In the pursuit of carbon neutrality, photovoltaic (PV) power generation systems have become a cornerstone of clean energy. However, their large-scale integration introduces challenges such as reduced grid inertia and stability, often termed the “double-high” characteristic. To ensure grid security, national standards mandate that PV on-grid inverters possess low voltage ride-through (LVRT) capability, allowing them to remain connected and support the grid during voltage sags. Traditional control methods like voltage-oriented control (VOC) offer simplicity but suffer from slow dynamic response and poor robustness under disturbances. In this paper, I propose a novel hybrid control strategy that combines virtual synchronous generator (VSG) control for normal operation with a predictive repetitive control approach derived from model predictive control (MPC) and proportional resonant control (PRC) for LVRT scenarios. This strategy enhances the dynamic performance, LVRT capability, and robustness of PV on-grid inverters, while significantly reducing total harmonic distortion (THD) in grid-connected currents. Through detailed mathematical modeling, simulation, and experimental validation, I demonstrate the effectiveness of this approach in meeting stringent grid codes.
The core of any on-grid inverter control system lies in its ability to regulate power flow while maintaining stability under varying grid conditions. The on-grid inverter serves as the interface between the PV array and the utility grid, converting DC power to AC and synchronizing it with the grid. Its performance directly impacts power quality and grid reliability. The proposed hybrid strategy addresses the limitations of conventional methods by leveraging the strengths of multiple control techniques, ensuring that the on-grid inverter can seamlessly transition between normal and fault conditions.
A typical PV on-grid inverter system includes a DC-AC inverter, an LCL filter for harmonic suppression, and a grid connection point. The filter parameters, such as inductance \(L_g\) and resistance \(R_g\), are critical for performance. For design, the filter inductance can be calculated as:
$$L_g = \frac{v_{\text{rms}}}{2 \sqrt{6} f_s \Delta \Gamma}$$
where \(v_{\text{rms}}\) is the RMS grid voltage, \(f_s\) is the switching frequency, and \(\Delta \Gamma\) is the current ripple. In the synchronous rotating \(dq\)-frame, with the \(d\)-axis aligned to the grid voltage vector (\(v_{g,d} = V_m, v_{g,q} = 0\)), the system enables decoupled control of active and reactive power. The state-space representation of the on-grid inverter in discrete-time, using zero-order hold and sampling frequency \(F_s\), is given by:
$$x_n(k+1) = A_d x_n(k) + B_d u(k)$$
$$y(k) = C_d x_n(k)$$
Here, \(x_n\) is the state vector, \(u\) is the input vector, \(y\) is the output vector, and \(A_d\), \(B_d\), \(C_d\) are matrices. For an on-grid inverter, this model forms the basis for control design.
However, real-world operation involves disturbances like grid voltage harmonics or imbalances. To account for these, I extend the model to include disturbance effects. Let \(\mu(k)\) be a disturbance signal modeled by an internal model \(D(z) = \prod_{k=1}^n (1 – z^{-1} e^{j\omega_k T_s})\), where \(\omega_k\) are harmonic frequencies. The filtered state-space equation becomes:
$$x_s(k+1) = A_d x_s(k) + B_d u_s(k)$$
$$y(k+1) = -d_1 y(k) – d_2 y(k-1) – \cdots – d_a y(k-a+1) + C_d [A_d x_s(k) + B_d u_s(k)]$$
where \(x_s = D(q^{-1}) x_n(k)\) and \(u_s = D(q^{-1}) u(k)\). Defining an augmented state vector \(x(k) = [x_s(k) \quad y(k) \quad y(k-1) \quad \ldots \quad y(k-a+1)]^T\), the perturbed system is:
$$x(k+1) = A x(k) + B u_s(k)$$
$$y(k) = C x(k)$$
This formulation is crucial for designing robust control strategies for on-grid inverters, especially under LVRT conditions.
The hybrid control strategy I propose operates in two modes: normal grid-connected mode and LVRT mode. During normal operation, the on-grid inverter employs VSG control to emulate the inertia and damping of synchronous generators, enhancing grid support. The VSG dynamics are described by:
$$J \frac{d(\omega – \omega_0)}{dt} = \frac{1}{\omega_0} (P_{\text{ref}} – P_e) – D (\omega – \omega_0)$$
$$\frac{d\theta}{dt} = \omega – \omega_0$$
where \(J\) is virtual inertia, \(D\) is damping coefficient, \(P_{\text{ref}}\) is reference power, \(P_e\) is electromagnetic power, and \(\theta\) is the phase angle. The reactive power control is:
$$U_V – U_0 = K_V (Q_{\text{ref}} – Q_e)$$
with \(K_V\) as the reactive droop coefficient. VSG control improves the on-grid inverter’s ability to participate in frequency and voltage regulation, making it more grid-friendly.
