Improved ES Model for Core Loss Calculation of Brushless Doubly Fed Machine with Hybrid Rotor.

Brushless doubly fed machine (BDFM), is a new type of machine with special structure, shows promising features for the field of variable frequency speed regulation and wind power generation due to its inherent characteristics, which has the advantages of reliable operation, adjustable power factor, lower operation and maintenance costs as well as requiring a smaller capacity converter [1], [2]. Since core loss has an important effect on efficiency and temperature distribution, it is vital to accurately calculate such component in an optimal design procedure. Furthermore, rotor core loss is also a significant factor which can affect the performance characteristics of BDFM due to the complex magnetic field distribution and relatively high value of slip. Specifically, a novel hybrid rotor structure which is combined with magnetic barrier and assisted cage has better coupling ability than the commonly used rotor structures such as cage rotor and reluctance rotor is presented but it also increases the difficulty of core loss calculation. E&S model is a vector magnetic hysteresis property model [3], [4], in which H (magnetic field intensity) is dependent not only on B (magnetic flux density) but also on time derivative of B. Increase of core loss when the phase difference between B and H occurs, is well expressed in this method, while the conventional analysis was not able to consider the phase difference between B and H. Furthermore, the total core loss including both alternating and rotational losses can be directly calculated from the fundamental terms of obtained $B_{x}$, $B_{y}$, $H_{x}$ and $H_{y}$ without other fitting data, which can improve the core loss computation accuracy of BDFM with hybrid rotor in contrast with conventional core models. In this paper, an improved E&S model based on a 2-D rotational magnetic property analysis for core loss of BDFM with hybrid rotor is proposed by considering the high-order harmonic magnetic field. The finite element analysis model of BDFM with hybrid rotor is established. The core loss calculation results are compared with the simulation results to verify the correctness and feasibility of the proposed E&S model. Fig. 1 shows the finite element model, hybrid rotor of prototype and special points distribution diagram of BDFM with hybrid rotor. As shown in Fig. 1 (a)-(b), the cage bars are added on the non-magnetic layer of the radial magnetic barrier rotor, and the cage bars are respectively divided into concentric cage bar and common cage bar. There are two kinds of rotating magnetic fields with different poles and frequencies in the air-gap of BDFM, which renders that the air-gap magnetic density harmonic contents are rich and the magnetic properties of each part of core are different. According to the basic principle, structure characteristics and magnetic field distribution of BDFM with hybrid rotor, some special points of stator and rotor are analyzed and calculated. The relationship between B vector and H vector, and the relationship between the waveform of $B_{x}$, $B_{y}$ and the waveform of $H_{x}$, $H_{y}$, obtained by the combination of the improved E&S model and finite element analysis, is shown in Fig. 1 (c), which is seen that the phase between B and H is different. The improved E&S model can consider higher order harmonic magnetic field than the conventional E&S model. As shown in Fig. 2 (a), the stator and rotor core loss calculation process of BDFM with hybrid rotor is described by the flow diagram. The datum of $B_{x}$, $B_{y}$, $H_{x}$, $H_{y}$ are obtained by the combination of the improved E&S model and finite element method, and all order harmonic of $B_{x}$, $B_{y}$, $H_{x}$, $H_{y}$ are computed by fourier series expansion. Therefore, the total core loss of BDFM with hybrid rotor can be calculated by the formula in the flow diagram, where, $\rho$ is the magnetic material density, T is the period, $m$ is the amount of the special points, $n$ is the harmonic order, and $M_{i}$ is the mass. In addition, in order to verify the accuracy of the core loss calculation, the 2-D finite element model of BDFM with hybrid rotor is established, and the simulation results are shown in Fig. 2 (b). The validity and feasibility of the improved E&S model is verified by comparing with the simulation results. In addition, the full paper will present the detailed calculation procedure and analysis.