models for transmission lines. transmission capacity hvdc ... · models for transmission lines....

10/19/2006

Fyrirlestur nr 15/EBH 1Greining raforkukerfa - 08.31.41

Models for Transmission Lines.Transmission Capacity HVDC Transmission

10/19/2006


Lecture topics

• Transmission line models– Short lines– Medium lines– Long lines

• Transmission capacity– Natural loading (Surge impedance loading=SIL)– Thermal limits– Stability limits

• HVDC (= High Voltage Direct Current Transmission)

10/19/2006


The Long Line Model for Transmission Lines - Distributed Parameters

(R+jX)∆x

i j

∆x

(r+jX)∆x (R+jX)∆x

∆x ∆x

C∆x C∆x C∆xC∆x

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The Long Line Model for Transmission Lines - Distributed Parameters

z∆x1 2

∆x

y∆x

V V V z x I+∆ = + ∆ ⋅

10

z R jX

y G jB jCω

= +

= + = − V V+ ∆ V

I I+ ∆ I

I∆

V z x I∆ = ∆ ⋅

dV z Idx

= ⋅

I I I y x V+ ∆ = + ∆ ⋅

I y x V∆ = ∆ ⋅

dI y Vdx

= ⋅

•Voltage and Current conditions lead to:

•Impedance and addmitance per unitlength of line:

x

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Voltage and current equationsz∆x

1 2

∆x

y∆xVV+∆ V

II+∆ I

I∆

dV z Idx

= ⋅We differentiate thevoltage equation a second time...

2

2d V dIz

dxdx= ⋅

....and plug in thecurrent equation

dI y Vdx

= ⋅ ....similarly for thecurrent equation

2

2d V zy Vdx

= ⋅....and we get

2

2d I zy Idx

= ⋅

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Propagation constant

( ) ( )

( ) ( )

zy R jX G jB

R j L G j C

γ

ω ω

= = + ⋅ +

= + ⋅ +

We can define the propagationconstant as follows

The real part of thepropagation constant isdefined as theattenuation constant

jγ α β= +The imaginary part of the propagationconstant is defined as the phase constant

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Long line model

We have 2 identicaldifferential equationsregarding bot voltage and current, which are complexphasors and are a function of the location, x along the line

22

2d V Vdx

γ= ⋅2

22

d I Idx

γ= ⋅

{ }( ) ( ) exp ( )VV V x V x j xδ= =

{ }( ) ( ) exp ( )II I x I x j xδ= =

1 2( ) x xV x A e A eγ γ−= +These differential equationshave a general solution:

( )1 21 ( )( ) x xdV xI x A e A eZ dx z

γ γγ −= = −dV z Idx

= ⋅ we getBy using

( )1 2( ) x xyI x A e A ez

γ γ−= −or...

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Characteristic Impedance

We can further define theimportant concept of theCharacteristic impedance(Also called SurgeImpedance)

cz R jX R j LZy G jB G j C

ωω

+ += = =

+ +

Then we get the followinggeneral formulas for thevoltage and current phasorsalong the line

1 2( ) x xV x A e A eγ γ−= +

( )1 21( ) x x

cI x A e A e

Zγ γ−= −

To calculate the constants A1and A2 we need to examinethe boundary conditions

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Boundary conditions

We must implemnet boundaryconditions to obtain the constantsA1 and A2. When x = 0 we havewhere x is the distance measuredfrom bus #2 and where V2 and I2are constants. This leads to:

2

2

(0)(0)

V VI I

==

2 2 2 21 2;

2 2c cV Z I V Z I

A A+ −

= =

2 2 2 2( )2 2

x xc cV Z I V Z IV x e eγ γ−+ −

= +The following relationis then obtained

2 2 2 21( )2 2

x xc c

c

V Z I V Z II x e e

Zγ γ−+ −⎛ ⎞= −⎜ ⎟

⎝ ⎠

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Model for long lines

2 2( ) cosh sinhcV x V x I Z xγ γ= +Next we get the followingrelations for voltage and current along the line

2 21( ) sinh coshc

I x V x I xZ

γ γ= +

1 2 2cosh sinhcV V I Zγ γ= +At bus #1 we get the followingrelation:

