The parameters of permanent magnet synchronous motor (PMSM) affect the performance of vector control servo system. Because of the complexity of nonlinear model of PMSM, it is very difficult to identify the parameters of PMSM. Aiming at the problems of large amount of data calculation, low identification accuracy and poor robustness in the process of multi parameter identification of permanent magnet synchronous motor, this paper proposes a weighted differential evolutionary particle swarm optimization algorithm based on double update strategy. By introducing adaptive judgment factor to control the proportion of weighted difference evolution (WDE) algorithm and particle swarm optimization (PSO) algorithm in each iteration process, and consider using PSO algorithm or WDE algorithm to update individuals according to the probability law. The individuals obtained from WDE operation are used to guide the individual evolution process in PSO operation through the information exchange mechanism. The proposed WDEPSO algorithm can ensure the diversity and effectiveness of the individual evolution of the population. The algorithm is applied to parameter identification of PMSM drive system. The simulation results show that the proposed algorithm has better convergence performance and has strong robustness, parameter identification of permanent magnet synchronous motor based on proposed method does not need to rely on more data sheet on the motor design value, can motor stator resistance identification at the same time, the rotor flux linkage, d/q-axis inductance and electrical parameters, and can effectively track the parameters value.

For Field-oriented control (FOC), the parameters of the current control loop will directly affect the overall performance of the system, with the stator resistance and stator inductance directly influencing the current control loop controller. In addition, the parameters of the speed and position loop controllers are also influenced by the current loop control parameters. In direct torque control (DTC), the electromagnetic torque and flux linkage are used as control variables, and the torque and chain deviations are directly controlled by a hysteresis comparator [

In order to obtain reliable permanent magnet synchronous motor parameters, suitable parameter identification methods are required, and the main methods for permanent magnet synchronous motor parameter identification are: model reference adaptive algorithm [

The reference [

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It provides a new idea for scientific research to combine the two methods to solve engineering problems by making full use of their respective advantages. In this paper, particle swarm optimization algorithm and weighted difference algorithm are combined for parameter identification of permanent magnet synchronous motor.

The main work of this paper:

(1) The advantages of the particle swarm optimization and the weighted differential evolution algorithm are combined, and a permanent magnet synchronous motor parameter identification method that combines the use of both algorithms is proposed.

Particle swarm optimization (PSO) algorithm has a fast convergence speed in the initial stage of solving the optimization problem, but in the later stage, because all particles are close to the optimal particle, the whole population loses diversity, and particles are easy to fall into local optimal. The weighted differential evolution (WDE) algorithm has the ability to maintain population diversity and explore local search, but it has no mechanism to store previous processes and use global information about the search space, so it can easily lead to waste of computing power. Therefore, in this paper, the advantages of PSO and WDE are combined to realize the identification of PMSM parameters.

(2) An adaptive judgment factor is proposed to control the ratio between the particle swarm optimization and the weighted differential evolution algorithm.

Adaptive judgment factors are introduced to control the proportion of particle swarm optimization and weighted differential evolution algorithm in each iteration process. According to the probability law, PSO algorithm or WDE algorithm is used to update individuals. The individuals obtained by WDE operation are used to guide the evolution process of individuals in PSO operation through information exchange mechanism, so as to ensure that the greater the crossover probability, the more information the new individuals inherit from the mutant individuals, and the richer the population diversity, thus ensuring the global solution accuracy and efficiency of the algorithm.

The permanent magnet synchronous motor has multivariable, nonlinear, and strongly coupled characteristics, and the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system (d/q-axis coordinate system) can be expressed as

The order of the

The differential evolution algorithm was proposed by Rainer Storn and Kenneth Price in 1995 while studying the Chebyshev polynomial fitting problem [

Step 1: population initialization. The current population can be described as follows:

Step 2: variant operation.

Step 3: crossover operations.

Step 4: select operation. The differential evolution algorithm uses a greedy strategy to compare the fitness of offspring individuals over their parents, and the individuals with better fitness will be selected to enter the next generation population.

The weighted differential evolution algorithm (WDE) [

Step 1: population initialization. The initial WDE population contains

In

Step 2: weighted operation. WDE algorithm randomly selects NP subpopulation

Step 3: cross-mutation operation. The crossover factor

One of the following two strategies is selected according to the probability of each pair to perform the variation operation.

Strategy 1. The variation factor is defined according to

Strategy 2. Generate different variation factors

Step 4: select operation. The differential evolution algorithm uses a greedy strategy to calculate the fitness values of individuals before and after the mutation, and selects the better solution with smaller fitness values to update and replace the initial values.

