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# STControl Systems and Critical Infrastructures ECE 504

UI

GPA 3.81

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This 150 page Class Notes was uploaded by Fredy Okuneva on Thursday October 22, 2015. The Class Notes belongs to ECE 504 at University of Idaho taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/227740/ece-504-university-of-idaho in ELECTRICAL AND COMPUTER ENGINEERING at University of Idaho.

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Date Created: 10/22/15

172 39OU NOISSEIS NOIJQELLOEId SWELLSAS HEMOd CEDNVACIV LLS dVbOS EDS y Ob nag nag T N 4 n wmm a wu Jur 2 H ova Em m rff QJCREf My MA m Universityafldam aqepw lgmmgun m m E amp wag agmwiabm mzca E m Universityofldahe Lw m Universityo dahe MM m Universityo daho 5w QsmEEbm QED asm t vbm gmg a 99 390quot NOISSEIS All39llEVlS SWELLSAS HEMOd 31 Sd39VOS EIGEI m Universityofldahc I E OVA Va A P quot39 MM 5 35 gt34 53 6 E1 value t39e 39ftc WK 1 will sdrr we 46 g Jov jo fg m Universityafldaho Gl B 9 C tar e a pig r lvy h A s m Universityofldaho I Er quotgaffer F r a JUamph cya mw 41 hf 00050 chor 0 whoa 5quot1395615 c g t 5 C4 tquot 99 VGO39L39 J A 4550c r 1 W at em pk u 3 QSQEDSEEQED g m Universityafidahc Simn IarLl 44c Ixn raw WKquot 0 0 MM jafy V67 A quot5 C6 39Ke W c W iov c 95 06er r k A z 3 m Universityofldaho L09 4r VI 6 VJ Q 59 if I g quot Fr 4 M Q 0 wiw are 0r 39 0 an L c f hf 340W g 0 5031 A0 rm asmvteb gmzcz g m Universityofldahc 39 L2H I rquot quot 9 quotquot quot 455 I L c 1 54 a wvt he fin Jeane arc a 117 2 a quotA03 3 m 6L 1 ozmutcb EZQD s H WW 7 137 2 NW5 05 3 Aquot f39 743 Swan3w 39IOW OHEPHOMQSJSAQUn m m II x g NH 2 I 3 ozmu ob gg z m Universityofldaho is 2 20 At A a 2 An 45quot a 9 At a C cw i3 m Universityafldmm L4 3 a 44 AU M N Hfquot O m ltasiniversityafEdahc K W a 6155 MM 0 EmEkbEgED g Emu Beige amp mumw OngKobEgED E f m Universitya daha I39M 9 R 3 91 1 4 1 M ON 2 mgtd n 3 a w w c r I a E l 37 c Emwtabm wzpi s m Universityafldaha 2 NW ozmntobmagtm3 E an oswngttmEgtED E m Universityofldam quot W I Cam 1 Z QC 39 34 f la y I 5 00w h s 33 S osmvicbwmgt53 17 39OU NOISSEIS NOLLDELLOHd SNELLSAS HHMOd JEDNVACIV 5LS dVbOS EDEI m Universityofidaha a C3mltmwmm awamrg 1 ha st gs 9 aomQ m Universityefldahm Te fps M 40Iw3 39 Je 1 Ah I les 7 W my 395 00st amp t 7t w l t er Mi 39 39 v 01 Lose W S 700 a f 7 quot ige f I d f 2 56x35 Universityofldaha 2 wquot M V amp J 5573 as Uh uh Lh 3 353 s m Universityofldaha W W w u M m Universityafidahm gmmgbmegmt g osmntobmmazc E 62 390 NOISSES All39IIEVlS SWHLSAS EEIMOd LLS Sd39VOS 333 V ER E OLMEEDEQED s Universityofldaho Universityofldaho ZS 39OU NOISSEIS NOLLDEIiOtld SIAIELLSAS HEMOd CEDNVACIV LLS dVbOS EDEI Universitycafldahg 66wan 40 s s or 75599 PM 75671010 ANSI 6 0 Factors Limiting the Active and Reactive Bower Delivered by a Generating Unit Generator capability curve Voltage limits Steadystate stability limit Minimumexcitation limiter 39 Overexcitation limiter OEI Generator Capability Curve 3r Current L quot 39 