Generalized Swing Control Framework for Inverter-based Resources

TL;DR

This paper addresses stability in low-inertia grids dominated by inverter-based resources by introducing Generalized Swing Control (GSC), a framework that extends the swing equation to the complex power domain to couple active and reactive power with voltage and frequency dynamics. GSC uses a second-order model with matrices $\mathbf{M}$ (inertia), $\mathbf{D}$ (damping), and $\mathbf{K}$ (stiffness), and derives a generalized eigenvalue problem via $\det(\lambda^2\mathbf{M} + \lambda\mathbf{D} + \mathbf{K}) = 0$ to analyze stability, while defining the generalized position $\boldsymbol{u}_v = [\ln v, \theta_v]^T$ and its complex-frequency $\boldsymbol{\eta}_v = [\rho_v, \omega_v]^T$ in the dynamic equations $\mathbf{M}\boldsymbol{\eta}_v' + \mathbf{D}(\boldsymbol{\eta}_v - \boldsymbol{\eta}_o) + \mathbf{K}(\boldsymbol{u}_v - \boldsymbol{u}_o) = \boldsymbol{s} - \boldsymbol{s}_o$. A new performance index $\mu_{\rm ts}$ combines transient and steady-state voltage and frequency deviations to quantify controller performance, and a Monte Carlo approach tunes parameters due to nonlinear grid dynamics. Case studies on the WSCC-9 bus and all-island Irish systems compare several GSC configurations: VSM, extended/decoupled VSM, coupled VSM, and DVSM, showing that coupling and DVSM variants can improve dynamic response and damping, albeit with trade-offs in stability margins and energy sharing. Overall, GSC provides a unified, tunable platform to enhance system stability in converter-dominated grids and can be extended to higher-dimensional formulations and additional features such as current limiting and advanced mode operation.

Abstract

This paper proposes a novel control framework designed for Inverter-Based Resources (IBRs), denoted as Generalized Swing Control (GSC). The proposed GSC framework generalizes the definition of Grid-Forming (GFM) control schemes and exploits the coupling between active and reactive power dynamics. To validate the proposed scheme, we conduct extensive time-domain simulations and small-signal analysis using a modified version of the WSCC 9-bus system and a 1479-bus dynamic model of the all-island Irish transmission system. The case studies focus on evaluating the dynamic performance of the proposed framework under different configurations, including Virtual Synchronous Machine (VSM), coupled-VSM and dual-VSM schemes. To address the nonlinear nature of power system dynamics, sensitivity analysis based on Monte Carlo methods are employed to improve parameter tuning and assess the stability of GSC configurations in the studied systems.

Figures (13)

• Figure 1: WSCC 9-bus system - Sensitivity analysis based on the Monte Carlo method for vsm case - Unstable simulation rate as a function of parameter values in logarithm scale under a load variation at bus 5 applied at second 1 of the simulations.
• Figure 2: WSCC 9-bus system - Sensitivity analysis based on the Monte Carlo method for vsm case - Performance metric $\mu_{\rm ts}$ as a function of parameter values in logarithm scale, $M_{22}$ in panel (a), $D_{11}$, in panel (b), $D_{22}$ in panel (c) and $K_{11}$ in panel (d). Top 5 configurations are highlighted in each panel indicating the lowest metric values.
• Figure 3: WSCC 9-bus system - Sensitivity analysis based on the Monte Carlo method analysis for the extended vsm case - Unstable simulation rate as a function of parameter values in logarithm scale under a load variation at bus 5 applied at second 1 of the simulations.
• Figure 4: WSCC 9-bus system - Sensitivity analysis based on the Monte Carlo method for the extended vsm case - Performance metric $\mu_{\rm ts}$ as a function of parameter values in logarithm scale, $M_{11}$ in panel (a) and $K_{22}$ in panel (b). Top 5 configurations are highlighted in each panel indicating the lowest metric values.
• Figure 5: WSCC 9-bus system - Extended & decoupled vsm analysis - Effect on frequency and magnitude of the voltage behavior at bus 1, for a variation in parameters $K_{22}$ and $M_{11}$.