# Understanding and Estimating Physical Parameters in Electric Motors using Mathematical Modelling

If you have a question about this talk, please contact Dr Vivien Gruar.

Rotating electrical machinery such as pumps, fans, and compressors underpin a lot of our modern-day infrastructure; they are used in the water industry, throughout manufacturing, and in turbines/ for power generation. These devices are generally powered by three-phase induction motors, and the reliable performance of these motors (and the driven equipment) is critical in many sections of industry.

Artesis is a small company that provides remote monitoring of this equipment, looking at only the voltage and current drawn by the motor to identify (mostly mechanical) faults in the motor and in the driven equipment.

To do this, we use a black-box modelling algorithm which approximates the motor as a linear system – from a sample of voltage and current data, the algorithm extracts the best-fit linear relationship between voltage and current, and the leftover ‘residual’ current is then further analysed by examining its Fourier spectrum. The model consists of a number of parameters which do not themselves have any physical meaning. However, these parameters should correspond to physical parameters of the motor itself such as winding resistances, impedances, and slip (a parameter related to the output torque) and the first aim of this project is to extract this meaningful physical data from the parameters produced by the model. Time permitting, we would then like the student to speculate (both using some physical insight and a bit of guesswork) how faults on the equipment, as well as operational changes, might influence these physical parameters and therefore the parameters in the mathematical model; and some of these hypotheses can be tested using a test rig.

This project is relatively open ended though it builds on work done in previous PMP project from 2016. There should be some time to visit either a real customer site or take at quick tour of the engineering department, and we hope this project will provide an opportunity for the student to see how mathematics interacts with the real world – and hopefully for them to develop a taste for solving problems that are important in industry.

This talk is part of the Cambridge Mathematics Placements Seminars series.

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