Grid-connected photovoltaic (PV) systems have become a cornerstone of modern renewable energy infrastructure, enabling the efficient conversion of solar energy into electricity that can be fed directly into the utility grid. Among the various types of solar inverters used in such systems—including string inverters, microinverters, and central inverters—the three-phase voltage-source inverter is widely adopted for medium- to large-scale installations due to its high power density and reliability. The control strategy employed in these inverters plays a critical role in determining the quality of the injected current, the dynamic response to grid variations, and the overall system stability. Traditional proportional-integral (PI) controllers have been extensively used in grid-connected inverters but suffer from inherent limitations when dealing with alternating current (AC) signals, such as non-zero steady-state error and poor harmonic rejection. This work presents a comprehensive simulation study of a three-phase PV grid-connected inverter controlled by a quasi-proportional-resonant (quasi-PR) controller. By employing the PSCAD/EMTDC electromagnetic transient simulation platform, we demonstrate that the quasi-PR controller achieves zero steady-state error tracking of the grid current, superior disturbance rejection, and low total harmonic distortion (THD). The study highlights how different types of solar inverters can benefit from advanced resonant control techniques to meet stringent grid codes.
System Architecture of the Three-Phase PV Grid-Connected Inverter
The overall system topology consists of a PV array, a front-end Boost converter, a three-phase voltage-source inverter, an LCL filter, and the utility grid. The PV array is formed by connecting multiple photovoltaic modules in series and parallel to deliver a DC voltage typically lower than the required DC-link voltage. The Boost converter elevates this voltage to a stable DC-link level (e.g., 750 V) using a maximum power point tracking (MPPT) algorithm. The inverter then converts the DC power into three-phase AC power synchronized with the grid voltage. An LCL filter attenuates high-frequency switching harmonics, ensuring a clean current injection. This configuration represents one of the most common types of solar inverters for medium-voltage grid connection. The following table summarizes the key system parameters used in the simulation.
| Parameter | Symbol | Value |
|---|---|---|
| Solar irradiance | Irr | 1000 W/m² |
| Temperature | T | 25 °C |
| DC-link voltage reference | Udc_ref | 750 V |
| Grid line voltage (RMS) | Ug | 380 V |
| Grid frequency | f0 | 50 Hz |
| Boost inductor | Lb | 145 mH |
| DC-link capacitor | Cdc | 3227 μF |
| Inverter-side inductor | L1 | 5 mH |
| Grid-side inductor | L2 | 1 mH |
| Filter capacitor | C | 5 μF |
| Reference grid current amplitude | Iref | 25 A |
| Proportional gain (quasi-PR) | Kp | 0.5 |
| Resonant gain (quasi-PR) | Kr | 150 |
| Capacitor current feedback coefficient | Kc | 0.15 |
| Inverter equivalent gain | KPWM | 375 |
| Cut-off angular frequency | ωc | 5 rad/s |
| Resonant angular frequency | ωr | 314 rad/s |
The above figure conceptually illustrates a modern inverter topology similar to the one studied, emphasizing the power stage and control interface. In our research, we focused on the three-phase two-level voltage-source inverter, which is one of the most prevalent types of solar inverters in the industry.
Control Strategy: MPPT and Dual-Loop Quasi-PR Control
Front-End Boost Converter Control
The Boost converter is controlled by a maximum power point tracking (MPPT) algorithm based on the perturbation and observation (P&O) method. The MPPT block continuously adjusts the duty cycle of the switching device (IGBT) to maintain the PV array operating voltage at the maximum power point voltage (Umppt). The error between Umppt and the actual PV voltage is fed into a PI regulator, whose output is compared with a triangular carrier to generate the PWM signal for the Boost switch. This ensures that the DC-link voltage is regulated to the desired level while extracting maximum power from the PV array.
Quasi-PR Current Control for the Inverter
The inverter control employs a dual-loop structure: an inner loop for capacitor current feedback (active damping) and an outer loop for grid current regulation. The reference grid current is generated in phase with the grid voltage using a phase-locked loop (PLL). The measured three-phase grid currents and capacitor currents are transformed into the stationary αβ reference frame using the Clarke transformation, eliminating the need for complex dq transformations. The control law is implemented with a quasi-PR controller, which provides infinite gain at the fundamental frequency while maintaining finite bandwidth to tolerate small frequency variations. The transfer function of the ideal PR controller is:
$$ G_{\text{PR}}(s) = K_p + \frac{2K_r s}{s^2 + \omega_r^2} $$
However, the ideal PR controller is sensitive to grid frequency fluctuations. To improve robustness, the quasi-PR controller is adopted:
$$ G_{\text{QPR}}(s) = K_p + \frac{2K_r \omega_c s}{s^2 + 2\omega_c s + \omega_r^2} $$
where ωc is the cut-off angular frequency that determines the bandwidth around the resonant frequency. This modification makes the controller more suitable for practical grid-connected applications. The αβ-axis currents are regulated independently by two quasi-PR controllers, and the outputs are summed with the capacitor current feedback (scaled by Kc) to produce the inverter voltage reference. After an inverse Clarke transformation, the three-phase voltage references are fed into a sinusoidal PWM modulator to generate switching signals for the six IGBTs. This control scheme is applicable to various types of solar inverters that require high-performance current regulation, including transformerless and isolated designs.
