Separation of Eddy Current and Hysteresis Losses

Laboratory Report Assignment N. 2 Separation of Eddy topical and Hysteresis departurees Instructor Name Dr. Walid Hubbi By Dante Castillo Mordechi Dahan Haley Kim November 21, 2010 ECE 494 A -102 Electrical Engineering Lab Ill slacken of Contents Objectives3 Equipment and leave-takings4 Equipment and separate ratings5 Procedure6 Final Connection Diagram7 reading Sheets8 Computations and Results10 Curves14 Analysis20 Discussion27 Conclusion28 Appendix29 Bibliography34 ObjectivesInitially, the purpose of this laboratory try out was to separate the eddy-current and hysteresis dischargees at various frequencies and flux densities utilizing the Epstein join way out Testing equipment. However, due to technical difficulties encountered when using the watt-meters, and duration 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 th e inductance value of an inductor with and without a magnetic warmheartedness. * To experimentally determine the total hurt in the core of the transformer.Equipment and carve ups * 1 low- bureau-factor (LPF) watt-meter * 2 digital multi-meters * 1 Epstein piece of running play equipment * Single-phase variac Equipment and parts ratings Multimeters Alpa 90 Series Multimeter APPA-95 Serial No. 81601112 WattmettersHampden Model ACWM-100-2 Single-phase variacPart 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 potency -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 expound procedure had been achieverful, 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 absolute oftenness and maximum take voltage available for your panel. 5. Adjust the variac to obtain voltages Es as cipher 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 control 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 withou t magnetic coreInductor Without Magnetic centre 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 ResultsPart 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 mensurable 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 TestingEquipment Table 5 counting 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- tease 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 HzW=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 index number ratio vs. frequency for Bm=0. 4 Figure 2 military unit ratio vs. frequency for Bm=0. 6Figure 3 superpower ratio vs. frequency for Bm=0. 8 Figure 4 federal agency ratio vs. frequency for Bm=1 . 0 Figure 5 tycoon 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 elongate fit through power frequency ratio vs. requency for Bm=0. 4 The plot in Figure 6 was giftd using Matlabs 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 atomic number 18 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 t he 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 expendd. The data points were well behaved therefore the exclusion was not undeniable. 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. 2The 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*Bmn) vs. log Bm For the plot in figure 11, exclusion was created to ignore the value in the bottom left field corner. T his 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=logKhKh=10b=10-1. 014=0. 097 n=m=1. 554 Figure 17 Linear fit through log (Ke*Bm2) vs. og Bm No exclusion rule was necessary to perform the linear fit through the data points. b=logKeKe=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 rolling wave must be affiliated 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 coil 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 E ddy-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 little 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 matlabs curve fitting toolbox made physical sense and allowed us to plot some(prenominal) 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. 21. % Maximum magnetic flux density f=301060 % 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 % mightiness 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 dimension W/Hz) grid on title(Power balance 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(Freque ncy 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*Bmn 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*Bmn) vs. log(Bm) figure(6) plot(log_Bm,log_b,rX,MarkerSize,12) xlabel(log(Bm)) ylabel(log(Kh*Bmn)) grid on title(Log of Normalized Hysteresis Loss vs. Log of Magnetic Flux niggardliness) %% Obtaining Ke m=0. 001125 0. 001325 0. 00341 0. 004135 0. 00695 % m=Ke*Bm2 log_m=log10(m) % Computing the log of m% Plotting log(Ke*Bm2) vs. log(Bm) figure(7) plot(log_Bm,log_m,rX,MarkerSize,12) xlabel(log(Bm)) ylabel(log(Ke*Bm2)) 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) out of date 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,M arkerSize,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