643_mid - ece643-exam #1 — au/O9 1. (20 points total)...

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Unformatted text preview: ece643-exam #1 — au/O9 1. (20 points total) Determine the inductance at the coil as a function at g1. Assume that the ermeabilit of the core material including the movable plunger isl infinite.) The plunger is constrained to move only in the vertical direction, thus the gaps identified as g2 are fixed [0.2 cm] whereas the gap g1 is a variable. Assume the cross sectional area of all parts of the core and plunger is the same — Acore = 4 cm2. N = 250 turns. a Movable ‘plunger it, i x W; ‘R L: V ~21 3;» t l N. {pr !%‘b yr , } 9' A!” M Page 2 of 7 ece643-exam #1 — au/O9 2. (20 points total) Misc. short answer questions: a. (4 points) What isithe permeability of an ideal magnetic structure: WI (yr —1 or 0 [zero] or 1 b. (4 points) For a salient gole synchronous machine, what is the relationshig between Xg and Kg? // I Xq > Xd or Xq = Xd or x .r’ c. (4 points) For a c lindrical rotor s nchronous machine, what is the relationship between Xg and XQ? r" /\ d. (8 points) Compare the BH curve for a permanent magnet [i.e., Bpm, Hpm] with that of ferro- magnetic material [i.e., Bferm, erm] typically used for transformer core. 1. B,- [remanent flux density], i.e., the value of B when H = 0: Br .pm > Br_ferro or or Br _pm < Br_ferro 2. Hc [coercivity], i.e., the value of H when B = 0: ch_pm| < chjerrol Page 3 of7 ece643-exam #1 — au/O9 3. (20 points) Consider a 3(3) salient pole synchrous machine. For the following machine information, [1nd the angle at Iq. Note: all values given are in actual volts, amps, ohms, etc. — not per unit. Ratings: 22,kV, 60 Hz, 600 MVA ' am“; e mm} 4A" M — _ I 0 Parameters. Xd — 1.1 ohms, Xq — 0.8 ohms 003 Ch); as .7314 I. 0 j»? “‘15” Zip?“ A Operating at: rated voltage; 12,590 amx _s at 0.9 power‘factoxilead ‘ / gmuadtoi a L8 «at,» « /——~ l Emle Von —\— :5“ ’77 {WSW g fl 0) / w R l 83/ f :7 Q 931 1095 __,/’-’—v’ Page 4 of 7 //? miV bi! (5 point Assuming the machine ' at M21. 0 er mg at steady state, angles 00 will the instahtaneous value of ' ' = itl ‘ . . . rotor winding ‘/ a T V ‘ a .4: V, l I f L , flw't ,/ I W ‘~ m 21,376) fl: k” 011%] KP?! xii/waged??? a”; M J 15“”‘4‘ Page 5 of 7 ece643-exam #1 — au/09 4,: L. "V 5. (20 points) Consider the inductance given below. Assuming a currenWhat is the resulting W to the magnetic field evaluated at x = ofAlsc“as‘sume'a’lihear system? L(x) = ax2+ bx +c L/ L L M Flimsy 9%” ” U a ’ r [L 9' m f :7 R. M"; G? “firm—"awflm .‘e 643 examl answers auZOQ 1. Note that because of the coil location, the two L _ gazmg1+ 2g2 5R _ g1 mgz : g2 N2 9? #0 * Acore g1 in #0 * Acore g2 gaps are in parallel. *A L=N2*fi9——%2re p0=4*7r*10”7 N=250 Acore=4*10‘4 Z-a- “ideal magnetic structure: 0° g1+ 2 b. Xq < Xd for salient pole machine 1* g2 =0.2*10—2 L: i c. Xq = Xd for cylindrical rotor machine 2502*4*7r*10—7*4*10—4 o.2*10‘2 2 g1+ d.1. B,_pm about the same as Brferro l 2' chwpm I > I Hc ferro I 3. Ea; = va + la*jXq va = 22*103 / v3 Ia = 12,500 @ +cos-1(o.9) Eaf' = 12,272 @ +47.17O angle of lq = angle of Eaf’ = 47.170 f Magnetic axis 0 rotor field 4. from Faraday’s