In recent years, the growing energy crisis and heightened environmental awareness have led to increased focus on renewable energy and distributed generation technologies. As a critical interface between renewable energy systems and the grid, photovoltaic inverters play a vital role in ensuring efficient power conversion and grid stability. Among the various types of solar inverter, those used in grid-connected applications must handle not only ideal conditions but also asymmetric grid faults, which can arise from grid disturbances or unbalanced loads. These faults introduce negative sequence components, leading to power oscillations, current distortions, and potential damage to inverter components. Therefore, it is essential to develop robust control strategies for photovoltaic inverters under asymmetric grid conditions. In this article, we explore and compare control methodologies based on synchronous and stationary reference frames, emphasizing grid synchronization, power control, and current regulation. We incorporate mathematical models, tables, and experimental insights to provide a comprehensive analysis, while highlighting the relevance of different types of solar inverter in these contexts.
The fundamental structure of a grid-connected photovoltaic inverter system under asymmetric faults involves three key components: grid synchronization, power control, and current regulation. Grid synchronization detects the grid voltage’s frequency, phase, and magnitude, which are crucial for accurate inverter operation. Power control generates reference currents based on desired active and reactive power outputs, while current regulation ensures that the actual grid currents track these references, producing PWM signals for the inverter switches. Two primary coordinate systems are employed for these tasks: the synchronous reference frame (SRF) and the stationary reference frame. Each approach offers distinct advantages and challenges, particularly when dealing with negative sequence voltages. We will delve into the specifics of these strategies, using equations and comparative tables to illustrate their performance. For instance, the power in a three-phase system can be expressed as:
$$ P = \frac{3}{2} (v_d i_d + v_q i_q) $$
$$ Q = \frac{3}{2} (v_q i_d – v_d i_q) $$
where \( v_d \) and \( v_q \) are the direct and quadrature components of voltage, and \( i_d \) and \( i_q \) are the current components in the synchronous frame. Under asymmetric conditions, these equations extend to include negative sequence terms, complicating the control design. Throughout this discussion, we will reference various types of solar inverter, such as string inverters and central inverters, to contextualize the applicability of these strategies.
Grid Synchronization Techniques
Grid synchronization is the first step in inverter control, as it provides the phase and frequency information needed for coordinate transformations and current regulation. Under asymmetric grid faults, the voltage waveform becomes unbalanced, containing both positive and negative sequence components. Traditional synchronization methods, like the single synchronous reference frame phase-locked loop (SSRF-PLL), struggle with such conditions due to the oscillatory nature of the detected values. To address this, advanced techniques have been developed for different types of solar inverter.
In the synchronous reference frame approach, the double synchronous reference frame PLL (DDSRF-PLL) is commonly used. It decouples the positive and negative sequence components by applying two rotating frames: one for the positive sequence and another for the negative sequence. The voltage vector transformation from the stationary frame to the synchronous frames is given by:
$$ \begin{bmatrix} v_d^+ \\ v_q^+ \end{bmatrix} = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} v_\alpha \\ v_\beta \end{bmatrix} $$
$$ \begin{bmatrix} v_d^- \\ v_q^- \end{bmatrix} = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} v_\alpha \\ v_\beta \end{bmatrix} $$
where \( \theta \) is the estimated phase angle, and \( v_\alpha \) and \( v_\beta \) are the stationary frame components. The DDSRF-PLL uses low-pass filters to extract the DC components of \( v_d^+ \) and \( v_q^+ \), which are then fed into a PI controller to adjust the frequency and phase. This method effectively mitigates the impact of negative sequence voltages but introduces complexity due to the decoupling network and slower dynamic response.
In contrast, the stationary reference frame approach employs the double second-order generalized integrator frequency-locked loop (DSOGI-FLL). This method directly tracks the grid frequency using SOGI blocks to generate orthogonal voltage components in the stationary frame. The SOGI transfer function for a voltage component \( v \) is:
$$ G(s) = \frac{v'(s)}{v(s)} = \frac{k \omega s}{s^2 + k \omega s + \omega^2} $$
where \( k \) is a damping factor, and \( \omega \) is the grid frequency. The DSOGI-FLL structure simplifies the synchronization process by eliminating the need for rotating transformations, resulting in faster frequency tracking and reduced computational burden. This makes it suitable for various types of solar inverter, especially in distributed generation systems where rapid response is critical.
