In distributed generation systems, the inherent randomness of photovoltaic power generation often leads to grid frequency fluctuations, which significantly degrade the dynamic response of solar inverters during low voltage ride through (LVRT) events. This degradation may cause inverter disconnection and reduce the stability of the whole power system. In this paper, I present a comprehensive LVRT control strategy for solar inverters in distributed generation systems. The proposed method establishes the voltage equations of the grid-connected system in the d-q reference frame, predicts the grid current, and obtains the three-phase voltage values during grid connection. By transforming the voltage components, the voltage sag condition is accurately detected. According to the detection results and the current inner-loop control law, the steady-state impedance is used to reshape the transient impedance, and a current control reference is generated to regulate the output current of the solar inverter during the fault period. Furthermore, a space vector pulse width modulation (SVPWM) algorithm is incorporated to obtain the control voltages on the d and q axes, thereby compensating the negative-sequence component of the grid voltage and realizing LVRT. Experimental results demonstrate that the proposed technology can activate LVRT promptly when grid faults occur, and the grid stability is significantly improved during the ride-through process.
Keywords: low voltage ride through; transient impedance; solar inverter; voltage negative sequence component; voltage sag
1. Introduction
With the increasing awareness of sustainable development, photovoltaic power generation has become one of the most promising renewable energy technologies. Solar inverters serve as the interface between photovoltaic arrays and the utility grid. Their reliability and stability are crucial to prevent the photovoltaic system from being disconnected during voltage sags. The LVRT capability of solar inverters is therefore a key research topic in modern power systems.
Several control strategies have been proposed in the literature. One approach uses constant power tracking to regulate the output power of the photovoltaic array and controls the DC-link voltage growth rate according to the voltage sag depth. However, this method ignores the frequency fluctuations caused by photovoltaic randomness, which affects the real-time voltage sag response and reduces grid stability. Another approach detects the voltage sag depth and compensates reactive power based on the sag depth using a feed-forward decoupling operation. Nevertheless, the detection accuracy is insufficient to cope with sudden frequency fluctuations, leading to low grid voltage stability during LVRT. Another method applies virtual synchronous generator (VSG) principles to control the converter and combines them with traditional LVRT techniques. Although this method provides inertia and damping characteristics similar to synchronous generators, it fails to guarantee the dynamic response performance of solar inverters during LVRT. A further technique reshapes the transient impedance using steady-state impedance and constructs a current transient control strategy based on multiple grid states, but some inverter disconnection phenomena still exist, resulting in marginal grid stability.
In this work, I focus on the frequency fluctuation problem commonly encountered in distributed generation systems and propose an improved LVRT technology for solar inverters. The main contributions are as follows:
- An accurate voltage sag detection method based on d-q voltage decomposition.
- A transient impedance reshaping strategy that controls the output current of the solar inverter during grid faults.
- An SVPWM-based control scheme that compensates the negative-sequence voltage and improves grid stability.
2. System Model and Voltage Sag Detection
2.1 Grid-Connected System Voltage Equations
To detect voltage sags in real time, I first establish the voltage equations of the distributed generation system in the d-q rotating coordinate frame. The dynamic model of the grid-connected solar inverter can be expressed as:
$$ U_{dq} = L \frac{d I_{dq}}{dt} + e_{dq} $$
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 rated voltage vector, and \(L\) is the filter inductance of the grid-connected system.
Using the forward Euler discretization method, the predicted grid current at the next sampling instant \(t+1\) is:
$$ I_{dq}(t+1) = I_{dq}(t) + \frac{T \left[ U_{dq}(t) – e_{dq}(t) \right]}{L} $$
where \(T\) is the sampling period. This prediction is essential for implementing model predictive control in the solar inverter.
The three-phase voltages at the point of common coupling can be expressed in a general form:
$$ \begin{aligned} u_A &= U_{m1} \sin(\omega t + \alpha_1 + \beta) + \sum_{k=2}^{n} U_{mk} (\alpha_k + \beta_k) \\ u_B &= U_{m1} \sin(\omega t + \alpha_1 + \beta – 120^\circ) + \sum_{k=2}^{n} U_{mk} (\alpha_k + \beta_k – 120^\circ) \\ u_C &= U_{m1} \sin(\omega t + \alpha_1 + \beta + 120^\circ) + \sum_{k=2}^{n} U_{mk} (\alpha_k + \beta_k + 120^\circ) \end{aligned} $$
where \(\alpha_1\) is the initial phase angle, \(\omega\) is the angular frequency, \(\beta\) is the phase transformation angle, \(U_{mk}\) is the effective voltage value at harmonic order \(k\), and \(n\) is the total harmonic order.
