Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems

TL;DR

This paper develops LIFE and LIVE, low-order, physics-based models for frequency and voltage evolution in grid-forming inverter–dominated power systems, addressing critical gaps left by traditional synchronous-generator–centric models. By explicitly modeling GFMs and exploiting DC power-flow reductions and matrix-exponential solutions, the authors produce fast, scalable representations that capture spatial-temporal frequency heterogeneity and Q-V dynamics, validated against EMT simulations on 9-bus and 39-bus benchmarks and demonstrated on a 25,000-bus synthetic grid. The results show substantial speedups over EMT while preserving key performance metrics (nadir, RoCoF, voltage changes), enabling new planning and operational analyses, including dynamic security assessment, parametric studies, and optimization-based planning with stability constraints. Collectively, LIFE and LIVE offer a practical, scalable framework for accurate transient analysis in future low-inertia, inverter-rich networks, supporting improved reliability and investment decisions in large-scale power systems.

Abstract

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the Newtonian mechanics of synchronous generators, assuming that the frequency dynamics across a system are approximately homogeneous, and assume the dynamics of nodal voltages for most operating conditions are negligible, and thus are not directly computed at all buses. As a result, the use of system frequency models results in the systematic underestimation of frequency minimum nadir and maximum RoCoF, and provides no insight into the reactive power-voltage dynamics. This paper proposes a low-order model of both frequency and voltage response in grid-forming inverter-dominated power systems. The proposed model accounts for spatial-temporal variations in frequency and voltage behavior across a system and as a result, demonstrates the heterogeneity of frequency response in future renewable power systems. Electromagnetic transient (EMT) simulations are used to validate the utility, accuracy, and computational efficiency of these models, setting the basis for them to serve as fast, scalable alternatives to EMT simulation, especially when dealing with very large-scale systems, for both planning and operational studies.

Figures (13)

• Figure 1: Frequency response block diagram and response shape for: 1) SGs (left) and 2) GFMs (right) sajadiSynchronizationElectricPower2022.
• Figure 2: PowerWorld simulation results of the WECC system following the outage of the Palo Verde Nuclear Generating Station, the system dimensioning contingency.
• Figure 3: One-line diagram of the WSCC 9-bus system.
• Figure 4: Sending-end reactive power with respect to $\delta_{SR}$ and receiving-end voltage. $V_S = 1.0$ and $X = 0.05$.
• Figure 5: Low-order model of reactive droop.