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Water distribution systems (WDSs) are designed to convey water from sources to consumers. Their operation is a main concern for engineers, researchers, and practitioners and is subject to demand, pressure, and quality constraints. Pumping stations require power to pump water and keep system pressure at a desired level. On the other hand, power is generally supplied through power grids (PGs), which require optimal operation while satisfying operational constraints, such as generation limits, power consumption, and voltage constraints. Since the two infrastructure systems are interconnected, decision-makers could benefit from a holistic approach that would allow solving the two operational optimization problems together as one conjunctive problem. This paper presents the full mathematical formulation of the conjunctive optimization problem, including a novel modelling approach for the operation of a variable speed pump, which does not include integer variables for pump status, thus allowing to solve the model as a non-linear programming (NLP) problem. The formulation is applied to two illustrative case studies, and the results are compared to the optimal operation of the independent WDS. The inclusion of the PG in the optimization problem is observed clearly in the results and influences them quite significantly. WDS operation is shown adjust to the PG constraints, and the application of the conjunctive model results in a cost reduction rate of more than 10 % for both case studies. |
