## 4 Proposed LVRT Enhancement Strategies
### DC-Link (DCL) Voltage Control Scheme  
The proposed DCL control scheme is shown in Figure 4. During normal operating conditions, the incremental conductance (IC) MPPT method is applied to track the maximum power from the PV arrays. Under three-phase fault conditions, the inverter cannot inject the SPV system with the maximum power into the grid owing to the sudden voltage sag. The surplus energy causes a sharp  
Figure 3: E.ON Netz GmbH code: (**a**) low voltage ride-through (LVRT) waveform and (**b**) reactive current injection requirement. increase in the DCL voltage, which will damage the inverter module and the DCL capacitor. Hence, the \"control without MPPT\" controller is proposed during the fault period to reduce DCL over-voltage. The PV system should instantly change the \"control without MPPT\" operation mode when voltage sag appears in the PCC. Thus, a quick voltage-sag monitoring method is essential for FRT voltage control. In this study, the simple root-mean-square (RMS) detection method is adapted to identify the grid fault. The proposed method calculates the grid voltage RMS value of the phase-locked loop (PLL) by using Equation (9) to signal the control system that it should switch to operating under the fault-operation mode. \[\mathrm{v_{sag}}\ =\sqrt{\mathrm{v_{d}}^{2}+\mathrm{v_{q}}^{2}} \tag{9}\]  
where \(\mathrm{V_{sag}}\) is the voltage sag, \(\mathrm{V_{d}}\) is the d-axis component voltage, and \(\mathrm{V_{q}}\) is the q-axis component voltage. The \"control without MPPT\" controller is designed using the PI controller, with an anti-windup mechanism to avoid the saturation of the integral gain (\(\mathrm{K_{i}}\)). The output of the controller is the duty cycle (\(\mathrm{d_{2}}\)), which is calculated using Equation (10):  
\[\mathrm{d_{2}}=\biggr{(}\mathrm{K_{P}}+\mathrm{K_{i}}\frac{\mathrm{T_{s}}\ \mathrm{Z}}{\mathrm{Z}-1}\biggr{)}\ (\mathrm{V_{DCL\_ref}}-\mathrm{V_{DCL\_meas}}). \tag{10}\]  
where \(\mathrm{d_{2}}\) is the duty cycle, \(\mathrm{K_{P}}\) is the proportional gain, \(\mathrm{K_{i}}\) is the integral gain, \(\mathrm{T_{s}}\) is the sample time, \(\mathrm{V_{DCL\_ref}}\) is the reference DC voltage, and \(\mathrm{V_{DCL\_meas}}\) is the measured DC voltage. The modified integrator gain is:  
\[\mathrm{K_{modified}}=\mathrm{K_{i}}+\mathrm{K_{aw}}\ (\mathrm{d_{sat}}- \mathrm{d_{unsat}}) \tag{11}\]  
The saturated control signal is calculated as follows:  
\[\mathrm{d_{sat}}=\mathrm{min}(\mathrm{max}(\mathrm{d_{unsat}},\mathrm{d_{min} }),\ \mathrm{d_{max}}) \tag{12}\]  
where, \(K_{aw}\) is the anti-windup gain, \(\mathrm{d_{unsat}}\) is the unsaturated duty cycle, \(\mathrm{d_{min}}\) is the lower limit for the duty cycle, and \(\mathrm{d_{max}}\) is the maximum limit for the duty cycle. The simple PI controller selected for this study provides immediate changes in the control signal according to the respective set value. The proposed control strategy controls the injected active power into the grid during voltage sag, while avoiding over-voltage in the DCL. When we use the PI controller under the \"control without MPPT\" mode, a problem may occur because the system works at a different point than the MPP under fault conditions. Therefore, the DCL voltage takes a long time to reach the nominal value after the fault is cleared, because the error in the DCL voltage promotes the accumulation of control action in an integral part of the PI controller at the end of voltage sag, which should be compensated for by an input error in the opposite direction. Therefore, the actual DCL voltage is reduced below the reference value, which may cause the inverter to lose control and be disconnected. To solve this issue, the anti-wind-up technique is applied to the PI controller to accumulate excessive control action when it exceeds a specified value. Thus, when the voltage sag ends, the DCL voltage recovers to the nominal value without perceptible overcompensation.