The increasing penetration of renewable energy sources into the power grid is a critical response to global energy challenges. Among these, solar photovoltaic (PV) generation has seen particularly rapid development. As the number of grid-connected solar inverters grows, their dynamic interaction with the grid becomes crucial for overall system stability and power quality. Consequently, modern grid codes mandate that solar inverters must possess Low Voltage Ride-Through (LVRT) capability, requiring them to remain connected and support the network during voltage sags instead of disconnecting. This requirement makes the research and development of advanced LVRT control strategies for solar inverters a subject of significant practical importance.
Traditional LVRT strategies for solar inverters primarily focus on maintaining connection and injecting reactive current to support grid voltage. However, many existing approaches employ a fixed reactive current injection scheme regardless of the specific type of voltage fault (e.g., symmetrical three-phase fault, single-phase-to-ground fault). This one-size-fits-all method may not optimally utilize the solar inverter’s capacity to support the grid under different unbalanced conditions. For instance, during an asymmetric fault, blindly boosting the positive-sequence voltage component could cause overvoltage in the healthy phases. Therefore, a more intelligent strategy that adapts the solar inverter’s response based on the fault type is highly desirable to provide “flexible voltage support.”
This article proposes an enhanced LVRT control strategy for solar inverters that incorporates grid fault classification to achieve flexible voltage support. The core of the strategy lies in a weighted distribution of reactive current references between positive- and negative-sequence components. By adjusting a single distribution factor, the solar inverter can prioritize boosting the positive-sequence voltage during symmetric faults or reducing voltage unbalance during asymmetric faults. The theoretical foundation, implementation details, and verification through simulation studies are presented in the following sections.
Theoretical Foundation for Current Reference Generation
The instantaneous power theory provides the basis for calculating current references for the solar inverter under unbalanced grid conditions. In the stationary $\alpha\beta$ reference frame, the general form for generating current commands $i^*_\alpha$ and $i^*_\beta$ to deliver active power $P^*$ and reactive power $Q^*$ is given by:
$$
i^*_\alpha = \frac{2}{3} \frac{P^* (v^+_\alpha + v^-_\alpha) + Q^* (v^+_\beta + v^-_\beta)}{(v^+_\alpha + v^-_\alpha)^2 + (v^+_\beta + v^-_\beta)^2}
$$
$$
i^*_\beta = \frac{2}{3} \frac{P^* (v^+_\beta + v^-_\beta) – Q^* (v^+_\alpha + v^-_\alpha)}{(v^+_\alpha + v^-_\alpha)^2 + (v^+_\beta + v^-_\beta)^2}
$$
where $v^+_{\alpha,\beta}$ and $v^-_{\alpha,\beta}$ are the positive- and negative-sequence components of the Point of Common Coupling (PCC) voltage in the $\alpha\beta$ frame. The denominator in these equations contains a double-grid-frequency oscillating term, as shown by its expansion:
$$ (v^+_\alpha + v^-_\alpha)^2 + (v^+_\beta + v^-_\beta)^2 = (V^+)^2 + (V^-)^2 – 2V^+V^-\cos(2\omega t + \phi^+ – \phi^-) $$
where $V^+$ and $V^-$ are the magnitudes of the positive- and negative-sequence voltage components, $\omega$ is the grid angular frequency, and $\phi$ represents the phase angle. Using the general form directly would lead to current references containing harmonics to achieve constant power output. Since a solar inverter has no rotating parts and is less sensitive to power oscillations, an alternative formulation that prioritizes sinusoidal output currents is often adopted:
$$
i^*_\alpha = \frac{2}{3} \frac{P^* (v^+_\alpha + v^-_\alpha) + Q^* (v^+_\beta + v^-_\beta)}{(V^+)^2 + (V^-)^2}
$$
$$
i^*_\beta = \frac{2}{3} \frac{P^* (v^+_\beta + v^-_\beta) – Q^* (v^+_\alpha + v^-_\alpha)}{(V^+)^2 + (V^-)^2}
$$
This formulation eliminates the oscillatory denominator, leading to better current waveform quality from the solar inverter, albeit with some inherent power oscillation.
Proposed Flexible Voltage Support Strategy
The proposed strategy builds upon the second formulation but introduces a key innovation: the reactive current command is calculated using a weighted sum of the positive- and negative-sequence voltage components. This allows the solar inverter to tailor its support based on the fault type.