Armatqg urr3nt M W 410 453 P MW Capability Curve of a 160MW Generator Including MEL and OEL 7 HziPte gr gU 39Ifff fquotquot39quotT T39fil gihqVJL WZOMPa EM L Factor v 6085 7 U quot39quotLe ading 39 7 Power39 Factor Voltage Phasors Determine System Power Flow LossofField Condition Reduces Machine Power Output t 1 T E3 13 E E 396 n5 A X RR 04 I If Tf0 time constant for open field condition Reducing Generator Excitation May a Cause Loss of SteadyState Stability LOF Simulation Cases Two initial load conditions 150 40 MW Two modes of loss of field 9 Field Short oilrouit o Field breaker opening with disoh insertion Two initial operating conditions plant one and two generators c and arge resistor in the power in he Field Short Circuit 150 MW enerators On Line mqg 5 i i w m mewpbwmw m mmom wvr r q s i g e D Q 5 l i i g I 9 s u E 391 x a 3 C3 HMquot 33 i f quot39 quotquot39quot393quotquot 39 quotquot quotquot39 Pquot 55 1 E 3 E Z ux m Generator Protection Functions Related to the CapabilityCurve o Statorthermal protection Rotorthermal protection i MotOring protection OverVoltage protection Undervoltage protectilt Lossof field protectiOI Effect of the LOF Condition 0n the Generator and the Power System 0 Generator 9 Rotor overheating o Stator overheating 0 Large pulsating torques 0 Power system 9 Lowvoltage conditions possible voltage coHapse o Possible loss of steadystate stability LossofField Protection Using a NegativeOffset Mho Element MP W R LassofField ImPGdance Trajectary Relay Operating Charac eristic TwoZone Lossof Field Protection Using NegativeOffset Mho Elements TwoZone LossofField Protection Using a Positive Offset Mho Element Supervised by a Directional Element Pour 4r PunMe a0 4 hunt5 1 ti s is i J u V sagging 39 1 e t a r e D x S e n 0 Z t any m H r m m E F O L h t 0 B Xt Representation Gives a Threea Dimension View of the LOF Process II R in Secondary Ohms2 sumo mpuoasg u T I JX Q PlaneBased LOF Element Detects LossofFieid Condition agSEQ Power Case l L P w m away Tyajxahtczzsry 5 as I 5 I Eif mmwmzeuaaaaw J E u l A A v verM39vanvgmN v tuwnmmir mwwma a m a i e a NWquot 2 i M wwwmmw 4 l i W 1 Di TWPJV SE 39OU NOISSEIS NOIJDELLOHd SIAELLSAS HEMOd GHDNVACIV LLS dVbOS EDEI 2 E i xo im 9E2 m Universityo dahm m ngamSJaxgun 53 m Universitya dahg HM ya u s39 1 i 37 um SS 8 390 NOISSEIS All39ll VlS SWELSAS EElMOd LLS Sd39VOS EIOEI Emu Sumac aw 2 235 Mam 0st Emsz amp 3 Un iversityof Idaho Pil m39 0 V39mn 0 Mg39n VVCNG EL A www 9 SE 0 N 8 53292 MW V 3 mm 3 3w Uh ozmnzoa mzca m 2 52552 amp LV H mm W 3 05mg 52562 WWW m v 72 W o Eng 52552 Mama Em U Bb mzca ax vux 37 E 08 32552 MW SE 39OU NOISSEIS NOLLDELLOEId SIAIELLSAS EEIMOd CEDNVAGV LLS dVbOS EDS m Universitya daho a 1WD it Iva7L1quot Qqepll lgSJaxgun m i szmwquclamrg ban h 91x glna Hw grw Ca 3 A c kN th 3a m Universityafldah m Universityofldahm m Univers tyefidahm Qsmut m mgtmc i m Universiaof idahm w am jF alI aoJe quot3 n 4 mg S eewa mmquot 4quot 0 in j mam M00 3 6 1 Emme 352 g 93Vxc mgtc3 s oxmn ex wzcs E 95 532 i acmntob kgfn i ECE 504 Special Topics