As a researcher focused on power quality enhancement in modern distribution networks, I have observed the growing integration of solar energy resources. The intermittent, volatile, and uncontrollable nature of photovoltaic (PV) output often leads to three-phase voltage asymmetry in distribution grids, making them prone to voltage sag faults. To address this, I propose an adaptive compensation control strategy for solar inverters based on positive and negative sequence virtual synchronous generator (VSG) technology. This approach aims to improve power quality by leveraging fault-induced negative sequence power for voltage support, thereby reducing system complexity and costs.
The proliferation of solar inverters in distribution systems has transformed passive networks into active ones, but the inherent lack of inertia and damping in power electronic interfaces exacerbates voltage and frequency fluctuations. Traditional synchronous generators provide inherent stability through rotational inertia, whereas solar inverters require emulation of such characteristics. Virtual synchronous generator technology has emerged as a key solution, mimicking the external output traits of synchronous generators to enhance grid stability. However, under unbalanced grid conditions such as voltage sags, conventional VSG methods may fail to compensate effectively, leading to increased current stress and potential inverter damage. My work focuses on developing a robust control strategy that adapts to various sag scenarios without relying on extensive grid parameter knowledge.
To understand the impact of voltage sags on point of common coupling (PCC) voltages, consider a simplified PV distribution system model. The grid bus voltage is denoted as $u_s \angle 0$, the PCC voltage as $u_{pcc} \angle \delta$, and the line impedance as $R + jX$. The relationship between these voltages can be expressed as:
$$ u_{pcc} – u_s = I(R_1 + jX_1) $$
where $I$ is the current flowing through the grid impedance $R_1 + jX_1$. During faults, the grid voltage $u_s$ dips, causing PCC voltage imbalance. The voltage drop $\Delta u_{pcc}$ can be derived as:
$$ \Delta u_{pcc} = \frac{P_P R_1 + Q_P X_1}{u_{pcc}} $$
Given that transmission line reactance typically dominates resistance ($X_1 \gg R_1$), this simplifies to:
$$ \Delta u_{pcc} \approx \frac{Q_P X_1}{u_{pcc}} $$
The positive and negative sequence currents at the PCC are:
$$ I^+ = \frac{Q^+_P}{u_{pcc}}, \quad I^- = \frac{Q^-_P}{u_{pcc}} $$
Thus, the grid and PCC voltages relate through sequence components as:
$$ u^+_s = u^+_{pcc} – \omega L_1 I^+, \quad u^-_s = u^-_{pcc} – \omega L_1 I^- $$
This analysis reveals that injecting positive sequence reactive power via solar inverters can boost the positive sequence voltage at the PCC, while injecting negative sequence reactive power suppresses the negative sequence component, thereby reducing voltage unbalance. My strategy capitalizes on this principle by designing a VSG-based control that adaptively compensates for voltage sags using negative sequence power.
The core of my approach lies in an enhanced VSG control scheme that incorporates separate positive and negative sequence power loops. Traditional VSG emulates synchronous generator dynamics through active power-frequency and reactive power-voltage droop controls. The active power-frequency loop is given by:
$$ \omega = \frac{1}{J} \int \left[ \frac{1}{\omega_0} (P_{ref} – P_m) – D(\omega – \omega_0) \right] dt $$
$$ \frac{d\theta^+}{dt} = \omega – \omega_0 $$
where $\omega_0$ is the rated angular frequency, $\omega$ is the output frequency, $\theta^+$ is the electrical angle, $J$ 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 reactive power-voltage loop generates the virtual excitation voltage amplitude $u_v$:
$$ u_v = u_0 + \Delta u_q + \Delta u_u $$
with $\Delta u_q = K(Q_{ref} – Q)$ and $\Delta u_u = K_u(U_{ref} – U_v)$, where $K$ and $K_u$ are droop coefficients, $Q_{ref}$ is the reactive power reference, $Q$ is the measured reactive power, $U_{ref}$ is the voltage amplitude reference, and $U_v$ is the measured voltage amplitude. For solar inverters, these basic VSG equations need extension to handle unbalanced conditions.
