In recent years, the rapid development of solar energy as a clean power source has led to a significant increase in the penetration of grid-connected photovoltaic (PV) systems. With declining costs, solar inverters have become crucial components in modern power grids, enabling the conversion of DC power from PV arrays to AC power for grid integration. However, as the proportion of solar inverters in the grid grows, their impact on grid stability becomes more pronounced, especially during grid faults. Grid codes and technical standards, such as those outlined in various national regulations, mandate that solar inverters must possess low-voltage ride-through (LVRT) capabilities to avoid disconnection during voltage sags, thereby preventing further grid instability. This requirement highlights the importance of effective control strategies for solar inverters under fault conditions to ensure uninterrupted operation and compliance with grid standards.
Grid faults can be categorized into symmetrical faults, where all three phases experience voltage dips equally, and asymmetrical faults, where voltage imbalances occur. During such events, solar inverters face challenges such as excessive peak currents, power fluctuations, and current distortion, which can compromise system reliability and performance. This paper explores the operational characteristics of solar inverters under different grid fault conditions and proposes advanced control strategies to address these issues. By focusing on peak current limitation and power fluctuation mitigation, the aim is to enhance the LVRT capability of solar inverters while maximizing active power output. The study is presented from a first-person perspective as a researcher in the field, drawing on simulation-based analysis and theoretical derivations.
The topology of a typical three-phase grid-connected solar inverter is shown in Figure 1, which illustrates a three-wire system without a neutral connection, thereby eliminating zero-sequence currents. The DC voltage from the PV array is controlled and converted to AC through an inverter, with output filters (resistance R and inductance L) ensuring sinusoidal current injection into the grid. The mathematical model of the solar inverter is fundamental to deriving control strategies. For phase a, the voltage equation is given by:
$$ u_a = R i_a + L \frac{di_a}{dt} + e_a $$
where $u_a$ is the inverter output voltage, $i_a$ is the output current, and $e_a$ is the grid voltage. Transforming this into the dq rotating reference frame, we obtain the positive and negative sequence components, which are essential for analyzing unbalanced conditions. The dq-model is expressed as:
$$ u^+_d = (R + sL)i^+_d – \omega L i^+_q + e^+_d $$
$$ u^+_q = (R + sL)i^+_q + \omega L i^+_d + e^+_q $$
$$ u^-_d = (R + sL)i^-_d + \omega L i^-_q + e^-_d $$
$$ u^-_q = (R + sL)i^-_q – \omega L i^-_d + e^-_q $$
Here, the superscripts $+$ and $-$ denote positive and negative sequence components, respectively, while $d$ and $q$ refer to the direct and quadrature axes. This model forms the basis for developing control strategies under fault conditions, as it allows for decoupled control of active and reactive power.
Under symmetrical grid faults, all three-phase voltages dip uniformly, often accompanied by phase jumps. For instance, if the voltage drops to $U_{fault}$ with a phase shift $\phi$, the grid voltages can be represented as:
$$ e_a = \sqrt{2} U_{fault} \cos(\omega t + \phi) $$
$$ e_b = \sqrt{2} U_{fault} \cos(\omega t – 2\pi/3 + \phi) $$
$$ e_c = \sqrt{2} U_{fault} \cos(\omega t + 2\pi/3 + \phi) $$
In the dq-frame, this simplifies to $e_d = \sqrt{2} U_{fault}$ and $e_q = 0$. The instantaneous active power output of the solar inverter is given by $P = 1.5 e_d i_d$. During a fault, if the solar inverter attempts to maintain pre-fault power levels, the current $i_d$ can surge beyond safe limits, potentially triggering overcurrent protection and causing disconnection. To prevent this, a power-limiting control strategy is adopted, where the active power reference is adjusted to keep the output current within the maximum allowable limit $I_{max}$. The maximum active power that can be delivered during a symmetrical fault is:
$$ P_{max} = 1.5 e_d I_{max} $$
This approach ensures that solar inverters remain connected during faults without exceeding current ratings, thereby fulfilling LVRT requirements. For distributed solar inverters, which often do not require reactive power support, the focus is solely on active power control, simplifying the implementation.
