class #30 review for exam 3 5-6-04

7/28/2019 Class #30 Review for Exam 3 5-6-04

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Class 30

Review for Exam 3


2/54

Class 17

Start Voltage Regulation Definitions

Review two winding transformers

Autotransformer


3/54

Class #18

Step-Voltage Regulators


4/54

Step-Voltage Regulator

+

-

V

SL

+

-

V

R

L

Source

Load

-

PreventiveAutotransformer

ReversingSwitch

Series

Winding

ShuntWinding

PTControl

ControlCT

S

L


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Control Circuit

Line Dr op

Co mpensato r Relay

Voltage Time

Delay

Motor

Operating

Circuit

Control Current TransformerLine C urrent

Control Po tential Transformer


6/54

Control Settings

Voltage level - voltage to hold at the load

center

Bandwidth - allowed variance from voltage

hold

Time delay - time before tap change takes

place

Line drop compensator - equivalent R and

X from regulator to the load center


7/54

Type A Step-Up Regulator

SL

SL

E2

N2

-

VL

+

+

+

- -

N1

E1

L

S +

-

VS

IS

LIL

R I2

I1

S

IS

SV

+

-

L

LI

+

-

VL


8/54

Type B Step-Up Regulator

+

-

V

S

SL

+

-

V

R

S

L

+

-

I1

E1

+

-

E

I2

2

IS

IS

IL

S

+

SV

-

SL

LV

L

LI

IS

+

-

L

N2

N1

L


9/54

Regulator Ratio as Function of

Tap Position1 0.00625_ _

1 0.00625_ _

0.00625 120 0.75 _ /

a TapR Type A

a TapR Type B

volts step


10/54

Generalized Matrices

Type A: Type B:

1

0

0

R

R

aa

b

cd a

0

0

1

R

R

a ab

c

da


11/54

Line Drop Compensator

Circuit

Voltage

Relay

R line + jX line

LoadCenter

MVA ratingkV hi - kV lo

R' X'

