Stability Analysis of Wholesale Electricity Markets under Dynamic Consumption Models and Real-Time Pricing

TL;DR

This paper investigates the stability of wholesale electricity markets with real-time pricing and consumption models that include memory, showing conditions for stability and how memory affects market convergence.

Contribution

It introduces a stability analysis framework for markets with dynamic consumption models incorporating memory, extending previous models without memory considerations.

Findings

Market stability depends on the ratio of consumers' disutility to supply cost.

Models with both price and consumption memory expand stability regions.

Memory in consumption models accelerates convergence to market equilibrium.

Abstract

This paper analyzes stability conditions for wholesale electricity markets under real-time retail pricing and realistic consumption models with memory, which explicitly take into account previous electricity prices and consumption levels. By passing on the current retail price of electricity from supplier to consumer and feeding the observed consumption back to the supplier, a closed-loop dynamical system for electricity prices and consumption arises whose stability is to be investigated. Under mild assumptions on the generation cost of electricity and consumers' backlog disutility functions, we show that, for consumer models with price memory only, market stability is achieved if the ratio between the consumers' marginal backlog disutility and the suppliers' marginal cost of supply remains below a fixed threshold. Further, consumer models with price and consumption memory can result in greater stability regions and faster convergence to the equilibrium compared to models with price memory alone, if consumption deviations from nominal demand are adequately penalized.