With the increasing penetration of renewable energy sources into power systems, the role of the grid connected inverter has evolved from a simple power conversion unit to a critical grid-supporting device. As a key interface between distributed generation, such as photovoltaic (PV) systems, and the utility grid, the grid connected inverter must ensure not only efficient energy transfer but also maintain grid stability during disturbances. One of the most challenging scenarios for a grid connected inverter is an asymmetric grid fault, where unbalanced voltages occur due to single-phase or phase-to-phase faults. Under such conditions, the grid connected inverter faces several issues, including output current peak overruns, significant power oscillations on the AC side, and instability of the DC-link voltage. These problems can compromise the safety of the grid connected inverter and lead to disconnection, violating grid codes that require fault ride-through (FRT) capability. In this paper, we propose a comprehensive reactive power support control strategy for grid-connected inverters in PV systems during asymmetric grid faults. Our approach aims to address these challenges by ensuring that the grid connected inverter provides necessary reactive power to support grid voltage while operating within safe limits defined by constraints on current peaks and power oscillations. By doing so, we enhance the reliability and functionality of the grid connected inverter, contributing to a more resilient power system.
To understand the operational challenges, we first analyze the behavior of a grid connected inverter under asymmetric grid faults. In a three-phase three-wire system, during an unbalanced fault, the grid voltage and the output current of the grid connected inverter contain both positive- and negative-sequence components. Transforming these quantities into the stationary αβ reference frame, the grid voltage can be expressed as:
$$u_{abc} = \begin{bmatrix} u_{g\alpha}^+ + u_{g\alpha}^- \\ u_{g\beta}^+ + u_{g\beta}^- \end{bmatrix} = \begin{bmatrix} U_g^+ \cos(\omega t + \theta^+) + U_g^- \cos(\omega t + \theta^-) \\ U_g^+ \sin(\omega t + \theta^+) – U_g^- \sin(\omega t + \theta^-) \end{bmatrix}$$
Here, \(U_g^+\) and \(U_g^-\) represent the magnitudes of the positive- and negative-sequence grid voltages, respectively, while \(\omega\) is the fundamental angular frequency, and \(\theta^+\), \(\theta^-\) are the corresponding phase angles. Similarly, the output current from the grid connected inverter can be decomposed into positive- and negative-sequence active and reactive components:
$$i_{abc} = \begin{bmatrix} i_{\alpha}^+ + i_{\alpha}^- \\ i_{\beta}^+ + i_{\beta}^- \end{bmatrix} = \begin{bmatrix} I_p^+ \cos(\omega t + \theta^+) + I_q^+ \sin(\omega t + \theta^+) \\ I_p^+ \sin(\omega t + \theta^+) – I_q^+ \cos(\omega t + \theta^+) \end{bmatrix} + \begin{bmatrix} I_p^- \cos(\omega t + \theta^-) – I_q^- \sin(\omega t + \theta^-) \\ -I_p^- \sin(\omega t + \theta^-) – I_q^- \cos(\omega t + \theta^-) \end{bmatrix}$$
In these equations, \(I_p^+\), \(I_q^+\) denote the magnitudes of positive-sequence active and reactive currents, and \(I_p^-\), \(I_q^-\) denote those for the negative-sequence. Using the instantaneous power theory, the active power \(P\), reactive power \(Q\), and their oscillation amplitudes \(\Delta P_g\) and \(\Delta Q_g\) at the point of common coupling (PCC) can be derived as follows:
$$P = 1.5(U_g^+ I_p^+ + U_g^- I_p^-)$$
$$Q = 1.5(U_g^+ I_q^+ + U_g^- I_q^-)$$
$$\Delta P_g = 1.5 \sqrt{(I_p^+ U_g^- + I_p^- U_g^+)^2 + (I_q^+ U_g^- – I_q^- U_g^+)^2}$$
$$\Delta Q_g = 1.5 \sqrt{(I_q^+ U_g^- + I_q^- U_g^+)^2 + (I_p^- U_g^+ – I_p^+ U_g^-)^2}$$
These equations highlight that unbalanced voltages lead to power oscillations, which can stress the grid connected inverter and the connected PV system. For safe operation, two primary constraints must be considered: the active power oscillation amplitude and the output current peak of the grid connected inverter. The active power oscillation amplitude \(\Delta P_g\) is directly linked to the DC-link voltage fluctuation \(\Delta U_{dc}\) through the relationship:
