The growing adoption of solar energy systems demands enhanced grid-interaction capabilities for photovoltaic (PV) inverters. This paper presents a novel composite control strategy combining quasi-proportional resonant (PR) control and enhanced repetitive control, enabling solar inverters to simultaneously perform grid-tie functions and active harmonic compensation. The proposed approach addresses the limitations of conventional control methods while leveraging the structural similarities between PV inverters and active power filters.
1. System Architecture and Harmonic Detection
The solar inverter system integrates three critical functional blocks:
$$ \begin{cases}
P_{PV} = I_{PV} \times V_{PV} \\
Q_{comp} = \sum_{h=2}^{50} I_h^2 \times X_h
\end{cases} $$
Where \( P_{PV} \) represents photovoltaic output power and \( Q_{comp} \) denotes harmonic compensation capacity. The harmonic detection employs an enhanced ip-iq method based on instantaneous power theory:
| Component | Transformation Matrix |
|---|---|
| αβ Conversion | $$ C_{32} = \frac{2}{3}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \end{bmatrix} $$ |
| dq Conversion | $$ C = \begin{bmatrix} \sin\omega t & -\cos\omega t \\ -\cos\omega t & -\sin\omega t \end{bmatrix} $$ |
2. Composite Control Strategy
The proposed quasi-PR + repetitive control architecture overcomes individual limitations through synergistic cooperation:
$$ G_{PR}(s) = K_p + \frac{2K_r\omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
$$ G_{RC}(z) = \frac{z^{-N}K_R S(z)}{1 – Q(z)z^{-N}} $$
| Parameter | Quasi-PR | Repetitive |
|---|---|---|
| Bandwidth | 5 Hz | 25th harmonic |
| Gain (K) | K_p=10, K_r=100 | K_R=1 |
| Phase Margin | 45° | 60° |
3. Harmonic Compensation Performance
The solar inverter demonstrates superior harmonic suppression capabilities:
$$ THD = \sqrt{\sum_{h=2}^{50}\left(\frac{I_h}{I_1}\right)^2} \times 100\% $$
| Control Method | Steady-State THD | Response Time |
|---|---|---|
| Pure PR | 4.65% | 2.5 ms |
| Pure Repetitive | 2.32% | 20 ms |
| Composite Control | 1.92% | 5 ms |
4. Dynamic Response Enhancement
The hybrid control strategy achieves rapid compensation during irradiance transients:
$$ \tau_{comp} = \frac{1}{2\pi f_c} \ln\left(\frac{1}{\sqrt{1-\zeta^2}}\right) $$
Where \( f_c \) represents crossover frequency (2 kHz) and \( \zeta \) denotes damping ratio (0.707). The solar inverter maintains grid synchronization within 10 ms under 30% step load changes.
5. Implementation Considerations
Critical design factors for practical solar inverter applications:
$$ L_{filter} = \frac{V_{dc}}{6f_{sw}\Delta I_{pp}} $$
- Switching frequency (\( f_{sw} \)): 10 kHz
- DC link voltage (\( V_{dc} \)): 600 V
- Current ripple (\( \Delta I_{pp} \)): <20% rated
This integrated control approach enables solar inverters to deliver 97.8% conversion efficiency while maintaining grid current THD below 2% across varying operating conditions. The strategy demonstrates particular effectiveness in weak grid scenarios with multiple harmonic sources, making it suitable for large-scale PV plant applications.