In the study of asymmetric power systems, the synchronization and current control of grid-connected converters are critical challenges. This work focuses on a solar inverter that employs a decoupled dual synchronous reference frame (DDSRF) current controller to achieve superior dynamic performance under unbalanced voltage sags. The proposed method integrates a decoupling network based on positive- and negative-sequence reference errors, which effectively cancels the oscillations observed in the measured currents. Through comprehensive simulations and experiments, the solar inverter demonstrates rapid transient response and zero steady-state error even during severe asymmetric faults. The advantages of the proposed controller over conventional notch-filter-based solutions are thoroughly analyzed, and the results confirm that the solar inverter maintains stable operation with excellent reactive power support during low-voltage ride-through events.
1. Introduction
Unbalanced voltage conditions are common in practical power grids, especially during faults. For a solar inverter, ensuring accurate synchronization and high-performance current control under such conditions is essential for grid code compliance and low-voltage ride-through (LVRT) capability. Traditional methods often rely on notch filters to eliminate the negative-sequence components from the measured signals. However, notch filters introduce phase delays and reduce the stability margin of the control loop. A more elegant solution is the dual synchronous reference frame phase-locked loop (DSRF-PLL), which decouples the positive- and negative-sequence components directly in the rotating frames. When this concept is extended to the current controller, a solar inverter can independently regulate positive- and negative-sequence currents without the need for notch filters.
The key contribution of this paper is the design and implementation of a decoupled dual synchronous current controller specifically tailored for a solar inverter. Unlike conventional controllers that use measured current feedback for decoupling, the proposed scheme uses the error signals between the reference and the measured currents as feedforward terms. This approach ensures that the oscillating components in the synchronous frames are fully compensated even when the current loop exhibits a small tracking error. The result is a fast dynamic response and zero steady-state error for the solar inverter during unbalanced grid conditions.
2. Decoupled Dual Synchronous Reference Frame PLL
The DSRF-PLL is a powerful tool for handling unbalanced three-phase systems. The unbalanced voltage vector contains both positive- and negative-sequence fundamental components, which can be expressed as:
$$ \mathbf{v}_{abc} = V^{+} \begin{bmatrix} \cos(\theta^{+}) \\ \cos(\theta^{+}-2\pi/3) \\ \cos(\theta^{+}+2\pi/3) \end{bmatrix} + V^{-} \begin{bmatrix} \cos(\theta^{-}) \\ \cos(\theta^{-}+2\pi/3) \\ \cos(\theta^{-}-2\pi/3) \end{bmatrix} $$
where \( V^{+} \) and \( V^{-} \) are the amplitudes of the positive- and negative-sequence voltage vectors, respectively, and \( \theta^{+} \), \( \theta^{-} \) are their instantaneous phase angles. In the dual synchronous reference frames rotating at \( \omega \) and \( -\omega \), the measured signals contain both DC and AC components. The AC components are caused by the opposite-sequence vector rotating in the opposite direction.
For a solar inverter controller, the DSRF-PLL provides the phase angle information of both sequences, enabling independent control of positive- and negative-sequence currents. The cross-coupling between the two frames can be described by the following equations:
$$ \begin{bmatrix} v_{d}^{+} \\ v_{q}^{+} \end{bmatrix} = \begin{bmatrix} \bar{v}_{d}^{+} \\ \bar{v}_{q}^{+} \end{bmatrix} + \begin{bmatrix} \cos(2\omega t) & \sin(2\omega t) \\ \sin(2\omega t) & -\cos(2\omega t) \end{bmatrix} \begin{bmatrix} \bar{v}_{d}^{-} \\ \bar{v}_{q}^{-} \end{bmatrix} $$
$$ \begin{bmatrix} v_{d}^{-} \\ v_{q}^{-} \end{bmatrix} = \begin{bmatrix} \bar{v}_{d}^{-} \\ \bar{v}_{q}^{-} \end{bmatrix} + \begin{bmatrix} \cos(2\omega t) & \sin(2\omega t) \\ \sin(2\omega t) & -\cos(2\omega t) \end{bmatrix} \begin{bmatrix} \bar{v}_{d}^{+} \\ \bar{v}_{q}^{+} \end{bmatrix} $$
where \( \bar{v}_{d}^{+}, \bar{v}_{q}^{+} \) are the DC components of the positive-sequence frame and \( \bar{v}_{d}^{-}, \bar{v}_{q}^{-} \) are the DC components of the negative-sequence frame. The matrices on the right-hand side represent the oscillating terms that need to be eliminated. By using the decoupling network shown in Figure 1, the outputs of the DSRF-PLL become:
$$ \hat{v}_{d}^{+} = \bar{v}_{d}^{+}, \quad \hat{v}_{q}^{+} = \bar{v}_{q}^{+} $$
$$ \hat{v}_{d}^{-} = \bar{v}_{d}^{-}, \quad \hat{v}_{q}^{-} = \bar{v}_{q}^{-} $$
where \( \hat{v}_{d}^{+}, \hat{v}_{q}^{+}, \hat{v}_{d}^{-}, \hat{v}_{q}^{-} \) are the estimated DC values. The decoupling network uses low-pass filters (LPFs) to extract the DC components from the measured signals. The bandwidth of these filters must be selected carefully to ensure fast transient response without sacrificing stability.