$$\Delta P_g = 2 \omega C_{dc} \Delta U_{dc} U_{dc}$$
Where \(C_{dc}\) is the DC-link capacitance and \(U_{dc}\) is the DC-link voltage. To prevent excessive voltage stress on DC components, \(\Delta U_{dc}\) should typically be limited to within 1% of the rated DC voltage. Thus, the constraint for the active power oscillation amplitude can be formulated as:
$$(I_p^- U_g^+ + I_p^+ U_g^-)^2 + (I_q^+ U_g^- – I_q^- U_g^+)^2 \leq \frac{4}{3} \omega C_{dc} U_{dc} \Delta U_{dc\_max}$$
Here, \(\Delta U_{dc\_max}\) is the maximum allowable DC-link voltage fluctuation. The output current peak \(I_{peak}^{max}\) of the grid connected inverter is another critical constraint, as overcurrent can damage semiconductor devices. The maximum current peak is derived from the current components and is given by:
$$I_{peak}^{max} = \sqrt{(I^+)^2 + (I^-)^2 + 2I^+ I^- \gamma_{max}}$$
Where \(I^+ = \sqrt{(I_p^+)^2 + (I_q^+)^2}\) and \(I^- = \sqrt{(I_p^-)^2 + (I_q^-)^2}\) are the magnitudes of the positive- and negative-sequence currents, and \(\gamma_{max}\) is the maximum value of the cosine function of the phase difference between sequences. According to grid standards such as GB/T 40427-2021, the power factor of the grid connected inverter should be maintained within 0.95 leading to 0.95 lagging. Therefore, the current constraint can be expressed as:
$$I_{peak}^{max} \leq \frac{2 \times P_N}{U_{gpeak}} \times 0.95 \times \sqrt{3}$$
In this inequality, \(P_N\) is the rated power of the grid connected inverter, and \(U_{gpeak}\) is the peak phase voltage of the grid. These constraints form the foundation for designing a safe reactive power support strategy for the grid connected inverter during asymmetric faults.
Our proposed control strategy for the grid connected inverter aims to fulfill grid code requirements for reactive power injection while strictly adhering to the aforementioned safety constraints. Modern grid codes often mandate that during voltage sags, the grid connected inverter must inject reactive current to support grid voltage recovery. We adopt a reference reactive current scheme based on the voltage deviation, which is commonly used in standards. The positive- and negative-sequence reactive current references for the grid connected inverter are set as:
$$I_{qref}^+ = 2.5 \times \frac{0.9U_N – U_g^+}{U_N} I_N$$
$$I_{qref}^- = 2.5 \times \frac{0.05U_N – U_g^-}{U_N} I_N$$
Where \(U_N\) is the nominal grid voltage, and \(I_N\) is the rated current of the grid connected inverter. The strategy is divided into two main operational modes for the grid connected inverter, depending on whether the reactive power support requirements can be met without violating the safety constraints.
In the first mode, when meeting the full reactive power support would cause the grid connected inverter to exceed the current peak or active power oscillation limits, we prioritize safety. In this case, we set the active current components to zero and adjust the reactive currents within the allowable limits. The constraints simplify to functions \(f_P\) and \(f_I\) as follows:
$$f_P = \frac{4}{3} \omega C_{dc} U_{dc} \Delta U_{dc\_max} – |I_q^+ U_g^- – I_q^- U_g^+| \geq 0$$
$$f_I = P_N – U_{gpeak} \times 0.95 \times 1.5 \times \sqrt{(I_q^+)^2 + (I_q^-)^2 + 2|I_q^+||I_q^-| \gamma_{max}} \geq 0$$
To provide partial reactive support, we allocate reactive currents based on their relative weights. If the positive-sequence reactive current reference \(I_{qref}^+\) is larger than the negative-sequence \(I_{qref}^-\), we prioritize injecting \(I_{qref}^+\) and set \(I_{qref}^- = 0\) initially. Then, we check if increasing \(I_{qref}^-\) within the constraints is possible. Conversely, if \(I_{qref}^-\) has a larger weight, we prioritize it. This approach ensures that the grid connected inverter contributes to grid voltage support while remaining within safe operating boundaries, even if full reactive support is not feasible.
