In modern power systems, the integration of renewable energy sources has heightened the importance of grid-connected inverters, particularly single phase inverters, which convert DC power to AC power compliant with grid standards. Single phase inverters often employ LCL filters to mitigate switching frequency harmonics, but the third-order nature of these filters introduces resonance peaks and phase lag, challenging control stability. Traditional inverter-side current feedback (ICF) control methods for single phase inverters struggle to maintain high-quality grid current under non-ideal grid voltages, as they lack mechanisms to suppress low-order harmonics. To address this, we propose an enhanced ICF control strategy incorporating capacitor current feedforward and active damping, utilizing a proportional multi-resonant controller for precise current tracking and harmonic suppression. This article details the mathematical modeling, control design, and validation through simulations and experiments, emphasizing the robustness of single phase inverters in distorted grid conditions.
The mathematical model of a single phase LCL-type grid-connected inverter forms the foundation for control design. The circuit comprises an inverter bridge, LCL filter, and grid connection, where \(L_1\) and \(L_2\) represent the inverter-side and grid-side inductances, respectively, \(C\) is the filter capacitance, and \(u_g\) denotes the grid voltage. Applying Kirchhoff’s laws, the dynamic equations are derived as:
$$L_1 \frac{di_1}{dt} = U_i – u_c$$
$$L_2 \frac{di_2}{dt} = u_c – u_g$$
$$C \frac{du_c}{dt} = i_1 – i_2$$
Here, \(i_1\) is the inverter-side current, \(i_2\) is the grid-side current, \(u_c\) is the capacitor voltage, and \(U_i\) is the inverter output voltage. These equations describe the interactions between the filter components and are essential for analyzing the system’s frequency response. The resonance frequency \(f_r\) of the LCL filter is given by:
$$f_r = \frac{1}{2\pi} \sqrt{\frac{L_1 + L_2}{L_1 L_2 C}}$$
This resonance can lead to instability if not properly damped, underscoring the need for advanced control strategies in single phase inverters.
Conventional ICF control for single phase inverters, as depicted in earlier works, relies on feedback of the inverter-side current \(i_1\) through a controller \(G_c(s)\), which could be a PI or PR type. The reference current \(i_{ref}\) is generated from the amplitude command and phase-locked loop (PLL) output. However, under non-ideal grid voltages with background harmonics, this approach fails to attenuate grid-side current distortions because the control loop does not incorporate harmonic information from the grid current. To overcome this, we introduce an improved ICF control strategy that includes capacitor current feedforward and active damping. The capacitor current \(i_c\) is fed forward to the current reference, enabling the inverter-side current loop to compensate for grid-side harmonics. Additionally, capacitor current feedback with a damping coefficient \(H\) is employed to suppress the LCL resonance peak, enhancing stability. The proportional multi-resonant controller \(G_c(s)\) is defined as:
$$G_c(s) = k_p + \sum_{h=1,3,5,7} \frac{2k_{rh}\omega_c s}{s^2 + 2\omega_c s + (h\omega_0)^2}$$
where \(k_p\) is the proportional gain, \(k_{rh}\) is the resonant gain for the \(h\)-th harmonic, \(\omega_0\) is the fundamental angular frequency, and \(\omega_c\) is the cutoff frequency to improve frequency adaptability. This controller ensures zero steady-state error for the fundamental and key low-order harmonics, critical for maintaining power quality in single phase inverters.
The design of controller parameters is pivotal for the performance of single phase inverters. First, the active damping coefficient \(H\) is determined based on the transfer function from the inverter output to the inverter-side current. The open-loop transfer function \(G_d(s)\) with active damping is expressed as:
$$G_d(s) = \frac{L_2 C s^2 + 1}{L_1 L_2 C s^3 + H L_2 C s^2 + (L_1 + L_2)s}$$
Bode plots analysis shows that increasing \(H\) reduces the resonance peak, with \(H = 4.5\) selected to balance damping and stability. Next, the proportional gain \(k_p\) is designed by considering the phase margin and bandwidth. The open-loop transfer function for the current control loop, ignoring resonant terms, is:
$$G_o(s) = \frac{k_p (L_2 C s^2 + 1) \exp(-1.5T_s s)}{L_1 L_2 C s^2 + H L_2 C s + L_1 + L_2}$$
where \(T_s\) is the sampling period. Setting the crossover frequency \(\omega_c = 4396 \, \text{rad/s}\) and ensuring a phase margin greater than \(35^\circ\) yields \(k_p = 9.5\). The resonant gains are chosen as \(k_{r1} = 200\), \(k_{r3} = 120\), \(k_{r5} = 60\), and \(k_{r7} = 20\) to achieve high gain at harmonic frequencies while maintaining adequate phase margin. The table below summarizes key parameters for a typical 5 kW single phase inverter system.
| Parameter | Value | Description |
|---|---|---|
| Rated Power | 5 kW | Output power of the single phase inverter |
| DC Voltage \(U_{dc}\) | 400 V | DC-link voltage |
| Grid Voltage \(u_g\) | 220 V (rms) | Grid voltage magnitude |
| Switching Frequency \(f_s\) | 10 kHz | PWM switching frequency |
| \(L_1\) | 1.1 mH | Inverter-side inductance |
| \(L_2\) | 1 mH | Grid-side inductance |
| \(C\) | 20 μF | Filter capacitance |
| \(H\) | 4.5 | Active damping coefficient |
| \(k_p\) | 9.5 | Proportional gain |
Simulation and experimental validations are conducted on a 5 kW single phase inverter platform to verify the proposed control strategy. Under ideal grid conditions, the grid current total harmonic distortion (THD) is 1%, demonstrating effective fundamental tracking. When the grid voltage contains 3rd, 5th, 7th, and 11th harmonics (voltage THD of 14.5%), the grid current THD remains below 2.5%, highlighting the robustness of the improved ICF control. Dynamic tests involving step changes from no-load to full-load show that the grid current stabilizes within 10 ms with less than 3% overshoot, confirming the system’s rapid response and stability. The performance metrics are summarized in the following table, illustrating the superiority of the proposed method for single phase inverters in harmonic-rich environments.
| Condition | Grid Voltage THD | Grid Current THD | Settling Time |
|---|---|---|---|
| Ideal Grid | 0% | 1.0% | N/A |
| Non-ideal Grid | 14.5% | 2.5% | 10 ms |
The enhanced performance is attributed to the multi-resonant controller’s ability to provide high gain at harmonic frequencies, as shown in the Bode plot of the current control loop. The plot indicates significant magnitude peaks at 50 Hz, 150 Hz, 250 Hz, and 350 Hz, corresponding to the fundamental, 3rd, 5th, and 7th harmonics, respectively, without compromising phase margin. This ensures accurate tracking and suppression of harmonic currents in single phase inverters. Furthermore, the capacitor current feedforward introduces grid-side harmonic information into the control loop, enabling active cancellation of distortions. The stability analysis using Nyquist criteria confirms that the system remains stable under various operating conditions, with sufficient gain and phase margins.
In conclusion, the improved ICF control strategy with capacitor current feedforward and active damping effectively addresses the limitations of traditional methods in single phase inverters under non-ideal grid voltages. The proportional multi-resonant controller ensures precise current tracking and harmonic suppression, while the active damping stabilizes the LCL filter resonance. Extensive simulations and experiments on a 5 kW single phase inverter validate the strategy’s effectiveness, demonstrating low THD and robust dynamic performance. This approach enhances the reliability and power quality of single phase inverters in modern grid applications, paving the way for wider adoption in renewable energy systems.