PSS model parameter solving method based on improved particle swarm optimization algorithm

Abstract

The invention relates to a PSS model parameter solving method based on an improved particle swarm optimization algorithm. The PSS model parameter solving method comprises the following steps: establishing a single-machine infinite-bus power system model; a PSS optimization model with the rotating speed deviation as an input signal and the voltage of a supplementary control loop as an output signal is established, and the supplementary control loop is a loop where a PSS is located; an MCPSO algorithm is designed; encoding and decoding PSS optimization model parameters, converting the PSS optimization model parameters into variables which can be identified by MCPSO, and designing constraint conditions and a target function; and optimizing and solving the parameters of the PSS optimization model based on an MCPSO algorithm. Compared with the prior art, the method has the advantages of effectively improving the damping ratio of a power system, inhibiting low-frequency oscillation and the like.

Description

Technical Field

[0001] The present invention relates to the field of power system service continuity, and in particular to a method for solving PSS model parameters based on an improved particle swarm optimization algorithm. Background Art

[0002] Service continuity is one of the most important features of power systems. With the expansion of the power grid and the increase in power transmission, low-frequency oscillations between regional power grids have gradually become a bottleneck for improving the transmission capacity of large-scale power systems. The main reasons for power system instability include local oscillations between generators in the same power plant, oscillations caused by adjacent power plants, and global oscillations of unstable generators connected to the same power grid. Obviously, these oscillations (even at low frequencies) have a negative impact on the power transmitted in the transmission line. Interferences such as sudden load changes or faults will cause an imbalance between the power delivered by the generator and the mechanical power generated by the turbine. The imbalance will cause shaft torque and accelerate or decelerate the axis. Therefore, it is necessary to consider the transient stability problem of maintaining synchronization between generators under severe disturbances. Since the single-machine infinite-bus power system model is a simplified power system model, it helps the study of power system stability and avoids considering unnecessary influencing factors. Therefore, the single-machine infinite-bus power system is used for research.

[0003] The basic function of a power system stabilizer (PSS) is to damp power oscillations by using the excitation system to generate electrical torque. To ensure the safe and reliable operation of the PSS, on-site tests must be carried out before the PSS is put into operation to verify whether the PSS parameters meet the requirements. At present, the on-site test of PSS parameters depends to a large extent on the experience of testers, with a large workload and a certain degree of blindness.

[0004] The particle swarm optimization (PSO) algorithm is a stochastic parallel optimization algorithm with the following advantages: it does not distinguish the optimization function, has a fast convergence speed, a simple algorithm, and is easy to program and execute. However, it also has some disadvantages: 1) For functions with multiple local optima, although the PSO algorithm provides the possibility of global search, it cannot guarantee convergence to the global optimum. 2) The PSO algorithm does not make full use of the information obtained during the calculation process, that is, due to the lack of an effective cooperative search method, it may not produce satisfactory results. Therefore, the PSS parameter optimization method needs to be further improved. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for solving PSS model parameters based on an improved particle swarm optimization algorithm, optimize and tune the single-machine infinite-bus power system stabilizer, so that the optimized parameters of the PSS have good adaptability, can effectively improve the damping ratio of the power system, and reduce the low-frequency oscillation of the single-machine infinite-bus power system under various conditions.

[0006] The object of the present invention can be achieved by the following technical solutions:

[0007] A method for solving the parameters of a PSS model based on an improved particle swarm optimization algorithm, comprising the following steps:

[0008] S1. Establish a single-machine infinite-bus power system model;

[0009] S2. Establish a PSS optimization model with the rotational speed deviation as the input signal and the voltage of the supplementary control loop as the output signal, wherein the supplementary control loop is the loop where the PSS is located;

[0010] S3. Design the MCPSO algorithm;

[0011] S4. Encode and decode the parameters of the PSS optimization model, convert them into variables recognizable by the MCPSO, and design the constraint conditions and the objective function;

[0012] S5. Optimize and solve the parameters (i.e., the time constants and the gains) of the PSS optimization model based on the MCPSO algorithm.

