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Abstract
—In this paper it is presented a proposal to get the squirrel cage induction motor parameters by means of a combined, new, trustworthy, simple and cheap process, in order to be used at the first design stages of variable speed drives. In this work three different approaches are combined: the easiest classical tests (stator resistance measurement), the parameter extraction based on the plate motor data, and finally, the three-phase induction motor modeling. The induction motor study field is very interesting, because it is a kind of motor with a simple, robust and low-cost mechanical structure. Moreover, analyzing the great use of these systems, it can be said that a third part of electrical energy is converted again to mechanical energy by means of induction motors, and it is thought they will cover (in ten years) between 60 and 70% of the electrical motors applications [1].
Key words
—Squirrel cage induction motors; parameters estimation.
I.I
NTRODUCTION
At the industry, the induction motor is used in a wide range of applications, for example as pumps, blowers, compressors, conveyors, etc. Because of its robustness and simplicity, the induction motor can be utilized in extreme working conditions. Their construction is simple: they don’t have collector, sliding rings, mobile contacts between rotor and stator; these features arise different advantages, like low maintenance levels in comparison with DC motors. Because of their great reliability and their low-cost, it can be understood why induction motors are preferred over DC motors. Nowadays, induction motor control strategies have been developed to scalar techniques as well as to vector techniques; vector techniques are highly dependent on the acute knowledge of the induction motor parameters values [2], and this is why it is necessary to get the values of these parameters. A set of trustworthy parameters values is essential to properly represent the dynamics of the induction motor. The tests to be done, as well as the required computations to get the induction motor parameters values, lead to necessity of a deep knowledge of the induction motor dynamics. In order to make the motor tests, it is needed to use a specific representation in which there usually exist some simplifications that should not affect the final result. There are different methods to estimate the induction motor parameters values, but it is not clear to distinguish a using trend, however it is clear that the per-phase induction motor circuit model is too much used. In this paper, it is used the classical circuit model for characterizing the induction motor (obtaining the induction motor parameters values), whose circuit can be illustrated in figure 1. This is the induction motor model in the stationary state, and it is created by means of rotor and stator resistances and reactances, as well as the magnetizing branch that it is modeled as a magnetizing reactance. This circuit is widely used in the stationary state for determining the motor static behavior. Despite the existing differences between classical transformer and induction machine models, the first approximation in the problem of parameter estimation lies on the exactly use of the hypothesis for transformers. So, according to this idea, the no-load and blocked-rotor tests were done to obtain an approximation of the parametric estimation [3]. In the regulation IEEE 112, section 5.9, it is established the procedure required to make the no-load test, the blocked-rotor test and the experimental resistance measurement of the stator winding. However, as it can be seen in [3], [4] and [5], these procedures are frequently applied in a simplified way taking into account that such a simplification can be ignored because of the final application: the development of a control system. From the no-load and blocked-rotor traditional tests, it is impossible to completely determine the 6 parameters values of the classical equivalent electrical circuit (the stator resistance R
1
, the stator reactance X
1
, the magnetizing reactance X
m
, the rotor reactance (referred to the stator) X
2
, and the rotor resistance (referred to the stator) R
2
. Each of the tests
Characterizing the Squirrel Cage Induction Motor
Velázquez-González Felipe de Jesús; Aguilar-Justo Marving Omar.
Figure 1.Circuit model (per phase) of the three-phase squirrel cage induction motor
2013 International Conference on Mechatronics, Electronics and Automotive Engineering
978-1-4799-2252-9/13 $31.00 © 2013 IEEEDOI 10.1109/ICMEAE.2013.23134
2013 International Conference on Mechatronics, Electronics and Automotive Engineering
978-1-4799-2252-9/13 $31.00 © 2013 IEEEDOI 10.1109/ICMEAE.2013.23134
2013 International Conference on Mechatronics, Electronics and Automotive Engineering
978-1-4799-2252-9/13 $31.00 © 2013 IEEEDOI 10.1109/ICMEAE.2013.23134
2013 International Conference on Mechatronics, Electronics and Automotive Engineering
978-1-4799-2253-6/13 $31.00 © 2013 IEEEDOI 10.1109/ICMEAE.2013.23134
establishes just two independent equations, so additional tests are needed to get an acute determination of all the parameters values. The resistance stator winding direct measurement eliminates one unknown quantity, but it is still necessary one additional equation. If it is considered that stator reactances and the rotor reactances (referred to the stator) are equal, or that both reactances maintain a known empirical relationship, it is srcinated another approximation.
