# Effect of Harmonics on Ferroresonance in Low Voltage Power Factor Correction System--A Case Study
## 4 Experimental Results and Discussion
### Experimental Results for C2  
Case C2 represents an operating point where the conditions for ferroresonance are satisfied, and ferroresonance occurs when the capacitor stage is switched on. The current and voltage waveforms, electrical quantities, and harmonic distortions of the studied system are analyzed with and without ferroresonance. The experimental results for C2 are given as follows. The steady-state data when the capacitor stage is switched on and off are given in Table 2. Before the capacitor stage is switched on, the transformer voltage and current harmonic distortions are high, as shown in Figure 13. After the capacitor stage is switched on, the voltage and current harmonic distortions are increased due to ferroresonance, as shown in Figure 14. In the presence of ferroresonance, the voltage and current waveforms are highly distorted. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**State** & \(P_{T1}\) [kW] & \(Q_{T1}\) [kvar] & \(cosp_{T1}\) & \(I_{T1}\) [A] & \(THD_{L7,T1}\) [\%] & \(THD_{u}\) [\%] \\ \hline Cap. stage off & 532.4 & 115.1 & 0.98 & 811.3 & 20.2 & 6.9 \\ Cap. stage on & 534.3 & 79.1 & 0.99 & 808.2 & 24.7 & 8.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: C2: Electrical quantities on the low-voltage side of the transformer station. Figure 11: C1—Harmonic spectrum of reactor voltage, capacitor voltage and stage current in normal steady state. Figure 12: C1—Medium voltage feeder voltage and current after switching on the capacitor stage. Before the ferroresonance was triggered, the high harmonic content of the transformer current with significant values of the 5 th, 7 th, and 11 th harmonics was present. In the presence of the ferroresonance, other even and odd harmonics occurred, and the current of the 5 th harmonic changed direction. Figure 15 shows the vector diagram of the 5 th harmonic of the secondary voltage and secondary current of transformer T1 before and after the capacitor stage was switched on. Before switching on the stage, the current of the 5 th harmonic of the transformer was \(I_{T1,5}=151.3\) A and flowed into the medium voltage grid. After switching on the stage, the current of the 5 th harmonic of the transformer was \(I_{T1,5}=184.1\) A and flowed from the medium voltage grid to the low voltage side of the transformer station. Figure 14: C2—Secondary voltage and current of transformer T1 after switching on the capacitor stage. Figure 13: C2—Secondary voltage and current of transformer T1 before switching on the capacitor stage. The voltage waveforms of transformer T1, reactor, and capacitor, and the current of the capacitor stage when the stage is switched on are shown in Figure 16. When the capacitor stage is switched on, the reactor goes into saturation, and the maximum values of the reactor current reach values that are about 15 times the nominal value. Unlike in C1, the reactor and capacitor remain in ferroresonance after the capacitor stage is switched on, supported by the grid. In this condition, the capacitor and detuned reactor are overloaded, resulting in high audible noise from the reactor and overheating of both components. Operation with ferroresonance is dangerous for the industrial equipment. RMS value of detuned reactor current is \(I_{S}=280.4\) A, the maximum peak value of reactor current is \(I_{S,max}=1167.5\) A, and the current THD is 387.3%. The RMS value of the reactor voltage is \(U_{L}=167.0\) V, and the maximum peak value of the reactor voltage is \(U_{L,max}=344.0\) V.  
Figure 16: C2—Transformer secondary voltage, capacitor voltage, reactor voltage and capacitor stage current when the stage is switched on. Figure 15: C2—Vector diagram of 5 th harmonic of the secondary voltage and current of transformer T1 (**a**) before and (**b**) after switching on the capacitor stage.