Contingency analysis of water distribution networks using quadratic sensitivity functions

Cyber-physical attacks on infrastructure systems take many forms. Here we consider coordinated cyber-attacks that are small in magnitude, and therefore hard to detect, but can result in catastrophic physical damage or loss. We cast the problem as an n - k contingency problem, with k perturbations to n network assets, e.g. tanks, variable frequency drive pumps, or digitally controlled valves. This is a challenging combinatorial problem, due to the nonlinear dynamics of headloss in water distribution networks. Starting from the nonlinear EPANET equations, we use a combination of implicit differentiation and sensitivity analysis to compute closed-form expressions of head-level sensitivity functions. We use these expressions to forecast nodal pressure disruption using a single baseline simulation, rather than enumerating all combinations of attacks. We illustrate the applicability of our method on an EPANET model in predicting pressure drop over all contingency scenarios.