Optimal Real-Time Pricing of Electricity Based on Switched Markov Chain Models and Welfare Maximization

Real-time pricing (RTP) of electricity is one of the key technologies in smart grid. In RTP, the electricity price is set according to power consumption. Information about the price and power consumption is communicated through a communication network. Electricity is supplied to consumers through a power line. In this sense, a RTP system can be regarded as a cyber-physical system (CPS). In this paper, we consider the optimal RTP problem that a welfare function is maximized, where a switched Markov chain (SMC) model is utilized as a mathematical model of power consumption. Using a welfare function, we can consider a balance of electricity conservation and consumers' utility. In an SMC model, a Markov chain expressing time evolution of power consumption is switched according to the price and the transient response. This problem is reduced to a mixed integer linear programming problem.