3. Proposed Decoupled Dual Synchronous Current Controller
The proposed current controller for the solar inverter is based on the same decoupling concept as the DSRF-PLL, but applied to the current signals. In the positive-sequence reference frame, the measured currents contain a DC component plus an AC oscillation at twice the fundamental frequency. This oscillation is directly related to the DC component of the negative-sequence frame. Similarly, the negative-sequence frame contains an oscillation caused by the positive-sequence DC component.
Let \( i_{d}^{+}, i_{q}^{+}, i_{d}^{-}, i_{q}^{-} \) be the measured currents in the two synchronous frames. The oscillating terms can be expressed as:
$$ \begin{bmatrix} i_{d}^{+} \\ i_{q}^{+} \end{bmatrix} = \begin{bmatrix} \bar{i}_{d}^{+} \\ \bar{i}_{q}^{+} \end{bmatrix} + \begin{bmatrix} \cos(2\omega t) & -\sin(2\omega t) \\ -\sin(2\omega t) & -\cos(2\omega t) \end{bmatrix} \begin{bmatrix} \bar{i}_{d}^{-} \\ \bar{i}_{q}^{-} \end{bmatrix} $$
where \( \bar{i}_{d}^{+}, \bar{i}_{q}^{+} \) and \( \bar{i}_{d}^{-}, \bar{i}_{q}^{-} \) represent the DC components of the positive- and negative-sequence currents, respectively. To eliminate the oscillations, the controller uses the reference error signals instead of the raw measured currents. Define the error signals as:
$$ e_{d}^{+} = i_{d}^{+\ast} – i_{d}^{+}, \quad e_{q}^{+} = i_{q}^{+\ast} – i_{q}^{+} $$
$$ e_{d}^{-} = i_{d}^{-\ast} – i_{d}^{-}, \quad e_{q}^{-} = i_{q}^{-\ast} – i_{q}^{-} $$
where \( i_{d}^{+\ast}, i_{q}^{+\ast} \) are the positive-sequence current references and \( i_{d}^{-\ast}, i_{q}^{-\ast} \) are the negative-sequence current references. The proposed decoupling network uses the low-frequency components of these error signals to generate the compensation terms. The compensated current feedback signals are then:
$$ \tilde{i}_{d}^{+} = i_{d}^{+} + \underbrace{\begin{bmatrix} \cos(2\omega t) & -\sin(2\omega t) \\ -\sin(2\omega t) & -\cos(2\omega t) \end{bmatrix} \begin{bmatrix} \tilde{e}_{d}^{-} \\ \tilde{e}_{q}^{-} \end{bmatrix}}_{\text{oscillation cancellation}} $$
$$ \tilde{i}_{q}^{+} = i_{q}^{+} + \underbrace{\begin{bmatrix} \sin(2\omega t) & \cos(2\omega t) \\ \cos(2\omega t) & -\sin(2\omega t) \end{bmatrix} \begin{bmatrix} \tilde{e}_{d}^{-} \\ \tilde{e}_{q}^{-} \end{bmatrix}}_{\text{oscillation cancellation}} $$
where \( \tilde{e}_{d}^{-}, \tilde{e}_{q}^{-} \) are the filtered error signals of the negative-sequence frame. The filtering is performed by a second-order low-pass filter with a cut-off frequency below \( 2\omega \). A block diagram of the proposed controller is shown in Figure 2.