[0013] The single-machine infinite-bus power system includes a synchronous generator and an automatic voltage regulator of an exciter connected to an infinite bus through a transmission line, wherein the synchronous generator includes an excitation circuit and an equivalent damping winding on the q-axis.

[0014] The output of the PSS is the input voltage signal of the automatic voltage regulator of the exciter.

[0015] The transfer function of the PSS optimization model is:

[0016]

[0017] Wherein, the time constant T 6 represents the transducer time constant, the gain of the PSS is set by K PSS , the signal washout is set by the time constant T 5 , the second-order module with parameters A 1 and A 2 is used to consider the low-frequency effect of the high-frequency torsional filter, T 1 to T 4 are the time constants of two lead-lag compensation modules, the output of the PSS is the voltage signal V ref of the supplementary control loop, the input signal is the deviation Δω(s) of the synchronous speed; the parameters to be identified are T 1 , T 2 , T 3 , T 4 , T 5 , T 6 and K PSS。

[0018] The specific MCPSO algorithm is as follows:

[0019] S31. Initialize two populations P1 and P2. Among them, population P1 processes constraints to converge within the constraint range, and the other population P2 does not consider constraints to maintain the diversity of the algorithm results;

[0020] S32. During the evolution process, population P1 adopts a dynamically changing ε-constraint relaxation processing mechanism to screen feasible solutions, including the following processes: selecting the individual optimal solution, the global optimal solution, generating the offspring population, environmental selection of the solution set, and dynamically updating the constraint boundary; population P2 only evolves for the objective function, including the following processes: selecting the individual optimal solution, the global optimal solution, generating the offspring population, and environmental selection;

[0021] S33. Populations P1 and P2 generate the next generation population;

[0022] S34. During the search process, populations P1 and P2 have two different co-evolution methods: Method 1 is heterologous co-evolution, that is, populations P1 and P2 have different initial information; Method 2 is homologous co-evolution, that is, sub-populations P1 and P2 have the same initial information;

[0023] Heterologous co-evolution is adopted in the first half of the search, aiming to quickly converge population P1 within the constraint range, and homologous co-evolution is adopted in the second half of the search, aiming to use population P2 to assist in expanding the diversity of population P1 without considering constraints.

[0024] In the above S32, the simulated annealing algorithm using the exponential function is used to dynamically shrink the ε-constraint boundary. Assuming the number of constraint conditions is p, the ε-constraint boundary at the t-th moment is:

[0025]

[0026] Among them, cp controls the decreasing trend of ε, δ is set to a value close to 0, the violation degree of the maximum constraint condition of the initial population is selected as the initial boundary of the ε-constraint feasible region, and the annealing constants A j and B j are designed as:

[0027]

[0028] Among them, ε(0) is the initial value of the constraint boundary, and T is the maximum number of changes.

[0029] In the above S33, populations P1 and P2 generate the next generation population using the following formula:

[0030] V(t + 1) = wV(t) + c 1 ×rand[Pbest - X(t)] + c2 ×rand[Gbest - X(t)]

[0031] X(t + 1) = X(t) + V(t + 1)

[0032] Wherein, V(t) represents the velocity of the particle at time t, X(t) represents the state of the particle at time t, c 1 and c 2 represent learning factors, rand is a random number uniformly distributed in the interval (0, 1), Pbest is the current individual optimal value of the particle, Gbest is the current optimal value in the population, w is the inertia weight factor, and t represents the number of iterations.

