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Date Submitted: 02/15/2013
Report Submitted: Instructor: Prof. David R. Haas
Omar Khalaf Course Title: Electrical Engr. Lab III
Garrett Dicken Course #: ECE 494
Anas Kabashi Lab Report Section #: 102
Spring 2013
Experiment Title
Separation of Eddy Current & Hysteresis Losses
Comments by Professor:
Corrected By: Grade:
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Table of Contents
1.1. Abstract of Synopsis...............................................................................................................1
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1. Abstract of Synopsis
Modeling and defining of a procedure leading to a good estimation of power losses in
electrical machines from materials is challenging. The standardized measurement device
for measuring the magnetic properties of soft magnetic materials is theEpstein Frame.
The sample used in this experiment is a Grain Oriented electrical steel which in contrast
to non-Grain provides more increased magnetic flux and also a decreased magnetic
saturation. The power losses are measured by means of a wattmetermethod in which the
primary current and secondary voltage are used. During the measurement the Epsteinframe behaves as an unloaded transformer
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http://en.wikipedia.org/wiki/Wattmeterhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Wattmeterhttp://en.wikipedia.org/wiki/Transformer7/28/2019 Part a- Lab 2 Draft
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3. Final Connection Diagram
Figure 1.1
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4. Data Sheet
Table 1.1 Magmatic Density (Wb/m)
0.4 0.6 0.8 1.0 1.2
Freq. =
30 (Hz)
Es Calculated
(V)20.76 31.14 41.52 51.9 62.26
Es Measured
(V)20.89 31.34 41.88 52.0 62.5
% Error 0.63 0.64 0.87 0.19 0.38
Power
Measured
(Watts)
1.5 3 4.8 7 10
Freq. =
40 (Hz)
Es Calculated 27.68 41.52 55.36 69.2 83.04
Es Measured 27.47 41.56 55.6 69.7 83.9
% Error 0.76 0.096 0.433 0.72 1.03
Power
Measured
(Watts)
2 3.9 6 9 13
Freq. =
50 (Hz)
Es Calculated 34.6 51.9 69.2 86.5 103.8
Es Measured 34.51 52.00 69.6 86.5 103.9
% Error 0.26 0.19 0.57 0.0 0.096
Power
Measured
(Watts)
2.6 5 8 12 17
Freq. =
60 (Hz)
Es Calculated 41.52 62.28 83.04 103.8 124.56
Es Measured 41.56 62.8 83.7 104.2 125.1
% Error 0.096 0.83 0.79 0.38 0.43
Power
Measured
(Watts)
3.2 6 10 15 20
Freq. =
70 (Hz)
Es Calculated 48.44 72.66 96.88 121.1 145.32
Es Measured 49.29 72.7 96.7 121.4 144.9
% Error 1.75 0.055 0.18 0.25 0.29
Power
Measured
(Watts)
4 7 12 17 24
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5. Computations and Results
1) Kg Core Loss vs. frequency at different flux densities
Figure 1.1
2)
Table 1.2Frequency
(Hz)
W/f at Bm= 0.4 W/f at Bm= 0.6 W/f at Bm= 0.8 W/f at Bm= 1.0 W/f at Bm= 1.2
30 0.005 0.01 0.016 0.023333 0.03333
40 0.005 0.00975 0.015 0.0225 0.0325
50 0.0052 0.01 0.016 0.024 0.034
60 0.005333 0.01 0.016667 0.025 0.0333370 0.005714 0.01 0.017143 0.024286 0.034286
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Figure 1.3
Table 1.3
Bm (Wb/m) Slope = Ke* B2m Y-intercept = Kh*Bnm
0.4 0.0002 0.00470.6 0.00002 0.0099
0.8 0.0004 0.015
1.0 0.0004 0.0225
1.2 0.0003 0.0327
Table 1.4
f = 30 Hz f = 40
Hz
f = 50
Hz
f =
60 Hz
f = 70
Hz
Bm
(Wb/m)Pe =Ke*
Bmf(Watts)
Ph=Kh*Bn
m *f(Watts)
Pe =Ke*
Bmf(Watts)
Ph=Kh*Bnm
*f(Watts)
Pe =Ke*Bm
f(Watts)
Ph=Kh*Bn
m *f(Watts)
Pe =Ke*Bm
f(Watts)
Ph=Kh*Bn
m *f(Watts)
Pe =Ke*Bm
f(Watts)
Ph=Kh*Bnm
*f(Watts)
0.4 0.18 0.141 0.32 0.188 0.5 0.235 0.72 0.282 0.98 0.329
0.6 0.018 0.297 0.032 0.396 0.05 0.496 0.07
2
0.594 0.098 0.693
0.8 0.36 0.45 0.64 0.6 1 0.75 1.44 0.9 1.96 1.05
1.0 0.36 0.675 0.64 0.9 1 1.125 1.44 1.35 1.96 1.575
1.2 0.27 0.981 0.48 1.308 0.75 1.635 1.08 1.962 1.47 2.289
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3)
