# Identification of Induction Motor Parameters in Industrial Drives with Artificial Neural Networks

Authors: Baburaj Karanayil; Muhammed Fazlur Rahman; Colin Grantham
Journal: Advances in Fuzzy Systems
 (2009)

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## Abstract

This paper presents a new method of online estimation of the stator and rotor resistance of the induction motor in the indirect vector-controlled drive, with artificial neural networks. The back propagation algorithm is used for training of the neural networks. The error between the rotor flux linkages based on a neural network model and a voltage model is back propagated to adjust the weights of the neural network model for the rotor
resistance estimation. For the stator resistance estimation, the error between the measured stator current and the estimated stator current using neural network is back propagated to adjust the weights of the neural network. The performance of the stator and rotor resistance estimators and torque and flux responses of the drive, together with these estimators, is  investigated with the help of simulations for variations in the stator and rotor resistance from their nominal values. Both types of resistance are estimated experimentally, using the proposed neural network in a vector-controlled induction motor drive. Data on tracking performances of these estimators are presented. With this approach, the rotor resistance estimation was found to be insensitive to the stator resistance variations both in simulation and experiment.


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## Body

## 1. Introduction

Indirect field oriented vector-controlled
induction motor drives are widely used in industrial applications for
high-performance drive systems. Because indirect field orientation utilizes an
inherent slip relation, it is essentially a feedforward scheme and hence
naturally parameter sensitive, particularly to the rotor resistance. A mismatch
between the actual rotor flux and the estimated rotor flux leads to error
between the actual motor torque and the estimated torque and hence leads to poor
dynamic performance. The accuracy of the estimated rotor flux is greatly influenced
by the value of rotor resistance (Rr)
used for control. Rotor resistance may vary up to 100% due to rotor heating,
and recovering this information with a thermal model or a temperature sensor is
not desirable. In addition, rotor resistance can change significantly with
rotor frequency due to skew/proximity effect in machines with double-cage and
deep-bar rotors. The problem related to stator and rotor resistance adaptation
has been investigated by various authors [1–5].Several
methods have been reported to minimize the consequences of parameter sensitivity
in indirect vector-controlled drives. The methods discussed in [6–8] are
based on model reference adaptation of either flux or reactive power. The second approach,
developed in [9, 10], was to compensate for rotor resistance variation by
adaptive feedback linearization control with unknown rotor resistance.  The third identification method is to detect
the output signal variation invoked by the artificial injection signal [11].
Also, an extended Kalman filter was used for rotor resistance identification in
[12, 13]. These methods assumed that there is no change in the stator
resistance during the rotor resistance estimation. To estimate stator
resistance, online identification has been developed using model reference
adaptation [14]. Combined stator and rotor resistance identification has been
reported [7, 15]. However, these methods are based on the assumption that the
stator resistance does not change during the estimation of rotor resistance.In
this paper, online estimators are developed to address the situation of similar
disturbances in both stator and rotor resistance simultaneously. Section2 describes an
online estimation of rotor resistance (Rr)
with multilayer feedforward artificial neural networks (ANNs) using online training [16].
Multilayer feedforward neural networks are regarded as universal approximations
and have the capability to acquire nonlinear input-output relationships of a
system by learning via the back propagation algorithm [17, 18]. It should be
possible that a simple two-layer feedforward neural network trained by the back
propagation technique can be employed in the rotor resistance identification.
In this estimator, two models of the state variable estimations can be used;
one to provide the actual induction motor output states and the other to give
the neural model output states. The total error between the desired and actual
state variables may then be back propagated as shown in Figure 1, to adjust the
weights of the neural model, so that the output of this model tracks the actual
output. When the training is completed, the weights of the neural network
should correspond to the parameters in the actual motor. However, the Rr  estimation algorithm
requires the knowledge of stator resistance (Rs) which may also vary up to 50% during operation. It
has been observed that the error in Rs leads to significant errors in Rr estimation. It is hypothesized in this paper that the problem may be overcome by adding
another online estimation for Rs to the system using recurrent neural network, discussed in Section 3, giving
the indirect vector control system, total immunity to both resistance
variations. The proposed stator resistance observer was
realized with a recurrent neural network trained using the standard back propagation learning algorithm. The recurrent neural network with feedback loops used in this paper is trained by standard back propagation
algorithm. Such architecture is known to be a more desirable approach [19], and
the implementation reported in this paper confirms this.Figure 1
Parameter identification using neural networks.The
rotor and stator resistance estimators described in Sections2 and 3
are investigated by modeling studies using SIMULINK, and the results are
discussed in Section 4. The new resistance estimators are also tested in an
experimental setup for both slip-ring and squirrel-cage induction motors. These
results are discussed in detail in Section 5.


