Stochastic quantum models for the dynamics of power grids

Area of Science:

• Physics
• Electrical Engineering
• Complex Systems

Background:

• Electric power grids are crucial for decarbonization, but renewable energy integration challenges their stability.
• Power oscillation modes are key indicators of grid stability, traditionally classified into inter-area and intra-area modes.
• Existing numerical methods may not fully capture the complex dynamics introduced by modern grid changes.

Purpose of the Study:

• To introduce a novel analogy using stochastic quantum models for analyzing power system stability.
• To demonstrate the applicability of this quantum model analogy to power grids.
• To provide a new framework for understanding power oscillation modes.

Main Methods:

• Development of an analogy based on stochastic quantum models.
• Application of the Courant-Fisher-Weyl theorem to analyze network eigenvectors.
• Numerical simulations on simple models and a realistic European power grid model.

Main Results:

• A frequency-dependent relationship (inversely cubic) for the mean free path induced by disorder was identified in simple models.
• The Courant-Fisher-Weyl theorem provided insights into eigenvector organization and disorder resistance at low frequencies.
• Three distinct power oscillation propagation regimes (ballistic, diffusive, localized) were confirmed in a realistic European power grid model.

Conclusions:

• The stochastic quantum model analogy offers a powerful new perspective on power grid stability.
• The identified three regimes challenge the conventional two-regime view of power oscillations.
• This framework enhances understanding of power oscillation dynamics, particularly with high renewable energy penetration.