In recent years, the increasing penetration of renewable energy, particularly wind power, has introduced new challenges to the security and stability of power systems. Among these challenges, voltage ride-through (VRT) capabilities of wind turbines under grid faults have been extensively studied, with a focus on low-voltage ride-through (LVRT). However, unbalanced high-voltage ride-through (UHVRT) scenarios, such as those caused by asymmetrical faults or grid imbalances, remain underexplored. In my research, I address the issue of grid-connected on-grid inverters for direct-drive permanent magnet synchronous generator (DD-PMSG) systems under unbalanced transient high-voltage conditions. The proposed strategy combines sliding mode control, virtual synchronous generator (VSG) technology, and positive/negative sequence voltage-current double closed-loop PWM control to enhance fault ride-through capability and operational stability. This article details the methodology, analysis, and simulation results, emphasizing the role of the on-grid inverter in managing power fluctuations and supporting grid voltage recovery.
The integration of wind energy into power grids often leads to voltage instability due to faults like single-phase load switching or grounding issues, which can cause unbalanced voltage sags or swells. For on-grid inverters in DD-PMSG systems, these conditions may result in disconnection if not properly managed. Traditional control strategies, such as PI-based methods, may not adequately handle the dynamic and nonlinear characteristics of unbalanced faults. Therefore, I propose an optimized approach that leverages the robustness of sliding mode control to improve the on-grid inverter’s response. The core of this strategy involves decoupling positive and negative sequence components in the dq coordinate system, calculating current references to regulate active and reactive power, and implementing a VSG-based outer loop for frequency and voltage support. Through this, the on-grid inverter can maintain stable operation during high-voltage transients, ensuring continuous power delivery to the grid.
The structure of this article is as follows: First, I discuss the control strategies for the machine-side converter (MSC) and on-grid inverter, highlighting the use of VSG technology for power regulation. Second, I analyze grid voltage imbalance and its impact on inverter performance. Third, I derive the sequence-based control framework for the on-grid inverter, including current reference calculations. Fourth, I introduce the optimized sliding mode control for the inner current loop to enhance stability. Finally, I present simulation results that validate the effectiveness of the proposed method, demonstrating improved fault ride-through ability for the DD-PMSG system. Throughout, I emphasize the critical function of the on-grid inverter in balancing power and supporting grid stability under adverse conditions.
Control Strategies for DD-PMSG System
The DD-PMSG system consists of a permanent magnet synchronous generator connected to the grid via a back-to-back converter, which includes a machine-side converter (MSC) and an on-grid inverter. The MSC controls the generator to maximize torque output while minimizing losses, typically achieved by setting the d-axis current to zero (i.e., \(i_{sd} = 0\)). The voltage equations in the dq rotating coordinate system are given by:
$$u_{sd} = R_s i_{sd} + L_{sd} \frac{di_{sd}}{dt} – \omega_s L_{sq} i_{sq}$$
$$u_{sq} = R_s i_{sq} + L_{sq} \frac{di_{sq}}{dt} + \omega_s L_{sd} i_{sd} + \omega_s \psi_f$$
where \(u_{sd}\), \(u_{sq}\), \(i_{sd}\), \(i_{sq}\), \(L_{sd}\), and \(L_{sq}\) are the d- and q-axis voltages, currents, and inductances; \(\omega_s\) is the synchronous angular velocity; and \(\psi_f\) is the rotor flux linkage. The MSC employs a double closed-loop control strategy, as shown in the conceptual diagram, to regulate torque and speed. This ensures efficient power extraction from the wind turbine, which is then fed to the DC link and subsequently to the on-grid inverter for grid integration.
For the on-grid inverter, I implement virtual synchronous generator (VSG) technology to mimic the behavior of traditional synchronous generators, providing inertia and damping to the system. The VSG control equations for active and reactive power regulation are:
$$\frac{P_{ref}}{\omega_0} – \frac{P_e}{\omega} + D(\omega_0 – \omega) = J \frac{d\omega}{dt}$$
$$Q_{ref} – Q_e = K \frac{d(E – e_n)}{dt}$$
Here, \(P_{ref}\) and \(P_e\) are the reference and output active power, \(Q_{ref}\) and \(Q_e\) are the reference and output reactive power, \(\omega\) and \(\omega_0\) are the VSG and grid angular frequencies, \(E\) and \(e_n\) are the virtual and rated voltages, and \(J\), \(D\), and \(K\) are the virtual inertia, damping coefficient, and integral gain, respectively. The VSG output generates a reference voltage \(e_{ref}\) for the on-grid inverter, which is used in PWM modulation to control power flow. This approach allows the on-grid inverter to participate in frequency and voltage regulation, similar to conventional generators, thereby enhancing grid stability during faults.