## 2. Rotor Resistance Estimation
Using Artificial Neural Networks

The basic structure of an adaptive scheme described by Figure1 is extended for rotor resistance estimation of an induction motor as
illustrated in Figure 2. Two independent observers are used to estimate the
rotor flux vectors of the induction motor.
Equation (1) is based on stator voltages and currents, and (2) is based
on stator currents and rotor speed: (1)[dλdrvmdtdλqrvmdt]=LrLm{[vdsvqs]−Rs[idsiqs]−σLs[didsdtdiqsdt]},(2)[dλdrimdtdλqrimdt]=[−1Tr−ωrωr−1Tr][λdrimλqrim]+LmTr[idsiqs].Figure 2
Structure of the neural network system forRr estimation.The current model (2) can also be written as (3)λrim→.=(−1TrI+ωrJ)λrim→+LmTris→, where (4)I=[1001],J=[0−110],is→=[idsiqs],vs→=[vdsvqs],λrim→=[λdrimλqrim],λrvm→=[λdrvmλqrvm].The sample data model of
(3) is shown as follows: (5)λrnm→(k)=(W1I+W2J)λrnm→(k−1)+W3is→(k−1), where (6)W1=1−TsTr;W2=ωrTs;W3=LmTrTs. Here, Ts  is the sampling period.
Equation (5) can also be written as(7)λrnm→(k)=W1X1+W2X2+W3X3, where (8)X1=Iλrnm→(k−1)=[λdrnm(k−1)λqrnm(k−1)],X2=Jλrnm→(k−1)=[−λqrnm(k−1)λdrnm(k−1)],X3=Iis→(k−1)=[ids(k−1)iqs(k−1)].The neural
network model represented by (7) is shown in Figure 3, where W1,W2,W3  represent the weights of the networks, and X1,X2,X3  are the three inputs to the network. If the network
shown in Figure 3 is used to estimate Tr, W2 is already known, and W1 and W3  need to be updated.Figure 3
Two-layered neural
network model.The weights of
the network,W1 and W3 are found from training,
so as to minimize the cumulative error function E1, (9)E1=12ε1→2(k)=12{λrvm→(k)−λrim→(k)}2, and the weight adjustment using generalized delta rule
is given by (10)ΔW1(k)=[λrvm→(k)−λrnm→(k)]TIλrnm→(k−1), where, (11)δ→=∂E∂λrnm→(k)=[λrvm→(k)−λrnm→(k)]T.To accelerate
the convergence of the error back propagation learning algorithm, the current
weight adjustments are
supplemented with a fraction of the most recent weight adjustment, as(12)W1(k)=W1(k−1)−η1δ→X2+α1ΔW1(k−1), where η1  is the training coefficient, and α1 is a user-selected
positive momentum constant.Similarly,
the changes inW3 can be
determined as follows: (13)W3(k)=W3(k−1)−η1δ→X3+α1ΔW3(k−1).The
rotor resistanceRr can
be calculated from either W1 or W3 from (14) or (15) as follows: (14)Rr=LrW3LmTs,(15)Rr=Lr(1−W1)Ts.The rotor resistance estimator described in this section, has used the
fluxesλdrvm,λqrvm derived from the voltage model of the
induction motor. This is dependent on stator resistance Rs of the motor (see (1)). Modeling results in Section
4 clearly show
that maximum possible variation in Rs introduces a significant variation in Rr.
In order to minimize the error in rotor resistance estimation, resulting from
the stator resistance variation, an online stator resistance estimator is
integrated, which is discussed in Section 3.


