In the context of achieving carbon neutrality goals, solar power generation technology has entered a new phase of development. However, solar inverters face challenges such as limited reactive power regulation range and slow dynamic response, leading to inefficient operation. Traditional solar inverters often remain idle during periods of insufficient light, resulting in low utilization rates. To address these issues, this paper proposes a reactive power regulation strategy for solar inverters based on dual constraints of Maximum Power Point Tracking (MPPT) and grid-connected point voltage. By leveraging the structural characteristics of solar inverters, this strategy maximizes the use of redundant capacity for reactive power compensation, thereby enhancing the flexibility and range of reactive power regulation.
The proposed strategy analyzes the reactive power regulation capability of solar inverters under different operating states and derives the maximum output reactive power constraints. This allows solar inverters to deliver spare reactive power to the distribution grid, improving their utilization during low-light conditions. The effectiveness of the strategy is validated through simulation and experimental results, demonstrating that solar inverters can achieve wide-range reactive power regulation under the dual constraints.
Mathematical Model of Solar Inverters
The topology of a grid-connected solar inverter typically includes solar panels, a Boost circuit with MPPT, a full-bridge inverter, and an LCL filter. The inverter converts DC power from the solar panels into AC power synchronized with the grid. In the rotating d-q coordinate system, the low-frequency mathematical model of the grid-connected inverter can be expressed as:
$$ u_d = L \frac{di_d}{dt} – \omega L i_q + u_{gd} $$
$$ u_q = L \frac{di_q}{dt} + \omega L i_d + u_{gq} $$
where \( L \) is the equivalent inductance of the filter, \( u_d \) and \( u_q \) are the d-axis and q-axis components of the grid voltage, and \( i_d \) and \( i_q \) are the active and reactive current components, respectively. The coupling between the d-axis and q-axis necessitates decoupling control to enable independent adjustment of active and reactive power. Introducing grid voltage components for feedforward compensation improves the quality of the grid-connected current. The decoupled control structure is shown below:
$$ u_d = K_p \left(1 + \frac{1}{T_i s}\right) (i_{d}^* – i_d) – \omega L i_q + u_{gd} $$
$$ u_q = K_p \left(1 + \frac{1}{T_i s}\right) (i_{q}^* – i_q) + \omega L i_d + u_{gq} $$
where \( K_p \) is the proportional coefficient, \( T_i \) is the integral time constant, and \( i_{d}^* \) and \( i_{q}^* \) are the reference currents for the d-axis and q-axis, respectively. By comparing the reference currents with the actual currents and applying decoupling control, the voltage signals are generated to regulate the output current through switching signals.
Reactive Power Regulation Strategy with Dual Constraints
The instantaneous power output of the solar inverter is given by:
$$ P = \frac{3}{2} u_d i_d $$
$$ Q = \frac{3}{2} u_q i_q $$
Assuming constant grid voltage, the active and reactive power outputs are proportional to \( i_d \) and \( i_q \), respectively. The DC-side input power is \( P_{dc} = U_{dc} I_{dc} \), and neglecting losses, the relationship between DC and AC power is:
$$ P = U_{dc} I_{dc} = \frac{3}{2} u_d i_d $$
Thus, the DC-side current \( I_{dc} \) is proportional to \( i_d \), and MPPT influences \( I_{dc} \), thereby constraining the reactive power output. Additionally, the grid-connected point voltage imposes another constraint. The voltage vector relationship when the inverter delivers lagging reactive power is:
$$ u_d^2 + u_q^2 = \left(\frac{U_{dc}}{\sqrt{3}}\right)^2 $$
The modulation index for SVPWM control is \( m = \sqrt{3} \frac{\sqrt{u_d^2 + u_q^2}}{U_{dc}} \). To ensure effective SVPWM control and output voltage quality, the maximum modulation index is 1, leading to the voltage constraint:
$$ u_d^2 + u_q^2 \leq \left(\frac{U_{dc}}{\sqrt{3}}\right)^2 $$
Combining with the power equations, the reactive power constraint due to grid voltage is derived as:
$$ Q \leq \frac{U_{dc}^2}{3 \omega L} – \frac{P^2}{\omega L} $$
The dual constraints from MPPT and grid voltage define the maximum reactive power output of the solar inverter. The overall constraint equation is:
$$ Q_{max} = \min \left( \sqrt{\left(\frac{U_{dc}^2}{3}\right) – \left(\frac{2P}{3}\right)^2}, \sqrt{S_{rated}^2 – P^2} \right) $$
where \( S_{rated} \) is the rated capacity of the solar inverter. This equation enables two operational modes:
- Mode 1: The solar inverter utilizes all redundant capacity for reactive power output without violating voltage limits.
- Mode 2: If grid voltage fluctuations occur, the solar inverter prioritizes voltage constraints to adjust reactive power output, ensuring stable operation.
The control strategy involves sampling the grid voltage to synchronize the inverter current, transforming the current into d-q components, and applying PI regulators with decoupling control. The power constraint module limits the reactive power output based on Equation (8), and SVPWM signals are generated to control the inverter. The overall control block diagram integrates these elements to achieve efficient reactive power regulation.
Simulation and Experimental Analysis
To validate the proposed strategy, a simulation model was built in MATLAB/Simulink with the following parameters: rated capacity \( S = 5 \, \text{kVA} \), DC-link voltage \( U_{dc} = 660 \, \text{V} \), grid line voltage \( U_g = 380 \, \text{V} \), inverter-side inductance \( L_1 = 1 \, \text{mH} \), filter capacitance \( C_f = 1 \, \mu\text{F} \), grid-side inductance \( L_2 = 1 \, \text{mH} \), and switching frequency \( f_s = 10 \, \text{kHz} \).
When the solar inverter operates with an active power output of \( P = 4 \, \text{kW} \), the maximum reactive power output is \( Q_{max} = 3 \, \text{kvar} \). The following table summarizes the simulation results under different reactive power commands:
| Reactive Power Command (kvar) | Active Power Output (kW) | Voltage THD (%) | Current THD (%) |
|---|---|---|---|
| 0 | 4.00 | 1.21 | 1.72 |
| 1 | 4.00 | 1.20 | 1.70 |
| 2 | 4.00 | 1.22 | 1.71 |
The results show that the solar inverter can regulate reactive power without affecting active power output, and the THD levels comply with standards. During changes in light intensity, the grid voltage fluctuates but remains within limits, and the output current adjusts dynamically. The experimental setup using dSPACE 1104 confirmed these findings, with the solar inverter achieving reactive power outputs of \( 1 \, \text{kvar} \) and \( -2.5 \, \text{kvar} \) while maintaining stable active power output.
The dynamic response of the solar inverter during reactive power adjustments is shown in the waveforms. Although brief current fluctuations occur during transitions, the system quickly stabilizes, demonstrating the strategy’s robustness. The experimental results validate that solar inverters can provide wide-range reactive power compensation under dual constraints, enhancing grid support capabilities.
Conclusion
This paper presents a reactive power regulation strategy for solar inverters based on dual constraints of MPPT and grid-connected point voltage. By deriving the maximum reactive power constraints and implementing a decoupling control scheme, the strategy enables solar inverters to utilize redundant capacity for reactive power compensation. Simulation and experimental results confirm that solar inverters can achieve wide-range reactive power regulation without compromising active power output. The proposed approach improves the flexibility and utilization of solar inverters, contributing to the stability and efficiency of distribution grids. Future work will focus on optimizing the control strategy for varying grid conditions and integrating energy storage systems with solar inverters.