Convex Relaxation of Line-Wise Power Systems Model for Optimal Planning and Operations

Recent developments in the field of power systems have rekindled interest in enhancing the performance of different power system iterative and optimization-based studies. Solution quality and computational complexity are particularly important metrics for comparing the performance of different algorithms used to solve such studies. Factors that include mathematical models used for representing the electrical systems under consideration and mathematical tools utilized for solving these problems are of major significance in determining the performance of algorithms used for conducting these studies. Hence, the contributions in the fields of power system modeling and optimization are of great interest.

Recent advances in the literature in the field of power system modeling include the introduction of the Line-Wise Model (LWM) for presenting meshed transmission networks, which has shown its potential in reducing the computational complexity of different power system studies compared to the Bus Injection Model (BIM). Moreover, the utilization of the concept of convex optimization for solving different power system mathematical challenges is considered a major milestone in terms of enhancing the performance of different power system studies.

In this dissertation, two main contributions are introduced to provide suitable responses to identified gaps in the recent literature. The first is to introduce an angle-free LWM-based formulation that is more suited for power system iterative and optimization-based studies involving Radial Distribution Systems (RDSs). The second is the convexification of the LWM through the utilization of different convex optimization techniques that include the Second Order Cone Programming (SOCP), Quadratic Convex (QC), and Semidefinite Programming (SDP). The convexified LWM formulations are then utilized for solving different power system optimization-based problems of continuous and mixed-integer natures that include Optimal Power Flow (OPF), Transmission Network Expansion Planning (TNEP), and Reactive Power Planning (RPP). Results are then compared with those obtained through the utilization of recently available formulations in the literature that are relevant to this research. These comparisons show the ability of the proposed formulations to provide significant reductions in the needed computational cost for solving such optimization problems while providing solutions of similar or better quality for most test cases under study.