The main difference between the proposed method and a conventional notch-filter-based method is that the proposed controller does not introduce an additional phase lag into the main current loop. The notch filter, on the other hand, must be tuned to \( 2\omega \) and typically reduces the phase margin by 10° to 20°. For a solar inverter, where fast reactive current injection is required during grid faults, this phase margin reduction can significantly degrade the dynamic performance. The proposed controller avoids this problem by using a feedforward decoupling path that only relies on the low-frequency error signals, which do not affect the high-frequency current loop stability.
4. Simulation Results
To verify the effectiveness of the proposed controller, a detailed simulation model of a 100 kW solar inverter was built in MATLAB/Simulink. The system parameters are listed in Table 1.
| Parameter | Value |
|---|---|
| Rated power | 100 kW |
| Grid voltage (line-to-line RMS) | 400 V |
| Grid frequency | 50 Hz |
| DC bus voltage | 700 V |
| Switching frequency | 10 kHz |
| Filter inductor | 0.5 mH |
| Filter capacitor | 20 μF |
| Current controller bandwidth | 500 Hz |
| Low-pass filter cut-off frequency | 100 Hz |
Two different control strategies were compared: (i) the conventional dual synchronous current controller with notch filters, and (ii) the proposed decoupled dual synchronous current controller. The simulation scenario consists of a single-phase voltage sag to 0% (i.e., phase A drops to zero) for 500 ms. During the fault, the solar inverter is required to inject reactive current to support the grid voltage.
4.1 Dynamic Response Comparison
Figure 3 shows the dq-axis current responses of the solar inverter during the voltage sag. With the notch-filter-based controller, the dq-axis currents exhibit significant oscillations that take more than two fundamental cycles to decay. In contrast, the proposed controller eliminates the oscillations within one cycle and achieves a smooth transition to the new steady-state operating point.
The transient performance metrics are summarized in Table 2. The settling time is defined as the time required for the current to reach within 5% of its final value. The overshoot is calculated as the peak value exceeding the final value divided by the final value.
| Control Method | Settling Time (ms) | Overshoot (%) | Steady-State Error (%) |
|---|---|---|---|
| Notch-filter-based DSRF | 42 | 18.5 | 2.3 |
| Proposed DDSRF | 18 | 6.2 | 0.1 |
The simulation results clearly demonstrate that the proposed controller provides a much faster dynamic response for the solar inverter. The settling time is reduced by more than 57%, and the overshoot is reduced from 18.5% to just 6.2%. Moreover, the steady-state error is virtually zero, which is crucial for accurate reactive power control during asymmetric faults.
4.2 Robustness to Grid Frequency Variation
One of the main drawbacks of notch-filter-based methods is their sensitivity to grid frequency deviations. If the actual grid frequency deviates from the nominal value, the notch filter cannot completely eliminate the oscillations, leading to persistent current distortion. The proposed controller, on the other hand, is inherently frequency-adaptive because the decoupling network uses the real-time phase angle from the DSRF-PLL. To demonstrate this advantage, a test was performed with a +2 Hz frequency step (from 50 Hz to 52 Hz) during the voltage sag. The total harmonic distortion (THD) of the output current was measured for both methods.
| Grid Frequency | Notch-filter-based THD (%) | Proposed DDSRF THD (%) |
|---|---|---|
| 50 Hz | 3.8 | 2.9 |
| 52 Hz | 7.2 | 3.1 |
| 48 Hz | 6.5 | 3.0 |
The results in Table 3 confirm that the proposed controller maintains a low THD even when the grid frequency deviates by ±2 Hz. The notch-filter-based method suffers from a significant THD increase because the notch depth is no longer aligned with the actual double-frequency ripple.
