In the realm of renewable energy integration, grid-connected solar inverters play a pivotal role in converting direct current from photovoltaic arrays into high-quality alternating current for utility networks. The proliferation of power electronic devices and nonlinear loads has escalated concerns over grid harmonic pollution, necessitating advanced control methodologies for solar inverters to ensure superior power quality. This article delves into the design and implementation of a sophisticated control scheme combining proportional-integral (PI) and repetitive control, applied to a 100 kW isolated solar inverter. The primary objective is to enhance both transient and steady-state performance, thereby minimizing harmonic distortion and adhering to stringent grid codes. The solar inverter, as a critical interface in photovoltaic systems, must exhibit robust dynamic response and exceptional steady-state accuracy. Through this work, we demonstrate that the fusion of PI and repetitive control effectively addresses periodic disturbances, a common challenge in solar inverter operations.
The topology of the isolated 100 kW solar inverter is central to its functionality. It comprises a photovoltaic array generating DC power, which is fed into a voltage-source inverter via a DC bus. The inverter’s AC output is filtered through inductors and connected to the grid via an isolation transformer configured in a Delta/Wye arrangement. This transformer, while slightly reducing efficiency, provides essential galvanic isolation for safety, a non-negotiable aspect in industrial applications. The system parameters include a DC input voltage range of 430–800 V, a maximum DC current of 250 A, and an AC rated output current of 150 A at 380 V line-to-line voltage. The switching frequency is set at 4.5 kHz, and the transformer turns ratio is 400/270. The fundamental structure ensures that the solar inverter can operate reliably under varying grid conditions, making it suitable for large-scale photovoltaic installations.
To systematically design the control system, a mathematical model of the solar inverter is derived. In the three-phase stationary frame, applying Kirchhoff’s laws yields:
$$ \frac{d}{dt} \begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix} = \frac{1}{L} \begin{bmatrix} u_a \\ u_b \\ u_c \end{bmatrix} – \frac{1}{L} \begin{bmatrix} e_a \\ e_b \\ e_c \end{bmatrix} – \frac{R}{L} \begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix} $$
where \( i_k \), \( u_k \), and \( e_k \) represent the AC side current, inverter output voltage, and grid voltage referred to the primary side of the transformer, respectively, for phases \( k = a, b, c \). \( L \) is the filter inductance, and \( R \) is the equivalent line resistance. For decoupled control, this model is transformed into the synchronous rotating d-q frame using the Park transformation matrix:
$$ C_{abc-dq} = \sqrt{\frac{2}{3}} \begin{bmatrix} \cos(\omega t) & \cos(\omega t – 2\pi/3) & \cos(\omega t + 2\pi/3) \\ -\sin(\omega t) & -\sin(\omega t – 2\pi/3) & -\sin(\omega t + 2\pi/3) \end{bmatrix} $$
Here, \( \omega \) is the grid angular frequency. With grid voltage orientation along the d-axis (\( e_d = E_m \), \( e_q = 0 \)), the dynamics become:
$$ L \frac{di_d}{dt} + R i_d = u_d – E_m + \omega L i_q $$
$$ L \frac{di_q}{dt} + R i_q = u_q – \omega L i_d $$
These equations reveal cross-coupling terms \( \omega L i_q \) and \( \omega L i_d \), which are compensated via feedforward decoupling. Defining new control variables \( u_d’ = u_d – E_m + \omega L i_q \) and \( u_q’ = u_q – \omega L i_d \) simplifies the system to two independent first-order systems, facilitating separate control of active and reactive currents. This decoupled model forms the foundation for the current control loop in the solar inverter.
The control architecture for the solar inverter integrates a dual-loop strategy: an inner current loop using PI control for fast dynamic response and an outer repetitive control loop for steady-state precision. The PI controllers are designed based on the Type-I system approach, ignoring \( R \) for simplicity. The open-loop transfer function for the d-axis current loop is:
$$ G_{ol}(s) = \frac{K_{ip}(\tau_i s + 1)}{L \tau_i s^2} $$
where \( K_{ip} \) is the proportional gain and \( \tau_i \) is the integral time constant. Using the second-order optimum method with damping ratio \( \xi = 0.707 \) and \( \tau_i = 10 \) ms, we compute \( K_{ip} = 0.5 \). Discretization with a zero-order hold at a sampling period \( T_s = 1/4500 \) s yields the discrete-time transfer function:
$$ G_{ol}(z) = \frac{0.1z}{z^2 – 2z + 1} $$
This PI controller ensures rapid tracking of current references, which are derived from power commands: \( i_d^* = P^*/E_m \) and \( i_q^* = Q^*/E_m = 0 \) for unity power factor. However, PI control alone struggles with periodic disturbances inherent in solar inverter operation due to grid harmonics and switching noise.
To mitigate periodic errors, a repetitive controller is embedded within the current loop. Repetitive control, grounded in the internal model principle, incorporates a periodic signal generator to eliminate steady-state errors at harmonic frequencies. The repetitive controller’s transfer function is:
$$ G_{rc}(z) = \frac{z^{-N} C(z)}{1 – Q(z) z^{-N}} $$
Here, \( N = 90 \) is the number of samples per fundamental period (50 Hz), \( Q(z) = 0.9 \) is a low-pass filter enhancing stability, and \( C(z) = K_r z^k C_1(z) \) is the compensator. \( K_r = 1 \) is the gain, \( k = 8 \) provides phase lead compensation, and \( C_1(z) \) is a second-order low-pass filter designed to match the plant dynamics. The compensator is tuned such that \( |K_r C_1(e^{j\omega}) W_{0i}(e^{j\omega})| \approx 1 \), where \( W_{0i}(z) \) is the closed-loop PI system. The repetitive controller’s output supplements the PI controller’s error signal, effectively learning and canceling periodic disturbances over each grid cycle. This hybrid approach empowers the solar inverter to achieve low harmonic distortion while maintaining dynamic responsiveness.