Pe & Ph vs. frequency at different flux densities
Figure 1.4
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6. Discussion and Conclusion
In this lab our main objective was to be able to separate between the eddy and hysteresis
losses that take place using Epstein core loss testing equipment.
To begin with, core losses arise in transformers and inductors as a result of alternating
currents. They are usually present in the form of heat energy and result in increasing the
temperature of the core. The total amount of core losses is dominated by the summation of the
hysteresis and eddy current losses.
The hysteresis loss is caused by continuous reversals in the alignment of the magnetic
domains in the magnetic core. Succinctly put, the energy that is required to cause these reversals
is the hysteresis loss.(Gonen) On the other hand, eddy current losses arise, Because iron is a
conductor, time-varying magnetic fluxes induce opposing voltages and currents called eddy
currents that circulate within the iron core. In the solid iron core, these undesirable circulating
currents flow around the flux and are relatively large because they encounter very little
resistance. Therefore, they produce power losses with associated heating effects and cause
demagnetization. As a result of this demagnetization, the flux distribution in the core becomes
non-uniform, since most of the flux is pushed toward the outer surface of the magnetic
material.(Gonen) In order to decrease the magnitude of the eddy currents, the resistance of thecore has to be increased drastically. This is achieved by laminating the core material or using non
conducting magnetic material for the core.
The power lost as a result of hysteresis losses (Ph) is summarized in the following
formula,
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We can see that the factors that affect the hysteresis losses are the volume of the material,
and hence the cross sectional area and the length of the core, the frequency and the maximum
flux density through the core. All these factors are directly proportional to the power lost due to
hysteresis; hence the increase of any of those factors will directly increase the hysteresis losses.
Similarly, the eddy current losses are also measured through the following formula,
The formula is very similar to that of the hysteresis power losses, except that as the
frequency or the magnetic flux doubles, the eddy current losses is quadrupled. Also for the eddy
current losses the lamination thickness has to be taken into consideration because as the
thickness gets smaller, the power loss due to eddy currents diminishes.
In this particular lab, we started off by following the procedure described earlier and by
preparing a circuit similar to the one present in the final connection diagram. A circuit breaker
was connected between the variable frequency supply and the variac which was later connected
in parallel with the primary side of the Epstein test equipment. At the secondary side a double
pole double throw (DPDT) switch was connected where one setting connected to a voltmeter andthe other connected to an LPF wattmeter. The wattmeter was connected because it has less
resistance in its wires than the voltmeter; as a result a high proportion of the current is going to
pass through the coils of the wattmeter than it would pass through the voltmeter. Consequently,
readings obtained were more accurate through the wattmeter than they were through the
voltmeter. The frequency was then altered and changed and at every setting the voltage input was
changed to obtain higher flux densities. The values were obtained before the lab and the numbers
were tested for errors afterwards. All the results obtained were tabulated in the datasheet portion
of the lab.
