The integration of solar energy into distribution networks has transformed these systems from passive to active grids, leveraging the advantages of renewable resources. However, the intermittent and unpredictable nature of photovoltaic (PV) output introduces challenges such as voltage fluctuations, flicker, and frequency instability, often leading to voltage sags and imbalances. Solar inverters, as critical interfaces between PV arrays and the grid, play a pivotal role in mitigating these issues. Traditional grid-tied inverters lack the inertia and damping characteristics of synchronous generators, exacerbating system instability during disturbances. To address this, Virtual Synchronous Generator (VSG) technology has emerged, emulating the dynamic behavior of synchronous machines to enhance grid support. In this article, I propose an adaptive voltage sag compensation control strategy for solar inverters based on sequence-separated VSG techniques. This approach leverages negative-sequence power control to improve voltage quality at the point of common coupling (PCC) during unbalanced voltage sags, without relying on grid parameters or additional energy storage. The strategy is designed to be robust under various sag conditions, including symmetric and asymmetric faults, and is validated through comprehensive simulations. Throughout this discussion, the term solar inverters will be emphasized to highlight their central role in modern power systems.
The increasing penetration of solar inverters in distribution networks has heightened concerns about power quality, particularly voltage sags caused by faults, load variations, or grid imbalances. Voltage sags, defined as short-duration reductions in voltage magnitude, can disrupt sensitive loads and lead to widespread outages if not properly managed. For solar inverters, which convert DC power from PV panels to AC power for grid injection, maintaining stable operation during sags is essential to ensure continuous energy supply and grid reliability. Conventional control methods for solar inverters often focus on maximum power point tracking (MPPT) and basic grid synchronization, but they may fail to provide adequate voltage support during disturbances. VSG technology addresses this by incorporating virtual inertia and damping, mimicking the frequency and voltage regulation capabilities of synchronous generators. However, standard VSG controllers are typically designed for balanced grid conditions and may not effectively handle unbalanced voltage sags, which are common in distribution networks due to single-phase loads or faults. This gap motivates the development of advanced control strategies that enhance the fault ride-through capability of solar inverters while improving overall voltage quality.
To understand the impact of voltage sags on solar inverters, consider a simplified grid-connected PV system. The PCC voltage is influenced by grid impedance and the power injected by the solar inverter. During a sag, the grid voltage dips, causing an imbalance at the PCC that can propagate through the network. Analyzing this effect requires examining the relationship between voltage, current, and power in sequence components. For instance, the voltage drop at the PCC can be expressed as:
$$ \Delta U_{pcc} = \frac{P_P R_1 + Q_P X_1}{U_{pcc}} $$
where \( \Delta U_{pcc} \) is the voltage deviation, \( P_P \) and \( Q_P \) are the active and reactive powers at the PCC, \( R_1 \) and \( X_1 \) are the grid resistance and reactance, and \( U_{pcc} \) is the PCC voltage magnitude. In practice, the reactance dominates (\( X_1 \gg R_1 \)), simplifying the equation to:
$$ \Delta U_{pcc} \approx \frac{Q_P X_1}{U_{pcc}} $$
This indicates that reactive power injection can directly influence voltage magnitude. By extending this to sequence components, we can derive positive- and negative-sequence currents. The positive-sequence current \( I^+ \) and negative-sequence current \( I^- \) relate to reactive powers as:
$$ I^+ = \frac{Q^+_P}{U_{pcc}}, \quad I^- = \frac{Q^-_P}{U_{pcc}} $$
where \( Q^+_P \) and \( Q^-_P \) are the positive- and negative-sequence reactive powers. The grid voltage in terms of sequence components is:
$$ U^+_s = U^+_{pcc} – \omega L_1 I^+, \quad U^-_s = U^-_{pcc} – \omega L_1 I^- $$
Here, \( U^+_s \) and \( U^-_s \) are the positive- and negative-sequence grid voltages, \( \omega \) is the angular frequency, and \( L_1 \) is the grid inductance. From this, it is evident that injecting positive-sequence reactive power can boost the positive-sequence voltage, while injecting negative-sequence reactive power can suppress the negative-sequence voltage, thereby reducing voltage unbalance at the PCC. This principle forms the basis of the proposed control strategy for solar inverters, enabling adaptive compensation during sags.
