This thesis is dedicated to the study of Complex Network Theory with applications in power systems. The focus of the study is to analyze and solve power system problems by treating and modelling it as a network and applying the concepts from this theory. The work can be broadly classified into two parts: vulnerability analysis and fault location. Two different centrality indices are proposed to analyze power system vulnerabilities. The first method utilizes shortest path betweenness approach and a centrality index is defined based on the power flow equation using reactance as the measure of portion of power flowing through any line. A few limitations of this method are improved in the second, where power system is considered to be capacitated and directed in any steady state and another centrality index based on the maximum flow algorithm is defined using admittance as weight to model the network. Based on Kirchhoff’s law, admittances are considered to be a measure of proportion and ease with which current or power flows through any line. Further, using maximum flow algorithm, lines are marked as important based on the fraction of total flow they carry between nodes. It is demonstrated by simulations on the IEEE 39 and IEEE 118 bus systems that failure of transmission lines identified as critical or vulnerable has a major impact on the efficiency and performance of the network, unlike the failure of random connections which have little or no effect. In another study, cascading failures in power systems are assessed using line outage distribution factor and power transfer distribution factor together with Complex Network Theory. This work identifies the group of transmission lines which may be affected if any one line fails and investigates the sequence and depth to which the failure may propagate. Using the IEEE 14 bus system, it explains how the failure of one line can sometimes lead to a cascading failure and eventual blackout. The next part of the research applies Complex Network Theory together with travelling wave based fault location techniques to locate faults in power systems. This study is further divided into two parts. The first part analyzes a power generation network, where the double-ended travelling wave theory is used to calculate the time stamp of fault transients at each node and then network topology of the system is used to first identify the faulty link and then calculate the fault distance. Finally, the single-ended travelling wave method is used to locate faults in power distribution systems. Due to the radial structure of transmission lines in such systems, more than one fault candidates may appear in the calculations, out of which only one is real. This ambiguity is resolved by taking advantage of the spanning tree like structure and using depth first search to identify the actual fault. The results reveal that the proposed methodologies are capable of locating single faults in power systems with reasonable accuracy.
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