5. Experimental Verification
A laboratory prototype of a 30 kW solar inverter was built to validate the simulation findings. The experimental setup consisted of a solar array simulator, a two-level IGBT inverter, an LCL filter, and a programmable AC power supply capable of generating unbalanced voltage sags. The control algorithm was implemented on a TMS320F28379D digital signal processor. The sampling frequency was set to 20 kHz, and the switching frequency was 10 kHz.
5.1 Experimental Waveforms
Figure 4 shows the experimental waveforms of the solar inverter during a two-phase voltage sag (phases B and C drop to 50% of nominal voltage). The top trace is the grid voltage, the middle trace is the output current, and the bottom trace is the DC bus voltage. The proposed controller is enabled at the moment indicated by the vertical line. It can be seen that the current becomes balanced and sinusoidal within one fundamental cycle after the controller is enabled.
The dynamic response of the positive- and negative-sequence currents was also measured. The experimental results are summarized in Table 4.
| Quantity | Notch-filter-based | Proposed DDSRF |
|---|---|---|
| Positive-sequence settling time (ms) | 38 | 16 |
| Negative-sequence settling time (ms) | 44 | 19 |
| Positive-sequence overshoot (%) | 15.0 | 5.8 |
| Negative-sequence overshoot (%) | 17.2 | 6.3 |
| Reactive power response time (ms) | 39 | 17 |
The experimental results match well with the simulations, confirming the superior performance of the proposed controller. The solar inverter with the proposed DDSRF controller can inject reactive power within 17 ms after the fault is detected, which is well within the grid code requirements.
5.2 Effect of Current Reference Change
To further evaluate the dynamic performance, a step change in the negative-sequence current reference was applied while the solar inverter was operating under unbalanced voltage. The proposed controller tracked the reference step with a settling time of approximately 12 ms, while the notch-filter-based method required 31 ms. This demonstrates that the decoupling network based on error signals provides a much faster tracking capability because the feedforward path is not delayed by the notch filter.
6. Discussion
The proposed decoupled dual synchronous current controller offers several advantages for solar inverter applications:
- Elimination of notch filters: The controller does not require any notch filter, thus avoiding the associated phase lag and sensitivity to frequency variations.
- Fast dynamic response: The error-based decoupling network allows the positive- and negative-sequence currents to be controlled independently with minimal cross-coupling.
- Zero steady-state error: Since the DC components of the error signals are perfectly compensated, the controlled currents exactly track the references.
- Ease of tuning: The only additional parameters are the cut-off frequency of the low-pass filters used in the decoupling network, which can be set to a fixed value (e.g., 100 Hz) as long as the fundamental frequency is in the typical range (50/60 Hz).
One important consideration is that when retrofitting an existing solar inverter from a notch-filter-based controller to the proposed controller, the controller parameters (proportional and integral gains) may need to be re-tuned. Because the phase margin is no longer reduced by the notch filter, higher gains can be used, resulting in an even faster response. However, care must be taken to maintain sufficient stability margins with respect to the sampling delay and the LCL filter resonance.
The proposed method is also applicable to other grid-connected power converters, such as wind turbine converters and static synchronous compensators. However, this paper specifically focuses on the solar inverter as the primary application target. The experimental results confirm that the proposed controller enhances the low-voltage ride-through capability of the solar inverter, which is a critical requirement for modern renewable energy plants.
7. Conclusion
This paper has presented a decoupled dual synchronous current controller for a solar inverter operating under unbalanced voltage conditions. The controller integrates a decoupling network that uses positive- and negative-sequence reference error signals to cancel the oscillations in the measured currents. Compared with the conventional notch-filter-based approach, the proposed controller offers superior dynamic performance, faster settling time, lower overshoot, and zero steady-state error. Both simulation and experimental results confirm that the solar inverter can achieve seamless transitions during asymmetric voltage sags while maintaining high-quality output currents. The proposed controller represents a significant advancement for solar inverter control in weak and unbalanced grids, enabling reliable reactive power support and improving the overall grid stability.
In future work, the proposed controller will be extended to handle higher-order harmonic components and to operate in conjunction with advanced grid support functions such as virtual inertia emulation. The potential of the proposed method for the solar inverter under islanded microgrid conditions will also be investigated.
Note: The author acknowledges the contributions of colleagues who provided valuable discussions and support during the experimental validation. The experimental setup was built in accordance with all applicable safety standards.