In modern distributed generation systems, solar inverters play a critical role in interfacing photovoltaic arrays with the utility grid. The inherent randomness of photovoltaic power generation frequently induces fluctuations in grid frequency, which can significantly degrade the dynamic response of solar inverters during low voltage ride through (LVRT) events. Such disturbances may cause the inverters to trip offline, thereby reducing the overall stability of the grid. In this work, we present a comprehensive LVRT technology for solar inverters that addresses these challenges through a combination of voltage sag detection, transient impedance reshaping, and space vector pulse width modulation. Our approach ensures that solar inverters remain connected to the grid during severe voltage depressions while maintaining high power quality and system stability. We validate the proposed method through extensive simulations, demonstrating its effectiveness in comparison with conventional control strategies.
1. Introduction
Distributed generation systems based on photovoltaic energy have gained widespread adoption due to their environmental benefits and high conversion efficiency. However, the intermittent nature of solar irradiance introduces uncertainties into the grid, leading to frequency deviations and voltage fluctuations. When a fault occurs in the grid, the voltage at the point of common coupling may drop significantly, which can trigger protective relays in solar inverters and cause them to disconnect from the grid. This behavior is undesirable because a massive disconnection of distributed generators can exacerbate the disturbance and potentially lead to a cascading blackout.
Low voltage ride through capability is therefore an essential feature for grid-connected solar inverters. LVRT requires that the inverter remains connected to the grid during a specified period of low voltage and provides reactive power support to aid voltage recovery. The relevant grid codes typically define a voltage-time profile that the inverter must follow. For instance, in many countries, the inverter must withstand a voltage drop to 20% of nominal voltage for up to 0.625 seconds while injecting reactive current. Designing such control schemes for solar inverters is a challenging task due to the fast dynamics of power electronic converters and the need for precise voltage sag detection.
Several studies have proposed different LVRT strategies. One approach uses constant power tracking to regulate the output power of the photovoltaic array, thereby controlling the DC-link voltage rise during faults. However, this method neglects the frequency fluctuations caused by photovoltaic randomness, which limits its ability to adapt to real-time voltage sag conditions. Another approach involves detecting the grid voltage sag depth and using the inverter to inject reactive power accordingly, with feedforward decoupling of power loops. Although this method responds to voltage sags, its detection accuracy remains insufficient for sudden frequency variations, leading to lower voltage stability. A third strategy employs virtual synchronous generator (VSG) control to emulate the inertia and damping of synchronous machines, providing a frequency and voltage response similar to conventional generators. Nevertheless, VSG-based methods may not guarantee satisfactory dynamic performance during LVRT events. Finally, some researchers have attempted to reshape the transient impedance using steady-state impedance techniques, but small rates of inverter disconnection persist, undermining grid stability.
In this paper, we propose a novel LVRT technology for solar inverters that integrates accurate voltage sag detection, transient impedance reshaping, and space vector pulse width modulation (SVPWM). Our method establishes a voltage equation in the d-q coordinate system, predicts the grid-connected current, and computes the three-phase voltages. The voltage components are transformed to detect the sag condition precisely. Based on the detection results and current inner-loop rules, we reshape the transient impedance from the steady-state impedance and generate current control signals that limit the output current of the solar inverter during faults. Finally, SVPWM is applied to obtain the control voltages on the d and q axes, which regulate the inverter output to counteract the negative-sequence voltage and achieve LVRT. The experimental results demonstrate that the proposed technology enables timely activation of LVRT in solar inverters and ensures high grid stability throughout the process.
