Unit – I Lecture 2

7/25/2019 Unit I Lecture 2

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UNIT I

LECTURE -2


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OVERVIEW OF LECTURE - 2

In this lesson, you are going tolearn about phase difference,

phasor diagram, power, energy

passive sign convention andpower factor


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PHASE DIFFERENCE

Thephase differenceor phase shift of a sinusoidalwaveform is the angle , in degrees or radians that

the waveform has shifted from a certain reference

point (t=0) along the horizontal zero axis.

3


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PHASOR DIAGRAM

A Phasor is a rotating vector- a scaled line whose length represents the maximum

value of the sinusoidal signal and direction is varying

from 0to 360

Reference

axis0

Vm

v = Vm

Sint

Vm

0

v = VmSin (t +)

Vm

0

v = VmSin (t -)

Anti-clockwise rotation(Lead) Clockwise rotation

(Lag)


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Exercise-1

Draw the phasor diagram for v1=10 sin (t+50) and v2=

20 sin ((t -30).Solution:

The sinusoid v1is leading the reference waveform by 50

and v2is lagging the reference waveform by 30.


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POWER


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ENERGY


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PASSIVE SIGN CONVENTION


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PSC: EXAMPLE I


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PSC: EXAMPLE II


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PSC: EXAMPLE III


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POWERIN AC CIRCUITS

Three types of power representation

1. Real power(P):I2R (or) V2/ RWatts

The average power consumed in an A.C circuit .

It is also called as true power.

True power goes only one way from source to load and

performs work on the load in terms of energy dissipation.

2.Reactive power(Q)=I2 X (or) VAR (Volt-Amp-reactive)

The power absorbed by a pure reactance (XLor Xc) in acircuit.

Reactive power simply goes back and forth between source

and load with zero resultant work being done.

2V

X


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3. Apparent power(S): V I = I2 Z = VA(Volt-Amp)

The combination of reactive power and true

power

S = P jQ

2V

Z

power is calculated with scalar quantities ofvoltage, current, resistance, and reactance.

POWER IN AC CIRCUITS

These three types of power are

trigonometrically related to one another.

In a right triangle, P = adjacent length,

Q = opposite length, and S = hypotenuse length.


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POWER TRIANGLE

Relationbetweenall the three powers is shown power

triangle

Phase angle for V or I represents a relative shift

in timing between two waves.Phase angle for power represents a ratio

between power dissipated and power returned


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POWER FACTOR

A power factor of 0.72 would mean that only 72%

of the power supplied is being used to do useful

work.Perfect power factor is 1.0, (unity); meaning

100% of the power is being used for useful work.

Ratio between true power and apparent power is

called the power factor for this circuit.Power factor ratio is also equal to the cosine of

that phase angle.

true power (watt)power actor =appare!t power (VA)

Unit less quantity


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ANALOGY OF POWER FACTOR


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SIGNIFICANCE OF POWER FACTOR

I = V / R = 240 / 48 = 5 A

True Power = V I cos= 240 x 5 x 1 =1200W

The generator has no problem, although it isoperating at the maximum current and power.

All the generated power is consumed by the load

GeneratorRatings : 5A

1200W,240V UPF


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SIGNIFICANCE OF POWER FACTORGenerator

Ratings : 5A

1200W,240V

Even though average power consumed is less, current

exceeds the maximum rating and will damage the

generator windings.True power rating is not appropriate for AC sources and

hence all the AC sources such as generator should be

rated at VA.The required generator rating is 1920 VA . Out of 1920

VA , only 60 % is useful (1152 W).

I= V / R

= 240 / 30 = 8 A

True Power = V I cos

240 x 5 x 0.6 =1152 W

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Unit – I Lecture 2