Distributed gradient algorithm for constrained optimization with application to load sharing in power systems

In this paper, a distributed constrained optimization problem is discussed to achieve the optimal point of the sum of agents’ local objective functions while satisfying local constraints. Here neither the local objective function nor local constraint functions of each agent can be shared with other agents. To solve the problem, a novel distributed continuous-time algorithm is proposed by using the KKT condition combined with the Lagrangian multiplier method, and the convergence is proved with the help of Lyapunov functions and an invariance principle for hybrid systems. Furthermore, this distributed algorithm is applied to optimal load sharing control problem in power systems. Both theoretical and numerical results show that the optimal load sharing can be achieved within both generation and delivering constraints in a distributed way.