A Framework for Capacity Expansion Planning in Failure-Prone Flow-Networks via Systemic Risk Analysis

In this article, a capacity expansion framework is proposed for failure-prone flow-networks. A systemic risk measure that quantifies the risk of unsatisfied demand due to cascaded edge failures is considered. To minimize the total cost of additional edge capacities, while keeping the risk of unsatisfied demand below a certain threshold, a general stochastic optimization problem is formulated. The distribution of unsatisfied demand is calculated via Monte-Carlo simulations embodied within a grid search algorithm that identifies the feasible region. Thereafter, the cost-optimal edge capacity expansion plan is computed by a differential evolution algorithm. Contributions of this article are: 1) consideration of both immediate investment and future risk costs of capacity expansion plans; 2) a generic flow-network model that can be tuned for different real-life applications; 3) addressing the stochastic nature of both supply and demand simultaneously within a systemic risk framework; 4) use of eigenvector centrality for edge grouping in systemic risk analysis. An extensive numerical study is performed to investigate the effects of different edge grouping methods, characteristics of stochastic components, and cost parameters on the feasible region and optimal solution. The proposed framework is also demonstrated on a case study adapted from ERCOT 13-bus test system.