## 3. Stator Resistance Estimation with
Artificial Neural Networks

The voltage and current model equations of the induction
motor, (1) and (2) in Section 1, can also be written as (16)σLsdidsdt=LmLrTrλdrim+LmLrωrλqrim−Lm2LrTrids+Vds−Rsids,(17)σLsdiqsdt=LmLrTrλqrim−LmLrωrλdrim−Lm2LrTriqs+Vqs−Rsiqs. Using the
discrete form of (16),(18)ids*(k)=W4ids*(k−1)+W5λdrim(k)+W6ωrλqrim(k)+W7Vds(k), where (19)W4=1−TsσLsLm2LrTr−TsσLsRs,W5=TsσLsLmLrTr,W6=TsσLsLmLrωr,W7=TsσLs.The weightsW5,
W6, and W7, are calculated from the
motor parameters, motor speed ωr,  and the sampling interval Ts.To examine the
effect of stator resistance variation in the amplitude of stator current,
modeling studies were carried out with a ramp change in stator resistance. The
stator current profile is shown in Figure4. The relationship between stator
current and stator resistance is nonlinear which could be easily mapped using a
neural network.Figure 4
Relationship betweenRs variation with amplitude of stator current.Equation (18) can be represented by a recurrent neural network as shown
in Figure 5. The standard back-propagation learning rule is then employed to
train the network. The weight W4 is the result of training so as to
minimize the cumulative error function E2: (20)E2=12ε22→(k)=12{ids(k)−ids*(k)}2.Figure 5
D-axis
stator current estimation using recurrent neural network based on (18).The weight
adjustment forW4 is given
by (21)ΔW4(k)α[ids(k)−ids*(k)]ids*(k−1).To accelerate
the convergence of the error back propagation learning algorithm, the current
weight adjustments are
supplemented with a fraction of the most recent weight adjustment, as in(22)W4(k)=W4(k−1)+η2ΔW4(k)+α2ΔW4(k−1), where η2  is the training coefficient, α2 is a user-selected
positive momentum constant.Similarly, using the discrete
form of (17), (23)iqs*(k)=W4iqs(k−1)+W5λqrim(k)−ωrW6λdrim(k)+W7Vqs(k).Equation (23)
can be represented by a neural network as shown in Figure 6.Figure 6
Q-axis
stator current estimation using recurrent neural network based on (23).The weightW4 is adjusted with training
based on (22).The stator resistanceRs can be
calculated from (24)R^s={1−W4−TsσLsLm2R^rLr2}σLsTs.The stator resistance of an induction motor can be thus
estimated from the stator current using the neural network system as indicated
in Figure7.Figure 7
Rs estimation using artificial neural network.


