Reluctance Network Model of Switched Reluctance Motor Considering Magnetic Hysteresis Behavior

Abstract

In recent years, it is strongly required to establish a practical calculation method for iron loss of electric machines including magnetic hysteresis behavior, in order to develop high-efficient electric machines. However, magnetic hysteresis is not considered in general-purpose numerical analysis programs due to a long calculation time.To overcome the above problem, this paper proposes a reluctance network analysis (RNA) [1]. The RNA expresses an analytical object by one reluctance network. All the reluctances can be determined by B-H curve of the material and dimensions. The RNA has some advantages such as a simple model, fast calculation, and easy coupling with external electric circuit and motion equation. The RNA has been applied to the calculation of characteristics of various electric machines including transformers and motors. In previous papers, a novel RNA model incorporating a play model [2], which is one of the phenomenological models of magnetic hysteresis behavior, was presented. So far, this method was applied to the analyses of a permanent magnet synchronous motor [3] and a variable inductor [4], and its calculation accuracy was proved by comparing the measured and calculated values. However, the voltage and current waveforms are almost sinusoidal in these devices. Therefore, in this paper, the versatility of this method is experimentally demonstrated by using a switched reluctance (SR) motor, which has stronger nonlinear magnetic properties and is excited by a square voltage waveform, as an object of discussion.In this paragraph, a deriving method for the RNA model of the SR motor incorporating the play model is described [5]. First, the analytical object is divided into multiple elements. To allow consideration of leakage flux flowing between the stator pole and yoke, and between the adjacent stator poles, surrounding space is also divided. In the core region, each reluctance is needed to be determined by considering magnetic hysteresis. Thus, the dc hysteresis is represented by the play model, which can express an arbitrary hysteresis loop by multiplying play hysterons with different widths by shape functions. Although the play model generally requires a large number of measured dc hysteresis loops with different maximum flux densities to derive the shape functions, the proposed method requires only one or two measured dc hysteresis loops because the Landau-Lifshitz-Gilbert (LLG) equation is used to calculate the dc hysteresis loops [6]. Fig. 1(a) shows the hysteresis loops calculated by the LLG equation. As shown in this figure, a large number of hysteresis loops which are used to derive the play model can be obtained without experiments. On the other hand, the classical and anomalous eddy current losses are denoted by the inductance and controlled-source, respectively. In addition, since an SR motor has a salient pole structure, the magnetic flux distribution around the stator and rotor pole tips change dynamically with rotation. Thus, the magnetic circuit around poles and the air gap is represented by variable reluctances depending on the rotor position angle as shown in Fig. 1(b), so that the local magnetic saturation and the fringing magnetic flux can be taken into consideration. Fig. 1(c) shows a schematic diagram of the proposed RNA model incorporating the play model. The controlled-sources at the stator poles are the MMFs generated from the winding current.Using the proposed RNA model, the characteristics of the SR motor are calculated when the excitation voltage is 9 V, the excitation starting angle is 0 deg., and the excitation width is 70 deg. Fig. 2(a) and (b) show the measured and calculated winding rms current density versus torque and torque versus rotational speed characteristics, respectively. As shown in these figures, the measured and calculated values are in good agreement. Next, Fig. 2(c) and (d) show the measured and calculated iron loss and efficiency characteristics, respectively. In the experiment, iron loss is measured by subtracting the sum of mechanical output and copper loss, and mechanical loss measured separately in advance, from electrical input. From these figures it is clear that the measured and calculated values are in good agreement. Furthermore, Fig. 2(e) indicates calculated hysteresis loops in certain divided elements of the RNA model. As shown in the figure, the magnetic hysteresis inside the core, which is generally difficult to measure and calculate, can be drawn by the proposed method. In the future, we plan to verify the validity of such local hysteresis loops in the experiment.This work was supported by Grant-in-Aid for JSPS Fellows (JP19J20572). **