Enhanced Grid Following Inverter (E-GFL): A Unified Control Framework for Stiff and Weak Grids

TL;DR

This paper addresses reliable Grid-Following Inverter (GFL) operation under both stiff and weak grids by developing a unified control framework that treats the line-inverter dynamics in the dq frame as a MIMO system perturbed by coupling. It recasts the MIMO closed-loop as a perturbed 2-SISO system with a nominal sensitivity $\tilde{S}$ and analyzes stability, robustness, and performance through disturbance-rejection objectives that obviate the need for a separate PLL. The key contributions include a decoupling strategy that bounds coupling effects, robust stability conditions under line-impedance uncertainty, and a design methodology that jointly optimizes reference-tracking, synchronization, harmonic attenuation, and filter-resonance suppression. The framework is validated via simulations and experiments, showing robust performance under asymmetric faults, grid disturbances, and low-voltage ride-through, with practical controller designs that integrate inverter dynamics into feedback synthesis. The work provides a systematic way to navigate the inherent trade-offs dictated by the Bode sensitivity integral, offering PLL-free synchronization with predictable stability margins and performance in weak-grid scenarios, thereby enhancing GFL reliability in modern power systems.

Abstract

This paper presents an extensive framework focused on the control design, along with stability and performance analysis, of Grid-Following Inverters (GFL). It aims to ensure their effective operation under both stiff and weak grid conditions. The proposed framework leverages the coupled algebraic structure of the transmission line dynamics in the $dq$ frame to express and then mitigate the effect of coupled dynamics on the GFL inverter's stability and performance. Additionally, we simplify the coupled multi-input, multi-output (MIMO) closed-loop system of the GFL into two separate single-input, single-output (2-SISO) closed-loops for easier analysis and control design. We present the stability, robust stability, and performance of the original GFL MIMO closed-loop system through our proposed 2-SISO closed-loop framework. This approach simplifies both the control design and its analysis. Our framework effectively achieves grid synchronization and active damping of filter resonance via feedback control. This eliminates the need for separate phase-locked loop (PLL) and virtual impedance subsystems. We also utilize the Bode sensitivity integral to define the limits of GFL closed-loop stability margin and performance. These fundamental limits reveal the necessary trade-offs between various performance goals, including reference tracking, closed-loop bandwidth, robust synchronization, and the ability to withstand grid disturbances. Finally, we demonstrate the merits of our proposed framework through detailed simulations and experiments. These showcase its effectiveness in handling challenging scenarios, such as asymmetric grid faults, low voltage operation, and the balance between harmonic rejection and resonance suppression.

Figures (16)

• Figure 1: (a) Conventional 3-phase PLL system that include $abc$ to $dq$ transform, PLL loop filter $K_\theta$ and voltage controlled oscillator (VCO) (integrator). (b) Linearized model of the PLL in (a) that is frequently used for stability and performance analysis of the PLL.
• Figure 2: (a) Inverter averaged model with output $RLC$ filter, interfaced to the grid via $RL$ impedance. (b) The $dq$ rotating frame.
• Figure 3: (a) The control structure with diagonal feedback controller $[K^d,K^q]$, MIMO line dynamics $G_L$ and exogenous inputs $[\hat{i}_0^d,\hat{i}_0^q]^{\top}$, $[\hat{d}^d,\hat{d}^q]^{\top}$.
• Figure 4: (a) The upper bound in (\ref{['eq:coupling_stability_upper_bound']}) for different values of $\lambda$. The lower values of $\lambda$ correspond to smaller upper bounds. (b) The RS boundary, as shown by the dashed line, consists of two distinct upper bounds. The SISO upper bound (\ref{['eq:first_RS_condition']}) and coupling upper bound. Any nominal closed-loop sensitivity $\widetilde{S}_0$ that remains below the RS boundary is considered to have RS property.
• Figure 5: (a) The quadrature closed-loop $\widetilde{T}^q$ is comprised of low-pass $\widetilde{T}_{\theta}^q$ and band-pass $\widetilde{T}_{v}^q$. This attenuates disturbances on $u_\theta$ beyond $\widetilde{T}_{\theta}^q$ cut-off frequency (dotted line) by shifting the high-frequency disturbances to $v_c^q$.

Theorems & Definitions (24)

• Proposition 3.1
• Remark 1
• Remark 2
• Proposition 3.2
• Remark 3
• Remark 4
• Proposition 4.1
• Proposition 4.2
• Remark 5
• Proposition 4.3