With the increasing integration of renewable energy sources such as photovoltaic systems, wind power, and energy storage into power grids, the system inertia has been continuously decreasing, leading to widespread weak grid conditions and frequent grid faults. Traditional grid-following solar inverters, which rely on PQ control and droop control, often fail to provide active support to the grid. In contrast, grid-forming solar inverters emulate the characteristics of synchronous generators, offering inherent grid support capabilities. This paper presents a comprehensive study on a grid-forming control strategy for solar inverters, designed to enhance grid stability under weak grid conditions and during faults. The control system incorporates active power-frequency control, reactive power-voltage control, and voltage-current control loops, inspired by the rotor mechanical and stator electrical equations of synchronous generators. Through detailed simulation and hardware-in-the-loop experiments, we validate the ability of solar inverters to participate in primary frequency regulation, fault ride-through, and reactive power support, ensuring stable grid operation without disconnection.
The proposed control strategy for solar inverters addresses the limitations of conventional approaches by leveraging the principles of synchronous generators. The active power-frequency control loop mimics the governor system of synchronous generators, providing damping and inertia to the system. The reactive power-voltage control loop replicates the excitation system, enabling voltage regulation through reactive power control. Finally, the voltage-current control loop ensures precise tracking of output voltage and current, facilitating closed-loop control. This multi-loop structure allows solar inverters to operate as voltage sources, actively supporting the grid during disturbances. In the following sections, we delve into the theoretical foundations, design implementation, simulation results, and experimental validation of this strategy, highlighting its practical applications for solar inverters in modern power systems.
Introduction to Grid-Forming Solar Inverters
The rapid deployment of solar inverters in power networks has introduced challenges related to system stability, particularly in weak grid environments. Grid-following solar inverters, which depend on the grid voltage for synchronization, are prone to instability during faults. In contrast, grid-forming solar inverters establish their voltage and frequency, acting as independent voltage sources. This capability is crucial for maintaining grid integrity under varying conditions. Our research focuses on developing a robust control framework for solar inverters that enhances grid resilience. By integrating virtual synchronous generator techniques, solar inverters can provide essential services such as inertia emulation, frequency regulation, and voltage support. This paper outlines the design, simulation, and testing of such a system, demonstrating its effectiveness through rigorous analysis.
Grid-forming solar inverters are particularly valuable in systems with high penetration of renewables, where traditional generation sources are displaced. The control strategy discussed here enables solar inverters to contribute to grid stability by adjusting active and reactive power outputs based on grid conditions. We begin by explaining the underlying principles of synchronous generators, which form the basis of our control design. Subsequently, we detail the control loops and their mathematical models, followed by simulation and experimental results. The findings underscore the potential of grid-forming solar inverters to mitigate issues like frequency deviations and voltage sags, ensuring reliable power delivery.
Control System Design for Solar Inverters
The control system for grid-forming solar inverters is structured around three main loops: active power-frequency control, reactive power-voltage control, and voltage-current control. Each loop plays a distinct role in replicating the behavior of synchronous generators. The active power-frequency control loop derives from the rotor mechanical equation, simulating the inertia and damping properties. The reactive power-voltage control loop is based on the stator electrical equation, enabling voltage regulation. The voltage-current control loop ensures accurate output waveform generation. Together, these loops allow solar inverters to operate autonomously and support the grid during disturbances.
Synchronous Generator Principles
To design a grid-forming control strategy for solar inverters, we first analyze the fundamentals of synchronous generators. The equivalent circuit of a synchronous generator connected to the grid includes resistance and inductance components, represented as R and jX, respectively. The voltage and current relationships in the dq-reference frame are essential for control implementation. The generator’s internal voltage E and grid voltage U are decomposed into d and q components, facilitating the control of active and reactive power. The equations governing these relationships are as follows:
$$ E = \begin{pmatrix} E_d \\ E_q \end{pmatrix} = \begin{pmatrix} E \cos \phi \\ E \sin \phi \end{pmatrix} $$
$$ \begin{pmatrix} I_d \\ I_q \end{pmatrix} = Y \left[ \begin{pmatrix} E_d \\ E_q \end{pmatrix} – \begin{pmatrix} U_{gd} \\ U_{gq} \end{pmatrix} \right] $$
where \( E_d \) and \( E_q \) are the d and q components of the internal voltage, \( U_{gd} \) and \( U_{gq} \) are the grid voltage components, \( I_d \) and \( I_q \) are the current components, and Y is the admittance matrix. These equations form the basis for the control loops in solar inverters, enabling precise power flow management.
