EEL-5270 Electrical Transients in Power Systems. Lecture Notes. Set No. 1. Professor Osama A. Mohammed. Miami, Florida Spring 2017

Transcription

1 Florida International Univerity Department of Eletrial & Computer Engineering EEL-570 Eletrial Tranient in Power Sytem Leture Note Set No. Profeor Oama A. Mohammed Miami, Florida Spring 07 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

2 FLORIDA INTERNATIONAL UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EEL-570 Eletrial Tranient in Power Sytem SPRING SEMESTER 07 INFORMATION SHEET AND COURSE TOPICS COURSE INSTRUCTOR: Profeor Oama A. Mohammed, Ph.D., Fellow IEEE Energy Sytem Reearh Laboratory Department of Eletrial & Computer Engineering Room EC-3983 Florida International Univerity Miami, Florida 3374 USA Tel: + (305) (Offie), Tel: + (305) (ESRL Lab) Fax: + (305) (Offie) mohammed@fiu.edu Cla Time/Room: OFFICE: Offie hour PHONE: PRE-REQUISITE: CREDIT HOURS: F: :00-4:30 pm, EC-40 EC-3983 F :00-:00 pm (305) /807 (offie/taff) EEL-43 or permiion of intrutor. 3 Hour TEXT_BOOK AND NOTES:. Eletrial Tranient in Power Sytem by Allan Greenwood, Wiley, Seleted leture note by Profeor Mohammed and other demontration material and example will be made available at the above Web ite and/or in la. Who Should Take Thi Coure? FIU Eletrial and Computer Engineering Student who took EEL43 (power I) and Graduate Student. Student at other Univeritie in Florida or out of State with the oure prerequiite. Engineer and tehnial peronnel in Indutry preparing for Engineering Liene Engineer and tehnial taff who want to keep urrent and reah a deep undertanding of energy onverion onept. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

3 Objetive:. Introduing Eletrial Tranient in power ytem. Cover the onept of traveling wave and propagation 3. Modeling of tranmiion line a ditributed parameter ytem. 4. Diu iue related to inulation oordination, grounding and limiting of urge effet 5. Develop tehnique related to refletion at tranition point in line and able 6. Multi ondutor tranient and ditributed parameter modeling for omponent and hielding iue. 7. Involve tudent in a pratial experiene through the term projet. Coure topi: Introdution to Eletrial Tranient in Power Sytem (Ciruit opening and loing tranient, Reovery tranient. Traveling wave on Tranmiion Sytem (Propagation of Surge) Modeling of Tranmiion Line by Ditributed Parameter Conept (Lole ae, lo ae, ditrotionle ae, Line with mall loe) Ditortion due to Corona Energy in Traveling Wave Charateriti of Traveling Wave (wave hape, tandard, impule and withing urge, lightning, Bai Impule Inulation Level (BIL), Flahover urge generator) Analytial approximation of Surge Wave Shape Tranition Point (Line, Cable, Voltage Buildup, variou type of Tranition point, termination) Lumped Serie and Shunt Impedane Tranition Point (Juntion at Cable, Subtation Diimilar Voltage and Current Surge Surge Arreter (Linear and Nonlinear Charateriti. Sueive Refletion on Tranmiion Sytem Grounding Inulation Coordination Multi-Condutor, Multi-veloity Sytem Tranient Performane of Ditributed parameter Sytem for Tranformer, Generator and Motor Winding Shielding Pratial Example, projet Referene: Appropriate lit and opie of tehnial paper will be ditributed or lited for your olletion. A lit of reent text-book and other tehnial reord will be uggeted to you. However, you are alo required to reearh and obtained other pertinent material related to the topi overed. ASSISTANCE: Pleae try to ee Dr. Mohammed during hi lited offie hour or through the ommuniation forum on the web page. If thi prove impoible, a peronal appointment hould arranged by alling my diret phone number or the ECE department eretary at extenion ( ). ABSENCE: Cla attendane (phyial or virtual) i very important and i onidered in your overall performane in the oure. Student are reponible for all material overed in that la. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

