TRANSIENTS. Lecture 5 ELEC-E8409 High Voltage Engineering

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1 TRANSIENTS Lece 5 ELECE8409 Hgh Volage Engneeng

2 TRANSIENT VOLTAGES A ansen even s a sholved oscllaon (sgnfcanly fase han opeang feqency) n a sysem cased by a sdden change of volage, cen o load. Tansen Popagaon wave (chaacesc) mpedance popagaon speed enegy ansfe avelng wave aenaon Tansen Reflecon Lace Dagam hps://noppa.aalo.f/noppa/kss/s8.50

3 TRANSIENT PROPAGATION The wave can be analyzed n elaon o me As he volage wave pogesses along lne, chage s also dsplaced Cen flows n we If lne s ndsoed, volage and cen waves ae dencal v v, x 0 0 Dx x x 0 A volage wave popagang along lne meased volage (cen) a pon A hps://noppa.aalo.f/noppa/kss/s8.50

4 SUPERPOSITION PRINCIPLE ð Conscve/descve nefeence of ovelappng waves Sqae wave Wedge wave S S ( 0 ) Sawooh/Tangle wave S S S ( 0 ) ( 0 ) hps://noppa.aalo.f/noppa/kss/s8.50 4

5 TRANSIENT PROPAGATION A lne consss of he followng componens (pe n lengh): Ressance Opposon of cen Indcance l Indced elecomove foce opposng he change n cen Condcance g Ease of eleccy flow hogh an eleccal elemen Capacance c Amon of elecc chage soed fo a gven poenal d x ldx dx x gdx c d x dx x x x dx hps://noppa.aalo.f/noppa/kss/s8.50 5

6 TRANSIENT PROPAGATION Wave Impedance l w c a (α aenaon faco) ð Dependan on lne popees, b no s lengh ð No dependan on volage o cen ð Indcance l and capacance c (pe n lengh) depend on pemeably μ degee of magnezaon of a maeal pemvy ε maeal's ably o ansm (o "pem") an Efeld of he nslaon maeal (bae condco/nslaed cable) hps://noppa.aalo.f/noppa/kss/s8.50 6

7 TRANSIENT PROPAGATION Fo a sngle a nslaed condco: l m0 ln p h c ln pe 0 ( h ) m0 h h w ln 60ln p e 0 W h condco hegh, condco ads μ 0 pemeably of vacm (4π 0 7 Vs/Am) ε 0 pemvy of vacm (8,85 0 As/Vm) c speed of lgh n vacm (00 m/µs) Popagaon velocy v me c m e Popagang wave avels a speed of lgh n a nslaed lossless cable ð In ealy, losses and coona decease popagaon velocy hps://noppa.aalo.f/noppa/kss/s8.50 7

8 TRANSIENT PROPAGATION Popagaon pah w [Ω] v [m/μs] Smple cen condco Bndled condco 0 65 Lghnng sheld we Cable Undegond condco Eahng condons (essance) can sgnfcanly ale vales As a le of hmb, bae condco wave mpedance s appoxmaely 0 mes geae han an nslaed cable hps://noppa.aalo.f/noppa/kss/s8.50 8

9 TRANSIENT PROPAGATION Popagang wave enegy and powe ð Insananeos powe p (,, ae nsananeos volage and cen) ð Enegy of popagang wave W T ò p d 0 T ò 0 d Enegy s soed n he elecomagnec feld of he popagang wave Half n he elecc feld Half n he magnec feld hps://noppa.aalo.f/noppa/kss/s8.50 9

10 TRAVELING WAVE ATTENUATION Lne losses Decease he enegy (amplde and fon) of he wave Skn effec Cen densy nea sface of he condco s geae han ha a s coe Effecve essance of he condco nceases wh he feqency of he cen Cased by Eddy cen: changng magnec feld cases a cclang flow of elecons (cen) whn he condco ndcng magnec felds ha oppose he change of he ognal magnec feld Coona Inceases effecve damee of condco whch deceases wave mpedance Eahng condons Peneaon deph and popagaon speed depend on feqency of popagang wave hps://noppa.aalo.f/noppa/kss/s8.50 0

11 TRANSIENT REFLECTION When a avellng wave eaches a dsconny egon, eflecons occ. If mpedance s geae afe anson pon: Cen deceases on ohe sde Chages accmlae a anson egon Volage nceases To manan balance, a new wave s podced whch s spl no:,,. Refleced wave. Tansmed wave, Balance Condon hps://noppa.aalo.f/noppa/kss/s8.50

12 TRANSIENT REFLECTION Tansmed Refleced Volage Cen Balance: Ohm s law: Þ ) ( ) ( hps://noppa.aalo.f/noppa/kss/s8.50

13 TRANSIENT REFLECTION Tansmsson coeffcen:,, Reflecon coeffcen:,, ( ), hps://noppa.aalo.f/noppa/kss/s8.50

14 Dsconny Eqvalen cc REFLECTED WAVE TRANSMITTED WAVE Open lne Change n mpedance Sho cc Temnaon wh essance Temnaon wh ndcance* Temnaon wh capacance* C L R R R R R R R R ø ö è æ L L e e C C e e ø ö è æ * specal case: () s a sep fncon 4 hps://noppa.aalo.f/noppa/kss/s8.50

15 INDUCTANCE ø ö è æ e L Tansmed wave: Refleced wave: ' ø ö è æ e ' ø ö è æ ø ö è æ e e 5 hps://noppa.aalo.f/noppa/kss/s8.50 L L

16 CAPACITANCE ø ö è æ e C ø ö è æ e ø ö è æ ø ö è æ e e 6 hps://noppa.aalo.f/noppa/kss/s8.50 C C Tansmed wave: Refleced wave:

17 LATTICE DIAGRAM ρ τ ρ τ τ ρ 500 Ω 50 Ω 500 Ω A B Tansmsson: Reflecon: ( ) 0.88 hps://noppa.aalo.f/noppa/kss/s8.50 7

18 0 4 5 A ( ) B x ( ) Tme Volage a A Volage a B [] [ A ] [ B ] 0 0 Δ Δ Δ 4Δ 5Δ nδ (n)δ ( ) ( ) [ ( )] n é ê å ë 0 ù ( ) úû ( ) [ ( ) ] n 0 å( ) é ù ê ú ë û hps://noppa.aalo.f/noppa/kss/s8.50 8

19 / B 0 A /Δ hps://noppa.aalo.f/noppa/kss/s8.50 9

20 hps://noppa.aalo.f/noppa/kss/s8.50 0

21 hps://noppa.aalo.f/noppa/kss/s8.50

22 hps://noppa.aalo.f/noppa/kss/s8.50

23 Nondeal machng of mpedance along ansmsson lne hps://noppa.aalo.f/noppa/kss/s8.50

24 SUMMARY Tansen Popagaon Lace Dagam Tansen Reflecon hps://noppa.aalo.f/noppa/kss/s8.50 4

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