Computationally Efficient Analytical Models of Frequency and Voltage in Low-Inertia Systems
Marena Trujillo, Amir Sajadi, Jonathan Shaw, Bri-Mathias Hodge
TL;DR
The work addresses the need for fast, accurate modeling of both frequency and voltage dynamics in low-inertia grids with high shares of inverter-based resources. It introduces reduced-order, linear-in-time models for frequency (via a Kron-reduced, DC-flow network and low-order SG/GFM blocks) and voltage (via per-bus Q/V dynamics coupled through reactive power), with analytic, closed-form solutions and parameter-estimation strategies. Validation against EMT simulations on WECC 9-bus and IEEE 39-bus networks shows high fidelity and orders-of-magnitude speedups, while a 2,000-bus scalability demonstration confirms practical applicability for planning and optimization. The approach offers EMT-screening capabilities and integration potential into stability-constrained optimization, enabling rapid multi-scenario and probabilistic analyses as grid-forming resources proliferate.
Abstract
In this paper, low-order models of the frequency and voltage response of mixed-generation, low-inertia systems are presented. These models are unique in their ability to efficiently and accurately model frequency and voltage dynamics without increasing the computational burden as the share of inverters is increased in a system. The models are validated against industry-grade electromagnetic transient simulation, compared to which the proposed models are several orders of magnitude faster. The accuracy and efficiency of the low-inertia frequency and voltage models makes them well suited for a variety of planning and operational studies, especially for multi-scenario and probabilistic studies, as well as for screening studies to establish impact zones based on the dynamic interactions between inverters and synchronous generators.