Optimization Model of Time-of-Use Electricity Pricing Considering Dynamical Time Delay of Demand-Side Response

Traditional time-of-use (TOU) pricing models ignore the delay characteristics of user behavior; consequently, the resulting load adjustments exhibit discrete patterns, whereas actual load variations follow gradual trajectories in reality. Hence, a dynamic process is to be considered when describing user behavior and designing pricing strategy, which will, however, add to the complexity of pricing. This paper proposes a TOU pricing strategy considering user response with delay. Firstly, based on the final state of user response, the time delay of the demand response is defined. Secondly, to describe the dynamic process of load transfer, a time-varying price elasticity matrix is proposed, and its parameters are newly identified by using the weighted least squares method. Finally, based on the elasticity matrix, a mixed-integer programming model is proposed with the multi-objective of minimizing the peak–valley difference of system load and maximizing user satisfaction. An improved non-dominated sorting genetic algorithm (NSGA-II) is applied to find the Pareto front solution and obtain the optimal price of the TOU. The simulation results based on a provincial load data in China show that the proposed optimization strategy to the TOU pricing can help the system reduce peak–valley load difference and effectively smooth the load curve.