# Synchronous Machine Winding Modeling Method Based on Broadband Characteristics
## 3 Experimental Verification  
The impedance characteristic curve of a 5-kW, three-phase, salient pole synchronous generator machine winding was measured by using a KESIGHT impedance analyzer (model E4990A) and the sweep frequency range was 20 Hz-120 MHz. The connection diagram is shown in Figure 5. The common mode and the differential mode measurements can prevent the influence of other phases in a single-phase measurement, and it can contain more characteristic curve information, which is closer to the actual machine working characteristic curve than single-phase measurements [9; 14; 16; 17; 18]. Because there are too many parameters to search, to avoid falling into the local optimal solution, some exploratory calculations need to be carried out before the parameter identification, this limits the upper and lower limits of the parameters to be identified to a certain range, and then the parameter search is carried out, thus the probability of the optimal value will be significantly improved. In order to highlight the superiority and adaptability of the proposed method, this paper only limits the lower limit of all parameters to be greater than 0 and then brings the result of the Equation (10) into the Equation (11) to construct the fitness function. The change in the fitness function is shown in Figure 6. Figure 6 shows the fitness Equation (11) trend between the impedance characteristic curve formed by the optimal solution, corresponding to each iteration, and the actual measured value during the iteration process. The smaller the fitness function value is, the closer the impedance characteristic curve simulated by the optimal solution is to the measured curve [19]. According to Figure 6, it can be seen that in the initial stage of a PSO search, the fitness of PSO is sharply reduced, which indicates that the impedance value calculated by the parameters searched  
Figure 4: Flow chart of particle swarm optimization. by the algorithm at each frequency point is very close to the value of the measured curve at each frequency point. However, in the later stage of the algorithm, there is no change in fitness, which indicates that the local change in the parameters identified in the later stage of the algorithm under the previous search results cannot significantly affect the change in the fitness value. This phenomenon also indicates that the search results of the algorithm are close to the optimal solution. To a certain extent, it shows that PSO is indeed suitable for multi-parameters identification problems and can achieve an optimal solution close to that of the actual measurement curve in a small number of iterations. Figure 5: Common mode and differential mode impedance measurement wiring diagram of synchronous machine: (**a**) common mode impedance measurement wiring; (**b**) differential mode impedance measurement wiring; and (**c**) measurement site map. Table 1 shows the results of parameter identification. The common mode and differential mode impedance curves of the machine are simulated using the identified circuit parameters and are then compared with the measured common mode and differential mode impedance curves, as shown in Figure 7. The results show that the trend of the identification results is the same as the measured results in the range of 20 Hz-30 MHz, and the curves in the low and medium frequency bands are in good agreement. However, there may be some errors between the identification results and the measured values in the high-frequency band due to the existence of measurement noise and the inherent defects of the single-phase parameter model. However, the model still has specific application scenarios in engineering.