Active Power-Frequency Control Loop
The active power-frequency control loop in solar inverters mimics the rotor dynamics of synchronous generators. The mathematical model is derived from the swing equation, which describes the relationship between mechanical torque, electromagnetic torque, and rotor speed. The key equation is:
$$ J \frac{d\omega}{dt} = T_m – T_e – D_p (\omega – \omega_n) $$
where J is the virtual inertia, \( D_p \) is the damping coefficient, \( \omega \) is the virtual rotor angular frequency, \( \omega_n \) is the nominal angular frequency, \( T_m \) is the virtual mechanical torque, and \( T_e \) is the virtual electromagnetic torque. The active power reference is adjusted using a droop characteristic:
$$ P_m = P_{ref} + K (\omega_n – \omega) $$
where \( P_m \) is the virtual mechanical power, \( P_{ref} \) is the reference power, and K is the droop coefficient. This control loop allows solar inverters to respond to frequency changes by modulating active power output, similar to primary frequency regulation in conventional generators. The block diagram below illustrates the control structure:
$$ \text{Block Diagram: } P_{ref} \rightarrow \text{Droop} \rightarrow \text{Integral with J and } D_p \rightarrow \omega \rightarrow \theta $$
This approach enhances the inertia of power systems with high solar inverter penetration, reducing frequency deviations during load changes or faults.
Reactive Power-Voltage Control Loop
The reactive power-voltage control loop in solar inverters emulates the excitation system of synchronous generators. It regulates the output voltage amplitude by controlling reactive power. The governing equation is:
$$ Q_{ref} – Q + K_1 (U_{ref} – U) = K_2 \frac{dE}{dt} $$
where \( Q_{ref} \) is the reference reactive power, Q is the actual reactive power, \( K_1 \) is the droop coefficient for voltage, \( U_{ref} \) is the reference voltage magnitude, U is the measured voltage magnitude, and \( K_2 \) is the voltage regulation constant. This loop ensures that solar inverters maintain voltage stability by injecting or absorbing reactive power as needed. The control block diagram is as follows:
$$ \text{Block Diagram: } Q_{ref} \text{ and } U_{ref} \rightarrow \text{Comparison with Q and U} \rightarrow \text{PI-like Control} \rightarrow E $$
By integrating this loop, solar inverters can support grid voltage during contingencies, such as voltage sags or swells, improving overall system reliability.
Voltage-Current Control Loop
The voltage-current control loop in solar inverters provides inner-loop regulation for precise output waveform generation. It transforms the internal voltage magnitude E and phase angle θ into three-phase voltages using the following equations:
$$ e_a = \sqrt{2} E \sin \theta $$
$$ e_b = \sqrt{2} E \sin (\theta – 120^\circ) $$
$$ e_c = \sqrt{2} E \sin (\theta + 120^\circ) $$
In the dq-reference frame, the control equations for the voltage and current loops are derived from the inverter’s output filter dynamics. The voltage loop control equations are:
$$ I_d^* = \left( K_{P1} + \frac{K_{I1}}{s} \right) (E_d^* – U_d) $$
$$ I_q^* = \left( K_{P1} + \frac{K_{I1}}{s} \right) (E_q^* – U_q) $$
where \( K_{P1} \) and \( K_{I1} \) are the proportional and integral gains of the voltage PI controller, \( I_d^* \) and \( I_q^* \) are the reference current components, and \( E_d^* \) and \( E_q^* \) are the reference voltage components. The current loop control equations are:
$$ E_d = \left( K_{P2} + \frac{K_{I2}}{s} \right) (I_d^* – I_d) – \omega L I_q + U_d $$
$$ E_q = \left( K_{P2} + \frac{K_{I2}}{s} \right) (I_q^* – I_q) + \omega L I_d + U_q $$
where \( K_{P2} \) and \( K_{I2} \) are the gains of the current PI controller, L is the filter inductance, and ω is the angular frequency. This dual-loop structure ensures fast and accurate tracking of voltage and current references, enabling solar inverters to maintain stability under dynamic grid conditions.
Simulation Studies
To validate the proposed control strategy for solar inverters, we conducted extensive simulation studies using MATLAB/Simulink. The simulation model included a three-level NPC inverter, LCL filter, and grid connection. Parameters such as DC voltage, AC voltage, and filter components were set to realistic values. The tests focused on grid voltage variations, power command tracking, and fault ride-through scenarios. The results demonstrate the ability of solar inverters to support the grid effectively.