[0033] In the S34, during the heterologous co - evolution process, the method for updating P1 is as follows:

[0034] Pop new = [Pop1, Offspring1, Offspring2]

[0035] P1 ← Pop new Adopt an environmental selection strategy with ε - constraint

[0036] Wherein, Pop1 is all individuals in the original P1 population, Offspring1 and Offspring2 are the next - generation individuals generated by two populations, P1 is the updated population, and the updated population of P2 is the better individuals in [Pop2, Offspring2];

[0037] During the homologous co - evolution process, the updated population of P2 is the same as that of P1;

[0038] flag is designed as a co - evolution state flag, which is determined by the number of individuals in P1 that satisfy the constraints. That is, when all individuals in P1 satisfy the constraints, flag changes from 0 to 1, and the heterologous co - evolution is replaced by the homologous co - evolution.

[0039] The S4 is specifically as follows:

[0040] According to the PSS transfer function and the actual application scenario, set the upper and lower limits of the parameters T 1 , T 2 , T 3 , T 4 , T 5 , T 6 , K PSS ;

[0041] Encode the PSS optimization model parameters as individuals in the MCPSO population:

[0042] x = [x 1 , x 2 , x3 , x 4 , x 5 , x 6 , x 7 , x min ≤x≤x max

[0043] where x represents a particle, x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 respectively correspond to T 1 , T 2 , T 3 , T 4 , T 5 , T 6 , K PSS , x min represents the lower limit of the parameter, x max represents the upper limit of the parameter;

[0044] Set the evaluation criteria of the MCPSO algorithm as:

[0045]

[0046] where F is the cost function, T is the system operation time, w(t) is the motor speed after system optimization, and w(t) is the desired motor speed.

[0047] The said S5 includes the following steps:

[0048] S51. Without considering the constraints, initialize the populations P1 and P2, and set the maximum violation degree of each constraint in the initial population P1, that is, ε(0) = InitialE, and the collaborative state flag flag = 0;

[0049] S52. Enter the loop, update the ε constraint boundary by the simulated annealing operator, select Gbest and Pbest in the two populations and generate the next generation population; The P1 population adopts the ε-constrained environmental selection strategy to select the individual with a smaller cost function from Pop new = [Pop1, Offspring1, Offspring2] as the new generation population, and the P2 population adopts the unconstrained environmental selection strategy to select the individual with a smaller cost function from [Pop2, Offspring2] as the new generation population; If the collaborative state flag becomes 1, the heterologous co-evolution becomes homologous co-evolution. At this time, the new generation population of P2 is the same as that of P1; Finally, output the voltage signal V ST to make the speed deviation Δω return to 0.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] (1) During the evolution process, the MCPSO algorithm can balance convergence, diversity, and feasibility simultaneously. Although the traditional PSO algorithm is simple and easy to implement, and has a fast convergence speed, it lacks information exchange between particles and is prone to falling into local optima. The multi-mode co-evolution optimized MCPSO algorithm proposed in the present invention adopts multiple populations to evolve independently, jointly search the unknown space, and share the individual position information of the populations, so as to improve the perception ability of a single population for the space. This optimized algorithm can not only ensure the diversity and feasibility of the population, but also accelerate the convergence speed of the algorithm.

[0052] (2) At present, the on-site test of PSS parameters largely relies on the experience of testers, with a large workload and certain blindness. In view of this situation, the present invention studies an intelligent solution method for PSS parameters. By applying the improved particle swarm optimization algorithm to parameter solving, the single-machine infinite-bus system has excellent performance under different conditions, can effectively suppress low-frequency oscillation, and improves the system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is the method flow chart of the present invention;

[0054] Figure 2 is the single-line diagram of the SMIB power system;

[0055] Figure 3 is the structural block diagram of the SMIB system with PSS;

[0056] Figure 4 is the schematic diagram of the PSS optimization model structure;

[0057] Figure 5 is the comparison diagram of the phase-frequency characteristics of the single-machine infinite-bus power system before and after adding PSS;

[0058] Figure 6 is the comparison diagram of the speed deviation of the single-machine infinite-bus power system under the step disturbance of electromagnetic torque;

