powerfactory emt model2

8/10/2019 PowerFactory EMT Model2

1/14


2/14

12

[ ] [ ];s m m s m m

abc m s m abc m s m

m m s m m s

Z Z Z Y Y Y

Z Z Z Z Y Y Y Y

Z Z Z Y Y Y

= =

[ ]0

012 1

2

0 0 2 0 0

0 0 0 0

0 0 0 0

s m

s m

s m

Z Z ZZ Z Z Z

Z Z Z

+ = =

[ ]0

012 1

2

0 0 2 0 0

0 0 0 0

0 0 0 0

s m

s m

s m

Y Y Y

Y Y Y Y

Y Y Y

+ = =

The models based on line types (TypLne) are by default non frequency-dependent

which the electrical parameters per unit-length of the line at power frequency are defined.These parameters remain unchanged; if the frequency of the simulation changes i.e. differs

from the power frequency, then the program will adjust the reactance and susceptance of the

line according to the new frequency. The inductances and capacitances remain however

unchanged. For certain functions (harmonic load flow, frequency sweeps) the user still has

the option to assign a frequency characteristic to the parameters in the line type.

PowerFactory further distinguishes between constant and frequency-dependent

parameters models. Models based on tower geometry types (TypTow or TypGeo) use

frequency dependent parameters; it means that the electrical parameters of the line per unit-

length are calculated from the mechanical characteristics of the tower and the conductors

accounting for skin effect, the frequency-dependent earth-return path of the line, etc. These

types should be preferred in simulations where a wide range of frequencies is involved or

frequencies other than the power frequency of the system.

The following figures will show the input data for Transmission Line model in

PowerFactory v15.1 and some note points according to Basic Data and EMT Simulation

Data.


3/14

13

Figure 4.7 New Selection option for Lumped Parameter (PI) model

Figure 4.8 Basic data input for Line Type


4/14

14

Figure 4.9 EMT-Simulation data input for Line Type

Figure 4.10 Basic data input (1) for Tower Type


5/14

15

Figure 4.11 Basic data input (2) for Tower Type

Figure 4.12 Calculation results (impedance and admittance matrices)


6/14

16

Figure 4.13 Select New Tower Geometry Type from Line Element

Figure 4.14 Data input for Tower Geometry Type


7/14

17

Figure 4.15 Basic Data input for Tower Geometry Type


8/14

18

This figures above describes the Data input of the electrical parameters of an

overhead line system from its configuration characteristics like tower geometry, conductor

types, number, phasing and grounding condition of its circuits, etc. The calculation function

is available for lines having a tower type (TypTow) or a tower geometry type (TypGeo).

The line parameters calculation function, or so-called line constants, supports

overhead lines systems with any number of parallel circuits of the same or different nominal

voltage, 3-ph, 2-ph and single phase, with or without earth wires and neutral conductors and

different types of transpositions. The calculation accounts for the skin effect in the conductors

and for the frequency dependency of the earth return path.

The calculation function can be used in a stand-alone mode, in which case

PowerFactoryprints the calculation results (impedance and admittance matrices) to the

output window, or it can be automatically called by the line (ElmLne) or line coupling

(ElmTow) elements when associated to a tower type (TypTow) or a tower geometry type

(TypGeo). In the last case, the parameters calculation function will automatically return

the resulting impedance and admittance matrices of the overhead line system to the

simulation model.

Finally, the tower type (TypTow) does also support the definition of the transmission

system in terms of its electrical parameters, so that the user has the option to enter the

impedance and admittance matrices either in natural or in sequence components. This is

especially useful when the user has to define an unbalanced system (eg. untransposed line)

with multiple circuits not supported by the line type (TypLne).

4.3.3.2.

Distributed Parameters Model

Besides the lumped parameter models described in the previous sections,

PowerFactoryalso supports distributed parameters models for three-phase line circuits. This

model accounts for the distributed nature of the line parameters and should be therefore the

preferred option for long lines. For short lines the lumped parameters models discussed in the

previous sections provide enough accurate solutions.


9/14

19

To make the model usable for EMT simulations, further assumptions have to be

made. These assumptions give rise to the different models available for the EMT-models of

distributed parameter lines are based on Bergerons methodfor the solution in time domain.