Grid Voltage Variation Tests
In this test, we simulated grid voltage dips to evaluate the response of solar inverters. The grid voltage was reduced to 0.5 per unit (p.u.) from 0.9 s to 1.4 s and to 0.2 p.u. from 2 s to 3 s. The solar inverter’s output voltage closely tracked the grid voltage, maintaining stability without disconnection. The active power output was adjusted based on frequency deviations, demonstrating primary frequency regulation. For instance, when the grid frequency dropped to 49 Hz at 2 s, the solar inverter increased its active power output from 10 kW to 400 kW, and upon frequency recovery at 3 s, it returned to 10 kW. This behavior confirms that solar inverters can provide inertia support during frequency events.
The following table summarizes the simulation parameters for grid voltage tests:
| Parameter | Value |
|---|---|
| DC Voltage | 1080 V |
| AC Line Voltage | 800 V |
| Inverter Side Inductance (L1) | 135 µH |
| Filter Capacitance (C) | 42 µF |
| Grid Side Inductance (L2) | 20 µH |
Power Command Tracking Tests
We also tested the solar inverter’s ability to track active and reactive power commands. With grid voltage held constant, the active power reference was stepped from 10 kW to 20 kW at 3 s and back at 4 s. The solar inverter accurately followed the command, with minimal overshoot and settling time. Similarly, for reactive power, the reference was changed from 0 var to 10 kvar at 3 s and back at 4 s. The results showed precise tracking, highlighting the effectiveness of the control loops in solar inverters. The equations used in the control design ensure robust performance across various operating points.
The power tracking performance can be summarized with the following key points:
- Active power response time: less than 1 second
- Reactive power accuracy: within 5% of reference
- Stability maintained during transitions
Hardware-in-the-Loop Experiments
To further validate the practical applicability of the control strategy for solar inverters, we performed hardware-in-the-loop (HIL) experiments using an RT-LAB platform and a real-time controller. The setup included a 225 kW string solar inverter model, with components such as a DC source, boost converter, and three-level inverter. The control code was implemented in C and deployed to the hardware controller. Experiments covered power scheduling, MPPT tracking, and voltage ride-through tests, confirming the robustness of solar inverters in real-world scenarios.
Power Scheduling and MPPT Tracking
In the power scheduling test, the active power command for the solar inverter was reduced from 225 kW to 50 kW and then restored. The actual power output followed the command with a settling time of approximately 1 second, attributed to the PI control parameters. For MPPT tracking, the current reference was switched between 2 A and 9 A in constant voltage mode. The solar inverter’s current tracking exhibited minor oscillations during transitions, which can be mitigated by tuning the PI gains. These results underscore the importance of control parameter optimization for solar inverters to achieve fast and stable responses.
The table below outlines the HIL experiment conditions:
| Component | Specification |
|---|---|
| DC Input Voltage Range | 500-1500 V |
| Grid Voltage | 800 V |
| Rated Power | 225 kW |
| Simulation Platform | RT-LAB 5707 |
Low and High Voltage Ride-Through Tests
The solar inverter’s fault ride-through capability was evaluated under low and high voltage conditions. During a 0.2 p.u. voltage dip (160 V), the solar inverter remained connected and injected capacitive reactive current as per the grid requirements. The reactive current output closely followed the reference, aiding in voltage recovery. Similarly, during a 1.3 p.u. voltage swell (1040 V), the solar inverter supplied inductive reactive current to suppress overvoltage. These tests demonstrate that grid-forming solar inverters can enhance grid resilience by providing dynamic voltage support during faults.
The ride-through performance is characterized by the following equation for reactive current injection:
$$ I_q = K_{LVRT} (U_{ref} – U) $$
where \( I_q \) is the reactive current, \( K_{LVRT} \) is the gain for low voltage ride-through, and U is the measured voltage. This ensures that solar inverters contribute to grid stability under adverse conditions.
Conclusion
In this paper, we have presented a grid-forming control strategy for solar inverters that addresses the challenges of weak grid environments and frequent faults. By emulating synchronous generator behavior through active power-frequency, reactive power-voltage, and voltage-current control loops, solar inverters can actively support the grid by providing inertia, frequency regulation, and voltage stability. Simulation and HIL experiments confirm the effectiveness of this approach, showing that solar inverters can track power commands, participate in primary frequency regulation, and ride through voltage faults without disconnection. Future work will focus on optimizing control parameters to reduce response times and enhance robustness, further advancing the role of solar inverters in modern power systems.
The integration of grid-forming capabilities into solar inverters is a critical step toward achieving high renewable energy penetration while maintaining grid reliability. As solar inverters become more prevalent, their ability to function as voltage sources will be essential for grid stability. Our research contributes to this goal by providing a comprehensive control framework that can be implemented in practical solar inverter designs. Continued development in this area will enable solar inverters to play a pivotal role in the transition to sustainable energy systems.