In recent years, the widespread adoption of photovoltaic power generation has made grid-connected solar inverters a critical component in renewable energy systems. The quality of power injected into the grid depends heavily on the control strategy employed in the solar inverter. While proportional-integral (PI) control is widely used in industrial applications due to its fast dynamic response, it suffers from limited ability to suppress periodic disturbances caused by grid harmonics and nonlinear loads. To overcome this limitation, we have developed a 100 kW isolated solar inverter that combines PI control with repetitive control. This hybrid approach ensures both excellent steady-state waveform quality and rapid transient response, effectively reducing harmonic pollution to the grid. In this paper, we present the detailed design, mathematical modeling, control architecture, and experimental validation of the proposed solar inverter system.
1. Topology of the 100 kW Isolated Solar Inverter
The topology of the 100 kW isolated solar inverter is shown in the figure below. The system consists of a photovoltaic array providing DC voltage, a voltage-source inverter (VSI), an L filter on the AC side, and a Δ/Y isolation transformer for grid connection. The isolation transformer enhances safety by eliminating galvanic coupling between the inverter and the grid, although it slightly reduces overall efficiency. In industrial products, safety is paramount, and thus most grid-tied solar inverters incorporate isolation transformers.
Key parameters of the solar inverter are listed in Table 1.
| Parameter | Value |
|---|---|
| Rated Power | 100 kW |
| DC Input Voltage Range | 430 – 800 V |
| Maximum DC Current | 250 A |
| Nominal AC Output Current | 150 A |
| Grid Voltage Range | 380 V (-10% ~ +15%) |
| Switching Frequency | 4.5 kHz |
| Transformer Ratio (Δ/Y) | 400 V / 270 V |
| Filter Inductance (L) | Designed per system requirements |
| Line Equivalent Resistance (R) | Negligible |
2. Mathematical Model of the Solar Inverter
Based on Kirchhoff’s voltage law, the three-phase stationary coordinate model of the grid-connected solar inverter is given by:
$$ \frac{d}{dt} \begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix} = \frac{1}{L} \begin{bmatrix} u_a \\ u_b \\ u_c \end{bmatrix} – \frac{1}{L} \begin{bmatrix} e_a \\ e_b \\ e_c \end{bmatrix} – \frac{R}{L} \begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix} $$
where \(u_k\) are the inverter output phase voltages, \(e_k\) are the grid phase voltages referred to the primary side of the transformer, and \(k = a, b, c\). To achieve decoupled control of active and reactive power, we apply the d-q transformation using the following matrix:
$$ C_{abc-dq} = \frac{2}{3} \sqrt{\begin{bmatrix} \cos\omega t & \cos(\omega t – 2\pi/3) & \cos(\omega t + 2\pi/3) \\ -\sin\omega t & -\sin(\omega t – 2\pi/3) & -\sin(\omega t + 2\pi/3) \end{bmatrix}} $$
After transformation, the d-q model becomes:
$$ L \frac{di_d}{dt} + R i_d = u_d – e_d + \omega L i_q $$
$$ L \frac{di_q}{dt} + R i_q = u_q – e_q + \omega L i_d $$
Using grid voltage orientation, we align the d-axis with the grid voltage vector, so \(e_d = E_m\) (peak grid voltage) and \(e_q = 0\). Then, we define new variables:
$$ u’_d = u_d – E_m + \omega L i_q $$
$$ u’_q = u_q – \omega L i_d $$
Thus, the system simplifies to two independent first-order systems:
$$ L \frac{di_d}{dt} + R i_d = u’_d $$
$$ L \frac{di_q}{dt} + R i_q = u’_q $$
The reference voltages for the d and q axes are:
$$ u^*_d = u’_d + E_m – \omega L i_q $$
$$ u^*_q = u’_q + \omega L i_d $$
3. Control System Design for the Solar Inverter
3.1 PI Controller Design
We design the PI controller for the current loops using the I-type system approach. The d-axis current loop (neglecting R) is shown in the block diagram. The closed-loop transfer function of the digital controller (with sampling period T = 1/4500 s) is:
$$ G(z) = \left. G(s) \right|_{s = \frac{1 – z^{-1}}{T}} = \frac{0.1 z}{z^2 – 2z + 1} $$
Using the second-order optimal tuning method with damping ratio \(\xi = 0.707\) and integral time constant \(\tau_i = 10\,\text{ms}\), we obtain the proportional gain \(K_{ip} = 0.5\). The open-loop transfer function in the s-domain is:
$$ G(s) = \frac{K_{ip} \tau_i s + K_{ip}}{L \tau_i s^2} $$
Discretizing with a zero-order hold yields the digital PI controller suitable for implementation in the solar inverter’s digital signal processor.