Asymmetrical faults introduce voltage imbalances, leading to negative sequence components that cause power fluctuations and current distortion. The grid voltage under unbalanced conditions can be expressed as:
$$ u_a = U^+ \sin(\omega t + \delta^+) + U^- \sin(\omega t + \delta^-) $$
$$ u_b = U^+ \sin(\omega t + \delta^+ – 120^\circ) + U^- \sin(\omega t + \delta^- + 120^\circ) $$
$$ u_c = U^+ \sin(\omega t + \delta^+ + 120^\circ) + U^- \sin(\omega t + \delta^- – 120^\circ) $$
where $U^+$ and $U^-$ are the positive and negative sequence voltage magnitudes, and $\delta^+$ and $\delta^-$ are their phases. In the dq-frame, this yields components $[u^+_d, u^+_q, u^-_d, u^-_q]$. Using instantaneous power theory, the active and reactive power outputs are derived as:
$$ P = P_0 + P_{c2} \cos(2\omega t) + P_{s2} \sin(2\omega t) $$
$$ Q = Q_0 + Q_{c2} \cos(2\omega t) + Q_{s2} \sin(2\omega t) $$
where $P_0$ and $Q_0$ are average powers, and the terms with subscripts $c2$ and $s2$ represent double-frequency oscillations. These oscillations can stress the solar inverter and affect grid stability, necessitating control strategies to mitigate them. Common control objectives for solar inverters under asymmetrical faults include: (I) injecting balanced three-phase currents (eliminating negative sequence currents), (II) delivering constant reactive power (eliminating reactive power oscillations), and (III) delivering constant active power (eliminating active power oscillations). Each objective has trade-offs in terms of current peaks and power fluctuations.
For objective I, the reference currents are set to eliminate negative sequence components, resulting in balanced currents but significant power fluctuations. The reference currents in the dq-frame are:
$$ i^+_d = \frac{2}{3} \frac{P_0}{u^+_d}, \quad i^+_q = 0, \quad i^-_d = 0, \quad i^-_q = 0 $$
The peak current in this case is $I_I = \frac{2}{3} \frac{P_0}{u^+_d}$, and the power fluctuations are $\Delta p_I = \epsilon P_0$ and $\Delta q_I = \epsilon P_0$, where $\epsilon = U^-/U^+$ is the voltage unbalance factor.
For objective II, the goal is to maintain constant reactive power, leading to zero reactive power oscillations but higher peak currents. The reference currents are:
$$ i^+_d = \frac{2}{3} \frac{P_0 u^+_d}{(u^+_d)^2 – (u^-_d)^2}, \quad i^+_q = 0, \quad i^-_d = \frac{2}{3} \frac{-P_0 u^-_d}{(u^+_d)^2 – (u^-_d)^2}, \quad i^-_q = 0 $$
The peak current is $I_{II} = \frac{2}{3} \frac{P_0}{u^+_d (1 – \epsilon)}$, and the reactive power fluctuation is $\Delta q_{II} = \frac{2\epsilon P_0}{1 – \epsilon^2}$.
For objective III, constant active power is maintained, resulting in zero active power oscillations but increased reactive power fluctuations. The reference currents are:
$$ i^+_d = \frac{2}{3} \frac{P_0 u^+_d}{(u^+_d)^2 + (u^-_d)^2}, \quad i^+_q = 0, \quad i^-_d = \frac{2}{3} \frac{P_0 u^-_d}{(u^+_d)^2 + (u^-_d)^2}, \quad i^-_q = 0 $$
The peak current is $I_{III} = \frac{2}{3} \frac{(1+\epsilon) P_0}{u^+_d (1+\epsilon^2)}$, and the active power fluctuation is $\Delta p_{III} = \frac{2\epsilon P_0}{1 – \epsilon^2}$.
