Mathematical modeling of the joint operation of pumping units including frequency regulated ones

Summary

The use of pumping units with variable speed drives in order to save energy and provide for effective operating modes in water supply and sanitation systems, sometimes without sufficient justification, does not always furnish the desired result. One of the reasons is the lack of a simple mathematical model describing the flow distribution in the process pipelines of pumping stations with account of all the limitations of the operating mode parameters while using variable speed drives in some or all pumping units. The flow distribution task itself should be represented in the form of an optimization problem where the objective function can be the total energy input of all the operating pumping units. Such an optimization model provides for describing the operating modes of both paralleled and compound pumps. Once the electricity costs for all significant modes throughout the year have been determined and compared with the existing modes without the use of variable speed drives, drawing a reasonable conclusion about the applicability of variable speed drives in one or several pumping units becomes possible. The proposed model provides for arranging both effective and technologically acceptable modes. Based on the obtained results of calculating the optimization task for several modes, it is possible to construct approximating functions of the total flow of the pumping station from the head losses in throttling devices and use them in case of the flow meter lack or failure.

Key words

pressure , frequency converter , hydraulic head , centrifugal pump , pumping unit , flow distribution task , optimization task , energy input , parallel and serial operation of pumps