3_Lines_Travelling_waves_VERA_2.pdf

7/28/2019 3_Lines_Travelling_waves_VERA_2.pdf

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Travelling waves on transmissionlines and line modeling in

EMTP/ATP

Oct 15, 2012 - Bp

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Electromagnetic wave propagation along ahorizontal, lossless overhead line

t

IxLV

=

V(x+x,t)I(x,t)V(x,t)

x x+x

V

I

t

UxCI

=

I(x+x,t)


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Wave eq. (telegraph equations)

IxLV= ILV

=

t

VxCI

=t

VC

I

=

2

22

2

2

2

t

VC

tx

I

txIL

xV

=

=

2

2

2

2

2

2

2

2

ILC

It

VLC

x

V

=

=

11/6/20124 / 64

Solution of wave equations

C

LZ

LCv

where

vtxfZvtxfZtxV

vtxfvtxftxI

==

+=

++=

0,1

)()(),(

)()(),(

2010

21

x

+vf1(x,t) -v f2(x,t)


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Example

1 p.u.

SRC V1 V3 V5 V7 V9 ENDV V V V V VV

10km 10km 10km 10km 10km 10km 10km 10km 10km 10km

Line parameters, L=1.6mH/km, C=10nF/km makes Zo=400 ohm, v=250m/us

(file AC2_Tr_waves.pl4; x-var t) v:SRC v:V1 v:V3 v:V5 v:V7 v:V9 v:END

0.0 0.4 0.8 1.2 1.6 2.0[ms]-0.5

0.0

0.5

1.0

1.5

2.0

2.5

[V]

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Example (cont.)

1 p.u.

SRCV

V1 V3 V5 V7 V9 ENDV V V V V V

Single phase distr. parameter line, Zo=400 ohm, v=250m/us

(file AC2_Tr_waves.pl4; x-var t) v:SRC v:V1 v:V3 v:V5 v:V7 v:V9 v:END

0.0 0.4 0.8 1.2 1.6 2.0[ms]-0.5

0.0

0.5

1.0

1.5

2.0

2.5

[V]


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Reflection and refraction of waves

V1

ZA ZB

V3V2

V2=(ZB-ZA)/(ZA+ZB) V1 = V1

V3=(2ZB)/(ZA+ZB) V1 = V1

ZB=infinite (open circuit) =2, =1ZB=zero (short circuit) =0, = -1

11/6/20128 / 64

Simulation time step selectionz Small enough to meet sampling requirements for signal

reconstruction (dT < 1 / 2 x fmax)

z Much smaller than smallest time constant or natural oscillation

period in circuit

(file AC2_Surge_DT_selection.pl4; x-var t) v:SRC

0 2 4 6 8 10[us]0

10

20

30

40

50

60

70[V]

t=3st=10ns

(file AC2_Surge_DT_selection.pl4; x-var t) v:SRC

0 2 4 6 8 10[us]0

20

40

60

80

100

[V]

H

SRCV


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Simulation time step selection (II)Vcap

V

10 nF

1 mH10 ohm

(file AC2_Surge_DT_selection.pl4; x-var t) v:VCAP0.00 0.02 0.04 0.06 0.08 0.10[ms]

0

40

80

120

160

200

[V]

t=0.1sfsample=10MHz

(file AC2_Surge_DT_selection.pl4; x-var t) v:VCAP0.00 0.02 0.04 0.06 0.08 0.10[ms]

0

20

40

60

80

100

120

140

160[V]

t=10sfsample=100kHz

fmax=50 kHz

Recommended dT (time step)

PhenomenaBeing S tudied

TypicalStudyDurations

TypicalTimeStep

Lightningsurges

100-200 s .1 -1 s

TransmissionLine S witchingSurges

.2 - 1 ms 1-20 s

Capacitorswitching

1 - 100 ms 10-100 s

Short circuits 0.1 - 1 s 10-200 s

Machine

dynamics

0.5 - 5 s 100-1000 s

(About 5 - 10 samples within a period of the highest frequency of interest)


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Overhead line models (single phase)

Zo,v Zo,v

length/2 length/2

Rl/4 Rl/2 Rl/4

Line Models in ATP-EMTP

z Nominal- model Frequency independent

Lumped-parameter model

Skin effect and earth return corrections

Multi-phase lines can be represented

No time step limit (often misleading!)

Not suitable for transient studies!

