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Time-of-use (TOU) is an effective price-based demand response strategy. A reasonable design of TOU strategy can effectively reduce the peak-valley difference, and then produce a lot of benefits (such as delaying power grid investment, reducing interruption cost, and improving reliability). However, changing peak-valley period has a great influence on the peak-valley difference and power supply reliability of power system. Therefore, this paper aims to investigate the optimal modification of peak-valley period considering reliability loss under multiple TOU schemes. Firstly, this paper presents a clustering model and algorithm of optimal load curve based on a minimum error iteration method. Secondly, an optimal modification of peak-valley period based on a dynamic load point method is proposed, and the traditional peak-valley difference is replaced by the global peak-valley difference to calculate the objective function. Thirdly, this paper establishes a load–reliability relation fitting model based on the back propagation neural network. Finally, the effectiveness and correctness of the proposed method are investigated by the Roy Billinton test system and reliability test system. [ABSTRACT FROM AUTHOR]

• A method of period partitioning based on the silhouette coefficient is proposed. • A TOU price optimization model considering benefits and reliability is established. • A multi-objective simulated annealing particle swarm optimization algorithm is developed. • A bi-level TOU price optimization model for high reliability demand system is presented. The reliability of power system will vary with different demand response strategies, and it is significant to make a decision on demand response for satisfying differential reliability demand of power system. First, a peak-valley period partition model with an objective of maximizing silhouette coefficient was established based on the fuzzy clustering and step-wise iteration technology. Second, this paper proposed a multi-objective time of use electricity price optimization model considering the interests of both supply and demand sides, as well as reliability demand, and a multi-objective simulated annealing particle swarm optimization algorithm was developed to obtain solution. Third, the Pareto front curve of the dual-objective function was fitted by using a third-order Hermite interpolation algorithm, and the time of use prices corresponding to the reliability demand was obtained by using the back propagation neural network algorithm. Finally, the proposed model and algorithm were verified by the RBTS system, and the results indicate good rationality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]