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Martin-Candilejo, ACorresponding AuthorMartin-Carrasco, FjAuthorSantillan, DAuthor

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June 21, 2021
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How to Select the Number of Active Pumps during the Operation of a Pumping Station: The Convex Hyperbola Charts

Publicated to: Water (WATER-SUI). 13 (11): 1474- - 2021-06-01 13(11), DOI: 10.3390/w13111474

Authors:

Martin-Candilejo, A; Martin-Carrasco, FJ; Santillán, D
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Affiliations

‎ Univ Politecn Madrid, Dept Ingn Civil, Hidraul Energia & Medio Ambiente, Madrid 28040, Spain - Author

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.
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Keywords

Analytic solutionComputational effortDrivesEfficiency analysisEnergyEnergy efficiencyGraphic methodsIterative algorithmIterative methodsMethodologyMultiobjective optimizationNetworksOperationOperation controlOperations technologyOptimal-designPumpPumpingPumping plantsPumping stationPumping stationsPumpsQualityResearch methodSpecific energySpeed pumpWater distribution-systemsWater supply systemsWater treatment

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Water (WATER-SUI) due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Geography, Planning and Development.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-25:

  • WoS: 4
  • Scopus: 4
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-25:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 8 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
    • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/85801/

    As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

    • Views: 126
    • Downloads: 68
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    Leadership analysis of institutional authors

    There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (MARTIN CARRASCO, FCO. JAVIER) and Last Author (SANTILLAN SANCHEZ, DAVID).

    the author responsible for correspondence tasks has been MARTIN CARRASCO, FCO. JAVIER.

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    Project objectives

    El presente trabajo tiene como objetivo principal optimizar la operación de estaciones de bombeo mediante la selección adecuada del número de bombas activas. Se pretende analizar la forma de las curvas energía específica-volumen (e*-V*) para identificar su estructura como hipérbolas convexas. Además, se busca desarrollar un método analítico directo que evite algoritmos iterativos complejos y reduzca el esfuerzo computacional. Otro objetivo es representar gráficamente estas curvas mediante los Convex Hyperbola Charts para facilitar la toma de decisiones operativas. Finalmente, se aspira a proporcionar una herramienta práctica y compatible con otras técnicas de control que permita determinar rápidamente la combinación óptima de bombas según el volumen deseado.
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    Most relevant results

    El estudio presenta una metodología innovadora para determinar el número óptimo de bombas activas en una estación de bombeo, optimizando el volumen de agua y el consumo energético. Los resultados más relevantes son: 1) las curvas energía específica-volumen (e*-V*) tienen forma de hipérbola convexa; 2) esta forma permite una solución analítica directa sin necesidad de algoritmos iterativos complejos; 3) los gráficos de hipérbolas convexas indican claramente la combinación óptima de bombas según el volumen deseado; 4) la elaboración de estos gráficos requiere únicamente una hoja de cálculo y se puede utilizar de forma permanente durante la operación; 5) esta metodología es compatible y complementaria con otras técnicas de control operativo.
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