Laboratory Report Assignment N. two Separation of Eddy Current and Hysteresis Losses Instructor Name: Dr . Walid Hubbi Simply by: Dante Errar Mordechi Dahan Haley Kim November 21 years old, 2010 ECE 494 A -102 Electrical Engineering Lab Ill Desk of Material Objectives3 Equipment and Parts4 Equipment and parts ratings5 Procedure6 Last Connection Diagram7 Data Sheets8 Computations and Results10 Curves14 Analysis20 Discussion27 Conclusion28 Appendix29 Bibliography34 Goals
Initially, the goal of this lab experiment was going to separate the eddy-current and hysteresis loss at different frequencies and flux densities utilizing the Epstein Main Loss Screening equipment.
However , due to technological difficulties experienced when using the watt-meters, and period constraints, i was unable to finish the experiment. Our teacher acknowledging the fact that it was not our wrong doing changed the objective of the experiment to the pursuing: * To experimentally determine the inductance value associated with an inductor with and without a magnetic core. * To experimentally decide the total loss in the key of the transformer.
Equipment and Parts 5. 1 low-power-factor (LPF) watt-meter * a couple of digital multi-meters * 1 Epstein piece of test equipment * Single-phase variac Tools and parts ratings Multimeters: Alpa 85 Series Multimeter APPA-95 Serial No . 81601112 Wattmetters: Hampden Model: ACWM-100-2 Single-phase variac: Part Number: B2E 0-100 Unit: N/A (LPF) Watt-meter: Item: 43284 Model: PY5 Epstein test products: Part Number: N/A Model: N/A Procedure The method for this laboratory experiment involves two levels: A. Watt-meters accuracy dedication -Recording used voltage -Measuring current streaming into test circuit Conspiring relative mistake vs . volts applied B. Determination of Inductance value for inductor w/ and w/o a magnetic main -Measuring the resistance worth of the inductor -Recording used voltages and measuring current flowing in to the circuit If perhaps part A of the above described treatment had been effective, we would possess followed this set of instructions: 1 . Total table 2 . 1 employing (2. 10) 2 . Hook up the signal as displayed in physique 2 . 1 3. Hook up the power source from the table panel to the INPUT of the single stage variac and connect the OUTPUT of the variac to the routine. 4.
Wait for an instructor to modify the consistency and optimum output voltage available for the panel. 5. Adjust the variac to get voltages Sera as worked out in table 2 . 1 . For each applied voltage, evaluate and record Es and W in table installment payments on your 2 . The above sets of instructions make references for the manual of our course. Final Connection Plan Figure one particular: Circuit for Epstein main loss evaluation set-up The above mentioned diagrams were obtained from the section that describes the experiment in the student manual. Data Bedding Part you: Experimentally Identifying the Inductance Value of Inductor Table 1: Measurements obtained with no magnetic key
Inductor Without Magnetic Core| V [V]| I [A]| Z [ohm]| P [W]| 20| 1 ) 397| 18. 31639| 28. 94| 10| 0. 78| 12. 82051| 7. 8| 15| 1 . 067| 18. 05811| 18. 005| Desk 2: Measurements obtained with magnetic main 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| zero. 35| 57. 14286| 7| Part a couple of: Experimentally Deciding Losses inside the Core from the Epstein Tests Equipment Stand 3: Main loss data provided by teacher | 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 5: Calculated beliefs of Ha sido 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| twenty. 76| 27. 68| 34. 6| forty one. 52| 0. 6| 23. 14| 41. 52| fifty-one. 9| 62. 28| 0. 8| forty one. 52| fifty five. 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
Portion 1: Experimentally Determining the Inductance Benefit of Inductor Table your five: Calculating beliefs of inductances with and without magnetic key Calculating Inductances| Resistance [ohm]| 2 . 50| Impedence w/o Magnetic Key (mean) [ohm]| 13. 73| Impedence w/ Magnetic Main (mean) [ohm]| 55. 84| Reactance w/o Magnetic Key [ohm]| 13. 50| Reactance w/ Magnetic Core [ohm]| 55. 79| Inductance w/o Magnetic Core [henry]| zero. 04| Inductance w/ Magnet Core [henry]| 0. 15| The principles in Table 4 had been calculated using the following remedies: Z=VI Z=R+jX X=Z2-R2 L=X2? 60 Portion 2: Experimentally Determining Deficits in the Primary of the Epstein Testing
Gear Table five: Calculation of hysteresis and Eddy-current losses Table 2 . 3: Info Sheet intended 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 6th: Calculation of relative mistake between evaluate core damage and the sum of the computed hysteresis and Eddy-current failures at f=30 Hz W=Pe+Ph @ f=30 Hz| Watts [Watts]| Pe [Watts]| Ph level [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 several: Calculation of relative problem between evaluate core damage and the quantity of the worked out hysteresis and Eddy-current failures at f=40 Hz