Current Reference Calculation with Weighted Voltage Components
The active power current reference is calculated considering only the positive-sequence voltage to ensure stable power transfer and is given by:
$$
i^*_{\alpha(p)} = \frac{2}{3} P^* \frac{v^+_\alpha}{(V^+)^2}, \quad i^*_{\beta(p)} = \frac{2}{3} P^* \frac{v^+_\beta}{(V^+)^2}
$$
The innovative reactive power current reference is calculated as follows:
$$
i^*_{\alpha(q)} = \frac{2}{3} Q^* \frac{k^+ v^+_\beta + k^- v^-_\beta}{k^+ (V^+)^2 + k^- (V^-)^2}
$$
$$
i^*_{\beta(q)} = \frac{2}{3} Q^* \frac{-k^+ v^+_\alpha – k^- v^-_\alpha}{k^+ (V^+)^2 + k^- (V^-)^2}
$$
Here, $k^+$ and $k^-$ are weighting factors for the positive- and negative-sequence components, respectively, with the constraint:
$$ k^+ + k^- = 1, \quad k^+ \in (0, 1) $$
The total current reference for the solar inverter controller is the sum of the active and reactive components:
$$ i^*_\alpha = i^*_{\alpha(p)} + i^*_{\alpha(q)}, \quad i^*_\beta = i^*_{\beta(p)} + i^*_{\beta(q)} $$
By adjusting $k^+$, the solar inverter can control the proportion of positive- and negative-sequence reactive current it injects. This is the mechanism that enables flexible voltage support.
Principle of Voltage Support
The impact of the solar inverter’s reactive current injection on the PCC voltage can be understood by considering the simplified grid connection model. The PCC voltage $\vec{V}$ is related to the grid source voltage $\vec{V}_g$ and the voltage drop across the grid inductance $L_g$: $\vec{V} = \vec{V}_g + j\omega L_g \vec{I}$. When the proposed reactive current is injected, the resulting positive- and negative-sequence PCC voltages can be approximated as:
$$
V^+ \approx V^+_g + \frac{2}{3} Q^* \omega L_g \frac{k^+ V^+}{k^+ (V^+)^2 + k^- (V^-)^2}
$$
$$
V^- \approx V^-_g – \frac{2}{3} Q^* \omega L_g \frac{k^- V^-}{k^+ (V^+)^2 + k^- (V^-)^2}
$$
Analysis of these expressions reveals the flexible support capability:
- When $k^+ \rightarrow 1$ (and $k^- \rightarrow 0$), the injection predominantly boosts the positive-sequence voltage $V^+$, which is most beneficial during symmetrical three-phase faults to raise the overall voltage level.
- When $k^+ \rightarrow 0$ (and $k^- \rightarrow 1$), the injection works mainly to reduce the negative-sequence voltage $V^-$, which is most beneficial during asymmetrical faults (e.g., single-phase faults) to improve voltage balance and prevent overvoltage in healthy phases.
Thus, a single solar inverter can be dynamically tuned to address different grid support needs by simply changing the weighting factor $k^+$ based on the detected fault type.
Power Command Allocation and Current Limiting
During an LVRT event, the solar inverter’s output current must remain within its maximum allowable limit $I_{max}$. The proposed strategy prioritizes reactive power support. The power commands are allocated based on the voltage sag depth $D$, defined as $D = 1 – V_{min}/V_N$, where $V_{min}$ is the minimum RMS phase voltage and $V_N$ is the rated voltage.
The apparent power capacity $S$ to be delivered is split as:
$$ Q^* = D \cdot S, \quad P^* = (1 – D) \cdot S $$
This allocation ensures reactive power injection increases with the severity of the voltage sag. The maximum allowable $S$ is determined by substituting $P^*$ and $Q^*$ into the expressions for the three-phase peak currents derived from the current reference equations and enforcing $I_{peak, phase} \leq \sqrt{2} I_{max}$. The smallest $S$ value from the three phases is selected to ensure the solar inverter operates safely within its current limits.
Overall Control Strategy Implementation
The overall LVRT control system for the solar inverter is structured as follows. First, the PCC voltages are measured and transformed into the $\alpha\beta$ frame. A sequence decomposition method (e.g., a Second Order Generalized Integrator – Frequency Locked Loop) extracts the positive- and negative-sequence voltage components ($v^+_{\alpha,\beta}$, $v^-_{\alpha,\beta}$, $V^+$, $V^-$).
The fault type is assessed based on the extracted sequence components. The sag depth $D$ is calculated. The weighting factor $k^+$ is then selected according to the fault type:
- For a symmetrical fault ($V^- \approx 0$), set $k^+ = 1.0$ to maximize positive-sequence voltage support.
- For an asymmetrical fault ($V^- > 0$), set $k^+ = 0.1$ to prioritize the reduction of voltage unbalance.
