Load flow and optimal power flow in power distribution systems - application of Riemannian optimization and holomorphic embedding
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Distribution networks are undergoing unprecedented challenges originated from the large-scale adoption of distributed energy resources, price responsive demand, electric storage resources, electric vehicles, etc. Power system analysis techniques such as Load Flow (LF) and Optimal Power Flow (OPF) are necessary to ensure secure and optimal operation in an increasingly active, distributed, and dynamic distribution grid operation. This dissertation presents robust and computationally efficient solution techniques for LF and OPF problems. In the first part of this dissertation, we utilize Riemannian optimization and present two solution methods. The first solution method is applicable to the LF problem and is shown to fall into the category of Riemannian approximate Newton methods, which guarantees descent at each iteration while maintaining a local superlinear convergence rate. The second solution method is a Riemannian Augmented Lagrangian Method (RALM) which applies to the OPF problem. The proposed solution approach exploits the geometrical properties of the power flow equations and ensures the physical feasibility of the solution. Computational experiments on several distribution networks provide encouraging results in terms of solution quality and speed. The second part of this dissertation employs Holomorphic embedding methods and presents two LF solution techniques. The first solution technique improves the computational efficiency of the Holomorphic Embedding Load flow Method (HELM). Numerical experimentation demonstrates overall time savings of up to 30% on IEEE radial distribution test cases. The second solution technique extends HELM to three-phase distribution networks with a generic topology and wye/delta connected ZIP load models. We demonstrate the efficacy of the proposed method through numerical results. The third part of this dissertation is focused on exploiting the existing network infrastructure to improve the system operation. We present an optimal line switching and bus splitting heuristic considering AC and N-1 contingency constraints and apply the proposed method to several IEEE standard test networks. We also provide directions for possible extensions to distribution networks. The proposed method identifies a network topology that reduces the operation cost while maintaining AC feasibility and initial system reliability level in the sense of N-1 contingency requirements.