With the rapid integration of large-scale photovoltaic (PV) power generation into electrical grids, the stability and reliability of power systems have become critical concerns. Solar inverters, as key interfaces between PV arrays and the grid, must ensure continuous operation during grid disturbances, particularly under voltage dips. Traditionally, solar inverters operate at unity power factor, maximizing active power output. However, during grid faults, this approach leads to underutilization of the inverter’s apparent power capacity and fails to support grid voltage recovery. Moreover, unbalanced faults—such as single-phase or phase-to-phase faults—are common in practical grids, posing challenges for solar inverters due to the presence of negative-sequence components. This paper addresses these issues by proposing a low voltage ride-through (LVRT) control strategy for solar inverters under unbalanced faults, focusing on reactive power injection to bolster grid voltage while maintaining balanced three-phase currents. The strategy leverages positive and negative sequence dual-current closed-loop control with feedforward decoupling, ensuring stable operation and compliance with grid codes. Extensive simulations validate the effectiveness of the approach, highlighting the role of solar inverters in enhancing grid resilience.
The proliferation of solar energy has transformed power systems, but grid-connected PV systems introduce vulnerabilities during faults. LVRT capabilities are mandated by grid standards, such as those from State Grid Corporation of China, requiring solar inverters to remain connected during voltage dips and provide reactive power support. Under unbalanced faults, negative-sequence currents can cause excessive stress on solar inverters, leading to tripping or damage. Existing LVRT methods often focus on symmetric faults, neglecting the complexities of unbalanced conditions. This work fills that gap by developing a control strategy that suppresses negative-sequence currents and exploits the reactive power capability of solar inverters. By doing so, solar inverters can contribute to voltage support, reducing reliance on external compensation devices and optimizing resource use. The following sections detail the mathematical modeling, control design, and simulation results, emphasizing the pivotal role of solar inverters in modern power grids.
To begin, consider the topology of a grid-connected PV system, which typically includes a PV array, a DC-DC converter, and a DC-AC solar inverter with an L-filter. The solar inverter interfaces with the grid, and its control system must manage power flow under normal and fault conditions. During unbalanced grid voltages, the system can be analyzed using symmetrical components. In the synchronous rotating reference frame (d-q axis), the grid-side equations for the solar inverter can be expressed as follows, accounting for positive and negative sequence components:
$$ L \frac{di_{pd}}{dt} = e_{pd} – u_{pd} – R i_{pd} + \omega L i_{pq} $$
$$ L \frac{di_{pq}}{dt} = e_{pq} – u_{pq} – R i_{pq} – \omega L i_{pd} $$
$$ L \frac{di_{nd}}{dt} = e_{nd} – u_{nd} – R i_{nd} – \omega L i_{nq} $$
$$ L \frac{di_{nq}}{dt} = e_{nq} – u_{nq} – R i_{nq} + \omega L i_{nd} $$
Here, \( L \) and \( R \) represent the grid-side inductance and equivalent resistance, respectively. The variables \( i \) and \( u \) denote the solar inverter output current and voltage, while \( e \) signifies the grid voltage. Superscripts \( p \) and \( n \) indicate positive and negative sequence components, and subscripts \( d \) and \( q \) refer to active and reactive components. The term \( \omega \) is the grid angular frequency. These equations reveal coupling between the d and q axes for both sequences, necessitating decoupling control for effective regulation of solar inverters.
The proposed control strategy employs feedforward decoupling to eliminate cross-coupling. Using proportional-integral (PI) controllers, the reference voltage signals for the solar inverter are derived as:
$$ u_{pd}^* = e_{pd} – \left( K_{iP} + \frac{K_{iI}}{s} \right) (i_{pd}^* – i_{pd}) + \omega L i_{pq} $$
$$ u_{pq}^* = e_{pq} – \left( K_{iP} + \frac{K_{iI}}{s} \right) (i_{pq}^* – i_{pq}) – \omega L i_{pd} $$
$$ u_{nd}^* = e_{nd} – \left( K_{iP} + \frac{K_{iI}}{s} \right) (i_{nd}^* – i_{nd}) – \omega L i_{nq} $$
$$ u_{nq}^* = e_{nq} – \left( K_{iP} + \frac{K_{iI}}{s} \right) (i_{nq}^* – i_{nq}) + \omega L i_{nd} $$
In these equations, \( K_{iP} \) and \( K_{iI} \) are the PI gains for the current loops, and \( i_{pd}^*, i_{pq}^*, i_{nd}^*, i_{nq}^* \) are the reference current values. The control objective is to set negative-sequence currents to zero, i.e., \( i_{nd} = 0 \) and \( i_{nq} = 0 \), ensuring balanced output from the solar inverter. This minimizes power quality issues and protects the inverter from undue stress. To determine the reference currents, we analyze the complex power output of the solar inverter under unbalanced conditions. The apparent power \( S \) is given by:
$$ S = 1.5 (u_{pdq} e^{j\omega t} + u_{ndq} e^{-j\omega t}) (i_{pdq} e^{j\omega t} + i_{ndq} e^{-j\omega t}) $$
Expanding this, the active and reactive power components include constant terms and oscillatory terms at twice the grid frequency. By imposing the condition \( i_{nd} = i_{nq} = 0 \), the power expressions simplify, allowing calculation of reference currents based on desired active and reactive power. Specifically, the positive-sequence reference currents are:
$$ i_{pd}^* = \frac{2(e_{pd} P_0^* + e_{pq} Q_0^*)}{(e_{pd})^2 + (e_{pq})^2} $$
$$ i_{pq}^* = \frac{2(e_{pd} P_0^* – e_{pq} Q_0^*)}{3(e_{pd})^2 + (e_{pq})^2} $$
Here, \( P_0^* \) and \( Q_0^* \) are the references for active and reactive power, respectively. Under normal operation, solar inverters typically set \( Q_0^* = 0 \) for unity power factor. However, during LVRT, reactive power injection becomes crucial. The grid standards define the relationship between voltage dip and required reactive current. For instance, German grid codes specify that solar inverters must inject reactive current proportional to the voltage deviation. Adapting this for unbalanced faults, the reactive current reference for the positive sequence is computed based on the positive-sequence voltage magnitude. Let \( U_p \) be the positive-sequence voltage magnitude, and \( U_N \) the nominal voltage. The reactive current reference \( i_{pq}^* \) is given by:
$$ i_{pq}^* =
\begin{cases}
k I_N \frac{U_N – U_p}{U_N} & \text{for } \left(1 – \frac{1.1}{k}\right) U_N \leq U_p \leq 0.9 U_N \\
1.1 I_N & \text{for } 0.2 U_N \leq U_p < \left(1 – \frac{1.1}{k}\right) U_N
\end{cases} $$
where \( k \geq 2 \) is a constant (e.g., \( k = 2 \)), and \( I_N \) is the rated current of the solar inverter. The active current reference \( i_{pd}^* \) is then limited to prevent overcurrent, ensuring the total current does not exceed 1.1 times the rated value. This approach enables solar inverters to provide dynamic reactive support during faults, enhancing grid stability. To implement this, accurate detection of positive and negative sequence components is essential. A phase-locked loop (PLL) with notch filters at twice the grid frequency can extract these components from the unbalanced grid voltage. The PLL ensures synchronization with the positive-sequence voltage, maintaining stable operation of the solar inverter.
The overall control block diagram for the solar inverter integrates these elements. It includes sequence decomposition, reference current calculation, and dual-current closed-loop control. The system switches between normal operation and LVRT mode based on grid voltage monitoring. During faults, the solar inverter prioritizes reactive power injection while suppressing negative-sequence currents. This not only complies with LVRT requirements but also optimizes the use of the inverter’s capacity. To illustrate, consider the following table summarizing key parameters and their values used in the control design for a typical solar inverter system:
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Grid-side inductance | L | 0.0003 | H |
| Equivalent resistance | R | 0.01 | Ω |
| DC-link voltage reference | UDC_ref | 690 | V |
| PI gain (current loop) | KiP | 0.8 | – |
| PI gain (current loop) | KiI | 0.02 | – |
| Switching frequency | fsw | 5000 | Hz |
| Rated current | IN | Depends on system | A |
These parameters are typical for a 50 kW solar inverter system, as used in simulations. The design ensures that solar inverters can handle unbalanced faults effectively. To further elucidate the power output characteristics, the active and reactive power under unbalanced conditions can be expressed as:
$$ P = P_0 + P_{c2} \cos(2\omega t) + P_{s2} \sin(2\omega t) $$
$$ Q = Q_0 + Q_{c2} \cos(2\omega t) + Q_{s2} \sin(2\omega t) $$
where the constant terms \( P_0 \) and \( Q_0 \) represent the average power, and the oscillatory terms account for imbalances. By controlling the negative-sequence currents to zero, the oscillatory components are minimized, leading to smoother power output from the solar inverter. This is crucial for protecting the DC-link capacitor and ensuring long-term reliability of solar inverters.
Simulation studies were conducted to validate the proposed strategy. A real-time digital simulator (RTDS) was used to model a 50 kW PV system connected to a grid with unbalanced faults. The solar inverter was tested under a single-phase fault where the voltage dipped to 40% of nominal. The results demonstrate that the dual-current control strategy quickly suppresses negative-sequence currents, maintaining balanced three-phase outputs. Moreover, the solar inverter injects reactive power according to the voltage dip, supporting grid recovery. For example, during the fault, the reactive current reference is set based on the aforementioned equations, and the solar inverter adapts its output accordingly. The following table summarizes simulation results under different fault scenarios:
| Fault Type | Voltage Dip | Negative-Sequence Current | Reactive Power Injection | Solar Inverter Status |
|---|---|---|---|---|
| Single-phase | 40% | Suppressed to near zero | Yes, per grid code | Stable, no tripping |
| Phase-to-phase | 50% | Suppressed to near zero | Yes, per grid code | Stable, no tripping |
| Three-phase symmetric | 30% | Not applicable | Yes, per grid code | Stable, no tripping |
These results confirm that solar inverters equipped with the proposed control can achieve LVRT under various unbalanced conditions. The dynamic response shows that current overshoot is limited to within 1.5 times rated current during transients, which is acceptable for solar inverters. Additionally, the DC-link voltage remains stable, avoiding excessive fluctuations that could damage components. The integration of reactive power control allows solar inverters to contribute to grid voltage support, reducing the need for external devices like STATCOMs or SVCs. This optimization is economically beneficial, as it leverages the existing capacity of solar inverters.