In the second mode, when the reactive power support requirements can be satisfied without constraint violations, we introduce a control parameter \(\mu\) to manage power oscillations and extend the active power output capability of the grid connected inverter. The parameter \(\mu\) defines the relationship between negative-sequence active current and positive-sequence active current:
$$I_{pref}^- = \mu I_{pref}^+$$
The range of \(\mu\) is from \(-\epsilon\) to \(\epsilon\), where \(\epsilon = U_g^- / U_g^+\) is the voltage unbalance factor. By substituting the reactive current references and the \(\mu\) relation into the constraint equations, we derive the safe operating region for the active power of the grid connected inverter. The active power oscillation constraint becomes:
$$f_P = \left( \frac{4}{3} \omega C_{dc} U_{dc} \Delta U_{dc\_max} \right)^2 – \left( \frac{9}{4} I_N U_g^- – \frac{1}{8} I_N U_g^+ \right)^2 – \left( \mu U_g^+ + U_g^- \right) |I_p^+| \geq 0$$
Similarly, the current constraint transforms into:
$$f_I = P_N – U_{gpeak} \times 0.95 \times 1.5 \times \sqrt{ A^2 – B^2 – (1+\mu^2)(I_p^+)^2 + (I_p^+)^2 + A^2 (\mu I_p^+)^2 + B^2 } \geq 0$$
With the terms \(A\) and \(B\) defined as:
$$A = \left( \frac{9}{4} – \frac{5}{2} \frac{U_g^+}{U_N} \right) I_N$$
$$B = \left( \frac{1}{8} – \frac{5}{2} \frac{U_g^-}{U_N} \right) I_N$$
For a given value of \(\mu\), these inequalities define permissible ranges for the positive-sequence active current \(I_p^+\), which in turn determine the active power \(P\) through the equation:
$$P = 1.5(U_g^+ + \mu U_g^-) I_p^+$$
By solving these constraints across the range of \(\mu\), we can map out the safe operating region for the grid connected inverter in terms of active power output. This region allows the grid connected inverter to provide full reactive power support while maximizing active power generation, thereby enhancing the utilization of the PV system during faults. The flexibility offered by \(\mu\) enables the grid connected inverter to trade off between minimizing power oscillations and maximizing active power output, depending on grid conditions and operator preferences.
To further ensure the stability of the entire PV system, we incorporate a non-maximum power point tracking (Non-MPPT) control strategy for the Boost converter that interfaces the PV array with the grid connected inverter. Under asymmetric faults, the power balance between the PV array and the grid connected inverter may be disrupted, leading to DC-link voltage instability. If the maximum power from the PV array \(P_{MPPT}\) exceeds the maximum power that the grid connected inverter can safely deliver \(P_{max}\), we switch the Boost converter from MPPT mode to Non-MPPT mode. In this mode, the duty cycle of the Boost converter is adjusted to reduce the power extracted from the PV array, aligning it with the inverter’s safe operating point. The adjusted duty cycle \(D_{non}\) is calculated as:
$$D_{non} = 1 – \frac{ \left[ \frac{P_{MPPT} – P_{max}}{P_{MPPT}} (U_{oc} – U_{MPPT}) + U_{MPPT} \right] + \left( k_p + \frac{k_i}{s} \right) (P_{MPPT} – P_{max}) }{U_{dc}}$$
Here, \(U_{oc}\) is the open-circuit voltage of the PV array, \(U_{MPPT}\) is the voltage at the maximum power point, and \(k_p\), \(k_i\) are the proportional and integral gains of a PI controller used to fine-tune the voltage reference. This Non-MPPT control ensures that the DC-link voltage remains stable, preventing overvoltage conditions that could damage the grid connected inverter or other components.
