## 3 Proposed LVRT Control Strategy for Grid-Connected ESSs and Analysis of PCC Voltage Variation
### Analysis of PCC Voltage Variation  
When the ESS operates under the discharging condition, the active current is injected into the three-phase grid from the ESS. In this case, the PCC voltages are changed by the phase of the reactive current injected into the three-phase grid. Figure 8 shows the variations of the PCC voltage in the discharging condition of the ESS depending on the phase of the reactive current. \(V_{G}\) is the grid voltage, and \(I_{G}\) is the grid current flowing between the ESS and the three-phase grid. In this paper, when \(I_{G}\) is positive, it flows to the three-phase grid from the ESS. The \(d\)-axis refers to the reactive component, and the \(q\)-axis refers to the active component. \(V_{PCC}\) is the PCC voltage, which is the sum of \(V_{G}\) and the voltage drops (\(V_{RG}\) and \(V_{LC}\)) of the resistor-inductor of the three-phase grid. In Figure 8a, \(I_{G}\) includes only the active current, which means that the reactive current is zero. \(V_{PCC}\) is occurred by \(V_{G}\), \(V_{RG}\), and \(V_{LG}\), and it has a phase equal to that of \(I_{G}\). When the inductive or capacitive reactive current is injected into the three-phase grid, \(V_{PCC}\) is changed by the variation of the phases of \(V_{RG}\) and \(V_{LG}\), as shown in Figure 8b,c. In other words, \(V_{PCC}\) decreases because of the injection of the inductive reactive current, and it increases because of the injection of the capacitive reactive current. As a result, in the discharging condition of the ESS, the active current with the capacitive reactive current injected into the three-phase grid contributes to an increase of \(V_{PCC}\) and meets the LVRT requirement.  
When the ESS operates under the charging condition, contrary to the discharging condition, the active current flows to the ESS from the three-phase grid. \(V_{PCC}\) is also changed by the phase of the reactive current flowing to the ESS. The variations of \(V_{PCC}\) in the charging condition of the ESS depending on the phase of the reactive current is shown in Figure 9. In Figure 9a, \(I_{G}\) includes only the active current without the reactive current. It does not contribute to the increase of \(V_{PCC}\) because \(I_{G}\) has a negative direction. In Figure 9b,c, \(V_{PCC}\) is changed by the injection of the inductive and capacitive reactive currents, respectively. \(V_{PCC}\) decreases when the inductive reactive current is injected, and it increases when the capacitive reactive current is injected. Therefore, in the charging condition of the ESS, the active current with the capacitive reactive current contributes to the LVRT requirement.  
Figure 8: Variations of the point of common coupling (PCC) voltage in the discharging condition of the ESS depending on the phase of the reactive current. (**a**) Reactive current is zero; (**b**) Inductive reactive current is injected; (**c**) Capacitive reactive current is injected.  
Figure 9: Variations of the PCC voltage in the charging condition of the ESS depending on the phase of the reactive current. (**a**) Reactive current is zero; (**b**) Inductive reactive current is injected; (**c**) Capacitive reactive current is injected.  
When the grid voltage drops in the grid-connected ESS, the proposed LVRT control strategy is required to comply with the LVRT requirement. The proposed LVRT control strategy determines the injection quantity of the active and reactive currents, and the strategy depends on the voltage drop ratio of the three-phase grid. In addition, regardless of the operating condition of the ESS, such as the charging and discharging conditions, the injection of the capacitive reactive current contributes to the LVRT requirement because of the increase of \(V_{\mathrm{PCC}}\). The validity of the proposed LVRT control strategy is demonstrated and the variations of the PCC voltage of the grid-connected ESS are analyzed by simulation and experimental results.