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# EEE229 Electrical Energy and Conversion - Coursework: A three-phase induction machine

EEE229Electrical Energy and ConversionUKThe University of Sheffield

Coursework - EEE229 Electrical Energy and Conversion (2022 -23)

Total score: 100 (Part I and Part II)

Submission details: You may complete your answers by using a word -processed document or as handwritten sheets (no preference or differential marks for submitting either), as long as you provide a detailed solution showing the individual steps and justification to reach your results. Please save or scan these respectively into a PDF file and submit this via the BlackBoard (BB) site in the ‘Assignment 202 2/23’ folder. Please do not zip your PDF file . Grades and feedback will be released 4 –5 weeks after the deadline. The questions in Part I contain data which are shown in RED CAPITAL TEXT , which is specific to each candidate. You can find the particular data for you to use in each question in Appendix A of this problem sheet.

Part I: Semester 1 (score 50) Introductory notes: This assignment contains several elements that have not been explicitly covered in the lecture notes. These, quite deliberately, require you to access manufacturer datasheets or research other source s of information in order to complete the question (s). This additional material is not examinable in the main examination – only material covered in the Lecture s, Tutorials, Slides, and Lecture Notes is game for an exam question. You should provide all workings and explanations in your solutions – these will variously count towards achieving full marks in a particular question. Answer all questions .

QUESTION 1

A three -phase induction machine is designed to operate at a near constant speed for the compressor of an environmental control system of an aircraft. The power system to which it is connected is a standard 400Hz, 115 Vrms (phase voltage) sinusoidal AC supp ly. The nominal speed for the compressor is NOM INAL _SPEED (i.e. the synchronous speed with zero slip). During manufacture, the stator resistance is measured to be R1. During a locked -rotor test at 400Hz after assembly , the measured input power per phase is LR_INPUT_POWER and the measured phase current is LR_CURRENT 2 when operated at standstill with a reduced stator voltage of LR_VOLTAGE . The machine as a core loss at 3% slip of CORE_LOSS . The magnetising reactance, 𝑋𝑚, is j30. a) Calculate the number of poles for the design to achieve the specified nominal speed. [4] b) Using the full approximate equivalent circuit, c alculate the torque produced by the machine for a slip of 3%. [8]

c) Calculate the total input current at this operating point. [8]

d) Calculate the efficiency at this operating point. [5]

QUESTION 2 A permanent magnet brushed DC machine is used to drive a geared mechanism in an aerospace valve actuator. The machine in an aerospace grade brushed DC motor manufactured by Maxon (www.maxonmotor.com ). The motor is part of their RE Programme range of high performance machines as has part number DC_PART_NO . The specification for this machine contains all the information you need to answer these questions (take care over units). a) Calculate the total friction and drag torque at the no -load sp eed (i.e. when there is no external load applied to the machine). [5] b) Starting from th e equivalent circuit parameters, calculate the no -load speed taking into account the friction and drag torque calculated in part (a) and compare this with the value i n the specification sheet. [5] c) Plot the torque (y -axis) versus speed (x -axis) characteristic for this machine design at its nominal voltage, taking care to include calculations of any key operating points (Note this will not match exactly the experimental measurements in the published specification, but should be a value close to it). [10] d) Using the value of the maximum continuous current for the machine (also referred to as the nominal current in the specification sheet), calculate the mac hine torque and speed when drawing this current. [5]

3 Part II: Semester 2 (score 50) Introductory notes: The following questions contain elements that were studied in Lecture 8. Elements such as motor equations (torque and p ower ) have been also studied in Semester 1. Additional effort is required to solve steady -state equations. We encourage you to use Wolfram Mathematica to facilitate your analysis, whose license is available for students, in such case please upload your own Math ematica notebook alongside your word -processed or hand -written notes. Consider the DC Motor control set -up in Fig. 1.

