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.Comment: 8 pages, 7 Figures, accepted to the 2017 American Control Conferenc