Stator resistance Measurement Test
With the rotor without movement, in each of the phase winding resistances is applied a DC voltage, so it is possible to measure the current in each of them; taking these data (current and voltage) the stator resistance can be calculated using the Ohm’s Law. However, to correct the effects of operating temperature and frequency there exist different recommendations, and the one used in this work is to add 5% of the measured value as it is reported in [10].
1
1.05
DC DC
V RI
(1)
Free acceleration test
In this test the magnetizing reactance X
m
and the resistance R
c
(that represents losses at the core) are found. The test is made by driving the motor up to the synchronous speed, without load, applying a nominal stator voltage. Under these conditions the input or the consumed power is measured at the stator terminals, as well as the applied voltage and the consumed current. The adopted criterion for simplifying is that rotor circuit presents very high impedance, because the slip is very close to zero, so the motor equivalent circuit is simplified like figure 2 shows. With the equations illustrated from (2) to (4), along with the obtained data, three elements are calculated: the power factor, the magnetizing current and the loss current.
cos
nlnlas as
PV I
(2)
sin
m as nl
I I
(3)
cos
c as nl
I I
(4) Now the stator impedance can be discarded, because it is very small in comparison with the magnetizing impedance and with the core losses impedance. This consideration simplifies the computations, so the magnetizing reactance can be obtained as follows:
asmm
V X I
(5) The core loss resistance is calculated as follows:
ascc
V RI
(6) According to [3],the procedure mentioned above is enough for most of the induction motor applications.
Blocked-rotor test
In this test, the motor rotor is blocked in order to avoid its movement, then a set of three-phase voltages is applied to the motor; these voltages must be increased in gradual form until in each stator winding flows the motor nominal current. Under these conditions, the consumed motor power, the applied voltage and the stator winding current are measured. When the rotor is blocked the slip is equal to one, so the circuit is similar to the transformer with its secondary in short-circuit. As the magnetizing branch impedance has a very high value related to the rotor impedance, the resulting impedance is approximately the same than the rotor impedance, so the resulting circuit is approximated to the shown in figure 3. Now it is necessary to compute the power factor, the rotor- blocked impedance, the rotor resistance (referred to the stator), and the rotor blocked reactance. By applying an empirical relation between the stator reactance X
1
and the rotor reactance X
2
the values can be calculated:
cos
abr br as br
PV I
(7)
Figure 2.Per phase equivalent circuit in the induction motor under the no-load testFigure 3.Per-phase equivalent circuit of the induction motor with the rotor blocked.
