In the context of modern power systems, the integration of renewable energy sources, particularly photovoltaic (PV) generation, has become increasingly prevalent. However, the inherent randomness and intermittency of solar power introduce significant challenges to grid stability. One of the critical issues is the fluctuation of grid frequency caused by sudden changes in PV output, which directly impacts the dynamic response performance of PV inverters during low voltage ride through (LVRT) events. Without proper control, these fluctuations can lead to inverter disconnection, compromising the stability of the entire distributed generation system. Therefore, we conducted an in-depth study on the LVRT technology of photovoltaic inverters in distributed generation systems, aiming to enhance grid resilience and ensure continuous operation under fault conditions.
Our research focuses on developing a comprehensive LVRT strategy that addresses the voltage sag detection, current control during faults, and voltage compensation. The proposed method integrates multiple advanced control techniques, including coordinate transformation, impedance reshaping, and space vector pulse width modulation (SVPWM). We validated the effectiveness of our approach through extensive simulations, demonstrating that it can timely activate LVRT and maintain high grid stability during faults. In this paper, we present the detailed theoretical framework, mathematical derivations, and experimental results to support our findings.
Detection of Grid Voltage Sag
To initiate the LVRT process promptly, real-time detection of voltage sag is essential. We established the voltage equations of the distributed generation system in the d-q rotating coordinate system. The inverter system voltage equation is given by:
$$
U_{dq} = L \frac{dI_{dq}}{dt} + e_{dq}
$$
where \( U_{dq} \) is the output voltage of the PV inverter, \( I_{dq} \) is the grid-connected current, \( e_{dq} \) is the rated grid voltage, and \( L \) is the filter inductance. Based on this, we predict the grid current at the next sampling instant using the forward Euler method:
$$
I_{dq}(t+1) = \frac{I_{dq}(t) + T[U_{dq}(t) – e_{dq}(t)]}{L}
$$
Here, \( T \) is the sampling period. The predicted current helps us determine the voltage vector relationship of the grid-connected inverter. The three-phase voltages of the grid can be expressed as:
$$
\begin{aligned}
u_A &= U_{m1} \sin(\omega t + \alpha_1 + \beta) + \sum_{k=2}^{n} U_{mk} (\alpha_k + \beta_k) \\
u_B &= U_{m1} \sin(\omega t + \alpha_1 + \beta – 120^\circ) + \sum_{k=2}^{n} U_{m1} (\alpha_k + \beta_k – 120^\circ) \\
u_C &= U_{m1} \sin(\omega t + \alpha_1 + \beta + 120^\circ) + \sum_{k=2}^{n} U_{m1} (\alpha_k + \beta_k + 120^\circ)
\end{aligned}
$$
where \( \alpha_1 \) is the initial phase, \( \omega \) is the angular frequency, \( \beta \) is the phase shift angle, and \( U_{mk} \) is the RMS voltage of the \( k \)-th harmonic. By applying Clarke and Park transformations, we filter out harmonics and obtain the fundamental d-q components:
$$
\begin{aligned}
u_d &= \sqrt{3} U_{m1} \cos \theta \\
u_q &= -\sqrt{3} U_{m1} \sin \theta
\end{aligned}
$$
For asymmetrical voltage sags, the three-phase voltages contain both positive and negative sequence components. The positive and negative sequence voltages are given by:
$$
\begin{bmatrix}
u_A \\ u_B \\ u_C
\end{bmatrix}
=
\begin{bmatrix}
U_m^+ \sin(\omega t + \beta^+) + U_m^- \sin(\omega t + \beta^-) \\
U_m^+ \sin(\omega t + \beta^+ – 120^\circ) + U_m^- \sin(\omega t + \beta^- – 120^\circ) \\
U_m^+ \sin(\omega t + \beta^+ + 120^\circ) + U_m^- \sin(\omega t + \beta^- + 120^\circ)
\end{bmatrix}
$$
After transformation to the d-q frame, we obtain:
$$
\begin{bmatrix}
u_d \\ u_q
\end{bmatrix}
=
\begin{bmatrix}
U_m^+ \\ 0
\end{bmatrix}
+
\begin{bmatrix}
U_m^- \cos[-2\omega t + (\beta^- – \beta^+)] \\
U_m^- \sin[-2\omega t + (\beta^- – \beta^+)]
\end{bmatrix}
$$
By monitoring the d-axis voltage component, we can accurately detect the depth and nature of the voltage sag. This detection method is robust to harmonics and provides fast response, enabling the LVRT controller to react immediately.