law, e(t) = N [d¢(t)/dt], thus when ‘ (Mt) at a max, e(t) = 0 and when (Mt) at 0 then (l)(t) is 7% either a positive or negative maximum. [a] vi-j-Ii-I-Z \ Therefore, eaa’(t) = 0 when 60 = nrt for n = 0,1, 2, [b] And eaa’(t) is a maximum (either pos or neg) at mt/Z for n = 1, 3, 5, [c] Positive magnetic axis of . g I _ V stator phases perpendicular to plane of coil —their ', orientation is NOT affected by the rotor for a ' ' ' ' ' cylindrical rotor machine. Iaa, = O at the instant of time indicated, whereas ice, = —ibb,. (bbb, is directed at +1200 and since ICC, is negative, (Dec, at + 600, thus the resultant at +900. p Magnetic axis of ¢a ‘ Plane of coil of rotor winding 1 aiWfidoxn ‘ 2 ffld: a Wfidz *L(x)*12 L(x)=a*x2+b*x+c x l ffld<10>X0)=E*(2*a*X0+b)*15 C ece643-exam #1 — au/08 m “magi /C.LL S“ fl Voltage Regulation is a measure of “quality” of the mode of operation for various power —-sY'Stem devices such as transformers and generators. What is the ideal value of voltage regulation? [Circle correct answe -1 or or +1 or 00 ~ b. Considering a synchroggmotofil is it more likely to become overheated when it is operating at which 0 ‘ o the following power factors? [A phasor diagram may be useful] 1. (20 points total) Misc. questions [each question of equal value]. or unity (1) or / 'Qding \ ,g/‘fl’w +ua _ ‘ Magnetic axis ctr/Assume the rotor is rotating at a constant smed. in ‘ of rotor 6014-90 Magnetic axis ' of phase a fad/The energy stored in a magentic field of a linear system is given by the following expression; what is the resulting force? Wad = K] + KZ/X where Kl & K2 are constants and x represents a variable air-gap spacing l : Awful. (:4 (Jx ‘ .— KZ x"’ = Page 2 of6 ece643-exam #1 — au/08 2; (20 points) Refer to the ferromagnetic system shown here; consider the permeabiligg to be infinite. All parts have the same cross-sectional area (Awe); assume the cross-section to form-a square. An N tum coil surrounds the movable part and the movable part is free to move up and down without any change in the gaps identified §§ g1. stationary part i ....... Li? movable What is the inductance at the N-turn coil? L Page 3 of6 ece643-exam #1 - au/08 C (20 points total) Consider a salient pole BQ , 60-Hz, 2-pole, sygchrous machine with the following inductances: ., _ . . - _ :5 .. it“); 18...,— 5.l+1.1*cos(28mc)rmlh-hennes ~ Val-l L : \WJL_%3 a- Leakage inductance of stator winding = 0.3 milli-henries A4 = 6.6*cos(6me) milli'hendes M” “H E A V L“: L14; [ékw‘vn/D') Determine the (allowing: {9/ o (6p0ints)Xd=: X Lu“ : Lwligdifgfit H '2 a; a: - X“ W “l m M = K Le) {X H fl: (6 PointS)Xq= , V <3 C I ‘m 0X (8 point rot?» current for a particular operating condition where E.f= 4000 @ 4513 volts. ,» L' y 2,2,03 A g. . {5.5 LLVWfi Page 4 of 6 ece643-exam #1 - arr/08 _4_. (20 points) Consider a salient pole 34> synchronous machine with the following direct- and quadrature-axis reactances: X, = 1.4 per unit Xq = 0.85 per unit Assume the machine is operating as a generator with rated terminal voltage and rated terminal current calculate Id and Iq [magnitudes and angles] when the generator is operating at 0.9 ggwer factor lead. [An appropriate