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135
135
135
asbr br
V ZI
(8)
2 1
cos
br br
R Z R
(9)
1 2
sin
br br br
X Z X X
(10) The method of classical tests in the induction motor is a traditional method usually used in Universities’ books. It has a direct relation with the exposed method in the IEEE 112 standard (IEEE Standard Test Procedure for Polyphase Induction Motors and Generators). However, as the machine parameters values change during operation and depend on the rotor speed, the nonlinear equations system that results could not represent the actual dynamics. To face this problem, a solution could be to focus on another operating point, which is reached making the test at the nominal operating point, identifying the parameter which is more sensitive to any specific test. Another solution could be obtaining the parameters set that minimize a certain cost function made by the errors between the actual values and the calculated values [6]. As it is shown in table I there are reported results like in [7] where it is compared the application of the standard IEEE 112 against the standard IEC60034-28 (Rotating electrical machines - Part 28: Test methods for determining quantities of equivalent circuit diagrams for three-phase low-voltage cage induction motors) where this last standard is oriented to the same kind of tests to estimate the induction motor parameters values; in addition to this, the standard establishes specifications that take into account different magnetic saturation levels, as well as the compensation to skin effects. Table I shows the results comparison for a specific application of the IEEE 112 and the IEC60034-28 standards. In table I also can be seen that there are differences between both methods (mentioned in Standards IEEE 112 and IEC 60034-28). This is because different operating points were considered, and the obtained equations system is solved applying some empirical criteria that help to eliminate some unknown variables from the system. Sometimes it is not a good practice the motor parameter estimation using a classical method, mainly when the motor is already installed in a plant, making a specialized function, so it cannot be stopped. That is why it is necessary to use other methods like those using technical information provided by the manufacturer of such a motor; in this sense, the information displayed at the motor data plate represents the first source of information in order to make the estimation of the motor parameters values. For standard drives, without high dynamic response, the calculation of the parameters from the plate is enough; however, the resulting deviation could be around 50%. For parameter estimation using just data from the motor plate, a method developed in [6] is chosen. It is based on stationary model of the motor, so we can take figure 4 as a reference obtaining the following formulas:
Parameters IEEE 112 Standard IEC 60034-28 Standard Stator Resistance 0.89 0.89 Stator Reactance 0.43 0.88 Core-Loss Resistance 491.8 521.18 Magnetizing Reactance 25.05 22.18 Rotor Reactance(referred to the stator) 0.65 1.77 Rotor Resistance (referred to the stator) 0.60 0.86
Table I.- Comparison between the obtained parameters values for the three-phase squirrel cage induction motor with 3 hp, 230/460 V, 9.0/4.5 A, 1745 rpm, 60 Hz.
Total Reactance
23
N hsdN
V X X I
(11) Stator and rotor resistance
ˆˆ2
rN sdN s r hN sqN
I R R X f I
(12) Total leakage factor
h
X X
(13) Stator time constant
2
hsN s
X T f R
(14) As the motor estimation parameters methods that yield higher accuracy are complex in the required equipment and their development, and considering that their srcinated results are changing just as the machine operating point changes too, it is proposed to define a procedure to get induction motor parameters with the following features:
The procedure can be supported on the existing methods,
The procedure can be applied with the minimum amount of tests and equipment,
The obtained parameters values can be reliable, quite similar to the actual values.
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II.D
EVELOPMENT
A.Proposed method
In this work was decided to join two methods, the classical tests and plate data, in order to establish a simple and cheap procedure to get the induction motor parameters. In addition, for any set of estimated parameters values it is verified the induction motor behavior using the three-phase dynamic model by means of a comparison with usual behavior established by the motor manufacturer, with no-load and with rated load. If there exists a deviation, an adjustment can be done to decrease the error.
B.Parameter estimation using classical tests
The plate data corresponding to the used induction motor are shown in Table II. De Lorenzo Motor, model DL 30115 ; IP55 Voltage 220 V / 380 V (/Y) Current 1.7 A / 0.98 A (/Y) Power 370 W Rpm 3350 Power factor 0.85 Frequency 60 Hz
Table II. Plate data for the De Lorenzo DL 30115 Motor
The parameters obtained in the experimental method, by means of the classical tests, are illustrated in Table III. De Lorenzo DL 30115 Parameters Values Stator Resistance R
1
27.38 Stator Reactance X
1
16.26 Stator Inductance L
1
37.77 mH Core losses Resistance R
c
2520 Magnetizing Reactance X
m
507.28 Magnetizing Inductance L
m
1.34 H Rotor resistance (referred to the stator) R
2
16.26 Rotor Reactance (referred to the stator) X
2
21.35 Rotor Inductance (referred to the stator) L
2
56.66 mH
Table III. Parameters of the de Lorenzo DL 30115 induction motor obtained by means of the classical experimental method.
C.Parameter estimation using plate data
As was previously pointed out, it is chosen the procedure exposed in [6], obtaining the parameters values shown in Table IV and considering that these values were calculated for the rated operating point of the motor.
