part a- lab 2 draft

7/28/2019 Part a- Lab 2 Draft

1/16

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:


2/16

Table of Contents

1.1. Abstract of Synopsis...............................................................................................................1


3/16

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

Page 1 of 14
http://en.wikipedia.org/wiki/Wattmeterhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Wattmeterhttp://en.wikipedia.org/wiki/Transformer


4/16


5/16

3. Final Connection Diagram

Figure 1.1

Page 3 of 14


6/16

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

Page 4 of 14


7/16

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

Page 5 of 14


8/16

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

Page 6 of 14


9/16

3)

Pe & Ph vs. frequency at different flux densities

Figure 1.4

Page 7 of 14


10/16

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,

Page 8 of 14


11/16

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

Page 9 of 14


12/16

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)

Page 10 of 14


13/16

- 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.

Page 11 of 14


14/16

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

Page 12 of 14


15/16

8. Observed Data Sheet

Page 13 of 14


16/16

Page 14 of 14

part a- lab 2 draft

Documents