phasor diagram could be beneficial for partial credit considerationsl] A v0 \Cad 1:13;” :QE‘Z‘ Va: ‘6‘) L PageSof6 15/ ,1 A II; I 1.; 3- _ l \ 3’ 7’ ece643-exam #1 — au/08 C (20 points total) Misc. questions. [Each question of equal value] Referring to the three different “machines” shown below, consider each device as being initially at rest in the position shown; then the indicated source as applied, what is direction of rotation for each of the circumstances given? Note that the stationary part and the movable part of each device are made of ferromagnetic material. Machine (a): with the rotor coil not energized, what the direction of rotation with a dc stator current in the direction indicated? "i * 7r" » ' Clo kWis A or ! no—motion _, or \ ! WM.” Machine (a): with the rotor coil not energized, what is the direction of rotation with a dc stator current in the direction 0 osite to that indicated? r N_ ./ ' Clockwise or nit-motion. or counte Machine (b): ne lectin the effect of the ermanent ma et, what is the direction of - n - - th a dc current in the dire tion indicated? c or downward .5 fl Machinejbzzl considering the effect of both the permanent magnet and the coil, is there a possibility that a current could be found where there is no motion? Briefly explain E LaifitUJL (fa :g)‘ l‘x [It .Vl r J-rrct‘? 4311;.[1‘ / Machine to): there is no coil on the rotor; what is the direction of rotation with an ac, 60 Hz, i'o'e‘c'o'o'o \ 9o‘o'o‘o‘o’c ‘- w .o'o°o‘o°¢‘a . ‘ ho’e’oy-‘o’. 999’. 096?. Magnetic material mass M NOTE: Rotor is elliptical (c) Page 6 of 6 '0 = an 19101 uaql gumu ausoddo pue Ienba ato 8J2 sasmos |N pue Wd uaqM 1 ND (3) 'SpJEMdn (q) My (2) 'qled xnl; all p aauepmaJ sq], aanpa; o1 uomanp e u! sAemle 3310:] 'uonow JO uogpwgp afiueqa 10u saop 3p JO De Jaqlaqm JO luaum 310 uomanp an1 ’paJenbs luaJJna 01 leuomodmd ASJaua plaH '(uonow Jeau” 40; x 73 UOnElOJ 10,19) mama/mu; on, lDSdSBJ LmM AEJaua play; u! afiueqa aql 01 paleleu ELIE 3310; pue aanol 'g 5X! * 271+ 0/1 = 3% 31119991 esnvosq ...f+.. ((fd)1~soo)u!sf+/d)*0'1= “I :suonnlos Jo;,,1aaqs dlaH” 8OOZ/n9 'I# lUBXEI E179 EDEI (""')UFS* [07* [1*‘0": [09 1 J 1m=0 ((9)soo*fvy*fnfi= P zxna [(231, 0991)*S'[ + '91]*091LZ = b1 * m : bx [(2% 099mg: +'E11*091LZ = “1 * ‘0 = pX “HUGH-HIM ("') 503*12'1 + SD + 8‘17 = ("')503*ZB1+'91+ 0991 =29: :sdgqsuonelaJ aouepnpug 1043 'ddv o; JQJQJ '2 WWW! 6 91°71 Ikeaasm ‘Jxrxrmx14kkm‘fl’i‘wzn'i‘r'mfi‘b'wxjfiizfl'm v‘mwavmi-anmxxmur- «m; [enmed u! 3J9 s 1323 0M1 am alou {(°‘°°V 011 )/q18ue| : 2/; -z {017.5133} 1u21suoo=;| x9 = ‘19sz i (x ‘1) P119149 __ = 7 x9 1/ {9Z.€ .ba} gumsuoozy _ = [7sz |(x ‘1') 101/1149 _p 'z 'I '0 z u aJaqM 1LU @ 910,91an, {o e. a ’xew s; 982w” an uaqM (— 1p/«(p = 9 ‘M21 S,AepeJed UJOJj '3 JOlOLU 103l8ugpea1 'q IPEOFIIYUAI APPOI—IWAI _ I PEOI'OUA” = uone'ngm BBBIIOA -e--[ ...
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This note was uploaded on 12/07/2011 for the course ECE 600 taught by Professor Clymer,b during the Fall '08 term at Ohio State.

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643_mid - ece643-exam #1 — au/O9 1. (20 points total)...

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