To validate the effectiveness of our proposed control strategy for the grid connected inverter, we conducted extensive simulations using MATLAB/Simulink. The system parameters used in the simulations are summarized in Table 1 below, which provides a comprehensive overview of the PV system and grid connected inverter configuration.
| Parameter | Value |
|---|---|
| PV Array Configuration | 20 series, 7 parallel |
| Open-Circuit Voltage per Module | 36.3 V |
| Short-Circuit Current per Module | 7.84 A |
| Voltage at Maximum Power Point (MPP) | 29 V per module |
| Current at MPP | 7.35 A per module |
| PV Side Filter Inductance | 5 mH |
| PV Side Filter Capacitance | 100 µF |
| DC-Link Voltage Rating | 800 V |
| DC-Link Capacitance | 4000 µF |
| Grid Connected Inverter Rated Power | 50 kW |
| Grid Connected Inverter Rated Current | 107.18 A |
| Grid Voltage Amplitude (Phase) | 311 V |
| Grid Frequency | 50 Hz |
| Inverter Output Filter Inductance | 8 mH |
| AC Filter Capacitance | 10 µF |
| Allowable DC-Link Voltage Fluctuation | 1% of rated (8 V) |
| Active Power Oscillation Limit | 16.09 kW |
| Output Current Peak Limit | 112.82 A |
We simulated two common asymmetric fault scenarios: single-phase-to-ground fault and two-phase-to-ground fault. For the single-phase fault, we assumed a voltage dip depth of 0.5 per unit, resulting in positive- and negative-sequence voltages of \(U_g^+ = 259.2\) V and \(U_g^- = 51.8\) V. The reactive current references were computed using the earlier equations, and the constraints indicated that the grid connected inverter could meet the full reactive support without violations. We varied the control parameter \(\mu\) during the simulation to demonstrate the safe operating region. The results showed that the grid connected inverter successfully injected reactive power while maintaining the output current peak below 112.82 A and the active power oscillation amplitude within 16.09 kW. The DC-link voltage remained stable around 800 V, with fluctuations less than 1%, confirming the effectiveness of the Non-MPPT control for the Boost converter.
For the two-phase fault scenario, we set a voltage dip depth of 0.3 per unit, with \(U_g^+ = 165.9\) V and \(U_g^- = 72.6\) V. In this case, meeting the full reactive support requirements would cause the grid connected inverter to exceed the current limit. Therefore, we operated in the first mode, prioritizing positive-sequence reactive current injection and limiting the negative-sequence reactive current to 24 A based on the constraint analysis. The simulation results demonstrated that the grid connected inverter provided partial reactive support, with the current peak at 112.30 A and active power output near zero, ensuring safe operation. The DC-link voltage stability was maintained throughout the fault duration.
To further illustrate the advantages of our control strategy, we compared the active power output capability of our grid connected inverter with that of a conventional method under the same fault conditions. The conventional method often fixes the active power output to a conservative value to avoid constraints, whereas our strategy leverages the safe operating region to maximize active power. Table 2 presents a quantitative comparison for the single-phase fault scenario, highlighting the enhanced performance of our approach.
| Control Strategy | Maximum Active Power Output | Reactive Power Support Level | Output Current Peak | Active Power Oscillation Amplitude |
|---|---|---|---|---|
| Conventional Fixed Active Power | 24.40 kW | Partial or None | Within limit | Within limit |
| Proposed Strategy with μ Adjustment | 26.77 kW | Full according to grid code | Within limit | Within limit |
As shown in Table 2, our proposed strategy allows the grid connected inverter to achieve a higher active power output—up to 26.77 kW—while providing full reactive power support as required by grid codes. This is made possible by the flexible safe operating region defined by the parameter μ, which optimizes the trade-off between active power and reactive power injection. In contrast, the conventional method limits active power to 24.40 kW to ensure safety, potentially reducing the energy yield from the PV system during faults. This comparison underscores the effectiveness of our strategy in enhancing the operational flexibility and economic performance of the grid connected inverter under asymmetric grid conditions.
In addition to the active power benefits, our control strategy also ensures robust performance of the grid connected inverter in terms of power quality and grid support. The injection of reactive current during faults helps to mitigate voltage sags, contributing to grid stability. Moreover, the constraints on active power oscillations prevent excessive torque pulsations in connected rotating machinery and reduce stress on the DC-link capacitor, thereby extending the lifespan of the grid connected inverter. The integration of Non-MPPT control further safeguards the system by preventing DC overvoltage, which is a common issue in PV systems during fault ride-through events.
