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# Note for ECE 350 with Professor Haskew at UA-SOLUTIONS FROM PREVIOUS SEMESTERS

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Date Created: 02/06/15

ECE 350 Electromechanics Homework 1 Solution Problem 119 Assume 7 20840quot V a zeq z1 22 25243750 Q L 82494 375o A Zeq 2524315quot pf cos375 079 lagging f Load defined with passive convention ssup W 17164 1425 kVA 1361 j1045 kVA ssup 1716 kVA Psup 1361kW qup 1045 kVAR b feq Z 22 23 3154750 Q L 66034 75 A 315475o pf cos75 099 lagging Load defined with passive convention Sup W 13734 1725 kVA 1361 j179 kVA Ssup 1373 kVA Psup 1361 kW qup 179 kVAR c The magnitude of the current was reduced and the current became less lagging The additional impedance was capacitive thus supplying a portion ofthe reactive power required by the load Special Assignment 2 ECE 350 Electric Power and Machines 2 5 w Consider the power system below 5259 X3 X2 5 133131 L4 132 9 Clool 39 A A HSM I 5 Yo I x1 TL23 I 9931quot G1 r 3C I X I 39 L3 6 495 s 0 1 1 AY 2 3 Yak 37 1 Cf Waite System Data 5 063 30quot 7quot X1 3 SinglePhase 75 MVA 138 kV664 kV X6 5V7 X82 6 X2 1 ThreePhase 50 MVA 115 kV25 kV X6 6 a 90quot L X3 3 SinglePhase 25 MVA 664144 kV X6 4 3 a 0 amt X 39 15w mc9053 zO108210649Qml 63 c 15 TL23 125 mlles 39 r y 1661 uSIm 5quot E 3 09 07 V L3 70 MVA 098 pf lagging 1148 kV 9 3 L4 zY 20 j4 o a 2 31r oeri is System Bases 100 MVA 115 kV at bus 3 2 2 C0Oa t39i04613 a Compute the line voltage bases at each bus b Compute the Y impedance bases at each bus 3 7 0055 0 Draw the perunit perphase equivalent circuit for the system 3 7 d Determine the required line voltage at the source in W e Determine the apparent power output in MVA and power factor of the source f Determine the line voltage magnitude at bus 4 in kV b7 e M lea 13068 116 L22 V 3E i it ZC 7games EX 63 L319 I 2 A 036 3393 I 5 lt1 3 WE N4 0 3 c we 1 I 0ae9ozkllq55 7 1ET 3 20 SdLlATloN quotquot SPECIAL ASSIGNMENT 1 ECE 350 Electromechanics A balanced threephase source operating with positive phase sequence supplies two loads through identical balanced transmission lines with series impedances of 10j50 2 One load is a balanced load of 125 MVA at 060 pf lagging and 230 kV The other load is a Aconnected load of 11j02 kQ Balanced 34gt Source Balanced 34 Load abc V 2 11j02 kc 1391Cw03 o6 Q 2 a f as Mquot 10 Asnomg Balanced 34gt Load 125 MVA W 060 pf lagging 230 kV W 2 3137 rw fl 5367 a Compute the equivalent Yconnected impedance of the complex power load b Compute the line current magnitude in the transmission line feeding the complex power load c Compute the line voltage magnitude at the source d Compute the line current delivered to the impedance load e Compute the line voltage magnitude at the impedance load f Compute the apparent power and power factor of the source g If the aphase linetoneutral39voltage at the source is the reference with a phase angle of zero degrees what are the three linetoline voltage phasors at the complex power load h Compute the Yconnected capacitance value required to correct the power factor of the complex power load to 098 laggingcc VA B goelgolqgo 7 50 O 22L DUE Tuesday June 22 2010 My a f c EA W 2393 7331 1 4o53f A V 2 37ae739mm a 3 x Jig 37339730 U 3 V9 2amp7359 3 673 6a67 13 z3lL1 e Z Ki 21R Vgnz if 5 7 269ng 3M A V Q q 12 9 9 0 Z 34 3926 M M K5590 a177 0 AN 9 57 99676 91 03 K 35 L 3 x r L 2 3 53951ku m Aswan m W m 5 39 V I 430 2230 LMW A I h Qt 115 631332goo WAR WAR o 9 2 00 0 l quot 539 OS was