PI sections can be connected in cascade for transient studies

with certain limitations:

Produces reflections at the cascading points

Computationally expensive

Sections must be kept very short { 5-10 km for frequencies up to about 2kHz}

z Frequency independent distributed parameter line model (CPDL)

z Frequency dependent distributed parameter line model (JMarti)


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Line Models for Transient Studiesz Constant parameter distributed line model (CPDL)

Model assumes that per unit R, L, & C are constant

L & C are distributed

Losses R*l are assumed to be lumped in three places Shunt losses are ignored

Use traveling wave solutions and valid over a wide frequencyrange

Require transformations between phase and modal domain

Keep track of modal waves traveling at different speeds

z Frequency dependent transmission line model (JMarti) Represents distributed nature and freq. dependency of all line

parameters accurately

Transformation matrix can be real or complex, but constant Most accurate model for transient studies

Approximations in the transformation matrix for untransposedlines

Can be used with compromise if asymmetry gets stronger

11/6/201214 / 64

Frq. dependency of l ine parameters

Zero sequence resistance vs. frequency


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Frq. dependency of line parameters

Zero sequence inductance vs. frequency

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For the lossless line

with characteristic impedance Z and travel time , the

expression v + Zi does not change if observer travels

forward with the wave (method of characteristics):

or

Equivalent

circuit:

)t(Zi)t(v)t(Zi)t(v 151515 =+

)t(I)t(vZ

)t(i += 151151

Transient solution in a larger network


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Input data needed for l ine modeling

z (x,y) coordinates of each conductor and shield wire;

z bundle spacing, orientations;

z sag of phase conductors and shield wires;

z phase and circuit designation of each conductor;

z phase rotation at transposition structures;

z physical dimensions of each conductor;

z DC resistance of each conductor and shield wire

z Ground resistivity of the ground return path.

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Overhead line modeling (LCC)


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Line/Cable modeling

z Line/Cable Constants, Cable Parameters

Bergeron, PI, JMarti, Semlyen, Noda(?)

z View

Cross section, grounding

z Verify

Frequency response, power frequency params.

z Line Check

Power freq. test of line/cable sections

0.0 2.0 4.0 6.0

log(freq)0.4

1.5

2.7

3.9 log(| Z |)

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Cable modeling (CC & CP)z Specify

Geometrical data

Electrical param.

1-21 phases

Max 42 overhead

cond.,16 cables

z Automatic ATP-

execution:

Bergeron

PI-equiv.

Semlyen

JMarti Noda

z View and Verify

modules


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Specification of data + View module

11/6/201222 / 32

Line Check

z The user selects a group in the circuit

z ATPDraw identifies the inputs and outputs (user modifiable)


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Line Check (cont.)

z ATPDraw reads the LIS-file and calculates the series

impedance and shunt admittance

Conclusions

z Use PI-exact model for steady state studies

z Use FD-line models for lines of main interest in

your study

z Use CPDL-line models for lines of secondary

interest


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Time controlled switches

Conventional deterministic switch

Model circuit breakers

Model short circuits Other similar switching devices

Modeled as ideal element:

I = 0 when open, R = 0 when closed

Statistics switch

Random closing/opening switch

Systematic switch

11/6/201226 / 32

Voltage controlled switch

Simulate protective gaps

Surge arrester gaps

Series capacitor gaps

Flashovers across insulators Normally open at the start of the simulation

Closes when the voltage across the switchexceeds a user-defined flashover value

Opening occurs at the first current zero,provided the user defined delay time haselapsed


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TACS controlled switches

Type 11 - Simulates diodes and thyristors

Type 12 - can be used to simulate triacs and spark

gaps

Type 13 - General TACS controlled switch

Load Models

Load models should satisfy two requirements The power frequency MVA load should be accurate in order to

set up the proper initial conditions

The low and high frequency characteristics should also match

the physical load to properly represent its effects on harmonicsand transients

Series RL and Parallel RL models Produce correct initial conditions

Inaccurate at higher frequencies

Series RL provides very little damping at high frequencies

Parallel RL provides a constant damping at higher frequencies


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Nonlinear branches

type 99 : Pseudo-nonlinear resistance

type 98 : Pseudo-nonlinear inductance

type 97 : Staircase time-varying resistancetype 96 : Pseudo-nonlinear hysteretic inductor

type 94 : User-defined component via MODELS

type 93 : True, nonlinear inductance

type 92 : Exponential ZnO surge arrester

Multi-phase, piece-wise linear resistance withflashover

type 91 : Multi-phase time-varying resistance

TACS/MODELS controlled resistance

User supplied Fortran nonlinear element

11/6/201230 / 32

L

VR IL

VL

A non-linear circuit


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iL

(t)

(t -t)

iL(t- t)

slope

kn

A piece-wise linear-i characteristic

( ) ( )[ ] ( ) ( )tttttitik LLn =

iL(t)

=dt

dvL

( ) ( )[ ] ( ) ( )ttttttvtv LL =+ 21

( ) ( )[ ] ( ) ( )tttttitik LLn =

( ) ( ) )( )(i t tk

v t i t tt

kv t tL L L L= + +

2 2

dtdt

tddttv

t

tt

t

tt

L

=)(

)(

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