A distributed approach to the optimal powerow flow problem and its privacy properties

Abstract: In this thesis we address the optimal power flow (OPF) problem, where the goal is to find an optimal operating point of an electric network, which agrees to laws of physics and other physical limitations of the network. Traditionally the OPF problem has only been solved in the transmission network, which is responsible for transmitting the electricity from the power plants to cities. But with the introduction of the smart grid, the OPF problem has become relevant, not only in transmission networks, but also in distribution networks, which deliver electricity to end users. Addressing the OPF problem in the distribution network is challenging in many aspects. Firstly, the general formulation is non-convex, and therefore designing algorithms, which are both efficient and optimal is usually challenging. However in practice, efficient algorithms are desirable, and therefore it is inevitable that one has to rely on heuristics to design solutions approaches for the general OPF problem. In this thesis we seek methods, based on con- vex optimization techniques to address the general OPF problem. During the solution approach, we capitalize on sequential approximations, in order to gracefully manipulate the non-convexity of the problem. Of course, the optimality of the algorithm is not guaranteed due to the non-convexity of the problem. Numerical results are provided to compare the proposed algorithm with other existing approaches. Another challenge is the scalability of the related algorithms. The large size of the electrical network ruins the possibility of relying on centralized solution approaches, which are usually poor in scalability. Therefore, it is desirable to seek distributed methods, which have rich scalability properties. In this thesis we employ the state-of-the-art alternating direction method of multiplier (ADMM) method to enrich the proposed algorithms with scalability properties. The original non-convex OPF problem is broke into sub problems (one for every bus), which are coordinated via a thin protocol to find a good operating point. Numerical results are provided to show the applicability of our algorithm in large electrical network setups. The proliferation of smart grid technologies, their processing information together with sophisticated statistical data mining and pattern recognition techniques have given rise to another threat, privacy breaches associated with the households life styles. Therefore, it is worth of investigating algorithms, which can suppress such threats. Even though, we do not model mechanisms for privacy guarantees as an explicit design criterion of our solution approach, we discuss the potentials of our proposed algorithm, which are inherently accomplished, for preserving the privacy of household power demands.