Power System Stability l Define the Situation Session 39 A machine connected to an infinite bus through a stepup transformer and a line The line is opened for a short period of time and reclosed Machine Xdp 00225 H 35 Pm 09 Vt 10 Transformer XT 015 Line XL 0 5 Tc 01 System 000 27560 00 376991 ll Goal a Determine the inital conditons ie the internal voltage and torque angle b Determine the torque angle at the time of reclosur c Determine the maximum torque angle PJLAVVCassesS05PSS HAN DOUTSs39 mcd Page 1 of 4 April 22 2005 ECE 504 Special Topics Power System Stability Session 39 quotI Take Action J H a X Xdp XT XL X 0672 s Pm jng I 3 Vt III 0949 argI 718435 deg Vinf 3 Vt 139le t XLI lvinfl 0995 argVnf 736006 deg Shift to using Vinf as the angle reference A9 7mgvmf A9 36006 deg jAe v 7 jAe in I IeJ39Ae lit 9 Calculate E E vt jXdpI HE 010 50 argE sod 4 PJLAWCIassesS05PSSHANDOUTSs39mcd Page 2 of 4 April 22 2005 Power System Stability ll Session 39 ECE 504 Special Topics 7 ImeIIIEI P 7149 max 397 X max 7 39 c 0 5C 7 0918 Pm 7 Pmax 51115 d5 Pm d5 7 Pm 7 PmaXsin5 d5 o JSO JSO J50 PmSC 7 50 PmSmax 7 5C PmaXcos5max 7 PmaXcos5c 0 7Pm 50 7 PmaXSc PmSmax PmaXcos5max 0 PmSO PmaXSc Pm smax constant Pm50 PmaXcos5c constant 1489 Smax 90 deg Given constant PmSmax PmaXcos5max smax 7 Find5max smax 7 1442 5 7E Pe55g PmaXsin 150 1 Pmax cos 5 max April 22 2005 PJLAVVCassesS05PSS HAN DOUTSs39 mcd Page 3 of 4 ECE 504 Special Topics Power System Stability Session 39 06 04 02 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 55g PJLAVVCassesS05PSSHANDOUTSs39mcd Page 4 of 4 April 22 2005 ECE 504PS ST POWER SYSTEMS STABELI39W SESSEON no 28 u gmm m leum a wax 3n b r mqg IF 3L3 x V P 3 ECE 504 Advanced Electric Machinery Session 12a Law JD amp AS Spring 2007 Page 16 DIRECT AXIS SYNCHRONOUs MACHINE EQUATION MANIPULATION FOR THE PURPOSE OF SIMULATION IGNORING DAMPER WINDINGs NonReciprocal Per Unit System B 7 l with Lmdu l and Rfd l 1 Variables Inputs Vfd and ids Output Vds Internal 139 fd and e LLfifZWfd Unknowns Vds 139 fd and 61 ie output plus internal variables Note There are 3 unknows Therefore we need 3 equations 11 Voltage Equation P 7 R 1 Vfd DB Vfd fdlfd III Flux Linkage Equations Vfd Lffdl39fd BLmdids 2 W Ldids Lmdifd 3 IV Solve for the Input to the Integrator Select 6 as the output of the integrator Modify Eq 1 such that it is in terms of 6 instead of Vfd L L Mult1ple Vfd by 1 1n the form of p Lffd Lmd if 7 R 4 W 03 Lmd Lfdefd fdlfd Equation 4 can be rewritten as L L we R 39 5 W DBLmd q fdlfd 0 I Lmd where e 7 d 6 q Lfdef ECE 504 Advanced Electric Machinery Session 12a Law JD amp AS Spring 2007 Page 26 Dividing Eq 5 by R fd yields Vfd Vfd Lffd I 7 Rfd 1 V fd P DB Lmd Rfd 6 lfd Solve for e DB Lmd Rfd quot t dt 0 8 eq Lffd 0 Vfd W A subscript u denotes the unsaturated value of an inductance Noting that L ff and Lmd change approximately proportional to each other ie LLmd gLLmdM ffd ffdu L d DBRfd quot e39 t L v z dte39 0 10 q Lffdu 0 fd fd q The directaxis opencircuit transient time constant is de ned as d 4 i d 17I Lff u