### Separation of Eddy Current and Hysteresis Losses

Laboratory Report Assignment N. 2 Separation of Eddy Current and Hysteresis Losses Instructor Name: Dr. Walid Hubbi By: Dante Castillo Mordechi Dahan Haley Kim November 21, 2010 ECE 494 A -102 Electrical Engineering Lab Ill Table of Contents Objectives3 Equipment and Parts4 Equipment and parts ratings5 Procedure6 Final Connection Diagram7 Data Sheets8 Computations and Results10 Curves14 Analysis20 Discussion27 Conclusion28 Appendix29 Bibliography34 Objectives

Initially, the purpose of this laboratory experiment was to separate the eddy-current and hysteresis losses at various frequencies and flux densities utilizing the Epstein Core Loss Testing equipment. However, due to technical difficulties encountered when using the watt-meters, and time constraints, we were unable to finish the experiment. Our professor acknowledging the fact that it was not our fault changed the objective of the experiment to the following: * To experimentally determine the inductance value of an inductor with and without a magnetic core. * To experimentally determine the total loss in the core of the transformer.

Equipment and Parts * 1 low-power-factor (LPF) watt-meter * 2 digital multi-meters * 1 Epstein piece of test equipment * Single-phase variac Equipment and parts ratings Multimeters: Alpa 90 Series Multimeter APPA-95 Serial No. 81601112 Wattmetters:Hampden Model: ACWM-100-2 Single-phase variac:Part Number: B2E 0-100 Model: N/A (LPF) Watt-meter: Part Number: 43284 Model: PY5 Epstein test equipment: Part Number: N/A Model: N/A Procedure The procedure for this laboratory experiment consists of two phases: A. Watt-meters accuracy determination -Recording applied voltage -Measuring current flowing into test circuit Plotting relative error vs. voltage applied B. Determination of Inductance value for inductor w/ and w/o a magnetic core -Measuring the resistance value of the inductor -Recording applied voltages and measuring current flowing into the circuit If part A of the above described procedure had been successful, we would have followed the following set of instructions: 1. Complete table 2. 1 using (2. 10) 2. Connect the circuit as shown in figure 2. 1 3. Connect the power supply from the bench panel to the INPUT of the single phase variac and connect the OUTPUT of the variac to the circuit. 4.

Wait for the instructor to adjust the frequency and maximum output voltage available for your panel. 5. Adjust the variac to obtain voltages Es as calculated in table 2. 1. For each applied voltage, measure and record Es and W in table 2. 2. The above sets of instructions make references to the manual of our course. Final Connection Diagram Figure 1: Circuit for Epstein core loss test set-up The above diagrams were obtained from the section that describes the experiment in the student manual. Data Sheets Part 1: Experimentally Determining the Inductance Value of Inductor Table 1: Measurements obtained without magnetic core

Inductor Without Magnetic Core| V [V]| I [A]| Z [ohm]| P [W]| 20| 1. 397| 14. 31639| 27. 94| 10| 0. 78| 12. 82051| 7. 8| 15| 1. 067| 14. 05811| 16. 005| Table 2: Measurements obtained with magnetic core Inductor With Magnetic Core| V [V]| I [A]| Z [ohm]| P [W]| 10. 2| 0. 188| 54. 25532| 1. 9176| 15. 1| 0. 269| 56. 13383| 4. 0619| 20| 0. 35| 57. 14286| 7| Part 2: Experimentally Determining Losses in the Core of the Epstein Testing Equipment Table 3: Core loss data provided by instructor | f=30 Hz| f=40 Hz| f=50 Hz| f=60 Hz| Bm| Es [Volts]| W [Watts]| Es [Volts]| W [Watts]| Es [Volts]| W [Watts]| Es [Volts]| W [Watts]| 0. | 20. 8| 1. 0| 27. 7| 1. 5| 34. 6| 3. 0| 41. 5| 3. 8| 0. 6| 31. 1| 2. 5| 41. 5| 4. 5| 51. 9| 6. 0| 62. 3| 7. 5| 0. 8| 41. 5| 4. 5| 55. 4| 7. 4| 69. 2| 11. 3| 83. 0| 15. 0| 1. 0| 51. 9| 7. 0| 69. 2| 11. 5| 86. 5| 16. 8| 103. 6| 21. 3| 1. 2| 62. 3| 10. 4| 83. 0| 16. 2| 103. 8| 22. 5| 124. 5| 33. 8| Table 4: Calculated values of Es for different values of Bm Es=1. 73*f*Bm| Bm| f=30 Hz| f=40 Hz| f=50 Hz| f=60 Hz| 0. 4| 20. 76| 27. 68| 34. 6| 41. 52| 0. 6| 31. 14| 41. 52| 51. 9| 62. 28| 0. 8| 41. 52| 55. 36| 69. 2| 83. 04| 1| 51. 9| 69. 2| 86. 5| 103. 8| 1. 2| 62. 28| 83. 04| 103. 8| 124. 56| Computations and Results

