In the field of renewable energy, solar energy has drawn significant global attention, and photovoltaic (PV) grid-connected technology is at the core of modern power systems. The solar inverter serves as the critical interface between the PV panels and the utility grid. Among the various control objectives, ensuring high-quality grid-injected current with low total harmonic distortion (THD) and unity power factor is paramount. In this study, I present a comprehensive investigation of an inductor current feedback control strategy applied to a single-phase solar inverter equipped with an LC output filter. The work focuses on achieving zero steady-state error for the grid current, improving dynamic response, and mitigating the impact of grid voltage distortion through feed-forward decoupling. A reference current phase advancement method is proposed to compensate for the phase shift introduced by the filter capacitor, enabling precise unity power factor operation. The control performance is validated using a 3 kW experimental prototype. The results demonstrate that the proposed strategy, combined with a quasi-proportional-resonant (PR) controller, yields a grid current THD below 3% and a power factor of 1.
The increasing penetration of solar inverters into the power grid demands high standards of power quality. Control techniques such as hysteresis control, PID control, repetitive control, model predictive control, and resonant control have been widely explored. Among these, the proportional-resonant (PR) controller offers infinite gain at the fundamental frequency, which is ideal for tracking sinusoidal references without steady-state error. Additionally, the quasi-PR controller improves robustness against frequency variations. In my work, I adopt a two-stage solar inverter architecture: a front-end boost converter stabilizes the DC-link voltage, and a full-bridge inverter with an LC filter interfaces with the grid. The inductor current feedback is selected as the inner loop due to its simplicity and inherent overcurrent protection capability. By analyzing the vector relationships and system transfer functions, I derive the necessary compensation to achieve unity power factor and low harmonic distortion.
System Configuration of the Solar Inverter
The topology of the solar inverter under study is illustrated conceptually. It consists of a DC-DC boost stage that extracts maximum power from the PV array and regulates the DC-link voltage, and a DC-AC full-bridge inverter stage that converts the DC power into AC power synchronized with the grid. The output of the inverter is filtered by a low-pass LC filter before connecting to the grid through a relay. The boost stage includes an inductor L, a diode D, and a switch T. The inverter uses four IGBT switches (T1–T4) operating at a switching frequency of 18 kHz with unipolar sinusoidal pulse-width modulation (SPWM) to reduce output voltage ripple and switching losses. The LC filter parameters are designed to attenuate high-frequency switching harmonics while maintaining low reactive power consumption.
When the phase-locked loop (PLL) detects the positive zero-crossing of the grid voltage, the controller initiates the grid-connected mode. Before the relay closes, the inverter output voltage is forced to match the grid voltage in amplitude, frequency, and phase via feed-forward control. After closing, the current loop and maximum power point tracking (MPPT) algorithm work cooperatively to inject power with unity power factor. The overall structure ensures stable and efficient operation.
LC Filter Design
The LC filter is chosen over L and LCL filters due to its balanced performance and simplicity. The transfer function of the LC filter is given by:
$$ G_{LC}(s) = \frac{U_o(s)}{U_i(s)} = \frac{\omega_L^2}{s^2 + 2\xi\omega_L s + \omega_L^2} $$
where $\omega_L = 1/\sqrt{L_f C_f}$ is the resonant angular frequency, and $\xi$ is the damping coefficient. The cutoff frequency $f_c$ is designed to be higher than the fundamental frequency (50 Hz) but lower than the lowest harmonic frequency in the PWM voltage. A typical range for $f_c$ is 100–500 Hz. The characteristic impedance $R = \sqrt{L_f/C_f}$ is chosen between 50% and 80% of the load resistance to ensure good damping and avoid resonance. The final parameters are derived as:
$$ L_f = \frac{R}{2\pi f_c}, \quad C_f = \frac{1}{2\pi f_c R} $$
Based on these guidelines, I selected $L_f = 6\,\text{mH}$ and $C_f = 16\,\mu\text{F}$, yielding a cutoff frequency of approximately 514 Hz, which satisfies the design criteria. A damping resistor may be added in series with the capacitor to suppress resonance, but in this implementation, the controller’s damping capability is sufficient.
| Parameter | Symbol | Value |
|---|---|---|
| Filter Inductance | $L_f$ | 6 mH |
| Filter Capacitance | $C_f$ | 16 μF |
| Cutoff Frequency | $f_c$ | ~514 Hz |
| Characteristic Impedance | $R$ | ~19.4 Ω |
| Switching Frequency | $f_{sw}$ | 18 kHz |
Vector Analysis of Grid-Connected Operation
To understand the phase relationships required for unity power factor, I analyze the fundamental-frequency vector diagram of the solar inverter. The inverter output voltage $u_{pwm}$, the grid voltage $u_g$, and the voltage drop across the inductor $u_L$ satisfy $u_{pwm} = u_g + u_L$. The injected grid current $i_g$ is in phase with $u_g$ for unity power factor. The capacitor current $i_C$ leads $u_g$ by 90° and has a fixed magnitude $I_C = 2\pi f C_f U_g$, where $U_g$ is the RMS grid voltage. Consequently, the inductor current $i_L$, which is the sum of $i_g$ and $i_C$, leads $u_g$ by an angle $\theta = \arctan(I_C / I_g)$. Similarly, the inductor voltage $u_L$ leads $i_L$ by 90°. Therefore, to achieve $i_g$ in phase with $u_g$, the reference current for the inductor $i_{ref}$ must be phase-advanced relative to $u_g$ by exactly $\theta$. This advancement is automatically accounted for when the controller tracks the inductor current, but the controller must have sufficient bandwidth and proper reference generation.
