problem to be solved by the present invention is to provide a control method for a three-phase rectifier system based on multi-objective hybrid elite particle swarm optimization in view of the deficiencies of the prior art.

[0011] The present invention focuses on key technologies such as multi-objective optimization, power electronics, SVPWM, and three-phase rectification. By establishing a three-phase rectification model based on SVPWM modulation, more efficient output of the three-phase rectification circuit is achieved. Through the analysis of the actual circuit performance, appropriate performance indicators are selected as objectives, an improved multi-objective particle swarm algorithm is used, and then through the analysis of archived particles, the selection of hybrid elite particles and the adjustment of adaptive flight parameters are completed to achieve optimal algorithm performance. Finally, the optimal Pareto solution set is obtained through the optimization of the algorithm, and through the objective function values of different performances in the Pareto solution set, the PI controller parameter solution most suitable for the environment can be selected. The method of the present invention specifically includes the following steps:

[0012] Step 1, select the performance indicators of the three-phase rectification circuit as the objective function of the multi-objective particle swarm algorithm, and the performance indicators include settling time ST (Settling Time, ST, the time required for the system response to reach and remain within a certain range of the final steady-state value), overvoltage OV (Over Voltage, OV, the difference between the maximum voltage and the reference voltage), and steady-state error SSE (Steady State Error, SSE, the voltage error when the system reaches the steady state);

[0013] Step 2, use the multi-objective particle swarm algorithm to minimize and optimize the objective function;

[0014] Step 3, substitute the values of the particles obtained by initialization into the PI controller, and obtain the required circuit values through the simulation operation of the circuit. The values of the particles obtained by initialization refer to three sets of proportional-integral parameters pi (Proportional-Integral) and proportional-derivative parameters pd (Proportional-Derivative), denoted as (kp1, ki1, kp2, ki2, kp3, ki3); where kp1 and ki1 respectively represent the proportional-integral parameter Pi and proportional-derivative parameter pd of the first set of PI controllers; kp2 and ki2 respectively represent the proportional-integral parameter Pi and proportional-derivative parameter pd of the second set of PI controllers; kp3 and ki3 respectively represent the proportional-integral parameter Pi and proportional-derivative parameter pd of the third set of PI controllers;

[0015] Then calculate the three objective values represented by each particle through three objective functions. The three objective values include settling time ST, overshoot OV, and steady-state error SSE;

[0016] Step 4, calculate the domination relationship among the objective values of all particles, find all non-dominated solutions, and store all non-dominated solutions in the archive;

[0017] Step 5, analyze the archived particles, use the entropy weight method to calculate the particle with the minimum entropy, use the roulette wheel method to select the particles with higher quality (better fitness), use the particle with the minimum entropy and the particles with higher quality to represent the global optimal particles in the velocity update process of the multi-objective particle algorithm, and use the particle with the minimum entropy and the particles with higher quality to jointly form a hybrid elite particle to represent the global optimal particle;

[0018] Step 6, when using the hybrid elite particles obtained in the above process, because the influence of the flight coefficient needs to be considered in the calculation process, the domination degree method is used. By calculating the proportion of the domination degree of the particle with the minimum entropy in the entire archived particles, normalization is performed through the proportion, so as to dynamically adjust the flight coefficient of the hybrid elite particles;

[0019] Step 7, update the particle velocity and position;

[0020] Step 8, repeat steps 3 to 7 until the set conditions are reached (such as reaching the maximum number of update generations);

[0021] Step 9, during the update process, when the number of archived particles exceeds the set maximum capacity, delete the particles in the archive;

[0022] Step 10, output the particles in the final archive. At this time, the solution set composed of all particles in the archive is the final Pareto solution set (the Pareto solution set is a concept in multi-objective optimization problems, referring to the set of solutions that cannot be further optimized among all objective functions. Specifically, a solution is called a Pareto optimal solution if it is better than other solutions in at least one objective and not worse than other solutions in other objectives. The set composed of all Pareto optimal solutions is the Pareto solution set).

[0023] In Step 1, space vector pulse width modulation SVPWM (Space Vector Pulse Width Modulation) is used to obtain the parameters of the three-phase rectifier circuit, including kp1, ki1, kp2, ki2, kp3, ki3.