W=Pe+Ph @ f=40 Hz| W [Watts]| Premature ejaculation rapid ejaculation, rapid climax, premature climax, [Watts]| Ph level [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 almost 8: Calculation of relative problem between measure core loss and the total of the computed hysteresis and Eddy-current failures at f=50 Hz W=Pe+Ph @ f=50 Hz| W [Watts]| Rapid climax premature climax, [Watts]| Ph level [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 being unfaithful: Calculation of relative error between measure core loss and the sum of the worked out hysteresis and Eddy-current losses at f=60 Hz W=Pe+Ph @ f=60 Hz| Watts [Watts]| Pe [Watts]| Ph level [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 Determine 1: Electricity ratio or frequency for Bm=0. some Figure 2: Power percentage vs . frequency for Bm=0. 6
Number 3: Power ratio vs . frequency intended for Bm=0. 8 Figure some: Power ratio vs . rate of recurrence for Bm=1. 0 Number 5: Electricity ratio or frequency for Bm=1. 2 Figure 6: Plot in the log of normalized hysteresis loss vs . log of magnetic débordement density Physique 7: Storyline of the record of normalized Eddy-current damage vs . journal of permanent magnetic flux denseness Figure almost 8: Plot of Kg main loss or frequency Number 9: Story of hysteresis power damage vs . consistency for different beliefs of Bm Figure 10: Plot of Eddy-current power loss or frequency several values of Bm Evaluation Figure 10: Linear fit through electrical power frequency ratio vs . requency for Bm=0. 4 The plot in Figure 6th was made using Matlab’s curve appropriate tool. In addition , in order to receive the straight collection displayed in figure 6th, an exclusion rule was created in which the info points in the centre were dismissed. The incline and the y-intercept of the range are p1 and p2 respectively. y=mx+b fx=p1x+p2 m=p1=0. 001125 b=p2=-0. 002083 Physique 12: Geradlinig fit through power frequency ratio or frequency pertaining to Bm=0. six The plan in determine 7 was generated in the same manner as the plot in figure 6. The slope and y-intercept obtained with this case are: m=p1=0. 001325 b=p2=0. 5058 Figure 13: Linear fit through electricity frequency proportion vs . rate of recurrence for Bm=0. 8 For the linear fit exhibited in number 8, simply no exclusion was used. The data details were well behaved, hence the exclusion was not necessary. The slope and y-intercept would be the following: m=p1=0. 00341 b=p2=0. 0493 Physique 14: Thready fit through power regularity ratio vs . frequency to get Bm=1. 0 The use of exclusions was not essential for this particular suit. The incline and y-intercept are the following: m=p1=0. 004135 b=p2=0. 1169 Figure 12-15: Linear match through electrical power frequency rate vs . frequency for Bm=1. 2
The usage of exclusions was not necessary for this specific fit. The slope and y-intercept are listed below: m=p1=0. 00695 b=p2=0. 1285 Determine 16: Geradlinig fit through log (Kh*Bm^n) vs . record Bm To get the story in number 11, exclusion was created to ignore the value inside the bottom kept corner. This was done as this value was negative which usually implies that the hysteresis reduction had to be bad, and this end result did not appear sensible. The slope of this directly line signifies the exponent n as well as the y intercept represents log(Kh). b=logKh>Kh=10b=10-1. 014=0. 097 n=m=1. 554 Figure seventeen: Linear in shape through journal (Ke*Bm^2) or og Bm No exclusion rule was necessary to carry out the thready fit through the data items. b=logKe>Ke=10b=0. 004487 Dialogue 1 . Discuss how eddy-current losses and hysteresis deficits can be decreased in a transformer core. To lower eddy-currents, the armature and field cores are made from laminated metallic sheets. The laminated bedsheets are insulated from one one more so that current cannot movement from one linen to the different. To reduce hysteresis losses, most DC armatures are constructed of heat-treated silicon steel, which has an inherently low hysteresis loss.. Using the hysteresis damage data, figure out the value pertaining to the constant d. n=1. 554 The details showing how this variable was computed are within the analysis section. 3. Make clear why the wattmeter voltage coil has to be connected over the secondary winding terminals. The watt-meter voltage coil should be connected through the secondary winding terminals as the whole purpose of this try things out is to evaluate and independent the losses that take place in the key of a transformer, and attaching the potential coils to the secondary is the only way of computing the loss.