In the case of a proportional (P) controller, a steady-state error inevitably exists. The error manifests as both magnitude and phase discrepancies. To compensate, I deliberately advance the reference current by an additional angle $\alpha$ beyond $\theta$. The required advance angle for a P controller is derived as:
$$ \alpha = \arctan\left(\frac{2\pi f L_f I_g}{k_p U_g}\right) + \arctan\left(\frac{2\pi f C_f U_g}{I_g}\right) $$
where $k_p$ is the proportional gain. For a PR controller, the resonant term provides zero steady-state error, so the reference should be advanced exactly by $\theta$ (the natural phase lead of the inductor current). The quasi-PR controller used in this work is expressed as:
$$ G_{PR}(s) = k_p + \frac{2k_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
where $\omega_0 = 2\pi f_0$ is the fundamental frequency, $\omega_c$ is the bandwidth parameter, and $k_r$ is the resonant gain.
System Model and Control Strategy
The control system model of the solar inverter is established. The plant includes the inverter bridge (modeled as a gain $K$), the LC filter, and the grid. The current controller $G_1(s)$ takes the error between the reference current $I^*$ and the feedback inductor current $I_f$. The feed-forward path $G_n(s)$ is used to decouple the grid voltage disturbance. The output current of the inverter (grid current $I_g$) is given by:
$$ I_g = \frac{K G_1(s)}{L_f s + R + K G_1(s)} I^* – \frac{1 – K G_n(s)}{L_f s + R + K G_1(s)} U_g $$
By selecting $G_n(s) = 1/K$, the influence of $U_g$ is completely eliminated. This feed-forward decoupling enhances the robustness of the solar inverter against grid voltage harmonics and distortions. The inner current loop uses either a P controller or a quasi-PR controller. The quasi-PR controller parameters are tuned for optimal steady-state and transient performance. The design procedure involves: selecting the bandwidth $\omega_c$ (typically 5–15 rad/s), choosing the resonant gain $k_r$ to achieve sufficient gain at 50 Hz, and tuning $k_p$ for stability and disturbance rejection.
| Controller Type | $k_p$ | $k_r$ | $\omega_c$ (rad/s) |
|---|---|---|---|
| Proportional (P) | 2.5 | – | – |
| Quasi-PR | 1.8 | 80 | 10 |
The inductor current feedback loop ensures fast dynamic response and inherent overcurrent protection. The reference current $i_{ref}$ is generated by the MPPT algorithm and multiplied by the grid voltage waveform from the PLL. To compensate for the capacitor current, the reference current is phase-advanced as described earlier. The steady-state error of the P controller is mitigated by increasing the reference phase angle, while the PR controller eliminates the error entirely. The experimental comparison shows that the PR controller achieves zero steady-state error with a smaller phase advance.
Experimental Results and Analysis
I built a 3 kW solar inverter prototype to validate the proposed control strategy. The experimental setup included a Chroma 62100H-600S programmable DC power source emulating a PV array at standard test conditions (1000 W/m², 25°C, MPP voltage 250 V). The DC-link voltage was regulated at 400 V. The inverter used IGBT switches with a switching frequency of 18 kHz and unipolar SPWM. The grid voltage was 220 V/50 Hz. The THD of the grid current was measured using a power analyzer.
Under an output power of 2.5 kW with the quasi-PR controller, the grid current THD was as low as 2.8%, and the power factor was measured to be 0.999 (essentially unity). The current waveform was nearly sinusoidal and perfectly in phase with the grid voltage. The phase advance angle of the reference current relative to the grid voltage was observed to vary with power level. At 1.5 kW, the required advance was larger than at 3 kW, as the capacitor current becomes more significant at lower power.
| Power (kW) | Phase Advance (°) | Power Factor | THD (%) |
|---|---|---|---|
| 1.5 | 8.5 | 0.998 | 2.5 |
| 2.0 | 7.2 | 0.999 | 2.7 |
| 2.5 | 6.1 | 1.000 | 2.8 |
| 3.0 | 5.3 | 1.000 | 3.0 |
For comparison, the P controller required a larger phase advance angle to compensate for the steady-state error, and the resulting THD was slightly higher (around 3.8% at 2.5 kW). The relationship between the phase advance angle and the power factor is nonlinear. By adjusting the reference phase, the solar inverter can operate at leading or lagging power factors if required by grid codes. However, in this study, I focused on unity power factor operation.
| Controller | Phase Advance (°) | THD (%) | Power Factor |
|---|---|---|---|
| Proportional (P) | 9.2 | 3.8 | 0.990 |
| Quasi-PR | 6.1 | 2.8 | 1.000 |
The ability to achieve zero steady-state error with the PR controller is clearly superior. The phase advance angle for the PR controller closely matches the theoretical $\theta$ calculated from the filter parameters. The experimental results confirm the theoretical analysis and demonstrate the effectiveness of the proposed inductor current feedback control with grid voltage feed-forward decoupling.
Conclusion
In this work, I have presented a detailed study of an inductor current feedback control strategy for a solar inverter equipped with an LC filter. By analyzing the vector relationships and system transfer functions, I derived the necessary phase advancement for the reference current to achieve unity power factor. The adoption of a quasi-PR controller together with grid voltage feed-forward decoupling effectively eliminates steady-state error and suppresses grid voltage disturbances. Experimental results from a 3 kW prototype verify that the output current of the solar inverter can faithfully track the grid voltage frequency and phase, achieving a THD below 3% and a power factor of 1. The proposed control strategy is robust, simple to implement, and well-suited for practical photovoltaic grid-connected systems. Future work may extend this approach to three-phase solar inverters and include adaptive phase compensation for varying grid conditions.