D.Behavior Test using the induction motor dynamic model and the parameters values recently estimated D.1 Induction motor dynamic model
In this section is presented the induction motor dynamic model presented in [5]. Vector currents equation:
1 1
P r
d dN dt dt
i iR i vL L
(15) Rotor position equation
r P r
dN dt
(16) Rotor speed equation
1
r e r L
ddt J
(17) Electromagnetic torque equation
2
T Pe abcs sr abcr r
N
i L i
(18) De Lorenzo DL 30115 Parameters Values Stator Resistance R
1
15.75 Stator Reactance X
1
15.19 Stator Inductance L
1
40.31 mH Core losses Resistance R
c
--------- Magnetizing Reactance X
m
502.04 Magnetizing Inductance L
m
1.331 H Rotor resistance (referred to the stator) R
2
15.75 Rotor Reactance (referred to the stator) X
2
22.79 Rotor Inductance (referred to the stator) L
2
60.46 mH
Table IV. Parameters of the de Lorenzo DL 30115 induction motor obtained from its data plate.
D.2 Final results
The adjustment process applied to the induction motor is:
To simulate the behavior of the induction motor without load during 0.8 s.
To apply the nominal torque other 0.8 s.
To register the values of torque, speed and stator current.
To compare the simulated values of torque, speed and stator current against the actual values (given by the manufacturer).
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To adjust the induction motor parameters values to improve the behavior of the motor model, getting closer values in the mentioned variables (torque, speed and stator current).
Without load With load Model Actual Error Model Actual Error T (Nm) 0.101 0.101 0% 1 1 0%
(rad/s) 375.5 375.6 0% 357.6 350.8 2% I
s
(A) 0.29 0.44 34% 0.75 0.98 23.4%
Table V. Test Results obtained in the de Lorenzo DL 30115 induction motor, by means of the experimental way, without adjustment.
After looking the behavior of the induction motor with the parameters values obtained by means of the experimental method, these values were adjusted and the model behavior improved, as it is shown in table VI.
Without load With load Model Actual Error Model Actual Error T (Nm) 0.101 0.101 0% 1 1 0%
(rad/s) 375.2 375.6 0.1% 353.2 350.8 0.6% I
s
(A) 0.49 0.44 11% 0.886 0.98 9.5%
Table VI. Test results obtained in the De Lorenzo DL 30115 induction motor, by means of the experimental method, with adjustment.
The same process of tests and adjustments were made in the induction motor using the parameters obtained from the data plate; in tables VII and VIII are shown the results.
Without load With load Model Actual Error Model Actual Error T (Nm) 0.101 0.101 0% 1 1 0%
(rad/s) 375.3 375.6 0% 357.6 350.8 2% I
s
(A) 0.29 0.44 34% 0.75 0.98 23.4%
Table VII. Test results obtained in the De Lorenzo DL 30115 induction motor, using the data plate, without adjustment.
Without load With load Model Actual Error Model Actual Error T (Nm) 0.101 0.101 0% 1 1 0%
(rad/s) 375.2 375.6 0.1% 354.7 350.8 1.1% I
s
(A) 0.29 0.44 34% 0.86 0.98 12.2%
Table VIII. Test results obtained in the de Lorenzo DL 30115 induction motor, using the data plate, with adjustment.
De Lorenzo DL 30115 Parameters Values Stator Resistance R
1
27.38 Stator Reactance X
1
21.11 Stator Inductance L
1
56 mH Core losses Resistance R
c
282.74 Magnetizing Reactance X
m
0.75 H Magnetizing Inductance L
m
16.26 Rotor resistance (referred to the stator) R
2
21.11 Rotor Reactance (referred to the stator) X
2
56 mH Rotor Inductance (referred to the stator) L
2
56.66 mH
Table IX. Final parameters values obtained for the De Lorenzo DL 30115indution motor.
After simulating the behavior of the motor under no load condition and nominal conditions, it was observed that the stator current is the variable that presents major deviation from its real value, therefore, the parameters obtained by both methods are capable of be improved To make adjustments to the motor parameters, it has to be considered the torque equations and the motor NEMA class.
2max22sin2
32
thththth
V T RRXX
(19)
22sin2
222
32
tharr th
th
VRT XX
RR
(20) The above equations allow seeing whether a motor parameter affects the value of the stator current, the maximum torque and the starting torque, that is why it has to be checked
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