Dynamic Complex-Frequency Control of Grid-Forming Converters

TL;DR

The paper addresses the limited dynamic responsiveness of static complex-frequency (dVOC) control in grid-forming converters. It introduces dynamic complex-frequency control by replacing static gains with transfer-function dynamics, enabling coupled and richer frequency ($\varepsilon$) and voltage ($\omega$) responses. The authors formulate single- and multi-converter designs with aggregate target dynamics, provide a disaggregation strategy via dynamic participation factors, and establish small-signal stability guarantees under a uniform network $R/X$ ratio. Case studies on the IEEE 9-bus system demonstrate inertial-like behavior and synchronized multi-converter operation, underscoring the method's potential for delivering dynamic ancillary services in future grids.

Abstract

Complex droop control, alternatively known as dispatchable virtual oscillator control (dVOC), stands out for its unique capabilities in synchronization and voltage stabilization among existing control strategies for grid-forming converters. Complex droop control leverages the novel concept of ``complex frequency'', thereby establishing a coupled connection between active and reactive power inputs and frequency and rate-of-change-of voltage outputs. However, its reliance on static droop gains limits its ability to exhibit crucial dynamic response behaviors required in future power systems. To address this limitation, this paper introduces dynamic complex-frequency control, upgrading static droop gains with dynamic transfer functions to enhance the richness and flexibility in dynamic responses for frequency and voltage control. Unlike existing approaches, the complex-frequency control framework treats frequency and voltage dynamics collectively, ensuring small-signal stability for frequency synchronization and voltage stabilization simultaneously. The control framework is validated through detailed numerical case studies on the IEEE nine-bus system, also showcasing its applicability in multi-converter setups.

Figures (7)

• Figure 1: Dynamic complex-frequency control architecture of a GFM converter.
• Figure 2: A multi-converter network and its Kron reduction for control design.
• Figure 3: Multi-converter control setup for dynamic complex-frequency control.
• Figure 4: IEEE nine-bus system with dynamic complex-frequency controlled converters at bus 2.
• Figure 5: Block diagram of the dynamic complex-frequency control and inner control loops in a single-converter setup.