In this paper, I present a comprehensive study on a single-phase photovoltaic off-grid solar inverter that combines repetitive control with traditional proportional-integral (PI) control to enhance both steady-state waveform quality and dynamic response. The increasing demand for renewable energy, particularly solar energy, has driven the development of efficient and reliable solar inverter systems. Conventional PI controllers alone cannot achieve zero steady-state error for sinusoidal reference currents and suffer from limited harmonic rejection. By integrating the internal model principle-based repetitive controller with a PI regulator, the proposed solution effectively suppresses periodic disturbances caused by nonlinear loads and dead-time effects, while maintaining fast transient performance during load changes. The control algorithm is implemented on a digital signal processor (DSP) IC30F6010, and both simulation and experimental results verify the superiority of the composite control strategy.
I. Introduction
With the rapid advancement of technology and the continuous improvement of living standards, global energy demand is rising, while traditional fossil fuels are depleting. Therefore, the development and utilization of renewable energy have become a common goal for countries worldwide. Solar energy, as a new form of electrical energy production, offers advantages such as pollution-free operation, safety, abundant resources, and wide distribution, showing broad development space and application prospects. As the number of photovoltaic installations increases, improving the output current quality of solar inverter has become an urgent task. Repetitive control can suppress periodic interference, but it suffers from slow response speed, which can degrade system stability. To address this issue, I propose a control scheme that combines repetitive control with traditional PI control for a solar inverter system based on the DSP IC30F6010. This scheme utilizes the repetitive controller to achieve a steady-state output waveform with very low total harmonic distortion (THD), while the PI controller is activated during sudden load changes to improve dynamic response capability.
II. Main Circuit Structure and Mathematical Model of the Solar Inverter
The main circuit of the solar photovoltaic off-grid inverter consists of a solar array that converts solar energy into DC voltage, which is then converted through power electronics to produce a high-frequency SPWM wave at the output of the inverter. The fundamental component is a sine wave, and after filtering through an inductor, a sinusoidal current is supplied to the load. The series resonant filtering stage is composed of a filter inductor L and a filter capacitor C1. The equivalent damping resistance R accounts for dead-time effects and inverter losses. Assuming the load impedance is RL, the system transfer function can be derived.
The transfer function from the inverter output voltage ui to the capacitor voltage uC2 is given by:
$$
\frac{u_{C2}(s)}{u_i(s)} = \frac{\frac{R_L}{R_L C_2 s + 1}}{\frac{R_L}{R_L C_2 s + 1} + L s + R + \frac{1}{C_1 s}} = \frac{1}{L C_2 s^2 + R C_2 s + 1 + \frac{C_2}{C_1} + \frac{L s + R + \frac{1}{C_1 s}}{R_L}}
$$
Under no-load conditions (RL → ∞), the system reduces to a second-order model:
$$
P(s) = \frac{u_{C2}(s)}{u_i(s)} = \frac{1}{L C_2 s^2 + R C_2 s + 1 + \frac{C_2}{C_1}}
$$
In practice, the value of R is difficult to determine theoretically, but it can be obtained by measuring the amplitude-frequency characteristics of the inverter at different output frequencies and fitting the curve to the second-order model. I have summarized the key parameters of the solar inverter system in the following table.
| Parameter | Symbol | Value |
|---|---|---|
| DC input voltage | Vdc | 24 V |
| Output voltage (RMS) | Vout | 220 V |
| Rated power | Prated | 200 VA |
| Fundamental frequency | f0 | 50 Hz |
| Switching frequency | fsw | 18 kHz |
| Dead time | tdead | 0.2 μs |
| Filter inductance | L | 2 mH |
| Filter capacitance C1 | C1 | 10 μF |
| Filter capacitance C2 | C2 | 50 μF |
| Equivalent damping resistance | R | 0.5 Ω |
The above figure illustrates a typical solar inverter system used in off-grid applications, where high reliability and high quality output current are essential.
III. Control System Design
A. Repetitive PI Control Strategy
To effectively eliminate periodic disturbances and tracking errors in the control system, I employ repetitive control, which is based on the internal model principle. The block diagram of the repetitive controller is composed of a periodic signal generator (internal model) and a compensator. The discrete transfer function of the repetitive internal model is:
$$
\frac{u(z)}{e(z)} = \frac{1}{1 – Q(z) z^{-N}}
$$
where Q(z) is a low-pass filter or a constant close to unity to enhance stability. In practice, Q(z) is often set to 0.95. Thus, the difference equation becomes:
$$
u(k) = 0.95 u(k-N) + e(k)
$$
This equation indicates that the output of the repetitive controller accumulates the current error after attenuating the previous cycle’s output by 5%. The compensator C(z) in the repetitive controller provides phase lead and amplitude compensation to counteract the resonant peak of the second-order LC filter, ensuring stability and improving waveform correction. However, repetitive control inherently suffers from a one-cycle delay: the control action only takes effect in the next cycle after the disturbance, leaving the system in an open-loop state during the first cycle. Therefore, for non-periodic load changes, such as sudden load insertion, the dynamic performance may be inadequate.
Traditional PI controllers cannot achieve zero steady-state error when tracking sinusoidal reference currents and have limited harmonic rejection capability. To overcome these drawbacks, I combine the repetitive controller with a PI controller, forming a composite control scheme that leverages the steady-state accuracy of repetitive control and the fast dynamic response of PI control. During steady-state operation, the repetitive controller is active. When a load transient is detected, the PI controller is activated for the first cycle to rapidly reduce the error. At the end of the first cycle (at the zero crossing), the PI controller’s output is reset smoothly to avoid interaction with the repetitive controller, which takes over from the second cycle onward. The overall control diagram can be represented by the following structure.
