In recent years, the widespread adoption of renewable energy sources has highlighted the importance of efficient grid integration, particularly for photovoltaic (PV) systems. As a key component, the three phase inverter plays a critical role in converting DC power from PV arrays into AC power suitable for grid connection. This paper investigates a control strategy for a two-stage three phase inverter system aimed at improving grid connection efficiency and current quality. The proposed approach leverages advanced transformations and modulation techniques to achieve stable operation under varying environmental conditions. I will begin by outlining the system topology, followed by a detailed explanation of the control methodology, simulation results, and conclusions.
The two-stage three phase inverter system consists of a PV array, a DC-DC boost converter, a three-phase full-bridge inverter, and an LCL filter for grid integration. The PV array, modeled using SunPower SPR-305E-WHT-D monocrystalline modules, is configured as a 4×8 array to deliver approximately 6 kW of power. Key parameters of the PV array are summarized in Table 1. The DC-DC boost converter employs a maximum power point tracking (MPPT) algorithm based on a variable-step perturb and observe method to optimize power extraction and provide a stable DC voltage to the inverter stage. The three phase inverter utilizes insulated gate bipolar transistors (IGBTs) in a three-level topology, with each phase comprising four IGBTs, four freewheeling diodes, and two clamping diodes. The DC link is supported by two series capacitors to balance voltage. Finally, the LCL filter mitigates high-frequency harmonics, ensuring compliance with grid standards for power quality.
| Parameter | Value |
|---|---|
| Short-Circuit Current (A) | 5.96 |
| Open-Circuit Voltage (V) | 64.2 |
| Maximum Power (W) | 305.226 |
| Voltage at Maximum Power Point (V) | 54.7 |
| Current at Maximum Power Point (A) | 5.58 |
The control strategy for the three phase inverter is centered on a dual-loop system comprising an inner current loop and an outer voltage loop. This structure enhances dynamic response and stability. The inner loop regulates the grid current using Park transformations to convert AC quantities from the stationary reference frame (abc) to the synchronous rotating frame (dq). Specifically, the grid voltages \(U_a\), \(U_b\), and \(U_c\) are transformed using the Clarke and Park transformations to obtain the phase angle \(\theta\) and the dq components. The transformations are defined as follows:
First, the Clarke transformation converts three-phase voltages to the \(\alpha\beta\) frame:
$$ e_\alpha = \frac{2}{3} \left( U_a – \frac{1}{2} U_b – \frac{1}{2} U_c \right) $$
$$ e_\beta = \frac{\sqrt{3}}{3} \left( U_b – U_c \right) $$
The phase angle \(\theta\) is derived as:
$$ \sin \theta = \frac{e_\beta}{\sqrt{e_\alpha^2 + e_\beta^2}} $$
$$ \cos \theta = \frac{e_\alpha}{\sqrt{e_\alpha^2 + e_\beta^2}} $$
Subsequently, the Park transformation converts currents \(i_a\), \(i_b\), and \(i_c\) to the dq frame:
$$ \begin{bmatrix} i_d \\ i_q \end{bmatrix} = \frac{2}{3} \begin{bmatrix} \sin \theta & \sin(\theta – \frac{2\pi}{3}) & \sin(\theta + \frac{2\pi}{3}) \\ \cos \theta & \cos(\theta – \frac{2\pi}{3}) & \cos(\theta + \frac{2\pi}{3}) \end{bmatrix} \begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix} $$
In the dq frame, the grid voltage vector is aligned with the d-axis, simplifying power control. The instantaneous active power \(p\) and reactive power \(q\) are expressed as:
$$ p = \frac{3}{2} (e_d i_d + e_q i_q) $$
$$ q = \frac{3}{2} (e_d i_q – e_q i_d) $$
With grid voltage orientation, \(e_q = 0\), so these simplify to:
$$ p = \frac{3}{2} e_d i_d $$
$$ q = \frac{3}{2} e_d i_q $$
Thus, by controlling \(i_d\) and \(i_q\), the active and reactive power outputs of the three phase inverter can be regulated independently. The reference for \(i_d\) is generated from the outer voltage loop, which maintains the DC link voltage, while \(i_q^*\) is set to zero to minimize reactive power and enhance efficiency.
The inner current loop employs proportional-integral (PI) controllers to track reference currents. The d-axis current reference \(i_d^*\) is derived from the DC voltage error, while the q-axis reference \(i_q^*\) is zero. The outputs of the PI controllers, \(U_d^*\) and \(U_q^*\), are transformed back to the abc frame using inverse Park transformations and fed into the space vector pulse width modulation (SVPWM) block. The SVPWM technique generates switching signals for the IGBTs, ensuring sinusoidal output currents with minimal harmonic distortion. The modulation process involves determining the sector of the voltage vector and calculating duty cycles for the inverter switches. This approach improves voltage utilization and reduces switching losses in the three phase inverter.
The outer voltage loop stabilizes the DC link voltage by comparing the measured voltage \(V_{dc}\) with the reference \(V_{dc}^*\). The error is processed through a PI controller to produce the reference current \(i_{dc}^*\), which is then used to adjust \(i_d^*\). The relationship between the DC current and d-axis current is given by:
$$ i_{dc} = \frac{3 e_d i_d}{2 U_{DC}} $$
where \(U_{DC}\) is the nominal DC voltage. This ensures that the three phase inverter maintains power balance under varying load conditions. The control parameters for the PI controllers are tuned to achieve fast response and stability, as summarized in Table 2.
| Parameter | Value |
|---|---|
| Proportional Gain (kp) for Current Loop | 0.5 |
| Integral Gain (ki) for Current Loop | 100 |
| Proportional Gain (kp) for Voltage Loop | 0.1 |
| Integral Gain (ki) for Voltage Loop | 10 |
| LCL Filter Inductance (H) | 500e-6 |
| LCL Filter Capacitance (F) | 500e-6 |
To validate the control strategy, I developed a simulation model in MATLAB/Simulink. The PV array was subjected to standard test conditions (irradiance of 1000 W/m² and temperature of 25°C). The MPPT algorithm successfully tracked the maximum power point, as shown in Figure 1, where the power stabilizes at approximately 6 kW after 0.07 seconds. The grid connection performance was evaluated by analyzing voltage and current waveforms. After synchronization, the three phase inverter output currents exhibited minimal distortion and maintained phase alignment with the grid voltages. The voltage waveform remained stable at around 380 V, with current peaks at 15 A, demonstrating effective grid integration.
The harmonic analysis of the output current revealed a total harmonic distortion (THD) of 4.67%, which is within the acceptable limit of 5% for grid-connected systems. The frequency spectrum, centered at 50 Hz, indicated that the LCL filter effectively suppressed high-frequency components. This underscores the robustness of the proposed control strategy for the three phase inverter in maintaining power quality. Additionally, the system showed rapid recovery under transient conditions, such as changes in irradiance, highlighting the adaptability of the MPPT and control loops.
In conclusion, this research presents a comprehensive control strategy for a two-stage three phase photovoltaic inverter, focusing on grid connection efficiency and current quality. The use of Park transformations and SVPWM enables precise power control and harmonic mitigation. Simulation results confirm that the three phase inverter achieves stable operation with low THD and fast dynamic response. Future work could explore advanced techniques for handling higher-order harmonics and improving power factor correction under diverse load conditions. Overall, the proposed approach offers a reliable solution for integrating photovoltaic systems into the grid, with potential applications in larger-scale renewable energy projects.