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Self-adaptive differential evolution algorithm with hybrid mutation operator for parameters identification of PMSM

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Abstract

Parameters identification of permanent magnetic synchronous motor (PMSM), which significantly influences the control performance of the drive system, is an important and challenging task of power electronic system. The problem requires both high solution quality and fast convergence speed due to the constraints of hardware. This paper presents a self-adaptive differential evolution algorithm with hybrid mutation operator (SHDE) for parameters identification problem. In this method, a novel mutation operator, called “current-to-archive-best,” is developed by mixing the best solutions randomly selected from archive set and current population. Thus, the algorithm could use the best searching memories so far to generate promising solutions, yielding a faster evolving procedure. Besides, the corresponding control parameters of SHDE are also self-adapted without tedious trial-and-error progress to get appropriate values. Moreover, the parameters estimation program is inserted into the PMSM simulation that is solved by using Newton–Raphson method without any pre-assumption and simplification. This framework, which may be used under any working conditions with large disturbance, is different from other publications, resulting in wider applications. The proposed method applied to parameters identification of PMSM is evaluated on a PMSM drive system with two different operations. The comprehensive results and statistical analyses, compared with other state-of-the-art algorithms, show that SHDE could find high-quality solutions with higher convergence speed and probability.

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Abbreviations

\(A_{\mathrm{v}}\) :

Amplification of speed loop after PI controller

\(A_{\mathrm{i}}\) :

Amplification of current loop after PI controller

Cr:

Crossover rate

D :

Optimization problem dimension

F :

Scaling factor

G :

Generation index of DE algorithm

J :

Inertia coefficient \((\hbox {kg}\,\hbox {m}^{2}\))

\(L_{d}\) :

d-Axis inductance (H)

\(L_{d}^\mathrm{min}\) :

Lower limit of d-axis inductance (H)

\(L_{d}^\mathrm{max}\) :

Upper limit of d-axis inductance (H)

\(L_{q}\) :

q-Axis inductance (H)

\(L_{q}^\mathrm{min}\) :

Lower limit of q-axis inductance (H)

\(L_{q}^\mathrm{max}\) :

Upper limit of q-axis inductance (H)

\(R_{\mathrm{s}}\) :

Stator resistance (\(\Omega )\)

\(R_{\mathrm{s}}^\mathrm{min}\) :

Lower limit of stator resistance \((\Omega )\)

\(R_{\mathrm{s}}^\mathrm{max}\) :

Upper limit of stator resistance \((\Omega )\)

\(T_{\mathrm{e}}\) :

Electromagnetic torque (\(\hbox {N}\,\hbox {m}\))

\(T_{\mathrm{l}}\) :

Load torque (\(\hbox {N}\,\hbox {m}\))

\(\mathbf{U}_{i}\) :

Trail vector for ith individual

\(\mathbf{V}_{i}\) :

Mutation vector for ith individual

\(\mathbf{X}_{i}\) :

Target vector, i.e., ith individual

\(i_{d}, i_{q}\) :

dq-Axis current (A)

\(i_{d\_\mathrm{ref}}, i_{q\_\mathrm{ref}}\) :

Reference dq-axis current (A)

h :

Step size (s)

k :

Iteration index of Newton–Raphson method

\(k_{\max }\) :

Max iteration number of Newton–Raphson method

p :

Number of pole pairs

ps:

Population size of DE algorithm

t :

Sampling time index of PMSM simulation

\(v_{d}, v_{q}\) :

dq-Axis voltage (V)

\(v_{a}, v_{b}, v_{c}\) :

abc-Axis voltage (V)

\(\varepsilon \) :

Small positive constant of termination criteria for Newton–Raphson method

\(\theta \) :

Rotor position (rad)

\({\psi }_{\mathrm{r}}\) :

Rotor flux linkage (Wb)

\({\psi }_{\mathrm{r}}^\mathrm{min}\) :

Lower limit of rotor flux linkage (Wb)

\({\psi }_{\mathrm{r}}^\mathrm{max}\) :

Upper limit of rotor flux linkage (Wb)

\({\omega }_{\mathrm{e}}\) :

Electrical angular speed (rad/s)

\({\omega }_{\mathrm{m}}\) :

Mechanical angular speed (rad/s)

\({\omega }_{m\_\mathrm{ref}}\) :

Reference mechanical angular speed (rad/s)

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Acknowledgments

The authors would like to thank Natural Science Foundation of Liaoning Province, China, under Contract No. 2014025006; Education Department General Project of Liaoning Province, China, under Contract No. L2014209; Fundamental Research Funds for the Central Universities under Contract No. 3132016011 for financially supporting this research.

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  1. Marine Engineering College, Dalian Maritime University, Dalian, 116026, Liaoning, People’s Republic of China

    Chuan Wang, Yancheng Liu, Xiaoling Liang, Haohao Guo, Yang Chen & Youtao Zhao

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  1. Chuan Wang
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  2. Yancheng Liu
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  3. Xiaoling Liang
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Correspondence to Chuan Wang.

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Wang, C., Liu, Y., Liang, X. et al. Self-adaptive differential evolution algorithm with hybrid mutation operator for parameters identification of PMSM. Soft Comput 22, 1263–1285 (2018). https://doi.org/10.1007/s00500-016-2413-6

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