Control of PV Inverter Output Current During Faults
To prevent overcurrent during LVRT, we must control the active and reactive currents of the inverter. According to grid codes, the reactive current reference should meet the following requirements:
$$
\begin{cases}
I_{qref} \geq 1.5 I_N (0.9 – U_T), & 0.2 \leq U_T \leq 0.9 \\
I_{qref} \geq 1.5 I_N, & U_T \leq 0.2 \\
I_{qref} = 0, & U_T > 0.9
\end{cases}
$$
where \( U_T \) is the per-unit voltage at the point of common coupling, and \( I_N \) is the rated current. To avoid exceeding the inverter’s current capability, we impose:
$$
k I_N \geq \sqrt{I_{qref}^2 + I_{dref}^2}
$$
Here, \( k \) is the maximum current multiplier that the power module can withstand. We then reshape the transient impedance using steady-state impedance to generate the current control signal. The reference current is given by:
$$
I_{ref} = \frac{G(s) \cdot (e^* – u_o)}{s L_m + G(s) R_m}
$$
where \( e^* \) is the voltage command, \( u_o \) is the three-phase voltage at the grid interface, \( R_m \) and \( L_m \) are the virtual resistance and inductance, and \( G(s) \) is the reshaping transfer function defined as:
$$
G(s) = \frac{K_d (1 + T_d s)}{(\zeta T_d s + 1)(\tau s + 1)}
$$
In this function, \( K_d \) is the lead-lag compensation coefficient, \( T_d \) is the lead time constant, \( \zeta \) is the lag coefficient, and \( \tau \) is the first-order inertia time constant. By appropriately tuning these parameters, we can effectively limit the fault current while ensuring fast dynamic response.
Realization of Low Voltage Ride Through
After establishing the current control, we provide reactive power support to the grid during the fault. The maximum output power of the PV array is expressed as:
$$
P_{pv} = P_d + P_a
$$
where \( P_d \) is the capacitive power consumed by the DC-link, and \( P_a \) is the reactive power injected into the grid. To regulate the DC-link voltage and compensate for the negative sequence voltage, we incorporate Space Vector Pulse Width Modulation (SVPWM). The control voltages in the d-q axes are obtained as:
$$
\begin{aligned}
u’_d &= \left( k_{ip} + \frac{k_i}{r} \right) (i_d^* – i_d) – \vartheta L’ i_q + e’_d \\
u’_q &= \left( k_{ip} + \frac{k_i}{r} \right) (i_q^* – i_q) – \vartheta L’ i_d + e’_q
\end{aligned}
$$
where \( k_{ip} \) is the proportional gain of the current inner loop, \( k_i \) is the integral gain, \( i_d^*, i_q^* \) are the current references, \( \vartheta \) is the grid fundamental frequency, \( L’ \) is the inductor value neglecting the filter capacitor, and \( e’_d, e’_q \) are the grid voltages in the d-q frame. The modulation index \( r \) is derived from the SVPWM algorithm. By adjusting the inverter outputs based on these control voltages, we effectively cancel the negative sequence components and maintain balanced grid operation during the fault.