Fig. 1. H -bridge drive system for DC motor

1) Considering bipolar switching, compute the average value of the voltage across the terminals of the DC motor as a function of the duty cycle 𝑉𝑜(𝐷). Justify your answer using a diagram of the circuit and the step -by-step averaging procedure. [5] 2) Compute the total electromagnetic torque 𝑇𝑒 and the rotor speed 𝜔 when the duty cycle is equal to 0. 8 in the following three cases. a) The separately excited connection in Fig. 2. Consider: 𝑉𝐷𝐶=200 𝑉,𝑅𝑎=1Ω,𝐿𝑎=80𝑚𝐻,𝐿𝑚=2𝐻,𝐽=0.005 𝑘𝑔𝑚2, 𝐵𝐿=0.0015 𝑁𝑚/𝑟𝑎𝑑,𝑖𝑓=1𝐴.

Fig. 2. H -bridge drive system for separately excited DC motor [10]

4 b) The shunt excited connection in Fig. 2. Consider: 𝑉𝐷𝐶=200 𝑉,𝑅𝑎=1Ω,𝐿𝑎=80𝑚𝐻,𝐿𝑚=2𝐻,𝐽=0.005 𝑘𝑔𝑚2,𝑅𝑓=200 Ω, 𝐿𝑓=20𝐻,𝐵𝐿=0.0015 𝑁𝑚/𝑟𝑎𝑑.

Fig. 2. H -bridge drive system for a shunt DC motor [10] c) The series connection in Fig. 4. Consider: 𝑉𝐷𝐶=200 𝑉,𝑅𝑎=1Ω,𝐿𝑎=80𝑚𝐻,𝐿𝑚=2𝐻,𝐽=0.005 𝑘𝑔𝑚2,𝑅𝑓=200 Ω, 𝐿𝑓=20𝐻,𝐵𝐿=0.0015 𝑁𝑚/𝑟𝑎𝑑. Hint: Consider only the case when 𝝎>𝟎.

Fig. 3. H -bridge drive system for a series DC motor [10] d) Considering the above three cases (separately excited, shunt and series configurations) with ideal switches and a switching frequency of 50kHz: Hint: Consider only the case when 𝝎>𝟎. 1) Compute the input and output power. 2) Compute the duty cycle that is required when the machine rotate at 800 RPM (Remember to convert the speed into rad/s). 3) Compute the drive’s tON, tOFF and switching period T. [15]