4 IMPORTANT RULE: Student are enouraged to diu the oure topi with the profeor and with eah other. Any work ubmitted (Homework, Tet, projet, et.) hould be pledged and igned a the tudent' own work, and that there i no any unauthorized help wa obtained. Violator will be ubjet to aademi miondut, whih might lead to dimial from the univerity. GRADING POLICY: Homework will be aigned regularly, olleted and graded. Effort in homework indiate that you are tudying and aring about the oure and therefore an have an impat on your final grade. Time for the mid-term will be announed one week in advane. Any work ubmitted mut be neat and detailed for partial mark. Your Grade will be alulated a Follow: TERM PROJECT: Homework and Cla Projet 0% Mid Term 5% Term Projet/Reearh Paper 0% Final Exam 35% Total 00% The projet will involve one or more of the topi of thi oure. Final preentation (oral and written) of the overall projet reult will be required. Software available for thi la an be utilized for the projet. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

5 The Eletromagneti Pule (EMP) Effet EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

6 The Influene of a Charged Cloud EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

7 I. HOW LIGHTNING IS FORMED AVERAGE THUNDERCLOUD USUALLY BOTTOMS AROUND MILES (0,000 ) AND TOPS OUT AROUND 8 MILES (50,000 feet ) IN ELEVATION. TEMPERATURE IS ABOUT 40 o F AT BASE T0-65 o AT THE TOP. WARM MOIST AIR ON LEADING EDGE ASCENDS RAPIDLY FROM 40 o F TO -65 o F FORMING ICE CRYSTALS AND WATER DROPLETS. IT IS THIS RAPID ASCENT AND SWIRLING MOTION THAT FORMS THE ELECTRIC CHARGE. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

8 THIS CREATES A HIGHLY POSITIVE CHARGE IN THE TOP OF THE CLOUD (6 MILES AT -65ºF), A HIGHLY NEGATIVE CHARGE IN THE LOWER CENTRAL PART (3 MILES AT 0ºF) AND A SMALL POSITIVE CHARGE AT THE BASE ( MILES AT 40ºF). THE DIFFERENCES IN POTENTIAL RESULTS IN THE LIGHTNING STROKE. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

9 TYPICAL STROKE TO EARTH IS AROUND 5 MILLION VOLTS, 0,000 AMPS, WITH TEMPERATURE AROUND 50,000 o F. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

10 POINTS OF INTEREST YOU CAN TELL HOW NEAR THE STORM IS BY COUNTING THE SECONDS BETWEEN LIGHNING AND THUNDER. DIVIDE THE NUMBER OF SECONDS BY 5. THUNDERSTORMS ARE RESPONSIBLE FOR MAINTAINING EARTH S NEGATIVE CHARGE. LIGHTNING PRODUCES NITROGEN COMPOUNDS THAT ARE ESSENTIAL FOR MOST PLANTS. LIGHTNING KILLS MORE PEOPLE IN THE U.S. EVERY YEAR THAN TORNADOES, HURRICANES, OR FLOODS. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

11 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

12 AVERAGE THUNDERSTORM DAYS PER YEAR IN U.S. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

13 ELECTROMAGNETIC COUPLING ELECTROMAGNETIC COUPLING IS THE MOST COMMON WAY LIGHNING GETS INTO THE SYSTEM. AS A CHARGED CLOUD MOVES INTO THE AREA (OR BUILDS UP IN THE AREA), THE LINE BECOMES IMMERSED IN THE ELECTROSTATIC FIELD. WHEN LIGHTNING STIKES IN THE VICINITY (WITHIN A FEW HUNDRED FEET), IT MAY RESULT IN A COUPLING EFFECT BETWEEN THE FIELD AROUND THE STROKE AND THE LINE SIMILAR TO THE WAY THE COILS OF A TRANSFORMER OPERATE. THIS RESULTS IN OVERVOLTAGES (SURGES) ON THE LINE WHICH TRAVEL UNTIL IT FINDS A PATH TO GROUND. THIS POINTS OUT THE NEED FOR MAINTAINING A GOOD GROUNDING SYSTEM. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

14 II. HOW LIGHTNING GETS INTO THE SYSTEM DIRECT HIT EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

15 ELECTROMAGNETIC COUPLING - UNDERGROUND A DIRECT STRIKE TO EARTH IN THE VICINITY OF BURIED CABLE OR SPILL OVER FROM THE OH THROUGH THE RISER CAN CAUSE AN OVERVOLTAGE ON THE CONCENTRIC CABLE. WHEN THESE HIGHER VOLTAGES ARE PRESENT, THE DIFFERENCE IN POTENTIAL BETWEEN THE PHASE CONDUCTOR AND CONCENTRIC NEUTRAL CAN RESULT IN TREEING AND DAMAGED EQUIPMENT. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

