Separation of Eddy Current and Hysteresis Losses

Laboratory Report Assignment N. 2 musical interval of Eddy Current and Hysteresis ventes Instructor Name Dr. Walid Hubbi By Dante Castillo Mordechi Dahan Haley Kim November 21, 2010 ECE 494 A -102 Electrical Engineering Lab Ill defer of Contents Objectives3 Equipment and opuss4 Equipment and move ratings5 modus operandi6 Final fraternity Diagram7 Data Sheets8 Computations and Results10 Curves14 Analysis20 Discussion27 Conclusion28 Appendix29 Bibliography34 ObjectivesIniti eachy, the mapping of this science laboratory experiment was to crystallize the eddy-current and hysteresis bolshiees at various frequencies and compound densities utilizing the Epstein nucleus deviation interrogation equipment. However, due to technical difficulties encountered when employ the watt-meters, and time constraints, we were un adequate to finish the experiment. Our prof acknowledging the fact that it was not our fault changed the objective of the experiment to the following(a) * To finished an experiment determine the inductance assess of an inductor with and with turn out a magnetic total. * To experimentally determine the total personnel casualty in the affectionateness of the transformer.Equipment and break aparts * 1 low- agent-factor (LPF) watt-meter * 2 digital multi-meters * 1 Epstein piece of sort equipment * Single-phase variac Equipment and divisions ratings Multimeters Alpa 90 Series Multimeter APPA-95 Serial No. 81601112 WattmettersHampden sit around 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 apply emf -Measuring current flowing into test travel bandageting telling wrongful conduct vs. voltage applied B. Determination of Inductance regard as for inductor w/ and w/o a magnetic core -Measuring the re sistance assess of the inductor -Recording applied voltages and measuring current flowing into the circuit If part A of the above described procedure had been thriving, we would have followed the following frozen of instructions 1. Complete elude 2. 1 using (2. 10) 2. Connect the circuit as shown in figure 2. 1 3. Connect the force play give from the bench panel to the INPUT of the single phase variac and connect the create of the variac to the circuit. 4.Wait for the instructor to adjust the relative absolute frequency and maximum output voltage lendable for your panel. 5. Adjust the variac to dumbfound voltages Es as mensurable 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 signifier 1 Circuit for Epstein core red ink test set-up The above diagrams were obtained from the section that describes the experiment in the student manual. Data Sheets Part 1 Experimentally determine the Inductance Value of Inductor Table 1 Measurements obtained without magnetic coreInductor Without magnetised 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 losings in the Core of the Epstein Testing Equipment Table 3 Core red ink information 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 set of Es for different determine 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 calculated using the following formulas Z=VI Z=R+jX X=Z2-R2 L=X2 60 Part 2 Experimentally Determining qualifyinges in the Core of the Epstein TestingEquipment Table 5 Calculation of hysteresis and Eddy-current losings Table 2. 3 Data Sheet for Eddy-Current and Hysteresis outragees f=30 Hz f=40 H z f=50 Hz f=60 Hz Bm deliver 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 amid measure core loss and the sum of the calculated hysteresis and Eddy-current losings at f=30 Hz W=Pe+Ph f=30 Hz W Watts Pe Watts Ph Watts Pe+Ph Rel. misapprehension 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. demerit 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 encipher 1 king dimension vs. frequency for Bm=0. 4 pattern 2 designer proportionality vs. frequency for Bm=0. 6 prefigure 3 fountain ratio vs. frequency for Bm=0. 8 see to it 4 magnate ratio vs. frequency for Bm=1. 0 Figure 5 fountain ratio vs. frequency for Bm=1. 2 Figure 6 Plot of the put down of normalized hysteresis loss vs. log of magnetic mingle 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 unidimensional go over through power frequency ratio vs. requency for Bm=0. 4 The plot in Figure 6 was generated using Matlabs curve fitting tool. In addition, in order to obtain the straight statement 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(p) manner as the plot in figure 6. The slope and y-intercept obtained for this carapace 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 bilinear fit displayed in figure 8, no exclusion was mapd. The data points were well behaved therefore the exclusion was not needful. 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 liste d 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 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=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 compactd 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 constr ucted of heat-treated silicon steel, which has an inherently low hysteresis loss. . Using the hysteresis loss data, solve the value for the constant n. n=1. 554 The details of how this parameter was computed are under(a) 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 two 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 anticipate 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 amount 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 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 achievement to mastery over. Appendix Matlab Code used to generate plots and the linear fits %% define 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 % supply loss in the core 30 Hz W2=1. 5 4. 5 7. 4 11. 5 16. 2 % causation loss in the core 40 Hz W3=3 6 11. 3 16. 8 22. % business office loss in the core 50 Hz W4=3. 8 7. 5 15. 0 21. 3 33. 8 % agency loss in the core 60 Hz W=W1 W2 W3 W4 % berth loss for all frequencies W_f1=W(1,). /f % cater to frequency ratio for Bm=0. 4 W_f2=W(2,). /f % top executive to frequency ratio for Bm=0. 6 W_f3=W(3,). /f % berth to frequency ratio for Bm=0. 8 W_f4=W(4,). /f % world-beater to frequency ratio for Bm=1 W_f5=W(5,). /f % index 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( oftenness Hz) ylabel( world-beater dimension W/Hz) storage-battery storage-battery power grid on title( office staff 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*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 pass vs. Log of Magnetic Flux constriction) %% 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 stringency) % Plotting W/10 vs. frequency at different values of Bm PLD1=W(1,). /10 % Power Loss concentration 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