# Dynamical and operational performance of shunt and permanent-magnet DC motors powered by lead–acid batteries for pumping applications

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## Abstract

This paper presents some dynamical and operational performance of shunt and permanent-magnet DC motors powered by lead–acid batteries for water pumping applications. Starting from fully charged battery, the dynamical analysis includes the starting of fully loaded DC motors and the response of the system after successive step changes in the pumping capacities. The strong nonlinearities of the lead–acid battery model are taken into account based on simulating the electrochemical interaction by the electrical equivalent circuit. The dynamics of the thermal part of the electrolyte of the cell is considered. Additionally, the nonlinearities of the dynamical model of the motors have also been included along with that of their ferromagnetic material. The state-of-charge (SOC), variation of the efficiency and internal resistance of the batteries are outlined. It is concluded that the lead–acid battery can effectively start a fully loaded shunt and permanent-magnet DC motors within a settling time of more than 1 h following direct switching. It can also run them steadily at different loading conditions and can withstand step changes in the mechanical loads coupled to motors. It is observed that about 25% of the SOC of the battery is consumed for starting. The energy efficiency of the battery at starting and running conditions for the two motors has been addressed. All of the study is conducted assuming an ambient temperature of 25 \(^{\circ }\)C. All numerical simulations are carried out using MATLAB software package by building the code required.

## Keywords

Dynamical analysis Lead–acid battery dynamical model Shunt and permanent-magnet DC motors## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflicts of interest.

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