[0059] Figure 7 is the comparison diagram of the speed deviation of the single-machine infinite-bus power system under the white noise disturbance of electromagnetic torque. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0060] The present invention will be described in detail below with reference to the drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives the detailed implementation manner and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0061] In order to make the optimized PSS adaptable to various operation modes of the power grid after asynchronous interconnection, the present invention proposes a method for solving the parameters of a new type of PSS based on an improved particle swarm optimization algorithm. First, according to the operation mode of the power system, a single-machine infinite-bus power system model and an objective function of the power system in the oscillation mode are established; then, based on the role of the PSS in the power system, a PSS optimization model with the speed deviation as the input signal and the voltage of the supplementary control loop as the output signal is built; finally, aiming at the shortcomings of the particle swarm optimization algorithm, a multi-mode collaborative evolution optimization (MCPSO) algorithm for constrained multi-objectives is proposed. The parameters of the PSS optimization model are selected as the optimization object, and the optimal compensation effect on the excitation system under typical working conditions is taken as the objective function, while providing sufficient compensation under the operating conditions with the strongest system structure and full load is used as a constraint, and the MCPSO algorithm is used to solve the parameters (i.e., time constant and gain) of the PSS optimization model.

[0062] This embodiment provides a method for solving the parameters of a PSS model based on an improved particle swarm optimization algorithm, as Figure 1 shown, including the following steps:

[0063] S1. Establish a single-machine infinite-bus power system model.

[0064] For stability analysis, a single machine is connected to an infinite bus through a transmission line (a Single Machine connected to an Infinite Bus, SMIB), as Figure 2 shown. The system includes a synchronous generator (Generator, G) connected to the power grid (infinite bus) through a transmission line, and an automatic voltage regulator (Automatic Voltage Regulator, AVR) of the exciter. Among them, the synchronous generator includes an excitation circuit and an equivalent damping winding on the q-axis.

[0065] S2. Establish a PSS optimization model with the speed deviation as the input signal and the voltage of the supplementary control loop as the output signal.

[0066] The Power System Stabilizer (PSS) is a device that provides an additional supplementary control loop for the AVR. In order to provide damping for the vibration of the generator rotor, the PSS must generate an electric torque component corresponding to the rotor speed deviation, that is, add a stable signal during the dynamic / transient state of the excitation system, compensate for the oscillation of the excitation system voltage error, and provide a damping component when in phase with the motor rotor speed deviation. The theoretical basis of the PSS can be illustrated by the Figure 3 block diagram shown, where the supplementary control loop is the loop where the PSS is located.

[0067] The common structure of the PSS optimization model implemented in the present invention is as follows Figure 4 as shown, and its transfer function is given by the following relational expression:

[0068]

[0069] where the time constant T 6 represents the transducer time constant, the gain of the PSS is set by K PSS , the signal washout is set by the time constant T 5 , and the second-order module with parameters A 1 and A 2 is used to consider the low-frequency effect of the high-frequency torsional filter. T 1 to T 4 are the time constants of two lead-lag compensation modules. The output of the PSS is the voltage signal V ref added to the generator AVR as a supplementary control loop, that is, the input voltage signal of the exciter system; the input signal of the PSS is the deviation Δω(s) of the synchronous speed; the parameters to be identified are T 1 , T 2 , T 3 , T 4 , T 5 , T 6 and K PSS .

[0070] S3. Design the MCPSO algorithm.

[0071] The MCPSO algorithm is specifically as follows:

[0072] S31. Initialize two populations P1 and P2. Among them, population P1 processes the constraints to converge within the constraint range, and the other population P2 does not consider the constraints to maintain the diversity of the algorithm results.

[0073] S32. During the evolution process, population P1 adopts a dynamically changing ε-constraint relaxation processing mechanism to screen feasible solutions, including the following processes: selecting the individual optimal solution, the global optimal solution, generating the offspring population, environmental selection of the solution set, and dynamically updating the constraint boundary; population P2 only evolves for the objective function, including the following processes: selecting the individual optimal solution, the global optimal solution, generating the offspring population, and environmental selection.

