Separation of Eddy Current and Hysteresis Losses

Laboratory Report Assignment N. 2 Separation of Eddy Current and Hysteresis passinges Instructor Name Dr. Walid Hubbi By Dante Castillo Mordechi Dahan Haley Kim November 21, 2010 ECE 494 A -102 galvanical Engineering Lab Ill shelve of content Objectives3 Equipment and separate4 Equipment and move ratings5 Procedure6 terminal relateion Diagram7 selective information airplanes8 Computations and Results10 Curves14 summary20 proveion27 Conclusion28 Appendix29 Bibliography34 ObjectivesInitially, the purpose of this laboratory try was to separate the eddy-current and hysteresis terminationes at various frequencies and flux densities utilizing the Epstein affectionateness acquittance Testing equipment. However, due to technical difficulties encountered when victimisation the watt-meters, and time constraints, we were unable to bring to an end the test. Our professor acknowledging the fact that it was non our fault changed the objective of the experiment to the pursuance * To experimentally determine the generalization value of an induction with and without a magnetic fondness. * To experimentally determine the total passing play in the bosom of the transformer.Equipment and initiates * 1 low- military unit-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 WattmettersHampden Model ACWM-100-2 Single-phase variacPart account 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 endeavor -Recording applied potency -Measuring current flowing into test electrical circuit bizting congeneric defect vs. voltage applied B. Determination of Inductance value for inductor w/ and w/o a magnetic shopping mall -Measuring the shelter value of the inductor -Recording applied voltages and measuring current flowing into the circuit If part A of the above described procedure had been sure-fire, we would have followed the following aim 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 interrelate the OUTPUT of the variac to the circuit. 4.Wait for the instructor to adjust the oftenness 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, notice 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 totality passing test set-up The above diagrams were obtained from the section that describes the experiment in the student manual. Data Sheets Part 1 experimentally ascertain th e Inductance Value of inductor card 1 Measurements obtained without magnetic aggregateInductor Without charismatic plaza 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 tabulate 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 dischargees in the Core of the Epstein Testing Equipment duck 3 Core outlet entropy 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 determine of Es for different determine of Bm Es=1. 73*f*Bm Bm f=3 0 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 reckon 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 going awayes in the Core of the Epstein TestingEquipment Table 5 enumeration of hysteresis and Eddy-current losings Table 2. 3 Data Sheet for Eddy-Current and Hysteresis passing playes f=30 Hz f=40 Hz f=50 Hz f=60 Hz Bm s ky 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 acquittance and the centre 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 source ratio vs. frequence for Bm=0. 4 Figure 2 force-out ratio vs. a bsolute frequency for Bm=0. 6Figure 3 federal agency ratio vs. frequency for Bm=0. 8 Figure 4 powerfulness ratio vs. frequency for Bm=1. 0 Figure 5 position ratio vs. frequency for Bm=1. 2 Figure 6 Plot of the record of normalized hysteresis loss vs. log of magnetic flux assiduity 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 analogue give out by means of power frequency ratio vs. requency for Bm=0. 4 The plot in Figure 6 was generated using Matlabs curve fitting tool. In addition, in indian lodge to obtain the rightful(a) line displayed in figure 6, an excommunication practice was created in which the data points in the middle were brush offd. The slope and the y-intercept of the line ar p1 and p2 respec tively. 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 be m=p1=0. 001325 b=p2=0. 5058 Figure 13 Linear fit through power frequency ratio vs. frequency for Bm=0. 8 For the running(a) fit displayed in figure 8, no exclusion was used. The data points were well behaved therefore the exclusion was not infallible. 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 on a lower floor 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 belo w 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 corner. This was done because this value was oppose 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 coiffure 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(prenominal) so that current cannot flow from one sheet to the other. To reduce hysteresis losses, virtually DC armature s 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 intertwine must be connected across the secondary winding terminals. The watt-meter voltage coil must be connected across the secondary winding terminals because the intact 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 government agency of measuring the loss.Recall that in an ideal transformer P into the primary is pertain 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 afterward 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 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 ab le to get the job done. In addition to fulfilling the goals of this experiment, I accept this laboratory was even more of a success because it provided us with the luck of using matlab for data analysis and visualization. I know this is a worthy 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 % bring on 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 % spot 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&8242 W2&8242 W3&8242 W4&8242 % 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 proportionality W/Hz) power system on title(Power Ratio vs. frequency For Bm=0. 4&8242) % Plotting W/f vs. frequency for Bm=0. 6 figure(2) plot(f,W_f2,rX,MarkerSize,12) xlabel( oftenness Hz) ylabel(Power Ratio W/Hz) grid on title(Power Ratio vs. frequency For Bm=0. 6&8242) % Plotting W/f vs. frequency for Bm=0. 8 figure(3) plot(f,W_f3,rX,MarkerSize,12) xlabel( absolute frequency Hz) ylabel(Power Ratio W/Hz) grid on title(Power Ratio vs. frequence For Bm=0. 8&8242) % Plotting W/f vs. frequ ency for Bm=1. figure(4) plot(f,W_f4,rX,MarkerSize,12) xlabel( oftenness Hz) ylabel(Power Ratio W/Hz) grid on title(Power Ratio vs. Frequency For Bm=1. 0&8242) % 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&8242) %% Obtaining Kh and n b=-0. 002083 0. 05058 0. 0493 0. 1169 0. 1285 % b=Kh*Bmn log_b=log10(abs(b)) % reason 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( enter of Normalized Hysteresis sacking vs. Log of Magnetic Flux density) %% 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 N ormalized Eddy-Current Loss vs. Log of Magnetic Flux stringency) % 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 t itle(Power Loss Density vs.Frequency)legend(Bm=0. 4&8242,Bm=0. 6, Bm=0. 8, Bm=1. 0, Bm=1. 2&8242) %% 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&8242,Bm=0. 6, Bm=0. 8, Bm=1. 0, Bm=1. 2&8242) % 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&8242,Bm=0. 6, Bm=0. 8, Bm=1. 0, Bm=1. 2) Bibliography Chapman, Stephen J. Electric Machinery Fundamentals. Maidenhead McGraw-Hill Education, 20 05. Print. http//www. tpub. com/content/doe/h1011v2/css/h1011v2_89. htm