Real Reactive Apparent Power

10
Power Engineering Foundation By Fuad Latip 2006 1 Real, Reactive and Apparent Power in AC Circuit P = V*I DC Circuit AC circuit more complex Phase different between V and I The Instantaneous Power supplied to an AC cct still P = V*I V = Instan. Voltage I = Instan. Current Average Power supplied to the load will affected by the θ (θ = phase angle between V and I) + - R I V DC DC Voltage source supplying a load with resistance R

Transcript of Real Reactive Apparent Power

Page 1: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 1

Real, Reactive and Apparent Power in AC Circuit

P = V*I DC Circuit

AC circuit more complex Phase different between V and I

The Instantaneous Power supplied to an AC cct still

P = V*I

V = Instan. Voltage

I = Instan. Current

Average Power supplied to the load will affected by the θ (θ = phase angle between V

and I)

+ -

R

I

VDC

DC Voltage source supplying a load with resistance R

Page 2: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 2

Inductive Load Capacitive Load

θ = +ve θ = -ve

Current LAG the voltage by θ degrees. Current LEAD the voltage by θ degrees.

rms

peak

rms

IItIti

VV

VVtv

tVtv

=−=

=

===

)cos(2)(

load this toflowingcurrent The

2

voltageinstant)(cos2)(

load this toapplied voltageThe

θω

ω

rms

peak

rms

IItIti

VV

VVtv

tVtv

=+=

=

===

)cos(2)(

load this toflowingcurrent The

2

voltageinstant)(cos2)(

load this toapplied voltageThe

θω

ω

+ -

I AC = I∠-θo

VAC = V∠0o

AC Voltage source supplying a load with resistance Z =Z∠θo

Z =Z∠θo

θo I Lead V

V

I θo I Lag V

V

I

Page 3: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 3

Power in AC

2sin2sin1)12(coscos

sin2sin)12(coscos

)(coscos

)()()(

ComponenttVIComponenttVI

where

tVItVI

tttVI

titvtPLoadInductiveFrom

>−−>−−+

++=

−=

=

θωωθ

θωωθ

θωω

The components of power supplied to a single phase load versus time. The first Component represents the power supplied by the component of current in phase with the voltage, while the second term represents the power supplied by the component of current 90o out of phase with the voltage

Page 4: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 4

• The 1st term of the instantaneous power expression is always +ve, but it produces

pulses of power instead of a constant value.

• The average value of this term is

P = VICosθ

• This is the AVERAGE or REAL POWER (P) supplied to the load.

• The unit of real power are WATT (W)

1W = 1V * 1 A

• The 2nd term of instantaneous power expression is +ve half and –ve half so that

the average power supplied by this term is zero.

• This term represents power that is first transferred from source to the load, and

then returned from the load to the source.

• It is known as REACTIVE POWER (Q)

• Reactive Power represents the energy that is first stored and then released in the

magnetic field of an inductor or in the electric field of a capacitor.

• The Reactive Power of load is given by

Q = VISinθ

• The unit of Reactive Power is volt-amperes reactive (var).

1var = 1V * 1A

• θ is the impedance angle of the load for both cases (Active Power and

Reactive Power)

Page 5: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 5

Apparent Power (S) is the product of the voltage across the load and the current through

the load whereby the phase angle are ignored.

S = V*I

The unit of Apparent Power is volt-amperes (VA)

1VA = 1V * 1A

Relative Forms of the Power Equations

θθ

θ

θ

θθ

sincos

impedanceloadtheofmagnitud

sincos

(3)and(2)(1),tongsubstituti

constantloadaif

)3()2(sin)1(cos

2

2

2

jZjXRZ

ZZISZIQZIP

IZV

VISVIQVIP

+=+=

==

=

=

==

−−−−−−=−−−−=−−−−=

S

Q

P

θ

Page 6: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 6

Complex Power (S)

S = P + jQ

Complex Power, S supplied to a load can be calculated from the equation below

jQPjVIVIS

jVIVIVI

IV

IIVV

lett) I conjugaI* VI* (S

+=+=

−=

−+−=−∠=

−∠∠=

∠=∠=

==

θθβαθ

βαβαβα

βα

βα

sincos

)sin()cos()(

))((

The Relationship between Impedance Angle, Current Angle and Power

Inductive Load

• Has a +ve impedance angle ,θ since the reactance of an inductor is +ve

• The phase angle of the current flowing through the load will lag the phase angle

of the voltage across the load by θ.

θθ

−∠=∠∠

==ZV

ZV

ZVI 0

• Load is said to be consuming both real and reactive power from source.

Page 7: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 7

Capacitive Load

• Has a -ve impedance angle ,θ since the reactance of an inductor is -ve

• The phase angle of the current flowing through the load will lead the phase angle

of the voltage across the load by θ.

θθ

∠=−∠

∠==

ZV

ZV

ZVI 0

• Load is said to be consuming real power from the source and supplying reactive

power to the source.

+ -

I AC = I∠-θo

VAC = V∠0o Z =Z∠θo

P

Q

+ -

I AC = I∠-θo

VAC = V∠0o Z =Z∠θo

P

Q

Page 8: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 8

The Power Triangle

PQSQSP

=

=

=

θ

θ

θ

tan

sin

cos

• cosθ = cos(-θ), so the power factor produced by an impedance angle of +θ is

exactly same as the power factor produced by and impedance angle of –θ.

• So we cannot know whether a load is inductive or capacitive from the power

factor alone.

• Then the current leading or lagging have to know whenever a power factor is

quoted.

Page 9: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 9

Example

Figure below shows an AC voltage source supplying power to a load with impedance Z =

20∠-30o Ω. Calculate the current, I supplied to the load, the power factor of the load, and

the real, reactive, apparent, and complex power supplied to the load.

+ -

I

VAC = 120∠0o VoltZ =20∠-30o

Page 10: Real Reactive Apparent Power

Power Engineering Foundation

By Fuad Latip 2006 10