Stability analysis of nonlinear stochastic flexibility function in smart energy systems

TL;DR

This paper conducts a rigorous stability analysis of nonlinear stochastic flexibility functions in smart energy systems, crucial for demand-side management and market integration, supported by simulations confirming theoretical findings.

Contribution

It introduces a stability analysis framework for both deterministic and stochastic flexibility functions, advancing understanding of their dynamic behavior in energy systems.

Findings

Stability conditions for deterministic flexibility functions derived.

Stability criteria established for stochastic flexibility functions.

Simulations confirm analytical stability results.

Abstract

Demand-side management provides a great potential for improving the efficiency and reliability of energy systems. This requires a mechanism to connect the market level and the demand side. The flexibility function is a novel approach that bridges the gap between the markets and the dynamics of physical assets at the lower levels of the energy systems and activates demand-side flexibility with the purpose of decision-making as well as for offering a new framework for balancing and grid services. Employing this function as a key for many decision-making and control algorithms reveals that a mathematically rigorous stability analysis is required for it. In this paper, we investigate the stability properties of two nonlinear flexibility functions, as a dynamic mapping between electricity price and power consumption. Specifically, we analyze the stability of a deterministic flexibility function and an It\^{o} stochastic flexibility function. Simulation results are also provided to demonstrate the dynamics of the flexibility functions and to show that the analytical results hold.