[0024] In Step 2, ST (Settling Time): is the time required for the system response to reach and remain within the allowable error range of the output voltage reference value (the voltage value after three-phase rectification that needs to be obtained). The allowable error range is defined by the threshold PCTvst, and the upper bound ub and lower bound lb of the error range are respectively:[[]]

[0025] (1),

[0026] (2),

[0027] The objective functions of ST, OV, and SSE are respectively:[[]]

[0028] ST is the time when the system response vol(t) (the function of the final output voltage changing with time) first enters [lb, ub] and remains within this range, and the objective function is:[[]]

[0029] (3),

[0030] where vol(t) is the function of the final output voltage changing with time t; represents for any time greater than time t , all satisfy ;

[0031] OV (Over Voltage): is the maximum deviation when the system response exceeds the reference value V ref , and the objective function is:[[]]

[0032] (4),

[0033] SSE (Sum of Squared Errors): It is the sum of the squared errors between the system response in the steady state phase (the last Ns time points) and the reference value V ref The objective function is:

[0034] (5),

[0035] where len is the length of time t, and Ns is the number of time points in the steady state phase.

[0036] In the experiment of this invention, V ref is set to 750V, PCTvst is set to 0.02, and Ns is set to 500.

[0037] Step 4 includes: setting a multi-objective optimization problem, and the objective function is , where m is the number of objectives. For two solutions x_1 and x_2, if for all objective functions , i ranges from 1 to m, and the objective function of solution x_1 is at least as good as that of solution x_2, that is For all hold, and there is at least one objective such that , then it is determined that solution x_1 dominates solution x_2, denoted as x_1 , expressed as:

[0038] (6).

[0039] In step 5, the analysis of the archived particles and the calculation of the particle with the minimum entropy using the entropy weight method specifically include:

[0040] Step 5-11, initialization of the multi-objective particle swarm algorithm: Initialize the parameters of the multi-objective particle swarm algorithm, including the population size, the setting of the initial particles, the maximum number of iterations, archiving, the capacity of the archived particles, the flight coefficient, and the mutation rate;

[0041] Step 5-12, finding the elite particles using the entropy weight method: Among the archived particles, calculate the particle with the minimum information entropy using the entropy weight method, which specifically includes the following steps:

[0042] Step 5-12-1, data input:

[0043] Take the solution set composed of the archived particles as the original matrix; the original matrix is an n×3 matrix, where 3 represents three dimensions - OV, ST, SSE, and n represents the number of particles in the archive;

[0044] Step 5-12-2, data normalization:

[0045] (7),

[0046] where is the element in the \(i\)-th row and \(j\)-th column of the normalized original matrix, is the element in the \(i\)-th row and \(j\)-th column of the original matrix, , are respectively the minimum and maximum values of the \(j\)-th column of the original matrix;

[0047] Step 5 - 12 - 3, calculate the probability distribution matrix:

[0048] (8),

[0049] where is the element in the \(i\)-th row and \(j\)-th column of the probability distribution matrix, is the sum of all elements of the normalized matrix;

[0050] Step 5 - 12 - 4, calculate the information entropy:

[0051] (9),

[0052] where is the information entropy of the \(j\)-th objective value (the objective value represents three specific objectives, namely ST, OV, SSE);

[0053] Step 5 - 12 - 5, calculate the information entropy weight:

[0054] (10),

[0055] where, is the information entropy weight of the \(j\)-th objective function;

[0056] Step 5 - 12 - 6, calculate the normalized weight:

[0057] (11),

[0058] where is the normalized weight, is the sum of all information entropy weights;

[0059] Step 5 - 12 - 7, calculate the weighted value:

[0060] (12),

[0061] where, is the weighted value of the \(i\)-th particle;

[0062] Step 5 - 12 - 8, obtain the index of the minimum weighted value:

[0063] L (13),

[0064] where L is the position index of the minimum value, that is, the index of the position where the weighted information entropy is the minimum.

[0065] By calculating the index of the particle with the minimum information entropy, the minimum information entropy of the particle indicates that the uncertainty of the particle in the target space is lower, the amount of information provided is larger, it can better reflect the distribution of the objective function, helps to maintain the diversity of the population, and the particle with the minimum information entropy can provide more useful information to help the algorithm better explore the new solution space and improve the global search ability.

[0066] In step 5, the roulette wheel selection is based on calculating the selection probability based on the fitness value of each particle and making the selection through the cumulative probability;

[0067] The use of the roulette wheel method to select particles with higher quality specifically includes:

[0068] Step 5-21, calculate the selection probability: For each particle i, the selection probability is:

[0069] (14),

[0070] where is the fitness value of the i-th particle, and N is the total number of archived particles;

[0071] Step 5-22, calculate the cumulative probability: The cumulative probability P i is used to implement the roulette wheel selection:

[0072] (15),

[0073] where represents the selection probability of the e-th particle, and P i represents the cumulative probability of the i-th particle;

[0074] Step 5-23, select a particle: Generate a random number r ∈ [0, 1], and select the smallest particle i that satisfies the following condition:

[0075] (16),

[0076] In the present invention, the roulette wheel method is based on the hypercube selection and includes the following steps:

[0077] Step 5-24, Select the hypercube: REP.quality is a matrix, where each row represents a hypercube and the quality of the hypercube. The second column REP.quality(:,2) of the matrix REP.quality contains the quality values of each hypercube;

[0078] Step 5-25, Calculate the selection probability of each hypercube h :

[0079] (17),

[0080] Step 5-26, Select the hypercube: Use the roulette wheel selection mechanism to select a hypercube based on the value of:

[0081] Generate a random number r between the set [0,1], and calculate:

[0082] (18),

[0083] where R represents generating a random number that conforms to within the maximum value range;

[0084] Find the first hypervolume h_1 that meets the roulette wheel condition:

[0085] R ≤ (19),

[0086] where represents the cumulative probability of the hypervolume h_1 that meets the roulette wheel condition;

[0087] Step 5-27, Randomly select a particle H within the hypervolume h_1 as the particle with higher quality selected by the roulette wheel method;

[0088] The calculation methods of the hypercube and REP.quality in this step: For all particles in the archived particles, in the solution space, since there are three objective functions in this technical design, the solution space is a three-dimensional space. In this three-dimensional space, the entire solution space is divided and numbered using a set grid, where each grid is a hypercube, the REP.quality() matrix, where REP represents archiving, the first column represents the hypercube number with particles, and the second column, that is, the quality calculation formula is 10 divided by the number of particles in each hypercube with particles. For example: There are two hypercubes, numbered 3 and 5, and the number of particles is 1 and 5 respectively, then:

[0089] REP.quality() = (20).

[0090] The roulette wheel selection tends to favor solutions with better quality, thus guiding the search towards known high-quality regions. Due to the randomness of the roulette wheel selection, it increases the exploration degree of particles, thereby helping the algorithm explore new solution spaces. The roulette wheel selection is based on the proportion of quality values for selection. The higher the quality value of a particle, the greater the probability of being selected. This mechanism can dynamically adjust the selection pressure to adapt to the search requirements at different stages. For example, in the initial stage of the search, the solution quality differences are large, and the roulette wheel selection can be more inclined towards high-quality particles; while in the later stage of the search, the solution quality differences are small, and the roulette wheel selection can select particles more evenly.

[0091] Step 6 includes:

[0092] Step 6-1, calculate the maximum and minimum values of each objective function value in the archive: For each objective value j, calculate the maximum and minimum values of all solutions in the archive:

[0093] , (21),

[0094] where represents the objective value of the i-th particle on the j-th objective function, , are the maximum and minimum values of the j-th objective function respectively;

[0095] Step 6-2, calculate the dominance degree: For each solution in the archive (the particles in the archive are solutions, and in multi-objective optimization, each generated particle is a solution), calculate the dominance degree of the particle X with the minimum information entropy on each objective function:

[0096] (22),

[0097] where represents the value of the j-th objective function of the particle X with the minimum information entropy, is the dominance degree of the particle X with the minimum information entropy on the j-th objective function over the i-th particle, represents the objective value of particle i on objective function j, represents the maximum value on objective function j, represents the minimum value on objective function j;

[0098] If the particle X with the minimum information entropy is superior to particle i on the j-th objective function, then accumulate the dominance degree on the j-th objective function:

[0099] When (23),

[0100] Among them, M is the number of objective functions (taking the value of 3), is the total dominance degree of the particle X with the minimum information entropy over the i-th particle;

[0101] Step 6-3, calculate the total dominance degree: Calculate the total dominance degree G of the particle X with the minimum information entropy over all solutions in the archive:

[0102] (24),

[0103] Step 6-4, find the minimum value in the dominance degrees: Find the minimum value in the dominance degrees of the particle X with the minimum information entropy over all solutions in the archive :

[0104] (25),

[0105] Step 6-5, calculate the ratio of the minimum dominance degree to the total dominance degree :

[0106] (26),

[0107] Step 6-6, calculate the adaptive flight coefficient:

[0108] , (27),

[0109] Among them is the flight coefficient of the roulette wheel high-quality particles, is the flight coefficient of the particle with the minimum information entropy, and C2 is the basic flight coefficient of the global optimal particle.

[0110] Here, by introducing the dominance degree, the flight coefficients before the two elite particles are adaptively adjusted, which can better regulate the global search ability of the algorithm during the search process and better balance the exploration of the positions of the two elite particles. In addition, through the dominance degrees of other particles in the archive, the relative positions of the particles in the target space can be better evaluated. The smaller the dominance degree, the more isolated the particle is in the target space, and the larger the change range of the surrounding target values, which can ensure the uniformity of the solution distribution and prevent the algorithm from converging to the local optimal solution prematurely.