To compare these synchronization methods, we present a table summarizing their key characteristics:
| Feature | DDSRF-PLL (Synchronous Frame) | DSOGI-FLL (Stationary Frame) |
|---|---|---|
| Complexity | High, due to decoupling and multiple transformations | Low, with minimal coordinate changes |
| Dynamic Response | Slower, with settling times around 20 ms | Faster, with settling times under 10 ms |
| Accuracy under Faults | Good, but prone to oscillations | Excellent, with stable frequency output |
| Suitability for Types of Solar Inverter | Central inverters with high processing capability | String and microinverters with resource constraints |
This comparison highlights that the stationary frame approach offers advantages in simplicity and performance, which is beneficial for a wide range of types of solar inverter.
Power Control Strategies
Power control in photovoltaic inverters under asymmetric faults aims to regulate active and reactive power while minimizing oscillations caused by negative sequence components. The positive-negative sequence compensation (PNSC) strategy is widely used, as it allows for flexible power management by setting reference values for active power (P) and reactive power (Q). For instance, if reactive power reference is set to zero, the controller focuses on active power delivery, reducing oscillations in the output.
The reference currents in the PNSC strategy are derived from the positive and negative sequence voltage components. In the synchronous frame, the current references are computed as:
$$ i_d^* = \frac{2}{3} \frac{P^* v_d^+ – Q^* v_q^+}{(v_d^+)^2 + (v_q^+)^2} $$
$$ i_q^* = \frac{2}{3} \frac{P^* v_q^+ + Q^* v_d^+}{(v_d^+)^2 + (v_q^+)^2} $$
where \( P^* \) and \( Q^* \) are the reference powers, and \( v_d^+ \), \( v_q^+ \) are the positive sequence voltages. Under asymmetric conditions, additional terms for negative sequence components are included to ensure accurate tracking. This approach is effective but requires precise sequence separation, which can be computationally intensive for some types of solar inverter.
In the stationary frame, power control leverages the instantaneous power theory, which directly manipulates the αβ components. The reference currents are generated using:
$$ i_\alpha^* = \frac{2}{3} \frac{P^* v_\alpha – Q^* v_\beta}{v_\alpha^2 + v_\beta^2} $$
$$ i_\beta^* = \frac{2}{3} \frac{P^* v_\beta + Q^* v_\alpha}{v_\alpha^2 + v_\beta^2} $$
This method avoids rotating transformations, simplifying the implementation and enhancing robustness against grid imbalances. It is particularly advantageous for modular types of solar inverter, such as those used in residential systems, where simplicity and reliability are paramount.
The following table contrasts the power control methods in both frames:
| Aspect | Synchronous Frame Power Control | Stationary Frame Power Control |
|---|---|---|
| Implementation Complexity | High, with sequence decoupling | Low, with direct calculations |
| Oscillation Suppression | Effective but slow | Rapid and efficient |
| Compatibility with Types of Solar Inverter | Suited for high-power central inverters | Ideal for distributed and string inverters |
By integrating these strategies, we can address the challenges of asymmetric faults across different types of solar inverter, ensuring stable power delivery.
Current Regulation Methods
Current regulation is critical for maintaining grid current quality and protecting the inverter from overcurrent conditions. Under asymmetric faults, the current controller must handle unbalanced currents without introducing harmonics or distortions. Two primary methods are employed: PI controllers in the synchronous frame and PR controllers in the stationary frame.
In the synchronous frame, dual PI controllers are used for the d and q axes. The control law for the d-axis current is:
$$ u_d = k_p (i_d^* – i_d) + k_i \int (i_d^* – i_d) dt – \omega L i_q + v_d $$
where \( k_p \) and \( k_i \) are the proportional and integral gains, \( L \) is the inductance, and \( \omega \) is the grid frequency. Similarly, for the q-axis:
$$ u_q = k_p (i_q^* – i_q) + k_i \int (i_q^* – i_q) dt + \omega L i_d + v_q $$
This approach benefits from transforming AC quantities to DC, allowing PI controllers to achieve zero steady-state error. However, it requires decoupling terms and feedforward compensation, increasing complexity. This can be challenging for certain types of solar inverter with limited processing resources.
In the stationary frame, PR controllers are utilized, as they provide infinite gain at the fundamental frequency, enabling accurate tracking of AC signals. The transfer function of a PR controller is:
$$ G_{PR}(s) = k_p + \frac{2 k_i \omega_c s}{s^2 + 2 \omega_c s + \omega^2} $$
where \( \omega_c \) is the cutoff frequency. The control outputs for α and β axes are:
$$ u_\alpha = k_p (i_\alpha^* – i_\alpha) + k_i \int (i_\alpha^* – i_\alpha) dt $$
$$ u_\beta = k_p (i_\beta^* – i_\beta) + k_i \int (i_\beta^* – i_\beta) dt $$
This method eliminates the need for coordinate transformations and decoupling, simplifying the design and improving dynamic response. It is highly suitable for various types of solar inverter, including those in fast-varying environments.
