Stochastic quantum models for the dynamics of power grids

TL;DR

This paper introduces a novel stochastic quantum model analogy to analyze power grid stability, revealing how different regimes of power oscillation propagation can occur, which enhances understanding beyond traditional methods.

Contribution

The paper presents a new stochastic quantum model framework for power grid dynamics, demonstrating the existence of ballistic, diffusive, and localized oscillation regimes in realistic grid models.

Findings

Low-frequency mean free path scales inversely with the cube of frequency

Lowest frequency modes are strongly protected from disorder

Realistic European grid model confirms three oscillation regimes

Abstract

While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to the stability of the grid, are traditionally studied numerically with the conventional view-point of two regimes of extended (inter-area) or localized (intra-area) modes. In this article we introduce an analogy based on stochastic quantum models and demonstrate its applicability to power systems. We show from simple models that at low frequency the mean free path induced by disorder is inversely cubic in the frequency. This stems from the Courant-Fisher-Weyl theorem, which predicts a strong protection of the lowest frequency modes from disorder. As a consequence a power oscillation, induced by some local disruption of the grid, can propagate in a ballistic, diffusive or localised regime. In contrast with the conventional view-point, the existence of these three regimes is confirmed in a realistic model of the European power grid.