Discovery and Characterization of Cross-Area and Intra-Area SSOs Sensitive to Delay in Droop Control of Grid-Forming Converters

TL;DR

This work investigates subsynchronous oscillations (SSOs) in grids with grid-forming converters (GFCs), revealing a novel cross-area SSO in a 2-area IEEE system with 100% IBR penetration. It develops both space phasor calculus (SPC) and quasistationary phasor calculus (QPC) models, showing that QPC fails to capture SSOs while SPC captures both intra- and cross-area modes; EMT simulations validate the SPC-based findings. The cross-area SSO comprises GFC groups from different areas oscillating against each other, with a dominant cross-area mode near $40.59$ Hz and damping around $-0.27\%$, and a second mode near $40.23$–$41.06$ Hz depending on case. Importantly, a delay in the power-frequency droop control ($\tau_p$) stabilizes these modes, with $\tau_p \ge 3$ ms stabilizing all cases, underscoring the need for SPC-based analysis and careful droop-delay tuning in high-IBR grids.

Abstract

Subsynchronous oscillations (SSOs) involving grid-forming converters (GFCs) are in a less familiar territory of power system dynamics. This letter reports a new phenomenon namely cross-area SSOs in grids with 100% droop-controlled GFC-based renewable penetration, which was discovered during our study on evaluating the adequacy of quasistationary phasor calculus (QPC) and space phasor calculus (SPC)-based models in capturing SSOs. We present frequency-domain characterization of such oscillatory modes in addition to intra-area SSOs in grids involving GFCs and study the impact of a delay in power-frequency droop feedback loop in regards to their stability. Electromagnetic transient (EMT) simulations validate our findings.

Figures (7)

• Figure 1: (a) Circuit model of GFC with dc-side representing functional model of a renewable source, (b) power-frequency droop with delay $\tau_p$.
• Figure 2: Inner current and voltage control loops, and outer voltage control loop of GFC.
• Figure 3: Case 4: Cross-area SSO modes forming distinct GFC groups in modified IEEE $2$-area test system with 100% IBR penetration.
• Figure 4: Case ($4$): (a) Comparison of maximum singular values of QPC and SPC models when $\tau_p = 2$ ms, (b) the loci of the SSO modes as the delay $\tau_p$ varies.
• Figure 5: Case (4): Compass plots of normalized participation factor magnitudes and modeshape angles of the dominant states contributing to the cross-area SSO modes for $\tau_p = 2$ ms.