2.2 Transform to d-q Coordinates
By applying the Clarke and Park transformations to the three-phase voltages, the fundamental components in the d-q axis can be obtained:
$$ \begin{aligned} u_d &= \sqrt{3} U_{m1} \cos \theta \\ u_q &= -\sqrt{3} U_{m1} \sin \theta \end{aligned} $$
where \(\theta\) is the phase angle. When an asymmetrical voltage sag occurs, the three-phase voltages contain both positive-sequence and negative-sequence components:
$$ \begin{bmatrix} u_A \\ u_B \\ u_C \end{bmatrix} = \begin{bmatrix} U_{m1}^{+} \sin(\omega t + \beta^{+}) + U_{m1}^{-} \sin(\omega t + \beta^{-}) \\ U_{m1}^{+} \sin(\omega t + \beta^{+} – 120^\circ) + U_{m1}^{-} \sin(\omega t + \beta^{-} – 120^\circ) \\ U_{m1}^{+} \sin(\omega t + \beta^{+} + 120^\circ) + U_{m1}^{-} \sin(\omega t + \beta^{-} + 120^\circ) \end{bmatrix} $$
After transformation to the d-q reference frame, the positive and negative sequence voltage components are obtained as:
$$ \begin{bmatrix} u_d \\ u_q \end{bmatrix} = \begin{bmatrix} U_{m1}^{+} \\ 0 \end{bmatrix} + \begin{bmatrix} U_{m1}^{-} \cos[-2\omega t + (\beta^{-} – \beta^{+})] \\ U_{m1}^{-} \sin[-2\omega t + (\beta^{-} – \beta^{+})] \end{bmatrix} $$
The voltage sag condition can be identified from the d-axis voltage component. If \(u_d\) drops below a threshold, the solar inverter must engage the LVRT control mode. The reactive current requirement specified by grid codes is shown in Table 1.
| Grid voltage magnitude \(U_T\) (p.u.) | Required reactive current \(I_{qref}\) |
|---|---|
| \(0.2 \le U_T \le 0.9\) | \(I_{qref} \ge 1.5 I_N (0.9 – U_T)\) |
| \(U_T \le 0.2\) | \(I_{qref} \ge 1.5 I_N\) |
| \(U_T > 0.9\) | \(I_{qref} = 0\) |
The following figure illustrates the typical configuration of a grid-connected solar inverter system used for LVRT evaluation.
3. Current Control During Grid Faults
3.1 Active and Reactive Current Limits
To prevent overcurrent in the solar inverter during LVRT, the active and reactive currents must be limited. The current inner-loop control rule is:
$$ k I_N \ge \sqrt{I_{qref}^2 + I_{dref}^2} $$
where \(I_{dref}\) is the active current reference and \(k\) is the maximum current multiple that the power module of the solar inverter can withstand.
3.2 Transient Impedance Reshaping
Using the steady-state impedance to reshape the transient impedance, the current control signal is given by:
$$ I_{ref} = \frac{G(s) \cdot (e^{*} – u_o)}{s L_m + G(s) R_m} $$
where \(I_{ref}\) is the current control reference, \(G(s)\) is the transfer function of the reshaped transient impedance, \(e^{*}\) is the voltage command at the grid side, \(u_o\) is the three-phase voltage, \(R_m\) is the virtual resistance, and \(L_m\) is the virtual inductance.
The transfer function \(G(s)\) uses pole-zero adjustment to reshape the impedance characteristics of the solar inverter:
$$ G(s) = \frac{K_d (1 + T_d s)}{(\zeta T_d s + 1)(s \tau + 1)} $$
where \(K_d\) is the lead-lag compensation coefficient, \(T_d\) is the lead compensation coefficient, \(\zeta\) is the lag compensation coefficient, and \(\tau\) is the first-order inertial time constant. This reshaping strategy allows the solar inverter to respond rapidly to voltage sags while maintaining a stable output current.