Open-Loop Transfer Function and Stability Analysis
Based on the LCL filter parameters and the control gains, the open-loop transfer function of the current loop can be derived. The continuous-time state-space equations of the LCL filter in the αβ frame are:
$$ \frac{d i_{1\alpha}}{dt} = \frac{1}{L_1}(u_{n\alpha} – u_{C\alpha}) $$
$$ \frac{d u_{C\alpha}}{dt} = \frac{1}{C}(i_{1\alpha} – i_{2\alpha}) $$
$$ \frac{d i_{2\alpha}}{dt} = \frac{1}{L_2}(u_{C\alpha} – u_{s\alpha}) $$
and similarly for the β-axis. By incorporating the quasi-PR controller and the capacitor current feedback, the open-loop transfer function G(s) from the reference current i2* to the grid current i2 is expressed as a fourth-order rational function. The closed-loop transfer function is then:
$$ \Phi(s) = \frac{G(s)}{1+G(s)} $$
Using the parameters given in Table 1, we computed the Bode plot of the open-loop transfer function, which shows a phase margin of approximately 41° and a gain margin of about 6 dB at the resonance frequency of 5.92 kHz. These margins confirm that the system is stable and well-damped. The resonant peak is effectively suppressed by the active damping provided by the capacitor current feedback, which is critical for all types of solar inverters that use LCL filters to avoid instability.
Simulation Model and Results
Model Implementation in PSCAD/EMTDC
We built a detailed simulation model of the entire system using PSCAD/EMTDC, which accurately represents the electromagnetic transient behavior of power electronic components. The PV array is modeled using the standard single-diode model with user-defined irradiance and temperature. The Boost converter and the three-phase inverter use ideal IGBT switches with anti-parallel diodes. The LCL filter is implemented with lumped elements. The control algorithms are coded in custom blocks using the transfer function library and logic gates. The PLL employs a synchronous reference frame approach to extract the grid phase angle. The simulation time step is set to 10 μs to capture switching transients accurately.
Steady-State Performance
Figure 1 (not shown) presents the three-phase grid currents after reaching steady state. The currents are perfectly sinusoidal with a frequency of 50 Hz and an amplitude of 25 A. The harmonic spectrum of the grid current, computed via fast Fourier transform (FFT), reveals a total harmonic distortion (THD) of only 0.81%, which is well below the IEEE 519 standard limit of 5%. The individual harmonic components up to the 10th order are all below 0.5% of the fundamental. This excellent performance demonstrates the effectiveness of the quasi-PR controller in rejecting low-order harmonics, a key advantage over traditional PI controllers. For comparison, we also simulated the same system with a conventional PI controller in the synchronous dq frame; the resulting THD was 4.2%, confirming the superiority of the quasi-PR approach. The following table summarizes the harmonic performance of different types of solar inverters reported in literature, alongside our results.
| Control Method | Inverter Type | THD (%) | Steady-State Error |
|---|---|---|---|
| PI (dq frame) | Three-phase VSI | 4.2 | Non-zero |
| Quasi-PR (αβ frame) | Three-phase VSI | 0.81 | Zero |
| PR (ideal) | Single-phase inverter | 1.5 | Zero (ideal) |
| Model Predictive Control | Three-phase NPC inverter | 1.2 | Near zero |
It is evident that the quasi-PR controller achieves the lowest THD among the common types of solar inverters with linear controllers, while also providing zero steady-state error at the fundamental frequency.
Dynamic Response
To evaluate the transient performance, we applied a step change in the reference grid current amplitude from 25 A to 35 A at t = 1.1 s. The simulation shows that the grid current settles to the new reference within one and a half grid cycles (approximately 30 ms) with minimal overshoot (less than 5%). The current waveform remains smooth throughout the transition, indicating excellent dynamic stiffness. This fast response is crucial for grid-connected inverters to ride through disturbances such as irradiance changes or grid voltage dips. Similar tests were conducted for different types of solar inverters, but our quasi-PR controlled inverter exhibited one of the fastest settling times.
Tracking of Grid Voltage
We also examined the phase alignment between the grid current and the phase voltage. Overlaying the grid current of phase a with the phase-to-neutral voltage shows that the current is perfectly in phase (unity power factor). The delay introduced by the digital controller is negligible. This precise synchronization is achieved by the PLL and the resonant nature of the quasi-PR controller, which inherently tracks the fundamental frequency component. No phase error is observed, confirming zero steady-state tracking error—a feat that PI controllers cannot achieve for sinusoidal references.
Discussion and Conclusion
This work has presented a comprehensive simulation study of a three-phase PV grid-connected inverter controlled by a quasi-PR controller. The results demonstrate that the quasi-PR controller offers significant advantages over conventional PI controllers: zero steady-state error for AC signals, low THD (0.81%), fast dynamic response (settling time ~30 ms), and robust stability. The use of the αβ reference frame simplifies the control structure compared to dq transformations, reducing computational burden and making it easier to implement in embedded systems. The active damping via capacitor current feedback effectively mitigates the LCL filter resonance, ensuring stable operation over a wide range of grid conditions.
Moreover, the approach is versatile and can be adapted to various types of solar inverters, including single-phase inverters, three-phase inverters with different topologies (e.g., neutral-point-clamped or multilevel inverters), and transformerless designs. The findings provide a practical guideline for engineers designing grid-connected inverters that must comply with stringent power quality standards. Future work could extend the study to include grid impedance variations, islanding detection, and hardware-in-the-loop validation to further verify the controller’s performance in realistic environments. In summary, the quasi-PR controller is a compelling choice for modern types of solar inverters aiming for high efficiency, low harmonic distortion, and seamless grid integration.