Noquot 2 Lag 7mg 6233395quot L 0 39 Z 4 V 7 VL H H W 13 aim m tr R m M 3 3 r 9 32gt 1 f9 2 10 66Lari15515493MAMMW P 207667Zw 392 39 77 kw lt9 15575o W2 2 1553 WAR V 5 3595824 VA 615016 WA 3539 5 391 3 3 quot 03 l t53mcd 5 53531 392 7205 A 113 90 1T M V J 39 J 7v w V e f atly Raf cm 4 g F F fR41245 1 7mg I 2 g 59f 5 v a quotquot 392 00 7 quot A1o 1 I c BE 1 1 g 39quot a 0 r 3 3 9W O Cquot EZSPOKD 36 3 729 L13 F 9 U QNLsLa zigm metqmilmwgspmausjsas z i iym if y r 0 9 2751 I if A a Iz 377 quot 8003 3355 70 01 RA 1 W 3904 5 as H 5 1 7 W a V a R We 39 39 J il T Jr 69 1 4171313 1 39 s L swhmm w w 3103111 Sooqoov YM 7 i 3 Mab tqa 1H 5 mus H i 24 I9 i i oowxanyw 39 35 i 3 mm A 7 H la REE mr qvlt bzqujxlggb 000 gb a 7 i QM Ifwihukrlazsmiwb 0062 ammoquot 39 Baa 16 1cm f9 qu BM Wzo39m L115 K153 4917 fin tr 0339 s 7 T W230 quot 0 1 5 Pg 66 125 32 353 9 EM 39 1635 9 gt2 1601742 a f 9 c 5 V A39sn39 uvs r Wham x w J gt w 1ltlt 1gt 394 u mun m nv Any quotnwr39x y Lquot M re SCVT 5 4 7 Raft Ra 302 2 L 501me N Homework Assignment 4 EC 350 Elenrl Power and Machines Summer 20m A 401260 14150 MVA 138 kV synchronous generator has the test data provided batow The generator unpvm a connecled Impedance luau wrm 77 15 j611 wmle oneratrng wuh rated termrnal voltage The generator has rotauuual losses or 2 MW 2 ug 117 Field Amps 175 200 225 1 250 275 0c Llne Vans 12000 13 000 13 800 1a 500 15100 sc Amps 1895 125 263611 Pr 9 XS a DENmime the required eld current quot 5 1 Determine the torque requrred or me nrlmc mover 1 c t 317 1 zs m swn TuesdayJulyZT 2010 Ea mwm mar m 53 raw 5 m 1 many Mew 31 quot m 17392 r1 619 40299 I 1U HaSEEquot 5717913 31 73719 7 M M5145 Homework Assignment 5 T gt m 5 Wm ECE 350 EIeancPowerand MachinesSummerzmo 39 VA An 8pole 50 111 20000 HP 133 kV synchronous molar has 19 test data prowde below The rumor has ruranonal losses or 1000 HP and 1 operamd at ratEd termmal volrage the load an he menu 1 15000 HP page m f at r15 7 7 two PPM L nerd Amps t 175 E25 1 1 a h ecu12vqu I12000 13300 I E 3 1M 51 Amps I 1395 1437 1 J Jim 11 7 Iquot um 39 a Deterrmrm me motor speed In RPM 1 Delermtne he eld current i he motor 15 to operate at unity uuwcr actor c Dulurmuuz the maxtmum power that can be delwered a me load wirhom requrrmg and nrl1l1Pnl tn held current d Under the condinons of pan what wlll be the magmlude or the Imu current drawn by 1hr motor 776739 r1 Elsa c1 7 say 2 DUE Tuesday 1111127 2010 NX 117 b WWWW W W stwa Shawn 79615 H E 11519191 24 dgtlgo1i 5u E mm 3219 17 3151 A G g33 0U A7337 LIIyI 39 1 M mm magi 514103519 rt 13km W114 1 6 o 3 55 0 1 OH 3M 1 L 6 Eq 3393 nag v 5amp2 1203 50 12 3 93 j 1 1e5 433quot N v a 0 anto sif szIquot l7 3 U 6390255 1 its M a 119 mobg3 0978 1 5HA 3 i magi A E01 2 Lg lgigj izg liigz g 35 173 3L A 1 V266 c39 S 1 quotLL70 ECE 350 Electromechanics System Level Practice Problem 1 15 points The induction machine in the provided system delivers a torque of 2621 Nm at a speed of 1100 RPM while operating at rated voltage Determine the threephase apparent power and power factor required from the transformer bank Note that the shunt branch of the induction motor is negligible Default Answers 414 kVA 085 pf lagging 2 10 points Determine the line voltage and line current required at the transmission line side ofthe transformer bank Default Answers 144 kV 15 A 08 pf lagging 3 10 points Compute the ABCD constants forthe transmission line in SI units Default Answers A099j0 B295j35 Q C0 D099j0 4 10 points Compute the sending end linetoneutral voltage and and