# Leakage Detection Method of Coal Mine Power Supply System Based on 3 AC
## 4 Simulation Verification  
Because the theoretical analysis of the previous section is in the ideal case, the calculated \(\hat{I}_{\text{C0}}\) does not consider the actual working conditions. This section will simulate the actual working conditions, collect the current \(\hat{I}_{\text{C0}}\) generated by the additional three-phase asymmetric capacitor, and then calculate the insulation resistance \(R_{d}\). Continuing to use the power supply system simulation model using the 3 AC method, the simulation operation needs to record seven fault conditions, and six sets of insulation resistance data under each condition. The insulation drops to 1 k\(\Omega\), 2 k\(\Omega\), 10 k\(\Omega\), 20 k\(\Omega\), 24 k\(\Omega\), and 100 k\(\Omega\). These six cases are closer to the 1140 V insulation resistance setting value of 20 k\(\Omega\), so it is more reference. By writing Matlab script code, the system experiences the above seven kinds of leakage faults in turn. When each fault occurs, six different sets of insulation resistance data are substituted into the model respectively, which means that the whole simulation process will run 42 times. In this way, we can analyze the behavior of the system under different conditions in detail. Taking phase A leakage as an example, simulation research is carried out. The simulation results are shown in the figure. In this diagram, the X axis represents the real part of the calculated insulation resistance, while the Y axis represents the imaginary part of the insulation resistance. In order to clearly distinguish different leakage faults, a variety of colors are used to represent different resistance values. In addition, each fault type is identified by a unique icon, which makes the results more intuitive and easier to understand. The simulation results of the phase A leakage fault are shown in the following figure. In view of the fact that the real and imaginary parts of the insulation resistance in the complex form cannot be negative, all measurement results with real or imaginary parts less than zero should be excluded in the analysis process. As shown in Figure 7, when the insulation performance is reduced to 1 k\(\Omega\) (corresponding to the blue icon in the figure), the imaginary part of the complex resistance calculated by the phase A leakage model is closest to the zero value.According to this, it can be judged that the real part represents the actual insulation resistance value, which is 1008 \(\Omega\), and the error is 0.8%. Similarly, when the insulation level is reduced to 24 k\(\Omega\) (corresponding to the orange icon in the figure), the imaginary part of the complex resistance obtained by the phase A leakage model is also closest to zero, thus confirming that the real part is the actual insulation resistance value, that is, 25,182 \(\Omega\), and the corresponding calculation error is 4.9%. Taking the 1 k\(\Omega\) leakage fault as an example, the calculation results of insulation resistance under different types of leakage faults are simulated. The results are shown in the following table. Formula (1) to Formula (7) sequentially represent the following: A phase, B phase, C phase, AB phase, BC phase, AC phase, and ABC phase leakage. After observing the data in the table and excluding the simulation results that do not meet the conditions, we adhered to the following rules: Among the calculation results of various hypothetical leakage conditions, we noted which hypothesis had the smallest ratio of the imaginary part to the real part, and confirmed that the hypothesis was valid. As shown in Table 3, for an A-phase leakage, the minimum imaginary part is calculated using Formula (1), and its real part matches the preset leakage resistance. As shown in Table 4, for a B-phase leakage, the minimum imaginary part is calculated using Formula (2), and