Call to mind that within an ideal transformer P in the primary is usually equal to P out of the extra, but in truth, P in the primary is definitely not equal to P from the secondary. The main reason for this is the core losses that we need to evaluate in this research. Conclusion I really believe that this lab experiment was successful since the objectives of both portion 1 and 2 were fulfilled, namely, to experimentally determine the inductance benefit of an inductor with and without a permanent magnetic core and also to separate the core deficits into Hysteresis and Eddy-current losses.
The inductance values were determined and the values obtained produced sense. Needlessly to say the inductance of an inductor without the addition of a magnetic core was less than regarding an inductor with a magnetic core. Furthermore, part two of this research was powerful in the sense that after our professor provided us with the important measurement beliefs, meaningful data analysis and calculations were made possible. Your data obtained using matlab’s competition fitting tool kit made physical sense and allowed us to storyline several necessary graphs.
Although analyzing in your first set of beliefs our professor provided all of us with was very difficult and time consuming, after receiving an email with more detailed information on how to investigate the data presented to all of us, we were capable to get the job done. Additionally to gratifying the goals of this try things out, I think about this laboratory was even more of any success because it provided all of us with the opportunity of employing matlab pertaining to data analysis and visualization. I know this can be a valuable skill to mastery over. Appendix Matlab Code used to make plots and the linear matches %% Defining range of factors Bm=[0. 4:. 2: 1 . ], % Maximum magnetic flux density f=[30: 15: 60], % range of frequencies in Hertz Es1=[20. 8 23. 1 forty one. 5 51. 9 sixty two. 3], % Induced volt quality on the secundary @ 40 Hz Es2=[27. several 41. your five 55. four 69. 2 83. 0], % Activated voltage around the secundary @ 40 Hertz Es3=[34. 6 51. 9 69. 2 eighty six. 5 ciento tres. 8], % Induced voltage on the secundary @ 40 Hz Es4=[41. five 62. a few 83. 0 103. 6th 124. 5], % Activated voltage on the secundary @ 60 Hz W1=[1 2 . your five 4. 5 7 twelve. 4], % Power loss in the core @ 31 Hz W2=[1. 5 4. 5 7. four 11. a few 16. 2], % Electrical power loss in the core @ 40 Hertz W3=[3 6 eleven. 3 sixteen. 8 22. ], % Power damage in the primary @ 55 Hz W4=[3. almost eight 7. a few 15. 0 21. 3 33. 8], % Electrical power loss in the core @ 60 Hz W=[W1, W2, W3, W4, ], % Electricity loss for all frequencies W_f1=W(1,: ). /f, % Power to frequency proportion for Bm=0. 4 W_f2=W(2,: ). /f, % Power to frequency rate for Bm=0. 6 W_f3=W(3,: ). /f, % Power to frequency rate for Bm=0. 8 W_f4=W(4,: ). /f, % Capacity to frequency ratio for Bm=1 W_f5=W(5,: ). /f, % Power to rate of recurrence ratio for Bm=1. two %% Creating plots of W/f versus frequency for diffrent beliefs of Bm Plotting W/f vs . regularity for Bm=0. 4 plot(f, W_f1, ‘rX’, ‘MarkerSize’, 12), xlabel(, Regularity [Hz]’), ylabel(, Power Proportion [W/Hz]’), main grid on, title(, Power Ratio vs . Frequency For Bm=0. 4, ), % Conspiring W/f or frequency pertaining to Bm=0. 6th figure(2), plot(f, W_f2, ‘rX’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Power Proportion [W/Hz]’), main grid on, title(, Power Percentage vs . Regularity For Bm=0. 6, ), % Plotting W/f or frequency to get Bm=0. eight figure(3), plot(f, W_f3, ‘rX’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Power Percentage [W/Hz]’), main grid on, title(, Power Percentage vs . Frequency For Bm=0. 8, ), % Conspiring W/f versus frequency to get Bm=1. figure(4), plot(f, W_f4, ‘rX’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Electric power Ratio [W/Hz]’), grid in, title(, Electric power Ratio versus Frequency Pertaining to 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(, Electric power Ratio versus Frequency Pertaining to Bm=1. 2, ), %% Obtaining Kh and n b=[-0. 002083 0. 05058 zero. 0493 0. 1169 zero. 1285], % b=Kh*Bm^n log_b=log10(abs(b)), % Computer the log of magnitude of b( y-intercept) log_Bm=log10(Bm), % Processing the record 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 . Sign of Magnet 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% Conspiring log(Ke*Bm^2) or log(Bm) figure(7), plot(log_Bm, log_m, ‘rX’, ‘MarkerSize’, 12), xlabel(, log(Bm)’), ylabel(, log(Ke*Bm^2)’), main grid on, title(, Log of Normalized Eddy-Current Loss or Log of Magnetic Flux Density’), % Plotting W/10 vs . consistency at different values of Bm PLD1=W(1,: ). /10, % Power Loss Denseness for Bm=0. 4 PLD2=W(2,: ). /10, % Electrical power Loss Density for Bm=0. 6 PLD3=W(3,: ). /10, % Electrical power Loss Thickness for Bm=0. 8 PLD4=W(4,: ). /10, % Power Loss Thickness for Bm=1. 0 PLD5=W(5,: ). /10, % Electric power Loss Density for Bm=1. 2 figure(8), plot(f, PLD1, ‘rX’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Electricity Loss Density [W/Kg]’), main grid on, title(, Power Loss Density vs . Frequency’), older, plot(f, PLD2, ‘bX’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Electrical power Loss Density [W/Kg]’), main grid on, title(, Power Reduction Density or Frequency’), plot(f, PLD3, ‘kX’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Power Damage Density [W/Kg]’), grid about, title(, Electricity Loss Denseness vs . Frequency’), plot(f, PLD4, ‘mX’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Electricity Loss Density [W/Kg]’), main grid on, title(, Power Loss Density or Frequency’), plot(f, PLD5, ‘gX’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Power Loss Density [W/Kg]’), grid in, title(, Electrical power Loss Thickness vs .
