The rapid integration of renewable energy sources, particularly solar photovoltaic (PV) systems, has become a cornerstone of modern power grids. Ensuring the reliable and stable operation of these grid-connected systems during network disturbances is paramount. Among various grid faults, unbalanced voltage sags are statistically more frequent than symmetrical ones. During such events, the presence of negative-sequence voltage components and the reduction in positive-sequence voltage amplitude can cause the output current of a grid-connected solar inverter to surge dramatically. This peak current can reach several times its nominal value, threatening to trigger overcurrent protection, damage power semiconductor devices, and ultimately lead to a failure in low-voltage ride-through (LVRT) requirements. Consequently, developing effective control strategies to suppress the output peak current of solar inverters under unbalanced grid conditions is a critical challenge for enhancing the reliability and stability of PV power generation systems.
This analysis delves into the mechanism behind excessive peak currents and proposes an advanced control strategy. The core of the strategy is a refined reference current calculation algorithm that incorporates multiple adjustment parameters. This algorithm provides a flexible means to regulate both the output peak current and the power oscillations that accompany unbalanced faults. Building upon this improved algorithm, a coordinated active and reactive power control strategy is formulated. This integrated approach effectively mitigates overcurrent issues, expands the feasible active power output range during faults, and ensures compliance with grid connection standards.
A solar inverter typically interfaces the PV array with the three-phase grid. A common topology for medium to high-power applications is the two-level, three-leg voltage source converter (VSC) connected via an LCL or L filter. The dynamics of the inverter in the stationary αβ-reference frame can be described by:
$$ u_{\alpha} = Ri_{\alpha} + L\frac{di_{\alpha}}{dt} + e_{\alpha} $$
$$ u_{\beta} = Ri_{\beta} + L\frac{di_{\beta}}{dt} + e_{\beta} $$
where \( u_{\alpha}, u_{\beta} \) and \( i_{\alpha}, i_{\beta} \) are the inverter output voltages and currents, \( e_{\alpha}, e_{\beta} \) are the grid voltages, and \( R, L \) represent the filter resistance and inductance.
Under normal, balanced grid conditions, the instantaneous active and reactive power delivered by the solar inverter are given by:
$$ p = 1.5(u_{\alpha}i_{\alpha} + u_{\beta}i_{\beta}) $$
$$ q = 1.5(u_{\beta}i_{\alpha} – u_{\alpha}i_{\beta}) $$
During an unbalanced sag, the grid voltage contains both positive- and negative-sequence components. These can be expressed as:
$$ u_{\alpha} = u_{\alpha}^+ + u_{\alpha}^- = U^+\cos(\omega t + \delta^+) + U^-\cos(\omega t + \delta^-) $$
$$ u_{\beta} = u_{\beta}^+ + u_{\beta}^- = U^+\sin(\omega t + \delta^+) – U^-\sin(\omega t + \delta^-) $$
where \( U^+, U^- \) are the magnitudes of the positive- and negative-sequence voltages, and \( \delta^+, \delta^- \) are their phase angles. The degree of unbalance is often defined by the ratio \( \epsilon = U^- / U^+ \).
The primary cause of excessive peak current lies in the conventional control objective. Under normal operation, a solar inverter often operates at unity power factor, injecting active power \( P_{ref} \) while maintaining \( Q_{ref} = 0 \). The reference currents are typically derived from the positive-sequence voltage to achieve this:
$$ i_{\alpha\_ref} = \frac{2}{3}\frac{u_{\alpha}^+}{ (U^+)^2 } P_{ref}, \quad i_{\beta\_ref} = \frac{2}{3}\frac{u_{\beta}^+}{ (U^+)^2 } P_{ref} $$
When an unbalanced fault occurs, \( U^+ \) decreases significantly while \( P_{ref} \) often remains unchanged from its pre-fault maximum power point tracking (MPPT) value. According to the equations above, the reference current magnitude is inversely proportional to \( (U^+)^2 \). Therefore, a deep voltage sag causes a drastic increase in the calculated reference current, potentially exceeding the inverter’s current rating. Furthermore, the negative-sequence voltage interacts with the injected currents, leading to double-frequency (2ω) oscillations in both active and reactive power, which can destabilize the DC-link voltage.