[0111] Step 7 includes: The particle velocity update formula is:

[0112] (28),

[0113] The particle position update formula is:

[0114] (29),

[0115] Among them represents the velocity of particle i at the next moment, represents the velocity of particle i at the current moment, is the weight ratio in the update process of the current velocity of particle i, C1 is the flight coefficient of the individual optimal position, is the individual optimal position of particle i, represents the current position of particle i, represents the position of particle i at the next moment, is the particle with the minimum information entropy, is the roulette high-quality particle, , , are random numbers between 0 and 1.

[0116] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the described method is implemented.

[0117] The present invention also provides a computer device, including: a memory for storing instructions; a processor for executing the instructions, so that the computer device executes the described method.

[0118] Beneficial effects: When optimizing the PI controller, the traditional particle swarm algorithm is abandoned. Because in the traditional particle swarm algorithm, if multiple performance indicators of the circuit need to be considered, when designing the fitness function of the particle swarm algorithm, multiple performance parameters need to be linearly combined together through weight coefficients. In this way, how to select the weight coefficients is crucial, and the performance of the algorithm will be greatly affected by subjectivity when designing the weight coefficients. However, in the present invention, multi-objective optimization is used, the fitness function is abandoned, the performance indicators are directly used as the objective function, and then mutual selection is carried out through the dominance relationship, maintaining the independence of the objectives, avoiding weight allocation, and better handling objective conflicts.

[0119] In the process of updating the velocity of the particles, two hybrid elite particles calculated based on the entropy weight method and the roulette method are used to represent the global optimal particle for updating. The particle with the minimum information entropy obtained by the entropy weight method, the smaller the information entropy, the lower the uncertainty of the particle in the target space, the greater the amount of information provided, and it can better reflect the distribution of the objective function, which helps to maintain the diversity of the population. The roulette high-quality particle represents the known high-quality region of the particle in the solution space, thus guiding the search to develop towards the known high-quality region and promoting the algorithm to find a more accurate pareto solution set.

[0120] When using hybrid elite particles, since the flight coefficients of each need to be considered, the dominance calculation method is sampled in this experiment to adaptively adjust the flight coefficients, enabling the algorithm to better adapt to environmental changes and providing its anti-interference ability, thereby better improving the quality of the solution set.

[0121] Through the design of an archive and the use of dominance, the multi-objective optimization algorithm will finally output a Pareto solution set, enabling the overall experiment, i.e., the three-phase rectifier circuit, to autonomously select appropriate PI controller parameters according to the requirements of the external environment to meet the requirements of different external environments. For example, if the external environment has higher performance requirements for time (ST), the solution with the best ST among other Pareto solutions can be selected. Similarly, it can be used in external environments with higher requirements for OV or SSE. Brief Description of the Drawings

[0122] Figure 1 is the flow chart of the multi-objective particle swarm algorithm based on hybrid elite particles of the present invention.

[0123] Figure 2 is the optimization diagram of the control system of the three-phase rectifier circuit in the embodiment.

[0124] Figure 3 is the comparison of the scatter plots of the Pareto solution set before and after improvement and the mutual dominance relationship.

[0125] Figure 4 is the curve diagram of the output voltage of particle 1, particle 2, and particle 3 in the archived particles changing with time.

[0126] Figure 5 is the curve diagram of the output voltage of particle 4, particle 5, and particle 6 in the archived particles changing with time.

[0127] Figure 6 is the curve diagram of the output voltage of particle 7, particle 8, and particle 9 in the archived particles changing with time.

[0128] Figure 7 is the curve diagram of the output voltage of particle 10, particle 11, and particle 12 in the archived particles changing with time.

[0129] Figure 8 is the curve diagram of the output voltage of particle 13, particle 14, and particle 15 in the archived particles changing with time.

[0130] Figure 9 is the curve diagram of the output voltage of particle 16, particle 17, and particle 18 in the archived particles changing with time.

[0131] Figure 10It is a curve graph showing the variation of the output voltages of Particles 19, 20, and 21 in the archived particles over time.

[0132] Figure 11 It is a curve graph showing the variation of the output voltages of Particles 22, 23, and 24 in the archived particles over time.

[0133] Figure 12 It is a curve graph showing the variation of the output voltages of Particles 25, 26, and 27 in the archived particles over time.

[0134] Figure 13 It is a comparison of the improved Pareto solution set with the solution scatter plot obtained by the PSO (Particle Swarm Optimization) algorithm, as well as the dominance relationship.