Part 1: Experimentally Determining the Inductance Value of Inductor Table 5: Calculating values of inductances with and without magnetic core Calculating Inductances| Resistance [ohm]| 2. 50| Impedence w/o Magnetic Core (mean) [ohm]| 13. 73| Impedence w/ Magnetic Core (mean) [ohm]| 55. 84| Reactance w/o Magnetic Core [ohm]| 13. 50| Reactance w/ Magnetic Core [ohm]| 55. 79| Inductance w/o Magnetic Core [henry]| 0. 04| Inductance w/ Magnetic Core [henry]| 0. 15| The values in Table 4 were calculated using the following formulas: Z=VI Z=R+jX X=Z2-R2 L=X2?? 60 Part 2: Experimentally Determining Losses in the Core of the Epstein Testing

Equipment Table 5: Calculation of hysteresis and Eddy-current losses Table 2. 3: Data Sheet for Eddy-Current and Hysteresis Losses| | f=30 Hz| f=40 Hz| f=50 Hz| f=60 Hz| Bm| slope| y-intercept| Pe [W]| Ph [W]| Pe [W]| Ph [W]| Pe [W]| Ph [W]| Pe [W]| Ph [W]| 0. 4| 0. 0011| -0. 0021| 1. 01| 0. 06| 1. 80| 0. 08| 2. 81| 0. 10| 4. 05| 0. 12| 0. 6| 0. 0013| 0. 0506| 1. 19| 1. 52| 2. 12| 2. 02| 3. 31| 2. 53| 4. 77| 3. 03| 0. 8| 0. 0034| 0. 0493| 3. 07| 1. 48| 5. 46| 1. 97| 8. 53| 2. 47| 12. 28| 2. 96| 1. 0| 0. 0041| 0. 1169| 3. 72| 3. 51| 6. 62| 4. 68| 10. 34| 5. 85| 14. 89| 7. 01| 1. 2| 0. 0070| 0. 1285| 6. 6| 3. 86| 11. 12| 5. 14| 17. 38| 6. 43| 25. 02| 7. 71| Table 6: Calculation of relative error between measure core loss and the sum of the calculated hysteresis and Eddy-current losses at f=30 Hz W=Pe+Ph @ f=30 Hz| W [Watts]| Pe [Watts]| Ph [Watts]| Pe+Ph| Rel. Error| 1. 0| 1. 0125| 0. 0625| 1. 075| 7. 50%| 2. 5| 1. 1925| 1. 5174| 2. 7099| 8. 40%| 4. 5| 3. 069| 1. 479| 4. 548| 1. 07%| 7. 0| 3. 7215| 3. 507| 7. 2285| 3. 26%| 10. 4| 6. 255| 3. 855| 10. 11| 2. 79%| Table 7: Calculation of relative error between measure core loss and the sum of the calculated hysteresis and Eddy-current losses at f=40 Hz

