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Determination of electric motor losses and critical temperatures through an inverse approach

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Abstract

In this study, a practical numerical method is proposed to estimate losses of high specific power density electric motors, using few simulated temperature data. In such electric motors, these losses generate high heat fluxes inside the motor components that can be critically sensitive to temperature. Electromagnetic and mechanical friction phenomena are behind the occurring of these thermal dissipations. For both phenomena, losses could be difficult to compute with electrical or mechanical approaches. However, thermal management of electric motors requires a precise knowledge of those losses, in particular for high-performance motors such as those considered in future hybrid planes. To determine electric motor losses in a permanent magnet synchronous motor (PMSM) in real time, an inverse method using a lumped parameter thermal model (LPTM) is elaborated. In the first step, the dynamic profile of losses is determined through the inverse method, based on temperature data at easy-access points of the motor. In a second step, the identified losses are used to find temperatures at critical non-accessible hot spot points of the motor through forward LPTM. The method is applied for three useful cases, from the simplest case scenario, where only one type of losses has to be identified, to the most complicated case where all losses are simultaneously estimated. A global strategy for the choice of the number of future time steps used for regularization of the ill-posed problem is also proposed. Results show that this method enables adequate real-time supervision of the critical motor temperatures, mainly rotor and winding core.

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Abbreviations

A (N,N):

State matrix

B c (N):

Command vector relative to environment

B P (N,n p):

Command matrix relative to heat sources

C p :

Specific heat, J·kg−1·K−1

C (n q ,N):

Output matrix

h :

Convective exchange coefficient, W·m­2·K−1

I :

Identity matrix

κ :

Thermal conductivity, W·m−1·K−1

N :

Number of nodes

nf :

Number of future times for specification function

n p :

Number of heat sources

n q :

Number of outputs

nt :

Number of time steps

P :

Heat source vector, W

U :

Vector of unknown heat sources

V :

Vector of known inputs

vol:

Volume, m3

Y (n q):

Output vector

FTS:

Future time steps

LPTM:

Lumped parameter thermal model

PMSM:

Permanent magnet synchronous machine

SM:

Surface mounted

Γ:

System boundary

Δt :

Time step, s

ρ :

Density, kg·m−3

σ U :

Mean quadratic error for U, W

σ Y :

Mean quadratic error for Y, °C

χ :

Characteristic space function

Ω:

System domain

ext:

Exterior

k :

Time index

* :

Noisy temperature

^ :

Estimated value

T :

Transposition sign

−1:

Inverse of a matrix

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Acknowledgements

This project has received funding from the European Union’s Horizon 2020 (Cleansky 2 JTI) research and innovation program, 2014-2024 under Grant Agreement No. 715483.

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Authors and Affiliations

  1. Department of Fluid, Thermal, and Combustion Sciences, Pprime Institute UPR 3346, CNRS, ENSMA, University of Poitiers, ENSMA, Téléport 2 – 1 avenue Clément Ader, BP 40109, 86961, Futuroscope Chasseneuil Cedex, Poitiers, France

    Amal Zeaiter, Etienne Videcoq & Matthieu Fénot

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  1. Amal Zeaiter
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  2. Etienne Videcoq
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  3. Matthieu Fénot
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Correspondence to Amal Zeaiter.

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Zeaiter, A., Videcoq, E. & Fénot, M. Determination of electric motor losses and critical temperatures through an inverse approach. Electr Eng 103, 621–631 (2021). https://doi.org/10.1007/s00202-020-01098-0

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