[0135] Figure 14 It is a graph showing the relationship between the output voltage and time of Particle 24 in the improved Pareto solution set and the solution obtained by the PSO algorithm. Specific implementation manner

[0136] The following further specifically describes the present invention in conjunction with the accompanying drawings and specific implementation manners, and the above and / or other advantages of the present invention will become clearer.

[0137] This embodiment introduces a multi-objective optimized three-phase rectification system based on hybrid elite particles, including the following steps:

[0138] Step 1: Determine the objective function of the multi-objective particle swarm optimization algorithm. Referring to the performance indicators of the three-phase rectification circuit, three performance indicators ST (time), OV (overshoot), and SSE (steady-state error) are selected as the objective functions. During the selection process, if too many objective functions (more than three) are selected, the optimization problem will be introduced into high-dimensional multi-objective optimization, which will greatly reduce the performance of the algorithm. If the number of objective functions is small, the final result cannot well represent the overall performance of the circuit. Therefore, in this experiment, the above three performance indicators are selected as the objective functions.

[0139] Step 2, as Figure 1 shown is the flowchart of the multi-objective particle swarm algorithm based on hybrid elite particles. First, initialize the settings of the multi-objective particle swarm algorithm.

[0140] Step 2.1: Initialize the initial values of the particles, that is, the control parameters ki1, kp1, ki2, kp2, ki3, and kp3 of the three groups of PI controllers.

[0141] Step 2.2, set the population size, which is set to 20 in the present invention. Set the archive particle capacity, which is set to 30 in the present invention. Set the basic flight coefficient, the individual flight coefficient C1 = 2, the hybrid elite particle basic flight coefficient C2 = 2, the maximum value of the current speed proportion weight , the minimum value .

[0142] Step 2.3, set the maximum number of iterations Gmax = 1000. The particle boundary var = [0.0001, 50].

[0143] Step 2.4, set the mutation probability. In the present invention, after multiple experimental verifications, the mutation probability with the best effect is taken .

[0144] Step 3, assign values to the initial generation of particles. Use random numbers to randomly assign values to the particles within the set boundary range, and then interact with the simulation. Substitute the parameters of all particles into the PI controller of the simulation circuit, and extract the required parameter variables, namely the simulation time and the output data of the load voltage. Then substitute the relevant variables into the three objective functions to calculate the values of the three objective functions respectively. Since they are the initial generation of particles, directly assign the positions of the particles and the values of the objective functions to the historical optimal positions Pbest of the current particles and the historical optimal objective values Pbest_fit of the particles. Then, confirm the dominance relationship among all particles. The definition of dominance among particles is as follows:

[0145] Suppose there is a multi-objective optimization problem, and its objective functions are , where m is the number of objectives. For two solutions x and y, if for all objective functions , the objective functions of solution x are at least as good as those of solution y, that is For all all hold, and there is at least one objective , such that , then we say that solution x dominates solution y, denoted as , which is mathematically expressed as:

[0146] (1),

[0147] By determining the dominance relationship among all particles, store all non-dominated particles in the archive. Since they are the initial generation of particles, there is no need to consider the capacity problem of the archive.

[0148] Step 4, update the speeds and positions of the particles in the multi-objective particle swarm algorithm.

[0149] Step 4.1, analyze the particles in the archive particles. Refer to the definition of information entropy calculation in the above content, calculate and select the particle with the minimum information entropy.

[0150] Step 4.2: Analyze the particles in the archived particles. Refer to the definition of roulette wheel calculation in the above content, calculate and select high-quality particles.

[0151] Step 4.3: Analyze the particles in the archived particles. Refer to the definition of dominance calculation in the above content, calculate the dominance of the particle with the minimum information entropy over the entire archived particles, and calculate the respective flight coefficients of the hybrid elite particles.

[0152] Step 4.4: According to the current generation number and the maximum generation number, and based on the maximum value of the current speed weight ratio , minimum value , adaptively update the current speed weight ratio during the adaptive update process. The formula is:

[0153] (2),

[0154] Where ger represents the currently updated generation number, and Gmax represents the maximum number of iterations, which is set to 1000 in the present invention. The design feature of this method is that in the early stage of the algorithm, by increasing the speed weight ratio, the global search ability can be enhanced, enabling the particles to explore the solution space more widely and avoiding premature convergence to the local optimal solution. In the later stage of the algorithm, by reducing the speed weight ratio, the local search ability can be enhanced, enabling the particles to search the local area more carefully and improving the accuracy of the solution.