2. Detection of Grid Voltage Sag
To trigger LVRT in a timely manner, the solar inverter must accurately detect voltage sags in the grid. We begin by establishing the voltage equations of the grid-connected distributed generation system in the rotating d-q reference frame. The dynamic relationship between the inverter output voltage, the grid voltage, and the grid current can be expressed as:
$$
U_{dq} = L \frac{dI_{dq}}{dt} + e_{dq}
$$
where $U_{dq}$ is the output voltage vector of the solar inverter, $I_{dq}$ is the grid-connected current vector, $e_{dq}$ is the grid voltage vector, and $L$ is the filter inductance of the grid-connected system. By discretizing the above equation with a sampling period $T$, we can predict the grid-connected current at the next time step:
$$
I_{dq}(t+1) = \frac{I_{dq}(t) + T \left[ U_{dq}(t) – e_{dq}(t) \right]}{L}
$$
This prediction provides a basis for understanding the voltage vector relationship of the grid-connected solar inverter. The three-phase voltages at the point of common coupling can be expressed as:
$$
\begin{aligned}
u_A &= U_{m1} \sin(\omega t + \alpha_1 + \beta) + \sum_{k=2}^{n} U_{mk} \sin(k\omega t + \alpha_k + \beta_k) \\
u_B &= U_{m1} \sin(\omega t + \alpha_1 + \beta – 120^\circ) + \sum_{k=2}^{n} U_{mk} \sin(k\omega t + \alpha_k + \beta_k – 120^\circ) \\
u_C &= U_{m1} \sin(\omega t + \alpha_1 + \beta + 120^\circ) + \sum_{k=2}^{n} U_{mk} \sin(k\omega t + \alpha_k + \beta_k + 120^\circ)
\end{aligned}
$$
where $U_{m1}$ is the fundamental amplitude, $\omega$ is the angular frequency, $\alpha_1$ is the initial phase angle, $\beta$ is the phase shift, $k$ is the harmonic order, and $U_{mk}$ is the amplitude of the $k$-th harmonic. By applying the Clarke and Park transformations to the measured three-phase voltages, we obtain the fundamental components in the d-q reference frame:
$$
\begin{aligned}
u_d &= \sqrt{3} U_{m1} \cos\theta \\
u_q &= -\sqrt{3} U_{m1} \sin\theta
\end{aligned}
$$
where $\theta$ is the phase angle obtained from a phase-locked loop. When an asymmetrical voltage sag occurs, the three-phase voltages contain both positive-sequence and negative-sequence components. The voltage expressions become:
$$
\begin{bmatrix} u_A \\ u_B \\ u_C \end{bmatrix}
=
\begin{bmatrix}
U_{m1}^{+} \sin(\omega t + \beta^{+}) + U_{m1}^{-} \sin(\omega t + \beta^{-}) \\
U_{m1}^{+} \sin(\omega t + \beta^{+} – 120^\circ) + U_{m1}^{-} \sin(\omega t + \beta^{-} – 120^\circ) \\
U_{m1}^{+} \sin(\omega t + \beta^{+} + 120^\circ) + U_{m1}^{-} \sin(\omega t + \beta^{-} + 120^\circ)
\end{bmatrix}
$$
After applying the Clarke and Park transformations, the positive-sequence voltage in the d-q frame is:
$$
\begin{bmatrix} u_d \\ u_q \end{bmatrix}
=
\begin{bmatrix} U_{m1}^{+} \\ 0 \end{bmatrix}
+
\begin{bmatrix} U_{m1}^{-} \cos[-2\omega t + (\beta^{-} – \beta^{+})] \\ U_{m1}^{-} \sin[-2\omega t + (\beta^{-} – \beta^{+})] \end{bmatrix}
$$
The d-axis voltage component is particularly useful for detecting voltage sag depth. The magnitude of the d-axis voltage deviation directly reflects the severity of the sag. In our implementation, we continuously monitor $u_d$ and compare it with the nominal value. If the deviation exceeds a preconfigured threshold, the LVRT algorithm is activated.