To compare these strategies, Table 1 summarizes the key characteristics under asymmetrical faults for solar inverters.
| Control Objective | Peak Current ($I$) | Active Power Fluctuation ($\Delta p$) | Reactive Power Fluctuation ($\Delta q$) | Maximum Active Power ($P_{max}$) |
|---|---|---|---|---|
| Objective I: Balanced Currents | $\frac{2}{3} \frac{P_0}{u^+_d}$ | $\epsilon P_0$ | $\epsilon P_0$ | $1.5 u^+_d I_{max}$ |
| Objective II: Constant Reactive Power | $\frac{2}{3} \frac{P_0}{u^+_d (1 – \epsilon)}$ | $0$ | $\frac{2\epsilon P_0}{1 – \epsilon^2}$ | $1.5 u^+_d (1 – \epsilon) I_{max}$ |
| Objective III: Constant Active Power | $\frac{2}{3} \frac{(1+\epsilon) P_0}{u^+_d (1+\epsilon^2)}$ | $\frac{2\epsilon P_0}{1 – \epsilon^2}$ | $0$ | $1.5 \frac{1+\epsilon^2}{1+\epsilon} u^+_d I_{max}$ |
From the table, it is evident that objective I allows the highest active power output but introduces power fluctuations, while objective II minimizes reactive power oscillations at the cost of reduced active power capacity. Objective III offers a compromise but still suffers from limitations. To overcome these drawbacks, coordinated control strategies are proposed, which combine multiple objectives to expand the active power output range while managing current peaks and power fluctuations.
The first coordinated strategy, termed flexible active power coordination, blends objectives I and II. By distributing the active power reference $P_{ref}$ between the two objectives, it ensures that the peak current does not exceed $I_{max}$. The power allocation is derived from:
$$ P_I + P_{II} = P_{ref} $$
$$ \frac{P_I}{u^+_d} + \frac{P_{II}}{u^+_d (1 – \epsilon)} = I_{max} $$
Solving these equations yields:
$$ P_I = \frac{P_{ref}}{\epsilon} – \frac{I_{max} u^+_d (1 – \epsilon)}{\epsilon} $$
$$ P_{II} = \frac{(\epsilon – 1) P_{ref}}{\epsilon} + \frac{I_{max} u^+_d (1 – \epsilon)}{\epsilon} $$
This strategy enables active power output between $P_{II max}$ and $P_{I max}$, with active power fluctuation $\Delta P_{ref} = \epsilon P_I$ and reactive power fluctuation $\Delta Q_{ref} = \epsilon P_I + \frac{2\epsilon P_{II}}{1 – \epsilon^2}$. It allows solar inverters to operate with higher active power while keeping currents within limits.
The second coordinated strategy, flexible reactive power coordination, combines objectives I and III. The power allocation is given by:
$$ P_I + P_{III} = P_{ref} $$
$$ \frac{P_I}{u^+_d} + \frac{P_{III}}{u^+_d} \cdot \frac{1+\epsilon}{1+\epsilon^2} = I_{max} $$
Solving these leads to:
$$ P_I = \frac{(1+\epsilon) P_{ref}}{\epsilon (1 – \epsilon)} – \frac{I_{max} u^+_d (1+\epsilon^2)}{\epsilon (1 – \epsilon)} $$
$$ P_{III} = -\frac{(\epsilon^2 + 1) P_{ref}}{\epsilon (1 – \epsilon)} + \frac{I_{max} u^+_d (\epsilon^2 + 1)}{\epsilon (1 – \epsilon)} $$
This strategy extends the active power range from $P_{III max}$ to $P_{I max}$, with minimal reactive power fluctuations. Both coordinated strategies enhance the flexibility of solar inverters under asymmetrical faults, allowing for tailored operation based on grid requirements—such as prioritizing active power output or reducing power oscillations.