[0155] Step 4.5: According to the variables obtained in the above steps 4.1 to 4.5, refer to the following formula to update the speed and position of the current generation particles:

[0156] Speed update formula:

[0157] (3),

[0158] Position update formula:

[0159] (4),

[0160] Step 5: Interact with the simulation, set all the PI controller parameters of the mutated particles into the PI controller, obtain the simulation data, i.e., the simulation time and the output voltage, by running the simulation circuit, and calculate all the target values.

[0161] Step 6: Referring to the objective values of all particles obtained in Step 5, determine the dominance relationship among all particles, store all non-dominated solutions in the archive, and then determine the dominance relationship among all particles in the archive, and delete all dominated particles from the archive. In this step, it is possible that the number of particles in the archive exceeds the archive particle capacity, so a deletion operation needs to be performed again. During this deletion process, in order to maintain the diversity and uniformity of the overall archive particles, the crowded comparison method is sampled for deletion. Calculate the crowding degree of each particle and delete the particles with smaller crowding degrees in turn until the archive particle capacity is reached.

[0162] Step 7: Update the historical best position and objective function value of the particles. This step updates the dominance relationship between the historical best objective function value of the particle and the current objective value.

[0163] Step 7.1: Determine whether the current particle position dominates the historical best position. If it does, update the historical best position of the individual particle.

[0164] Step 7.2: Determine whether the personal best position is not dominated by the current particle position.

[0165] Step 7.3: In Step 7.2 where it is determined whether the personal best position is not dominated by the current particle position, introduce a random mechanism. Set a reference value, which is set to 0.5 in the present invention. By generating a random number, if the random number is greater than or equal to 0.5, no update is performed. If the random number is less than 0.5, the historical best position of the particle is updated. This step introduces randomness, which helps to maintain the diversity of the population and avoid the algorithm from converging to the local optimal solution prematurely.

[0166] Step 8: Repeat Steps 4 - 8 until the iteration reaches the set maximum iteration algebra Gmax = 1000.

[0167] Step 9: Output the archive particles. At this time, these archive particles represent the found Pareto optimal solutions and Pareto optimal solution sets.

[0168] Step 9.1: According to the above steps, the algorithm of the present invention has been run in MATLAB, and a set of Pareto results is shown in Table 1 below.

[0169] Table 1

[0170]

[0171] Step 9.2: Substitute the Pareto optimal solution set obtained in Step 10 into the system and compare it with the multi-objective particle swarm algorithm before improvement. The comparison results are shown in Table 2 below.

[0172] Table 2

[0173]

[0174] Among them, the domination rate measures the coverage of one solution set (set A) over another solution set (set B). Specifically, calculate the number of points in set B that are dominated by set A, and divide it by the total number of points in set B. A higher domination rate indicates better performance of set A relative to set B. Comparison reference of the scatter plot of the Pareto solution space Figure 3 , for the reference of the voltage curve diagram of all outputs of the pareto solutions Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 、 Figure 12 Among them, the finally output Pareto solution set has a total of 27 groups of Pareto solutions. To avoid the clutter of drawing 27 groups of solutions on one graph, every three groups of solutions are drawn on one graph, with a total of 9 graphs, which completely show the output voltage curve diagrams of the Pareto solution set.

[0175] Step 9.3, the Pareto optimal solution set obtained in step 9 is brought into the system and compared with the solutions obtained by the ordinary particle swarm optimization algorithm, referring to the scatter plot of the solution space Figure 13 It can be seen that among the Pareto solutions, there is at least one group of solutions that dominate the solutions obtained by the particle swarm optimization algorithm, that is, the optimization effect is stronger than that of the particle swarm optimization algorithm. Among them, a comparison diagram of the output voltage of a group of domination relationships is as Figure 14 。

[0176] The present invention provides a control method for a three-phase rectification system based on multi-objective hybrid elite particle swarm optimization. There are many methods and ways to specifically implement this technical solution. The above is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by existing technologies.

