As the global demand for renewable energy continues to rise, photovoltaic (PV) power generation has become one of the most promising technologies. The increasing penetration of large-scale PV power plants into the grid imposes higher requirements on the stability and reliability of power systems. Among these requirements, the low voltage ride-through (LVRT) capability of grid-connected solar inverters is critical. When a grid fault causes voltage sag, the solar inverter must remain connected to the grid and provide reactive power support to help the grid recover. This paper presents a comprehensive study on a LVRT strategy for a three-phase grid-connected solar inverter, focusing on reactive current injection. The proposed method uses a current single-loop control scheme during voltage sags, replacing the conventional voltage-current dual-loop control. Additionally, the Boost converter switches from maximum power point tracking (MPPT) to voltage regulation mode to stabilize the DC-link voltage. Simulation results obtained using PSCAD/EMTDC demonstrate the effectiveness of the proposed strategy. This article provides detailed mathematical models, control diagrams, tables summarizing key parameters, and LaTeX-formulated equations to illustrate the principles. The discussion emphasizes the role of the solar inverter in maintaining grid stability during faults.
Introduction
With the rapid development of the world economy, the demand for energy is growing significantly. Solar energy, as a clean and renewable resource, has gained widespread attention. The proportion of PV power in the grid supply has been increasing steadily. However, the intermittent and random nature of PV generation makes it difficult to predict power changes or perform flexible scheduling. To reduce the impact of grid-connected PV systems, grid codes impose constraints on normal operation and also require that during grid faults, PV power plants remain connected for a specified period before disconnection is allowed. The LVRT capability directly affects the large-scale application of PV systems. The low voltage ride-through strategy of a solar inverter is a key research topic. Many studies have been conducted on wind turbine LVRT, and similar concepts can be applied to PV systems. In this paper, we propose a LVRT strategy based on reactive current injection, which does not require additional hardware such as energy storage or reactive compensation devices. The control scheme is applicable to distributed energy resources as well. The main idea is to switch the solar inverter from dual-loop control to single-loop current control during voltage sags, while the Boost converter shifts from MPPT to constant voltage control. This approach ensures that the solar inverter can effectively support grid voltage recovery without tripping due to overcurrent.
System Topology of Grid-Connected PV System
The topology of a three-phase grid-connected PV system is illustrated in the figure below. The system consists of a PV array, a Boost converter, a DC/AC inverter, a filter inductor, and the grid. The Boost converter matches the PV output voltage to the inverter DC-link voltage and implements MPPT. The inverter converts DC power to AC power and delivers it to the grid. The filter inductor attenuates harmonics generated by the inverter. In the control system, the Boost converter uses a perturbation and observation MPPT algorithm to track the maximum power point. The inverter employs a dual-loop control structure with an outer DC voltage loop and an inner dq current loop. For simplicity, an inductor is used as the filter.
The detailed mathematical modeling of the Boost converter and the inverter is presented in the following subsections.
Boost Converter Model and Its Control
The Boost converter (step-up chopper) is shown in the topology. Its input voltage is \(U_{in}\) and output voltage is \(U_0\). When the switch S is ON, the inductor voltage equals \(U_{in}\); when S is OFF, the inductor voltage equals \(U_{in} – U_0\). According to the volt-second balance principle over one switching period \(T_s\),
$$ \int_{0}^{T_s} u_L(t) dt = U_{in} D T_s + (U_{in} – U_0)(1-D) T_s = 0 $$
Solving yields the voltage gain:
$$ \frac{U_0}{U_{in}} = \frac{1}{1-D} $$
where \(D\) is the duty cycle (0 ≤ D ≤ 1). The Boost converter in a PV system is mainly used to implement MPPT. The energy conversion efficiency of a PV cell depends on internal characteristics and external conditions (irradiance, temperature, load). Therefore, a control system is required to operate the PV array at its maximum power point. The perturbation and observation method is widely used. It compares the power before and after a voltage perturbation. If the current power is larger than the previous, the perturbation direction is maintained; otherwise, it is reversed. This algorithm continuously adjusts the PV voltage toward the maximum power point. The flowchart is described in the original paper but omitted here for brevity.
