05 - Unbalanced Load Flow

8/17/2019 05 - Unbalanced Load Flow

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ETAP Workshop Notes © 1996-2009 Operation Technology, Inc.

Unbalanced Load Flow


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Slide 2© 1996-2009 Operation Technology, Inc. – Workshop Notes: Unbalanced Load Flow Analysis

Real Unbalanced Power

Systems• Distribution System

– 3-phase, 2-phase, and single-phase network

components

– Unbalanced loads

• Transmission System

– Untransposed long transmission line

– Abnormal operation with one phase out of service

– Unbalanced loads (e.g., electrical railway traction

motors)


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Harmful Effects of System

Unbalance• Overheating of generators

• Nuisance tripping of protective relays

• Increased real power losses

• Transformer failure

• Radio communication interference


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Unbalance Factors/Indexes

• System unbalance is considered by power

quality standards as a disturbance

• Voltage/Current unbalance factors

• Ratio of zero/negative sequence to positivesequence

• Voltage/Current unbalance indexes

• Ratio of average values to maximum

deviation of average values


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Unbalanced Load Flow

Analysis

• Current Injection (CI) method

• The most robust algorithm ever developed

• Converge in less iterations than othermethods, especially for heavily loaded

systems

• Sparse matrix technique

• Unique modeling concepts


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Sequence Models of

3-Phase Machines


7/18Slide 7© 1996-2009 Operation Technology, Inc. – Workshop Notes: Unbalanced Load Flow Analysis

Unique Concepts of

3-Phase Machines

• Swing Machine

– The specified magnitude and the phase angle of the

positive sequence voltage only at the swing machine

terminal

• PV Machine

– The specified total output of 3-phase real powers and

the magnitude of the positive sequence voltage

• PQ Machine

– The specified total outputs of 3-phase real and reactive

powers



Concepts of Load

Connections

• Single-Phase Loads

• Connected in the phase connection types of

AB, BC, CA, AN, BN or CN• Three-Phase Loads

• Connected in Delta, Wye or Wye-G

• The constant individual powers in Wye are

not allowed due to multiple solutions



Modeling Capabilities

• A mixture of 3-phase, 2-phase and single-phase network components

• 3-phase machines with internal impedance

being considered

• Built-in calculator for overhead line

impedances

• Mutual coupling among overhead lines

• Transformers combined with load tap

changers (LTC) and phase shifters



Modeling Capabilities

• 2-winding and 3-winding transformers ofvarious winding connections

• Lumped loads consisting of constant power,

constant impedance and constant currentcomponents

• Generator exciters with AVR or Mvar / PF

controllers

• Robust library of of commonly used

overhead transmission lines and cables



Study Case

• Same pretense as Balanced Load Flow withmore detailed modeling, calculations, and

results



Output Results

• State-of-the-art graphic display ofresults

• Graphical display of marginal andcritical under/over voltages

• Alert View displays

limit violations



Reporting

• Customized output reports using Crystal Reports

®

• Individual phase and sequence voltage, current,

and power

• Voltage drops, losses,

power flows, power

factor, voltage/currentunbalance factors, etc.


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Example 1

© 1996-2009 Operation Technology, Inc. – Workshop Notes: Unbalanced Load Flow Analysis

j l . 5

- j0 . 3

j0 04

T2

10 MVA

Gen1

? 5 MlJ

2 .1 - j0 . 1

2

1 .6

1 .5

~ : : : : I : S u b 2 ~ B ~ ~ - - ~ _ ,

Sub2A . s - j0 . 5 z j l . 4

l

Z j l Z

0 .9 - j0 . 2

1 .2

- j0 . 5

- j0 . 1

Z . 1 - j0 . 1 t

l

6

. 2 . 30.1

0 .2 j0 .1 0 .3

0 .2 j0 .1 0 .3

~ \ 1 taP)

~ \ 1

t Pc)

~ \ I t &

Syn1

-0 .9 j0 .2

-0.8

j0 .2

-0.9 j0 .3

T

1 5 / 1 0 / 5 MVA

jO .

SW)

3

jO

- j0 .08

- j Lb . .

- j0 . 2 0 .5

- j0 . 2 0 .5

Sub3 H e t

0.

1

0 j0 .1

0 j0 .1

j0 . 2

j0 .1

j0 .2

:r

CAP1

450

kva r

Syn3

3500

HP

1250 HP

0 .2 j0 .1

I..A.IVOU. 2

j

0 . 1

T

1 5

MVA

T4

)

CB22 ~ \ 1 taP)

Bus

0

.469 ~ \ 1 t Pc)

jo .1

o

.4

1

; .

