The integration of distributed photovoltaic (PV) systems into power distribution networks has transformed traditional radial networks into multi-source, multi-load coexistence networks. This evolution complicates power flow and voltage distribution characteristics, often leading to three-phase imbalance issues. As a solar inverter is a critical component in grid-connected PV systems, its control strategy must address these imbalances to ensure stable operation. This article explores a reactive power control (RPC)-based adaptive method for suppressing three-phase imbalance in solar inverters, enabling unbalanced compensation and stable active power output. The approach leverages the inverter’s idle capacity to provide grid support, enhancing reliability without requiring extensive communication infrastructure.
With the proliferation of distributed solar energy, the power distribution network faces increased volatility due to fluctuating PV output. Three-phase imbalance, characterized by negative-sequence components, induces secondary ripple currents and voltages in the solar inverter’s DC side, degrading control performance and potentially causing tripping events. Traditional voltage regulation methods under balanced conditions may exacerbate unbalanced reactive power flow, worsening grid conditions. Therefore, developing adaptive control strategies for solar inverters is essential to mitigate these effects. This article proposes a novel RPC-based technique that adjusts reactive power injection or absorption based on local measurements, reducing voltage imbalance and ensuring continuous operation of PV generation units.
The voltage characteristics of distributed PV integration under balanced conditions can be described by a simple model. Consider a solar inverter connected to the grid at the point of common coupling (PCC), where the grid voltage is denoted as \(V_G\), the PCC voltage as \(V_n\), and the line impedance as \(R + jX\). The active and reactive power outputs from the solar inverter are \(P_n\) and \(Q_n\), respectively. The PCC voltage magnitude is approximated by:
$$|V_n| = |V_G| + \frac{P_n \cdot R + Q_n \cdot X}{|V_G|}$$
This equation shows that both active and reactive power can influence voltage regulation in balanced networks. However, under three-phase imbalance, this model becomes inadequate due to the presence of negative-sequence components. The line voltage unbalance rate (LVUR) is a common metric for assessing imbalance, defined as:
$$\text{LVUR\%} = \frac{\max\{\Delta |V_{AB}|, \Delta |V_{BC}|, \Delta |V_{CA}|\}}{|V_{\text{ave}}|} \times 100$$
where the average line voltage is:
$$|V_{\text{ave}}| = \frac{|V_{AB}| + |V_{BC}| + |V_{CA}|}{3}$$
Reducing the deviation in line voltage magnitudes lowers the LVUR, but achieving this in unbalanced networks requires coordinated control of the solar inverter’s reactive power.
To address this, the proposed method utilizes the solar inverter’s available capacity for reactive power exchange. The maximum reactive power capacity of a solar inverter, given its rated apparent power \(S_{\text{max}}\) and active power output \(P_{\text{PV}}\), is:
$$Q_{\text{max}} = \pm \sqrt{(S_{\text{max}})^2 – (P_{\text{PV}})^2}$$
This capacity allows the solar inverter to inject or absorb reactive power dynamically, compensating for voltage imbalances. The core of the approach is an adaptive control strategy based on RPC, which adjusts control gains according to grid conditions. The control框图 involves sequence decomposition of grid voltages and currents, transformation to the \(\alpha\beta\) coordinate system, and generation of reference currents for active and reactive power control.
The grid voltage and current at the PCC are decomposed into positive, negative, and zero-sequence components. For a three-wire system without neutral grounding, zero-sequence components are negligible. In the \(\alpha\beta\) coordinate system, the positive and negative-sequence voltages are expressed as functions of time:
$$\begin{bmatrix} v^+_\alpha \\ v^+_\beta \end{bmatrix} = V^+ \begin{bmatrix} \cos(\omega t + \psi^+) \\ \sin(\omega t + \psi^+) \end{bmatrix}$$
$$\begin{bmatrix} v^-_\alpha \\ v^-_\beta \end{bmatrix} = V^- \begin{bmatrix} \cos(\omega t – \psi^-) \\ -\sin(\omega t – \psi^-) \end{bmatrix}$$