Frequency’), legend(, Bm=0. 4, ‘Bm=0. 6′, , Bm=0. 8′, , Bm=1. 0′, , Bm=1. 2, ), %% Defining Ph level and Rapid ejaculationature climax, Ph=abs(f’*b), Pe=abs(((f’). ^2)*m), %% Plotting Ph for different ideals of frequency % To get Bm=0. 4 figure(9), plot(f, Ph(:, 1), ‘r’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Hysteresis Power Loss [W]’), grid on, title(, Hysteresis Electricity Loss versus Frequency’), % For Bm=0. 6 carry, plot(f, Ph(:, 2), ‘k’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Hysteresis Electricity Loss [W]’), grid on, title(, Hysteresis Power Reduction vs . Frequency’), % To get Bm=0. almost 8 lot(f, Ph(:, 3), ‘g’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Hysteresis Electric power Loss [W]’), grid upon, title(, Hysteresis Power Damage vs . Frequency’), % For Bm=1. 0 plot(f, Ph(:, 4), ‘b’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Hysteresis Power Loss [W]’), grid on, title(, Hysteresis Power Loss vs . Frequency’), % For Bm=1. zero plot(f, Ph(:, 5), ‘c’, ‘MarkerSize’, 12), xlabel(, Regularity [Hz]’), ylabel(, Hysteresis Electrical power Loss [W]’), grid on, title(, Hysteresis Power Reduction vs . Frequency’), legend(, Bm=0. 4, ‘Bm=0. 6′, , Bm=0. 8′, , Bm=1. 0’, , Bm=1. 2, ), % Plotting Rapid climax premature climax, vs consistency for different values of Bm % Pertaining to Bm=0. four figure(9), plot(f, Pe(:, 1), ‘r’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Hysteresis Power Reduction [W]’), main grid on, title(, Hysteresis Power Loss or Frequency’), % For Bm=0. 6 hold, plot(f, Pe(:, 2), ‘k’, ‘MarkerSize’, 12), xlabel(, Consistency [Hz]’), ylabel(, Hysteresis Electrical power Loss [W]’), grid about, title(, Hysteresis Power Damage vs . Frequency’), % To get Bm=0. 8 plot(f, Pe(:, 3), ‘g’, ‘MarkerSize’, 12), xlabel(, Rate of recurrence [Hz]’), ylabel(, Hysteresis Electricity Loss [W]’), grid in, title(, Hysteresis Power Loss vs . Frequency’), For Bm=1. 0 plot(f, Pe(:, 4), ‘b’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Hysteresis Power Reduction [W]’), main grid on, title(, Hysteresis Electricity Loss vs . Frequency’), % For Bm=1. 0 plot(f, Pe(:, 5), ‘c’, ‘MarkerSize’, 12), xlabel(, Frequency [Hz]’), ylabel(, Eddy-Current Power Damage [W]’), grid on, title(, Eddy-Current Electrical power Loss or Frequency’), legend(, Bm=0. 4, ‘Bm=0. 6′, , Bm=0. 8′, , Bm=1. 0′, , Bm=1. 2’), Bibliography Chapman, Stephen J. Electric powered Machinery Basics. Maidenhead: McGraw-Hill Education, 2006. Print. http://www. tpub. com/content/doe/h1011v2/css/h1011v2_89. htm
