# A Novel Method for Modeling the Electromagnetic Characteristics of Switched Reluctance Motors
## 1 Introduction  
The switched reluctance motor (SRM) has received great attention in many fields due to its simple and rugged structure with high efficiency, strong reliability and low cost [1; 2; 3; 4]. Fast and accurate acquisition of electromagnetic characteristics is very important for advanced control and performance assessment of SRM. The core of obtaining the electromagnetic characteristics of SRM is to accurately describe the relationship among the flux-linkage \(\psi\), rotor position \(\theta\) and current \(i\)[5; 6]. However, it is difficult to depict the flux-linkage characteristic of the SRM accurately because of the double saliency structure and high nonlinearity of magnetic material [7]. Hence, in order to build an accurate model for the flux-linkage characteristic of SRM, many research studies have been carried out in the past few decades. Most of the existing flux-linkage models of SRM are developed by look-up tables [8], intelligent methods [9; 10; 11; 12; 13; 14] and analytical methods [15; 16; 17; 18; 19; 20]. Generally, look-up tables are based on interpolation and extrapolation. In [8], a 2D bicubic spline interpolation is proposed to express the nonlinear electromagnetic characteristics of SRM. However, the accuracy of the look-up tabletechnique depends largely on the number of sample data. The multilayer feed forward neural network is widely applied in the modeling and control field of SRM because of its nonlinear mapping and self-learning ability. In [9], an artificial neural network is used for the modeling of the magnetic nonlinearity of the SRM. In [10], the nonlinear inductance and resistance of the phase winding of SRM are identified from operating data by a two-layer recurrent neural network. In [11], a dynamic simulation model of SRM is established based on the multi-output least square support vector machine (LSSVM), which can enhance the generalization abilities and reduce the cascade error. In [12], the electromagnetic characteristics of SRM under the stator winding fault are estimated based on a four-layer back-propagation (BP) artificial neural network. In [13], a radial basis function (RBF) neural network-based adaptive fuzzy system is developed to predict the dynamic performances of SRM. In [14], the comparison studies among fuzzy logic, neuro-fuzzy and neural network techniques for the modeling of SRM were carried out, and the results show that these methods have good modeling accuracy. The final modeling accuracy of these intelligent methods is relatively high, but on the other hand, intelligent methods require a large number of sample data and considerable time to train the network. Alternatively, the analytical methods can partly overcome these shortcomings. In [15], a geometry-based analytical flux-linkage model is developed, which is suitable for real-time implementation. In [16], based on the transformation from the time to the position domain, a novel modeling method is developed to determine the best current waveforms for SRM. In [17], an improved analytical method is proposed to calculate the natural frequencies of the SRM stator. A main advantage is that this method considers the effect of the stiffness and mass of the stator poles and windings on natural frequencies. In [18], an invertible flux-linkage model for SRM is built based on the Fourier series. This model can achieve the desired accuracy by selecting the number of terms of the Fourier series expansion. Compared with intelligent methods, these methods do not need the sample data, but they require the detailed properties and geometric dimensions of materials, which are usually difficult to obtain. To solve this problem, some modeling methods based on small quantities of sampling data have been proposed in [19; 20]. In [19], a decoupled analytical flux model is proposed by a two-order Fourier series expansion. The key feature of the model is that only 21 sampling data are required. In [20], an improved flux-linkage model for SRM is developed by using a simplified Fourier series expansion.