where \(\omega\) is the grid angular frequency, and \(V^+\), \(\psi^+\), \(V^-\), \(\psi^-\) are the magnitudes and phase angles of the positive and negative sequences. The instantaneous active power \(p\) and reactive power \(q\) are derived from:
$$\begin{bmatrix} p \\ q \end{bmatrix} = \frac{3}{2} \begin{bmatrix} v_\alpha & v_\beta \\ v_\beta & -v_\alpha \end{bmatrix} \begin{bmatrix} i_\alpha \\ i_\beta \end{bmatrix}$$
Using the sequence components, the reference currents for active and reactive power control are calculated. The active current references in the \(\alpha\beta\) frame are:
$$\begin{bmatrix} i^{(p)}_\alpha \\ i^{(p)}_\beta \end{bmatrix} = \frac{2}{3} \frac{P^+}{(v^+_\alpha)^2 + (v^+_\beta)^2} \begin{bmatrix} v^+_\alpha \\ v^+_\beta \end{bmatrix} + \frac{2}{3} \frac{P^-}{(v^-_\alpha)^2 + (v^-_\beta)^2} \begin{bmatrix} v^-_\alpha \\ v^-_\beta \end{bmatrix}$$
Similarly, the reactive current references are:
$$\begin{bmatrix} i^{(q)}_\alpha \\ i^{(q)}_\beta \end{bmatrix} = \frac{2}{3} \frac{Q^+}{(v^+_\alpha)^2 + (v^+_\beta)^2} \begin{bmatrix} v^+_\beta \\ -v^+_\alpha \end{bmatrix} + \frac{2}{3} \frac{Q^-}{(v^-_\alpha)^2 + (v^-_\beta)^2} \begin{bmatrix} v^-_\beta \\ -v^-_\alpha \end{bmatrix}$$
Here, \(P^+\), \(P^-\), \(Q^+\), and \(Q^-\) are the reference active and reactive powers for positive and negative sequences. To enable flexible power control under voltage imbalance, control gains \(k_p\) and \(k_q\) are introduced:
$$k_p = \frac{P^+}{P}, \quad k_q = \frac{Q^+}{Q}$$
where \(P\) and \(Q\) are the total active and reactive powers. The magnitudes of positive and negative-sequence currents are then:
$$I^+_p = \frac{2}{3} \frac{k_p P}{V^+}, \quad I^-_p = \frac{2}{3} \frac{(1 – k_p) P}{V^-}$$
$$I^+_q = \frac{2}{3} \frac{k_q Q}{V^+}, \quad I^-_q = \frac{2}{3} \frac{(1 – k_q) Q}{V^-}$$
These equations allow the solar inverter to adjust its output based on real-time grid conditions, effectively compensating for imbalance.
Under normal operation, the solar inverter operates at unity power factor within a voltage range of 0.95 to 1.05 per unit. When voltage deviations occur, the inverter injects or absorbs reactive power. The reactive current reference \(I_q\) is determined by:
$$I_q = \begin{cases} \mu(1 – V_{\text{gp}}) \times I, & 1 – \frac{1}{\mu} \leq V_{\text{gp}} \leq 0.95 \\ I, & V_{\text{gp}} < 1 – \frac{1}{\mu} \end{cases}$$
where \(I\) is the rated apparent current, \(V_{\text{gp}}\) is the instantaneous grid voltage in per unit, and \(\mu\) is a reactive current regulation coefficient. This adaptive mechanism ensures that the solar inverter responds promptly to voltage sags or swells, enhancing grid stability.
To validate the proposed control strategy, a simulation model was developed on the PSCAD/EMTDC platform. The system includes a three-phase solar inverter with a bridge topology, connected to a distribution network. Key parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Simulation Environment | PSCAD/EMTDC |
| Distribution Network Voltage | 0.4 kV |
| Line Impedance | 0.268 + j0.101 Ω |
| Solar Inverter Maximum Capacity | 51 kVA |
| Solar Inverter Maximum Active Output | 0.05 MW |
| Simulated Three-Phase Imbalance Rate | 23% |
| Target Maximum Voltage Unbalance | <2% |
The solar inverter circuit employs a three-phase bridge with a switching frequency of 10 kHz. Filter components include inductors \(L_1 = 3 \, \text{mH}\) and \(L_2 = 1.5 \, \text{mH}\), and a capacitor \(C = 9.4 \, \mu\text{F}\). A damping resistor of 10 Ω is connected in parallel with \(L_2\) to suppress oscillations. The DC link voltage is set to 250 V, with an active power reference of 40 kW. To simulate grid imbalance, a single-phase voltage regulator is inserted in series with the AC side at 6 seconds, creating a 23% three-phase imbalance rate.
Simulation results demonstrate the effectiveness of the RPC-based control. Before intervention, the grid exhibits significant current imbalance and fluctuations in DC voltage and power output. After the solar inverter activates the control strategy at 6.1 seconds, the three-phase currents rapidly balance within 0.05 seconds, reducing the imbalance rate from 23% to 2%. The DC-side voltage ripple decreases from ±0.005 pu to ±0.0002 pu, and the active power output stabilizes with minimal oscillation. This confirms that the solar inverter can effectively suppress negative-sequence components, ensuring stable grid connection.
