Comparing network-centric and power flow models for the optimal allocation of link capacities in a cascade-resilient power transmission network

In this paper, we tackle the problem of searching for the most favorable pattern of link capacity allocation that makes a power transmission network resilient to cascading failures with limited investment costs. This problem is formulated within a combinatorial multiobjective optimization framework and tackled by evolutionary algorithms. Two different models of increasing complexity are used to simulate cascading failures in a network and quantify its resilience: A complex network model [namely, the Motter-Lai (ML) model] and a more detailed and computationally demanding power flow model [namely, the ORNL-Pserc-Alaska (OPA) model]. Both models are tested and compared in a case study involving the 400-kV French power transmission network. The results show that cascade-resilient networks tend to have a nonlinear capacity-load relation: In particular, heavily loaded components have smaller unoccupied portions of capacity, whereas lightly loaded links present larger unoccupied portions of capacity (which is in contrast with the linear capacity-load relation hypothesized in previous works of literature). Most importantly, the optimal solutions obtained using the ML and OPA models exhibit consistent characteristics in terms of phrase transitions in the Pareto fronts and link capacity allocation patterns. These results provide incentive for the use of computationally cheap network-centric models for the optimization of cascade-resilient power network systems, given the advantages of their simplicity and scalability.