Analysis of Grid Voltage Imbalance
When the grid experiences unbalanced high-voltage conditions, such as during single-phase faults, the on-grid inverter must handle positive and negative sequence components to avoid power oscillations and potential damage. In a three-wire system without a neutral connection, zero-sequence components are negligible, so only positive and negative sequences are considered. Using instantaneous symmetrical component theory and Clarke transformation, the grid voltage and current in the αβ stationary frame can be expressed as vectors in the positive sequence synchronous rotating dq frame:
$$u_g = u^+_{g\alpha} + j u^+_{g\beta} + u^-_{g\alpha} + j u^-_{g\beta} = (u^+_{gd} + j u^+_{gq}) e^{j\omega_0 t} + (u^-_{gd} + j u^-_{gq}) e^{-j2\omega_0 t} e^{j\omega_0 t}$$
$$i_g = i^+_{g\alpha} + j i^+_{g\beta} + i^-_{g\alpha} + j i^-_{g\beta} = (i^+_{gd} + j i^+_{gq}) e^{j\omega_0 t} + (i^-_{gd} + j i^-_{gq}) e^{-j2\omega_0 t} e^{j\omega_0 t}$$
where superscripts \(+\) and \(-\) denote positive and negative sequences, respectively. The complex power output of the on-grid inverter is given by:
$$S = \frac{3}{2} u_g i_g^* = P_g + j Q_g$$
The instantaneous active and reactive powers can be decomposed into average and oscillatory components:
$$P_g = P_0 + P_{c2} \cos(2\omega_0 t) + P_{s2} \sin(2\omega_0 t)$$
$$Q_g = Q_0 + Q_{c2} \cos(2\omega_0 t) + Q_{s2} \sin(2\omega_0 t)$$
with the coefficients related to sequence currents as:
$$
\begin{bmatrix}
P_0 \\
P_{c2} \\
P_{s2} \\
Q_0 \\
Q_{c2} \\
Q_{s2}
\end{bmatrix}
= \frac{3}{2}
\begin{bmatrix}
u^+_{gd} & u^+_{gq} & u^-_{gd} & u^-_{gq} \\
u^-_{gd} & u^-_{gq} & u^+_{gd} & u^+_{gq} \\
u^-_{gq} & -u^-_{gd} & -u^+_{gq} & u^+_{gd} \\
u^+_{gq} & -u^+_{gd} & u^-_{gq} & -u^-_{gd} \\
u^-_{gq} & -u^-_{gd} & u^+_{gq} & -u^+_{gd} \\
-u^-_{gd} & -u^-_{gq} & u^+_{gd} & u^+_{gq}
\end{bmatrix}
\begin{bmatrix}
i^+_{gd} \\
i^+_{gq} \\
i^-_{gd} \\
i^-_{gq}
\end{bmatrix}
$$
This formulation shows that negative sequence components introduce double-frequency oscillations in power, which can degrade the performance of the on-grid inverter and cause DC-link voltage fluctuations. Therefore, controlling these sequence currents is essential for stable operation during unbalanced faults. The on-grid inverter must regulate \(i^+_{gd}\), \(i^+_{gq}\), \(i^-_{gd}\), and \(i^-_{gq}\) to suppress power ripples and maintain grid support.