1 2 21 sinh coshc

I V IZ

γ γ= +is the line length

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Conclusion: The “per phase” Equivalent for (Medium) Long Transmission Lines

' sinhcZ Z γ=

1 2

' 1 tanh2 2c

YZ

γ=

= line length

Source: Textbook; Saadat, chapter # 5

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The “per phase” Circuit Equivalent for Short Transmission Lines

R+jX1 2

Bus #1 Bus #2

Load impedance

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Conclusion: The “per phase” Equivalent for Medium Length Transmission Lines

C/2

R+jX1 2

C/2

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Long lines

• Wavelength at f = 50 Hz• Frequency multiplied wavelength equals the wave

velocity: f·λ=c (c is the velocity of light)• Wavelength: λ = 300000 [km/s]/50[Hz] = 6000 km• Line length more than 1000 km is significant

compared to the wavelength

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Transmission Capacity (reference): Surge Impedance Loading (SIL)

• SIL is reached, when thegenerated reactivepower equals theconsumed powerin the high voltageline.

• SIL is not maximum loadingbut a “charactersiticloading”

2 2consumed LQ X I L Iω= =

2 22

1generatedc

V VQ C V

X Cω

ω= = =

2 2

generated consumedQ Q

L I C Vω ω

=

=

c

XLZC C

ω= =

22

2 cV L Z

CI= =

2 2

* ( )SIL SILc

V VS PLZC

= = =

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Surge Impedance Loading

• Surge Impedance: – Also called characteristic

impedance this is theimpedance with which youcan insert a surge thesending end of the line and not get any reflection backat the receiving end.

• X is the reactance of theline– (in Ohm/km or in Ohm)

• B is the succeptance of theline– (in Siemens/km or in

Siemens)

Surge impedance

Receivingend

Sending end

c

XL XZC C B

ω= = = (≅ 250 – 400 ohm)

C/2

R+jXi j

C/2

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Transmission capacity definitions

• Thermal limits:– With V being constant, I

is the limiting factor(Imax)

• Steady State StabilityLimits:

• Natural Loading– Surge impedance

Loading or (SIL)

3 cosP V I φ= ⋅ ⋅

max max3 cosP V I φ= ⋅ ⋅

1 2 sinV VPX

δ⋅

= 1 2max

V VPX⋅

=

2 2

* ( )SIL SILc

V VS PLZC

= = =cLZC

=

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HVDC Transmission

High Voltage Direct CurrentTransmission

Orkuflutningar með jafnstraumstækni

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HVDC Transmission

• Point to point (from “A” to “B”) rather than meshednetwork. No commercially available DC circuitbreakers

• Used exclusively for long underground/submarinecable transmission

• Flexible Computer or Electronic control of power flow• Transmission over long distances by HVDC overhead

line• Recently “HVDC light”. Lower cost of AC/DC

converters

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HVDC projects around the world- conversion to/from DC to AC 50 or 60 Hz

Source: http://www.spectrum.ieee.org/

10/19/2006


HVDC submarine projects in Scandinavia

Gemmell, B.; Loughran, J. “HVDC offers the key to untapped hydro potential”, IEEE Power Engineering Review , Volume: 22 Issue: 5 , May 2002 Page(s): 8 - 11

10/19/2006


Different types of HVDC links

a) Monopolar withearth/sea return

b) Bipolar link e.g. +/-400 kV. Earth return in the case of a single pole failure

c) Unipolar link e.g. with 2 * -400 kVand earth/sea return

DCAC AC

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HVDC applications

e.g. 50 Hz

e.g. 50 Hze.g. 50 Hz

• HVDC links can be used to connect 2 AC powersystems with different frequencies and/or phase

• HVDC is and asynchronous connecting link

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HVDC terminal station

• The design of theterminal stationwith:– a YY

transformer– a YD

transformer• A thyristor stack

as a 12 pulseGaetz bridge

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The functioning of the 12 pulseGraetz bridge

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Áhrif kveikihorns thýristora

Spenna á jafnspennuhlið af-eða áriðils fyrir mismunandi kveikitíma (kveikihorn) þýristora.

