Distributed Quasi-Newton Method and its Application to the Optimal Reactive Power Flow Problem

We consider a distributed system of N agents, on which we define a quadratic optimization problem subject to a linear equality constraint. We assume that the agents can estimate the gradient of the cost function element-wise by measuring the steady state response of the system. Even if the cost function cannot be decoupled into individual terms, and the linear constraint involves the whole system state, we are able to design a distributed, quasi-Newton optimization algorithm. We prove finite time convergence in its centralized version, and by using the tool of average consensus we design its distributed implementation in the case in which a communication graph is given. As a testbed for the proposed method, we consider the problem of optimal distributed reactive power compensation in smart microgrids.