Parameter identification of Preisach model based on the conjugate gradient method and velocity-controlled particle swarm optimization

Abstract

I. INTRODUCTIONFerromagnetic materials have complex nonlinear hysteresis characteristics, which play a decisive role in simulating electrical equipment's magnetic properties, such as the power loss and the magnetic remanence of the core in transformers and motors[1]. Therefore, the accurate and efficient hysteresis model is fundamental to improving the power equipment's operational efficiency. As a fast and precise hysteresis model, the Preisach model is widely used in analyzing the magnetic properties of the electromagnetic device coupled with the FEM method. However, some problems remain to exist in the current Preisach model parameter identification methods, such as the convergence speed and the accuracy need to be further improved[2,3]. To develop a more efficient parameter identification method of the Preisach model, a hybrid algorithm combining conjugate gradient method (CGM) and velocity-controlled particle swarm optimization (VCPSO) algorithm is proposed in this paper: Firstly, a one-dimensional magnetic property test system is built to measure the hysteresis loop data of B30P150 steel sheet under quasi-static conditions. Secondly, the parameters of the Preisach model with closed-form Everett function are identified based on the proposed hybrid optimizing algorithm. Finally, in the full paper, the proposed method's accuracy is discussed by comparing the convergence speed and calculation accuracy of the proposed hybrid algorithm with other single intelligent algorithms.II. THE IMPLEMENT AND IDENTIFICATION OF PREISACH MODELA. The Preisach model based on the closed-form Everett functionThe traditional Preisach model is implemented by the double integral of the distribution function in the Preisach plane, which is time-consuming and inefficient. To overcome the complex parameters identification process of the traditional Preisach model, the distribution function is simplified to the product of two single-valued functions, and a numerical Preisach model based on the closed-form Everett function is established. The improved model only needs a series of basic operations and a few parameters to be identified, which implement efficiency is much improved.B. Parameters identification of the Preisach model by combing the CGM and VCPSO algorithmA hybrid intelligent algorithm based on the conjugate gradient method (CGM) and a velocity-controlled particle swarm optimization (VCPSO) algorithm is proposed to overcome the low convergence speed and easily fall into a locally optimal solution. The identification process of a hybrid algorithm is shown in Fig 1. Firstly, according to the fast optimization of the VCPSO algorithm, finding the optimal solution range of parameters. Secondly, the searching range of VCPSO is taken as the initial parameter of the conjugate gradient method. Then the optimal solution is determined by local search. Finally, the optimal parameters are obtained by CGM. The measured and simulated hysteresis loop are compared after the identification process. The efficiency of the hybrid algorithm with other single optimal identification algorithms will be discussed in the full paper.III. RESULT AND DISCUSSIONThe simulated and measured hysteresis loops of the B30P150 silicon steel sheet are shown in Fig 2. It can be found that the model parameters identification results can well simulate the hysteresis loop of the B30P150 silicon steel sheet. The error is due to the approximate substitution of the Everett function, and increasing the number of relevant terms of the Everett function can improve the Model accuracy. What’s more, considering the reversible and irreversible magnetization, the simulation accuracy at the model's turning point can also be improved.IV. CONCLUSIONIn this paper, a hybrid optimization algorithm combining a velocity-controlled particle swarm optimization algorithm and the conjugate gradient method is proposed to identify the parameters of the Preisach model. The hybrid algorithm is an effective means for parameter identification of the Preisach model and contributes to the design and upgrading of electrical equipment. **