Following options are supported:

Constant parameters model Frequency-dependent parameters model

2 2

2 2

( ) ' ; ( ) '

' ' ( ) ; ' ' ( )

V II x Z V x Y

x x

V IZ Y V x Z Y I x

x x

= =

= =

(2)

General Solution of this form:

1 2

1 2

( )( )

' ' '

'

x x

x x

C

C

U x K e K eZ I x K e K e

Zwith Z and Z Y

Y

= +

= +

= =

(3)

Both the surge (or characteristic) impedance ZC and the propagation factor are

frequency dependent and uniquely characterize the behavior of the transmission line,

therefore the impedance and admittance of the equivalent circuit are:

Figure 4.16 Incremental model for a line of elemental length


10/14

20

sinhsinh '

tanhcosh 1 1 2

'

sinh 22

C

C

lZ Z l Z l

l

l

lY Y l

lZ l

= =

= =

(4)

Considering up to the second order terms, equations (4) of the distributed parameter

model go into equations (1) of the lumped parameter model:

' ( ' ')

1 1

' ( ' ')2 2

Y Z Z l R j L l

Y Y Y l G j C l

= = = +

= = = +

(5)

The accuracy of the lumped model depends then on the weight of truncated terms in

the series expansion of the hyperbolic functions, which in turns depends on the factor f l

(frequency x length). For overhead lines less than 250 km and power frequency, this

approximation is very satisfactory and the error can be neglected. For longer lines or higher

frequencies, a distributed parameter model will give then a more accurate solution.

Longer lines can be alternatively modelled connecting line sections in cascade. In

general, the longer the line or the higher the frequency, the more line sections are required for

the same accuracy. Increasing the number of line sections to infinity will turn the lumped

parameter model into the distributed parameters model discussed before.

To make the model usable for EMT simulations, further assumptions have to be

made. These assumptions give rise to the different models available for the EMT-models of

Figure 4.17 Equivalent PI-Circuit for distributed line parameters in frequency domain


11/14

21

distributed parameter lines are based on Bergerons methodfor the solution in time domain.

Following options are supported:

Constant parameters model

Frequency-dependent parameters model

For the distributed constant parameters modelthe settings are adjusted on the EMT

page of the line element (ElmLne) or line coupling element (ElmTow) as following:

- Line Model: Constant parameter

- Frequency for travel time estimation: enter a representative frequency for the

transient under analysis. This frequency is used in matrix model to calculate the propagation

constant. In case of a non-transposed line, the frequency-dependent modal transformation

matrix is calculated at this frequency as well. A travel time(frequency independent) as,

' 'l

l L C

= =

To handle frequency dependent parameters PowerFactory supports the approach

proposed by J. Marti. The characteristic impedance and the propagation factor are developed

in rational functions and then the poles and zeros of the rational expressions calculated using

a Bodes approximation.

For the propagation factor ( )( ) :lA e =

min 1 2 1 2

1 2 1 2

( ) ( ) ( )( ) ...

( ) ( ) ( ) ( ) ( ) ( )

s n napp

n n

s z s z s z k k kA s e k

s p s p s p s p s p s p

+ + += = + + ++ + + + + +

1 2 1 20

1 2 1 2

( ) ( ) ( )( ) ...

( ) ( ) ( ) ( ) ( ) ( )

n n

C app

n n

s z s z s z k k kZ s k k

s p s p s p s p s p s p

+ + += = + + + +

+ + + + + +

The accuracy of the model depends on the quality of the rational function

approximations for Aand Zc. To verify the approximation PowerFactoryplots the exact and

approximated solutions of Aand Zc in the EMT-Simulation tab page of the line (ElmLne)

and line coupling (ElmTow) elements as shown in Figure below.


12/14

22

For the distributed frequency-dependent parameter modelthe settings are adjusted

on the EMT page of the line element (ElmLne) or line coupling element (ElmTow) as

following:

- Line Model: frequency-dependent parameter

- Frequency for travel time estimation:Frequency for travel time estimation: enter

a representative frequency for the transient under analysis. The frequency-dependent modal

transformation matrix is calculated at this frequency.

- Min and Max. Frequency of parameter fitting:enter the minimum and maximum

frequency for the approximation by rational functions of the propagation factor and the

characteristic impedance.

- Tolerance for Bode approximation: defined the maximum error in % that is

desired for the Bode approximation of the propagation factor and the characteristic

impedance. The lower the tolerance, the higher the number poles and zeros of the

approximated rational expressions.

Figure 4.18 Equivalent circuit with controlled current sourcesfor FD model


13/14

23

Figure 4.19 Data input for frequency-dependent for line model

Figure 4.20 Bode approximations of A and Zc for the zero-sequence


14/14

24

Figure 4.21 Data input for frequency-dependent for line model

powerfactory emt model2

Documents