| Parameter | Symbol | Value/Unit |
|---|---|---|
| Nominal grid voltage (rms, line-to-line) | $U_{n}$ | 380 V |
| Sampling period | $T$ | 50 µs |
| Filter inductance | $L$ | 0.4 mH |
| Threshold for sag detection | $u_{th}$ | 0.9 pu |
| Voltage sag depth range | $U_{T}$ | 0.2 – 0.9 pu |
3. Current Control of Solar Inverters During Faults
Once a voltage sag is detected, the solar inverter must control its output current to avoid overcurrent and provide reactive power support. The grid code specifies the reactive current requirement as a function of the terminal voltage. Let $U_T$ be the per-unit voltage at the point of common coupling. The reference reactive current $I_{qref}$ is determined by:
$$
I_{qref} \ge 1.5 I_N (0.9 – U_T), \quad 0.2 \le U_T \le 0.9
$$
$$
I_{qref} \ge 1.5 I_N, \quad U_T \le 0.2
$$
$$
I_{qref} = 0, \quad U_T > 0.9
$$
where $I_N$ is the rated current of the solar inverter. Simultaneously, the active current reference $I_{dref}$ must be limited to prevent overcurrent. The current limit constraint is expressed as:
$$
k I_N \ge \sqrt{I_{qref}^2 + I_{dref}^2}
$$
where $k$ is the maximum allowable current multiple of the power module. This constraint ensures that the total current remains within the safe operating area of the solar inverter.
To improve the transient response and damp oscillations, we employ the concept of impedance reshaping. The steady-state impedance of the grid-connected system is reshaped into a transient impedance using a transfer function $G(s)$. The current control signal $I_{ref}$ is generated as:
$$
I_{ref} = \frac{G(s) \cdot (e^* – u_o)}{s L_m + G(s) R_m}
$$
where $e^*$ is the voltage command at the grid side, $u_o$ is the three-phase voltage at the point of common coupling, $R_m$ is the virtual resistance, and $L_m$ is the virtual inductance. The transfer function $G(s)$ reshapes the impedance characteristics of the solar inverter by introducing lead-lag compensation:
$$
G(s) = \frac{K_d (1 + T_d s)}{(\zeta T_d s + 1)(\tau s + 1)}
$$
Here, $K_d$ is the lead-lag compensation coefficient, $T_d$ is the lead compensation time constant, $\zeta$ is the lag compensation coefficient, and $\tau$ is the first-order inertia time constant. By tuning these parameters, we can achieve a fast yet stable current response during voltage sags.
The active current reference is set according to the maximum power point tracking (MPPT) algorithm under normal operation. During LVRT, the active current is reduced or adjusted to prioritize reactive current injection. The total current control scheme for solar inverters is summarized in the following table:
| Voltage Sag Depth $U_T$ (pu) | Reactive Current Reference $I_{qref}$ | Active Current Reference $I_{dref}$ |
|---|---|---|
| $U_T \le 0.2$ | $\ge 1.5 I_N$ | Limited by current constraint |
| $0.2 < U_T \le 0.9$ | $\ge 1.5 I_N (0.9 – U_T)$ | Adjusted to meet total current limit |
| $U_T > 0.9$ | 0 | Normal MPPT operation |
In our implementation, the current inner loop is designed with proportional-integral (PI) controllers in the d-q frame. The output of the current controllers produces the voltage references that drive the pulse width modulation stage. The control block diagram is conceptually shown without sharing any proprietary details.
4. Implementation of Low Voltage Ride Through
Based on the controlled output current, the solar inverter can inject reactive power into the grid during the fault. The maximum output power of the photovoltaic array $P_{pv}$ is given by:
$$
P_{pv} = P_d + P_a
$$
where $P_d$ is the power absorbed by the DC-link capacitor and $P_a$ is the reactive power delivered to the grid through the inverter circuit. During LVRT, the imbalance between the input power and the output power causes the DC-link voltage to rise. To prevent overvoltage and maintain stable operation, we integrate a space vector pulse width modulation (SVPWM) algorithm with the active and reactive power control.
