Optimal operation of multi-quality water supply systems – I: Introduction and the Q-C model

One of three complementary models for optimal operation of multi-quality water supply systems is presented. The other two models are the subject of companion papers. The model, which is known as the Q-C (flow-quality) model, includes mass continuity of water and constituents. However, the hydraulic constraints do not appear explicitly. To prevent infeasibilities or unreasonable hydraulic conditions arising from the lack of hydraulic constraints, limits and a cost are associated with the flow in each pipe. The constraints in the model include dilution conditions which depend on flow direction. These dilution conditions are introduced into the model by an exponential function, resulting in a smooth continuous nonlinear programming problem, which is transformed into an equivalent problem and solved by a modified projected gradient method. The method is insensitive to scaling of variables, and the computational complexity depends only slightly on the number of water quality parameters. The method is demonstrated by application to two examples: the solution for a small network is presented in detail, and main results are shown for a larger one. The results of these two applications indicate the method's applicability to real networks.