Reliability analysis of water distribution networks in consideration of equity, redistribution, and pressure-dependent demand

A goal programming model has been developed to analyze the system behavior for the water distribution networks under contingency situations due to failures of pipes and pumps, taking into account three aspects: (1) equity, or sharing inconvenience equally among consumers; (2) redistribution of the network flows to reduce the negative consequences of a failure of one portion on other portions of the network; and (3) consideration of pressure-dependent demand delivery due to insufficient head, namely, if a nodal head falls below a desired level, the flow delivered to that node is reduced. The first priority of the goal program is to maximize the lowest nodal demand supply ratio (or the ratio of actually delivered demand to the required demand at a node). The second priority is to maximize the system demand supply ratio (or the ratio of actually delivered water to the required total system demand). Link flow directions in the model are not fixed but are determined by a set of criteria. The system behaviors with respect to the three aspects of reliability factors are examined through extensive numerical experiments. The impact of equity requirements on redistribution of network flows, link flow directions, nodal demand supply ratio, and system demand supply ratio when failure events become serious is examined in particular detail. It is found that equity requirements can satisfactorily bring about fair sharing of inconvenience among consumers. The model proposed also suggests that network operations should reverse some link flow directions in order to meet equity requirements under severe contingencies.