5 APPENDIX A – Individual parameters for Part I Question 1 Reg. No. NOMINAL_SPEED (rpm) LR_VOLTAGE (Vrms) LR_CURRENT (Arms) LR_INPUT_POWE R(W) R1 () CORE_LOSS (W) 1 190148267 12000 35 18 219 0.30 43 2 190148614 12000 55 39 1027 0.30 22 3 200139847 4800 25 16 173 0.30 12 4 200138611 4800 45 23 357 0.30 21 5 200138688 6000 35 23 238 0.20 32 6 200138622 24000 55 33 735 0.30 87 7 200138079 8000 35 25 281 0.20 39 8 200138367 6000 60 35 965 0.35 54 9 200189093 12000 60 37 1232 0.40 33 10 210161373 12000 50 25 563 0.40 33 11 210161409 4000 50 44 1525 0.35 9 12 200345747 12000 45 32 461 0.20 64 13 200345770 4800 30 14 132 0.30 17 14 200345068 4800 40 21 496 0.50 11 15 200344946 6000 50 25 352 0.25 26 16 200344913 6000 25 23 298 0.25 20 17 200344968 8000 30 14 221 0.50 17 18 200345035 4000 30 15 203 0.40 16 19 200345301 4000 55 27 656 0.40 25 20 200345046 24000 25 22 218 0.20 130 21 200344957 4000 35 21 447 0.45 11 22 200344865 6000 45 24 648 0.50 13 23 200345220 8000 60 33 1103 0.45 44 24 200344902 4800 60 42 1786 0.45 12 25 200345057 4800 25 17 260 0.40 45 26 200345378 8000 60 41 1324 0.35 25 27 200344681 8000 45 29 473 0.25 35 28 200344588 12000 50 45 911 0.20 22 29 200344603 8000 25 15 253 0.50 18 30 200344924 6000 30 13 171 0.45 15 31 200345312 24000 50 28 617 0.35 75 32 200344599 8000 50 40 900 0.25 25 33 200345781 4000 45 26 761 0.50 22 34 200345323 4800 60 30 506 0.25 15 35 200345356 4000 40 26 380 0.25 17 36 200345367 8000 55 31 1081 0.50 18 37 200339517 12000 35 17 325 0.50 26 6 38 200345183 4000 35 17 195 0.30 26 39 200345895 4800 50 28 617 0.35 27 40 200344625 4000 25 12 65 0.20 30 41 200345242 4000 50 30 608 0.30 14 42 200345231 4000 25 20 270 0.30 15 43 200345297 12000 35 17 260 0.40 47 44 200345736 4000 30 13 133 0.35 12 45 200344979 4000 60 32 922 0.40 21 46 200345194 4800 55 34 1040 0.40 28 47 200345714 8000 50 26 304 0.20 42 48 200345769 24000 35 21 298 0.30 64 49 200345208 4800 35 22 436 0.40 13 50 200345024 12000 25 16 173 0.30 48 51 200344614 24000 50 39 1369 0.40 12 52 200345345 6000 50 30 1013 0.50 33 53 200345219 12000 55 30 709 0.35 37 54 200345150 8000 40 29 662 0.35 25 55 200345013 4000 60 41 1891 0.50 9 56 200345161 4800 40 29 378 0.20 26 57 200345264 4800 60 61 2093 0.25 21 58 200344636 6000 55 40 1260 0.35 44 59 200344577 6000 45 37 924 0.30 39 60 200345116 6000 40 21 447 0.45 15 61 200344670 24000 25 17 163 0.25 45 62 200344980 8000 45 23 595 0.50 22 63 200344669 4000 35 28 441 0.25 20 64 210159680 24000 45 30 810 0.40 66 65 210161362 12000 25 20 225 0.25 52 66 210161421 12000 45 33 858 0.35 38 67 210161384 24000 40 26 532 0.35 58 68 210168453 24000 55 30 1013 0.50 88 69 210171246 4800 55 30 709 0.35 32 70 210172737 8000 45 37 924 0.30 29 71 210184280 4800 50 28 794 0.45 12 72 210186608 24000 40 26 608 0.40 73 73 220140168 8000 35 21 248 0.25 34 74 220139689 6000 60 46 1428 0.30 22 75 220140146 24000 30 18 146 0.20 85 76 220140283 8000 55 28 706 0.40 22 77 220140397 24000 60 30 911 0.45 54 78 220140364 6000 25 15 228 0.45 15 79 220139667 8000 50 33 1103 0.45 12 80 220140249 4800 45 35 551 0.20 25 81 220140191 24000 45 30 405 0.20 87 82 220140319 24000 35 17 293 0.45 58 83 220140179 12000 30 16 144 0.25 51 84 220140261 12000 45 28 441 0.25 37 85 220139955 6000 45 22 490 0.45 32 7 86 220140353 12000 55 31 973 0.45 29 87 220140320 4000 55 30 911 0.45 27 88 220140250 6000 40 26 608 0.40 16 89 220139678 6000 55 29 378 0.20 32 90 220140294 24000 60 38 1625 0.50 97 91 220140216 4000 30 19 244 0.30 19 92 220139531 4800 30 15 152 0.30 28 93 220140180 6000 30 21 198 0.20 43 94 220140205 8000 30 15 228 0.45 29 95 220140308 12000 30 19 406 0.50 90 96 220140342 24000 30 15 127 0.25 60 97 220140375 4000 45 24 518 0.40 27 98 220140386 4800 45 22 327 0.30 19 99 220140401 6000 45 25 352 0.25 17 100 220140238 8000 45 20 315 0.35 51 101 220140331 6000 50 24 454 0.35 22 102 220140227 24000 45 22 436 0.40 18 103 220140272 12000 55 28 706 0.40 57 104 220139542 4800 45 25 563 0.40 30 105 220231363 4000 55 29 757 0.40 15 106 220241845 4800 55 28 882 0.50 27 107 220241856 6000 55 27 656 0.40 30 108 220241867 6000 45 20 270 0.30 25 109 220245854 24000 45 20 225 0.25 22 110 220245843 4800 50 31 973 0.45 24 111 SPARE 12000 45 26 532 0.35 80 112 SPARE 8000 50 26 380 0.25 22 113 SPARE 4000 45 19 406 0.50 23 114 SPARE 24000 50 29 946 0.50 34 115 SPARE 4000 50 26 532 0.35 19 116 SPARE 8000 45 24 389 0.30 40 117 SPARE 12000 45 23 238 0.20 70 118 SPARE 8000 55 42 794 0.20 34 119 SPARE 12000 50 23 357 0.30 62 120 SPARE 24000 55 33 735 0.30 43