[0074] In this embodiment, the simulated annealing algorithm using the exponential function is used to dynamically shrink the ε-constraint boundary. Assuming the number of constraint conditions is p, the ε-constraint boundary at the t-th moment is:

[0075]

[0076] Among them, cp controls the decreasing trend of ε, δ is set to a value close to 0, and the violation degree of the maximum constraint condition of the initial population is selected as the initial boundary of the ε constraint feasible region, and the annealing constants A j and B j can be designed as:

[0077]

[0078] Among them, ε(0) is the initial value of the constraint boundary, and T is the maximum number of changes. In this embodiment, cp = 5 and δ = 1e-8 are set.

[0079] S33. The next-generation population is generated from populations P1 and P2 using the following formula:

[0080] V(t + 1) = wV(t) + c 1 ×rand[Pbest - X(t)] + c 2 ×rand[Gbest - X(t)]

[0081] X(t + 1) = X(t) + V(t + 1)

[0082] Among them, V(t) represents the velocity of the particle at time t; X(t) represents the state of the particle at time t; c 1 and c 2 represent learning factors. In this embodiment, constants are used, with a value of 2.05; rand is a random number uniformly distributed in the interval (0, 1), Pbest is the current individual optimal value of the particle, Gbest is the current optimal value in the population, w is the inertia weight factor, and t represents the number of iterations.

[0083] S34. During the search process, populations P1 and P2 have two different co-evolution methods: Method 1 is heterologous co-evolution, that is, populations P1 and P2 have different initial information; Method 2 is homologous co-evolution, that is, sub-populations P1 and P2 have the same initial information;

[0084] Heterologous co-evolution is adopted in the first half of the search to quickly converge population P1 within the constraint range, and homologous co-evolution is adopted in the second half of the search to use population P2 to assist in expanding the diversity of population P1 without considering the constraints.

[0085] During the heterologous co-evolution process, the method for updating P1 is:

[0086] Pop new = [Pop1, Offspring1, Offspring2]

[0087] P1 ← Pop new Adopt an environmental selection strategy with ε constraints

[0088] Among them, Pop1 are all individuals in the original P1 population, Offspring1 and Offspring2 are the next-generation individuals generated by the two populations, P1 is the updated population, and the updated population of P2 is the better individuals in [Pop2, Offspring2].

[0089] During the homologous co-evolution process, the updated population of P2 is the same as P1;

[0090] flag is designed as a co-evolution state flag, which is determined by the number of individuals in P1 that meet the constraints. That is, when all individuals in P1 meet the constraints, flag changes from 0 to 1, and the heterologous co-evolution is replaced by homologous co-evolution.

[0091] S4. Encode and decode the parameters of the PSS optimization model, convert them into variables recognizable by MCPSO, and design the constraint conditions and objective function.

[0092] Set the parameter T to be identified according to the PSS transfer function 1 , T 2 , T 3 , T 4 , T 5 , T 6 , K PSS The upper and lower limits of are [3, 3, 3, 0.1, 0, 0, 5] and [30, 3, 30, 1, 0.5, 0.5, 30] respectively;

[0093] Encode the parameters of the PSS optimization model as individuals in the MCPSO population:

[0094] x = [x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x min ≤ x ≤ x max

[0095] where x represents a particle, and x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 correspond to T 1 , T 2 , T 3 , T 4 , T 5 , T 6 , K PSS , x min= [3, 3, 3, 0.1, 0, 0, 5], x max = [30, 3, 30, 1, 0.5, 0.5, 30];

[0096] Set the evaluation criteria for the MCPSO algorithm as:

[0097]

[0098] Among them, F is the cost function, T is the system operation time, w(t) is the motor speed after system optimization, and w(t) is the expected motor speed.

[0099] S5. Optimize and solve the parameters (i.e., time constant and gain) of the PSS optimization model based on the MCPSO algorithm.