## 4. Modelling Results

The block
diagram of a rotor flux oriented induction motor drive, together with both
stator and rotor resistance identifications, is shown in Figure8. The use of
artificial neural networks in identification algorithms in Sections 2 and 3 is verified by
simulations with the aid of SIMULINK.Figure 8
Schematic of the indirect vector-controlled
induction motor drive with online stator and rotor resistance tracking.In order to investigate the performance of the drive for
parameter variations in rotor resistanceRr,
a series of simulations were conducted by introducing error between the actual
value Rr‐motor and the value used in the controller Rr‐control Similarly, another series of simulations were conducted by
introducing error between the actual stator resistance Rs‐motor and the one used in the controller Rs‐control.  All these investigations were conducted for
the drive running at 1000 rev/minute and a constant load torque of 7.4 Nm. The
parameters of the motor used for modeling studies are in Table 1.Table 1
Induction motor parameters.
1.1 kW, 1415 RPM, 415 V,
2.77 A, 3 phases, 4 pole, 50 HzStator resistanceRs: 6.03 ΩRotor leakage inductanceLrs:  29.9 mHStator leakage inductanceLls: 29.9 mHMagnetizing inductanceLm: 489.3 mHRotor resistanceRr:  6.085 Ωat 50 HzMoment of inertiaJT:  0.011787 kgm2Initially, a 40% error was introduced betweenRr‐motor and Rr‐control and Rs‐motor and Rs‐control simultaneously at 1.5 seconds,
after switching off both the rotor resistance estimation (RRE) and stator resistance
estimation (SRE) blocks in Figure 8. The steady-state values of the torque,
rotor flux linkage, and the amplitude of the stator current vector are shown in
Figure 9(a). The rotor flux linkage in the motor increases by 21% compared to
its estimated value, when the error in rotor resistance is introduced, as shown
in Figure 9(a) (iv). The estimated torque is 4% lower than the actual motor
torque, as shown in Figure 9(a) (ii). Also, there is a 3.25% drop in the
amplitude of the stator current vector starting at 1.5 seconds, when the error is introduced, as
in Figure 9(a) (vi).Performance
of the drive with and without rotor and stator resistance compensations.
(a)
40% step change
inRr‐motor and Rs‐motor,Rs‐motor and Rs‐control  uncompensated(b)
40% step change
inRr‐motor and Rs‐motor, Rs‐motor and Rs‐control compensatedLater, simulations were repeated after switching on
only the rotor resistance estimation block with the SRE block switched off, for
the same errors introduced in Figure9(a). The estimated Rr, in this case, is higher than the Rr‐motor by 1.7% as shown in Figure 9(b) (i). The estimated torque is 1.35% higher
than the real motor torque, as shown in Figure 9(b) (ii). But the estimated
rotor flux linkage is 1.5% lower than the actual rotor flux linkage as
indicated in Figure 9(b) (iv). The stator current amplitude increases only by
0.4% in this case, as shown
in Figure 9(b) (vi).Finally, the simulations were carried out with both the
RRE and SRE blocks switched on. The results of torque, rotor flux linkage, and
stator current amplitude are shown for both of the cases, in Figure9(b). The
errors reported in the previous paragraph, between estimated and real
quantities of torque rotor flux linkage and stator current amplitude, have
largely disappeared in this case. The estimated rotor resistance has tracked
the real rotor resistance of the motor very well, as the estimation error now
drops to 0.3% as in Figure 9(b) (i).However, there was a small but insignificant error of 4.4%, as shown Figure9(b) (v), for the estimated stator resistance with respect to the real stator
resistance.The Figures9(a) and 9(b) also described the possible
steady-state errors encountered in a situation, where a step change in
resistance is applied, only for the purpose of investigation. However, the
practical variation in resistance
is very slow, and a corresponding analysis is also carried out, and the results
are indicated in Figure 10. The simulations are done in three steps. At first,
the drive system is analyzed after introducing error between Rr‐motor  and Rr‐control  and Rs‐motor and Rs‐control  keeping both RRE and SRE turned OFF. Repeated simulations were also carried
out, with RRE ON and SRE OFF. The estimated Rr,  in this case, is higher than the Rr‐motor by 1.1% as shown in Figure 10 (i). The estimated torque is 1.3% higher
than the real motor torque, as shown in Figure 10 (ii). But the estimated rotor
flux linkage is 1.5% lower than the actual rotor flux linkage as indicated in
Figure 10 (iv). The stator current amplitude increases only by 0.4% in this
case, as shown in Figure 10 (vi).Figure 10
Performance of the induction motor drive with a ramp change in stator
and rotor resistance
with and without RRE and SRE.Finally, both
rotor and stator resistance estimators are investigated with both RRE and SRE
switched ON. The estimated rotor resistance has tracked the real rotor
resistance of the motor very well, as the error now drops to 0.3% as in Figure10 (i). However, there was a small but insignificant error of 5%, as shown Figure
10 (v), for the estimated stator resistance with respect to the real stator
resistance. But its effect on the rotor flux oriented control is negligible, as
the errors between torques, rotor flux linkages, and stator current amplitudes
are virtually eliminated.


## 5. Experimental Results

In
order to verify the proposed stator and rotor resistance estimation algorithms,
a rotor flux oriented induction motor drive was implemented in the laboratory
as shown in Figure11.Figure 11
Experimental setup for the resistance
identification in induction motor drive.The experimental setup was built for
the 1.1 kW  squirrel cage induction motor around a dSPACE DS1104 controller
board residing in PC, as shown in Figure12. An IGBT inverter with a switching
frequency of 5 kHz was used for driving the induction motor. Hand-coded C
programs with the real-time reference library functions were used to develop
the control programs. The current and flux controllers were implemented with
100 microsecond sampling interval and the speed controller with
500 microsecond.
The proposed rotor resistance estimation block used 1000 microsecond sampling
time, and the stator resistance estimation block used 100 μmicrosecond. An
encoder with 5000 pulses per revolution was used for position and speed
feedbacks. A permanent magnet DC motor coupled to the induction motor was used
to load the induction motor. A constant load torque was maintained by using the
current control loop in the load circuit.Figure 12
Photograph of the experimental setup
of the 1.1 kW squirrel cage induction motor drive.


