VOLTAGE DROPS IN POWER SYSTEM Simple DC line (LV, MV) Double-wire circuit. Assumption: constant cross-section and resistivity. El.

Transcription

1 VOLTAGE DROPS N POWER SYSTEM Simpe DC ie (LV, MV) Doube-wire circuit. Assumptio: costat cross-sectio ad resistivity. E. tractio, eectrochemistry, ight sources, og-distace trasmissio, power eectroics. Sige oads suppied rom oe side

2 a) additio method t adds votage drops aog the power ie sectios. (Votage drops are aways i both coductors i the sectio.) th sectio ) A m,, m m, (V; S Curret i th sectio y y Maximum votage drop y y S

3 b) superpositio method t adds votage drops or idividua discrete oads: S curret momets to the eeder Reative votage drop: V V, ; Note. Losses must be cacuated oy by meas o the additio method! ) A m,, m m, (W; S P ) ( P P

4 Sige oads suppied rom both sides the same eeders votages Rig grid, higher reiabiity o suppy. Two oe-eeder ies ater a aut. Cacuatio o curret distributio ad votage drops.

5 Cosider B as a egative oad: B B A AB S S 0 Hece (momet theorem) B Aaogous (curret momets to other eeder) A O course y y B A

6 Curret distributio idetiies the pace with the biggest votage drop = the pace with eeder divisio spit-up ito two oe-eeder ies. Sige oads suppied rom both sides dieret eeders votages Two dieret sources, meshed grid.

7 Superpositio: ) Curret distributio with the same votages. ) Dieret votages ad zero oads baacig curret S B A v 3) Sum o the soutios + Further cacuatio is the same. Or directy: B B A S S S S S B A B

8 Direct curret trasmissio HV Log distace trasmissio or oca statios (AC-DC-AC). Reasos: trasmissio stabiity, short-circuit coditios, parameters compesatio, power osses, ecoomic aspects, power systems coectio. Possibiity o smaer isuatio distaces ad higher trasmissio capacity tha or AC systems. Cotro by DC votage. Pricipe DC ie Rectiier verter verter Rectiier

9 Coiguratios:

10 a) Groud as retur coductor. Groud resistace does ot deped o ie egth but o groud coectio. Suitabe or uoccupied regios (corrosio, EMC). b) Two wires ie. Compared to 3ph ess materia, ighter towers. c) Two covertors i series. Low baacig groud curret caused by ubaace. Durig a aut it trasorms to a), ha power. 450 V DC Caada

11 Compex power i AC grids 3 phase P 3 cos 3 cos (W) Q 3 si 3 si S 3 3 P Q Compex ( phase) Ŝ P jq cos jsi Sig accordig a covetio. (VAr) (VA) j S e ductive oad ju ji Û e, e Compex cojugated curret * j u i Ŝ Û e * ND Ŝ Û P jq CAP j e

12 3 phase power ies LV, MV Series parameters are appied, or LV X 0. 3 phase power ie MV, oad at the ed Symmetrica oad phase diagram, operatioa parameters. Compex votage drop Û Ẑ ND CAP R jx č j j Û R č X j j X č R j ND CAP magitude phase

13 Phasor diagram (iput,, φ ) (age υ usuay sma, up to 3) magi. part egectig ad modiicatios R3 č X3 j RP XQ 3 3 Percetage votage drop RP XQ 3 RP XQ 3 phase active power osses Ŝ 3Û 3 P 3R * 3Ẑ R jx 3R j3x 3R * 3Ẑ (W;, A) č j

14 ! Eve the reactive curret causes active power osses! reactive power compesatio 3 phase MV power ie suppied rom oe side Costat series impedace R jx ( / m) Ẑ

15 Votage drop at the ed (eed t be the highest oe, it depeds o oad character) A Ẑ Û Ater imagiary part egectig CAP ND X R j č A CAP ND 3 Q X P R A Votage drop up to the poit X (superpositio) X AX X AX Ẑ Ẑ Û

16 3 phase MV power ie suppied rom both sides Cacuatio as or DC ie (eeder is a egative oad, zero votage drop). Û AB 0 Ẑ Ẑ B

17 Momet theorems B A y y B A ( pricipe it is the curret divider or each oad.) Active ad reactive curret sig chage coud be i dieret odes maximum votage drop shoud be checed i a grid poits.

18 NO! Meshed grids MV

19 YES!

20 Node votage method Grid with odes. Set series brach parameters, oad currets (oda currets), mi. ode votage Û (betwee the ode ad the groud). Ẑ m

21 Cacuatio with series admittaces Ŷm Ẑ m R m jx m Node m 0 0 m m 0 Û Ŷ 0 Braches, m m Û Ater modiicatios: m m Û m Ŷ m Û Ûm Ŷm ÛŶ 0

22 Û Ŷm Ŷ0 ÛmŶ m m m m Admittace matrix parameters deiitio: Noda se-admittace (diagoa eemet) Ŷ (,) Ŷm Ŷ0 m m Betwee odes admittace (o-diagoa eemet) Ŷ Ŷ Ŷ or m Hece (,m) (m,) m (or o-coected odes Ŷ (,m) 0 ) m Ŷ (,m) Û m m

23 Matrix orm Ŷ Û Set votages at odes to (x), currets at odes + to (y) Ŷ xx Ŷ x xy Û x T y Ŷ Ŷ Ûy xy yy Hece Ŷ Û Ŷ Û x T Ŷ Û Ŷ Û y xx xy x x Cacuate x, Û y T Û Ŷ Ŷ Ŷ Û y yy y xy yy yy y y xy x

24 some odes are coected to the groud (through a admittace), the the admittace matrix is reguar to set a oda curret is eough. Û Ŷ Note : Simiar or DC grid. G Note : For power egieerig powers are set, currets are cacuated rom the powers. * Ŝ 3Û Resuts are ot precise i omia votages are used iteratio methods.