The image above illustrates a typical energy storage inverter, which shares similarities with solar inverters in terms of grid interface and control challenges. While this paper focuses on solar inverters, the principles can be extended to hybrid systems involving storage, further enhancing grid stability. The control strategy for solar inverters is thus part of a broader effort to modernize power electronics for renewable integration.
In-depth analysis of the control dynamics reveals the importance of tuning the PI gains. For solar inverters, the current loop bandwidth must be high enough to track reference changes during faults. Using the symmetrical optimum method, the PI parameters can be designed based on the system time constants. The transfer function of the current loop for the solar inverter can be approximated as:
$$ G_i(s) = \frac{1}{Ls + R} $$
With PI compensation, the open-loop transfer function becomes:
$$ G_{open}(s) = \left(K_{iP} + \frac{K_{iI}}{s}\right) \frac{1}{Ls + R} $$
Setting the crossover frequency appropriately ensures stability and fast response. For instance, for a solar inverter with \( L = 0.0003 \, H \) and \( R = 0.01 \, \Omega \), a crossover frequency of 500 Hz might be chosen, leading to \( K_{iP} = 0.8 \) and \( K_{iI} = 0.02 \) as previously noted. This tuning allows solar inverters to effectively manage fault transients. Additionally, the sequence decomposition relies on notch filters with quality factor \( Q \). The transfer function for a notch filter at frequency \( \omega_0 \) is:
$$ F(s) = \frac{s^2 + \omega_0^2}{s^2 + \frac{\omega_0}{Q} s + \omega_0^2} $$
For grid applications, \( \omega_0 = 2\omega \) (twice the grid frequency) and \( Q = 5 \) provide adequate filtering without excessive phase lag. This ensures accurate extraction of sequence components for the solar inverter control.
Furthermore, the reactive power capability of solar inverters is constrained by their apparent power rating. During faults, the active power output may be reduced to accommodate reactive injection. The relationship between active and reactive currents in a solar inverter can be expressed as:
$$ I_{pd}^2 + I_{pq}^2 \leq (1.1 I_N)^2 $$
This inequality ensures that the solar inverter operates within safe limits. By dynamically adjusting \( I_{pd}^* \) and \( I_{pq}^* \), the control strategy maximizes reactive support without overloading the solar inverter. For severe voltage dips below 45% of nominal, the solar inverter may prioritize reactive power entirely, setting \( I_{pd}^* = 0 \) and \( I_{pq}^* = 1.1 I_N \). This aligns with grid code requirements and underscores the flexibility of modern solar inverters.
To illustrate the economic and technical benefits, consider a case study where a 100 MW solar farm employs the proposed LVRT strategy. During unbalanced faults, the solar inverters provide reactive support, potentially deferring investments in additional grid reinforcement. The table below compares traditional approaches with the proposed strategy for solar inverters:
| Aspect | Traditional Solar Inverters (Unity PF) | Proposed Solar Inverters (LVRT Reactive Control) |
|---|---|---|
| Reactive Power Source | External devices (e.g., capacitors, SVC) | Solar inverters themselves |
| Grid Support During Faults | Limited; may trip or disconnect | Active voltage support via reactive injection |
| Cost Implications | Higher due to extra equipment | Lower, leveraging existing inverter capacity |
| Reliability | Reduced if inverters trip | Enhanced through continuous operation |
| Compliance with Grid Codes | May require additional measures | Directly meets LVRT requirements |
This comparison highlights the advantages of optimizing solar inverters for reactive power control. As grid standards evolve, such capabilities become essential for large-scale PV integration. The proposed strategy not only improves fault ride-through but also enhances the overall value proposition of solar inverters in power systems.
In conclusion, this paper presents a comprehensive LVRT control strategy for solar inverters under unbalanced faults. By employing positive and negative sequence dual-current closed-loop control, solar inverters can suppress negative-sequence currents and maintain balanced outputs. The integration of reactive power injection based on voltage dip magnitude allows solar inverters to support grid voltage recovery, complying with international standards. Simulations confirm the strategy’s effectiveness, demonstrating stable operation and dynamic response. Future work could explore integration with energy storage systems or advanced predictive controls. Ultimately, the role of solar inverters is expanding beyond mere power conversion to active grid support, driving the transition to sustainable energy systems. The continued innovation in solar inverter technology will be pivotal for achieving resilient and efficient power grids worldwide.