W=Pe+Ph @ f=40 Hz| W [Watts]| Pe [Watts]| Ph [Watts]| Pe+Ph| Rel. Error| 1. 5| 1. 8| 0. 0833| 1. 8833| 25. 55%| 4. 5| 2. 12| 2. 0232| 4. 1432| 7. 93%| 7. 4| 5. 456| 1. 972| 7. 428| 0. 38%| 11. 5| 6. 616| 4. 676| 11. 292| 1. 81%| 16. 2| 11. 12| 5. 14| 16. 26| 0. 37%| Table 8: Calculation of relative error between measure core loss and the sum of the calculated hysteresis and Eddy-current losses at f=50 Hz W=Pe+Ph @ f=50 Hz| W [Watts]| Pe [Watts]| Ph [Watts]| Pe+Ph| Rel. Error| 3. 0| 2. 8125| 0. 1042| 2. 9167| 2. 78%| 6. 0| 3. 3125| 2. 529| 5. 8415| 2. 64%| 11. 3| 8. 525| 2. 465| 10. 99| 2. 1%| 16. 8| 10. 3375| 5. 845| 16. 1825| 3. 39%| 22. 5| 17. 375| 6. 425| 23. 8| 5. 78%| Table 9: Calculation of relative error between measure core loss and the sum of the calculated hysteresis and Eddy-current losses at f=60 Hz W=Pe+Ph @ f=60 Hz| W [Watts]| Pe [Watts]| Ph [Watts]| Pe+Ph| Rel. Error| 3. 8| 4. 05| 0. 125| 4. 175| 11. 33%| 7. 5| 4. 77| 3. 0348| 7. 8048| 4. 06%| 15. 0| 12. 276| 2. 958| 15. 234| 1. 56%| 21. 3| 14. 886| 7. 014| 21. 9| 3. 06%| 33. 8| 25. 02| 7. 71| 32. 73| 3. 02%| Curves Figure 1: Power ratio vs. frequency for Bm=0. 4 Figure 2: Power ratio vs. frequency for Bm=0. 6

Figure 3: Power ratio vs. frequency for Bm=0. 8 Figure 4: Power ratio vs. frequency for Bm=1. 0 Figure 5: Power ratio vs. frequency for Bm=1. 2 Figure 6: Plot of the log of normalized hysteresis loss vs. log of magnetic flux density Figure 7: Plot of the log of normalized Eddy-current loss vs. log of magnetic flux density Figure 8: Plot of Kg core loss vs. frequency Figure 9: Plot of hysteresis power loss vs. frequency for different values of Bm Figure 10: Plot of Eddy-current power loss vs. frequency for different values of Bm Analysis Figure 11: Linear fit through power frequency ratio vs. requency for Bm=0. 4 The plot in Figure 6 was generated using Matlab’s curve fitting tool. In addition, in order to obtain the straight line displayed in figure 6, an exclusion rule was created in which the data points in the middle were ignored. The slope and the y-intercept of the line are p1 and p2 respectively. y=mx+b fx=p1x+p2 m=p1=0. 001125 b=p2=-0. 002083 Figure 12: Linear fit through power frequency ratio vs. frequency for Bm=0. 6 The plot in figure 7 was generated in the same manner as the plot in figure 6. The slope and y-intercept obtained for this case are: m=p1=0. 001325 b=p2=0. 5058 Figure 13: Linear fit through power frequency ratio vs. frequency for Bm=0. 8 For the linear fit displayed in figure 8, no exclusion was used. The data points were well behaved; therefore the exclusion was not necessary. The slope and y-intercept are the following: m=p1=0. 00341 b=p2=0. 0493 Figure 14: Linear fit through power frequency ratio vs. frequency for Bm=1. 0 The use of exclusions was not necessary for this particular fit. The slope and y-intercept are listed below: m=p1=0. 004135 b=p2=0. 1169 Figure 15: Linear fit through power frequency ratio vs. frequency for Bm=1. 2

The use of exclusions was not necessary for this particular fit. The slope and y-intercept are listed below: m=p1=0. 00695 b=p2=0. 1285 Figure 16: Linear fit through log (Kh*Bm^n) vs. log Bm For the plot in figure 11, exclusion was created to ignore the value in the bottom left corner. This was done because this value was negative which implies that the hysteresis loss had to be negative, and this result did not make sense. The slope of this straight line represents the exponent n and the y intercept represents log(Kh). b=logKh>Kh=10b=10-1. 014=0. 097 n=m=1. 554 Figure 17: Linear fit through log (Ke*Bm^2) vs. og Bm No exclusion rule was necessary to perform the linear fit through the data points. b=logKe>Ke=10b=0. 004487 Discussion 1. Discuss how eddy-current losses and hysteresis losses can be reduced in a transformer core. To reduce eddy-currents, the armature and field cores are constructed from laminated steel sheets. The laminated sheets are insulated from one another so that current cannot flow from one sheet to the other. To reduce hysteresis losses, most DC armatures are constructed of heat-treated silicon steel, which has an inherently low hysteresis loss. . Using the hysteresis loss data, compute the value for the constant n. n=1. 554 The details of how this parameter was computed are under the analysis section. 3. Explain why the wattmeter voltage coil must be connected across the secondary winding terminals. The watt-meter voltage coil must be connected across the secondary winding terminals because the whole purpose of this experiment is to measure and separate the losses that occur in the core of a transformer, and connecting the potential coil to the secondary is the only way of measuring the loss.