To address power quality issues, several conventional control targets for solar inverters under unbalance exist: 1) Inject balanced sinusoidal currents (eliminate negative-sequence current), which results in large power oscillations; 2) Maintain constant reactive power, which eliminates reactive power ripple but allows active power oscillation; and 3) Maintain constant active power, which eliminates active power ripple but allows reactive power oscillation. Given that active power oscillations directly impact DC-link voltage stability and MPPT efficiency, the third objective—constant active power—is often a preferred basis. The standard reference currents for achieving constant active power \( P_{ref} \) and reactive power \( Q_{ref} \) are given by a complex vector formulation. However, this method does not inherently limit the peak phase current.
The proposed strategy introduces a flexible reference current algorithm with multiple degrees of freedom. The new algorithm in the αβ-frame is:
$$ i_{\alpha\_ref}(p) = \frac{2}{3} \frac{ u_{\alpha}^+ – k_1 u_{\alpha}^- }{ (U^+)^2 – k_1 (U^-)^2 } \cdot mP_{ref} $$
$$ i_{\beta\_ref}(p) = \frac{2}{3} \frac{ u_{\beta}^+ – k_1 u_{\beta}^- }{ (U^+)^2 – k_1 (U^-)^2 } \cdot mP_{ref} $$
$$ i_{\alpha\_ref}(q) = \frac{2}{3} \frac{ u_{\beta}^+ + k_2 u_{\beta}^- }{ (U^+)^2 + k_2 (U^-)^2 } \cdot nQ_{ref} $$
$$ i_{\beta\_ref}(q) = -\frac{2}{3} \frac{ u_{\alpha}^+ + k_2 u_{\alpha}^- }{ (U^+)^2 + k_2 (U^-)^2 } \cdot nQ_{ref} $$
$$ i_{\alpha\_ref} = i_{\alpha\_ref}(p) + i_{\alpha\_ref}(q), \quad i_{\beta\_ref} = i_{\beta\_ref}(p) + i_{\beta\_ref}(q) $$
Here, \( m, n, k_1, k_2 \) are adjustable parameters within the range [0, 1]. Their roles are pivotal:
• Parameters \( k_1 \) and \( k_2 \) primarily regulate the trade-off between peak current suppression and power oscillation. Adjusting them away from 1 reduces the peak current but reintroduces active and/or reactive power oscillations.
• Parameters \( m \) and \( n \) directly scale the active and reactive power references. Reducing them lowers the power injection, which is a straightforward but less efficient method to limit current, used only when adjustment via \( k_1, k_2 \) is insufficient.
The peak value of the three-phase output current \( I_{max} \) when using this algorithm can be derived as:
$$ I_{max} = \frac{2}{3} \left[ \frac{ mP_{ref} + \epsilon nQ_{ref} } { U^+(1 – k_1 \epsilon^2) } + \frac{ \epsilon m k_1 P_{ref} + n k_2 Q_{ref} } { U^+(1 + k_2 \epsilon^2) } \right] $$
This equation clearly shows the influence of the unbalance factor \( \epsilon \), the power references, and the four tuning parameters on the peak current. By strategically selecting these parameters, the peak current can be constrained below the inverter’s maximum allowable limit \( I_{max\_allow} \).