16 PRE-DISCHARGE BUILD UP - B Ø WHEN SURGE IS PRESENT ON LINE, ALL 3 PHASES ARE AFFECTED. ARRESTERS, ON ALL PHASES, WHICH ARE COMMONLY GROUNDED LIMIT THE SURGE OVER VOLTAGES BETWEEN PHASES. IF THE GROUND RESISTANCE IS NOT LOW WNOUGH THE SURGE REMAINS ON THE LINE LONGER, POSSIBLY RESULTING IN DAMAGE TO THE ARRESTERS AS WELL AS OTHER EQUIPMENT. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

17 MULTI-GROUNDED WYE CIRCUITS MULTI-GROUNDED WYE CIRCUITS DEPEND ON INTERMEDIATE LOW RESISTANCE GROUND STATIONS FOR THE SYSTEM TO OPERATE PROPERLY UNDER ABNORMAL CONDITIONS. BECAUSE OF HIGH SURGE IMPEDENCE IN THE NEUTRAL CONDUCTOR, IT SHOULD NOT BE COUNTED ON TO DISSIPATE THE SURGE & OVERVOLTAGES OR TO CARRY THE SURGES TO THE SUBSTATION FOR DISSIPATION. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

18 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

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20 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

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22 Comparion of variou ditribution line protetive meaure. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

23 B.I.L. - BASIC IMPULSE INSULATION LEVEL THE ABILITY OF ANY MATERIAL OR DEVICE TO WITHSTAND A PRE-DETERMINED IMPULSE LEVEL. EXAMPLES: PIN INSULATOR - 00 KV 35 KV INSULATOR (POST) - 80 KV ANY POLE IN SALT SPRAY AREA - 0 KV CONCRETE POLE - 0 KV WOOD POLE WET - 75 KV/FT DRY - 00 KV/FT WOOD X-ARM WET - 75 KV DRY - 00 KV/FT AIR - 86 KV/FT 3 KV TRANSFORMER - 95 KV 3 KV TRANSFORMER - 5 KV EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

24 B.I.L. - BASIC IMPULSE INSULATION LEVEL BIL OF 35 KV SKIRTED INSULATOR IS 80 KV - WHEN BOLT EXTENDS OUT TO COVER - 3 SKIRTS, BIL IS REDUCED. EXAMPLE: BOLTS EXTENDS OVER 3 SKIRTS 80 KV - 90 KV = 90 KV AIR GAP BETWEEN BOLT & INSULATOR = + INSULATIONS VALUE OF AIR = 5 KV PER THEREFORE BIL IS APPROXIMATELY 05 KV EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

25 B.I.L. - BASIC IMPULSE INSULATION LEVEL CONCRETE POLE 35 KV INSULATOR - 80 KV CONCRETE POLE - _ 0 TOTAL BIL 80 KV WOOD POLE 35 KV INSULATOR - 80 KV WOOD POLE (WET) - 75 KV/FT 75 KV 80 KV x_ 3_ 5 KV 5 KV TOTAL BIL 405 KV EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

26 INSTALLATION OF GROUND RODS -----PREFERRED METHOD----- RODS DRIVEN VERTICALLY IN TANDEM DOUBLING ROD LENGTH REDUCES OHM READING BY ABOUT 40% EXAMPLE: 0 FT DEEP ROD - 30 OHMS 40 FT DEEP ROD - 8 OHMS EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

27 INSTALLATION OF GROUND RODS ALTERNATIVE TO DEEP DRIVEN ROD CLUSTERED RODS - MULTIPLE RODS DRIVEN IN PARALLEL AND CONNECTED TOGETHER - WHEN - ONLY WHEN INITIAL ROD(S) ARE DRIVEN TO REFUSAL BEFORE SPECIFIED RESISTANCE IS REACHED EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

28 ALTERNATIVE TO DEEP DRIVEN ROD INSTALL GROUND ROD AT ANGLE RECOMMENDED ONLY FOR AREAS WHERE HARD ROCK PROHIBITS DRIVING RODS VERTICALLY DEEP ENOUGH TO ACHIEVE SPECIFIED OHMS. EXAMPLE: - ROD DRIVEN VERTICALLY TO 0 DEPTH - WHEN DRIVEN AT 45 ANGLE WILL HAVE 8 OF ROD IN CONTACT WITH EARTH MAY LOWER RESISTANCE BY 0% - 40% OVER RODS DRIVEN VERTICALLY EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

