A Combined Model and Data-Driven Approach for the Determination of Rotor Temperature in an Induction Machine

. 2021 Jun 30;21(13):4512. doi: 10.3390/s21134512

$V_{d s}$ , $V_{q s}$	[V] voltage equilibrium of the stator in rotating frame;
$V_{d r}$ , $V_{q r}$	[V] voltage equilibrium of the rotor in rotating frame;
$ω$	[rad/s] mechanical angular velocity;
$ω_{r}$	[rad/s] electrical angular velocity;
$i_{d s}$ , $i_{q s}$	stator currents in rotating frame;
$i_{d r}$ , $i_{q r}$	[A] rotor currents in rotating frame;
$ψ_{q s}$ , $ψ_{d s}$	[Wb] stator fluxes in rotating frame;
$ψ_{q r}$ , $ψ_{d r}$	[Wb] rotor fluxes in rotating frame;
$L_{s}$	[H] inductance of the stator;
$L_{r}$	[H] inductance of the rotor;
$L_{m}$	[H] mutual inductance;
$L_{l s}$	[H] leakage inductance of the stator;
$L_{l r}$	[H] leakage inductance of the rotor;
$i_{r}$	[A] estimated value of the magnetization current;
$i_{s}$	[A] stator current;
$τ_{r}$	[s] time constant of the rotor electrical dynamics;
$f_{s}$	[Hz] inverter switching frequency;
$R_{r}$	[ $Ω$ ] nominal rotor resistance;
$R_{s}$	[ $Ω$ ] nominal stator resistance;
$R_{m}, R_{n e t}$	normal distribution variances of observation and transition model;
$τ$	[s] time constant of the low-pass filter introduced for realizability;
$α_{1}, α_{2}$	coefficients of the thermal model;
$T_{s}$	[ $^{\circ}$ C] stator temperature;
$T_{r}$	[ $^{\circ}$ C] rotor temperature;
$T_{α}$	[ $^{\circ}$ C] predicted temperature with the thermal model;
$T_{n e t}$	[ $^{\circ}$ C] predicted temperature with the NARX model;
${\hat{T}}_{r}$	[ $^{\circ}$ C] posterior-estimated value of the rotor temperature;
h	[s] sample time;
$η$	[RPM] mechanical speed of the rotor measured in revolutions per minute;
$Δ$	gradient;
∗	reference value;
w	[-] particle filter sample weights;
$f_{1}$	sigmoid activation function of the hidden layer;
$f_{2}$	linear activation function of the output layer;