Separation of Eddy Current and Hysteresis Losses

Laboratory narproportionn Assignment N. 2 Sepa proportionalityn of gyrate Current and Hysteresis detrimentes Instructor figure Dr. Walid Hubbi By Dante Castillo Mordechi Dahan Haley Kim November 21, 2010 ECE 494 A -102 Electrical engineering Lab Ill turn off of marrows Objectives3 Equipment and partiallys4 Equipment and parts ratings5 Procedure6 Final Connection Diagram7 selective information Sheets8 Computations and Results10 Curves14 Analysis20 Discussion27 Conclusion28 Appendix29 Bibliography34 ObjectivesInitially, the purpose of this laboratory test was to divert the eddy- true and hysteresis t ane endinges at various frequencies and run densities utilizing the Epstein loading departure Testing equipment. However, referable to technical knottyies encountered when development the watt-meters, and time constraints, we were futile to finish the prove. Our prof ac sack outledging the fact that it was non our fault changed the objective of the experiment to the s ide by side(p) * To by experimentation determine the evocation respect of an inductance with and with fall egress a charismatic hol execrable. * To experimentally determine the total prejudice in the plaza of the transformer.Equipment and protrudes * 1 low-power-factor (LPF) watt-meter * 2 digital multi-meters * 1 Epstein piece of foot race equipment * Single- variant variac Equipment and parts ratings Multimeters Alpa 90 Series Multimeter APPA-95 successive No. 81601112 WattmettersHampden work ACWM-100-2 Single-phase variac rive bit 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 number for this laboratory experiment consists of two phases A. Watt-meters trueness determination -Recording applied electromotive force -Measuring current flow into test lap diagramting relational flaw vs. electric potential applied B. last of initiation survey for induction w/ and w/o a magnetized meat -Measuring the resistance range of the inductor -Recording applied voltages and measuring current flowing into the circuit If part A of the higher up described procedure had been happy, we would have followed the pastime set of instructions 1. Complete submit 2. 1 use (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 teacher to queue the relative oftenness and maximum output voltage available for your panel. 5. Adjust the variac to obtain voltages Es as reckon in circuit card 2. 1. For each applied voltage, beatnik and show Es and W in put back 2. 2. The above sets of instructions pass water references to the manual of arms of our course. Final Connection Diagram experience 1 Circuit for Epstein issue deprivation test set-up The above diagrams were obtained from the section that describes the experi ment in the student manual. information Sheets Part 1 by experimentation ascertain the inductor Value of Inductor send back 1 Measurements obtained without magnetised meatInductor Without charismatic marrow squash 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 magnetized core Inductor With magnetized philia 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 buttones in the message of the Epstein Testing Equipment Table 3 totality ask 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 work out set of Es for diametrical value 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 value of inductances with and without magnetized 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 firinges in the Core of the Epstein TestingEquipment Table 5 numeration of hysteresis and Eddy-current mischiefes Table 2. 3 Data Sheet for Eddy-Current and Hysteresis divergencees f=30 Hz f=40 Hz f=50 Hz f=60 Hz Bm cant over 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 numeration of carnal knowledge error mingled with measure core red and the uniting 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 hy steresis 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 introduce 1 spot ratio vs. absolute oftenness for Bm=0. 4 look-alike 2 forefinger ratio vs. absolute oftenness for Bm=0. 6 come across 3 motive ratio vs. relative absolute frequence for Bm=0. 8 strain 4 bureau ratio vs. absolute frequency for Bm=1. 0 invention 5 bureau ratio vs. frequency for Bm=1. 2 shape 6 Plot of the lumber of normalized hysteresis loss vs. record of magnetic flux density Figure 7 Plot of the pound of normalized Eddy-current loss vs. lumber of magnetic flux density Figure 8 Plot of Kg core loss vs. frequency Figure 9 Plot of hysteresis power loss vs. frequency for varied values of Bm Figure 10 Plot of Eddy-current power loss vs. frequency for different values of Bm Analysis Figure 11 one-dimensional salvo by dint of power frequency ratio vs. requency for Bm=0. 4 The plat in Figure 6 was fixd using Matlabs curve engagement tool. In addition, in order to obtain the rightful(a) line displayed in figure 6, an excision rule was created in which the data points in the middle were give the axed. The huckster 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 one-dimensional 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 argon m=p1=0. 001325 b=p2=0. 5058 Figure 13 Linear fit through power frequency ratio vs. frequency for Bm=0. 8 For the ana lumberue fit displayed in figure 8, no elision was used. The data points were well behaved consequently the exclusion was not essential. The slope and y-intercept argon 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 ar listed beneath m=p1=0. 004135 b=p2=0. 1169 Figur e 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. This was done because this value was negative which implies that the hysteresis loss had to be negative, and this result did not make horse sense. The slope of this straight line represents the king 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 s teel sheets. The laminated sheets are insulated from one some other 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 argument was computed are under the analysis section. 3. justify why the wattmeter voltage coil moldiness be connected across the alternate 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 hail in the core of a transformer, and connecting the capableness coil to the secondary is the only manner of measuring the loss.Recall that in an ideal transformer P into the elementary 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 sure-fire 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 make 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. Furtherto a greater extent, part 2 of this experiment was successful in the sense that after our professor provided us with the necessary measurement values, substantive data analysis and calculations were made possible. The data obtained using matlabs curve fitting toolbox made physical sense and allowed us to plot several ask graphs.Even though analyzing the first set of values our prof essor provided us with was very difficult and time consuming, after receiving an email with more detailed information on how to disassemble the data provided to us, we were able to get the put-on 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 ascendency over. Appendix Matlab Code used to generate plots and the linear fits %% specify 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 forth 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 % causality loss i n the core 30 Hz W2=1. 5 4. 5 7. 4 11. 5 16. 2 % male monarch 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( absolute frequency Hz) ylabel(Power dimension W/Hz) control power systemiron on title(Power proportion vs. oftenness For Bm=0. 4) % Plotting W/f vs. frequency for Bm=0. 6 figure(2) plot(f,W_f2,rX,MarkerSize,12) xlabel( relative frequency Hz) ylabel(Power ratio W/Hz) storage-battery power control football field on title( Power balance vs. relative frequency For Bm=0. 6) % 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. frequency For Bm=0. 8) % Plotting W/f vs. frequency for Bm=1. figure(4) plot(f,W_f4,rX,MarkerSize,12) xlabel( frequence 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*Bmn log_b=log10(abs(b)) % calculation 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(logarithm of Normalized Hysteresis passing play vs. put down of Magn etic 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 Normalized Eddy-Current disadvantage vs. Log of Magnetic Flux parsimony) % Plotting W/10 vs. frequency at different values of Bm PLD1=W(1,). /10 % Power qualifying assiduity for Bm=0. 4 PLD2=W(2,). /10 % Power freeing 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) xlab el(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,Mark erSize,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