Biblio
The advent of smart grids offers us the opportunity to better manage the electricity grids. One of the most interesting challenges in the modern grids is the consumer demand management. Indeed, the development in Information and Communication Technologies (ICTs) encourages the development of demand-side management systems. In this paper, we propose a distributed energy demand scheduling approach that uses minimal interactions between consumers to optimize the energy demand. We formulate the consumption scheduling as a constrained optimization problem and use game theory to solve this problem. On one hand, the proposed approach aims to reduce the total energy cost of a building's consumers. This imposes the cooperation between all the consumers to achieve the collective goal. On the other hand, the privacy of each user must be protected, which means that our distributed approach must operate with a minimal information exchange. The performance evaluation shows that the proposed approach reduces the total energy cost, each consumer's individual cost, as well as the peak to average ratio.
In this paper, we consider distributed algorithm based on a continuous-time multi-agent system to solve constrained optimization problem. The global optimization objective function is taken as the sum of agents' individual objective functions under a group of convex inequality function constraints. Because the local objective functions cannot be explicitly known by all the agents, the problem has to be solved in a distributed manner with the cooperation between agents. Here we propose a continuous-time distributed gradient dynamics based on the KKT condition and Lagrangian multiplier methods to solve the optimization problem. We show that all the agents asymptotically converge to the same optimal solution with the help of a constructed Lyapunov function and a LaSalle invariance principle of hybrid systems.