## 4 Proposed LVRT Enhancement Strategies
### Reactive Power Injection Scheme  
For the grid-connected operation, the real power is regulated using i\({}_{\text{d}}\), and the reactive power is regulated using i\({}_{\text{q}}\). The equations of the grid inverter can be given in d-q frame rotating at the line frequency, as follows:  
\[\frac{\text{d}\text{i}_{\text{d}}}{\text{dt}} =-\ \frac{\text{R}}{\text{L}}\text{i}_{\text{d}}+\frac{\text{v}_{ \text{d}}}{\text{L}}-\frac{\text{v}_{\text{gd}}}{\text{L}}+\omega\text{i}_{ \text{q}} \tag{13}\] \[\frac{\text{d}\text{i}_{\text{q}}}{\text{dt}} =-\ \frac{\text{R}}{\text{L}}\text{i}_{\text{q}}+\frac{\text{v}_{ \text{q}}}{\text{L}}-\frac{\text{v}_{\text{gq}}}{\text{L}}+\omega\text{i}_{ \text{d}} \tag{14}\]  
where i\({}_{\text{d}}\) and v\({}_{\text{d}}\) are the d-axis components of the inverter current and voltage, i\({}_{\text{q}}\) and v\({}_{\text{q}}\) are the q-axis components of the inverter current and voltage, and v\({}_{\text{gd}}\) and v\({}_{\text{gq}}\) are the d-axis and q-axis components of the grid voltage. When controlling P and Q independently, the d-axis reference voltage (v\({}_{\text{d-ref}}\)) and q-axis reference voltage (v\({}_{\text{q-ref}}\)) will be obtained. They are converted into the stationary reference frame using the dq-abc transformation, and sinusoidal pulse width modulation (SPWM) signals are then generated accordingly. To provide the reactive power support to the grid under fault conditions, this work proposes a modified control system for the voltage source converter (VSC), as shown in Figure 6. During normal operating conditions, the inverter control system generates a d-axis reference current to maintain the DCL voltage by using an external voltage regulator, and maintaining the unity power factor. The d-axis reference current controller, designed with the back-calculation anti-windup method, is used to avoid the error accumulation of the integral part under fault conditions. The quadrature axis reference current (Iq\({}_{\text{q-ref}}\)) is fixed to zero to keep the unity power factor under normal conditions. The PLL measures the system frequency, and provides the phase synchronous angle for the dq transformation block. When voltage sag is created on the grid, the reactive current injection level is calculated based on Equation (7). During the occurrence of voltage sag on the grid point (PCC), the inverter active power injection control mode is changed to the reactive-power injection control mode. At that time, the PI controller controls the q-axis reference current (Iq\({}_{\text{q-ref}}\)). Under fault conditions, the difference between the actual grid voltage (V\({}_{\text{grid-actual}}\)) and the measured grid voltage (V\({}_{\text{grid-meas}}\)) is used to calculate the required amount of reactive power (Q) needed for the grid by using Equation (15), and Iq\({}_{\text{q-ref}}\) is calculated using Equation (16):  
\[\text{Q}= \left(\text{k}_{\text{P}}+\frac{\text{k}_{\text{i}}}{\text{S}} \right)\ \left(\text{V}_{\text{grid\_actual}}-\text{V}_{\text{grid\_meas}}\right) \tag{15}\]  
\[\text{Iq\_ref}=\left(2\text{S}\right)/\left(3\,V_{\text{grid}}\right) \tag{16}\]  
\[\text{Iq\_max}=\left(2\text{Q}\right)/\left(3\,V_{\text{grid}}\right) \tag{17}\]  
where S is the apparent power, and the current Iq\({}_{\text{q-ref}}\) is limited based on the inverter current rating. Therefore, the range of the active power (P) during fault conditions is given by:  
\[0\ \leq\ \text{P}\ \leq\sqrt{\text{S}^{2}-Q^{2}} \tag{18}\]  
The reactive power capacity of the inverter can be utilized to compensate for the voltage sag under fault conditions. The maximum range of the inverter reactive power injection capacity is determined as follows:  
\[\text{Q}_{\text{max}}=\sqrt{\text{S}_{\text{max}}{}^{2}-\text{P}_{\text{spv}}{} ^{2}} \tag{19}\]  
where S\({}_{\text{max}}\) is the maximum apparent power, and P\({}_{\text{spv}}\) is the PV power. The proposed scheme, based on reactive power injection, is presented in Algorithm 1.