With $D$ and $k^+$ known, the power commands $P^*$ and $Q^*$ are calculated according to the current-limiting algorithm described above. Finally, the current references $i^*_\alpha$ and $i^*_\beta$ are computed using the proposed weighted formulas. These references are then tracked by the solar inverter’s inner current controller, typically a Proportional-Integral (PI) or Proportional-Resonant (PR) controller in the stationary frame, which generates the pulse-width modulation (PWM) signals for the power switches. This entire process allows the solar inverter to provide adaptive, fault-type-specific voltage support.
Simulation Verification and Results Analysis
The proposed LVRT control strategy for solar inverters was validated using a detailed simulation model of a 100 kW single-stage PV system in the PSCAD/EMTDC environment. The system parameters include a 220 V, 50 Hz grid, an inverter-side filter inductance $L_1=0.17$ mH, a filter capacitance $C=200 \mu$F, a grid-side inductance $L_2=0.05$ mH, and a DC-link capacitor of 6000 $\mu$F. The solar inverter’s maximum current is 155.6 A RMS (approx. 240 A peak).
Case 1: Three-Phase Symmetrical Fault
A balanced three-phase fault was applied at the grid side, causing the PCC voltage to drop to approximately 66 V RMS. Initially, the solar inverter operated with only active power. At $t=0.4$s, the proposed strategy was activated with $k^+=1.0$. The results confirmed that the solar inverter remained connected without overcurrent. Upon reactive power injection, the PCC voltage was successfully boosted to about 113 V RMS, demonstrating effective positive-sequence voltage support.
Case 2: Single-Phase-to-Ground Fault
An ‘a’-phase-to-ground fault was simulated. The response was divided into three stages for comparison:
- Stage 1 ($t=0.3$s to $0.4$s): Active power only.
- Stage 2 ($t=0.4$s to $0.5$s): Reactive power enabled with $k^+=0.9$.
- Stage 3 ($t=0.5$s to $0.6$s): Reactive power enabled with $k^+=0.1$.
Table 1 summarizes the key outcomes, illustrating how the solar inverter’s behavior changes with the weighting factor.
| Stage & Parameter ($k^+$) | Primary Current Characteristic | Effect on Positive-Seq. Voltage $V^+$ | Effect on Negative-Seq. Voltage $V^-$ | Result on Phase Voltages & Unbalance |
|---|---|---|---|---|
| Stage 2 ($k^+=0.9$) | Nearly balanced, positive-seq. dominant. | Significantly increased (~ +28 V). | Largely unchanged. | Faulted phase (a) raised to 103 V, healthy phases (b,c) raised to ~237 V (slight overvoltage). Unbalance reduced from initial fault. |
| Stage 3 ($k^+=0.1$) | Highly unbalanced, negative-seq. dominant. | Smaller increase than Stage 2. | Significantly reduced. | All phase voltages moderately raised. Three-phase voltage unbalance is further minimized compared to Stage 2. |
The results clearly show that using a high $k^+$ value (Stage 2) effectively raises the average voltage but can lead to overvoltage in healthy phases. In contrast, a low $k^+$ value (Stage 3) directs the solar inverter’s effort towards balancing the voltages, which is a more appropriate and “flexible” support objective for an asymmetric fault.
Case 3: Two-Phase-to-Ground Fault
A similar test was conducted for an ‘ab’-phase-to-ground fault. The results were consistent with the single-phase fault case. Setting $k^+=0.1$ again proved more effective in reducing the negative-sequence component and mitigating voltage unbalance compared to a high $k^+$ setting, validating the strategy’s adaptability for different asymmetric fault types.
Conclusion
This article has presented a novel Low Voltage Ride-Through control strategy for solar inverters designed to provide flexible voltage support by considering the grid fault type. The strategy is centered on a weighted distribution of reactive current references between positive- and negative-sequence components, controlled by a single parameter $k^+$. By setting $k^+ \approx 1$ for symmetrical faults, the solar inverter prioritizes boosting the positive-sequence voltage to elevate the overall voltage profile. By setting $k^+ \approx 0.1$ for asymmetrical faults, the solar inverter prioritizes injecting negative-sequence reactive current to reduce voltage unbalance and prevent overvoltage in healthy phases. A coordinated power command allocation scheme ensures the solar inverter operates within its current limits while prioritizing reactive power support during deep sags.
The strategy offers several advantages: 1) It enhances the grid-friendliness of solar inverters by providing targeted voltage support. 2) Its implementation in the stationary $\alpha\beta$ frame avoids the need for multiple rotating coordinate transformations and decoupled current controllers, simplifying the control structure. Simulation studies under various fault conditions have confirmed the strategy’s effectiveness in achieving safe LVRT and its flexible support capabilities. Future work will focus on optimizing the strategy’s performance under varying grid strength conditions and integrating it with other grid-supporting functions of modern solar inverters.