A Combined Model and Data-Driven Approach for the Determination of Rotor Temperature in an Induction Machine
Abstract
:1. Introduction
- The algorithm consumes data that is already available on most standard architectures of power electronics used in electric machine control (i.e., phase currents sensors, stator temperature sensor, position, and speed encoder).
- The method does not require additional components (e.g., real-time precision impedance measurement, search coils, etc.)
- The method is not invasive and does not alter the control commands to the electrical machine.
- In the common NARX network, the state is updated with the actual output of the network. In the proposed algorithm, we update the state of the NARX network with the posterior estimate. The posterior estimate is obtained after merging with the particle filter the two information channels: the NARX and the thermal model. This corrects the prediction of the neural network in the prediction stage. Thus, is obtained a conditioned output of the NARX model with the thermal model which in the end improves the precision of the estimated value. This approach is distinctive, and it was not investigated before to the problem of temperature estimation.
2. System Description—Belt-Driven Booster
3. The Mathematical Models of the State Transition and Observation Functions
Data Acquisition and Network Training
4. Particle Filter for Rotor Temperature Estimation
Algorithm 1 Particle filter for rotor temperature estimation |
Initialization Initialize posterior distribution: Generate particles with initial distribution and place them in a set called . Run Compute while do Calculate the weight associated with each projected state: i = i + 1 end while Sample the discrete distribution w to generate random samples which will represent the posterior : ; fetch values from a uniform distribution ; for j = 1: do ; Cumulative Sum of W; end for for j = 1: do ; will be the index of the posterior after re-sampling end for for j = 1: do end for |
5. Results and Discussions
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
BDB | Belt-Driven Booster |
CAN | Controller Area Network |
ECU | Electronic Control Unit |
HEV | Hybrid Electrical Vehicle |
IM | Induction Machine |
LM | Levenberg-Marquardt |
Mild-HEVs | Mild-hybrid Electrical Vehicles |
NARX | Nonlinear AutoRegressive network with eXogenous inputs |
Probability Density Function | |
PF | Particle Filter |
PMSM | Permanent Magnet Synchronous Machine |
List of Symbols
, | [V] voltage equilibrium of the stator in rotating frame; |
, | [V] voltage equilibrium of the rotor in rotating frame; |
[rad/s] mechanical angular velocity; | |
[rad/s] electrical angular velocity; | |
, | stator currents in rotating frame; |
, | [A] rotor currents in rotating frame; |
, | [Wb] stator fluxes in rotating frame; |
, | [Wb] rotor fluxes in rotating frame; |
[H] inductance of the stator; | |
[H] inductance of the rotor; | |
[H] mutual inductance; | |
[H] leakage inductance of the stator; | |
[H] leakage inductance of the rotor; | |
[A] estimated value of the magnetization current; | |
[A] stator current; | |
[s] time constant of the rotor electrical dynamics; | |
[Hz] inverter switching frequency; | |
[] nominal rotor resistance; | |
[] nominal stator resistance; | |
normal distribution variances of observation and transition model; | |
[s] time constant of the low-pass filter introduced for realizability; | |
coefficients of the thermal model; | |
[C] stator temperature; | |
[C] rotor temperature; | |
[C] predicted temperature with the thermal model; | |
[C] predicted temperature with the NARX model; | |
[C] posterior-estimated value of the rotor temperature; | |
h | [s] sample time; |
[RPM] mechanical speed of the rotor measured in revolutions per minute; | |
gradient; | |
∗ | reference value; |
w | [-] particle filter sample weights; |
sigmoid activation function of the hidden layer; | |
linear activation function of the output layer; |
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@ 20 °C | @ 20 °C | Pole Pairs | |||
---|---|---|---|---|---|
0.0023 | 0.0024 | 4 | |||
200 | 6 | 48 | 60 | 18,000 | 4500 |
Model Coefficient | Model Coefficient | Filter Time Constant |
14.8052 | 1.3332 | 0.01 |
Sample Time | Measurement Noise | Number of Particles |
[°C] | ||
0.0015 | 4.3641 | 60 |
Test Scenario | MSE | MAE | MAX | VAF |
---|---|---|---|---|
I | 3.42 | 1.30 °C | 6.90 °C | 98.15% |
II | 2.86 | 1.16 °C | 6.31 °C | 98.52% |
III | 3.80 | 1.79 °C | 7.21 °C | 97.56% |
0.1403 | 1.2166 | 0.1194 | 0.9794 | 0.0861 | 1.1758 | ||||
2.0016 | 1.8543 | 0.0046 | |||||||
0.5346 | 0.1372 | 1.0812 | 0.7085 | 0.3366 | |||||
0.7925 | 0.6204 | 0.8561 | 2.0562 | 1.2913 | |||||
0.8833 | 0.0223 | 1.0860 | 1.4808 | 1.6212 | |||||
0.4766 | 0.5783 | 0.7903 | |||||||
2.0631 | 0.1600 | 1.7474 | 2.1912 | ||||||
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Mocanu, R.; Onea, A.; Dosoftei, C.C. A Combined Model and Data-Driven Approach for the Determination of Rotor Temperature in an Induction Machine. Sensors 2021, 21, 4512. https://doi.org/10.3390/s21134512
Mocanu R, Onea A, Dosoftei CC. A Combined Model and Data-Driven Approach for the Determination of Rotor Temperature in an Induction Machine. Sensors. 2021; 21(13):4512. https://doi.org/10.3390/s21134512
Chicago/Turabian StyleMocanu, Razvan, Alexandru Onea, and Constantin Catalin Dosoftei. 2021. "A Combined Model and Data-Driven Approach for the Determination of Rotor Temperature in an Induction Machine" Sensors 21, no. 13: 4512. https://doi.org/10.3390/s21134512