Optimal real-time pricing of electricity with consideration for decrease in price effect

A real-time pricing method of electricity is one of the important methods in smart grid technologies. When electricity conservation is needed, the price is set to a high value, and electricity conservation is achieved. The authors have proposed a theoretical framework for real-time pricing of electricity. In this method, power consumption of consumers is modeled by a switched Markov chain (SMC) model in which a Markov chain is switched according to the price and the transient response. In addition, the pricing problem is formulated as a finite-time optimal control problem for the SMC model. However, in the SMC model, decrease in price effect has not been considered. In the case where a high price is continuously set, its effect is not sustained, and becomes gradually decreased. In this paper, considering decrease in price effect, a more sophisticated version of the SMC model is proposed. For the improved SMC model, the price problem is given, and its solution method is derived.