Claims

1. A control method for a three-phase rectifier system based on multi-objective hybrid elite particle swarm optimization, characterized in that: The following steps are involved: Step 1, selecting performance indicators of the three-phase rectifier circuit as the objective function of the multi-objective particle swarm algorithm, the performance indicators including the stabilization time ST, overshoot OV and stabilization error SSE; Step 2, using a multi-objective particle swarm algorithm to minimize and optimize the objective function; Step 3, bringing the value of the particle obtained by initialization into the PI controller, and obtaining the required circuit value by simulating the circuit. The value of the particle obtained by initialization refers to three groups of proportional integral parameters pi and proportional differential parameters pd, expressed as (kp1, ki1, kp2, ki2, kp3, ki3); wherein kp1, ki1 respectively represent the proportional integral parameters Pi and proportional differential parameters pd of the first group of PI controllers; kp2, ki2 respectively represent the proportional integral parameters Pi and proportional differential parameters pd of the second group of PI controllers; kp3, ki3 respectively represent the proportional integral parameters Pi and proportional differential parameters pd of the third group of PI controllers; Then, three target values ​​represented by each particle are calculated respectively through three sets of target functions, wherein the three target values ​​include the stabilization time ST, the overshoot OV and the stabilization error SSE; Step 4, calculate the mutual dominance relationship of the target values ​​of all particles, find all non-dominated solutions, and store all non-dominated solutions in the archive; Step 5, analyze the archived particles, use the entropy weight method to calculate the minimum entropy particles, use the roulette method to select the particles with higher quality, use the minimum entropy particles and the particles with higher quality to represent the global optimal particles in the speed update process of the multi-objective particle algorithm, and use the minimum entropy particles and the particles with higher quality to form a mixed elite particle to represent the global optimal particle; Step 6, using the dominance method, by calculating the dominance ratio of the particle with the minimum entropy in the entire archived particles, and normalizing the ratio, so as to achieve dynamic adjustment of the flight coefficient of the hybrid elite particles; Step 7, update the particle speed and position; Step 8, repeat steps 3 to 7 until the set conditions are met; Step 9: During the update process, when the number of archived particles exceeds the set maximum capacity, the particles in the archive are deleted; Step 10, output the particles in the final archive. At this time, the solution set composed of all particles in the archive is the final Pareto solution set; In step 2, ST is the system response to reach and maintain the output voltage reference value V ref The time required to be within the allowable error range is defined by the threshold PCTvst, and the upper bound ub and lower bound lb of the error range are: ub=V ref +V ref ×PCTvst (1), lb=V ref -V ref ×PCTvst (2), The objective functions of ST, OV, and SSE are: The ST objective function is: Where vol(t) is the final output voltage as a function of time t; It means that for any time τ greater than time t, vol(τ)∈[lb,ub] is satisfied; The OV objective function is: OV=max(max(vol(t))-V ref ,0) (4), The SSE objective function is: Where len is the length of time t and Ns is the number of time points in the steady-state phase.

2. The method according to claim 1, characterized in that In step 1, space vector pulse width modulation SVPWM is used to obtain the parameters of the three-phase rectifier circuit, including kp1, ki1, kp2, ki2, kp3, and ki3.

3. The method according to claim 2, characterized in that Step 4 includes: setting a multi-objective optimization problem, the objective functions are f1, f2, ..., f m , where m is the number of objectives, for two solutions x_1 and x_2, if for all objective functions f i , i takes values ​​from 1 to m, the objective function of the solution x_1 is at least as good as the solution x_2, that is, f i (x_1)≤f i (x_2) holds for all i=1,2,....,m, and there is at least one target f j So that f j (x_1) <f j (x_2), then we determine that solution x_1 dominates solution x_2, denoted by It is expressed as:

4. The method according to claim 3, characterized in that In step 5, the archived particles are analyzed and the entropy weight method is used to calculate the particle with the minimum entropy, which specifically includes: Step 5-11, initialization of multi-objective particle swarm algorithm: Initialize and design the parameters of the multi-objective particle swarm algorithm, including the population size, the setting of the first generation of particles, the maximum iteration number, archiving, the capacity of the archived particles, the flight coefficient and the mutation rate; Step 5-12, use the entropy weight method to find elite particles: among the archived particles, use the entropy weight method to calculate the particle with the smallest information entropy, which specifically includes the following steps: Step 5-12-1, data input: The solution set consisting of archived particles is taken as the original matrix; the original matrix is ​​an n×3 matrix, where n represents the number of particles in the archive; Step 5-12-2, data normalization: Where front_norm ij is the normalized element of the original matrix in row i and column j. ij is the element in the i-th row and j-th column of the original matrix, min(front .j ), max(front .j ) are the minimum and maximum values ​​of the j-th column of the original matrix respectively; Step 5-12-3, calculate the probability distribution matrix: where p ij is the i-th row and j-th column element of the probability distribution matrix, is the sum of all elements of the normalized matrix; Step 5-12-4, calculate information entropy: Among them, H j is the information entropy of the jth target value; Step 5-12-5, calculate the information entropy weight: oh j =1-H j (10), Among them, ω j is the information entropy weight of the jth objective function; Step 5-12-6, calculate the normalized weight: in is the normalized weight, is the sum of all information entropy weights; Step 5-12-7, calculate the weighted value: Among them, v i is the weighted value of the i-th particle; Step 5-12-8, get the index of the minimum weighted value: L=min(v i ) (13), Where L is v i The position index of the minimum value is the index of the minimum position of the weighted information entropy.