DC/AC Inverter Model and Its Control
Assume the grid line voltages \(e_a, e_b, e_c\) are balanced sinusoidal, and the filter inductances are identical. The switching functions \(S_a, S_b, S_c\) are defined as:
$$ S_k = \begin{cases} 1 & \text{upper switch on, lower off} \\ 0 & \text{lower switch on, upper off} \end{cases} $$
where \(k = a, b, c\). The dynamic equations in the stationary abc frame are:
$$
\begin{aligned}
L \frac{di_a}{dt} &= u_{ca} – R i_a – e_a \\
L \frac{di_b}{dt} &= u_{cb} – R i_b – e_b \\
L \frac{di_c}{dt} &= u_{cc} – R i_c – e_c \\
C_2 \frac{du_{dc}}{dt} &= i_D – i_{dc} = i_D – (S_a i_a + S_b i_b + S_c i_c)
\end{aligned}
$$
where \(u_{dc}\) is DC-link voltage, \(i_{dc}\) is DC-link current, \(i_D\) is diode current, \(u_{ca}, u_{cb}, u_{cc}\) are inverter output voltages, \(L\) is filter inductance, \(R\) is equivalent resistance. The inverter output voltages are related to the DC-link voltage by:
$$
\begin{aligned}
u_{ca} &= S_a u_{dc} + u_{on} \\
u_{cb} &= S_b u_{dc} + u_{on} \\
u_{cc} &= S_c u_{dc} + u_{on}
\end{aligned}
$$
Using the balanced condition \(e_a+e_b+e_c=0\) and \(i_a+i_b+i_c=0\), we obtain:
$$ u_{on} = -\frac{S_a+S_b+S_c}{3} u_{dc} $$
Transforming to the synchronous rotating dq frame using the equal-magnitude transformation gives:
$$
\begin{aligned}
L \frac{di_d}{dt} &= u_{cd} – e_d – R i_d + \omega L i_q \\
L \frac{di_q}{dt} &= u_{cq} – e_q – R i_q – \omega L i_d \\
C_2 \frac{du_{dc}}{dt} &= i_D – \frac{3}{2} S_d i_d – \frac{3}{2} S_q i_q
\end{aligned}
$$
To improve stability, a dual-loop control strategy is employed. The inner current loop uses direct current control with decoupling and feedforward compensation:
$$
\begin{aligned}
u_{cd} &= K_{p\_id} (i_d^* – i_d) + K_{i\_id} \int (i_d^* – i_d) dt – \omega L i_q + e_d \\
u_{cq} &= K_{p\_iq} (i_q^* – i_q) + K_{i\_iq} \int (i_q^* – i_q) dt + \omega L i_d + e_q
\end{aligned}
$$
The outer voltage loop generates the active current reference:
$$ i_d^* = K_{p\_dc} (u_{dc}^* – u_{dc}) + K_{i\_dc} \int (u_{dc}^* – u_{dc}) dt $$
where \(u_{dc}^*\) is the DC voltage reference. Under normal conditions, the reactive current reference \(i_q^*\) is set to zero to achieve unity power factor.
Low Voltage Ride-Through Requirements
LVRT capability refers to the ability of a solar inverter to remain connected to the grid during voltage sags caused by faults, and to support grid voltage recovery. When the grid voltage dips, the output power of the inverter decreases, causing a rise in DC-link voltage and potential overcurrent. Without proper control, the inverter will trip due to overcurrent protection. International standards, such as German standards and Chinese GB/T 19964-2012, specify the required voltage vs. time characteristics. For example, the German standard requires that the inverter stay connected for 150 ms even if voltage drops to zero, while the Chinese standard requires 150 ms for voltages below 20% of nominal. Additionally, reactive current injection requirements are defined. The Chinese standard demands that when voltage drops to 80% of nominal, the inverter must inject 105% of rated reactive current. The reactive current reference during LVRT is given by:
$$
i_{qref} =
\begin{cases}
0, & U_T \geq 0.9 \\
1.5 \times (0.9 – U_T) I_N, & 0.2 \le U_T < 0.9 \\
1.05 I_N, & U_T < 0.2
\end{cases}
$$
where \(U_T\) is the per-unit grid voltage at the point of common coupling (PCC), and \(I_N\) is the rated current.
Proposed LVRT Strategy
The main challenge for solar inverter LVRT is to prevent overcurrent while maintaining grid connection and providing reactive support. The proposed strategy is illustrated in the control block diagram (omitted in text but described). Under normal conditions, the inverter operates with dual-loop control (voltage outer loop, current inner loop). When a voltage sag is detected (e.g., \(U_T < 0.9\)), the controller switches to single-loop current control. The voltage outer loop is disabled. The active current reference \(i_{dref}\) is derived from the available current capacity and the required reactive current. To avoid exceeding the inverter current rating, the active current limit is computed as:
$$ i_{dref} = \sqrt{I_{max}^2 – i_{qref}^2} $$
where \(I_{max}\) is the maximum allowed current (usually 1.1 to 1.2 pu). Simultaneously, the Boost converter changes from MPPT mode to constant voltage regulation mode to stabilize the DC-link voltage. The DC voltage reference is set to a fixed value (e.g., 0.7 pu of nominal) during the sag. This ensures that the PV array does not output maximum power, allowing the inverter to prioritize reactive power injection. When the voltage recovers above a threshold (e.g., 0.9 pu), the system returns to normal dual-loop control and MPPT mode.