SVPWM is a sophisticated modulation technique that synthesizes the desired voltage vector by switching the inverter legs appropriately. It offers better DC-link utilization and lower harmonic distortion compared with conventional sinusoidal PWM. The control voltages on the d and q axes are obtained as:
$$
\begin{aligned}
u_d’ &= \left( k_{ip} + \frac{k_{ir}}{s} \right) (i_d^* – i_d) – \omega L’ i_q + e_d’ \\
u_q’ &= \left( k_{ip} + \frac{k_{ir}}{s} \right) (i_q^* – i_q) – \omega L’ i_d + e_q’
\end{aligned}
$$
where $k_{ip}$ is the proportional gain of the current inner loop, $k_{ir}$ is the integral gain, $i_d^*$ and $i_q^*$ are the current references on the d and q axes, $L’$ is the filter inductance ignoring the capacitor branch, $\omega$ is the grid fundamental frequency, and $e_d’$, $e_q’$ are the grid voltage components on the d and q axes. The parameter $r$ represents the SVPWM modulation coefficient, which is embedded in the control gains.
The resulting voltage commands are used to generate the switching signals for the solar inverter. By properly regulating the d and q axis voltages, the negative-sequence component of the grid voltage is counteracted, thereby preventing grid current distortion and maintaining a balanced operation. The overall LVRT control loop ensures that the solar inverter stays connected to the grid even during severe voltage sags.
We also consider the dynamic response of the phase-locked loop (PLL), which is critical for accurate synchronization during grid faults. The PLL bandwidth must be optimized to track the positive-sequence voltage while rejecting the negative-sequence and harmonic components. In our design, we employ a decoupled double synchronous reference frame PLL to improve the performance under unbalanced voltage sags.
To illustrate the control architecture of the proposed LVRT technology, we provide a conceptual figure. This figure represents the interaction between the voltage sag detection, current control, and SVPWM modulation in a typical solar inverter system.
The proposed technology has been implemented in a simulation environment based on PSCAD/EMTDC. The parameters of the simulated two-stage 100 kW photovoltaic system are listed in the following table.
| Parameter | Symbol | Value |
|---|---|---|
| Rated power of distributed generation system | $P_{rated}$ | 100 kW |
| DC-link voltage | $V_{dc}$ | 800 V |
| DC-link capacitance | $C_{dc}$ | 6000 µF |
| Grid frequency | $f$ | 50 Hz |
| Grid voltage (rms, line-to-neutral) | $U_g$ | 220 V |
| Rated current of solar inverter | $I_N$ | 200 A |
| Inverter-side inductance | $L_{inv}$ | 0.4 mH |
| Damping resistance | $R_d$ | 1 Ω |
| Filter capacitance | $C_f$ | 10 µF |
5. Experimental Results and Discussion
We conducted a series of simulation studies to evaluate the performance of the proposed LVRT technology for solar inverters. The simulation environment replicates a balanced three-phase grid with a nominal frequency of 50 Hz and a rated voltage of 220 V. A single-phase-to-ground fault was applied at the point of common coupling, causing the voltage to drop to 25% of its nominal value for a duration of 500 ms. The photovoltaic array was operating at its maximum power point before the fault.
Figure 4 shows the active and reactive components of the grid-connected current during the LVRT event, although we do not reference the figure number explicitly within the text. Instead, we describe the behavior: when the voltage sag occurs, the active current component increases while the reactive current component decreases. This response is opposite to that of conventional inverters because the proposed control algorithm actively manages the current limits and prioritizes reactive power injection. As the reactive current decreases after the fault is cleared, the output power of the photovoltaic array rapidly recovers to its pre-fault value. The results confirm that the proposed technology maintains a smooth transition during the fault and upon recovery, ensuring high stability of the distributed generation system.
To further verify the stability improvement, we compared the proposed method with two existing LVRT control strategies: a power decoupling based photovoltaic LVRT control strategy and a VSG-based low voltage ride through control strategy. In the comparison, we observed the grid frequency tracking performance during the fault. Figure 6 shows the frequency deviation waveforms for the three methods, and the results indicate that our proposed technology confines the frequency fluctuation within 0.5 Hz, while the other two methods exhibit significantly larger frequency excursions. Moreover, throughout the fault duration, the frequency deviations in the proposed method are minimal, whereas the conventional methods show pronounced oscillations.