[0100] Specifically, S5 includes the following steps:

[0101] S51. Without considering constraints, initialize populations P1 and P2, and set the maximum violation degree of each constraint in the initial population P1, that is, ε(0) = InitialE, and the collaborative state flag flag = 0;

[0102] S52. Enter the loop, update the ε constraint boundary using the simulated annealing operator, select Gbest and Pbest in the two populations and generate the next generation of populations; The P1 population adopts an environmental selection strategy with ε constraints to select the individual with a smaller cost function from Pop new = [Pop1, Offspring1, Offspring2] as the new generation population, and the P2 population adopts an environmental selection strategy without constraints to select the individual with a smaller cost function from [Pop2, Offspring2] as the new generation population; If the collaborative state flag becomes 1, the heterologous coevolution becomes homologous coevolution. At this time, the new generation population of P2 is the same as P1; Finally, output the voltage signal V ST Make the speed deviation Δω return to 0.

[0103] So far, from S1 to S5, the effective suppression of low-frequency oscillation in the single-machine infinite bus power system under various conditions has been completed, improving the system stability. Figure 5 Shows the comparison of the phase-frequency characteristics of the single-machine infinite bus power system before and after adding PSS, Figure 6 Shows the comparison of the speed deviation of the single-machine infinite bus power system under the step disturbance of electromagnetic torque, Figure 7 Shows the comparison of the speed deviation of the single-machine infinite bus power system under the white noise disturbance of electromagnetic torque. It can be seen that the performance of the method proposed in the present invention is far superior to that of the single-machine infinite bus power system without PSS.

[0104] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A method for solving PSS model parameters based on an improved particle swarm optimization algorithm, characterized in that, it includes the following steps: S1. Establish a single-machine infinite-bus power system model; S2. Establish a PSS optimization model with the speed deviation as the input signal and the voltage of the supplementary control loop as the output signal, where the supplementary control loop is the loop where the PSS is located; S3. Design the MCPSO algorithm; S4. Encode and decode the PSS optimization model parameters, convert them into variables recognizable by MCPSO, and design the constraint conditions and the objective function; S5. Optimize and solve the PSS optimization model parameters based on the MCPSO algorithm.

2. The method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, the single-machine infinite-bus power system includes a synchronous generator and an automatic voltage regulator of the exciter connected to an infinite bus through a transmission line, where the synchronous generator includes an excitation circuit and an equivalent damping winding on the q-axis.

3. The method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 2, characterized in that, the output of the PSS is the input voltage signal of the automatic voltage regulator of the exciter.

4. The method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, the transfer function of the PSS optimization model is: Among them, the time constant T 6 represents the transducer time constant, and the gain of the PSS is set by K PSS , the signal washout is set by the time constant T 5 with parameters A 1 and A 2 The second-order module is used to consider the low-frequency effect of the high-frequency torsional filter. T 1 to T 4 are the time constants of two lead-lag compensation modules. The output of the PSS is the voltage signal V ref of the supplementary control loop, and the input signal is the deviation Δω(s) of the synchronous speed; the parameters to be identified are T 1 , T 2 , T 3 , T 4 , T 5 , T 6 and K PSS .

5. The method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, the specific MCPSO algorithm is: S31. Initialize two populations P1 and P2, where population P1 processes the constraints to converge within the constraint range, and the other population P2 does not consider the constraints to maintain the diversity of the algorithm results; S32. During the evolution process, population P1 adopts a dynamic ε-constraint relaxation processing mechanism to screen feasible solutions, including the following processes: selecting the individual optimal solution, the global optimal solution, generating the offspring population, environmental selection of the solution set, and dynamically updating the constraint boundary; Population P2 only evolves for the objective function, including the following processes: selecting the individual optimal solution, the global optimal solution, generating the offspring population, and environmental selection; S33. Populations P1 and P2 generate the next generation population; S34. During the search process, populations P1 and P2 have two different co-evolution methods: Method 1 is heterologous co-evolution, that is, populations P1 and P2 have different initial information; Method 2 is homologous co-evolution, that is, sub-populations P1 and P2 have the same initial information; Heterologous co-evolution is adopted in the first half of the search to quickly converge population P1 within the constraint range, and homologous co-evolution is adopted in the second half of the search to use population P2 to assist in expanding the diversity of population P1 without considering the constraints.

