# Zero-Voltage Ride-Through Capability of Single-Phase Grid-Connected Photovoltaic Systems
## 4 Control Strategy in Zero-Voltage Ride-Through Operation  
Once the grid phase-to-ground fault is detected by the grid synchronization, the photovoltaic (PV) system should switch to the grid fault operational mode with reactive power injection to support  
Figure 6: Performance comparison of the selected PLLs under a grid voltage fault with a 0.6 p.u. voltage drop: (**a**) grid voltage; (**b**) PLL estimated voltage amplitude output; (**c**) PLL estimated frequency output. Figure 7: Performance comparison of the selected PLLs under a voltage sag depth of 100% (i.e., zero-voltage fault): (**a**) grid voltage; (**b**) PLL estimated voltage amplitude output; (**c**) PLL estimated frequency output. the grid recovery. In different countries, to fulfill various local conditions under national realities, the suitable grid code has been proposed [15; 16; 17]. Figure 8 exemplifies the voltage profiles for the possible fault condition in some countries, where the PV systems should operate under the specific condition when the grid voltage is above the curves [15; 16; 17]. According to the requirements in Figure 8, it is clear that different from the anti-islanding protection, the ZVRT requires that in a short-time interval (e.g., 150 ms) even with a grid voltage amplitude of 0 V in Germany and China [15; 16], the system should remain connected. Thus, in order to support the grid recovery, the controller should provide additional functionality to adjust the current reference for reactive power injection. The reactive current injection profile in China is presented in Figure 9[16]. As it is shown in Figure 9, the required reactive current \(I_{q}\) to support the grid voltage in the Chinese grid regulations is defined. The characteristic in the grid code is the injected reactive current increased with the depth of the grid voltage sag (i.e., the fault severity). At certain critical points, it should inject one p.u. of the reactive current. The required reactive current \(I_{q}\) in the Chinese grid code can be given as [16]  
\[I_{q}=\left\{ \begin{array}{ll}0&(\Delta U\leq 0.1U_{N})\\ 1.5I_{N}(\frac{\Delta U}{U_{N}}-0.1)&(0.1U_{N}\leq\Delta U\leq 0.8U_{N})\\ 1.05I_{N}&(\Delta U\geq 0.8U_{N})\\ \end{array} \right. \tag{15}\]  
where \(U_{N}\) and \(I_{N}\) are the nominal grid voltage and the nominal inverter current, \(\Delta U\) is the depth of grid voltage sag, and \(I_{q}\) is the required injected reactive current when the fault occurs. Figure 8: Low-voltage (and zero-voltage) ride-through requirements for grid-connected systems in different countries [15; 16; 17]. Figure 9: Reactive current injection requirements under low-voltage ride-through/zero-voltage ride-through (LVRT/ZVRT) operations in China [16]. As in the above discussions, it is known that the current reference should be properly generated under grid faults. Hence, the conventional dual-loop control structure for single-phase PV systems can be applied, where the current references can be directly calculated. The control diagram of the single-phase dual-loop control structure is shown in Figure 10. Based on the single-phase instantaneous power control theory, the current reference of the inner control loop can be obtained through the active power and reactive power references (i.e., \(P^{*}\) and \(Q^{*}\)), as shown in Figure 10. As aforementioned, the reactive current injection is dependent on the voltage sag depth. It is calculated considering the amplitude detection of the PLL system. According to the single-phase \(PQ\) theory [13; 14; 31; 34], the active and reactive power can be controlled independently in the outer power control loop, and then the grid current references are generated, being a dual-loop control structure [30]. In order to regulate the power reference, an OSG system is needed to generate the quadrature components, \(v_{\alpha}\) and \(v_{\beta}\). The grid current references are given by  
\[\left[ \begin{array}{c}{i_{\alpha}}^{*}\\ {i_{\beta}}^{*}\end{array} \right]=\frac{2}{v_{g\alpha}^{2}+v_{g\beta}^{2}} \left[