The core of the proposed method lies in a sequence-separated VSG control scheme that independently manages positive- and negative-sequence powers. Traditional VSG controllers for solar inverters typically use a swing equation to emulate inertia and a voltage regulation loop to mimic excitation. The active power-frequency control is given by:
$$ \omega = \frac{1}{J} \int \left[ \frac{1}{\omega_0} (P_{ref} – P_m) – D(\omega – \omega_0) \right] dt $$
where \( \omega \) is the output angular frequency, \( \omega_0 \) is the nominal frequency, \( J \) is the virtual inertia, \( D \) is the damping coefficient, \( P_{ref} \) is the reference active power, and \( P_m \) is the mechanical power input. The voltage amplitude control is:
$$ U_v = U_0 + K(Q_{ref} – Q) + K_u(U_{ref} – U_v) $$
where \( U_v \) is the virtual excitation voltage, \( U_0 \) is the base voltage, \( K \) is the reactive power droop coefficient, \( Q_{ref} \) is the reference reactive power, \( Q \) is the measured reactive power, \( K_u \) is the voltage regulation gain, and \( U_{ref} \) is the reference voltage. For solar inverters, this standard VSG framework is enhanced by incorporating sequence separation. Using Clarke transformation, the three-phase voltages and currents are converted to αβ coordinates:
$$ \begin{bmatrix} F_\alpha \\ F_\beta \end{bmatrix} = T_{abc/\alpha\beta} \begin{bmatrix} F_a \\ F_b \\ F_c \end{bmatrix} = \begin{bmatrix} F^+_\alpha + F^-_\alpha \\ F^+_\beta + F^-_\beta \end{bmatrix} $$
with the transformation matrix:
$$ T_{abc/\alpha\beta} = \sqrt{\frac{2}{3}} \begin{bmatrix} 1 & -1/2 & -1/2 \\ 0 & \sqrt{3}/2 & -\sqrt{3}/2 \end{bmatrix} $$
To separate positive and negative sequences, a reduced-order vector controller is employed, with transfer functions:
$$ G^+_{OVPI}(s) = \frac{k_v}{s – j\omega}, \quad G^-_{OVPI}(s) = \frac{k_v}{s + j\omega} $$
where \( k_v \) is an integral gain. This allows independent control of sequence components. The negative-sequence power control is then designed to compensate for voltage sags. The negative-sequence active power-frequency loop is:
$$ \omega^-_q = \frac{1}{J} \int \left[ (P_{ref} – P^-) – D(\omega^-_q – \omega_0) \right] dt $$
and the negative-sequence reactive power-voltage loop is:
$$ U^- = U + K^-_p (Q^-_{ref} – Q^-) $$
where \( U^- \) is the negative-sequence output voltage, \( K^-_p \) is the droop coefficient for negative-sequence reactive power, and \( Q^-_{ref} \) is the reference negative-sequence reactive power. To achieve adaptive compensation, \( Q^-_{ref} \) is generated based on the voltage unbalance at the PCC:
$$ Q^-_{ref} = \epsilon \left( K_q + \frac{K_i}{s} \right) (U^-_{pcc} – U^-_{ref}) $$
with \( \epsilon = d – \frac{U^-_v}{U^+_v} \), where \( d \) is the reference voltage unbalance factor, \( U^-_{pcc} \) is the measured negative-sequence PCC voltage, \( U^-_{ref} \) is its reference value, and \( K_q \) and \( K_i \) are proportional and integral gains. This ensures that solar inverters dynamically inject negative-sequence reactive power to mitigate voltage sags, improving the overall voltage quality without requiring precise grid parameters.
For implementation in solar inverters, a dual-loop control structure is used in the αβ frame. The outer loop employs a quasi-proportional resonant (PR) controller for voltage regulation, and the inner loop uses a proportional controller for current tracking. The PR controller has the transfer function:
$$ G_v(s) = k_{pv} + \frac{2k_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
where \( k_{pv} \) is the proportional gain, \( k_r \) is the resonant gain, \( \omega_c \) is the cutoff frequency, and \( \omega_0 \) is the resonant frequency (typically 100 Hz for negative-sequence compensation). The system output voltage can be expressed as:
$$ U_o(s) = G(s) U_{con} – Z_o(s) I $$
with \( G(s) \) as the voltage gain and \( Z_o(s) \) as the output impedance. By tuning the controller parameters, the output impedance at 100 Hz is reduced, enhancing the injection of negative-sequence current and thereby improving voltage compensation. This control strategy is particularly effective for solar inverters, as it leverages their fast response capabilities without additional hardware.
