Power system is vulnerable to disastrous climate events due to sequential or successive equipment failure. In this dissertation, the problem of identifying the critical k-transmission lines that fail one after another in quick succession, and the distribution system restoration problem using tie-lines/sectionalizing switches formulated as a mixed-integer non-linear programming problem (MINLP) that determines load shed under various k-line removal scenarios are solved. These problems are combinatorial that have huge search space, and solution through enumeration is intractable for large power systems. For reduction of search space, the following mathematical tools are derived, (i) two power flow methods due to k-transmission line removal using the sparse perturbation matrices and power flow sensitivities, (ii) a power flow sensitivity namely k-th order LODF computed using a vector of non-zero numbers stored from the matrix multiplication terms of the first-order sensitivity equation for single line removal cases which reduces its computational complexity, and the sensitivity is computed for any k-line removal case without the necessity of storing it for all k-line removal cases, and (iii) a topological metric based on Laplacian of unweighted graph to identify some important lines between highly connected subgraphs whose disconnection partitions the power system into a few islands. Algorithms are presented using these mathematical tools to identify a reduced number of k-transmission lines in linear time that initiate cascading overload failure and islanding of power system, that are used to solve the MINLP iteratively for identification of critical k-line contingencies as compared to the exponential time complexity of brute-force search for solutions of the MINLP. To reduce the complexity of the restorative problem, a method is developed that exploits the information on pre-contingency power flow solution, network topology together with post-contingency line congestion requirements, and in combination with a greedy search algorithm, which reduces the search space of the problem. Case studies show that the algorithms significantly reduce the search space and computation time of the MINLPs.


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Graduation Date





Batarseh, Issa


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Electrical and Computer Engineering

Degree Program

Electrical Engineering


CFE0009254; DP0026858





Release Date

August 2022

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)