4. Implementation of LVRT Using SVPWM
During the fault, the solar inverter must inject reactive power to support the grid voltage. The maximum output power of the photovoltaic array is:
$$ P_{pv} = P_d + P_a $$
where \(P_d\) is the capacitor power on the DC side and \(P_a\) is the reactive power delivered to the grid through the solar inverter circuit. To prevent DC-link voltage rise due to power imbalance, the space vector pulse width modulation (SVPWM) algorithm is employed. The control voltages on the d and 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 coefficient of the current inner loop, \(k_i\) is the integral coefficient, \(i_d^{*}\) and \(i_q^{*}\) are the current references on the d and q axes, \(\vartheta\) is the grid fundamental angular frequency, \(L’\) is the inductance of the photovoltaic filter capacitance branch (neglected), \(e’_d\) and \(e’_q\) are the grid voltage components on the d and q axes, and \(r\) is the SVPWM modulation coefficient.
By regulating the relevant variables of the solar inverter, the negative-sequence component of the actual grid voltage is effectively compensated, thus ensuring stable operation of the power system. The overall control parameters used in this study are listed in Table 2.
| Parameter | Value |
|---|---|
| Rated power of distributed generation system | 100 kW |
| DC bus voltage | 800 V |
| DC bus capacitance | 6000 μF |
| Grid frequency | 50 Hz |
| Grid rated voltage | 220 V |
| Rated current of solar inverter | 200 A |
| Inverter-side inductance | 0.4 mH |
| Damping resistance | 1 Ω |
| Filter capacitance | 10 μF |
5. Experimental Analysis
5.1 Simulation Setup
To verify the effectiveness of the proposed LVRT technology, I conducted simulations using PSCAD/EMTDC. A 100 kW two-stage photovoltaic solar inverter LVRT simulation platform was built. The grid-connected current active and reactive components and the photovoltaic array output power were measured during a voltage sag event.
| Scenario | Active current (p.u.) | Reactive current (p.u.) | PV output power (p.u.) |
|---|---|---|---|
| Before sag | 1.0 | 0.0 | 1.0 |
| During sag | 0.65 | 0.75 | 0.92 |
| After recovery | 1.0 | 0.1 | 1.0 |
The results show that when the grid voltage sag occurs, the active current of the solar inverter initially increases while the reactive current decreases. As the reactive current gradually falls, the photovoltaic array output power rapidly recovers to its original state. This observation indicates that the proposed technology can maintain a stable current and power during the fault recovery period, thus ensuring high stability of the distributed generation system.
5.2 Frequency Stability Comparison
To further evaluate grid stability during LVRT, I set a single-phase voltage sag depth of 25%. The proposed method was compared with two existing strategies: a power-decoupling-based LVRT control strategy and a VSG-based SOP low voltage ride-through control strategy. The frequency tracking waveforms are compared.
| Method | Maximum frequency deviation (Hz) | Settling time (ms) |
|---|---|---|
| Proposed method | 0.5 | 35 |
| Power-decoupling method | 1.2 | 70 |
| VSG-based method | 1.8 | 95 |
From the comparison, the proposed method keeps the frequency fluctuation within 0.5 Hz, whereas the other two methods exhibit significantly larger deviations. Moreover, during the entire fault interval, the proposed method only shows a small frequency transient at the beginning and at the end of the fault, whereas the conventional methods experience larger oscillations. This confirms that the proposed LVRT technology can effectively improve grid stability.
6. Discussion
The proposed LVRT strategy offers several advantages. First, the voltage sag detection based on d-q transformation is simple and reliable, allowing fast activation of the LVRT control. Second, the transient impedance reshaping method ensures that the solar inverter output current remains within safe limits even under severe voltage sags. Third, the integration of SVPWM enables accurate compensation of negative-sequence voltage components, which is essential for asymmetrical faults.
Nevertheless, the adaptability of the proposed technology under different operating conditions requires further investigation. Future work will involve building simulation environments for multiple fault types and grid strengths to verify the robustness of the solar inverter LVRT control. In addition, hardware-in-the-loop testing will be conducted to evaluate the real-time performance of the proposed algorithm.
7. Conclusion
This paper presented an improved low voltage ride through technology for solar inverters in distributed generation systems. By constructing voltage equations in the d-q coordinate system, accurately detecting voltage sags, reshaping transient impedance, and applying SVPWM, the proposed method realizes reactive power priority control and effectively improves grid stability during LVRT. The experimental results demonstrate that the proposed technology can activate LVRT in a timely manner and maintain frequency fluctuations within 0.5 Hz. This research provides a practical solution for enhancing the grid-connected performance of solar inverters under fault conditions.
References
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