## 5 Case Analysis and Results  
For a theoretical illustration, suppose that a power supply station area is a three-phase, four-wire system with a balanced load of 100 kW and a power factor of 0.85 (lag). In addition, phase \(B\) has a single-phase pure resistance load of 10 kW. The grid voltage is sinusoidal and symmetrical, and its phase voltage \(U\) is 220 V. The program is written in MATLAB to optimize the compensation according to the above, and the effectiveness and feasibility of the reactive power compensation optimization strategy under the CPC theory are verified.  
According to the above-known conditions, the three-phase load current RMS values can be obtained, and the admittance (conductance and susceptance) value of each phase can be obtained according to (4). The results are shown in Table 1.  
The amplitude of the physical component of the current is \(\sqrt{6}/3\) times the three-phase current RMS values. The amplitudes of active current component \(I_{a\max}\), inductive reactive current component \(I_{r\max}\), negative-sequence reactive current component \(I_{n\max}\), and zero-sequence reactive current component \(I_{z\max}\) are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Load Current RMS Value (A)** & **Conductance (S)** \\ \hline Phase \(A\) & 151.51 & 0.5854 \\ Phase \(B\) & 191.65 & 0.7920 \\ Phase \(C\) & 151.51 & 0.5854 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The three-phase load current RMS values and the admittance value of each phase.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Current Component** & **Three-Phase RMS Value (A)** \\ \hline \(\|i_{i}\|\) & 249.3 \\ \(\|i_{r}\|\) & 138.2 \\ \(\|i_{u}\|\) & 26.24 \\ \(\|i_{z}\|\) & 26.24 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Three-phase RMS values of different current components.  
Based on these calculations, the peak current of the compensation device needs to reach 120.7 A to achieve full compensation. The power supply-side waveforms of phase \(A\) current \(i_{A}\), phase \(B\) current \(i_{B}\), phase \(C\) current \(i_{C}\), and phase \(A\) voltage \(u_{A}\) before compensation are shown in Figure 3, and the sum of squares of the amplitudes of all reactive current components is 13,658 A\({}^{2}\).  
As long as the peak current of the compensation device can reach the peak current that needs to be completely compensated for, complete compensation can be achieved. Suppose that the peak current compensated for by the compensation device is 100 A, and incomplete compensation is performed under this constraint condition. When other power theories are adopted under this condition, if the reference compensation current cannot be effectively constrained, the current flowing through the compensation device will exceed the limit current of the compensation device, which will cause the device to be cut off or even damaged. Therefore, in order to continue to use the compensation device, through the previous description, based on CPC theory, the reactive current compensation scheme that can minimize the loss can be selected from different compensation schemes to improve the power quality and different optimization compensation objectives can be selectively achieved.