The instantaneous active and reactive powers resulting from this algorithm contain both constant and oscillatory components. The double-frequency oscillatory components \( \tilde{P} \) and \( \tilde{Q} \) are:
$$ \tilde{P} = \frac{ (1-k_1)\epsilon U^+ }{ (U^+)^2 – k_1 (U^-)^2 } mP_{ref} \cos(2\omega t) + \frac{ (1+k_2)\epsilon U^+ }{ (U^+)^2 + k_2 (U^-)^2 } nQ_{ref} \sin(2\omega t) $$
$$ \tilde{Q} = -\frac{ (1+k_2)\epsilon U^+ }{ (U^+)^2 + k_2 (U^-)^2 } nQ_{ref} \cos(2\omega t) + \frac{ (1-k_1)\epsilon U^+ }{ (U^+)^2 – k_1 (U^-)^2 } mP_{ref} \sin(2\omega t) $$
Setting \( k_1 = k_2 = 1 \) eliminates these oscillations, reverting to the classic constant-active-power strategy, but typically at the cost of higher peak current. The proposed algorithm thus allows for a continuous compromise between current limiting and power smoothing.
Based on this algorithm, a coordinated active and reactive power control strategy for solar inverters is established, following a logical hierarchy compliant with common grid codes:
1. Detection & Power Reference Setting: Upon detecting an unbalanced voltage sag, the positive-sequence voltage \( U^+ \) is measured. The required reactive current support \( I_{q\_ref} \) is determined according to grid code specifications (e.g., inject 2% of rated current for every 1% of voltage dip below 0.9 pu). This sets the reactive power reference \( Q_{ref} \). The active power reference \( P_{ref} \) is initially set to utilize the remaining inverter capacity \( S_{rated} \), i.e., \( P_{ref} = \sqrt{S_{rated}^2 – Q_{ref}^2} \), with \( m=n=1 \).
2. Primary Current Limiting via \( k_1, k_2 \): The parameters \( k_1 \) and \( k_2 \) are adjusted as the primary control knobs. The goal is to find the pair \( (k_1, k_2) \) that minimizes the power oscillations \( \tilde{P} \) (or a weighted sum of \( \tilde{P} \) and \( \tilde{Q} \)) while strictly satisfying the constraint \( I_{max} \leq I_{max\_allow} \). An offline optimization algorithm like Improved Particle Swarm Optimization (IPSO) can be used to pre-compute a lookup table relating the optimal \( (k_1, k_2) \) to the measured grid conditions \( (U^+, \epsilon) \) and power references.
3. Secondary Power Scaling via \( m, n \): If the voltage sag is very deep (high \( \epsilon \)), adjusting \( k_1 \) and \( k_2 \) may be insufficient to keep the current within limits, or may lead to unacceptably large power oscillations. In this case, \( k_1 \) and \( k_2 \) are fixed at 1 (prioritizing non-oscillatory active power). The parameters \( m \) and \( n \) are then reduced to scale down the power references. Priority is given to meeting the grid code’s reactive power support requirement; thus, \( n \) is set to 1 initially. The active power scaling factor \( m \) is then calculated from the peak current equation to ensure \( I_{max} = I_{max\_allow} \), yielding:
$$ m = \frac{ \frac{3}{2} U^+ I_{max\_allow} – \epsilon n Q_{ref} }{ P_{ref\_available} (1 + \epsilon) } $$
where \( P_{ref\_available} \) is the active power corresponding to the remaining capacity after reserving for \( Q_{ref} \).
The overall control block diagram for the solar inverter implements this strategy. The grid voltages are measured and separated into positive and negative sequence components using a method like a dual second-order generalized integrator (DSOGI). The sequence voltages, along with the power references and the optimized parameters from the lookup table (or the online calculation block), are fed into the proposed reference current algorithm. The calculated αβ-reference currents are then tracked using high-bandwidth proportional-resonant (PR) current controllers, which provide zero steady-state error for sinusoidal signals at the fundamental frequency. The output of the current controllers is modulated to generate the switching signals for the inverter.