### 5.1. Results for Slip Ring Induction Motor

The
induction motor in Table1 is of squirrel cage type, and its rotor resistance
measurement with a dc current measurement is not possible, the initial rotor
resistance estimation experiment was conducted on a slip ring induction motor
with specifications in Table 2. The experimental setup for the 3.7 kW slip-ring
induction motor is shown in Figure 13. A separately excited DC motor coupled to
the induction motor was used to load the induction motor. The estimated rotor
resistance was noted using the estimation principles described in Sections 2 and 3, when
the motor was running at 1000 rev/min and drawing 75% of full load current. The
drive was shut down, and the rotor resistance was measured immediately, using a
dc current injection. Both the estimated and measured rotor resistance of this motor
are shown in Table 3.Table 2
Induction motor parameters.
3.7 kW, 1410 RPM, 415 V, 7.8 A,
3 phases, 4 pole, 50 HzStator resistanceRs = 1.54 ΩStator leakage inductanceLls = 11.65 mHRotor leakage inductanceLrs  = 11.65 mHMagnetizing inductanceLm  = 184.61 mHRotor resistanceRr  = 2.62 ΩMoment of inertiaJT = 0.08 kgm2Table 3
Rotor resistance measurements.
Measured rotor resistanceEstimated rotor resistance
usingthe proposed estimator2.62 Ω2.51 ΩFigure 13
Photograph of the experimental setup of the 3.7 kW slip-ring
induction motor drive.


### 5.2. Results for Squirrel Cage Induction Motor

After establishing the
validity of the proposed rotor resistance estimation with the slip-ring
induction motor, experimental investigations are repeated with the squirrel
cage induction motor which was used for the modeling studies.In order to examine the
capability of tracking the rotor resistance of the induction motor with the
proposed estimator, a temperature rise test was conducted, at a motor speed of
1000 rev/min. The results ofRr estimation obtained from the experiment are shown in Figure 14, after logging the data for
60 minutes. Figure 15 shows the d-axis rotor
flux linkages of the current model (λdrim), the voltage model (λdrvm), and the neural model (λdrnm), taken at the end of heat run. All of
the flux linkages are in the stationary reference frame. The flux linkages λdrim and λdrvm are updated with a sampling time of 100 microseconds, whereas the flux λdrnm is updated only at 1000 microseconds.
The flux linkage λdrnm follows the flux linkage λdrvm due to the online training of the neural
network. The coefficients used for training are η1  = 0.005  and α1  = 10.0e−6.Figure 14
EstimatedRr in experiment.Figure 15
Rotor fluxes inRr estimation.To test
the stator resistance estimation, an additional 3.4 Ωper
phase was added in series with the induction motor stator, with the motor
running at 1000 rev/min with a load torque of 7.4 Nm. The estimated stator
resistance together with the actual stator resistance is shown in Figure16. The
estimated stator resistance converges to 9.4 Ωwithin less than 200 milliseconds. Figure 17 shows both the
measured d-axis stator current and the one estimated by the neural network model.
The neural model output ids*(k) follows the measured values ids(k) due to the online training of the network. The neural model current estimate is updated with
a sampling time of 100 microseconds. The coefficients used for training are η2 = 0.00216 and α2 = 10.0e−6.Estimated stator resistanceRs in experiment.
(a)(b)Figure 17
Stator currents inRs estimation.


