This paper defines a security injection region (SIR) to guarantee reliable operation of water distribution systems (WDS) under extreme conditions. The model of WDSs is highly nonlinear and nonconvex. Understanding the accurate SIRs of WDSs involves the analysis of nonlinear constraints, which is computationally expensive. To reduce the computational burden, this paper first investigates the convexity of the SIR of WDSs under certain conditions. Then, an algorithm based on a monotone inner polytope sequence is proposed to effectively and accurately determine these SIRs. The proposed algorithm estimates a sequence of inner polytopes that converge to the whole convex region. Each polytope adds a new area to the SIR. The algorithm is validated on two different WDSs, and the conclusion is drawn. The computational study shows this method is applicable and fast for both systems.
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