From the algorithm steps, it can be seen that the weighting operation is an important difference between WDE and DE. Through the weighting operation of

The particle swarm optimization is inspired by observing the foraging messaging of a flock of birds. In the algorithm, each individual is a particle representing a feasible solution. Let

In each iteration of the particle, its update equation is:

The evolution criterion of the differential evolution algorithm is based on adaptive information and does not require additional conditions such as function derivability and continuity. In addition, differential evolution is inherently parallel and suitable for massively parallel distributed processing. However, differential evolution algorithms do not utilize individual prior knowledge, i.e., there is no mechanism to store prior processes and use global information about the search space. The particle swarm optimization algorithm, on the other hand, makes decisions based on its own and other particles’ experience, so it can effectively compensate for the deficiencies of the differential evolution algorithm. The WDE algorithm and PSO algorithm are fused, and an adaptive judgment factor is introduced to control the ratio between the use of particle swarm optimization and differential evolution algorithms in each iteration, and the PSO algorithm or WDE algorithm is considered to update individuals according to the law of probability, which ensures that the greater the crossover probability, the more information the new individuals inherit from the mutant individuals, and the richer the population diversity. Judgment factor is used to select the update method of individuals, it is calculated as:

Then when the i-th individual generates a new individual, first a random number

According to

The basic idea is that according to the difference between the actual output of the system and the output of the adjustable model, the parameters of the model to be identified are continuously adjusted by the identification algorithm to minimize the value of the error adaptation function between the actual output value and the adjustable model, the smaller the adaptation value, the closer the input of the identification model and the measured input, and the closer the parameters to be identified and the real value.

The fitness function is:

Parameter identification steps of permanent magnet synchronous motor based on WDEPSO:

Step 1: sampling current and angular velocity.

Step 2: initialize the two algorithms.

Step 3: judge the relationship between

Step 4: select one of the two algorithms for iteration according to the results of step 3.

Step 5: if the maximum number of iterations is not reached, re-enter step 3 for circulation.

Step 6: reach the maximum number of iterations and output identification parameters.

The algorithm flow is shown in

In this simulation, a simulation model based on the WDEPSO is built on the MATLAB/Simulink platform for the parameter identification of permanent magnet synchronous motor. The parameters of the simulation model are set as in

Symbol | Quantity | Value |
---|---|---|

P | Rated power | 1.0 kW |

N | Rated speed | 2000 r · min^{−1} |

T | Nominal torque | 4 N · m |

U | Rated line voltage | 220 V |

R | Stator resistance | 1.454 |

L_{d} |
d-axis inductance | 7.53 mH |

L_{q} |
q-axis inductance | 13.25 mH |

_{f} |
Flux linkage | 0.224 Wb |

p_{n} |
Number of pole pairs | 4 |

To make the results comparable, the WDEPSO is compared with the WDE, DE, PSO, and particle swarm optimization with inertial weight variation (LPSO). To ensure the rationality of simulation, the WDEPSO, PSO, LPSO are set with the same parameters, and the WDE and DE algorithms are set with the same crossover factor and variation factor. In order to test the performance of the algorithms in global search, the initial domain of all parameters to be identified is set to (−2, 10), far from the real values set in the simulation. The simulations were run 50 times independently in order to reduce the testing error caused by the randomness of the single algorithm.

In order to fully verify the computational performance of various algorithms, the effectiveness of algorithm recognition is tested under changing working conditions. The algorithms are tested under two conditions: load change and speed change. The speed of the permanent magnet synchronous motor is designed to first accelerate to the rated speed, then run steadily, and finally decelerate to 20% of the rated speed until the end. Each speed change strategy accounts for one-third of the total sampling time, and the motor load increases from 0 to the rated value during stable operation, and decreases to 0 when the motor starts to decelerate.

The simulation data are presented in the following

Identified parameter | WDE | DE | LPSO | PSO | WDEPSO |
---|---|---|---|---|---|

R/ |
1.447 | 1.544 | 1.438 | 1.438 | 1.453 |

L_{d}/mH |
6.829 | 7.554 | 7.484 | 7.484 | 7.541 |

L_{q}/mH |
17.05 | 12.70 | 13.50 | 14.89 | 13.43 |

_{f}/Wb |
0.2299 | 0.2227 | 0.2295 | 0.2273 | 0.2242 |

Fitness | 15210 | 20570 | 5659 | 11005 | 45.9 |

From the data in the

The results of the five algorithms to identify each parameter of the permanent magnet synchronous motor are shown in

From

Parameter identification of PMSM is subject to large fluctuations or mis-convergence due to the high degree of nonlinearity of the PMSM model and the local extreme value points of the objective function, which makes it difficult to find the optimal solution for algorithms with low search degree, small solution space and poor stability. All five algorithms in this paper can converge quickly to near the true value, which indicates that all five algorithms have good global search performance. When the identified values of all five algorithms are close to the stable values, it can be seen that the WDEPSO converges faster than the other algorithms, and the identification accuracy is higher than the other algorithms, and it can be seen from the data in Table I that the identified values of the WDEPSO are closer to the design values, the average fitness value is smaller, and the WDEPSO can better track the motor in speed and load torque mutation. This shows that the WDEPSO has good robustness and convergence, which verifies the superiority of the algorithm.

In this paper, based on vector control, the motor electromechanical mathematical model is brought to full rank by injecting weak magnetic negative sequence current with