## 5.1. Results for Slip Ring Induction Motor

The
induction motor in Table1 is of squirrel cage type, and its rotor resistance
measurement with a dc current measurement is not possible, the initial rotor
resistance estimation experiment was conducted on a slip ring induction motor
with specifications in Table 2. The experimental setup for the 3.7 kW slip-ring
induction motor is shown in Figure 13. A separately excited DC motor coupled to
the induction motor was used to load the induction motor. The estimated rotor
resistance was noted using the estimation principles described in Sections 2 and 3, when
the motor was running at 1000 rev/min and drawing 75% of full load current. The
drive was shut down, and the rotor resistance was measured immediately, using a
dc current injection. Both the estimated and measured rotor resistance of this motor
are shown in Table 3.Table 2
Induction motor parameters.
3.7 kW, 1410 RPM, 415 V, 7.8 A,
3 phases, 4 pole, 50 HzStator resistanceRs = 1.54 ΩStator leakage inductanceLls = 11.65 mHRotor leakage inductanceLrs  = 11.65 mHMagnetizing inductanceLm  = 184.61 mHRotor resistanceRr  = 2.62 ΩMoment of inertiaJT = 0.08 kgm2Table 3
Rotor resistance measurements.
Measured rotor resistanceEstimated rotor resistance
usingthe proposed estimator2.62 Ω2.51 ΩFigure 13
Photograph of the experimental setup of the 3.7 kW slip-ring
induction motor drive.


## 5.2. Results for Squirrel Cage Induction Motor

After establishing the
validity of the proposed rotor resistance estimation with the slip-ring
induction motor, experimental investigations are repeated with the squirrel
cage induction motor which was used for the modeling studies.In order to examine the
capability of tracking the rotor resistance of the induction motor with the
proposed estimator, a temperature rise test was conducted, at a motor speed of
1000 rev/min. The results ofRr estimation obtained from the experiment are shown in Figure 14, after logging the data for
60 minutes. Figure 15 shows the d-axis rotor
flux linkages of the current model (λdrim), the voltage model (λdrvm), and the neural model (λdrnm), taken at the end of heat run. All of
the flux linkages are in the stationary reference frame. The flux linkages λdrim and λdrvm are updated with a sampling time of 100 microseconds, whereas the flux λdrnm is updated only at 1000 microseconds.
The flux linkage λdrnm follows the flux linkage λdrvm due to the online training of the neural
network. The coefficients used for training are η1  = 0.005  and α1  = 10.0e−6.Figure 14
EstimatedRr in experiment.Figure 15
Rotor fluxes inRr estimation.To test
the stator resistance estimation, an additional 3.4 Ωper
phase was added in series with the induction motor stator, with the motor
running at 1000 rev/min with a load torque of 7.4 Nm. The estimated stator
resistance together with the actual stator resistance is shown in Figure16. The
estimated stator resistance converges to 9.4 Ωwithin less than 200 milliseconds. Figure 17 shows both the
measured d-axis stator current and the one estimated by the neural network model.
The neural model output ids*(k) follows the measured values ids(k) due to the online training of the network. The neural model current estimate is updated with
a sampling time of 100 microseconds. The coefficients used for training are η2 = 0.00216 and α2 = 10.0e−6.Estimated stator resistanceRs in experiment.
(a)(b)Figure 17
Stator currents inRs estimation.


## 6. Analysis of Results

The modeling results as described
in Figure9(b) indicate
that the proposed rotor and stator resistance estimators can converge in a
short time, as low as 200 milliseconds
corresponding to a 40% step change for both stator and rotor resistance
simultaneously.  In order to compare the
stator resistance estimation for simulation and experiment, simulation is
repeated with SRE and RRE blocks in Figure
8. Then, a step change in Rs‐motor  is applied without a step change in Rr‐motor, and the results are recorded as the upper trace in Figure 18.  The bottom trace in this figure is the same
as the top trace of Figure 16. The estimation time in modeling is in very close
agreement with that obtained from experiment.Comparison of stator resistance estimations.
(a)(b)


## 7. Conclusions

This
paper has presented a new online estimation technique for the rotor resistanceRr  in the presence of  Rs  variations for the
induction motor drive. The Rr  estimation was found to be totally insensitive to Rs variations, as a result of the stator resistance
estimation which is embedded separately.Investigations
carried out in this paper have clearly shown that two ANNs can be used in
estimatingRr in the face
of significant variations in Rs, which can occur due to motor heating. Both the rotor and stator resistance variations
can be successfully estimated using the adaptation capabilities of neural
networks. The implementation of these techniques required only a small increase
of the computation times. The feasibility and validity of the proposed
identification have
been proved by the excellent experimental results.



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*Source: 241809-2009-04-08.xml*