To validate the proposed strategy for solar inverters, a detailed simulation model of a 0.5 MW grid-connected PV system was built. The system parameters are summarized below:
| Parameter | Value |
|---|---|
| Rated Power (Prated) | 0.5 MW |
| DC-link Voltage (Udc) | 800 V |
| DC-link Capacitance (C) | 5700 µF |
| Grid-side Filter Inductance (L) | 1 mH |
| Switching Frequency | 6 kHz |
| Maximum Allowable Peak Current | 1.2 × Rated Current |
The system operates at MPPT (0.5 MW, unity power factor) under normal conditions. An unbalanced grid fault is applied at t = 2.0 s. The proposed control strategy is activated at t = 2.4 s to demonstrate its effect.
Case 1: Moderate Sag (\( U^+ = 0.95 \) pu, \( \epsilon = 0.18 \)). According to the grid code, no reactive power support is required (\( Q_{ref}=0 \)). The conventional constant-active-power strategy causes a peak current of ~1.3 pu, exceeding the 1.2 pu limit. The lookup table provides optimal parameters \( k_1=0.645, k_2=0, m=n=1 \). With these, the peak current is successfully limited to ~1.2 pu. The trade-off is observed in the power plots: active power now exhibits a small double-frequency oscillation, while the reactive power oscillation present before 2.4 s is slightly reduced.
Case 2: Deeper Sag with Reactive Support (\( U^+ = 0.887 \) pu, \( \epsilon = 0.3 \)). The grid code mandates reactive support, resulting in \( Q_{ref} = 0.113 \) Mvar and \( P_{ref} = 0.487 \) MW. The conventional method yields a peak current of ~1.6 pu. The optimized parameters from the strategy are \( k_1=0.163, k_2=0.264, m=n=1 \). Applying these parameters successfully brings the peak current down to the 1.2 pu limit. The active power output remains high at 0.487 MW, demonstrating the strategy’s ability to extend the feasible active power output region compared to methods that simply derate power.
Case 3: Severe Sag (\( U^+ = 0.688 \) pu, \( \epsilon = 0.6 \)). This is a severe case requiring significant reactive support (\( Q_{ref} = 0.312 \) Mvar). Adjusting only \( k_1, k_2 \) is insufficient to limit the current, which would be ~3.6 pu with the conventional method. Therefore, the strategy switches to mode 3: \( k_1=k_2=1 \) (to avoid excessive power oscillation), \( n=1 \) (prioritize reactive support), and \( m \) is calculated to limit the current. This results in \( m \approx 0.15 \), meaning the active power is reduced to about 0.0725 MW. The peak current is effectively clamped at 1.2 pu. The active power is constant (no oscillation), and reactive power oscillates but at a reduced magnitude compared to the uncontrolled pre-2.4 s period.
The simulation results confirm the analysis and validate the effectiveness of the proposed coordinated control strategy for solar inverters. The key achievements are:
1. Effective Peak Current Suppression: The peak phase current is reliably constrained below the predefined safety limit (e.g., 1.2 pu) under various unbalanced sag conditions.
2. Enhanced Active Power Delivery: By utilizing the parameters \( k_1 \) and \( k_2 \) as the primary control lever, the strategy maximizes active power injection while respecting current limits, outperforming methods that rely solely on power derating.
3. Grid Code Compliance: The strategy seamlessly integrates reactive current injection requirements as per modern grid codes, ensuring system support during faults.
4. Managed Trade-offs: It provides a systematic and flexible framework to manage the inherent trade-offs among peak current, power oscillation, and power output level.
In conclusion, the challenge of overcurrent in grid-connected solar inverters during unbalanced voltage sags is effectively addressed by the proposed control strategy. The introduction of a multi-parameter reference current algorithm offers a versatile tool for current shaping. The hierarchical, coordinated control logic—prioritizing parameter-based current limiting followed by necessary power scaling—ensures robust and reliable LVRT operation. This strategy enhances the resilience of PV power plants, contributes to grid stability during disturbances, and facilitates the higher penetration of renewable energy sources into the power system.