To validate these control strategies, simulation models were developed in PSCAD/EMTDC for a 0.5 MW grid-connected solar inverter system. The parameters are listed in Table 2, which provides a detailed overview of the system configuration used in the study.
| Parameter | Value |
|---|---|
| Rated Power ($P_{rated}$) | 0.5 MW |
| DC Link Voltage ($U_{dc}$) | 800 V |
| DC Capacitance ($C$) | 5700 μF |
| Grid-Side Filter Inductance ($L$) | 1 mH |
| Switching Frequency ($f$) | 6 kHz |
| Maximum Allowable Current ($I_{max}$) | 1.2 × Rated Current |
For symmetrical faults, a three-phase voltage dip to 0.6 per unit (pu) was simulated at t = 2 s. Without control, the solar inverter’s output current surged to approximately 1.65 times the rated current, exceeding $I_{max}$. By applying the power-limiting strategy, the active power was reduced to maintain the current at 1.2 times the rated value, achieving successful LVRT. The maximum active power output during the fault was calculated as $P_{max} = 1.5 \times 0.6 \times I_{max}$, aligning with simulation results.
For asymmetrical faults, a voltage unbalance factor $\epsilon = 0.3$ was introduced, corresponding to a positive sequence voltage of 0.887 pu. Initially, the solar inverter operated under objective II, resulting in a peak current of 1.6 times the rated current—above the limit. After 0.2 s, the flexible active power coordination strategy was activated, enabling active power output from $P_{II max} = 0.373$ MW to $P_{I max} = 0.5$ MW. Throughout this range, the peak current remained at $I_{max}$, with active power fluctuations increasing from zero to $\epsilon P_I$ and reactive power fluctuations decreasing accordingly. Similarly, the flexible reactive power coordination strategy allowed output from $P_{III max} = 0.45$ MW to $P_{I max} = 0.5$ MW, with current limits respected. The simulations confirmed the theoretical derivations, demonstrating that coordinated control strategies can effectively expand the operational range of solar inverters during faults.
The performance of solar inverters under these strategies is further analyzed through power quality metrics. For instance, total harmonic distortion (THD) of output currents was monitored, remaining below 5% in all cases, compliant with grid standards. Additionally, the response time of control loops was within 10 ms, ensuring rapid adaptation to fault conditions. These aspects highlight the robustness of the proposed methods for real-world applications, where solar inverters must dynamically adjust to grid disturbances.
In conclusion, this study presents comprehensive control strategies for grid-connected solar inverters under both symmetrical and asymmetrical grid faults. For symmetrical faults, a power-limiting approach is recommended to constrain output currents within safe limits. For asymmetrical faults, coordinated control strategies that blend multiple objectives are proposed to maximize active power output while managing current peaks and power fluctuations. The flexible active power coordination strategy prioritizes active power expansion with controlled fluctuations, whereas the flexible reactive power coordination strategy focuses on minimizing reactive power oscillations. Simulation results validate the effectiveness of these strategies, showing that solar inverters can achieve LVRT compliance without sacrificing performance. Future work may explore the integration of energy storage systems with solar inverters to further enhance fault ride-through capabilities, as well as real-time implementation using digital signal processors. As solar penetration continues to grow, advanced control schemes for solar inverters will remain critical for grid stability and renewable energy integration.
The implications of this research extend to the design and operation of modern power grids, where solar inverters play a pivotal role. By adopting the proposed strategies, grid operators can ensure reliable solar power delivery even during disturbances, contributing to a resilient and sustainable energy infrastructure. Moreover, the methodologies discussed here can be adapted for other inverter-based resources, such as wind turbines and battery energy storage systems, underscoring their broad applicability. In summary, the continuous evolution of control techniques for solar inverters is essential to harnessing the full potential of solar energy in the transition toward cleaner power systems.