# Analysis of Permanent Magnet Motors in High Frequency--A Review
## 1 Introduction  
Typically, an electrical drive consists of a power source, an inverter that applies the desired voltage and frequency to the electrical machine, usually with Pulse Width Modulation (PWM) technique and the electrical motor, as shown in Figure 1. The straight arrows indicate the radiated noise caused by the switching circuits of the converter. Figure 1: Radiated and Conducted Electromagnetic Interference (EMI) in an electric drive. The dashed line represents the differential-mode EMI, which is going through one phase and returns across the other phases to the DC bus of the power source. Finally, the dotted line is the common-mode EMI, which goes across the common ground, connecting all elements to the disturbance [1]. Even if PWM technique is the most used control technique, its pulses generate a Common-mode voltage (CMV) in the output connection to the motor causing diverse problems such as leakage current, shaft voltage and bearing currents. The rapid voltage changes (high \(du/dt\)) also deteriorate the winding insulation and can cause protection failures in the case of short-circuit or contact defects [2; 3; 4]. Moreover, the generated EMI can affect the power source grid and the elements connected to it, for instance, sensors and safety systems in electric cars [5]. Specifically, bearings are affected by the CMV variations, as leakage currents flow through them [6; 7]. Those currents damage the bearings, and together with the winding insulation damage due to voltage stress, the reliability and lifetime of the complete electric drive are decreased. Some solutions are proposed to mitigate this EMI in electric drives. Different inverter typologies and modulation algorithms are proposed to reduce CM voltage [1; 6; 8]. Filters and other types of add-ons, such as shields or insulation are also widely used to avoid EMI flowing to the power grid as shown in [6; 9; 10; 11], but they increase the cost of the drive, as well as the volume and the weight as they are bulky and heavy. Hence, those factors can reduce considerably the competitiveness of the final product on the market, for example, in the electric car. Thus, to reduce the development cost of the product, an EMI strategy-based design should be added early in the product development cycle to reduce costs and achieve the best solution. Consequently, understanding and predicting EMI noise using high-frequency models during the design stage is essential to manage EMI problems. According to the literature, the most extended modeling techniques for representing the behavior of electrical machines in high-frequency are based on electrical equivalent circuits or Lumped Parameter Models (LPM). These models consist of electrical circuits that comprise several resistances, inductances, and capacitances. The values of this electrical parameters can be obtained applying different procedures. For instance, by experimental measurements [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36], by analytical calculations considering the main design parameters [11; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50], by Finite Element Method (FEM) [28; 39; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70] or even by hybrid methods [71; 72; 73]. The High-Frequency LPM models are developed for many purposes in the literature. For example, to analyze the influence of the winding placement and the winding connection on the bearing currents [32; 57], to analyze the common-mode currents [73] or to analyze the over-voltages at motor terminals due to modulated supplying voltages [61]. Although all LPM approaches share the same basis, there are many diversified proposals for accounting for different high-frequency phenomena. In addition, as aforementioned, the calculation of the LPM parameters can be faced in different manners.