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

Yanru Ma, Pingping Wang, Dengshan Hou, Yue Yu, Shenghu Li () and Tao Gao
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Yanru Ma: Institute of Economy and Technology, State Grid Anhui Electric Power Company, Hefei 230022, China
Pingping Wang: Development and Planning Department, State Grid Anhui Electric Power Company, Hefei 230022, China
Dengshan Hou: Institute of Economy and Technology, State Grid Anhui Electric Power Company, Hefei 230022, China
Yue Yu: Institute of Economy and Technology, State Grid Anhui Electric Power Company, Hefei 230022, China
Shenghu Li: Anhui Province Key Laboratory of Renewable Energy Utilization and Energy Saving, Hefei 230009, China
Tao Gao: Anhui Province Key Laboratory of Renewable Energy Utilization and Energy Saving, Hefei 230009, China

Energies, 2025, vol. 18, issue 10, 1-16

Abstract: 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.

Keywords: power market; demand side response; time-of-use pricing; time delay; time-varying price elasticity matrix; weighted least squares method (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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