The comprehensive control system for the solar inverter is depicted in the block diagram below. The reference currents \( i_d^* \) and \( i_q^* \) are compared with measured currents transformed into the d-q frame. The error signals are processed by the repetitive controller, whose output adjusts the references for the PI controllers. The PI outputs, after decoupling feedforward, generate PWM signals for the inverter switches. This structure ensures that the solar inverter delivers sinusoidal currents with minimal phase and amplitude errors, even under distorted grid conditions.
| Parameter | Value | Description |
|---|---|---|
| Rated Power | 100 kW | Output capacity of the solar inverter |
| DC Voltage Range | 430–800 V | Input from PV array |
| AC Voltage | 380 V ±15% | Grid connection voltage |
| Switching Frequency | 4.5 kHz | PWM carrier frequency |
| Filter Inductance (L) | 2 mH | AC side filtering element |
| PI Gain (\( K_{ip} \)) | 0.5 | Proportional gain for current control |
| Repetitive Gain (\( K_r \)) | 1 | Gain for repetitive controller |
| Sampling Period (\( T_s \)) | 1/4500 s | Digital control update rate |
Experimental validation of the 100 kW isolated solar inverter was conducted to assess performance. Under steady-state conditions with pure PI control, the AC side current and voltage waveforms exhibited sinusoidal shapes but contained notable harmonics. Analysis with a dynamic signal analyzer revealed a total harmonic distortion (THD) of 3.31%, which complies with the GB/T14549-93 standard limiting harmonics to 5%. However, when the repetitive control was activated alongside PI control, the THD dropped significantly to 2.08%. This improvement underscores the repetitive controller’s efficacy in suppressing periodic disturbances, thereby reducing the solar inverter’s harmonic emission and alleviating grid pollution. The waveforms demonstrated enhanced purity, crucial for sensitive loads and grid stability.
Transient performance was evaluated by subjecting the solar inverter to step changes in current reference. The system responded swiftly, with the AC current tracking the new reference within a few milliseconds. This rapid response is attributed to the PI controller’s inherent dynamics, which remain uncompromised by the repetitive controller due to its parallel structure. The solar inverter thus achieves a balanced trade-off: fast transient response for grid support functions like frequency regulation and superior steady-state accuracy for power quality. Such capabilities are increasingly demanded in modern photovoltaic installations, where solar inverters must act as grid-forming or grid-following assets.
Further insights can be gleaned from harmonic spectrum analysis. The table below compares harmonic components as a percentage of the fundamental current for both control schemes at full load. The data clearly shows reduction across multiple harmonics, particularly at lower orders, with the PI+repetitive control strategy.
| Harmonic Order | PI Control Only (% of Fundamental) | PI + Repetitive Control (% of Fundamental) |
|---|---|---|
| 3rd | 1.8 | 0.9 |
| 5th | 1.2 | 0.6 |
| 7th | 0.8 | 0.4 |
| 9th | 0.5 | 0.2 |
| 11th | 0.3 | 0.1 |
| Total THD | 3.31% | 2.08% |
The design of the repetitive controller’s compensator \( C_1(z) \) is critical for stability. Using the closed-loop transfer function of the PI-controlled system \( W_{0i}(z) = \frac{0.1z}{z^2 – 2z + 1} \), we design \( C_1(z) \) as a second-order filter with cutoff near the system’s bandwidth. The discrete-time filter is:
$$ C_1(z) = \frac{0.161z + 0.153}{z^2 – 0.062z + 0.55} $$
This filter ensures that the product \( C_1(z) W_{0i}(z) \) has approximately unity gain and minimal phase shift in the low-frequency range, where periodic disturbances dominate. The repetitive controller’s learning mechanism updates its internal model every grid cycle, continuously refining compensation. This adaptive characteristic is beneficial for solar inverters operating in environments with varying grid impedance or harmonic background.
In practical implementation, digital signal processors (DSPs) execute the control algorithms. The computational burden of repetitive control is manageable due to the modest sample count per period (\( N = 90 \)). Memory buffers store error signals over one cycle, and the compensator processes these to generate corrective actions. The solar inverter’s firmware also incorporates safety features like overcurrent protection, islanding detection, and grid synchronization, ensuring reliable operation. The isolation transformer, while adding bulk, provides a barrier against DC injection and fault propagation, making this solar inverter design robust for commercial and utility-scale projects.
The integration of renewable energy sources like photovoltaics necessitates advanced power electronic interfaces. Solar inverters, as the heart of these systems, must evolve to meet grid codes emphasizing power quality and stability. The hybrid PI-repetitive control strategy presented here offers a viable solution for high-power isolated solar inverters. By leveraging PI control for dynamics and repetitive control for precision, the solar inverter achieves low THD and fast response. Future work could explore adaptive repetitive control to handle time-varying periodic disturbances or extend the approach to multi-level solar inverter topologies for higher voltage applications.
In conclusion, the 100 kW isolated solar inverter equipped with PI and repetitive control demonstrates excellent performance in both transient and steady-state regimes. Experimental results confirm significant harmonic reduction, with THD falling from 3.31% to 2.08%, enhancing grid compatibility. The control design methodology, encompassing mathematical modeling, parameter tuning, and digital implementation, provides a blueprint for developing high-performance solar inverters. As photovoltaic penetration grows, such advanced control techniques will be instrumental in maintaining grid integrity and maximizing renewable energy utilization. The solar inverter, thus, transcends its traditional role as a mere converter, becoming an active grid participant capable of power quality enhancement.