# Mathematical Model with Pressure Constraints to Minimize Electric Energy Costs in the Operation of Hydraulic Pumps

## Authors

• Letícia Maria Miquelin Postgraduate Program in Electrical Engineering, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Av. Luiz Edmundo Carrijo Coube, 14-01, Bauru, SP, 17033-360 Brazil. https://orcid.org/0000-0003-1539-843X
• Maristela Oliveira dos Santos Department of Applied Mathematics and Statistics, Universidade de São Paulo (USP), Av. Trabalhador São-carlense, 400, São Carlos, SP, 13560-970 Brazil. https://orcid.org/0000-0003-0822-3439
• Edilaine Martins Soler Department of Mathematics, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Av. Luiz Edmundo Carrijo Coube, 14-01, Bauru, SP, 17033-360 Brazil. https://orcid.org/0000-0002-7615-5768

## Keywords:

Electricity, water supply systems, hydraulic pumps, optimization

## Abstract

Water supply systems are responsible for providing quality water to the population in sufficient quantity. As sanitation companies are major energy consumers of electrical power, they have a contract of power in which the cost of electricity varies according to the period of the day. Thus, for these companies, at peak times the price of electricity is much higher. Most of the expenditure on electricity in water supply systems is due to hydraulic pumps, which are activated when the level of the tanks reaches the minimum level and remain on until the maximum levels are reached, without taking into account the time where this operation is performed. This work proposes a mathematical model for the optimization of electricity costs in water supply systems through the planning of the operation of hydraulic pumps. Numerical tests were performed through the implementation of the proposed model in GAMS software and solved by the CPLEX optimization package for different demand scenarios, in order to validate the proposed model. A model that simulates the operation performed in the practice of water supply systems is also presented, and its results are compared to the proposed optimization model. The obtained results proof of the efficiency of hydraulic pumps operation planning provided by the proposed model in relation to the operation performed in practice in water supply systems.

## Author Biographies

### Letícia Maria Miquelin, Postgraduate Program in Electrical Engineering, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Av. Luiz Edmundo Carrijo Coube, 14-01, Bauru, SP, 17033-360 Brazil.

Letícia Maria Miquelin received the degree in Mathematics from Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Bauru-SP, Brazil, in 2017, having obtained the M.Sc. degree in Electrical Engineering from the same university, in 2019. Currently, is degree student by Postgraduate Program in Electrical Engineering at Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Bauru-SP, Brazil, where develops research in the areas of energy optimization in water supply systems.

### Maristela Oliveira dos Santos, Department of Applied Mathematics and Statistics, Universidade de São Paulo (USP), Av. Trabalhador São-carlense, 400, São Carlos, SP, 13560-970 Brazil.

Maristela Oliveira dos Santos received the degree in Mathematics from Universidade Federal de Mato Grosso (1994), having obtained the M.Sc. and Ph.D. degrees in Science Computing and Computational Mathematics from Universidade de São Paulo (USP) (1996, 2000). Currently, she is an Associate Professor of the Department of Applied Mathematics and Statistics at Universidade de São Paulo (USP), São Carlos, SP, Brazil. She works with the development of mathematical models and solution methods for problems of production planning, scheduling, among others.

Marcos Mansano Furlan received the bachelor’s degree in Computer Science from Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP) (2008)., having obtained the M.Sc. and Ph.D. degrees in Science Computing and Computational Mathematics from Universidade de São Paulo (USP) (2011, 2015). Currently, he is an Assistant Professor in the Exact Sciences and Technology Faculty at Universidade Federal da Grande Dourados (FACET/UFGD).
He works mainly on topics related to batch sizing, heuristics, metaheuristics and hybrid methods.

### Edilaine Martins Soler, Department of Mathematics, Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Av. Luiz Edmundo Carrijo Coube, 14-01, Bauru, SP, 17033-360 Brazil.

Edilaine Martins Soler received the bachelor’s degree in Mathematics from Universidade de São Paulo (USP), São Paulo, Brazil, in 2006. She received the M.Sc. degree in Science Computing and Computational Mathematics in 2008 and Ph.D. degree in Electrical Engineering, in 2011, both from Universidade de São Paulo (USP), São Paulo, Brazil. Currently, she is an Assistant Professor of the Mathematics Department in the Science Faculty at Universidade Estadual Paulista (UNESP), Bauru, SP, Brazil. Her areas of expertise involve applied optimization, nonlinear optimization, discrete optimization and its applications to the power flow problem.

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2023-01-17

## How to Cite

Miquelin, L. M., Santos, M. O. dos ., Mansano Furlan, M. ., & Soler, E. M. (2023). Mathematical Model with Pressure Constraints to Minimize Electric Energy Costs in the Operation of Hydraulic Pumps. IEEE Latin America Transactions, 21(3), 483–489. Retrieved from https://latamt.ieeer9.org/index.php/transactions/article/view/7401

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