branch modeling

7/28/2019 Branch Modeling

1/19

Lecture #16

EEE 574Dr. Dan Tylavsky

Branch Modeling


2/19

Branch Modeling Copyright 1999 Daniel Tylavsky

There are two types of branches we wish to model:

Transmission Lines

Transformers

Lets first look at transmission line modeling.

(Assuming nominal or equivalent pi model:)

R + j X

BSHBSH


3/19


R + j X

BSHBSH

Node specification may

include a fixed reactor or

shunt capacitor.

BSH may be specified in:

per unit (PU).

MVAR = QSH=V2BSH, BSH>0 (where V is the nominal system

voltage.)

Branch/node may also include a switched reactor or

capacitor.

Data format may not allow enough info to tell if shunt branch

is lost when T-line is lost.


4/19


Power flow data formats: (Many!) IEEE Common Format for Exchange of Solved Load

Flow Data.

Well use and discuss this format.

PECO (Philadelphia Electric Co.) Format.

WSCC (Western Systems Coordination Council)

Format.

Etc.


5/19


IEEE Format

T-Line (Branch) Data

Terminal Identifier - 4 digit right justified bus numbers

Node From Cols. 1-4

Node To Cols. 6-9

Circuit Number Cols. 17

Integer 1-9 used to identify parallel lines

Branch Type Col. 19

0 Transmission Line

Branch Impedance Cols. 20-39

R, X in 2F10.6

Line Charging Cols. 41-49

2*BSH


6/19



7/19


Transformer Modeling:

We want to find an equivalent circuit in the form:

Ya

YcYb

I2

+

V2

-

+

V1

-

I1

R + j X=Z=Y-1 1:a

+

V2

-

+

V1

-

I1 I2

Tap

Side

Impedance

Side


8/19


Calculate the short-circuit

admittance parameters forthis two-port circuit.

2221212

2121111

VYVYI

VYVYI

ca

V

a

a

V

a

a

V

ba

V

YYV

IY

YV

YV

V

I

Y

YV

YV

V

IY

YYV

IY

02

2

22

1

1

01

2

21

2

2

02

1

12

01

1

11

1

2

1

2

We want to find an equivalent circuit in the form:

Ya

YcYb

I2+

V2

-

+

V1

-

I1


9/19


Calculate the short-circuit

admittance parameters for

the xfmr as a two port.

For the ideal transformer:

R + j X=Z=Y-11:a

+

V2-

+

V1-

I1 I2

Tap

Bus

Impedance

Bus

a

VV21

1

By power balance:1

*

2*

1

2

*

1

2*

22

*

11IaIor

a

III

a

VIVIV

21

*

1

02

2

22

*

1

*

1

01

2

21

2

2

02

1

12

01

1

11

'1

2

1

2

a

Y

aVa

I

V

IY

a

Y

Va

I

V

IY

a

Y

V

Ya

V

V

I

Y

YV

IY

V

V

V

V

a

VV

2

1


10/19


Equating like coefficients.

222

*21

12

11

a

Y

YYY

a

YYY

a

YYY

YYYY

ca

a

a

ba

With 4 equations & 3

unknowns, the system is

over-determined.

Can be solved if one

constraint is redundant.

22

22

1

1

a

aY

a

Y

a

YY

a

YY

a

Y

a

YYY

a

a

Ya

Y

YY

YYa

YYYY

a

YY

c

cca

b

bba

a

This is the case if a=a*.

Turns ratio is real (no phase shift.)


11/19


I2

+

V2-

+

V1-

I1

a

aY

1

aY

2

1

a

aY

Tap

Bus

Impedance

Bus


12/19


Y1:a

+

V2

-

+

V1

-

I1 I2

Teams: For the following circuit show the equivalent

model is.

I2

+

V2-

+

V1-

I1

aaY 2

aY

aY 1

This model cannot be used simply with IEEE format.

No division by a is somewhat of an advantage.


13/19


IEEE Format

Transformer (Branch) Data

Terminal Identifier - 4 digit right justified bus numbers

Tap Bus Cols. 1-4

Impedance Bus Cols. 6-9

Circuit Number Cols. 17

Integer 1-9 used to identify parallel transformers


14/19


IEEE Format

Transformer (Branch) Data contd

Branch Type Col. 19

0 transmission line

1 fixed voltage ratio and/or fixed phase angle.

2 fixed phase angle and variable voltage ratio with

voltage control (ULTC).

3 fixed phase angle and variable voltage ratio w/

MVAR control. (rare) 4 fixed voltage ratio and variable phase angle w/ MW

control.


15/19


IEEE Format

Transformer (Branch) Data contd

Branch Impedance Cols. 20-39

R, X in per-unit

Line Charging Cols. 41-49

2*BSH

Control Bus Cols. 69-72

Specifies where the quantity being controlled is

measured. Side Col. 74

0 - controlled bus is at the transformers terminals

1 - the remote controlled bus is near the tap side

2 - the remote controlled bus is near the impedance side.


16/19


R + j X=Z=Y-11:a

+

V2-

+

V1-

I1 I2

Tap

Bus

Impedance

Bus

a

VV

2

1

Increase a to increase voltage of buslocated on tap side of xfmr.

Decrease a to increase voltage of buson impedance side of the xfmr.


17/19



18/19


Transformer Types0 transmission line

1 fixed voltage ratio and/or fixed phase angle.

2 fixed phase angle and variable voltage ratio with voltage control (ULTC).

3 fixed phase angle and variable voltage ratio w/ MVAR control. (rare)

4 fixed voltage ratio and variable phase angle w/ MW control.


19/19

The End

branch modeling

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