A refined consumer behavior model for energy systems: Application to the pricing and energy-efficiency problems. (15th February 2022) - Zhang, Chao; Lasaulce, Samson; Wang, Li; Saludjian, Lucas; Poor, H. Vincent
Abstract: Sum-utility maximization is an important problem in the optimization of energy systems. A conventional assumption in addressing this problem is that the utility to be maximized is concave. But for some key applications, such an assumption is not reasonable and does not reflect well the actual behavior of the consumer. To address this issue, the authors pose and address a more general optimization problem, namely by assuming the consumer's utility to be sigmoidal and in a given class of functions. The considered class of functions is attractive for at least two reasons. First, the classical NP-hardness issue associated with sum-utility maximization is circumvented. Second, the considered class of functions encompasses well-known performance metrics used to analyze problems of pricing and energy-efficiency. This allows one to design a new and optimal inclining block rate (IBR) pricing policy which also has the virtue of flattening the power consumption and reducing the peak power. We also show how to maximize the energy-efficiency using a low-complexity algorithm. When compared to existing policies, simulations fully support the benefit of using the proposed approach. Highlights: Using prospect theory to refine consumer behavior models with sigmoidal functions. Solve the structured sigmoidal programming problem to maximize the sum-utility. Formally demonstrate the optimality of inclining block rates to maximize the social welfare. Propose a low-complexity bisection-based algorithm to maximize the profit associated with a unit power consumption.