In the pursuit of carbon peak and carbon neutrality goals, renewable energy sources are increasingly integrated into power systems through inverter-based generation. As the penetration of renewable energy rises, challenges such as reduced system inertia and stability issues become more pronounced. To address these challenges, I have focused on enhancing the utilization of renewable energy inverters, specifically through the development of advanced control strategies. The primary types of solar inverter in modern power systems are grid-following (GFL) and grid-forming (GFM). While GFL inverters behave as current sources, GFM inverters emulate voltage sources, offering superior grid support capabilities. In this work, I propose a flexible grid-connected power control method for the grid-forming inverter, targeting improvements in dynamic performance and control flexibility.
I begin by analyzing the limitations of conventional power control methods for grid-forming inverters. Traditional droop control and virtual synchronous generator (VSG) control often result in a second-order power loop, leading to overshoot and oscillations during transient events. Moreover, the coupling between droop coefficients, inertia, and damping makes controller design cumbersome and limits the ability to achieve a customizable settling time. To overcome these issues, I introduce a proportional-integral (PI) droop-based power control scheme with feedforward terms. This approach allows the configuration of system zeros, effectively reducing the order of the system from second-order to first-order. As a result, both power reference tracking and grid frequency response exhibit improved dynamics with no overshoot, while the settling time can be flexibly designed according to application requirements.
The core of my proposed method lies in the power control loop design. For active power control, I incorporate a PI controller with parameters kiω and kip to achieve power tracking and frequency synchronization. By introducing feedforward gains kset and kD, I enable zero-pole cancellation, which transforms the second-order system into a first-order one. This not only eliminates overshoot but also makes the settling time independently adjustable. The droop coefficient Dp is solely used for primary frequency regulation, decoupled from the dynamic response. Similarly, for reactive power control, an integral controller with gain kiq is employed, and the droop coefficient Dq governs voltage support. The reactive power loop naturally behaves as a first-order system, simplifying design and ensuring predictable dynamics.
To systematically present the design, I derived mathematical models for the active and reactive power loops. The small-signal block diagram for active power control is shown in the following analysis, where Grp(s) represents the transfer function from setpoint pset to output p, and Gωp(s) represents the transfer function from grid frequency deviation Δωg to output p. The coupling coefficient Cp is defined as Cp = UCUg/X, where UC and Ug are the inverter output voltage and grid voltage magnitudes, and X is the equivalent reactance.
$$ G_{rp}(s) = \frac{C_p (k_{ip} + k_{set}) s + C_p k_{i\omega}}{s^2 + C_p k_{ip} s + C_p k_{i\omega}} $$
$$ G_{\omega p}(s) = \frac{C_p (D_p k_D + D_p k_{ip} + 1) s + C_p D_p k_{i\omega}}{s^2 + C_p k_{ip} s + C_p k_{i\omega}} $$
By configuring the zero of Grp(s) to cancel one pole, the transfer function simplifies to a first-order low-pass filter. The pole p1 determines the settling time TPset as TPset = 4.6 / p1. Similar zero-pole cancellation is applied to Gωp(s) to achieve a first-order response. The control parameters are then calculated based on the desired p1 and an auxiliary pole p2. Table 1 summarizes the key control parameters used in different scenarios.
| Settling Time | Dp | Dq | kip | kiω | kset | kD | kiq |
|---|---|---|---|---|---|---|---|
| 1.0 s | 1000 | 100 | 5.9765 × 10-5 | 1.3746 × 10-4 | -2.9882 × 10-5 | -0.1 | 0.0093 |
| 0.2 s | 1000 | 100 | 2.9882 × 10-4 | 0.0034 | -1.4941 × 10-4 | -0.1001 | 0.0465 |
| 0.5 s | 1000 | 100 | 1.1953 × 10-4 | 5.4984 × 10-4 | -5.9763 × 10-5 | -0.10006 | 0.0186 |
I validated the proposed controller through extensive simulations using MATLAB/Simulink. The simulation model includes a grid-forming inverter with an LC filter and grid impedance. The parameters are listed in Table 2. The inverter rating is 10 kW, with a DC link voltage of 700 V and a switching frequency of 20 kHz.
| Symbol | Description | Value |
|---|---|---|
| udc | DC link voltage | 700 V |
| fN | Nominal frequency | 50 Hz |
| fsw | Switching frequency | 20 kHz |
| Lf | Filter inductance | 2 mH |
| Rf | Filter resistance | 0.3 Ω |
| Cf | Filter capacitance | 20 μF |
| RC | Damping resistor | 0.1 Ω |
| Rg | Grid side resistance | 0.1 Ω |
| Lg | Grid side inductance | 2 mH |
Simulation results confirm the effectiveness of the proposed method. For a settling time of 1.0 s, the active and reactive power responses to a step change in reference show no overshoot and match the designed settling time. In contrast, conventional droop control exhibits similar performance only at slower dynamics. When the settling time is reduced to 0.2 s, the proposed method maintains a first-order response, while conventional droop control begins to show overshoot. At 0.1 s, conventional control exhibits significant overshoot and oscillations, whereas the proposed method still achieves near-ideal performance.
Further tests on grid frequency and voltage support demonstrate the primary control capabilities. A 1 Hz grid frequency step triggers an active power change of Dp times the deviation, with smooth dynamics. A 5 V grid voltage step results in a corresponding reactive power change of Dq times the deviation. The system also shows robustness under voltage sag conditions, with only a minor overshoot in active power and a maintained settling time. Under unbalanced grid voltage conditions, the power responses exhibit double-frequency oscillations but retain the first-order characteristic, providing a solid foundation for fault ride-through control design.
I also investigated the influence of the frequency-locked loop (FLL) noise on system performance. The transfer function Gωp(s) shows that high-frequency measurement noise is attenuated at a rate of -20 dB/dec, ensuring acceptable performance. Simulations with added white noise on the FLL output confirm that while steady-state power ripple increases, the dynamic settling time remains unaffected.
Experimental validation was performed on a 10 kV·A inverter platform using a TMS320F28379 digital signal processor. The experiments confirm the simulation findings. For a 5 kW step in power reference, the settling time tracks the designed values of 2.0 s and 5.0 s without overshoot. When the grid frequency drops by 0.2 Hz, the inverter increases its active power output by 0.2 kW, consistent with the droop setting. Similarly, a 5 V grid voltage increase results in a 0.5 kvar reduction in reactive power. All experimental waveforms align with theoretical expectations, confirming the method correctness and practical feasibility.
Analyzing different types of solar inverter reveals that the proposed grid-forming control method is particularly suited for applications requiring high stability and grid support. While types of solar inverter like string inverters or microinverters often operate in grid-following mode, the grid-forming approach enables autonomous grid support. By offering flexible settling times and no overshoot, the method enhances integration of various types of solar inverter into weak grids or high-penetration renewable systems. The design decouples droop coefficients from dynamic response, allowing system operators to independently specify primary frequency response and dynamic performance. This is a significant advantage over conventional methods where these parameters are tightly coupled.
In conclusion, I have developed a flexible power control strategy for grid-forming inverters that achieves customizable settling time with no overshoot. Both active and reactive power loops behave as first-order systems, simplifying design and ensuring predictable dynamics. The method leverages zero-pole cancellation via feedforward terms, enabling independent control of droop and damping. Simulation and experimental results validate the effectiveness and robustness of the approach. The proposed control enhances the performance and flexibility of grid-forming inverters, supporting the reliable operation of modern power systems with high penetration of renewable energy sources. The ability to customize dynamic response without affecting steady-state droop characteristics makes this method a valuable tool for engineers working with various types of solar inverter in diverse grid environments.