Recall that in an ideal transformer P into the primary is equal to P out of the secondary, but in reality, P into the primary is not equal to P out of the secondary. This is due to the core losses that we want to measure in this experiment. Conclusion I believe that this laboratory experiment was successful because the objectives of both part 1 and 2 were fulfilled, namely, to experimentally determine the inductance value of an inductor with and without a magnetic core and to separate the core losses into Hysteresis and Eddy-current losses.

The inductance values were determined and the values obtained made sense. As expected the inductance of an inductor without the addition of a magnetic core was less than that of an inductor with a magnetic core. Furthermore, part 2 of this experiment was successful in the sense that after our professor provided us with the necessary measurement values, meaningful data analysis and calculations were made possible. The data obtained using matlab’s curve fitting toolbox made physical sense and allowed us to plot several required graphs.

Even though analyzing the first set of values our professor provided us with was very difficult and time consuming, after receiving an email with more detailed information on how to analyze the data provided to us, we were able to get the job done. In addition to fulfilling the goals of this experiment, I consider this laboratory was even more of a success because it provided us with the opportunity of using matlab for data analysis and visualization. I know this is a valuable skill to mastery over. Appendix Matlab Code used to generate plots and the linear fits %% Defining range of variables Bm=[0. 4:. 2:1. ]; % Maximum magnetic flux density f=[30:10:60]; % range of frequencies in Hz Es1=[20. 8 31. 1 41. 5 51. 9 62. 3]; % Induced voltage on the secundary @ 30 Hz Es2=[27. 7 41. 5 55. 4 69. 2 83. 0]; % Induced voltage on the secundary @ 40 Hz Es3=[34. 6 51. 9 69. 2 86. 5 103. 8]; % Induced voltage on the secundary @ 50 Hz Es4=[41. 5 62. 3 83. 0 103. 6 124. 5]; % Induced voltage on the secundary @ 60 Hz W1=[1 2. 5 4. 5 7 10. 4]; % Power loss in the core @ 30 Hz W2=[1. 5 4. 5 7. 4 11. 5 16. 2]; % Power loss in the core @ 40 Hz W3=[3 6 11. 3 16. 8 22. ]; % Power loss in the core @ 50 Hz W4=[3. 8 7. 5 15. 0 21. 3 33. 8]; % Power loss in the core @ 60 Hz W=[W1′ W2′ W3′ W4′]; % Power loss for all frequencies W_f1=W(1,:). /f; % Power to frequency ratio for Bm=0. 4 W_f2=W(2,:). /f; % Power to frequency ratio for Bm=0. 6 W_f3=W(3,:). /f; % Power to frequency ratio for Bm=0. 8 W_f4=W(4,:). /f; % Power to frequency ratio for Bm=1 W_f5=W(5,:). /f; % Power to frequency ratio for Bm=1. 2 %% Generating plots of W/f vs frequency for diffrent values of Bm Plotting W/f vs. frequency for Bm=0. 4 plot(f,W_f1,’rX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Ratio [W/Hz]’); grid on; title(‘Power Ratio vs. Frequency For Bm=0. 4′); % Plotting W/f vs. frequency for Bm=0. 6 figure(2); plot(f,W_f2,’rX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Ratio [W/Hz]’); grid on; title(‘Power Ratio vs. Frequency For Bm=0. 6′); % Plotting W/f vs. frequency for Bm=0. 8 figure(3); plot(f,W_f3,’rX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Ratio [W/Hz]’); grid on; title(‘Power Ratio vs. Frequency For Bm=0. 8′); % Plotting W/f vs. frequency for Bm=1. figure(4); plot(f,W_f4,’rX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Ratio [W/Hz]’); grid on; title(‘Power Ratio vs. Frequency For Bm=1. 0′); % Plotting W/f vs. frequency for Bm=1. 2 figure(5); plot(f,W_f5,’rX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Ratio [W/Hz]’); grid on; title(‘Power Ratio vs. Frequency For Bm=1. 2′); %% Obtaining Kh and n b=[-0. 002083 0. 05058 0. 0493 0. 1169 0. 1285]; % b=Kh*Bm^n log_b=log10(abs(b)); % Computing the log of magnitude of b( y-intercept) log_Bm=log10(Bm); % Computing the log of Bm Plotting log(Kh*Bm^n) vs. log(Bm) figure(6); plot(log_Bm,log_b,’rX’,’MarkerSize’,12); xlabel(‘log(Bm)’); ylabel(‘log(Kh*Bm^n)’); grid on; title(‘Log of Normalized Hysteresis Loss vs. Log of Magnetic Flux Density’); %% Obtaining Ke m=[0. 001125 0. 001325 0. 00341 0. 004135 0. 00695]; % m=Ke*Bm^2 log_m=log10(m); % Computing the log of m% Plotting log(Ke*Bm^2) vs. log(Bm) figure(7); plot(log_Bm,log_m,’rX’,’MarkerSize’,12); xlabel(‘log(Bm)’); ylabel(‘log(Ke*Bm^2)’); grid on; title(‘Log of Normalized Eddy-Current Loss vs. Log of Magnetic Flux Density’); % Plotting W/10 vs. frequency at different values of Bm PLD1=W(1,:). /10; % Power Loss Density for Bm=0. 4 PLD2=W(2,:). /10; % Power Loss Density for Bm=0. 6 PLD3=W(3,:). /10; % Power Loss Density for Bm=0. 8 PLD4=W(4,:). /10; % Power Loss Density for Bm=1. 0 PLD5=W(5,:). /10; % Power Loss Density for Bm=1. 2 figure(8); plot(f,PLD1,’rX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Loss Density [W/Kg]’); grid on; title(‘Power Loss Density vs. Frequency’); old; plot(f,PLD2,’bX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Loss Density [W/Kg]’); grid on; title(‘Power Loss Density vs. Frequency’); plot(f,PLD3,’kX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Loss Density [W/Kg]’); grid on; title(‘Power Loss Density vs. Frequency’); plot(f,PLD4,’mX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Loss Density [W/Kg]’); grid on; title(‘Power Loss Density vs. Frequency’); plot(f,PLD5,’gX’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Power Loss Density [W/Kg]’); grid on; title(‘Power Loss Density vs.

