Implementation of Bidirectional Power Flow Based Centrality Measure in Bulk and Smart Power Transmission Systems A. B. M. Nasiruzzaman, Member, IEEE, H. R. Pota, Member, IEEE and M. A. Barik, Student Member, IEEE Abstract—Bidirectional or two way power flow based central- ity measure has been implemented in bulk and smart power transmission systems. Proposed model can identify critical nodes from the system whose removal would affect the system severely. A combination of two models has been adopted to capture the power flow scenario of smart grid. Impacts of removal of critical nodes have been analyzed in terms of increase in path length, connectivity loss and load loss. Rank similarity analysis has been carried out to check the numerical stability of rank of the critical nodes found from proposed method based on complex network theory. Index Terms—Betweenness centrality, bidirectional power flow, path length, connectivity loss, load loss, rank similarity. I. I NTRODUCTION P OWER system is the most complex man-made system and its complexity is increasing day by day. In broad sense, a typical power system consists of generation, transmission, distribution and loads [1], [2]. Large scale generating plants are built where primary energy sources are plenty and usable. These generating stations are connected with high voltage transmission network to transport the transformed energy in electrical form to load centers. At the suitable location of the load center i.e., in substations the voltage is reduced and distributed through medium/low voltage distribution network. Consumers or loads are at the end of the transmission system. This is what a typical scenario of complex power grid where the demand and supply needs to be balance very carefully at every instant to avoid undesirable catastrophe. In future power grid i.e., the smart power grid some more complexity are going to be introduced [3], [4]. The future grid will be very large scale, nonlinear, switched, uncertain, multi agent and multi objective. Moreover, there will be bidirectional power flow [5], [6]. The grid behavior would be random due to switching on and off as well as large PHEV charging. Number of nodes will be massive with the inclusion of renewable sources and smart meters. Various intricate social behaviors like flocking, swarming and human psychology will also be integrated with the grid more and more. Recent years have seen several very large scale blackouts initiating from small disturbances. In August 1996, a cascading outage occurred in the Western power grids of North America A. B. M. Nasiruzzaman, H. R. Pota and M. A. Barik are with the School of Engineering and Information Technology (SEIT), The University of New South Wales at the Australian Defence Force Academy (UNSW@ADFA), Northcott Drive, Canberra, ACT 2612, Australia. E-mail: nasiruzza- man@ieee.org h.pota@adfa.edu.au and md.barik@student.adfa.edu.au in USA and Mexico [7], [8]. More than 4 million people suffered the consequences. Most affected areas were out of electricity for about 4 days. Another large scale blackout which affected around 55 million people happened in August 2003. Several northeast and midwestern states of USA and some provinces of Canada were affected [9]. Recent series of blackouts occurring all over the world have attracted the attention of researchers the model and analyze the power grid as a complex network. Social network researchers pioneered in this field of research. Statistical physicist tried to explain underlying structural property for large scale cascading blackout in power system [10]–[15]. Then engineers came trying to explore what precaution measures could be taken to prevent such large scale events and thereby saving lots of money from being wasted [16]–[29]. Vulnerability assessment methods based on complex net- work theory were used by many electrical engineering re- searchers to identify critical links and nodes of the power grid. The target is to invest most resources to protect most vulnerable ones. Commonly used centrality measures include degree centrality, closeness centrality and betweenness cen- trality [30]–[32]. The number of edges of a node is called its degree. The node with highest degree centrality has got largest number of connections in the network. Removal of degree central node from a network would destroy largest number of edges from the network. Thus to maintain the reliability and redundancy of the network, preservation of degree central node is essential. Calculation of degree centrality is fairly simple and requires just counting of number of edges per node. Edges can have centrality indices as well. The concepts of degree, closeness and betweenness based measures can be extended edges to measure the importance of links within a network [31]. Although exclusion of nodes have can have more impact than the removal of edges, generally nodes are well protected than nodes. For this reason, analysis of criticality of edges have importance in network science and almost every centrality measures have both edge and node version. The set of nodes or links whose removal would have most negative impact on the system are of importance. Various sets of attack vectors could have various impacts on the system. But the worst case is of highest importance since it severely affects network robustness and resilience. Several worst case connectivity statistics have been proposed in the graph theoretic literature but according to the author’s these measures have not yet been explored in terms of power grid vulnerability analysis.