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Change of power flow in a HVDC system

Source: http://www.spectrum.ieee.org/

10/19/2006


Symbols and the composition of semiconductor parts

• Light triggeredthyristor

Gate

http://images.google.com/imgres?imgurl=www.lxoindustries.com/Website%2520Pictures/Broadcast/New%2520Broadcast%2520Images/thyristor-1.jpg&imgrefurl=http://www.lxoindustries.com/broadcast.html&h=480&w=640&prev=/images%3Fq%3Dthyristor%26svnum%3D10%26hl%3Dis%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26sa%3DG

10/19/2006


The Cross Section of a High Voltage Thyristor

• The valve is the basic power-switching element of a converter. It consists of series-connected, fully protectedthyristor levels, each havinghigh power thyristors of up to125mm diameter, 8.5kV rating

10/19/2006


Thyristor characteristics

• Anode current as a function of voltagefor a thyristor

Anóðustraumur

Anóðuspenna

Kennilína fyrir straumrof áfram

gegnumbrot aftur á bak

Kennilína fyrir straumleiðni áfram

Kennilína fyrir straum-

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Thyristor unit

• Þýristoreining með 7 þýristorumvatnkældum hitagleypum og viðeigandi spennujöfnunar og tengibúnaði

LTT=light triggered thyristor

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The thyristor valve hall

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Dannebo converter station(Fennoskan)

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Baltic Cable converter stationAC line AC switchyard

Q compValvehall

DC lineAC filter

ActiveDC filter

Transformer building

Smoothing reactor

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HVDC : Thyristor Valve

Technology

Valve coolingsystem diagram

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The evolution of a thyristor’s currentand voltage capacity 1970-1995

0

1

2

3

4

5

6

1970 1975 1980 1985 1990

Málgildi jafnstraumsí gegnum þýristor

Hæsta lokunarspennaþýristors

Straumur (kA)

2

4

6

8Spenna (kV)

10/19/2006


HVDC link between Norway and Denmark (Skagerak)

Riðstraums-háspennulínur

Launaflsvél

Varaaflgjafi

Yfirtónasíur

Hápasssíur

Thyristor valves

Thyristor valves

Varaaflgjafi

Riðstraums-háspennulínur

Launaflsvél

Yfirtónasíur

Hápasssíur

10/19/2006


Strengur milli Svíþjóðar og Finnlands (Fennoskan)

• Koparleiðarinn er 1200 mm2

• Strengurinn vegur 54 kg/m

• Tvöföld armering• Flutningsgeta 500

MW• Spenna 400 kV DC• Lengd 200 km• Gangsetning 1989

Starfsmaður SINTEF með HVDC strengbút

Heimild: http://www.energy.sintef.no

10/19/2006


Sæstrengsverkefni í Malasíu

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HVDC cable cross

sectionFennoskan(Sweden-Finland)

Source: Vattenfall, Stockholm, Sweden

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The Break-even Distance for HVDC

Gemmell, B.; Loughran, J. “HVDC offers the key to untapped hydro potential”, IEEE Power Engineering Review , Volume: 22 Issue: 5 , May 2002 Page(s): 8 -11

10/19/2006


Cost of HVDC converter stations

The cost of theDC/AC converters showsa significanteconomies of scale

10/19/2006


From a HVDC submarine cable factory

Sæstrengurinn er vafinn upp áláréttu kefli sem fer síðan í skipið sem leggur hann á sjavarbotninn

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Ractive power ballance of a transmission line

• For light loadingthe line producesmore Mvars than it consumes

• For heavy loadingthe line is a net consumer of reactive power

10/19/2006


References

• Gemmell, B.; Loughran, J. “HVDC offers the key to untapped hydropotential”, IEEE Power Engineering Review , Volume: 22 Issue: 5 , May 2002 Page(s): 8 –11

• The rise of high-voltage, direct-current systems by Narain G. Hingorani, Consultant (1996) http://www.spectrum.ieee.org/

models for transmission lines. transmission capacity hvdc ... · models for transmission lines....

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