5. The method according to claim 4, characterized in that In step 5, the roulette wheel selection is based on the fitness value of each particle to calculate the selection probability and make the selection by cumulative probability; The roulette wheel method is used to select particles with higher quality, specifically comprising: Step 5-21, calculate the selection probability: For each particle i, the selection probability p i for: where f i is the fitness value of the ith particle, and N is the total number of archived particles; Step 5-22, calculate the cumulative probability: Cumulative probability P i For implementing roulette selection: where p e represents the selection probability of the e-th particle, P i represents the cumulative probability of the i-th particle; Step 5-23, select particles: Generate a random number r∈[0,1] and select the smallest particle i that satisfies the following conditions: r≤P i (16)， The roulette method is based on hypercube selection and includes the following steps: Step 5-24, select the hypercube: REP.quality is a matrix, where each row represents a hypercube and the quality of the hypercube. The second column of the matrix REP.quality REP.quality(:,2) contains the quality value of each hypercube; Step 5-25, calculate the selection probability prob of each hypercube h h : Step 5-26, select the hypercube: use the roulette wheel selection mechanism, based on P i The value of selects a hypercube: Generate a random number r between the set [0,1] and calculate: R=r×max(P i ) (18), Where R represents a random number r that generates a i A random number within the maximum range; Find the first hypervolume h_1 that satisfies the roulette condition: R≤P h_1 (19), Where P h_1 represents the cumulative probability of the hypervolume h_1 meeting the roulette condition; Step 5-27, randomly select a particle H in the hypervolume h_1 as a particle with a higher mass selected by the roulette method; For all particles in the archived particles, in the solution space, since there are three objective functions, the solution space is a three-dimensional space. The entire solution space is divided and numbered using a set grid in the three-dimensional space, where each grid is a hypercube.

6. The method according to claim 5, characterized in that Step 6 includes: Step 6-1, calculate the maximum and minimum values ​​of each objective function value in the archive: For each objective value j, calculate the maximum and minimum values ​​of all solutions in the archive: where f ij represents the target value of the i-th particle on the j-th objective function, are the maximum and minimum values ​​of the jth objective function respectively; Step 6-2, calculate the dominance: For each solution x in the archive r , calculate the dominance of the particle X with the minimum information entropy on each objective function: Among them U j It represents the value of the jth objective function of the particle X with the minimum information entropy, g ij is the dominance of particle X with the minimum information entropy over particle i on the j-th objective function, f j (i) represents the target value of particle i on the objective function j, represents the maximum value of the objective function j, Represents the minimum value of the objective function j; If the particle X with the smallest information entropy is better than particle i in the jth objective function, the dominance degree on the jth objective function is accumulated: Where M is the number of objective functions, g i is the total dominance of particle X with the smallest information entropy over the i-th particle; Step 6-3, calculate the total dominance: Calculate the total dominance G of the particle X with the smallest information entropy over all solutions in the archive: Step 6-4, find the minimum value in the dominance: find the minimum value g of the dominance of the particle X with the minimum information entropy over all solutions in the archive min : Step 6-5, calculate the ratio p of the minimum dominance to the total dominance: Step 6-6, calculate the adaptive flight coefficient: C quality =(1-p)×C2,C Entropy =p×C2 (26), Among them C quality is the flight coefficient of the roulette high-mass particle, C Entropy is the flight coefficient of the particle with the minimum information entropy, and C2 is the basic flight coefficient of the global optimal particle.

7. The method according to claim 6, characterized in that Step 7 includes: The particle velocity update formula is: v i (t+1)=ωv i (t)+c1γ1(pbest i (t)-x i (t))+C Entropy γ2(Entropy(t)- x i (t))+C quality γ3(quality(t)-x i (t))(27), The particle position update formula is: x i (t+1)=x i (t)+v i (t+1) (28), where v i (t+1) represents the velocity of particle i at the next moment, v i (t) represents the speed of particle i at the current moment, ω is the weight ratio of particle i in the current speed update process, c1 is the flight coefficient of the individual optimal position, pbest i (t) is the individual optimal position of particle i, x i (t) represents the current position of particle i, x i (t+1) represents the position of particle i at the next moment, Entropy(t) is the particle with the smallest information entropy, quality(t) is the roulette high-quality particle, and γ1, γ2, and γ3 are random numbers between 0 and 1.

8. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

9. A computer device, characterized in that: include: A memory for storing instructions; A processor is used to execute the instructions so that the computer device executes the method according to any one of claims 1 to 7.

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