Energy Management Considering Unknown Dynamics Based on Extremum Seeking Control and Particle Swarm Optimization

This brief studies an energy management (EM) problem with unknown dynamics of consumer appliances. A two-level optimization model is established between the utility company and the consumers. In this model, the utility company maximizes its profit by setting the electricity price, and the consumers respond to the price by regulating power usage to minimize their costs. The aforementioned process is performed in multiple stages. In each stage, the consumer response is formulated as a constrained optimization problem, which can be transformed into an unconstrained optimization problem using the penalty function method, and then an extremum seeking control (ESC) algorithm is developed to search for the quasi-optimal power consumption of the consumers. The ESC algorithm has noncontinuous first and second derivatives with respect to the variables. We propose an approximation method to make the ESC algorithm continuous and prove that the algorithm is semiglobally practically asymptotically (SPA) stable. After the consumer response in the same stage, the utility company updates the electricity price by the particle swarm optimization (PSO) algorithm. Then, we give an EM algorithm that integrates the ESC with PSO. In simulations, the algorithm is applied to achieve EM of heating, ventilation, and air conditioning (HVAC) systems, and the results show that the algorithm can converge to a neighborhood of the optimal solution and reduce the peak load and daily load.