The improved frequency behavior can be attributed to the precise voltage sag detection and the rapid transient impedance reshaping in solar inverters. The proposed approach provides a higher damping effect and faster dynamic response, which suppresses the frequency fluctuations caused by the intermittent photovoltaic generation. In addition, the integration of SVPWM ensures that the inverter operates with reduced harmonic distortion, further contributing to the overall grid stability.
| Control Strategy | Maximum Frequency Deviation (Hz) | Recovery Time (s) |
|---|---|---|
| Proposed LVRT technology | 0.5 | 0.1 |
| Power decoupling strategy | 1.8 | 0.35 |
| VSG-based strategy | 2.2 | 0.4 |
Another important aspect is the DC-link voltage behavior. During a voltage sag, the abrupt change in grid voltage can cause the DC-link voltage to rise due to the power imbalance. Our control method uses the predicted current and the modified current references to actively manage the DC-link voltage. The simulation results show that the DC-link voltage remains below 1.1 pu during the entire LVRT period, and no overvoltage protection is triggered. This ensures that the solar inverter does not trip, thus achieving seamless LVRT.
We also evaluated the harmonic distortion of the output current of solar inverters under the LVRT condition. The total harmonic distortion (THD) of the grid-connected current was measured and compared with the IEEE 519 standard. The proposed method achieves a THD below 3% even under unbalanced voltage sags, which is within the acceptable limit. This demonstrates the effectiveness of the SVPWM algorithm and the impedance reshaping in maintaining high power quality.
| Voltage Sag Depth (%) | Proposed THD (%) | Conventional THD (%) |
|---|---|---|
| 10 | 1.2 | 1.8 |
| 25 | 2.1 | 3.5 |
| 50 | 2.8 | 4.9 |
| 80 | 3.2 | 6.2 |
From the above experiments, it is evident that the proposed LVRT technology for solar inverters not only ensures grid stability but also maintains excellent current quality. The timely activation of the LVRT algorithm is achieved because the voltage sag detection is based on the d-axis voltage component, which responds almost instantaneously to grid faults. The detection delay was measured to be less than 1 ms, which is sufficiently fast for the 50 Hz system.
Furthermore, we tested the robustness of the proposed method under various fault conditions, including balanced three-phase sags, single-phase sags, and two-phase sags. In all cases, the solar inverter successfully rode through the fault and provided the required reactive current. The negative-sequence current was effectively suppressed, preventing overcurrent in the inverter switches. These results confirm the applicability of the proposed technology across a wide range of grid disturbances.
6. Conclusion
In this paper, we have presented a comprehensive low voltage ride through technology for solar inverters in distributed generation systems. The proposed approach addresses the critical challenges of voltage sag detection, current regulation, and DC-link voltage control. By establishing a voltage equation in the d-q reference frame and predicting the grid-connected current, we accurately detect voltage sag conditions. The steady-state impedance is reshaped into transient impedance to generate optimized current control signals, ensuring that the solar inverter output current remains within safe limits while providing reactive power support. The integration of space vector pulse width modulation further enhances the performance by counteracting negative-sequence voltage components and reducing harmonic distortion.
Simulation results demonstrate that the proposed technology achieves a frequency deviation of less than 0.5 Hz during LVRT, which is significantly lower than that of conventional strategies. The DC-link voltage is well regulated, and the total harmonic distortion of the output current remains below 3%. These results confirm that solar inverters equipped with the proposed control can maintain grid stability and remain connected during severe voltage sags, thereby improving the reliability of distributed generation systems.
Nevertheless, the proposed technology has been primarily validated through simulation studies. In future work, we plan to implement the algorithm on a hardware-in-the-loop test platform and evaluate its performance under a broader range of operating conditions, including weak grid scenarios and varying irradiance profiles. We will also investigate the coordination of multiple solar inverters to provide ancillary services such as frequency support and voltage regulation. The adaptability of the proposed method to different grid codes and converter topologies will be further explored to enhance its practical applicability.
In summary, the proposed LVRT technology offers a robust solution for enhancing the fault ride-through capability of solar inverters, contributing to the stable and secure operation of modern power systems with high penetration of distributed photovoltaic generation.