Robustness of Ontario power network under systemic risks

ABSTRACT

A failure of one or even a few components would have a limited impact on the network-level performance if the negative consequences are compensated for by neighboring components. However, under certain conditions, this component-level failure may not remain localized, but may rather propagate along other components, thus inducing an entire network/system-level cascade (i.e., systemic) risks. In this respect, the current study develops a simplified model of the Ontario Power Network (OPN) to simulate its topology and load demands. The study then evaluates the different OPN characteristics and develops robustness bands for the OPN under both random failures and targeted threats. Finally, the study presents two dynamic vulnerability indices to facilitate detecting the most critical components within power networks. This study is expected to not only expand the Canadian and the international power network topological analysis database, but also to provide the foundation for innovative network-level systemic robustness enhancement solutions.

KEYWORDS:

• Cascade failure
• giant component
• network-level
• power network
• robustness
• systemic risk
• vulnerability

Notation

BC:	=	The initial total betweenness centrality values of operational nodes in the OPN (state = 0);
BC’:	=	The total betweenness centrality values of operational nodes (state = 0) after cascade failure;
Ci:	=	The capacity of node i;
f:	=	The fraction of removed nodes/links;
<k>:	=	The average degree of the network;
Li:	=	The load demand on node i;
Lsti:	=	The state of all links connected to node i (Lsti = 0 operational and Lsti = 1 nonoperational);
N:	=	The total number of nodes in the OPN;
N’:	=	The total number of operational nodes in the OPN (state = 0);
Nsti:	=	The state of node i (Nsti = 0 operational and Nsti = 1 nonoperational);
R:	=	The network robustness;
V:	=	The set of all nodes in the OPN;
Vi:	=	The set of operational nodes/links in the OPN (state = 0);
ρ(l,k):	=	The number of shortest paths connecting node l to node k and
ρ(i,l,k):	=	The number of shortest paths connecting node l to node k that traverse node i.

Acknowledgments

The financial support for this study was provided through the Canadian Nuclear Energy Infrastructure Resilience under Systemic Risk (CaNRisk)-Collaborative Research and Training Experience (CREATE) program of the Natural Science and Engineering Research Council (NSERC) of Canada. Additional support was provided through the McMaster Institute for Multi-hazard Systemic Risk Studies (INTERFACE).

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Mohamed Ezzeldin

Mohamed Ezzeldin is an Assistant Professor in the Department of Civil Engineering and the Institute for Multi-hazard Systemic Risk Studies (INTERFACE) at McMaster University. He focuses on simulating the complex interdependence within large civil infrastructure systems to enhance their overall resilience. He is also interested in testing systems and integrating the resulting performance data with numerical simulation and analytical modeling approaches to develop system-level risk assessment and resilience quantification tools.

Wael E. El-Dakhakhni

Wael E. El-Dakhakhni, PhD, serves as the CaNRisk CREATE Program Director. He is a professor in the Department of Civil Engineering, the Director of the Institute for Multi-hazard Systemic Risk Studies (INTERFACE) and the Director of the Applied Dynamics Laboratory, all at McMaster University. A Fellow of the American Society of Civil Engineers (ASCE), he expertise is in the area of component- and system-level performance evaluation and risk and resilience quantification under extreme events. He has been actively involved in knowledge mobilization to practice through chairing or voting on several codes and standards committees in Canada and the USA. He is a member of the ASCE Risk & Resilience Measurements Committee and the Disaster Response and Recovery Committee.