When a voltage sag is detected, the system switches to LVRT mode, utilizing a predictive repetitive control (PRC) scheme. This integrates the fast response of MPC with the harmonic rejection of resonant control. Based on the perturbed model, I design a predictive controller that minimizes a cost function over a control horizon \(N_c\):
$$J = X^T \Gamma_x X + U_s^T \Gamma_u U_s$$
where \(U_s = [u_s(k) \quad u_s(k+1) \quad \ldots \quad u_s(k+N_c-1)]^T\), \(X\) is the predicted state vector, and \(\Gamma_x\), \(\Gamma_u\) are weighting matrices. The PRC ensures zero steady-state error for harmonic frequencies and provides rapid tracking during faults. To avoid transients during mode switching, I implement a vector signal holder that retains the pre-switch control signals as initial conditions for the new mode. This ensures smooth transitions, which is vital for the stability of the on-grid inverter.
The effectiveness of the hybrid control strategy is validated through simulations and experiments on a 0.5 MW PV on-grid inverter system with parameters: \(L_g = 3.4 \, \text{mH}\), \(R_g = 0.2 \, \Omega\), \(f_s = 15 \, \text{kHz}\), \(F_s = 50 \, \text{Hz}\), and DC bus voltage of 500 V. Tests include single-phase and three-phase ground faults to assess LVRT capability. The results show that the hybrid strategy maintains stable voltage and current profiles during faults, unlike traditional VOC which exhibits poor performance. Key metrics are summarized in Table 1.
| Control Strategy | THD in Steady-State (%) | THD during LVRT (%) | Voltage Recovery Time (ms) | Robustness to Disturbances |
|---|---|---|---|---|
| Traditional VOC | 4.37 | >5.0 | >100 | Low |
| Proposed Hybrid | 2.52 | <3.0 | <50 | High |
The hybrid control reduces THD to 2.52% under normal operation, well below the 5% limit, and maintains low distortion during LVRT. This is achieved through the combined action of VSG’s inertia and PRC’s harmonic suppression. The on-grid inverter’s response to disturbances is also improved, as shown in Table 2, which compares voltage deviation under grid imbalances.
| Disturbance Type | Voltage Deviation with VOC (p.u.) | Voltage Deviation with Hybrid (p.u.) | Improvement (%) |
|---|---|---|---|
| 10% Voltage Unbalance | 0.15 | 0.05 | 66.7 |
| 5 Hz Frequency Swing | 0.12 | 0.03 | 75.0 |
| Harmonic Injection (5th) | 0.08 | 0.02 | 75.0 |
The mathematical formulation of the control laws further illustrates the advantages. For the on-grid inverter, the VSG controller generates reference voltages \(v_d^*\) and \(v_q^*\) in the \(dq\)-frame:
$$v_d^* = U_V \cos \theta – \omega L_g i_q$$
$$v_q^* = U_V \sin \theta + \omega L_g i_d$$
where \(i_d\) and \(i_q\) are grid currents. During LVRT, the PRC controller adjusts these references based on error minimization. The resonant part for harmonic \(h\) is:
$$G_{\text{res},h}(s) = \frac{K_{r,h} s}{s^2 + (\omega_h)^2}$$
with \(\omega_h = 2\pi h F_s\). The overall control signal for the on-grid inverter is a combination of proportional, resonant, and predictive terms. The discrete-time implementation uses the state-space model to predict future states and optimize switching actions.
In conclusion, the hybrid control strategy significantly enhances the performance of PV on-grid inverters. By integrating VSG control for grid support and predictive repetitive control for LVRT, it addresses the limitations of conventional methods. Experimental results confirm improved dynamic response, robustness, and power quality, with THD reduced to 2.52%. This approach ensures compliance with grid codes and supports the reliable integration of renewable energy. Future work will focus on extending this strategy to multi-inverter systems and optimizing computational efficiency for real-time implementation.
The development of advanced control strategies for on-grid inverters is essential for the future power grid. As PV penetration increases, the role of the on-grid inverter evolves from mere power conversion to active grid stabilization. The proposed hybrid method represents a step forward in this direction, offering a scalable solution for various renewable energy systems. Further analysis could explore adaptive tuning of control parameters based on real-time grid conditions, enhancing the adaptability of the on-grid inverter.