# Synchronous Machine Winding Modeling Method Based on Broadband Characteristics
## 4 Contrast Experiment  
As mentioned above, finite element analysis of a winding structure is complex and it is challenging to achieve the desired effect; multi-unit circuits are not conducive to measuring the common mode and differential mode impedance [12; 13], so they are not compared here. Figure 8 shows a comparison of the impedance characteristics. Under the condition that the high frequency lumped parameter model is used as the single-phase winding model of synchronous machine, 2,3 represents the parameters identification based on the proposed method and engineering exploratory calculation method [14; 15]. The 1 represents the black box model as a result of the single-phase model parameter identification of synchronous machine winding [9; 10; 11].  
Mean absolute percentage error (MAPE) can be used to evaluate the quality of the model. Root mean square error (RMSE) is sensitive to the maximum or minimum error in a group of results and can also reflect the identified curve accuracy [27; 28]. With the same measured curve, the smaller the MAPE and RMSE are, the more accurate the identified curve. Therefore, this paper uses MAPE and RMSE to evaluate the accuracy of each identified curve, and the expression is as follows:  
\[E_{MAPE}=\frac{1}{n}\underset{i=1}{\overset{N}{\underset{i=1}{\sum}}}\frac{ \left|Z_{measure}-Z\right|}{Z_{measure}}\times 100\% \tag{12}\]  
\[E_{RMSE}=\sqrt{\underset{n}{\overset{N}{\underset{i=1}{\sum}}}\left(Z_{measure }-Z\right)^{2}} \tag{13}\]  
where \(n\) is the sampling number of the measurement curve, and \(Z_{measure}\) and \(Z\) are the measured value and the impedance simulation value under each method, respectively.  
Table 2 shows the MAPE and RMSE results under three methods. From Table 2, it can be seen that the proposed method's MAPE and RMSE values calculated between the simulated impedance characteristic curve (\(Z_{cm}\) and \(Z_{dm}\)) and the measured curve are the smallest compared with those of the other two methods. Therefore, it can be said that the proposed method is superior to the other two methods, and its accuracy is the highest.  
Figure 8: Comparison diagram of impedance characteristics: (**a**) comparison of common mode impedance characteristic curves; (**b**) comparison of differential mode impedance characteristic curves.  
**Author Contributions:** [PERSON] derived formulas, program verification and data analyses, wrote and revised manuscript; [PERSON] contributed data analysis, literature review, and grammar corrections; [PERSON] provided an experimental platform and ideas. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 51807166, the Natural Science Foundation of Chongqing, grant number cstc2019 cyj-msxmX0236, and the Venture and Innovation Support Program for Chongqing Overseas Returnees, grant number cx2019123.  
**Institutional Review Board Statement:** All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional.  
**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.  
**Data Availability Statement:** No data available.  
**Conflicts of Interest:** The authors declare no conflict of interest.