We present a comprehensive study on a frequency adaptive proportional resonant (PR) control strategy designed for F-type three-level grid-connected inverters. The proposed method addresses the key challenge of high harmonic distortion in grid-connected currents under unbalanced grid voltage and frequency fluctuation conditions. Our work demonstrates that by dynamically adjusting the resonant frequency of the PR controller to match the actual grid frequency, the total harmonic distortion (THD) of the injected current is significantly reduced compared to conventional quasi-PR control. Experimental validation on a 2.2 kW F-type inverter prototype confirms the effectiveness of our approach, with THD reductions of 0.35% under voltage imbalance and 0.45% under frequency deviation. This study provides a robust solution for improving power quality in modern renewable energy systems, particularly for various types of solar inverters used in distributed generation.
Introduction
In the process of China’s energy structure transformation and the goal of achieving carbon peak and carbon neutrality, three-level inverters have become a key technology for promoting efficient grid-connected renewable energy generation due to their low current harmonic content and high efficiency. However, traditional three-level inverter topologies, such as NPC and T-type, suffer from significant cost and loss increases as power levels grow. The T-type topology, in particular, requires switches with higher voltage ratings, leading to high costs and reduced efficiency. The F-type three-level inverter topology was proposed to solve this issue, as it requires no clamping diodes and only one switch per phase leg sustains the full DC bus voltage, while the others endure only half. This design minimizes cost at the same power level. Our research focuses on improving the control performance of this promising topology under non-ideal grid conditions.
The control objective of grid-connected inverters is to synchronize the frequency and phase of the output current with the grid voltage, ensuring unity power factor operation and reducing current harmonics. Proportional resonant (PR) control is widely used in power electronic converters, especially grid-connected inverters, due to its ability to provide high gain at a specific frequency without introducing additional phase lag. However, traditional PR control suffers from performance degradation when the grid frequency deviates from its nominal value. Multi-resonant PR control architectures introduce stability concerns due to high-order resonance. Researchers have proposed parameter adaptive tuning strategies and capacitive current feedback mechanisms to mitigate these issues. Nevertheless, under unbalanced and frequency-varying grid conditions, the steady-state error suppression capability of conventional quasi-PR control remains insufficient.
To overcome these limitations, we propose a frequency adaptive PR control strategy for the F-type three-level grid-connected inverter. Our method continuously monitors the grid frequency and updates the resonant frequency of the PR controller in real time, ensuring infinite gain at the fundamental frequency even under grid frequency deviations. This approach significantly enhances the grid-connected power quality, making it suitable for various types of solar inverters operating in weak grid environments.
Working Principle of the F-Type Three-Level Inverter
The main circuit of the F-type grid-connected inverter is shown in the conceptual diagram (not referenced by number). The DC side voltage $U_{dc}$ can be provided by batteries or a front-end DC/DC converter. All switching devices are fully controlled. The three-phase bridge outputs $U_a$, $U_b$, $U_c$ are connected to the grid through an LCL filter. The F-type inverter can connect each phase output to the positive (P), neutral (O), or negative (N) DC bus capacitors, requiring a switching state transition mechanism independent of the load current direction.
Taking phase A as an example, the relationship between switching device states and phase current is summarized in the following table. The operation principle ensures that regardless of the current direction, the current flows smoothly through the inverter branches.
| $S_{x1}$ | $S_{x2}$ | $S_{x3}$ | $S_{x4}$ | Output Voltage $U_{xo}$ | State |
|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | $U_{dc}/2$ | P |
| 0 | 1 | 1 | 0 | 0 | O |
| 0 | 1 | 0 | 1 | $-U_{dc}/2$ | N |
The switches $S_{x1}$ and $S_{x2}$, $S_{x3}$ and $S_{x4}$ operate in a complementary manner. The F-type topology thus achieves three-level voltage output with reduced device voltage stress, making it an attractive candidate for high-performance types of solar inverters.
Proportional Resonant Control Principle
Current Proportional Resonant Control
The F-type grid-connected inverter operates as a grid-following current source. We adopt a single current loop control architecture to reduce complexity. The closed-loop control block diagram is conceptually represented. The output current $I_g$ can be expressed as:
$$I_g = \frac{K_{PWM} G_1(s) G_2(s)}{1 + K_{PWM} G_1(s) G_2(s)} I_{ref} – \frac{G_2(s)}{1 + K_{PWM} G_1(s) G_2(s)} U_g$$
where $G_1(s)$ is the controller transfer function, $G_2(s)$ is the filter transfer function, $K_{PWM}$ is the PWM gain, $I_{ref}$ is the reference current, and $U_g$ is the grid voltage. The PR controller achieves high gain at the resonant frequency $\omega_0$, enabling zero steady-state error tracking of sinusoidal signals. The ideal PR controller transfer function is:
$$G_{PR}(s) = K_p + \frac{2 K_r s}{s^2 + \omega_0^2}$$
where $\omega_0 = 2\pi f_r$, with $f_r = 50$ Hz. The magnitude at the resonant frequency is theoretically infinite. However, the narrow bandwidth of the PR controller makes it sensitive to grid frequency variations.