29 TESTING OF GROUND RODS EQUIPMENT FUSE TESTER VIBOGROUNG ( M&S # ) MEGGER EARTH TESTER (M&S # ) EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

30 EARTH RESISTANCE VS. INSULATION RESISTANCE METERS EARTH RESISTANCE METERS OPERATE ON FREQUENCIES BETWEEN 97 Hz AND 5 Hz. INSULATION RESISTANCE METERS OPERATE ON FREQ. IN 60 Hz RANGE. INSULATION RESISTANCE METERS ARE SUSCEPTIBLE TO STRAY GROUND CURRENTS OR D.C. CURRENTS WHICH INFLUENCE READINGS. INSULATION RESISTANCE METERS ARE NOT TO BE USED FOR EARTH RESISTANCE TESTING. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

31 FUSE TESTER 3 AMP > 5 OHMS 8 AMP > 0 OHMS FUSE IS DESIGN TO BLOW AT - / TIMES ITS RATED VALUE 3 AMP FUSE WILL BLOW AT 4-/ AMPS 8 AMP FUSE WILL BLOW AT AMPS OHMS LAW E = R X R = E / R = 5 / 4.5 = 5.5 OHMS R=RESISTANCE I=CURRENT E=VOLTS EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

32 VIBROGROUND AND MEGGER EARTH TESTER NULL BALANCE INSTRUMENTS USED FOR MEASURING EARTH RESISTANCE METHOD FOR USE: POINT METHOD 3 POINT METHOD EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

33 POINT (DIRECT METHOD) MEASURE RESISTANCE BETWEEN GROUND ROD AND SURROUNDING EARTH USING THE SYSTEM NEUTRAL AS REFERENCE. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

34 3 POINT (FALL OF POTENTIAL) MEASURE RESISTANCE OF GROUND ROD AND SURROUNDING EARTH USING POTENTIAL AND CURRENT PROBES AS REFERENCE. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

35 TESTING GROUNDS AT EXISTING LOCATIONS TEST FOR 5 OHMS OR LESS IF 5 OHMS OR LESS NOT ACHIEVED, THEN: OPTIONS:. DRIVE ADDITIONAL RODS ON TOP OF EXITING RODS TO ACHIEVE 5 OHMS.. MOVE OVER 0 IF POSSIBLE (6 MINIMUM) AND CLUSTER RODS 5 OHMS. 3. ABANDON EXISTING INSTALLATION AND DRIVE NEW RODS TO ACHIEVE 0 OHMS IF POSSIBLE WITH 40 OR LESS (AS PREVIOUSLY SPECIFIED) EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

36 GOOD CONSTRUCTION PRACTICES RELATING TO GROUNDING THERE ARE MANY THINGS WE CAN DO TO IMPROVE OUR GROUNDING SYSTEM AND SERVICE RELIABILITY. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

37 INSTALLATION AND ATTACHMENT OF GROUND RODS ALL GROUNDING CONNECTIONS ARE ELECTRICAL WIRE BRUSH AND USE INHIBITOR TIGHTEN COUPLINGS FOR EACH SECTION OF GROUND ROD USE SEPARATE CLAMP OR CONNECTOR FOR EACH CONNECTION EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

38 SURGE ARRESTERS AND LEADS MAKE ALL LEADS AS SHORT AS POSSIBLE AVOID SHARP BENDS AND KINKS (EACH KINK INCREASES IMPEDANCE BY 0%) DO NOT COIL WIRE AVOID KINKS ON ANY BONDING WIRE EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

39 I. Eletrial Tranient in Power Sytem. Ciruit Cloing Tranient What i of importane?. The loing of a iruit breaker to energize a load.. The opening of a iruit breaker to lear a fault. Conider the following iruit: R R Steady tate power fator = z R L EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

40 Auming an ideal oure (mall impedane ompared to load) v( t) V in( t ) m = arbitrary phae angle to allow a general tudy of the intant of withing At loing of the with,, we an write: Ri di L dt V m in( t ) Rewriting the ame equation a: di Ri L Vm[int o dt ot in ] Laplae tranforming both ide give: o in RI ( ) LI ( ) Li( o) Vm For i( o) o initial value of i EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