Frequency’);legend(‘Bm=0. 4′,’Bm=0. 6’, ‘Bm=0. 8’, ‘Bm=1. 0’, ‘Bm=1. 2′); %% Defining Ph and Pe Ph=abs(f’*b); Pe=abs(((f’). ^2)*m); %% Plotting Ph for different values of frequency % For Bm=0. 4 figure(9); plot(f,Ph(:,1),’r’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=0. 6 hold; plot(f,Ph(:,2),’k’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=0. 8 lot(f,Ph(:,3),’g’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=1. 0 plot(f,Ph(:,4),’b’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=1. 0 plot(f,Ph(:,5),’c’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); legend(‘Bm=0. 4′,’Bm=0. 6’, ‘Bm=0. 8’, ‘Bm=1. 0’, ‘Bm=1. 2′); % Plotting Pe vs frequency for different values of Bm % For Bm=0. 4 figure(9); plot(f,Pe(:,1),’r’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=0. 6 hold; plot(f,Pe(:,2),’k’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=0. 8 plot(f,Pe(:,3),’g’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); For Bm=1. 0 plot(f,Pe(:,4),’b’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Hysteresis Power Loss [W]’); grid on; title(‘Hysteresis Power Loss vs. Frequency’); % For Bm=1. 0 plot(f,Pe(:,5),’c’,’MarkerSize’,12); xlabel(‘Frequency [Hz]’); ylabel(‘Eddy-Current Power Loss [W]’); grid on; title(‘Eddy-Current Power Loss vs. Frequency’); legend(‘Bm=0. 4′,’Bm=0. 6’, ‘Bm=0. 8’, ‘Bm=1. 0’, ‘Bm=1. 2’); Bibliography Chapman, Stephen J. Electric Machinery Fundamentals. Maidenhead: McGraw-Hill Education, 2005. Print. http://www. tpub. com/content/doe/h1011v2/css/h1011v2_89. htm