I propose a decoupled sequence control strategy where positive and negative sequence components are independently regulated. Using Clarke transformation, three-phase quantities are converted to two-phase stationary components:
$$ \begin{bmatrix} F_\alpha \\ F_\beta \end{bmatrix} = T_{abc/\alpha\beta} \begin{bmatrix} F_a \\ F_b \\ F_c \end{bmatrix} = \begin{bmatrix} F^+_\alpha + F^-_\alpha \\ F^+_\beta + F^-_\beta \end{bmatrix} $$
with $T_{abc/\alpha\beta} = \sqrt{\frac{2}{3}} \begin{bmatrix} 1 & -1/2 & -1/2 \\ 0 & \sqrt{3}/2 & -\sqrt{3}/2 \end{bmatrix}$. Sequence separation is achieved via reduced-order vector controllers:
$$ G^+_{OVPI}(s) = \frac{k_v}{s – j\omega}, \quad G^-_{OVPI}(s) = \frac{k_v}{s + j\omega} $$
where $k_v$ is an integral gain and $\omega$ is the resonant frequency. The virtual impedance $Z_v = R_v + jX_v$ yields the positive sequence voltage command:
$$ u_v = Z_v I^+ = (R_v + jX_v)(i^+_\alpha + j i^+_\beta) = (R_v i^+_\alpha – X_v i^+_\beta) + j(R_v i^+_\beta + X_v i^+_\alpha) $$
Instantaneous power theory provides the sequence power calculations:
$$ P^+ = u^+_\alpha i^+_\alpha + u^+_\beta i^+_\beta, \quad Q^+ = -u^+_\alpha i^+_\beta + u^+_\beta i^+_\alpha $$
$$ P^- = u^-_\alpha i^-_\alpha + u^-_\beta i^-_\beta, \quad Q^- = -u^-_\alpha i^-_\beta + u^-_\beta i^-_\alpha $$
For negative sequence power control, I design a dedicated VSG model. The negative sequence active power-frequency loop is:
$$ \omega^-_q = \frac{1}{J} \int \left[ (P_{ref} – P^-) – D(\omega^-_q – \omega_0) \right] dt $$
$$ \frac{d\theta^-}{dt} = \omega^-_q $$
The negative sequence reactive power-voltage loop is:
$$ u^- = u + K^-_p (Q^-_{ref} – Q^-) $$
where $u^-$ is the negative sequence voltage output, $u$ is the rated voltage amplitude, $K^-_p$ is the negative sequence droop coefficient, and $Q^-_{ref}$ is the reference negative sequence reactive power. The adaptive compensation for voltage sags is realized by setting $Q^-_{ref}$ based on PCC voltage unbalance:
$$ Q^-_{ref} = \varepsilon \left( K_q + \frac{K_i}{s} \right) (u^-_{pcc} – u^-_{ref}) $$
$$ \varepsilon = d – \frac{U^-_v}{U^+_v} $$
Here, $\varepsilon$ is the voltage unbalance compensation coefficient, $d$ is the reference unbalance degree, $u^-_{ref}$ is the rated negative sequence voltage, and $K_q$ and $K_i$ are proportional and integral gains. This formulation allows solar inverters to dynamically inject negative sequence reactive power to mitigate voltage sags, regardless of fault type.
To ensure precise tracking under fault conditions, I incorporate a dual-loop voltage-current control within the VSG framework. The outer loop uses proportional-resonant (PR) controllers for error minimization in the stationary frame, while the inner loop employs proportional controllers for fast current response. The PR controller transfer function is:
$$ G_v(s) = k_{pv} + \frac{2 k_r \omega_c s}{s^2 + 2\omega_c s + \omega_o^2} $$
where $k_{pv}$ is the proportional gain, $k_r$ is the resonant gain, $\omega_o$ is the resonant frequency (e.g., 100 Hz for negative sequence), and $\omega_c$ is the cutoff frequency. The system output voltage in the $\alpha$-axis is:
$$ u_{o\alpha}(s) = G(s) u_{\alpha con} – Z_o(s) I $$
with $G(s)$ as the equivalent voltage gain and $Z_o(s)$ as the output impedance. Parameter tuning of $k_r$ and $\omega_c$ influences bandwidth and impedance characteristics, enabling effective negative sequence current injection for voltage support.