line current for the transmission line Default Answers 8241quot kV 204 30 A 5 15 points Compute the require eld current for the synchronous generator Default Answers NOT REQUIRED 6 10 points Compute the required input torque forthe synchronous generator Default Answers 1900 Nm 7 15 points An adjustable resistor is inserted in series with the shunt eld winding of the dc motor to allow control of the shunt field current Determine the dc source voltage and field rheostat setting required for the dc motor if the armature current is not allowed to exceed 8608 A Default Answers NOT REQUIRED DC Source DC Motor Induction Motor 2400 V 750 HP 60 Hz 6 Pole 10 HP Rotational Losses R1125QX14Q R2084QX24Q Transformer Bank 3 SinglePhase 500 WA 60 Hz 79674 V2400 V 6 Reactance Transmission Line Q S 5 MIle Length 2 059210714 A7 y 0 A Synchronous Generator Synchronous Generator Transmission Line Transformer Bank 0 Induction Motor 0 o 15 W 5 MVA 4 Pole 60 Hz 35 kW Rotational Losses Field Current A 150 195 00 Line Voltage kV 12 15 SC Current A 400 520 DC Motor 1000 HP 1800 RPM 500 V Cum Compounded Long Shunt Ra 008 Q Rf 25 Q Rs 006 Q NsNf11000 Rotational Losses 100 Nm eff 0 5 10 15 20 25 30 If A Ea V 0 115 230 345 460 575 690 skan ssIENMENT 1 r 39 man We don 44 M9 1 L Vl 23a quot5 11a if 531313 9 2Tms3m152 b if 33 BIZ591532 A iiq39 agggaggmqm J2 3 q M7955 55561Lj A 1556541 A at 53 aaamnf ogsc mg mm m i a VA T35M3L31 r lmr gsa f 5 lszssstw 7 31531 ii a sz f i 3M Sacakjg M H 39 394 CSHX39 7 0512 Ja sjha 41 l 3L5i34337hg i quotSnc Cream law L W 739 39 7 LB 1 1esEfz q zL wisfw W 5 56l Lag A c e nru1 A 7 H i a 9 7 i 39 A 3 gig 3 31531L1391LM1rl ib loL1M QIQA39 zm 7 ampLLLoai1 n n imaiqj 1W 31 1 no 7 9 u M His Wigsf 37543 An quot5quot 937quot r r i quot H631 S75 11 6 179741 116422 7 1 fig 23545 g 1 WM PFL39 m QLEL IQJL M1115 7 3 7 Y J l m 7 3t1Ho L5x 73 3 Mamp i IL 31915n435 113 Ml h i it Li 1 7 H He 4gu39mtga 9mg 39 7i i39l quotquotTuf 379711 7 i9 7 befji mM MEXWU SoLuKoN Special Assignment 2 ECE 350 Electromechanics Consider the power system below 4 25 W T3 gas 57 3E AA T2 I4 AA l T1 TL23 I G10 I I gt L3 1 A Y 2 3 2 395 System Data quot6 2quot 31 25 5239 32quot25 52 game 2 905 Vimquot T1 3 SinglePhase 75 MVA 138 kV664 kV Xe 5 Ya 3 2 25 quot 939 Z T2ampT3 1 ThreePhase 50 MVA 115 kV25 1ltVXe 6 39 Klgf Z 011082 j0649 Qmi y 5 3 2 MT TL23 125 mlles Z 3 k DX Q T Q 7 y 1661 uSml 3 525 w 39 L3 50 MVA 095 pflagging 1148 kV 2 C125 1 9 l o39er L4 Zy20j4 2 413118 7 System Bases 100 MVA 115 kV at bus 3 if 1 12203 L25 3 005 75 3 29 I 2 7 32147 03964 a Compute the line voltage bases at each bus gt See oumapqm 6 15 a b Compute the Y impedance bases at each bus 5 05 c 39 Draw the perUnit perphase equivalent circuit for the system o d Determine the required line voltage at the source in W V quot 9393 E e Determine the apparent power output in MVA and power factor of the source Determine the line volta e ma nitude at bus 4 in W 2 f 9 9 l a 53sz25 0353012 M a 33quot 0 50quot quot 39 DUE Mondav Julv 20 2009 QL Us Hlo 2136 A 3 1 Z 05 LL 036 3 I gt03512010 7 70 i lz tia 0393lL 4 4 mam 83 evflassuas 637 W 93 521000 SSXO Q Oquot6 139191 7 7 3 151 a 2 3611 we t05161559quot SOLUTION Special Assignment 3 ECE 350 Electric Power and Machines A three phase 60 Hz 2250 HP 4 pole 2300 V induction motor has the following equivalent circuit parameters R1 0029 0 X1 X2 0226 0 R2 0022 a Xm 13040 The motor is operated at rated voltage 1 Determine the magnitude of the starting current if started across the line 2 Determine the