ffi 7 X 1 1 do 13 R fd DB R fd m pu ffdu ffdu Using the de nition of 1710 Eq 10 can be rewritten as Lmdu it 810 if vfd zfddte0 12 Rewriting Eq 12 to take advantage of selecting Lmdu 10 yields 1 it em A vfd ifddreq0 13 ECE 504 Advanced Electric Machinery Session 12a Law JD amp AS Spring 2007 Page 36 V Solve for 139 fd in terms of e and ids Solve Eq 2 for Lffdifd Lffdifd Vfd BLmdids 14 Divide by L ffd V d L d wif 6 quot ms 15 Lffd Lffd Multiple Vfd by l in the form of 2 L L lfd id Wfd B mdl Lmd Lffd Lffd Using the de nition of e from Eq 6 rewrite Eq 16 1 d i4 BLmdzd 17 f Lmd Lffd S The de nition of the directaxis transient inductance is given below L2 L E Ld M 18 Lffd Solvin E 18 for a ieldS39 g q Lm y L2 BdeLdLI 19 Lffd Dividing both sides of Eq 19 by Lmd yields L L L39 5 md d d 20 Lffd Lmd ECE 504 Advanced Electric Machinery Session l2a Law JD amp AS Spring 2007 Page 46 Noting that Ld L21 and Lmd change approximately proportional to each other BLmd Ldu Ldu Lffd Lmdu Rewriting Eq 21 to take advantage of selecting Lmdu 10 yields L M Ldu Lu 22 Lffd Substituting Eq 22 in to Eq 17 yields eq lfd i Ldu Ldulds 23 Lmd VI Solve for Vds in terms of e and ids Copying Eq 3 here for ease of reading st LdidsLmdifd 24 Substituting 139 fd from Eq 17 into yields Eq 24 elq BLmd st Ldlds39l Lmd i Ids 25 Lmd L ffd Using the distributive property of multiplication Eq 25 is rewritten as L2 Vds Ldids39l 6 E mdids 26 ff1 Combining terms that include ids yields 3L2 wds e Ld 39quotd m 27 Lffd ECE 504 Advanced Electric Machinery Law JD amp AS Spring 2007 Session 12a Page 56 Equation 27 can be rewritten making use of the de nition of the directaxis transient induc tance st e Lizids Noting that Lg 2 Lg Equation 28 can be rewritten as Ids eq Ldulds VII Summary e39titv z39 dte 0 1 goo fquot fquot 1 e ide Lid Ldu leuids quotI Q stU 8 L1uid3 X d L d Tl ff 1 ff 1 L X do mBRfd DBRfd 1n pu ff 51 ff 51 2 BLmdu L39 Ld dquot u Lffdu 28 29 30 31 32 33 34 35 9 390quot NOISSEIS AJJ39IIEVLS SWELLSAS HEIMOd LLS Sd39VOS 333 ocmnto mhmzcs 17 390 NOISSEIS All39IIEVlS SWELLSAS HEMOd 31 Sd39VOS 333 osmntob ggEn E ocmvTab gg a w Universityofldaho ko o fmv f MIAu Z 3 204 ZHA a a T g KWu w 2 m Universityofldaho Ageme 2 oqeplloJQSJaAgun Universityofldaho 5 ceJ rial m Universityofldaho O MU kobmmgwgtr3 I K osmvtob ggEa s avg Viabigmzcn E ocwniob hng g 72 390 NOISSBS II ILLI IIEI VLS SWELLSAS dBMOd VOQ 333 WNW 95652 8530 lt N 1 Pm KW 94 iv Q 3 429 2 a 73aux 4 id w a 5L5 392 CHEM Magmanun 35 313 Universityof Idaho WW7 Ho v is if 7 at N 0 w W 4 quotquot1 town5 lo 9 A uvyr A thc mac1W9 lace w ouep JUMSJeuun gig X3 Ni i 31375 Q 6 c XS 0 2 k A OVSDWOL N kn tut Rb i amp1 2x ng 05mg Bbmmgt3 luv Wm 931 Universityof Idaho 5 ha I I 5 17 5 5 5417 5 rt 90 wtf39 PE 0532 BEEQED luv Mm Universityof Idaho 010 4 r 5 W 42quotquot hC39 5 IO 9 10k 9 I 39m quotOVMGIIY s 3 skul 0002 f Universityof Idaho V 5 16 7c 47 UdJDL 00g Emu o2mmgt3 WWW 332 Universityof Idaho 5 3m w 39fquot l L W 5 R 2L0 W W Ly11 39 Es T L Cap W 3 ULTC

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