Ch. 5-1(수정)S [호환 모드]contents.kocw.net/KOCW/document/2014/sungkyunkwan/kimcheolhwan/8.pdfFor medium-length lines, typically ranging from 80 to 250 km at 60Hz, it is common

전력시스템해석및설계

제 5 장– Transmission Lines :

Steady –State Operation -

성균관대학교김 철 환

CENTER FORPOWER IT

Center for Power ITCENTER FOR POWER IT

전력IT인력양성센터

Transmission Line Models

l Previous lectures have coveredhow to calculate the distributed inductance,

capacitance andresistance

of transmission lines.

l In this section we will usethese distributed parameters

to develop the transmission line modelsused in power system analysis.

Chapter 5: Transmission Lines: Steady-State Operation

© 2012 Cengage Learning Engineering. All Rights Reserved.

2



CONTENTS

5.1 Medium and Short Line Approximations

5.2 Transmission-Line Differential Equations

5.3 Equivalent π-Circuit

5.4 Lossless Lines

5.5 Maximum Power Flow

5.6 Line Loadability

5.7 Reactive Compensation Techniques

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▣ 단거리 및 중거리 송전선로(short and medium-length transmission-line) - ABCD parameters

▣ the two-port network ▣ 단거리 송전선로 - 80 km ▣ 중거리 송전선로 - 80 ~ 250 km ▣ 장거리 송전선로 - 250 km 이상

:, ss IV sending-end voltage and current

:, RR IV receiving-end voltage and current

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▣ The relationship between the sending-end and receiving-end quantities can be written as

Or, in matrix format, where A, B, C, and D are parameters the

depend on the transmission-line constant R, L, C, and G.▣ Network theory texts [5] show that ABCD parameters apply to linear, passive,

bilateral two-port networks, with the following general relation :

RRS

RRS

DICVIBIAVV

+=+=

úû

ùêë

éúû

ùêë

é=ú

û

ùêë

é

R

R

S

S

IV

DCBA

IV

1=- BCAD

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▣ The circuit in Figure 5.2 represents a short transmission line, usually applied to overhead 60-Hz lines less than 80km long.

Only the series resistance and reactance are included.(shunt admittance is neglected.)The circuit applies to either single-phase or completely transposed three-phase lines operating under balanced conditions

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For a completely transposed three-phase line, Z is the series impedance,are positive-sequence line-to-neutral voltages, and are

positive-sequence line currents.

▣ Parameter’s notation is followings.z = R+jωL Ω/m, series impedance per unit lengthy = G+jωC S/m, shunt admittance per unit lengthZ = zl Ω, total series impedanceY= yl S, total shunt admittance l = line length m

RS VandV RS IandI

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▣ ABCD parameters for the short line is obtained by KVL, KCL.

▣ By comparing (5.1.7) and (5.1.3), (A,B,C,D) and (1,Z,0,1)

For medium-length lines, typically ranging from 80 to 250 km at 60Hz, it is common to lump the total shunt capacitance and locate half at each end of the line.

RS

RRS

IIZIVV

=+=

úû

ùêë

éúû

ùêë

é=ú

û

ùêë

é

R

R

S

S

IVZ

IV

101

0

1

==

==\

CZBDA

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▣ 중거리 송전선로- lump the total shunt capacitance - a nominal π-circuit - Figure 5.3.

▣ ABCD parameter of π-circuit(using KVL, KCL)

RRR

RRS ZIVYZYVIZVV ++=++= )2

1()2

(

RR

RRR

RSR

RS

IYZVYZY

YZIVYZYVIYVYVII

)2

1()4

1(

2])

21[(

222

+++=

++++=++=

(Writing a KVL equation)

(Writing a KCL equation)

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Writing these equations in matrix format,

Thus, comparing them

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전력IT인력양성센터11/67




▣ ABCD parameters of common networks in Figure 5.4

Including a series impedance network that approximates a short line and a π circuit that approximates a medium-length line.A medium-length line could also be approximated by the T circuit shown in Figure 5.4, lumping half of the series impedance at each end of the line.

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▣ 전압변동(Voltage regulation )The change in voltage at the receiving end of the line when the load varies fromno-load to a specified full load at a specified power factor, while the sending-end voltage is held constant.

▣ Phasor diagram for short transmission line

100||

||||´

-=

RFL

RFLRNL

VVV

VRpercent VRNL = no-load receiving-end voltage (=Vs/A)VRFL = full-load receiving-end voltage

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▣ 송전능력(line loadability) : 선로가 얼마만큼의 전력을 송전할 수 있는가 하는 능력

▣ 3가지 line-loading limits 열적한계(Thermal limit)-도체의최대허용온도(단거리선로)전압강하한계(Voltage-drop limit) - (중거리선로)정상상태안정도한계(Steady-state stability limit) –동기발전기의동기유지능력 (장거리선로)

▣ Example 5.1Q) A three-phase, 60-Hz, completely transposed 345-kV, 200-km line has two

795,000-cmil 26/2 ACSR conductors per bundle and the following positive-sequence line constants :

z = 0.032+j0.35 Ω/kmy = j4.2 [s/km]

Full load at the receiving end of the line is 700MW at 0.99 p.f. leading and at 95% of rated voltage. Assuming a medium-length line, determine the following :

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a. ABCD parameters of the nominal π circuitb. Sending-end voltage , current , and real power c. Percent voltage regulationd. Thermal limit, based on the approximate current-carrying capacity

listed in Table A.4e. Transmission-line efficiency at full load

Sol) a. The total series impedance and shunt admittance values are

sV sI sP

SCZB

puDASjylY

jjzlZ

°Ð´=°Ð+°Ð´=

W°Ð==°Ð=°Ð°Ð´+==

°Ð´=´==

W°Ð=+=+==

--

-

--

08.9010277.8)78.17401476.01)(90104.8(78.8429.70

159.09706.0)5.0)(78.8429.70)(90104.8(190104.8)200)(102.4(

78.8429.70704.6)200)(35.0032.0(

44

4

46

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b. The receiving-end voltage and current quantities are

°Ð=+=

°Ð=´

Ð=

°Ð=°Ð=

==

-

14.266.199))(())((

11.8246.1)99.0)(34595.0)(3(

99.0cos700

02.18903

8.3278.327)345)(95.0(

1

RRS

R

R

R

IZVAV

I

V

V LLkV

LNkV

kA

LNkV

현재 이 이미지를 표시할 수 없습니다 .

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c. The no-load receiving-end voltage is

MWP

IpukVV

S

S

LLS

5.730)5.1514.26cos()241.1)(8.345)(3(

5.15241.1)11.8246.1)(159.09706.0()02.189)(08.9010277.8(

00.18.34536.1994

=°-°=

°Ð=°Ð°Ð+°Ð°Ð´=

»==-

%7.8%1008.327

8.3273.356

3.356

=´-

=

==

VRpercent

kVA

VV LLS

RNL

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d. From Table A.4, the approximate current-carrying capacity of two 795,000-cmil 26/2 ACSR conductors is

e. The full-load line losses are

and the full-load transmission efficiency is

kA8.19.02 =´

MWPP RS 5.307005.730 =-=-

%8.95100 =´=S

R

PPEFFpercent

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Documents

Ch. 5-1(수정)S [호환 모드]contents.kocw.net/KOCW/document/2014/sungkyunkwan/kimcheolhwan/8.pdfFor medium-length lines, typically ranging from 80 to 250 km at 60Hz, it is common