Figure 1.1 in the computation and results shows the relationship between the density of
power loss per kg of core material as a function of frequency. We observed how an increase in
frequency resulted in an increase in the power loss. Moreover, as the flux density increased the
magnitude of power loss also increased. These results match other work of literature that
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indicates that the power loss is directly proportional to both the frequency and the magnetic flux
passing through the core material.
In table 1.2, the ratio between the power lost and the frequency was obtained as the
frequency and the magnetic flux changed. Amazingly, the ratio was almost constant for a given
magnetic flux, only slightly increased as the frequency increased. However, when the magnetic
flux was increased from 0.4 to 1.2 Wb/m2, the resultant ratio of power lost to frequency was over
six times larger. Hence, at a given frequency, the major factor affecting the power lost would be
the magnetic flux density. All the various ratios of power losses and frequencies were plotted
against frequency, for different values of maximum magnetic flux density, the slopes and the y-
intercepts of these lines were viewed on the plot and were later tabulated in table 1.3. The slope
when multiplied by the square of the frequency yields the power losses due to eddy currents.
Whereas, the product of the y-intercept and the frequency yielded the magnitude of the power
lost due to hysteresis. The hysteresis losses and the eddy currents losses were then calculated
tabulated as they changed with frequency and magnetic flux density in table 1.4 and they were
then plotted in figure 1.4. We concluded from the previous plot, that the hysteresis losses are
usually much higher at lower frequencies and they only increase slightly as the frequency is
increased. On the other hand, eddy losses are much smaller at lower frequencies but increase
drastically as the frequency is increased relative to hysteresis power losses.
As for the Kh and Ke calculations, we used traditional computation methods as the
graphical approach did not prove helpful in our case. The following steps and measures were
taken to figure out these values,
To calculate n and Kh:
For Bm = 0.4 T/m
Log (0.047) = Log Kh + n Log (0.4)
- 1.33 = Log Kh (0.398) n (1)
For Bm = 0.6 T/m
Log (0.0979) = Log Kh + n Log (0.6)
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- 1.0092 = Log Kh (0.223) n (2)
From Equation (1):
Log Kh = (0.398) n 1.33 .. (3)
Substitute (3) in (2):
- 1.0092 = (0.398) n 1.33 (0.223) n
n = 1.833
and Kh = 0.251
- To Calculate Ke:
For Bm = 0.4 T/m
Log (0.0018) = Log Ke + 2 Log (0.4)
- 2.744 = Log Ke 0.796
Ke = 0.0021
Similarly:
For Bm = 0.6 Ke = 0.0013
For Bm = 0.8 Ke = 0.0064
For Bm = 1.0 Ke = 0.0046
For Bm = 1.2 Ke = 0.0043
Keava. = (0.0021+0.0013+0.0064+0.0046+0.0043)/5 = 0.00374
All in all, most of the outcomes of the lab were expected; the power loss increased
drastically as frequency and the magnetic flux density consumed larger values. The plots and
data from the tables shoed that. However, we faced a stumbling block when it came to measuring
the proportionality constants of the material with respect to hysteresis and eddy current losses of
the core material of the Epstein test equipment. Consequently, we had to use an unorthodox
method of calculating the values Steinmetz exponent as well as the proportionality constants.
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7. Bibliography
M. I.T.Sta_, MagneticCircuitsandTransformers,pp.144-154,John Wiley andSons,1985.
Vincent Del Toro, Basic Electric Machines , pp. 34-38, Prentice Hall, 1990
Turan Gnen,Electrical Machines with MATLAB, pp. 17-41, 2nd Edition, CRC Press, BocaRaton, Fla, 2012
Dr. Edwin Cohen, Dr. Sol Rosenstark,NJIT Electrical Engineering Laboratory IV, version 1.3,Revised by Dr. David R. Haas, 2013
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8. Observed Data Sheet
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