To validate the proposed control strategy for solar inverters, simulation studies were conducted using Matlab/Simulink. The test system includes a PV array connected to the grid via a VSG-controlled solar inverter, with parameters summarized in Table 1. The simulations cover both symmetric and asymmetric voltage sags over a 3-second period, with normal operation from 0 to 1 s, a sag event from 1 to 2 s, and recovery thereafter. The performance is compared between traditional VSG control and the proposed sequence-separated VSG control.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| DC Link Voltage | 700 V | Filter Inductance L1 | 2.5 mH |
| AC Phase Voltage (RMS) | 220 V | Filter Capacitance C | 8 μF |
| Switching Frequency | 10 kHz | Filter Inductance L2 | 3 mH |
| Active Power Setpoint | 10 kW | Reactive Power Setpoint | 0 Var |
| Proportional Gain (Voltage) | 100 | Resonant Gain | 10 |
| Virtual Inertia J | 0.5 kg·m² | Damping Coefficient D | 25 N·m·s/rad |
| Negative-Sequence Droop K⁻_p | 0.1 | Voltage Unbalance Reference d | 0.02 |
For symmetric voltage sags, where all three phases experience a 20% drop, traditional VSG control fails to compensate, resulting in a sustained voltage of 180 V at the PCC. In contrast, the proposed control enables solar inverters to inject reactive power, restoring the voltage to 220 V within the sag period. This is achieved by adjusting the positive-sequence reactive power based on the sag depth. The compensation mechanism can be quantified using the reactive power reference:
$$ Q_{ref} = K_u (U_{ref} – U_{pcc}) + \frac{K_i}{s} (U_{ref} – U_{pcc}) $$
which is integrated into the VSG voltage loop. For asymmetric sags, such as single-phase or two-phase faults, the negative-sequence control becomes crucial. In a single-phase sag, one phase voltage drops to 178 V (20% reduction) with traditional VSG, but with the proposed method, the solar inverter injects negative-sequence reactive power to suppress the unbalance, bringing the voltage back to nominal. Similarly, for two-phase sags, the compensation works effectively, demonstrating the adaptability of the strategy. The key equations governing this process include the instantaneous power calculations in sequence components:
$$ P^+ = U^+_\alpha I^+_\alpha + U^+_\beta I^+_\beta, \quad Q^+ = -U^+_\alpha I^+_\beta + U^+_\beta I^+_\alpha $$
$$ P^- = U^-_\alpha I^-_\alpha + U^-_\beta I^-_\beta, \quad Q^- = -U^-_\alpha I^-_\beta + U^-_\beta I^-_\alpha $$
These allow the solar inverter to precisely control power flow during unbalanced conditions. The simulation results confirm that the proposed approach enhances voltage stability without overloading the solar inverter, as current limits are maintained through the dual-loop control.
Further analysis involves the impact of controller parameters on system performance. For instance, varying the resonant gain \( k_r \) in the PR controller affects the output impedance at 100 Hz. As \( k_r \) increases from 5 to 20, the impedance magnitude decreases, improving negative-sequence current injection. This is critical for solar inverters to compensate deeper sags. Additionally, the virtual inertia \( J \) and damping \( D \) can be tuned to balance response speed and stability. A larger \( J \) slows down frequency deviations, while a larger \( D \) reduces oscillations. For solar inverters operating in weak grids, these parameters must be optimized to ensure grid support during faults. The adaptive nature of the control strategy allows it to handle various sag types, including those with phase jumps or simultaneous frequency variations. This is achieved by continuously updating the sequence references based on real-time measurements, making it suitable for dynamic distribution networks with high PV penetration.
The proposed control strategy offers several advantages for solar inverters in modern power systems. First, it eliminates the need for additional devices like static VAR compensators or energy storage for voltage support, reducing costs. Second, it enhances the fault ride-through capability of solar inverters, ensuring compliance with grid codes during disturbances. Third, by leveraging VSG technology, it provides virtual inertia and damping, contributing to grid stability. However, challenges remain, such as handling harmonic distortions or multiple sag events. Future work could integrate harmonic compensation or predictive control to address these issues. Moreover, the strategy can be extended to hybrid systems combining solar inverters with other renewable sources, such as wind or battery storage, for comprehensive grid management.
In conclusion, the adaptive voltage sag compensation control based on sequence-separated VSG technology significantly improves the performance of solar inverters in distribution networks. By independently controlling positive- and negative-sequence powers, solar inverters can dynamically compensate for both symmetric and asymmetric voltage sags, enhancing voltage quality at the PCC. The control strategy is parameter-independent, easy to implement, and does not require extra hardware, making it a cost-effective solution for existing and future solar installations. Simulation results validate its effectiveness under various fault conditions, demonstrating rapid voltage restoration and stable operation. As solar inverters become increasingly prevalent, such advanced control methods will be essential for maintaining grid reliability and power quality in the era of renewable energy integration.