8 Question 2 Reg. No. DC_PART_NO 1 190148267 148866 2 190148614 148867 3 200139847 148877 4 200138611 218009 5 200138688 353295 6 200138622 353297 7 200138079 353298 8 200138367 353300 9 200189093 578296 10 210161373 578298 11 210161409 618571 12 200345747 618573 13 200345770 148866 14 200345068 148867 15 200344946 148877 16 200344913 218009 17 200344968 353295 18 200345035 353297 19 200345301 353298 20 200345046 353300 21 200344957 578296 22 200344865 578298 23 200345220 618571 24 200344902 618573 25 200345057 148866 26 200345378 148867 27 200344681 148877 28 200344588 218009 29 200344603 353295 30 200344924 353297 31 200345312 353298 32 200344599 353300 33 200345781 578296 34 200345323 578298 35 200345356 618571 36 200345367 618573 37 200339517 148866 38 200345183 148867 39 200345895 148877 40 200344625 218009 41 200345242 353295 42 200345231 353297 43 200345297 353298 44 200345736 353300 45 200344979 578296 9 46 200345194 578298 47 200345714 618571 48 200345769 618573 49 200345208 148866 50 200345024 148867 51 200344614 148877 52 200345345 218009 53 200345219 353295 54 200345150 353297 55 200345013 353298 56 200345161 353300 57 200345264 578296 58 200344636 578298 59 200344577 618571 60 200345116 618573 61 200344670 148866 62 200344980 148867 63 200344669 148877 64 210159680 218009 65 210161362 353295 66 210161421 353297 67 210161384 353298 68 210168453 353300 69 210171246 578296 70 210172737 578298 71 210184280 618571 72 210186608 618573 73 220140168 148866 74 220139689 148867 75 220140146 148877 76 220140283 218009 77 220140397 353295 78 220140364 353297 79 220139667 353298 80 220140249 353300 81 220140191 578296 82 220140319 578298 83 220140179 618571 84 220140261 618573 85 220139955 148866 86 220140353 148867 87 220140320 148877 88 220140250 218009 89 220139678 353295 90 220140294 353297 91 220140216 353298 92 220139531 353300 93 220140180 578296 10 94 220140205 578298 95 220140308 618571 96 220140342 618573 97 220140375 148866 98 220140386 148867 99 220140401 148877 100 220140238 218009 101 220140331 353295 102 220140227 353297 103 220140272 353298 104 220139542 353300 105 220231363 578296 106 220241845 578298 107 220241856 618571 108 220241867 618573 109 220245854 148866 110 220245843 148867 111 SPARE 148877 112 SPARE 218009 113 SPARE 353295 114 SPARE 353297 115 SPARE 353298 116 SPARE 353300 117 SPARE 578296 118 SPARE 578298 119 SPARE 618571 120 SPARE 618573

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