+ -V drop

I line

I comp

Npt:1

CTp:CTs

+

-

V reg

+

-

V R

1:1


12/54

Compensator Equations

Zcomp Zlinepu pu

VLN

Zcomp Rline jXlineohms ohms ohm N CTPT S

VLNZcomp Rline jXlinevolts ohms ohmNPT


13/54

Class 19

Three-Phase Voltage Regulators


14/54

Three-Phase Regulators

Single-phase

Three regulators connected in grounded

wye

Two regulators connected in open wye

Two regulators connected in open delta

Three regulators connected in closed delta


15/54

Grounded Wye Type A

Equations

10 0

10 0

1

0 0

0 0

0 0

0 0

1 0.00625

VLN a VLN b I ABC abc abc

I c VLN d IABC abc abc

aR

aaR

aR

aR

d aR

aR

a TapR


16/54

Grounded Wye Type B

Equations

0 0

0 0

0 0

10 0

10 0

10 0

1 0.00625

VLN a VLN b I ABC abc abc

I c VLN d IABC abc abc

aR

a aR

aR

aR

daR

aR

a TapR


17/54

Class #20

IEEE 13 Node Test Feeder


18/54

Class 21

Design Project


19/54

Class 22

Single-Phase Transformer Model


20/54

Center Tapped Transformer

+

-

V1

+

-

V2

+

-

E1

+

E2

-

Z0

+ I0 +

E0

- -

V

Z1

Z1

I1

I2

n :1t

n :1t

V

+

-

LS


21/54

Center Tapped Transformer

Equations_ 1 2 _

_ _1 2

0.5

0 1

0 2

0 1 2

0.5 0.80

0.41 2

V Rated H H voltageS

V Rated X X voltageL

VSntVL

E n Et

E n Etn I I I t

Z R j XT T

Z Z R j XT T


22/54

Class #23

Secondary Systems


23/54

Triplex Secondary Included

I1

I2

In

+

-

E1

+

E2

-

Z0

+ I0 +

E0

- -

Z1

Z1

H1

H2

VSZL2

ZL1

X1

X0

X2

VL

+

-

v1

v0

v2

+

-

V2

+

-

V1


24/54

Triplex Cable

212

12

1 212

Dia TD

Dia TD DN N

1 2

N


25/54

Triplex Cable Impedance

Plug into Carson for a 3x3 matrix

No Kron reduction


26/54

Class #24

Three-Phase Transformer

ConnectionsPart 1


27/54


28/54

Transformer ConnectionsA

B

C

N

a

bc

n

VAN

VABVCNVCA

VBN

VBC


29/54

Delta-Grounded Wye Standard

30 Degree Connection

Ztb Ztc

+ + +_ _ _

Zta

VCA VAB VBC

Vta

Vtb

Vtc

VabVbc+

_+

_

tn

g

+ _Vag

X3-cX2-b

X1-a

H3-CH2-BH1-A

_+ _+ _+

Ia

Ib

Ic


30/54

General Three-Phase

Transformer BanksI

I

I

I

V

V

V

V

V

AN

BN

CN

AB

BC

A

B

C

N

+

+

+

- - -

+

+

+

-

-

-

VCA

V

V

V

V

V

V

an

bn

cn

ab

bcca

I

I

I

a

b

c

In

+

---

+

+

+

+

+

-

-

-

Source Side Load Side

H0

H1 X1

H2

H3

X2

X3

X0


31/54

Generalized Matrix Equations

for All Connections

ABC t abc t abc

ABC t abc t abc

abc t ABC t abc

VLN a VLN b I

I c VLN d I

VLN A VLN B I


32/54

Class #25

Transformer Models - 2


33/54

Constant Z Loads

*2

1

2

3

1

1

1

*1000

0 0

0 0

0 0

ABC t abc t abc

ii

i

abc

abc abc abc

ABC t t abc abc abc

abc ABC

VLN a VLG b I

VLGZL

SL

ZL

ZL ZL

ZL

I ZL VLG

VLN a b ZL VLG X VLG

VLG X VLN


34/54

Serving Single-Phase and Three-Phase

Loads Wye-Delta

Ungrounded wye

Grounded wye

Open Wye-Delta

Leading connection

Lagging connection


35/54

Wye-Delta Connection

A

B

C

N

ab

cMotor

S-3

VBN

VAN

VCN


36/54

Leading Open Wye - Open Delta

A

B

C

N

a

b

cMotor

S-3

VBN

VAN

VCN


37/54

Lagging Open Wye-Open Delta

A

B

C

N

ab

cMotor

S-3

VBN

VAN

VCN


38/54

DeltaGrounded Wye

Common substation transformer connection

Provides 4-wire grounded wye feeder

Isolates LG faults

Distribution transformer

Used for providing balanced single-phase

loadingNot good for three-phase motor loads


39/54

Ungrounded Wye - Delta

Primary use

Supply combination single-phase and three-

phase loads Ungrounded wye so that upstream LG fault

currents do not flow thru transformers

Loss of one transformer will cause single-phasing on three-phase load

Really bad if the three-phase load is aninduction motor


40/54

Grounded Wye - Delta

Seldom used

Upstream ground faults can flow thru

transformersLoss of one transformer and the connection

becomes an open wye-open delta and will

continue to provide three-phase voltages to the

three-phase load


41/54

Open WyeOpen Delta

Can supply combination single-phase and

three-phase loads

Leading connection lightingtransformer on leading phase voltage

Lagging connection lighting

transformer on lagging phase voltage Reduced ratings (chalk board)


42/54

Class #26

Catch Up


43/54

Class 27

Induction Motor


44/54

Three-Phase Induction Motor

Balanced Three-Phase Voltages

1 ii ii

sRL Rr

s

Rs jXs jXr Rr

Ir RL

Is

Vs

-

+

jXm Im


45/54

Three-Phase Induction Motor

Unbalanced Voltages

abc abc abcIM YM VLL

InductionMotor

IMb

IMa

IMc

+

_

+_

+

_

Vab

Vbc

Vca


46/54

Class #28

Ladder Network Iterative Method


47/54

This is what it is all about

Transformer

Substation

Regulator

Voltage

Primary Feeder

Transformer

DistributionInductionMotor

Static

Load

A B

a b

c d

A B

a b

c d

A B

a b

c d

A B

a b

c d abcYM

Sabc

ABC abc abc

ABC abc abc

abc ABC abc

VLN a VLN b I

I c VLN d I

VLN A VLN B I


48/54

Class #29

Short Circuit Analysis

Distribution Feeder Protection


49/54

Three-Phase Equivalent Circuit

c

b

a+

+

+

x-

-

-

Vax

Vbx

Vcx+

-

VxgFaultedNode

Ea Eb Ec

+++

---

[ZTOT]

Zf

Zf

Zf

Ifa

Ifb

Ifc


50/54

Basic Equations

1

ZEQ ZTOT ZF

IP ZEQ Eabc


51/54

Common Equations

0 0

0 0

0 0

Simplify:

Z VE Z Z Z If If Vf xga aa ab ac a a ax

E Z Z Z If Z If V Vb ba bb bc b f b bx xg

E Z Z Z If If VZ Vc ca cb cc c c cxf xg

IP Ifa a

IP Ifb b

IP Ifc c

0 0

0 0

0 0

VY Y Y V Ys xgaa ab ac ax a

Y Y Y V Ys V ba bb bc bx b xg

Y Y Y V Ys Vca cb cc cx c xg


52/54

Matrix Equation to Solve

1 0 0

0 1 0

0 0 1

0

0

0

0

IfIP Y Y Y Ys aa aa ab ac aIfIP Y Y Y Ys bb ba bb bc b

IfIP Y Y Y Ys cc ca cb cc cVax

Vbx

Vcx

Vxg


53/54

Exam 3

(Given) Open Book

You will be given a floppy disk with a system that needs

to be fixed

You will be given an exam booklet

General questions

Transformer connection

Numerical problems


54/54

Exam 3

(Turn in) Turn in

Floppy

Fixed System Mathcad problems

Exam booklet

class #30 review for exam 3 5-6-04

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