Sequence-Based Virtual Synchronous Generator Control for On-Grid Inverter
To address unbalanced conditions, I integrate sequence decomposition with VSG control for the on-grid inverter. The circuit equations in the dq frame for positive and negative sequences are:
$$e^+_d = u^+_{gd} – L \frac{di^{+*}_{gd}}{dt} – R i^{+*}_{gd} + \omega_0 L i^{+*}_{gq}$$
$$e^+_q = u^+_{gq} – L \frac{di^{+*}_{gq}}{dt} – R i^{+*}_{gq} – \omega_0 L i^{+*}_{gd}$$
$$e^-_d = u^-_{gd} – L \frac{di^{-*}_{gd}}{dt} – R i^{-*}_{gd} – \omega_0 L i^{-*}_{gq}$$
$$e^-_q = u^-_{gq} – L \frac{di^{-*}_{gq}}{dt} – R i^{-*}_{gq} + \omega_0 L i^{-*}_{gd}$$
where \(e^+_d\), \(e^+_q\), \(e^-_d\), and \(e^-_q\) are the inverter output voltage sequences, and \(i^{+*}_{gd}\), \(i^{+*}_{gq}\), \(i^{-*}_{gd}\), and \(i^{-*}_{gq}\) are the current reference values. Under normal grid conditions, negative sequence currents are zero, and the positive sequence references are derived from the VSG output. However, during unbalanced high-voltage faults, the on-grid inverter must prioritize active power stability and reactive power support. To eliminate double-frequency oscillations in active power, I set \(P_{c2} = 0\) and \(P_{s2} = 0\), leading to the following relationship for negative sequence current references:
$$
\begin{bmatrix}
i^{-*}_{d} \\
i^{-*}_{q}
\end{bmatrix}
=
\begin{bmatrix}
\frac{-u^+_{gq} u^-_{gq} + u^+_{gd} u^-_{gd}}{(u^+_{gd})^2 + (u^+_{gq})^2} & \frac{u^+_{gq} u^-_{gq} + u^+_{gd} u^-_{gq}}{(u^+_{gd})^2 + (u^+_{gq})^2} \\
\frac{u^+_{gd} u^-_{gq} + u^+_{gq} u^-_{gd}}{(u^+_{gd})^2 + (u^+_{gq})^2} & \frac{-u^+_{gd} u^-_{gd} + u^+_{gq} u^-_{gq}}{(u^+_{gd})^2 + (u^+_{gq})^2}
\end{bmatrix}
\begin{bmatrix}
i^{+*}_{d} \\
i^{+*}_{q}
\end{bmatrix}
$$
Substituting the positive sequence references from VSG control, the negative sequence currents are computed to cancel power oscillations. This sequence-based control enables the on-grid inverter to maintain balanced active power output and provide dynamic reactive power injection, supporting grid voltage recovery during faults. The overall control structure involves an outer VSG loop for power and frequency regulation and an inner sequence current loop for precise tracking. This dual-loop design ensures that the on-grid inverter adapts to grid imbalances while preserving stability.
Optimized Sliding Mode Control for Enhanced Stability
While traditional PI control can manage sequence currents, its performance may degrade under severe transients due to parameter variations and disturbances. To enhance robustness, I propose an optimized sliding mode control (SMC) for the inner current loop of the on-grid inverter. SMC offers inherent invariance to uncertainties and fast dynamic response, making it suitable for unbalanced fault conditions. The state variables for the negative sequence system are \([e^-_d, e^-_q]^T\), with inputs \([i^-_d, i^-_q]^T\). The system dynamics are:
$$\dot{i}^-_d = \frac{di^-_d}{dt} = L^{-1}(u^-_d – e^-_d + R i^-_d – \omega_0 L i^-_q)$$
$$\dot{i}^-_q = \frac{di^-_q}{dt} = L^{-1}(u^-_q – e^-_q + R i^-_q + \omega_0 L i^-_d)$$
I define a linear sliding surface as:
$$S = C_1 i^-_d + C_2 i^-_q + C_3 \text{sgn}(\Delta i^-_d) + C_4 \text{sgn}(\Delta i^-_q)$$
where \(\Delta i^-_d = i^-_d – i^{-*}_d\), \(\Delta i^-_q = i^-_q – i^{-*}_q\), and \(C_i > 0\) for \(i=1,2,3,4\). The control law is designed to ensure convergence:
$$\Delta e^-_d = e^-_d – e^{-*}_d = R \Delta i^-_d + L \dot{i}^{-*}_d – C_3 \text{sgn}(\Delta i^-_d)$$
$$\Delta e^-_q = e^-_q – e^{-*}_q = R \Delta i^-_q + L \dot{i}^{-*}_q – C_4 \text{sgn}(\Delta i^-_q)$$
Using Lyapunov stability analysis with \(V = \frac{1}{2} S^2\), I derive \(\dot{V} = S \dot{S} \leq -L^{-1} |S| < 0\), guaranteeing finite-time convergence of the sliding surface to zero. This ensures that current errors vanish rapidly, improving the on-grid inverter’s tracking performance. The SMC replaces the PI controller in the inner loop, with its output fed to the voltage outer loop for coordinated control. This optimization strengthens the on-grid inverter’s ability to withstand unbalanced high-voltage transients, reducing power fluctuations and enhancing overall system resilience.
