How to Select the Number of Active Pumps during the Operation of a Pumping Station: The Convex Hyperbola Charts

Abstract

This research aims to identify the number of pumps that should be working at any moment during the operation of a pumping station in order to provide the desired volume of water whilst consuming the least amount of energy. This is typically done by complex iterative algorithms that require much computational effort. The pumping station should pump the desired volume of water V* using the least specific energy e* (energy per volume). In the methodology of this article, the shape of the curves e*–V* was analyzed. The result is that such curves present a convex hyperbola shape. This is a straightforward analytic solution that does not require any iterations. The representation of the Convex Hyperbolas Charts will indicate the best pump combination during the operation of a pumping station. Therefore, this is a straightforward resource for practitioners: the curves immediately tell engineers the number of pumps that should be turned on, depending on the desired volume of water to pump. The elaboration of such charts only requires the use of any calculation sheet, only once, and it is a permanent resource that can be used at any time during the operation. In addition, the Convex Hyperbolas Charts are completely compatible and complementary with any other operation control technique.