To illustrate the differences, we present a comparative table:
| Parameter | PI Controller (Synchronous Frame) | PR Controller (Stationary Frame) |
|---|---|---|
| Control Structure | Complex, with transformations and decoupling | Simple, with direct AC tracking |
| Steady-State Error | Zero for DC components only | Zero for AC components at fundamental frequency |
| Computational Load | High, due to additional calculations | Low, enabling faster execution |
| Application in Types of Solar Inverter | Best for centralized systems with robust hardware | Preferred for string and microinverters |
Overall, the stationary frame with PR controllers offers a more straightforward and effective solution for current regulation, accommodating diverse types of solar inverter.
Simulation Analysis
To validate the control strategies, we conducted simulations using a MATLAB/Simulink model of a grid-connected photovoltaic inverter under asymmetric faults. The system parameters included a grid voltage of 57.4 V, frequency of 50 Hz, grid-side inductance of 7 mH, DC-link voltage reference of 150 V, DC-side capacitance of 1980 μF, and a resistive load of 60 Ω. Control parameters were tuned based on system transfer functions, with DDSRF-PLL gains set as \( k_p = 0.7 \) and \( k_i = 30 \), DSOGI-FLL gains as \( k = 1.41 \) and \( \gamma = 100 \), PI current controller gains as \( k_p = 150 \) and \( k_i = 200 \), and PR controller gains as \( k_p = 200 \) and \( k_i = 30 \).
We simulated a two-phase voltage dip at 2 seconds, observing the grid synchronization, current waveforms, and DC-link voltage. The DDSRF-PLL exhibited frequency oscillations between 46.25 Hz and 52.5 Hz, with a settling time of approximately 20 ms, while the DSOGI-FLL showed a narrower range of 48.75 Hz to 50 Hz and settled within 10 ms. For current regulation, the PR controller in the stationary frame produced smoother grid currents with lower harmonic distortion compared to the PI controller. The DC-link voltage remained stable in both cases, but the stationary frame approach demonstrated superior performance in reducing oscillations and improving dynamic response. These results underscore the effectiveness of the stationary frame strategy for various types of solar inverter, particularly in fault conditions.
The active power and reactive power outputs were also analyzed using the equations:
$$ P = v_\alpha i_\alpha + v_\beta i_\beta $$
$$ Q = v_\beta i_\alpha – v_\alpha i_\beta $$
Under asymmetric faults, the stationary frame control minimized power ripples, highlighting its advantage for grid support functions in different types of solar inverter.
Experimental Validation
We built an experimental platform based on the TMS320F28335 digital signal processor to verify the simulation findings. The control algorithms, including voltage outer loops and current inner loops, were implemented on the DSP, with a carrier frequency of 10 kHz and sinusoidal PWM modulation. To emulate asymmetric grid faults, we used a voltage inverter controlled by a dSPACE 1104 system to generate unbalanced voltage conditions.
The experimental results aligned with the simulations: the DSOGI-FLL achieved faster frequency tracking with less oscillation than the DDSRF-PLL, and the PR controller in the stationary frame yielded cleaner current waveforms. For instance, during a two-phase voltage dip, the grid currents maintained sinusoidal shapes with minimal distortion when using the stationary frame approach, whereas the synchronous frame method introduced slight harmonics. This validates the practicality of the stationary frame strategy for real-world applications across different types of solar inverter, enhancing grid resilience under faults.
Conclusion
In this article, we have explored and compared control strategies for photovoltaic inverters under asymmetric grid faults, focusing on synchronous and stationary reference frames. From grid synchronization to power and current control, the stationary frame approach, utilizing DSOGI-FLL and PR controllers, demonstrated superior performance in terms of simplicity, dynamic response, and accuracy. This makes it highly suitable for a wide range of types of solar inverter, including string, central, and microinverters. By leveraging mathematical models, simulations, and experimental data, we have shown that the stationary frame strategy effectively suppresses negative sequence voltages, ensuring stable operation and grid compatibility. Future work could extend these methods to hybrid systems incorporating energy storage, further enhancing the reliability of photovoltaic generation.