41 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved, in o ) ( L R L V I m Try to put thi equation in a imple form. Define. L R L V B L V A m m in o ) ( B A I L give after arranging t m e t L R V t i in ) ( The firt Term i the Steady State Part The eond Term i the Tranient Part

42 If the breaker loe at time, t, uh that the tranient term beome zero, and the urrent wave beome ymmetrial. If the breaker loe at time, t, when the tranient term i maximum and the peak of i(t) will approah (x teady rate) [Pratial onideration in iruit breaker deign] EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

43 . Ciruit Opening (Fault Removal) Tranient Reovery Tranient: The tranient aompanie the removal of a fault from a power ytem. Aume L= indutane of a tranmiion ytem (line and a tranformer, et.) C= natural apaitane of the ytem adjaent to the breaker (apaitane to ground through buhing, CT, main tranformer, T-Line, et. Ciruit Reitane and other type diipation element are ignored. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

44 When a fault our on a ytem, a ignifiant (in fat very large) amount of fault urrent flow. The opening of a iruit breaker ontat by itelf doe not interrupt the urrent. (An ar will be etablihed between the ontat, the urrent will ontinue to flow. ) Sueful interruption depend upon the ontrol of the ar. In an a iruit, the urrent pae through zero twie per yle. At one of thee intane, urrent will be interrupted. In the iruit under diuion, the urrent lag the voltage by and i limited by the indutane. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

45 The voltage at the breaker ontat will be the ar voltage. Ignoring the ar voltage ine the oure voltage i inuoidally varying and i at it peak at the intant of fault urrent i interrupted. Hene: v( t) Vm ot The interrupted iruit equation i given by: and o di L v dt dv i dt di dt d v dt v( t) Therefore; d v dt L v V L m ot Before the breaker interrupt the fault urrent at t=0 v i (0) 0 0 dv (0) (0) 0 0 v (0) 0 0 dt EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

46 Tranforming into Laplae v ( ) 0Vm 0 L v (0) v 0 (0) v 0 L ( ) Applying the initial ondition, give the following for () v v 0Vm ( ) 0 Obtaining the invere Laplae Tranform, yield 0 v ( t) Vmot o0t 0 Repreent the voltage aro the iruit breaker ontat whih i alled Reovery (Retriking) Tranient Voltage ine v 0 then ( t) V ot o t m o EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

47 Reovery Tranient (voltage) Aro Breaker Contat For 0 v ( t) V o t m 0 It an be eaily een that for, 0 t, the value of v (t) would be v t V m 0 0 If the natural frequeny i high (L or or both are mall), the voltage v will rie very quikly with time. If the rate of appliation of the reovery voltage hould exeed the rate of build up of the dieletri trength in the medium between the ontat of the breaker, EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

48 the breaker will not be able to hold off and ar from reigniting. Thi reult in the breaker and the power ytem omponent arrying the fault urrent for at leat another / yle until the urrent beome zero again. Thi phenomenon i of o great importane for hort T-Line in whih both L & C are mall. The effet i alled kilometri fault EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

49 Example: for a partiular hort tranmiion line 3 L 0 Hene, Farad. 0 3 f Hz T0 ( period) 4 0 e If thi line i rated 3.8 kv, the voltage ould poibly rie to twie the peak line to neutral value in a period of T 0 i.e. v T Rate of 0 voltage rie = K.volt.to neutral Per Phae voltage TimePeriod kv / e. Suh aral from pratial experiene i beyond the apability of any C.B. (Notie Dieletri trength of air i 30 kv/m) 6 Vel. of Separation of breaker ont..= m / e. 3.5km / e. (Mehanially impoible) km / hr 3800mile / hr EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

50 Example of Fore Calulation (Subequent to S.C.) or loing of a breaker I i p. u (max) A i Intantaneou wort ae A.. I 0I H, B r r F / meter I B IB F / m 8000 F / m.8 Newton/Meter Cond. Length (H.V. Side 345 F / m Newt 0 3 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved, / M -50

51 Effet of Current Aymmetry on Reovery Voltage: When a iruit breaker i loed at random, it i likely that the urrent during the tranient period will lak ymmetry a hown below: In a three phae ytem, the voltage are 0 apart. During the tranient period, aymmetry will reult in one or more of the phae. The aymmetry will depend on the time in the yle at whih the fault our. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