For implementation, key parameters of the VSG control for solar inverters are summarized in the following table:
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| DC link voltage setpoint | 700 V | Filter inductor L1 | 2.5 mH |
| AC phase voltage (rated) | 220 V | Filter capacitor C | 8 μF |
| Switching frequency | 10 kHz | Filter inductor L2 | 3 mH |
| Active power setpoint | 10 kW | Reactive power setpoint | 0 Var |
| Proportional gain (PR) | 100 | Resonant gain (PR) | 10 |
| Virtual inertia J | 0.5 | Damping coefficient D | 25 |
Extensive simulations were conducted to validate the proposed strategy under various voltage sag conditions. The test system comprises a solar inverter rated at 10 kW, connected to a distribution grid with programmable faults. Simulation time is set to 3 seconds: from 0 to 1 second, the grid operates normally; from 1 to 2 seconds, a voltage sag occurs; after 2 seconds, the grid recovers. Both symmetric and asymmetric sags are considered to demonstrate adaptability.
In symmetric three-phase voltage sags, where all phases experience a 20% drop (from 220 V to 176 V), conventional VSG control fails to compensate, leaving the PCC voltage depressed. With my sequence-based VSG control, the solar inverter injects compensatory reactive power, restoring PCC voltage to approximately 220 V within cycles. The negative sequence power loop remains inactive due to the absence of unbalance, but the positive sequence control effectively mitigates the sag.
For asymmetric sags, such as single-phase faults (one phase drops by 20%), conventional VSG results in sustained low voltage and elevated currents. My control activates the negative sequence compensation loop, driving $Q^-_{ref}$ to counteract the unbalance. The PCC voltage recovers to balanced conditions, with the faulty phase voltage returning to nominal levels. Similarly, in two-phase faults, the adaptive strategy minimizes voltage unbalance by injecting appropriate negative sequence reactive power.
The effectiveness of the control is further quantified by analyzing voltage unbalance factors and total harmonic distortion (THD). With the proposed method, the voltage unbalance factor during asymmetric sags is reduced to under 2%, compared to over 10% with conventional VSG. THD remains below 5%, meeting power quality standards. These results underscore the capability of solar inverters equipped with this VSG-based strategy to enhance grid resilience.
To delve deeper into the control dynamics, consider the mathematical formulation of power flow during compensation. The apparent power output of the solar inverter can be expressed as:
$$ S = P + jQ = \frac{3}{2} (u^+ i^{+*} + u^- i^{-*}) $$
where $*$ denotes complex conjugate. Expanding this yields oscillatory components at twice the grid frequency during unbalance. My control suppresses these oscillations by regulating negative sequence power to follow the reference $Q^-_{ref}$, which is dynamically adjusted per the adaptive law. The stability of the system is ensured by proper selection of VSG parameters $J$ and $D$, which provide virtual inertia and damping akin to synchronous generators.
Another aspect is the scalability of this approach for multiple solar inverters in a distribution network. By implementing the same sequence-based VSG control on each unit, coordinated voltage support can be achieved without central communication. The droop coefficients $K$ and $K^-_p$ can be tuned to share reactive power contributions proportionally among inverters, preventing overloading. This decentralized operation aligns with the plug-and-play philosophy of modern solar installations.
Furthermore, the integration of energy storage systems with solar inverters can enhance the compensation capability during prolonged sags. The proposed VSG control can be extended to manage battery power, ensuring sustained reactive power injection even when solar generation is low. This hybrid approach leverages the versatility of solar inverters as multi-functional grid assets.
In conclusion, I have presented an adaptive voltage sag compensation strategy for solar inverters using virtual synchronous generator technology. By decoupling positive and negative sequence power control and incorporating an adaptive negative sequence reactive power loop, the method effectively mitigates both symmetric and asymmetric voltage sags without requiring detailed grid parameters. The control design maintains the inherent inertia and damping benefits of VSG while adding robustness to unbalanced conditions. Simulation results validate significant improvements in PCC voltage stability and power quality. Future work will explore application to other power quality issues like voltage flicker and harmonics, as well as hardware-in-the-loop testing for real-world validation. The advancement of such intelligent controls is pivotal for enabling high penetration of solar energy into modern distribution grids.