TRANSMISSION AND DISTRIBUTION LINES & CABLES

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1 ELEC46 Power ystem Analysis TANMON AND DTBUTON LNE & CABLE eading: hapters 4 and 5 of textbook (Glover et al). EE ETANCE Current in ondutor real power losses k = skin effet fator (.0) l = resistivity k A A = ross setional area l = ondutor length Temperature effets. EE NDUCTANCE Current in ondutor magneti fields mag. flux L = magneti flux linkage = urrent in ondutor mutual indutane between two ondutors = mag. flux linkage in ondutor L = urrent in ondutor 0 geometry of ondutors self and mutual indutane ELEC46: Transmission and distribution lines and ables p. 3. HUNT CAPACTANCE voltage on ondutor eletri fields apaitane of single line to ground mutual apaitane between two ondutors geometry of ondutors self and mutual apaitane 4. TANMON LNE MODEL: equivalent x line voltage phasor x km from x line urrent phasor x km from x sing x inremental (distributed) model: x z x x km km ELEC46: Transmission and distribution lines and ables p. y x series impedane: z j L (/m) shunt admittane: y G jc (/m) x

2 5. HOT TANMON LNE less than 80km shunt admittane is negligible distributed effets are negligible total series impedane (single phase) lumped model: sing zl where l length of line and 6. MEDUMLENGTH TANMON LNE from 80km to 40km distributed effets are negligible (single phase) equivalent model: sing zl Y yl ELEC46: Transmission and distribution lines and ables p LONG TANMON LNE longer than 40km distributed effets an be important transmission line equations d where: yz jl G jc d (in m ) is alled propagation onstant x osh x sinh x x sinh x osh x where: ELEC46: Transmission and distribution lines and ables p. 4 z = harateristi impedane y (single phase) equivalent model sing sinh l zl and l Y yl l tanh l

3 8. LOLE TANMON LNE approximation for highvoltage lines: G 0 sing lossless line: sinl Y jcl tan l / j Ll and l l / where: LC (m ) harateristi impedane: L/ C. t is purely resistive, also alled surge impedane. propagation onstant j is purely imaginary. flat voltage profile: x flat urrent profile: x omplex power profile: x Px jqx i.e. line absorbs and arries no reative power flat real power flow profile (lossless) Thus at rated ( pu) voltage, rated L kw pu propagation veloity v / LC urge impedane loading (L): line terminated with resistane x sing x L C oltage profiles: unompensated lossless line, fixed sing voltage (line length < /4) x km ELEC46: Transmission and distribution lines and ables p. 5 ELEC46: Transmission and distribution lines and ables p. 6

4 9. MAXMUM POWE TANFE (lossless line) jx oure P jb jb jq P jq Load hoose 0 (referene phasor) set ( = voltage phase shift aross line) sing omplex power: * jb P jq jx B j 90 X X equating real parts: P X sin (f. synhronous m/) 0 * 0. EACTE COMPENATON shunt reators (indutors or synhronous ondensers) to improve voltage regulation: sing installed during light load onditions: to absorb reative power and thus redue overvoltages removed during heavy loading to maintain voltage series or shunt apaitors (apaitors or stati var ompensators) to inrease line loadability: sing deliver reative power and inrease transmission voltage during heavy loading redue effetive x of line, hene inrease P max steady state stability limit = maximum power transfer = P max X 0 (in pratie 35 usually) ELEC46: Transmission and distribution lines and ables p. 7 ELEC46: Transmission and distribution lines and ables p. 8

5 Appix: represent tx line by twoport network Twoport _ network _ n matrix form: A B C D A B C D where A,B,C,D are parameters that dep on transmission line onstants. A and D are dimensionless, B has units of ohms and C has units of siemens. A=D B C hort line 0 Mediumlength Y Y line Y 4 Example: mediumlength transmission line sing Y Y Y Y hene: Y Y Y Y Y Y 4 n matrix form: Y Y 4 ELEC46: Transmission and distribution lines and ables p. 9 ELEC46: Transmission and distribution lines and ables p. 0