The control strategy can be summarized in the following table:
| Operation Condition | Inverter Control | Boost Control | Reactive Current Reference |
|---|---|---|---|
| Normal (U_T ≥ 0.9 pu) | Dual-loop (voltage + current) | MPPT | 0 |
| Moderate sag (0.2 ≤ U_T < 0.9 pu) | Single-loop current control | Constant voltage regulation | 1.5×(0.9-U_T)×I_N |
| Deep sag (U_T < 0.2 pu) | Single-loop current control | Boost disabled (DC voltage = PV open-circuit voltage) | 1.05×I_N |
| Recovery (U_T ≥ 0.9 pu) | Dual-loop | MPPT | 0 |
Mathematical Formulation of the Control
The overall control during LVRT can be expressed in the following equations. In the dq frame, the inverter output voltage references are given by the current controllers (PI) without the outer voltage loop. The active and reactive current references are as defined. The DC-link voltage is regulated by the Boost converter via a PI controller:
$$ u_{dc}^{ref} = 0.7 \, \text{pu} \quad \text{(during sag)} $$
The Boost duty cycle is adjusted to maintain this voltage. The PV output power is automatically reduced because the constant voltage reference is below the MPP voltage, thus preventing excess power from raising the DC-link voltage.
Simulation Results and Discussion
A simulation model was built in PSCAD/EMTDC to verify the proposed strategy. The system parameters are listed in the table below:
| Parameter | Value | Unit |
|---|---|---|
| Rated power | 100 | kW |
| Grid line voltage (rms) | 380 | V |
| DC-link nominal voltage | 700 | V |
| Filter inductance | 0.5 | mH |
| Boost inductor | 1.0 | mH |
| DC-link capacitor | 3000 | μF |
| Switching frequency | 10 | kHz |
The simulation scenario: Initially, the PV system operates under MPPT and dual-loop control, delivering about 1 pu of active power to the grid. At t=1 s, the grid voltage drops to 0.5 pu due to a three-phase fault. At t=1.5 s, the voltage recovers to 1.0 pu. The proposed LVRT strategy is activated upon detection of the sag.
The key simulation results (not shown as figures but described) indicate:
- DC-link voltage: When the sag occurs, the DC-link voltage initially rises due to power imbalance, but the Boost controller quickly switches to constant voltage regulation (0.7 pu). After a short transient, the DC-link voltage stabilizes at the reference value. When the grid recovers, the Boost returns to MPPT and the DC-link voltage returns to the MPPT operating point.
- Grid voltage: The voltage at the PCC drops to 0.5 pu during the fault. The inverter injects reactive current according to the reference. The grid voltage waveform shows a smooth recovery after fault clearance.
- Grid current: The inverter current remains within safe limits. During the sag, the current magnitude is slightly above rated (due to reactive injection) but does not exceed the maximum allowable (e.g., 1.1 pu). The current waveform is sinusoidal.
- Active and reactive power: Before the fault, active power is about 1 pu, reactive power near 0. During the sag, active power reduces significantly, and reactive power increases to about 0.6 pu (since 1.5×(0.9-0.5)=0.6). After recovery, active power returns to 1 pu and reactive power returns to zero.
The simulation confirms that the proposed single-loop current control strategy, combined with Boost voltage regulation, enables the solar inverter to ride through low voltage events effectively. The system provides reactive power support to aid grid voltage recovery, and the DC-link voltage is well controlled. No overcurrent protection tripping occurs. The transition between control modes is smooth.
Comparison with Other LVRT Methods
Several LVRT strategies have been proposed in the literature, including those using energy storage, dump loads, or advanced modulation schemes. The advantage of the proposed method is that it does not require additional hardware components such as crowbar circuits, DC choppers, or energy storage devices. It relies solely on modifying the control algorithm of the solar inverter and the Boost converter. This reduces cost and complexity. The reactive current injection follows grid code requirements, ensuring compliance. However, one limitation is that during deep sags (below 0.2 pu), the DC-link voltage drops to the PV open-circuit voltage, which may be lower than the nominal value. The inverter may not be able to fully supply the required reactive current if the DC voltage is too low. In such cases, a boost transformer or additional DC-DC stage might be needed. Nonetheless, for most practical faults (voltage not dropping below 0.2 pu), the strategy is effective.
Conclusion
This paper presents a low voltage ride-through strategy for a grid-connected solar inverter based on reactive current injection. The method uses a current single-loop control during voltage sags and switches the Boost converter from MPPT to constant voltage regulation. The control equations and parameters are provided. Simulation results using PSCAD/EMTDC demonstrate that the solar inverter can remain connected, inject reactive power to support grid voltage, and avoid overcurrent. The transition between normal and fault modes is stable. The strategy is simple, requires no additional hardware, and complies with grid codes. This work contributes to the reliable integration of PV systems into modern power grids.
Future work could include the experimental validation on a hardware platform and the extension to unbalanced faults. The impact of multiple solar inverters operating in parallel during LVRT also deserves further study.