speed at which maximum torque is developed in RPM 3 Using a spreadsheet or MATLAB plot the following versus speed a Developed torque b Developed power c Line current magnitude DUE Thursday July 29 2010 Induction Motor TorquePowerCurrent vs R10029 X1O226 R20022 X2O226 Xml304 VL2300 zlRljXl zmjXm VinVLsqrt3j0 zthzmzlzmzljx2 VthVinzmzmzlL IstartVthzthR2 Imagabslstart smaxR2abszth wsm12060P2pi60 nmaxl smax12060P kO for sl 00lO kkl nkl s12060P RR2s ZzthR 1kabsVthZ if 50 Speed Tk0 Pconvk0 Tk31kA2R2swsm PconvkTkl swsm end plotnT xlabel39n RPM39 ylabel39Tem N m39 title39Torque SpeedW figure plotnPconv xlabel39n RPM39 ylabel39Pconv W39 title39Power Speed39 figure plotnI xlabel39n RPM39 ylabel39IL A39 title39Line Current Speed39 lma 28942e003 smax 00490 nn1ax 17118e003 Tem Nm Pconv W 10 TorqueS peed 1 200 1 400 1 600 1 1 800 1 000 1 1 1 1 200 1 400 1 600 1 800 n RPM 106 PowerSpeed 1 1 1 1 1 1 1 1 1 200 400 800 800 1 000 1 200 1 400 1 800 1 800 n RPM Line Current 8 peed 3000 1 1 2500 2000 i 1 500 1 1 000 500 O 1 1 1 1 1 1 1 1 0 200 400 600 800 1000 1200 1400 1600 1800 n RPM 1 A threephase 5 MVA 115kVY25kVA transformer has a series reactance of 6 The transformer supplies a 4 MVA load of at 085 pf lagging and rated voltage on the low voltage side Compute the line voltage magnitude in W on the highvoltage side 2 A bank of three singlephase 5 MVA 124734 kV transformers are connected AA Each transformer has a series reactance of 7 The bank draws a 08 pu apparent power at 09 pf lagging and rated voltage from a source on the low voltage side On the low side of the bank the system bases are 20 MVA and 127 W a Compute the high side line voltage magnitude in W b Compute the complex power in MVA and in rectangular form delivered to the load on the high voltage side 3 The bank of three singlephase transformers below is to be connected as indicated Make the remaining connections such that the appropriate standards for negative phase sequence operation are enforced Be sure to draw a phasor diagram A B C a b c 25kV72kV O O o T 0 O O O 4 Consider the machine stator and source illustrated below Connect the numbered phases to the lettered phases of the source such that the magnetic field will rotate in the counterclockwise direction Bahnced ThreePhase Source 60 Hz Poste Phase Sequence 5 Open and shortcircuit test data for an 900 rpm 60 Hz 50 MVA 138 kV Yconnected smooth rotor synchronous machine is provided below Field Current A 175 200 225 250 275 00 Line Voltage kV 120 130 138 145 151 SC Line Current A 1895 2166 2437 2707 2978 a Compute the saturated synchronous reactance in Q b The machine supplies A Yconnected load of impedance 625j150 Q at rated terminal voltage Compute the backemf voltage phasor c Under these conditions determine the required field current d Without changing the field current what is the maximum amount of real power the generator could supply to a load and remain stable 6 A threephase 300 HP 2000 V 6 pole 60 Hz Yconnected squirrelcage rotor induction motor has the following data R102 2 R2 0203Q X1 0707 Q X2 0707 Q RC Xm gt00 The machine has rotational losses of 4100 W a Determine the starting current that the motor will draw if started across the line b At starting how much torque will the motor produce c lfthe motor is operating at a 3 slip how fast is the rotor turning in RPM d With a 3 slip and rated terminal voltage how much power will be delivered to the load e At what slip will the motor produce maximum torque

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