~ t e a )

CB2;1 : .2 j0 .1 o.41

0 .2 j0 .1

Ill

DC Sys t e m



Example 2

IEEE Four Node Test Feeder

• Characteristics of the Feeder

1. Two line segments with a 3-phase

transformer bank connected between the twosegments

2. Data is specified for balanced and

unbalanced loading at the most remote node

3. Transformer is specified for different

connection testing



U1

U7

us

99999992

MVAsc:

99999992

MVAsc:

99999992 MVAsc:

1853

j516

\(\1 ~ ' * ' )

15 4

2

j1361

\(\1

' * ' )

19 6

3

j1699

2164 j1644

4 7

2316

j9 90

'\z.4.7 17 4

j l l 2 2

\(\1

Bus1

\_1.. \(\1

Bu s

31

+2

97

j2 46

4 7

Bus27

+2

2

5

j1846

'\z.4.7

+2

368 j l l 9 6

'\z.4.7

' I ( ' J

\1.. \(\1

h 853

j516

\_1.. 4.

h 54 2

j1361

\_1..

4

+19 6 3

j1699

\_1.

_4 7 \(\1 ~

2164 j1644

2316

j99

17 4 j l l 2 2

\_1..

4.

2 97

j2 46

225 j1846

2368 j l l 9 6

Line1

Line1

2

Line14

44

'- \]

~ - ' )

\(\1 ~ ' * ' )

'$1 '- \] ~ - ' )

Bus3

\_1. (' .:)

r:>? '- \]

\_1.. (' .:)

Bu s 32

\_1.. (' .:)

\1.

~ . : ; : . )

Bus28

1. \

'- \]

e;,

'- \]

h 849

j499

~ ' - \ ]

h

528

\_1..

~ . : ; : . )

h

943

j1667

\_1..

~ . : ; : . )

' \ _ 1 . - ~

j1341 ¢ '---r

\ 6 '- \]

214 j1622

23 3

j9 62 \_1. ·

1696 j l l

4

\z.Z

2 75

j1993

22 3

1

j18 5

j l l 6 1

T1

T8

6

MVA

\(\1 ~ ' * ' )

T7

6 MVA

Bus4

< ; ~ 7 ' \

6 MVA

\(\1 ~ ' * ' )

' J O J ' ~ ~ )

'- \] ~ - p . : ) Bus3

< ; 1 7 ~ ' 1 ( \ J ~ ~ )

Bu s

3 4

~ - < ; 1 ' 1 ( \ J ~ ~ )

+

1325

~ . i i o ' i l

B



Example 3

IEEE 13 Node Test Feeder

• Characteristics of the Feeder

1. Short and relatively highly loaded for a 4.16

kV feeder

2. Overhead lines with variety of phasing

3. Shunt capacitor banks

4. In-line transformer

5. Unbalanced loading


18/18Slide 18© 1996-2009 Operation Technology Inc – Workshop Notes: Unbalanced Load Flow Analysis

Line603 BC300

Line605 CN300

LUI lp6

188 kVA

CAP1

100 kvar

U1

Bus650

T1

1000000 00 liVAs c

T

500 kVA

Line60

3

BC500 Line60

2

l t r 31

170 kUJ

Line604 ACN300

Load2

154 kVA

Bus632

16 3

121

t 1 22

+

1059

j479

504 j98

1026 j3 32

Line

01 22

LUI lp9

116 kVA

Li ne6 0 1 33

Bus680

LUI lp7

116

kVA

-0

- j O

0 - j O

+-

o j o

- - r l - ' ~

_1. 3 < \( I ltl

~ 1 9 1

o > - ~

- 1 ) 1 . 1

Bus633

162

121

t122

115

9 2

9 3

LUI lp1

494

kVA

j

11

0

j90

j90

1 .

8 l VAb

Cab1e6

06 500

488

j1

68

- j1 8 1

t2

91 j 3 7

+

44 j121

0

jO

120

j 2

5

- ' ~

LUI lp 5

3

\(\( I t l ' ~

227

kVA

.1-9

1

\ ( I d > - ~

Bu s675

+485 j 190 t j 1 91

68

j60 0

j2 42

290

j 2

1 2 0 j 1 75

LUI lp4

971

kVA

r

CAP2

6 00 k

var

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