Simulation Analysis and Results
To validate the proposed control strategy, I conducted simulation studies using MATLAB/Simulink. The DD-PMSG system parameters are listed in Table 1, representing a typical 2.5 MW setup. The on-grid inverter was tested under unbalanced high-voltage faults, specifically single-phase voltage swells to 1.15 p.u. and 1.3 p.u., each lasting 1 second. The performance was compared between traditional PI control and the optimized sliding mode control for the on-grid inverter.
| Parameter | Value |
|---|---|
| Rated Power | 2.5 MW |
| Stator Resistance | 0.78 Ω |
| Pole Pairs | 32 |
| Filter Inductance | 0.05 H |
| DC-Link Capacitance | 0.04 F |
| Rated Frequency | 50 Hz |
| d-axis Inductance | 0.835 mH |
| q-axis Inductance | 0.835 mH |
| Rotor Flux Linkage | 0.4 Wb |
| Grid Voltage (Line-to-Line) | 690 V |
| Filter Resistance | 0.01 Ω |
| DC Voltage | 1200 V |
| PI Gains (K_ip / K_ii) | 0.5 / 3 |
For the 1.15 p.u. voltage swell, the on-grid inverter with VSG and sequence control maintained active power fluctuations within ±10% of rated power during fault inception and clearance, and within ±5% during the sustained fault. Frequency deviations were limited to ±0.2% at transients and ±0.1% during the fault, with reactive power responding within 40 ms to support voltage recovery. This demonstrates the effectiveness of the sequence-based approach in stabilizing the on-grid inverter under moderate imbalances.
For the more severe 1.3 p.u. swell, the traditional PI control showed larger oscillations: active power varied up to ±30% at transients and ±6% during the fault, while frequency deviations reached ±0.5% and ±0.2%, respectively. In contrast, the optimized sliding mode control for the on-grid inverter reduced these fluctuations significantly. As summarized in Table 2, active power transients decreased by 1.7% and 1.2%, steady-state oscillations dropped by 3.4%, and frequency deviations improved by 0.04% to 0.12%. Reactive power response was faster and smoother, enhancing grid voltage support. These results highlight the superiority of sliding mode control in enhancing the on-grid inverter’s robustness during unbalanced high-voltage conditions.
| Control Method | Time (s) | Active Power Fluctuation (%) | Frequency Fluctuation (%) |
|---|---|---|---|
| PI Control | 2 (inception) | 10.8 | 0.160 |
| 2–3 (sustained) | 5.4 | 0.079 | |
| 3 (clearance) | 28.9 | 0.480 | |
| Sliding Mode Control | 2 (inception) | 9.1 | 0.120 |
| 2–3 (sustained) | 2.0 | 0.050 | |
| 3 (clearance) | 27.7 | 0.360 |
The simulations confirm that the proposed strategy, combining VSG, sequence decomposition, and sliding mode control, enables the on-grid inverter to achieve effective unbalanced high-voltage ride-through. The on-grid inverter not only regulates power flow but also contributes to grid stability by providing inertial and damping support. This is critical for modern power systems with high renewable penetration, where on-grid inverters must act as active grid-forming units rather than passive sources.
Conclusion
In this study, I have presented an optimized control strategy for on-grid inverters in DD-PMSG systems to address unbalanced transient high-voltage ride-through challenges. The approach integrates virtual synchronous generator technology for power and frequency regulation, positive/negative sequence decomposition for handling grid imbalances, and sliding mode control for enhanced current tracking robustness. By deriving current references to cancel power oscillations and implementing a robust inner loop, the on-grid inverter maintains stable operation during faults, reducing active power fluctuations and providing dynamic reactive support. Simulation results under single-phase voltage swells validate the method’s effectiveness, showing improved performance over traditional PI control. The on-grid inverter plays a pivotal role in this framework, ensuring continuous grid connection and supporting voltage recovery. Future work could explore adaptive tuning of control parameters and integration with energy storage systems to further enhance the on-grid inverter’s capabilities in diverse fault scenarios. Overall, this research contributes to advancing the fault ride-through ability of wind energy systems, promoting the reliable integration of renewables into power grids.