Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory (2105.13094v3)

Abstract: Power electronic converters for integrating renewable energy resources into power systems can be divided into grid-forming and grid-following inverters. They possess certain similarities, but several important differences, which means that the relationship between them is quite subtle and sometimes obscure. In this article, a new perspective based on duality is proposed to create new insights. It successfully unifies the grid interfacing and synchronization characteristics of the two inverter types in a symmetric, elegant, and technology-neutral form. Analysis shows that the grid-forming and grid-following inverters are duals of each other in several ways including a) synchronization controllers: frequency droop control and phase-locked loop (PLL); b) grid-interfacing characteristics: current-following voltage-forming and voltage-following current-forming; c) swing characteristics: current-angle swing and voltage-angle swing; d) inner-loop controllers: output impedance shaping and output admittance shaping; and e) grid strength compatibility: strong-grid instability and weak-grid instability. The swing equations are also derived in dual form, which reveal the dynamic interaction between the grid strength, the synchronization controllers, and the inner-loop controllers. Insights are generated into cases of poor stability in both small-signal and transient/large-signal. The theoretical analysis and simulation results are used to illustrate cases for simple single-inverter-infinite-bus systems and a multi-inverter power network.

• The paper introduces a duality theory that unifies grid-forming frequency droop control with grid-following PLL synchronization.
• The paper recasts inverter roles by defining grid-forming as current-following voltage-forming and grid-following as voltage-following current-forming in power grids.
• The paper reveals stability implications and swing dynamics for both inverter types, guiding robust control strategies for renewable integration.

Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory

The paper "Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory" presents a comprehensive examination of power electronic converters used in integrating renewable energy resources into power systems, specifically focusing on the duality between grid-forming (GFM) and grid-following (GFL) inverters. The authors propose a new perspective based on duality theory, which unifies the grid-synchronization and interfacing characteristics of these two inverter types. This theory provides fresh insight into their operation and interaction within power systems.

Key Concepts and Findings

1. Duality in Synchronization: The paper delineates a duality between the synchronization mechanisms of grid-forming and grid-following inverters. A grid-forming inverter employs frequency droop control to synchronize with the grid, akin to a synchronous generator. In contrast, a grid-following inverter utilizes a phase-locked loop (PLL) for grid synchronization. The duality theory posits that these synchronization methods are essentially duals, with frequency droop being equivalent to $i_d$-$\omega$ droop and the PLL corresponding to $v_q$-$\omega$ droop under certain conditions.
2. Grid-Interfacing Characteristics: The duality perspective recasts the traditional roles of these inverters into a current-following voltage-forming inverter for grid-forming inverters, and a voltage-following current-forming inverter for grid-following inverters. This reclassification offers a more precise understanding of their grid-interfacing characteristics.
3. Swing Characteristics: The paper introduces the concept of swing dynamics to describe the synchronization properties of both inverters. Grid-forming inverters exhibit current-angle or $P$-angle swing characteristics, whereas their dual, the grid-following inverters, show voltage-angle or $Q$-angle swing characteristics.
4. Stability Implications: The research provides insights into stability implications for both inverter types. It illustrates that both types are susceptible to instability under certain grid strengths due to interactions between the grid and synchronization controllers. Notably, grid-forming inverters can become unstable in strong grids with low impedance, while grid-following inverters are unstable in weak grids due to high grid impedance.
5. Transient Stability and Islanding Operation: The paper explores the implications of duality for transient stability. It is shown that just as two grid-forming inverters can synchronize with each other in island operation, two grid-following inverters can also synchronize when passive loads are involved, extending conventional perceptions of their operational capabilities. Moreover, duality also implies that both inverter types have swing characteristics driven by virtual inertia and damping, analogous to synchronous machines.

Practical and Theoretical Implications

The duality theory has significant implications for designing and operating power systems with high penetration of inverter-based resources (IBRs). By uncovering the symmetry in the operational principles of grid-forming and grid-following inverters, the theory can guide the development of more robust control strategies and enhance the stability of power systems. This unified approach can also shed light on the previously observed phenomena such as poor stability in certain configurations and provide a foundation for new inverter technologies and methodologies in smart grids.

Future Developments

Future research might explore applying this duality framework to more complex, multi-inverter systems, potentially leading to new interpretations of dynamic interactions in power systems. The theory could also inform the development of advanced grid codes and standards for IBR integration. Additionally, the exploration of this duality in other domains such as power quality and voltage stability could provide further insights and innovations.

In conclusion, the duality theory proposed in this paper establishes a coherent framework for understanding the intricate dynamics of grid-forming and grid-following inverters, paving the way for advancements in both theoretical analysis and practical applications in modern power systems.