# Synchronous Machine Winding Modeling Method Based on Broadband Characteristics
## 1 Introduction  
A power system's safe operation determines whether human activities are carried out normally, so the reliability of a power system is a very relevant issue for people today [1, 2, 3]. At the heart of the power industry's energy supply are large-scale synchronous machines, of which regular operation determines whether a power system is adequately supplied with energy [4, 5]. As a critical component of a synchronous machine, winding may cause defects, such as winding turn-to-turn faults and grounding short-circuits during synchronous machine operation [6]. With the continuous development of battery energy storage technology and increasingly severe environmental pollution problems, which have caused the constant increase in fuel vehicle emissions restrictions, it is bound to be the case that electric vehicles will replace traditional fuel vehicles [7, 8]. The electromagnetic interference of a machine drive system is an essential factor affecting the operation of the machine [9]. Before starting research on the above-mentioned machine problems, modeling the equivalent broadband circuit of the winding is the fundamental base of this study. At present, there are three broadly applicable methods for winding modeling: (1) Using the resonant unit of a black box model to simulate the information of each resonant point, and then cascade each resonant unit to construct a circuit model [9, 10, 11]; (2) a model is established using the physical properties of a machine, such as magnetic flux leakage, copper consumption, leakage current, etc. [12, 13, 14]; and (3) a whole machine winding's physicalstructure is analyzed using finite element method, and then the winding is modeled using the analysis results [15]. For the first method, a fast-modeling method of the equivalent circuit of machine winding is proposed in References [9; 10; 11]. The method aims to measure the amplitude-frequency characteristics of the end impedance of machine winding, determine the resonance points on the amplitude-frequency characteristic curve, and each resonance point uses an \(R\), \(L\), \(C\) resonance unit as the equivalent circuit model. Finally, a topology structure diagram of a wide-band equivalent circuit of the machine is constructed. However, the machine winding model constructed using this method has no actual physical meaning, and the frequency band is low (1 Hz-1 MHz). In the second method [12; 13], the physical meaning of the winding is firstly analyzed, and the fundamental circuit components that can represent the single-unit circuit are obtained. Then, the number of circuit units and the single-phase multi-unit circuit topology are obtained by analyzing the structure of the actual synchronous machine. Finally, the parameters of each fundamental circuit component are identified using the measured characteristics curve. However, the circuit parameters of the multi-stage unit constructed using this method are equal and cannot reflect the differences in winding in the winding process, and the interference of other phases cannot be prevented when measuring the broadband characteristic curve of single-phase winding; thus, the coincidence degree of its broadband equivalent characteristic curve is low. The literature [14] provides a method of modeling by indirectly measuring the characteristics of a port and uses the single-phase high-frequency lumped parameter model to build an equivalent model of the machine winding. Although this method uses common mode and differential mode measurement methods to prevent the interference of other phases to a certain extent when only measuring single-phase winding, this method uses an engineering exploratory calculation method to obtain parameters, which has inevitable human subjectivity and a low accuracy. In the third method [15], starting from the internal geometric structures of the synchronous machine, two-dimensional and three-dimensional solid modeling of the machine is carried out in actual scale in the electromagnetic finite element analysis software.