A Novel Distributed Approach for Optimal Power Flow Problem in Smart Grids

Abstract: In this thesis we study a classical problem of the electrical field; the optimal power flow (OPF) in an electrical network. Given a power grid, the problem is to find the optimal production of generators respecting all the constraints imposed by physics, like Kirchhoff’ equations and power bounds on each part of network. The goal of a power flow problem is to obtain complete voltage angle and magnitude information for each bus in a power system for operating conditions.Solving this problem in a centralized manner for a very large networks becomes difficult due to computational limitations and become undesirable due to safety reasons. The development of computational ability in each component of the network has opened new horizons, linking the electrical and ICT engineering. With the rapid development of smart grid infrastructures, the OPF problem is becoming very important.Scalability and the fast convergent properties of the associated solution methods are highly desirable in a practical point of view. One of the main challenge in the OPF problem is the decoupling of the constraints enforced by the Kirchhoff’ laws. Our contribution has been to propose a new formulation of the problem so that the bigger problem can be decomposable into a number of subproblems (one for each node), which relies on only the local information available. As a result, our proposed protocols are scalable. Moreover, we adopt the state-ofthe-art alternating direction method of multipliers (ADMM), which blends fast convergent properties into the proposed protocol. We also propose a partially distributed protocol based on ADMM, which relies on an intelligent central controller to handle the associated constraints of the OPF problem. In this case, the computational burden at nodes are very small, thus, the nodes can be unintelligent. Finally, we provide numerical experiments to illustrate the behavior of proposed algorithms.