A Novel Distributed Approach to the Optimal Power Flow Problem in Smart Grids

In this thesis,  the classical problem of the optimal power flow (OPF) in an electrical network is studied. Given a power grid, the problem is to find the optimal production of generators respecting all the constraints imposed by physics, such as Kirchhoff’ equations, and power bounds on each part of the  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 is notoriously hard due to computational limitations, and it is also undesirable due to safety reasons. The development of computational ability in each component of the network has opened new horizons, linking electrical and networking engineering. Scalability and the fast convergent properties of the OPF solution methods are highly desirable in practice. One of the main challenge in the OPF problem is the decoupling of the constraints enforced by the Kirchhoff’ laws. The groundbreaking contribution of this thesis consists in proposing a new transformation of the original problem so that it can be decomposed into a number of subproblems (one for each node) that relies on only the local information available. As a result, the proposed solution method is highly scalable. Moreover, the state-of-the-art alternating direction method of multipliers (ADMM) is adopted, which blends fast convergent properties into the proposed solution method. A partially distributed protocol based on ADMM is also proposed, 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, numerical experiments to
illustrate the behavior of proposed algorithms are provided.