Optimal operation of multi-quality water supply systems – II: The Q-H model

This paper describes the second in a series of three models for optimal operation of multi-quality water supply systems. This second model, which is termed the Q-H (flow-head) model, seeks to determine the optimal operation of pumps and valves, and does not consider water quality aspects. However, the model belongs to the group of three models for multi-quality systems because it is one of the two building blocks (the other is the flow-quality Q-C) of a full-flow-quality-head (Q-C-H) model. This Q-H model is based on continuous representations of the head-flow and power-flow functions of the pumping stations, which in turn results in a continuous non-convex optimization model. For a given flow distribution in the network, Q0, the Q0-H model is solved for the optimal operation of pumps and valves. The flow distribution is then modified by changing the circular flows, using a projected gradient method combined with the Complex Method which employs the results of the Q0-H solution, such that the locally optimal solution at the next point has a better value of the objective function. The process is continued until one of the termination criteria is satisfied. The circular flows thus serve as decision variables in an external problem, while in the internal problem the decisions are the operation of pumps and valves. The method is demonstrated by application to a sample problem.