Quasi-Proportional Resonant Control
To improve robustness, a damping term is introduced, leading to the quasi-PR (QPR) controller:
$$G_{QPR}(s) = K_p + \frac{2 K_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2}$$
where $\omega_c$ is the cutoff frequency. The Bode plot shows a high gain (e.g., 100 dB) at $\omega_0$ but with a finite bandwidth. While this reduces sensitivity to small frequency deviations, the gain still drops significantly when the grid frequency deviates beyond the bandwidth. This limitation motivates our frequency-adaptive approach.
Frequency Adaptive PR Control Analysis
In power systems with complex industrial loads, the grid fundamental frequency can experience dynamic deviations. According to Chinese standards, the allowable deviation is $\pm 0.5$ Hz under normal conditions and $\pm 1$ Hz under abnormal conditions. We design a frequency-adaptive PR (APR) controller that operates effectively in the 49–51 Hz range. The key idea is to update the resonant frequency in real time based on the measured grid frequency $f_r$. The transfer function becomes:
$$G_{APR}(s) = K_p + \frac{2 K_r s}{s^2 + (2\pi f_r)^2}$$
where $f_r$ is the instantaneous grid frequency. The block diagram of the APR controller is depicted conceptually. When the grid frequency is stable at 50 Hz, the APR controller behaves identically to the ideal PR controller. When the frequency deviates, $f_r$ is updated, and the controller’s gain at the actual fundamental frequency remains theoretically infinite, as shown by the magnitude expression:
$$A(\text{dB}) = \sqrt{K_p^2 + \left( \frac{2 K_r \cdot 2\pi f_r}{-(2\pi f_r)^2 + (2\pi f_r)^2} \right)^2} \rightarrow \infty$$
This ensures that the output current perfectly tracks the reference current $I_{ref}$, and the system becomes robust to grid voltage disturbances, as the transfer function from $U_g$ to $I_g$ approaches zero. The following table compares the theoretical behavior of the three controllers.
| Controller | Gain at resonant frequency | Sensitivity to frequency deviation | Bandwidth |
|---|---|---|---|
| Ideal PR | $\infty$ | Very high | Narrow |
| QPR | Finite (high) | Moderate | Adjustable |
| APR | $\infty$ (adaptive) | Low | Adaptive |
The APR controller preserves the infinite gain benefit of the ideal PR while adapting to frequency changes, making it superior for practical grid-connected inverters, including various types of solar inverters in weak grids.
Experimental Validation
We built a 2.2 kW experimental platform to verify the proposed APR controller. The setup includes a DC power supply, the F-type inverter, a three-phase voltage regulator, and the grid. Key parameters are listed below.
| Parameter | Value |
|---|---|
| Rated output power | 2.2 kW |
| Input voltage | 600 V |
| Switching frequency | 100 kHz |
| Grid voltage | 380 V |
| Grid-side inductance | 5 $\mu$H |
| Filter capacitor | 4.7 $\mu$F |
| Inverter-side inductance | 1 mH |
Performance Under Unbalanced Grid Voltage
We tested the case where phases A and B experienced a voltage drop to 198 V (90% of nominal) while phase C remained at 220 V. The grid-connected current waveforms and FFT analysis were recorded for both QPR and APR controllers. The THD values are summarized in the following table.
| Control Strategy | THD (%) |
|---|---|
| Quasi-PR | 1.20 |
| Adaptive PR | 0.85 |
The APR controller reduced THD by 0.35 percentage points, demonstrating superior harmonic suppression under unbalanced grid conditions. This improvement is critical for types of solar inverters operating in weak or unbalanced grids.
Performance Under Grid Frequency Variation
We also tested the system when the grid frequency shifted to 51 Hz while maintaining balanced voltage. The current THD values are shown below.
| Control Strategy | THD (%) |
|---|---|
| Quasi-PR | 1.65 |
| Adaptive PR | 1.20 |
The APR controller achieved a 0.45% reduction in THD. The results confirm that frequency-adaptive PR effectively mitigates harmonic distortion caused by grid frequency fluctuations, which is a common issue in distributed generation systems using various types of solar inverters.
Comprehensive Comparison
The following table summarizes the experimental results across different operating conditions.
| Condition | QPR THD (%) | APR THD (%) | Improvement (%) |
|---|---|---|---|
| AB phase voltage drop (10%) | 1.20 | 0.85 | 0.35 |
| Grid frequency 51 Hz | 1.65 | 1.20 | 0.45 |
The APR controller consistently outperforms the QPR controller, validating its effectiveness for improving power quality in practical grid-connected inverters, especially for modern types of solar inverters designed for complex grid conditions.
Conclusion
We have presented a frequency adaptive proportional resonant control strategy for F-type three-level grid-connected inverters. The proposed method addresses the high harmonic distortion issue under grid voltage imbalance and frequency fluctuations, which are common challenges for types of solar inverters. By dynamically updating the resonant frequency of the PR controller based on real-time grid frequency measurement, the controller maintains infinite gain at the fundamental frequency, enabling zero steady-state error and strong disturbance rejection. Experimental results on a 2.2 kW prototype demonstrate that the APR controller reduces THD by 0.35% under voltage imbalance and by 0.45% under frequency deviation compared to traditional quasi-PR control. These findings confirm the superiority of our approach in enhancing grid-connected power quality. Future work will extend this strategy to other multilevel inverter topologies and further optimize the controller for a wider range of types of solar inverters in renewable energy systems.