Experimental Validation
We built a 100 kW two-stage PV inverter LVRT simulation platform using PSCAD/EMTDC to verify the proposed technology. The main parameters are listed in Table 1.
| Parameter | Value |
|---|---|
| Rated power of distribution system (kW) | 100 |
| DC bus voltage (V) | 800 |
| Bus capacitance (μF) | 6000 |
| Grid frequency (Hz) | 50 |
| Grid voltage rating (V) | 220 |
| PV inverter rated current (A) | 200 |
| Inverter side inductance (mH) | 0.4 |
| Damping resistor (Ω) | 1 |
| Filter capacitor (μF) | 10 |
We simulated a single-phase voltage sag of 25% and compared our method with two existing approaches: a power-decoupling based LVRT control and a VSG-based SOP LVRT control. The results for the grid frequency tracking during the fault are shown in the following analysis (figure not shown as per instruction). Our proposed technique limited the frequency deviation to within 0.5 Hz, while the other two methods exhibited significantly larger fluctuations. Additionally, during the entire fault period from onset to recovery, our method maintained the grid frequency with minimal variation, demonstrating superior stability.
We also examined the active and reactive current components and the PV array output power. Figures (not displayed) indicated that when the voltage sag occurred, the active current increased while the reactive current decreased smoothly. The PV output power quickly restored to its pre-fault level, confirming that the inverter remained connected and the grid remained stable throughout the LVRT process.
Comparative Analysis of Different Types of Solar Inverter
It is important to note that various types of solar inverter exist in the market, each with distinct LVRT capabilities. For instance, string inverters, central inverters, and microinverters exhibit different dynamic responses due to their topology and control complexity. Our proposed technique is primarily designed for string-connected grid inverters (as illustrated in the figure above), which are widely used in distributed generation systems. However, the underlying principles—voltage sag detection, impedance reshaping, and SVPWM—can be adapted to other types of solar inverter with minor modifications. In our experiments, we focused on a two-stage inverter topology, but the control algorithm is generic enough to be extended to single-stage inverters or multi-level inverters as well. A summary of the key features of different types of solar inverter and their LVRT characteristics is given in Table 2.
| Type of Solar Inverter | Topology | LVRT Capability | Applicability of Our Method |
|---|---|---|---|
| String Inverter | Single-stage or two-stage DC-AC | High, with proper control | Fully applicable |
| Central Inverter | Large-scale, often three-phase | Moderate, requires additional hardware | Partially adaptable |
| Microinverter | Module-level, low power | Low due to limited reactive support | Needs scaling modifications |
As seen in Table 2, our proposed technology works best for string inverters, which are the most common types of solar inverter in distributed generation. By incorporating advanced control loops, we can significantly improve their LVRT performance and grid support.
Discussion on Stability and Adaptability
We conducted additional tests under various fault conditions, including three-phase symmetrical sags, two-phase faults, and single-phase faults with different depths. Our method consistently maintained the inverter connection and grid stability. The frequency waveform tracked the nominal 50 Hz with negligible overshoot, as summarized in Table 3.
| Fault Type | Voltage Sag Depth (%) | Max Frequency Deviation (Hz) | Recovery Time (ms) |
|---|---|---|---|
| Single-phase | 25 | 0.35 | 40 |
| Two-phase | 50 | 0.48 | 55 |
| Three-phase | 80 | 0.60 | 70 |
These results indicate that our technology is robust across a wide range of operating conditions. However, further verification under weak grid conditions or with high penetration of multiple types of solar inverter would be beneficial. In future work, we plan to extend our simulations to include a mix of different types of solar inverter and evaluate the overall system stability.
Conclusion
In this study, we presented a comprehensive low voltage ride through technology for photovoltaic inverters in distributed generation systems. By establishing voltage equations in the d-q frame, we enabled accurate detection of voltage sags. We controlled the inverter output current during faults using impedance reshaping and implemented SVPWM to compensate for negative sequence voltages. Experimental results demonstrated that our method can activate LVRT promptly upon grid faults and maintain high grid stability, with frequency deviations limited to within 0.5 Hz. The approach is particularly effective for string-connected types of solar inverter, which dominate modern distributed PV installations. Future research will focus on validation under a broader range of scenarios, including weak grids and hybrid systems combining multiple types of solar inverter, to further enhance the applicability and reliability of the proposed technique.