Power Plexus: A network based analysis

Malvika Singh DA-IICT Gandhinagar, India. 20140 142 8@ daiict.ac.in

Sneha Mandan DA-IICT Gandhinagar, India 20140 142 2@ daiict.ac.in

Smriti Sharma DA-IICT Gandhinagar, India 20140 100 3@ daiict.ac.in

Abstract—Power generation and distribution remains an im- portant topic of discussion since the industrial revolution. As the system continues to grow, it needs to evolve both in infrastructure, robustness and its resilience to deal with failures. One such potential failure that we target in this work is the cascading failure. This avalanche effect propagates through the network and we study this propagation by Percolation Theory and implement some solutions for mitigation. We have extended the percolation theory as given in [1] for random nodes to targeted nodes having high load bearing which is eliminated from the network to study the cascade effect. We also implement mitigation strategy to improve the network performance.

I. INTRODUCTION Cascading failures have tremendous impact on power grid networks. When the failure of a few nodes triggers the failure of other nodes which in turn cause the failure of other large number of nodes, it results in complete failure of power system. While some of such failures are smaller in magnitude because their growth is checked, in other cases it causes avalanche mechanisms. This was evident in the power failure mishap of 10th August 1996 [2], [3], when a 1300 Mega Watts electrical line in Oregon had failed and a chain reaction started which culminated in loss of power to more than 4 million people in 11+ states. This is also suspected to be the reason behind the last major power failure in the United States on August 14, 2003. Moreover, the redistribution of the power after failure of certain nodes leads to congestion and bottlenecks in the network as has been in the case of Internet congestion collapse, first recorded officially in October 1986, when the speed of connection between Lawrence Berkeley Laboratory and the University of Berkeley, two spots separated by a distance of 200m suffered a decline by a factor of
100 [2]. There have been works regarding the mitigation of such blackouts by considering inter-dependent networks of communication and network topology [4]. Other works include studying actual electromagnetic constructions and applications that go in power generation and transmission. However, such detailed analysis are extremely difficult to scale to networks
of sizes having thousands of nodes. In our analysis, we have followed two approaches (i) Network performance based on

Fig. 1: Network of US power grid 2014

substations or transformers) and the K edges are the transmis- sion lines. To each edge between nodes i and j is associated a number eij in the range [0; 1] measuring how efficiently nodes i and j communicate through the direct connection. For instance eij = 1 means that the arc between i and j is perfectly working, while eij = 0 indicates that there is no direct connection between nodes i and j. The weight of each edge can be understood as the cost of power transmission and is taken to be inversely proportional to the efficiency of the edge. With each node i are associated the characteristics- load (Li) and threshold capacity of node (Ci) [7]. In our case, the load of a node is the betweenness centrality. (Betweenness centrality of a node v is the sum of the fraction of all-pairs shortest paths that pass through v). The capacity of the node is taken proportional to the initial load (betweenness centrality). Ci = α ∗ Li; α ≥ 1, i = 1, 2, .., N (1) where Ci is the capacity of ith node, Li is the load of ith size of giant component (ii) Cascading effect due to failure
of a single node and dynamic redistribution of flows on the network [5]. Lastly we talk about a mitigation strategy.

II. DESCRIPTION OF THE DATA SET We have taken the data-set of US Electricity department [6] in this study, with N=4941 nodes and K=6594 edges. The electric power grid is represented as an undirected graph, in which the N nodes are the substations (generators, distribution node and α is the tolerance parameter

III. MODEL Percolation Theory as suggested in [1] refers to removal
of nodes randomly from a network and study its effect on the remainder network. Here, in this work, we initially remove
a node in two ways: 1. Randomly remove a node and 2. Remove node with highest betweenness centrality (modified i percolation) and then after that the system is left to study the cascading effect on the remainder of the network as
the threshold capacity of the remaining nodes exceeds its maximum capacity.

A. Assumptions In this work, the load of a node is taken to be the measure of the metric - betweenness centrality. This is done because the load a node can carry is determined by the sho

…(Full text truncated)…