52 The iruit breaker interrupt at an intant of the yle at whih the urrent i zero. The reovery voltage will oillate around the intantaneou value of upply voltage. With aymmetrial fault urrent, the upply voltage (ytem voltage) will no longer be at it peak. The tranient reovery voltage i not a high a wa hown earlier. Effet of Current Aymmetry on Reovery Voltage EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

53 Effet of Ar Reitane on Reovery Tranient In ae where the ar voltage drop (aro ar reitane) annot be ignored, from a quai-quantitative tand point, the ar drop i heavily reitive. Thi ha the effet of bringing the urrent to be interrupted no more in phae with the voltage. Thi ha the effet of making the point of zero urrent our at point in the yle at whih the ytem voltage i not at it peak. Thi ha the effet of reduing the firt (harpet) peak of the tranient reovery voltage. Effet of Ar Reitane on Reovery Voltage EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

54 3 More Complex Reovery Tranient Conider an elementary power ytem whih may onit of a oure and an unloaded tranformer a hown below: Suh a ytem an be repreented from iruit point of view a follow: L and C repreent the indutane and tray apaitane on the oure ride of the breaker. L and C may repreent the indutane and tray apaitane of the unloaded tranformer. When the iruit breaker open in uh a power ytem it ompletely iolate the load ide from the upply ide. After the intant of breaker operation, the two halve of the ytem behave independently. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

55 What happen following uh a withing operation? () Before the breaker open, the upply voltage will divide in proportion to the indutane (apaitor repreent a high reatane path). The voltage aro the apaitor i: v ( t) L L v( t) L () For all pratial purpoe, the tranformer indutane, L, will be muh larger than the oure indutane, L. Hene, C and C have a voltage v (t), whih i approximately equal to the full upply voltage v(t). (3) Following the urrent interruption, C will diharge through L and a natural frequeny f. f L C Figure (b) on the next page how that thi tranient will be damped by iruit reitane. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

56 Double Frequeny Reovery Voltage (4) C, on the oure ide, harged to a voltage near oure voltage level, will exhibit a reovery tranient voltage wave hape hown on the next page. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

57 In thi ae the natural frequeny i maller than the ae diued earlier due to the initial harge on the apaitor C. f L C Thi i hown in figure (a) on the previou page. (5) The voltage aro the breaker i made of the differene between v (t) and v (t). The reult i hown in Figure () on the previou page, whih i (wave(a)-wave(b)) The above ae how a reovery voltage wave with two ditint frequenie f & f. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

58 An even more omplex ae Conider the following ae whih i enountered quite frequently in the ae of a iruit breaker learing the fault on the eondary ide of a tranformer a hown below: Elementary Power Sytem With Double Frequeny Reovery Voltage. The equivalent iruit beome a hown: Equivalent Ciruit of Sytem EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

59 In the equivalent above L repreent the indutane up to the tranformer and L i the leakage indutane of the tranformer. C and C are the ytem natural apaitane on either ide of the tranformer. Aume that during the period of interet, the oure voltage will remain ontant at a value V than: v ( t) V Under 60 Hz, C repreent a very high reatane path. At t=o before fault i leared L (0) V L L v and hene v (0) 0 0 Alo, the fault will be leared at an intant when i (t)=i (t)=0 So, from the equivalent iruit EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,

60 EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved, dt di L dt di L t v t v dt i v t v dt i i v dt di L t v t v t t 0 0 ) ( ) ( (0) ) ( (0) ) ( ) ( 0 Sine v(t)=v, Laplae tranform to the following: ) ( ) ( ) ( ) ( ) ( (0) ) ( (0) ) ( ) ( ) ( ) ( (0) (0) ) ( ) ( ) ( ) ( (0) (0) ) ( V V L V L I v I i L I L L i L I V V I V L i v V I I L I I v L i L I V OR and and and 0 0 0

61 Let A B L L L L L L and,one ha V ( B ) AV ( )( ) ( )( ) Uing the partial fration tehnique one an how that the invere Laplae tranform i: v ( t) AV B AV o t B ot If, we an obtain a ondition under whih the voltage v whih will how aro the breaker ontat might reah a high a (3V). *The algebra get rather involved quikly a more iruit element are added. The propagation of urge on power T-Line i diued next. EEL-570 Eletrial Tranient in Power Sytem, Prof. Mohammed, Copyright All right reerved,