per-unit system2009-3.ppt

7/22/2019 Per-Unit System2009-3.ppt

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Per-Unit System

In power systems there are so many different

elements such as Motors, Generators and

Transformers with very different sizes and

nominal values. To be able to compare the performances of a

big and a small element, per unit system is

used.


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Power System Representation

Physical Components in the system arerepresented by a mathematical model.

Mathematical models of components areconnected in exactly the same way as thephysical components to obtain the systemrepresentation.

Various physical components have differentratings or basis.

It is convenient to obtain the representation with

respect to a common basis.


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Per Unit And Percent Representation

The numerical per uni tvalue of any

quantity is its ratio to the chosen base

quantity of the same dimensions.

Thus a per unit quantity is a normalized

quantity with respect to a chosen base

value.

Percent is the per unit quantity multiplied

by a 100.


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Per Unit And Per Cent Representation

Advantages

In the per-unit system of representation, deviceparameters tend to fall in a relatively fixed range,

making erroneous values prominent.

Ideal transformers are eliminated as circuit

elements. This results in a large saving in

component representation and reduces

computational burden.

The voltage magnitude throughout a given power

system is relatively close to unity in the per-unit

system for a power system operating normally.

This characteristic provides a useful check on the


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Base Quantities

In power system calculations the nominalvoltage of lines and equipment is almost

always known, so the voltage is a

convenient base value to choose.

The apparent power (volt-ampere) is

usually chosen as a second base. In

equipment this quantity is usually knownand makes a convenient base.


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Base Quantities

The choice of these two base quantities will

automatically fix the base of current,

impedance, and admittance.

In a system study, the volt-ampere base can

be selected to be any convenient value such

as 100 MVA, 200 MVA, etc.


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Base Quantities

The same volt-ampere base is used in all

parts of the system. One base voltage in

a certain part of the system is selected

arbitrarily. All other base voltages mustbe related to the arbitrarily selected one

by the turns ratio of the connecting

transformers.


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Per Unit System

Power system quantities such as voltage,current and impedance are often expressed inper unit or percent of specified values.

Per unit quantities are calculated as:

ValueBaseValueActualValuePer Unit


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Per Unit Values

base

puSS

S

base

puII

I

base

puVV

V

base

puZZZ

ZZ

2

base

base

base

puV

S

ZZ

pu

base

2

base

pubase ZS

VZZ Z

Conversion of Per Unit Values

Per Unit System


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Per Unit System

Usually, the nominal apparent power (S) and

nominal voltage (V) are taken as the base

values for power (Sbase) and voltage (Vbase).

The base values for the current (Ibase) andimpedance (Z

base) can be calculated based on

the first two base values.


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Per Unit System

100%Zbase

actual%

Z

Z

The percent impedance

e.g. in a synchronous generator with 13.8 kV

as its nominal voltage, instead of saying the

voltage is 12.42 kV, we say the voltage is 0.9

p.u.


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Per Unit in 3 Circuit

Simplified:

Concerns about using phase or line voltages are

removed in the per-unit system

Actual values of R, XC and XL for lines, cables,and other electrical equipment typically phase

values.

It is convenient to work in terms of base VA (base

volt-amperes)


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Per Unit in 3 Circuit

,3

3

B

BB

BBB

VSI

IVS

B

B

B

BB

BBB

SV

IVZ

ZIV

2

3/

3

Usually, the 3-phase SB or MVAB and line-to-line VB or kVB

are selected

IB and ZB dependent on SB and VB


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Change of Base

The impedance of individual generators &

transformer, are generally in terms of

percent/per unit based on their own ratings.

Impedance of transmission line in ohmic value When pieces of equipment with various

different ratings are connected to a system, it

is necessary to convert their impedances to a

per unit value expressed on the same base.


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Z

VS

ZZZ

old

B

old

Bold

B

oldpu 2

Z

V

S

Z

ZZ

new

B

new

B

new

B

new

pu 2

new

B

new

B

Vbasevoltagenew&

Sbasepowernewon theimpedanceunitpernewthebenewpuZ

old

B

old

B

Vbasevoltage&

Sbasepoweron theimpedanceunitperthebeoldpuZ

1

2

Change of Base


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2

newB

old

B

old

B

new

Bold

pu

new

puV

V

S

SZZ

old

B

new

Bold

pu

new

puS

SZZ

From (1) and (2), the relationship between the

old and the new per unit value

If the voltage base are the same,

Change of Base


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General Relations Between Circuit

Quantities

3

2

3

3

3

2

3

3033*303

303

3

30

3

30

303

*3

30

S

V

S

VV

I

V

I

VZ

V

S

Z

VII

Connection

S

V

S

VV

I

V

Z

ConnectionY

o

LLLLo

LL

L

o

LL

D

LL

D

LL

o

D

LL

o

LD

o

LLLL

o

LL

L

LN

Y


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Base Conversion

2

)(

2

)(

)(

)(

)()( **

newbase

oldbase

oldbase

newbase

oldpunewpu

KV

KV

MVA

MVAZZ


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Example One: Base Conversion

A 50-MVA, 34.5:161 kV transformer with 10%

reactance is connected to a power system where all

the other impedance values are on a 100 MVA, 34.5

or 161 kV base. The reactance of the transformerunder new base is:

2.0*50

100*1.0

2

)(

2)(

)( newbase

oldbase

newpuKV

KVZ


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Example Two: Base Conversion

A generator and transformer, as shown below, are to

be combined into a single equivalent reactance on a

100 MVA, 110 kV (high voltage side) base.


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Advantages

More meaningful when comparing different voltagelevels

The per unit equivalent impedance of the transformer

remains the same when referred to either the primaryor the secondary side

The per unit impedance of a transformer in a three-phase system is the same, regardless the winding

connection The per unit method is independent of voltage

changes and phase shifts through transformers


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Advantages

Manufacturers usually specify the impedance of the

equipment in per unit or percent on the base of its

nameplate ratings

The per unit impedance values of various ratings ofequipment lie in a narrow range


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Advantages

Transformer equivalent circuit can besimplified by properly specifying basequantities.

Give a clear idea of relative magnitudes ofvarious quantities such as voltage, current, powerand impedance.

Avoid possibility of making serious calculationerror when referring quantities from one side of

transformer to the other.


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Advantages

Per-unit impedances of electrical equipment ofsimilar type usually lie within a narrownumerical range when the equipment ratingsare used as base values.

Manufacturers usually specify the impedances ofmachines and transformers in per-unit or percentin nameplate rating.


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Advantages

The circuit laws are valid in per unit systems,

and the power and voltage equation are

simplified since the factor 3 and 3 are

eliminated in the per-unit systems. Ideal for the computerized analysis and

simulation of complex power system problems.


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per-unit system2009-3.ppt

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