The performance of the solar inverter under various imbalance conditions is further analyzed through additional simulations. Table 2 compares key metrics before and after applying the RPC control.
| Metric | Without Control | With RPC Control |
|---|---|---|
| Three-Phase Current Imbalance Rate | 23% | 2% |
| DC Voltage Ripple (peak-to-peak) | 0.01 pu | 0.0004 pu |
| Active Power Fluctuation | High | Low |
| Reactive Power Exchange | Negligible | Adaptive |
| Grid Voltage Stability | Poor | Improved |
The solar inverter’s ability to dynamically adjust reactive power based on local measurements allows for real-time compensation without extensive communication. This is particularly advantageous in distributed PV systems where centralized control may be impractical. The control strategy also incorporates a proportional-resonant (PR) controller for precise current tracking, enhancing the solar inverter’s response to grid disturbances. The PR controller transfer function in the \(\alpha\beta\) frame is:
$$G_{\text{PR}}(s) = K_p + \frac{2K_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2}$$
where \(K_p\) is the proportional gain, \(K_r\) is the resonant gain, \(\omega_c\) is the cutoff frequency, and \(\omega_0\) is the fundamental frequency. This ensures zero steady-state error for sinusoidal references, critical for unbalanced conditions.
Moreover, the economic and operational benefits of using solar inverters for grid support are significant. By utilizing idle inverter capacity, no additional hardware is required for reactive power compensation, reducing costs. The solar inverter’s participation in voltage regulation also defers grid infrastructure upgrades, especially in areas with high PV penetration. To quantify these benefits, consider the reactive power capability of a typical solar inverter over a day. Assuming a 50 kVA solar inverter with a capacity factor of 20%, the available reactive power range can be calculated using:
$$Q_{\text{available}}(t) = \pm \sqrt{S_{\text{max}}^2 – P_{\text{PV}}(t)^2}$$
where \(P_{\text{PV}}(t)\) varies with solar irradiance. This capability enables continuous grid support, even during low PV generation periods.
In practice, implementing this control strategy requires coordination among multiple solar inverters in a distribution network. A decentralized approach can be adopted, where each solar inverter adjusts its reactive power based on local voltage measurements and pre-defined droop characteristics. The droop equation for reactive power control is:
$$Q_i = Q_{i0} + K_q (V_{\text{ref}} – V_i)$$
where \(Q_i\) is the reactive power output of the i-th solar inverter, \(Q_{i0}\) is the nominal reactive power, \(K_q\) is the droop coefficient, \(V_{\text{ref}}\) is the reference voltage, and \(V_i\) is the local voltage measurement. This ensures proportional sharing of reactive power among solar inverters, preventing overloading and maintaining voltage within limits.
The impact of solar inverter control on overall grid harmonics must also be considered. Under unbalanced conditions, the solar inverter may introduce low-order harmonics due to nonlinear control actions. However, the use of PR controllers and careful filter design can mitigate this. The total harmonic distortion (THD) of the solar inverter output current should be maintained below 5%, as per grid standards. The THD is computed as:
$$\text{THD\%} = \frac{\sqrt{\sum_{h=2}^{H} I_h^2}}{I_1} \times 100$$
where \(I_h\) is the harmonic current magnitude at order \(h\), and \(I_1\) is the fundamental current magnitude. Simulations show that with the proposed control, the THD remains within acceptable limits, ensuring compatibility with grid codes.
Future work could explore integration with energy storage systems to enhance the solar inverter’s flexibility. By combining battery storage with the solar inverter, both active and reactive power can be managed more effectively, providing inertia support and frequency regulation. The control framework can be extended to include predictive algorithms for forecasting PV generation and grid imbalance, enabling proactive adjustments. Additionally, standardization of communication protocols for solar inverter coordination in unbalanced grids will be crucial for large-scale deployment.
In conclusion, the proposed RPC-based adaptive control strategy for solar inverters offers a robust solution for mitigating three-phase imbalance in distribution networks with high PV penetration. By leveraging the solar inverter’s reactive power capacity, the method compensates for negative-sequence components, stabilizes DC voltage, and ensures continuous active power output. Simulation results validate its effectiveness, demonstrating rapid imbalance suppression and improved grid stability. This approach not only enhances the reliability of solar inverters but also contributes to the overall resilience of power systems, supporting the transition to renewable energy. As distributed PV adoption grows, such advanced control techniques will be essential for maintaining power quality and enabling sustainable grid operation.
The versatility of the solar inverter as a grid-support device underscores its importance in modern power networks. Through adaptive reactive power control, solar inverters can address voltage imbalance, reduce losses, and defer infrastructure investments. Future developments should focus on scalability and interoperability, ensuring that solar inverters from different manufacturers can collaborate seamlessly. With ongoing advancements in power electronics and control theory, the solar inverter will continue to play a pivotal role in achieving a clean and stable energy future.