Conditions for Regional Frequency Stability in Power System Scheduling -- Part I: Theory

TL;DR

This paper develops a mathematical framework to determine conditions ensuring regional frequency stability in power systems, accounting for inter-area oscillations, and enabling optimized ancillary service co-optimization.

Contribution

It introduces the first explicit mathematical conditions for regional frequency stability considering inter-area oscillations, integrating analysis with regression methods.

Findings

Derived conditions are linear inequalities for stability.

Conditions enable co-optimization of ancillary services.

Framework applicable to various power system configurations.

Abstract

This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are discussed, demonstrating that the post-fault frequency evolution in any given region is equal to the frequency evolution of the Centre Of Inertia plus certain inter-area oscillations. This finding leads to the deduction of conditions for guaranteeing frequency stability in all regions of a power system, a deduction performed using a mixed analytical-numerical approach that combines mathematical analysis with regression methods on simulation samples. The proposed stability conditions are linear inequalities that can be implemented in any optimisation routine allowing the co-optimisation of all existing ancillary services for frequency support: inertia, multi-speed frequency response, load damping and an optimised largest power infeed. This is the first reported mathematical framework with explicit conditions to maintain frequency stability in a power system exhibiting inter-area oscillations in frequency.