Optimal Portfolio of Distinct Frequency-Response Services in Low-Inertia Systems

TL;DR

This paper introduces a novel optimization framework for designing cost-effective frequency response services in low-inertia power systems, accounting for multiple service types and demand-side uncertainties.

Contribution

It provides a closed-form solution for frequency dynamics, enabling algebraic security constraints in optimization, and incorporates demand-side inertia uncertainty via chance constraints.

Findings

Efficient MISOCP formulation for frequency response optimization.

Exact convex reformulation of chance constraints.

Case studies demonstrating improved frequency security.

Abstract

A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper we propose a closed-form solution to the differential equation describing frequency dynamics, which allows to obtain frequency-security algebraic constraints to be implemented in optimisation routines. This is done while considering any finite number of FR services with distinguished characteristics, such as different delivery times and activation delays. The problem defined by these frequency-security constraints can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), which can be efficiently handled by off-the-shelf conic optimisation solvers. This paper also takes into account the uncertainty in inertia contribution from the demand side by formulating the frequency-security conditions as chance constraints, for which an exact convex reformulation is provided. Finally, case studies highlighting the effectiveness of this frequency-secured formulation are presented.