08 voltage regulation and per unit system

8/10/2019 08 Voltage Regulation and Per Unit System

1/19

Transformer Voltage Regulation


2/19

UCF Transformer Voltage Regulation (1)

Ideal:

Non-ideal:

S

P

N

Nn

n

V

V

S

P


3/19


No load (open circuit):

n

PSnl

VV

Full load : ( )P Sfl eqs eqs S R jXn

V V I

%100/

%100

Sfl

SflP

Sfl

SflSnl

V

VnV

V

VVVRVoltage regulation:


4/19


Discussions:

(1) Load is lagging (inductive)

%100/

Sfl

SflP

V

VnVVR

0/ VRVnV SflP

SeqsSeqsSflP jXR

n

IIVV

0sI


5/19

UCF

(2) Load is resistive (unit power factor)

0/ VRVnV SflP

(3) Load is leading (capacitive)

/ may be may be


6/19

UCF

Discussions on Phasor Diagram

0sI

0sI

PS eqs S eqs S R jX

n

VV I I

Assume the angle of is 0.SV

cos cos sin

( cos sin )

s s

P

S eqs S I eqs S I

S eqs eqs S

V

V R I X I n

V R X I

sin sin cos

( sin cos )

s s

Peqs S I eqs S I

eqs eqs S

VR I X I

n

R X I

lagging load

leading load

Real part:

Imaginary part:


7/19

UCF

Given: (1) VS (fixed)

(2) rated apparent power (VA) of the load

(3) power factor (pf) of the load

Find: ISand thenVP

Transformer VR Calculation Case I

/S rated S I S V

S SI V

%100/

S

SP

V

VnVVR

IS:

( )P S eqs eqs S R jXn

V

V I

1cos ( )pf + lagging, - leading


8/19

UCF

Given: (1) VP (fixed)

(2)IS

of the load

(3) power factor (pf) of the load

Find: VS

Transformer VR Calculation Case II (1)

ISj

S SI e

IS SI V

%100/

S

SP

V

VnVVR

IS: 1cos ( )pf + lagging, - leading

0SV

set

( )P S eqs eqs S R jXn V

V I


9/19

UCF

Transformer VR Calculation Case II (2)

0sI

( )

PS eqs eqs S

S eqs S

R jXn

Z

VV I

V I

cos ( cos sin ) ReP S eqs eqs S S eqs S V

V R X I V Z n

I

sin ( sin cos ) = Im( )Peqs eqs S eqs S

VR X I Z

n I

lagging load

Real part:

Imaginary part:

1 1

sin ( sin cos ) / ( / ) = sin Im( ) / ( / )eqs eqs S P eqs S PR X I V n Z V n

I

cos ( cos sin ) cos ReP PS eqs eqs S eqs S V VV R X I Z n n

I

Or: jP PV e

n n

V P

S eqs S Zn

V

V I


10/19

UCF

Given: (1) VP (fixed)

(2)ZL

Find: VS

Transformer VR Calculation Case III

%100/

S

SP

V

VnVVR

Assume the angle of is 0.PV0jP PV e

n n

V

( )

PS eqs eqs S

S eqs S

R jXn

Z

V V I

V I

L P

S L Seqs L

ZZ

Z Z n

VV I

/PS

eqs L

n

Z Z

VI


11/19

UCF

Example 3

For a 15 kVA, 2300/230 V, 60 Hz transformer, the equivalent circuit

parameters are:

Find voltage regulation:

(1) The secondary voltage 230 V (fixed), full load at (a) 0.8 pf lagging;

(b)1.0 pf; (c) 0.8 pf leading;(2) The primary voltage 2300 V (fixed), load current 65 A at

(a) 0.8 pf lagging; (b)1.0 pf; (c) 0.8 pf leading;

(3) The load resistance

k10,k100,6,5 MCeqeq XRXR

trans3.m.

3+j2 .L

Z


12/19

Per Unit System


13/19

UCF Per Unit System (1)

Define Base Values

Normalization:

quantityofvalueBasequantityActualunitperinQuantity


14/19

UCF Per Unit System (2)Analysis Procedure:

unitperinquantitysolvedvaluebase

resultsofvaluesactual(6)

unitperinquantitiesallwithanalysiscircuitstandardaperform(5)

unit)perquantitiesget:(orquantitiestheallnormalize)4(

basecurrent

basevoltagebaseresistance)3(

basevoltage

baseVAbasecurrent(2)

basevoltageandbaseVAselect(1)


15/19

UCF Example 4 (1)


16/19

UCF Example 4 (2)

Process is in trans4.m.


17/19

UCF

Non-ideal Transformer in Per Unit System

Or


18/19

UCF

Voltage Regulation in Per Unit System

%100/

%100

Sfl

SflP

Sfl

SflSnl

V

VnV

V

VVVRVoltage regulation:

Voltage regulation in per unit:

%100,

,,

puS

puSpuP

V

VV

VR

, , , , ,( )P pu S pu eq pu eq pu S puR jX V V I


19/19

UCF

Per-Unit Phasor Diagram

, , , , , ,P pu S pu eq pu S pu eq pu S puR jX V V I I

,Assume the angle of is 0.S puV

, , , , , ,

, , , ,

cos cos sin

( cos sin )s sP pu S pu eq pu S pu I eq pu S pu I

S pu eq pu eq pu S pu

V V R I X I

V R X I

, , , , ,

, , ,

sin sin cos

( sin cos )

s sP pu eq pu S pu I eq pu S pu I

eq pu eq pu S pu

V R I X I

R X I

,P puV

,S puV

, ,eq pu S puR I

, ,eq pu S pujX I

, ,eq pu S pujX I

, ,eq pu S puR I

,S puV

,P puV

lagging load

leading load

Real part:

Imaginary part:

08 voltage regulation and per unit system

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