6. The method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 5, characterized in that, in S32, the simulated annealing algorithm using an exponential function is used to dynamically shrink the ε-constraint boundary. Assuming the number of constraint conditions is p, the ε-constraint boundary at the t-th moment is: Among them, cp controls the decreasing trend of ε, δ is set to a value close to 0, the violation degree of the maximum constraint condition of the initial population is selected as the initial boundary of the ε constraint feasible region, and the annealing constants A j and B j are designed as: Among them, ε(0) is the initial value of the constraint boundary, and T is the maximum number of changes.

7. A method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 5, characterized in that in S33, the populations P1 and P2 generate the next generation population using the following formula: V(t + 1) = wV(t) + c 1 ×rand[Pbest - X(t)] + c 2 ×rand[Gbest - X(t)] X(t + 1) = X(t) + V(t + 1) Among them, V(t) represents the velocity of the particle at time t, X(t) represents the state of the particle at time t, c 1 and c 2 represent learning factors, rand is a random number uniformly distributed in the interval (0, 1), Pbest is the current individual best value of the particle, Gbest is the current best value in the population, w is the inertia weight factor, and t represents the number of iterations.

8. A method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 5, characterized in that in S34, during the heterologous co-evolution process, the method for updating P1 is: Pop new = [Pop1, Offspring1, Offspring2] P1 ← Pop new Adopt an environmental selection strategy with ε-constraint where Pop1 are all individuals in the original P1 population, Offspring1 and Offspring2 are the next generation individuals generated by the two populations, P1 is the updated population, and the updated population of P2 is the better individuals in [Pop2, Offspring2]; during the homologous co-evolution process, the updated population of P2 is the same as P1; flag is designed as a co-evolution state flag, which is determined by the number of constraints satisfied in P1. That is, when all individuals in P1 satisfy the constraints, flag changes from 0 to 1, and the heterologous co-evolution is replaced by the homologous co-evolution.

9. A method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 4, characterized in that S4 is specifically: Set the parameter T to be identified according to the PSS transfer function and the actual application scenario 1 , T 2 , T 3 , T 4 , T 5 , T 6 , K PSS the upper and lower limits of Encoding the PSS optimization model parameters as individuals in the MCPSO population: x = [x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x min ≤ x ≤ x max Among them, x represents a particle, x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 respectively correspond to T 1 , T 2 , T 3 , T 4 , T 5 , T 6 , K PSS , x min represents the lower limit of the parameter, x max represents the upper limit of the parameter; Setting the evaluation criteria of the MCPSO algorithm as: Among them, F is the cost function, T is the system running time, and w(t) is the motor speed after system optimization, which is the expected motor speed.

10. A method for solving PSS model parameters based on an improved particle swarm optimization algorithm according to claim 8, characterized in that S5 includes the following steps: S51. Without considering the constraints, initialize the populations P1 and P2, and set the maximum violation degree of each constraint in the initial population P1, that is, ε(0) = InitialE, and the co-evolution state flag flag = 0; S52. Enter the loop, update the ε-constraint boundary using the simulated annealing operator, select Gbest and Pbest from the two populations and generate the next-generation population; The P1 population adopts an environmental selection strategy with ε-constraint to select individuals with smaller cost functions from Pop new =[Pop1, Offspring1, Offspring2] as the new-generation population, and the P2 population adopts an environmental selection strategy without constraint to select individuals with smaller cost functions from [Pop2, Offspring2] as the new-generation population; If the collaborative state flag becomes 1, the heterologous coevolution becomes homologous coevolution. At this time, the new-generation population of P2 is the same as that of P1; Finally, output the voltage signal V ST to make the rotational speed deviation Δω return to 0.

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