# Zero-Voltage Ride-Through Capability of Single-Phase Grid-Connected Photovoltaic Systems
## 4 Control Strategy in Zero-Voltage Ride-Through Operation
\begin{array}{cc}{v_{g\alpha}}&{v_{g\beta}}\\ {v_{g\beta}}&-{v_{g\alpha}}\end{array} \right]\left[ \begin{array}{c}P^{*}\\ Q^{*}\end{array} \right] \tag{16}\]  
where \({i_{\alpha}}^{*}\) is the grid current reference \({i_{\beta}}^{*}\), \({v_{g\alpha}}\), \({v_{g\beta}}\), \({i_{g\alpha}}\), and \({i_{g\beta}}\) are the orthogonal components in the \(\alpha\beta\)-frame, \(P^{*}\) and \(Q^{*}\) are the active power and reactive power references, respectively. For the inner current control loop, a hybrid controller including a proportional resonant (\(PR\)) and a harmonic compensator (\(HC\)) is selected considering both control complexity and power quality [6; 13; 14; 30]. The \(PR\) controller overcomes the most drawbacks of the classical \(PI\) controller, which is steady-state error [30]. In addition, the \(HC\) controller provides a good capability of harmonics rejection. As a consequence, the hybrid PR with HC controller shows a better performance. The current controller relating PR controller \(G_{c}\)(s) and HC controller \(G_{h}\)(s) can be expressed as  
\[G_{\text{PR}+\text{HC}}=G_{c}+G_{\text{HC}}=\underbrace{k_{p}+\frac{k_{i}s}{s^ {2}+\omega_{0}^{2}}}_{\text{PR}}+\underbrace{\sum_{h=3,5,7}\frac{k_{i\beta}s}{ s^{2}+\left(h\omega_{2}\right)^{2}}}_{\text{HC}} \tag{17}\]  
where \(k_{p}\) is the proportional gain, \(k_{i}\) and \(k_{i\beta}\) are the resonant and harmonic compensator gains, \(h\) is the harmonic order, and \(\omega_{0}\) is the fundamental frequency. During ZVRT operation, the system loses all the grid information. The PV system should switch to the ZVRT operation mode from the normal condition or the LVRT operation mode, when the grid voltage sags to zero. The injection current from the grid-connected inverter should totally be reactive current in order to support the grid recovery. As the requirement of the grid code, the system must achieve the voltage fault detection, operation mode switch, and reactive current injection as soon as possible. The fast dynamics and accuracy of the grid fault detection are then essential. Figure 10: Control diagram of the single-phase PV system based on the single-phase instantaneous active and reactive powers (PQ) theory. However, in the ZVRT operation, the estimated grid voltage is in an undefined and abnormal condition caused by no grid information. As discussed previously, the steady-state error of the PLL estimated frequency output is not zero in the case of ZVRT faults. Therefore, the common implementation of PLL methods does not provide the ride-through ability. A feasible solution is to adjust the parameters of the LF (i.e., \(k_{p}\), \(k_{i}\)) to reduce the steady-state error. However, the dynamics will be sacrificed during fault ride-through, making it not very practical. Hence, a novel approach is proposed. Basically, the idea is that the detected grid voltage controls a switch to change the operational mode of the PLL, as shown in Figure 11. According to the Chinese grid code [16], the system should inject only reactive current in the case of voltage faults (below 0.8 p.u.). Therefore, the voltage sag of 0.8 p.u. can be set as the threshold to change the PLL operational mode. More specifically, when the grid voltage level is above 0.8 p.u., the PLL continuously estimates the grid phase angle, frequency, and amplitude. Once the grid voltage sags (i.e., below 0.8 p.u. ), a fixed frequency (i.e., being the nominal grid frequency) is imposed to the VCO, and then the phase angle for the control system is generated, as shown in Figure 11.