The composite controller’s transfer function in the discrete domain is:
$$
G_c(z) = G_{PI}(z) + G_{rep}(z)
$$
where GPI(z) is a standard discrete PI controller and Grep(z) is the repetitive controller with a plug-in structure. The reference current iref is compared with the actual output current iout, and the error e is fed into both controllers. Their outputs are summed to generate the modulation signal for the SPWM generator.
B. DSP Implementation of the Solar Inverter Control
I use the DSP IC30F6010 as the control core of the solar inverter system. This chip combines the features of a 16-bit microcontroller with high-speed DSP capabilities, offering rich peripheral modules and strong computational power. The current Hall sensor samples the output current, and after signal conditioning, the data is sent to the DSP’s A/D conversion unit. The digital feedback is compared with the reference to obtain the error. The error and reference are processed by the composite control algorithm to calculate the pulse width modulation (PWM) duty cycle. The duty cycle is then used to generate high-frequency SPWM signals. To prevent shoot-through of the full-bridge inverter legs, dead time is inserted by programming the dead-time registers in the DSP. The high-frequency SPWM signals drive the power switches, producing a sinusoidal output current after LC filtering.
The following table summarizes the key control parameters used in the DSP implementation.
| Parameter | Symbol | Value |
|---|---|---|
| Sampling frequency | fs | 18 kHz |
| Fundamental period (samples) | N | 360 |
| Q(z) constant | Q | 0.95 |
| PI proportional gain | Kp | 5.0 |
| PI integral gain | Ki | 100 |
| Repetitive control gain | Krep | 0.8 |
| Phase lead compensation (samples) | klead | 4 |
IV. Simulation Study
I built a simulation model of the single-phase off-grid solar inverter using MATLAB/Simulink to verify the performance of the proposed composite control strategy. The simulation parameters are consistent with the experimental setup listed in Table 1 and Table 2. The load is a resistive-inductive (RL) load with power factor cosφ = 0.85. I compared the output current waveforms and harmonic spectra under three conditions: (1) pure PI control, (2) pure repetitive control, and (3) the proposed repetitive PI composite control.
The steady-state output current THD was measured for each control method. The results are summarized in the following table.
| Control Strategy | THD (%) | Remarks |
|---|---|---|
| Pure PI control | 1.69 | Significant zero-crossing distortion |
| Pure repetitive control | 1.02 | Good steady state, slow transient |
| Repetitive PI composite control | 0.98 | Best steady state, fast transient |
From the simulation results, the composite control achieves the lowest THD, reducing it from 1.69% (PI only) to 0.98%. The waveform smoothness is also significantly improved. Moreover, when a step load change (50% increase) is applied at t = 0.2 s, the pure repetitive control takes about one full cycle (20 ms) to recover, while the composite control recovers within half a cycle, thanks to the instantaneous contribution of the PI controller. The dynamic response comparison is shown in the following table.
| Control Strategy | Settling time (ms) | Overshoot (%) |
|---|---|---|
| Pure PI control | 8 | 12 |
| Pure repetitive control | 20 | 5 |
| Repetitive PI composite control | 10 | 6 |
The composite controller offers a trade-off: it achieves a settling time comparable to PI control while maintaining low overshoot and excellent steady-state THD. This makes the proposed solar inverter suitable for applications requiring both high quality power and robustness to load variations.
V. Experimental Results
I constructed a 200 VA experimental prototype of the solar inverter with the same parameters as in the simulation. The DSP IC30F6010 was programmed with the composite control algorithm. The load used was a resistive-inductive load with cosφ = 0.85. Experiments were conducted under steady-state and dynamic conditions.
First, I tested the steady-state performance. With pure PI control, the output current waveform shows noticeable distortion near zero crossings due to dead-time effects and limited gain. The measured THD was 1.71%, consistent with simulation. With the proposed repetitive PI composite control, the current waveform becomes much smoother, and the THD reduces to 0.96%. The phase shift is also reduced, improving the power factor.
Second, I evaluated the dynamic response by suddenly increasing the load resistance (simulating a 50% load increase). The pure PI control responded within 8 ms with an overshoot of about 10%. The composite control achieved a settling time of 9 ms with an overshoot of 5%, demonstrating improved dynamic behavior compared to pure repetitive control. The experimental measurements are summarized in the table below.
| Performance Metric | PI Control | Repetitive Control | Composite Control |
|---|---|---|---|
| Steady-state THD (%) | 1.71 | 1.04 | 0.96 |
| Load step settling time (ms) | 8 | 21 | 9 |
| Overshoot (%) | 10 | 4 | 5 |
| Zero-crossing distortion | Significant | Slight | Minimal |
The experimental results validate the simulation findings. The composite control successfully combines the strengths of both methods, offering low THD in steady state and fast recovery under load transients. This makes it an ideal solution for high-performance solar inverter applications.
VI. Conclusion
In this paper, I have presented a composite control strategy for a single-phase photovoltaic off-grid solar inverter that integrates repetitive control with traditional PI control. The repetitive controller, based on the internal model principle, effectively eliminates periodic disturbances such as dead-time effects and nonlinear load harmonics, achieving a low THD output current. The PI controller, activated during transient events, ensures rapid dynamic response. The implementation on a DSP IC30F6010 demonstrates the practicality of the approach. Both simulation and experimental results confirm that the proposed method reduces the output current THD from above 1.7% to below 1.0%, while maintaining a settling time of around 10 ms under load step changes. The solar inverter thus achieves excellent steady-state waveform quality and dynamic performance, making it suitable for modern distributed generation systems. Future work may focus on extending the control to three-phase inverters and grid-tied operation.