Introduction

Climate change is causing significant shifts in weather patterns and temperatures, leading to environmental degradation, natural disasters, and resource scarcity. Sustainable practices are crucial to mitigate these effects, particularly in the energy and water sectors. This paper presents a mathematical model aimed at optimizing the use of electric energy in water supply networks while ensuring water quality. The focus is on minimizing energy consumption by electric pumps and maintaining the integrity of the pumps through controlled on/off cycles.

Methods

The proposed optimization model considers a hydraulic network with multiple water sources, each with different quality indices. Key assumptions include maintaining minimum pressure throughout the network and ensuring the total volume of water meets demand. The model involves a non-linear formulation, which is later linearized for practical application. Decision variables indicate whether a pump is on or off at given times, and the objective function aims to minimize the total energy consumption of the pumps.

Results

The model's non-linear formulation calculates the energy used by each pump based on its flow rate, head, and efficiency. Constraints ensure that the water volume in each reservoir stays within capacity limits and that the mixed water quality remains within specified bounds. The model also limits the number of pump switches to prevent system wear. Application of the model to a real-world scenario demonstrated its effectiveness in reducing energy consumption while maintaining water quality and operational constraints.

Conclusions

This study addresses the need for energy-efficient water supply systems by optimizing pump operation schedules. The model successfully balances energy use with water quality requirements and system durability. Future work could involve further refining the model to incorporate more dynamic factors and expanding its application to larger and more complex water networks.