The mathematical foundation of our strategy can be extended to other types of grid-connected inverters, such as those used in wind energy systems or battery energy storage systems. The core principles—defining safe operating regions based on constraints and optimizing control parameters—are universally applicable. For instance, in a battery energy storage system, the grid connected inverter can similarly provide reactive power support while managing state-of-charge limits through analogous constraint formulations. This versatility highlights the broad relevance of our work for modern power electronics-based grid interfaces.
To further elaborate on the control implementation, we can summarize the decision-making process for the grid connected inverter in a flowchart-like manner using equations. The overall algorithm for the grid connected inverter during an asymmetric fault is as follows:
- Detect fault and sequence components: Use a phase-locked loop (PLL) or sequence separation technique to obtain \(U_g^+\), \(U_g^-\), \(\theta^+\), \(\theta^-\).
- Compute reactive current references: Calculate \(I_{qref}^+\) and \(I_{qref}^-\) using the grid code formula.
- Check constraints with full reactive support: Evaluate \(f_P\) and \(f_I\) with \(I_q^+ = I_{qref}^+\), \(I_q^- = I_{qref}^-\), and \(I_p^+ = I_p^- = 0\).
- If constraints satisfied: Enter Mode 2. Select a value for μ (e.g., based on optimization for maximum active power or minimal oscillation). Solve for \(I_p^+\) from the safe operating region inequalities. Set \(I_p^- = μ I_p^+\). Generate current references for the grid connected inverter control loop.
- If constraints violated: Enter Mode 1. Prioritize reactive current with larger weight. Adjust \(I_q^+\) and \(I_q^-\) within limits using the constraint functions. Set \(I_p^+ = I_p^- = 0\). Generate current references accordingly.
- Coordinate with Boost converter: Compare \(P_{MPPT}\) with \(P_{max}\) (maximum safe active power from inverter). If \(P_{MPPT} > P_{max}\), switch Boost converter to Non-MPPT mode with duty cycle \(D_{non}\). Otherwise, keep MPPT mode.
- Implement current control: Use proportional-resonant (PR) controllers or other suitable techniques to track the current references in the αβ frame, then generate PWM signals for the grid connected inverter.
This algorithm ensures that the grid connected inverter operates safely and effectively under all fault conditions. The computational burden is manageable, as the constraint evaluations involve simple algebraic calculations that can be performed in real-time by modern digital signal processors.
In conclusion, we have developed a comprehensive reactive power support control strategy for photovoltaic grid-connected inverters during asymmetric grid faults. The strategy is designed to address the critical challenges faced by the grid connected inverter, including output current peak overruns, active power oscillations, and DC-link voltage instability. By incorporating safety constraints derived from system limitations, we define safe operating regions that allow the grid connected inverter to provide necessary reactive power support while maximizing active power output. The introduction of a control parameter μ offers flexibility to balance between power oscillation minimization and active power enhancement. Additionally, the integration of Non-MPPT control for the Boost converter ensures overall system stability. Simulation results under single-phase and two-phase fault scenarios validate the effectiveness of our strategy, demonstrating that the grid connected inverter can maintain safe operation and comply with grid code requirements. This work contributes to the advancement of grid-connected inverter technologies, enabling higher penetration of renewable energy sources into power systems without compromising grid stability. Future research may focus on extending this strategy to multi-inverter systems, incorporating predictive control techniques, and testing under real-world grid conditions to further optimize the performance of the grid connected inverter.
The grid connected inverter is undoubtedly a cornerstone of modern power electronics, and its ability to provide ancillary services like reactive power support is essential for the transition to a sustainable energy future. Our proposed strategy enhances the resilience and functionality of the grid connected inverter, making it a more reliable asset in the grid. As power systems continue to evolve with increasing levels of distributed generation, the role of the grid connected inverter will only grow in importance. Therefore, continuous innovation in control strategies for the grid connected inverter is crucial to meet the dynamic demands of future grids. We believe that our work provides a solid foundation for such innovations, paving the way for more intelligent and adaptive grid connected inverter systems.