3.2 Repetitive Controller Design
To suppress periodic disturbances (e.g., grid harmonics), we integrate a repetitive controller in parallel with the PI controller. The repetitive controller is based on the internal model principle and consists of a repetitive signal generator and a compensator. Its z-domain model is:
$$ G_{rp}(z) = \frac{z^{-N} C(z)}{1 – Q(z) z^{-N}} $$
where \(N = 90\) is the number of samples per fundamental period (sampling frequency 4.5 kHz, fundamental 50 Hz). \(Q(z)\) is typically a constant slightly less than 1 (we use \(Q(z) = 0.9\)) or a low-pass filter. \(C(z)\) is the compensator, chosen as:
$$ C(z) = K_r z^k C_1(z) $$
We set the repetitive control gain \(K_r = 1\), the phase-lead steps \(k = 8\), and \(C_1(z)\) as a second-order low-pass filter with cutoff frequency similar to the plant. The resulting compensator satisfies \(K_r C_1(z) W_{0i}(z) \approx 1\) in magnitude. The discrete-time form of \(C_1(z) W_{0i}(z)\) is:
$$ G_1(z) = \frac{0.161 z + 0.153}{z^2 – 0.062 z + 0.55} $$
The combined control structure for the d-axis current loop is shown in the block diagram (refer to the earlier figure). The error between the reference current \(i_d^*\) and the actual current \(i_d\) passes through the repetitive controller, generating a compensation signal that is added to the PI controller input. Thus, the PI controller receives a modified reference that effectively rejects periodic disturbances.
4. Experimental Results and Discussion
We built a 100 kW isolated solar inverter prototype using the proposed control strategy. Steady-state and transient tests were conducted under grid-connected conditions. The grid voltage was 380 V (-10% ~ +15%), and the DC side voltage ranged from 430 V to 800 V. The switching frequency was 4.5 kHz.
Table 2 summarizes the harmonic performance comparison between the pure PI control and the combined PI+repetitive control.
| Control Strategy | Current THD (%) |
|---|---|
| Pure PI Control | 3.31 |
| PI + Repetitive Control | 2.08 |
The results clearly show that the combined control reduces the THD from 3.31% to 2.08%, both within the IEEE 519 and GB/T14549-93 limits (5%). The repetitive controller effectively attenuates low-order harmonics caused by grid distortion and nonlinear loads.
Dynamic performance was also evaluated. When the reference current was stepped, the solar inverter’s AC current responded quickly, tracking the new reference within a few cycles. The transient overshoot and settling time remained comparable to the pure PI case, confirming that the repetitive controller does not degrade the dynamic response.
Figure 7 (not shown here) displays the steady-state voltage and current waveforms under PI+repetitive control. The sinusoidal quality is excellent, with minimal distortion. The solar inverter operates reliably and efficiently, delivering high-quality power to the grid.
5. Conclusion
We have developed a 100 kW isolated solar inverter that combines PI control with repetitive control. The PI loop ensures fast current tracking, while the repetitive controller compensates for periodic disturbances, significantly reducing output current harmonics. Experimental results confirm that the total harmonic distortion is reduced from 3.31% to 2.08%, well below the standard limit. The dynamic response remains fast and stable. This hybrid control strategy is well-suited for large-scale grid-tied solar inverter applications where both power quality and transient performance are essential.