  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.
