AC Power

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AC PowerAC Power

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As in the case with DC power, the instantaneous electric power in an AC circuit is given by P = VI, but these quantities are continuously varying. Almost always the desired power in an AC circuit is the average power, which is given by

AC PowerAC Power

Pavg = V I cos

where is the phase angle between the current and the voltage and V and I are understood to be the effective or rms values of the voltage and current. The term cos is called the "power factor" for the circuit.

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Instantaneous Power

As in DC circuits, the instantaneous electric power in an AC circuit is given by P=VI where V and I are the instantaneous voltage and current.

then the instantaneous power at any time t can be expressed as

Since

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the power becomes:

Averaging this power over a complete cycle gives the average power.

Average PowerAverage PowerNormally the average power is the power of interest in AC circuits. Since the expression for the instantaneous power is a continuously varying one with time, the average must be obtained by integration. Averaging over one period T of the sinusoidal function will give the average power. The second term in the power expression above averages to zero since it is an odd function of t. The average of the first term is given by

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Since the rms voltage and current are given by

the average power can be expressed as

and

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Average Power Integral

Finding the value of the average power for sinusoidal voltages involves the integral

The period T of the sinusoid is related to the angular frequency and angle by

Using these relationships, the integral above can be recast in the form:

Which can be shown using the trig identity:

which reduces the integral to the value 1/2 since the second term on the right has an integral of zero over the full period.

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RLC Series CircuitRLC Series Circuit

The RLC series circuit is a very important example of a resonant circuit. It has a minimum of impedance Z=R at the resonant frequency, and the phase angle is equal to zero at resonance.

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Single-phase SystemSingle-phase System

The Sinusoidal voltage

v(t) = Vm sin twhere

Vm = the amplitude of the sinusoid

= the angular frequency in radian/s

t = timev(t)

Vm

-Vm

t

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v(t)

Vm

-Vm

t

2

TT

1f

f2The angular frequency in radians per second

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Single-phase SystemSingle-phase SystemA more general expression for the sinusoid (as shown in the figure):

v(t) = Vm sin (t + )

where is the phase anglev(t)

Vm

-Vm

t

V1 = Vm sin t

V2 = Vm sin t + )

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A sinusoid can be expressed in either sine or cosine form. When comparing two sinusoids, it is expedient to express both as either sine or cosine with positive amplitudes. We can transform a sinusoid from sine to cosine form or vice versa using this relationship:

sin (ωt ± 180o) = - sin ωt

cos (ωt ± 180o) = - cos ωt

sin (ωt ± 90o) = ± cos ωt

cos (ωt ± 90o) = + sin ωt

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Apparent Power, Reactive Power and Power FactorThe apparent power is the product of the rms values of voltage and current.

The reactive power is a measure of the energy exchange between the source and the load reactive part.

)sin( ivQ rmsrmsIV

rmsrmsIVS

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Single-phase Single-phase SystemSystem

The power factor is the cosine of the phase difference between voltage and current.

The complex power:

)cos( ivfactor Power S

P

iv

jQP

rmsrms IV

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Three-phase SystemThree-phase System

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In a three phase system the source consists of three sinusoidal voltages. For a balanced source, the three sources have equal magnitudes and are phase displaced from one another by 120 electrical degrees.

A three-phase system is superior economically and advantage, and for an operating of view, to a single-phase system. In a balanced three phase system the power delivered to the load is constant at all times, whereas in a single-phase system the power pulsates with time.

Generation of Three-phaseGeneration of Three-phase

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Suppose three similar loops of wire with terminals R-R’, Y-Y’ and B-B’ are fixed to one another at angles of 120o

and rotating in a magnetic field.

R

R1

B

B1

Y

Y1

N S

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The instantaneous e.m.f. generated in phase R, Y and B:vR = VR sin t

vY = VY sin (t -120o)

vB = VB sin (t -240o) = VBsin (t +120o)

v(t)

t

vR

vY vB

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Phase sequences:(a) RYB or positive sequence

120o

-120o

120oVR

VY

VB

o

)rms(YY 120VV

o

)rms(RR 0VV

o

)rms(B

o

)rms(BB

120V

240VV

VR leads VY, which in turn leads VB

This sequence is produced when the rotor rotates in the counterclockwise direction

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(b) RBY or negative sequence

o

)rms(BB 120VV

o

)rms(RR 0VV

o

)rms(Y

o

)rms(YY

120V

240VV

120o

-120o

120oVR

VB

VY

VR leads VB, which in turn leads VY

This sequence is produced when the rotor rotates in the clockwise direction

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Star and Delta ConnectionStar and Delta Connection

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Star Connection

Three wire system R

Y

B

ZR

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Four wire system

VRN

VBN VYN

ZR

R

BN

Y

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Wye connection of Load

Z1

Z3

Z2

R

B

Y

NLoad

Z3

R

Y

B

Load

N

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Delta Connection

R

Y

B

Y

B

R

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Zc

Za

Zb

R

B

Y

Load

Za

R

Y

B

Load

Delta connection of load

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N

R

Y

B

VRY

VYB

VBR

VYN

VBN

VRN

IR

IY

IB

Line-to-neutral voltages:

240V

120V

0V

phaseBN

phaseYN

phaseRN

V

V

V

linephase

linephase

V

II

V

# Reference: VRN

# Positive sequence

Wye Connection

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N

R

Y

B

VRY

VYB

VBR

VYN

VBN

VRN

IR

IY

IB

303

120j1200j0

1200

seph

oooophase

phasephase

YNRNRY

aV

V

VV

VVV

)sin()(cos()sin(cos

The two other can be calculated similarly.

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BNBNBR VVV

The line to line voltages

1503

2103

903

303

phase

phaseBR

phaseYB

phaseRY

V

VV

VV

VV

BNYNYB VVV YNRNRY VVV

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VRY

VBR

VYB

VRY

R

Y

BV

YB

VBR

Delta Connection

Line-to-line currents:

240II

120II

0II

phaseBR

phaseYB

phaseRY

linephase

linephase

II

VV

# Reference: IRY

# Positive sequence.

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30I3

120j1200j0I

120I0I

III

seph

oooophase

phasephase

BRRYR

a

sin(cos)sin(cos

The two other can be calculated similarly.

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YBBRB III

903

2703

1503

303

phase

phaseB

phaseY

phaseR

I

II

II

II

RYYBY III BRRYR III

The line currents:

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30°

-120°

VBR VRY

VYB

VYN

VRN

VBN

-VYN

• Phasor diagram is used to visualize the system voltages• Wye system has two type of voltages: Line-to-neutral, and line-to-line• The line-to-neutral voltages are shifted with 120 degrees• The line-to-line voltage leads the line to neutral voltage with 30 degrees• The line-to-line voltage is times the line-to-neutral voltage

Vector diagram

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TNB SUPPLY SYSTEMTNB SUPPLY SYSTEM

Voltage 3 phase, 50 Hz

The main transmission and substation network are: - 275 kV - 132 kV - 66 kV

The distribution are: - 33 kV - 22 kV - 11 kV - 6.6 kV - 415 volts - 240 volts (single phase) drawn from 415 volts 3 phase (phase voltage), between line (R, Y, B) and Neutral (N)

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SYSTEMSYSTEM

The low voltage system (415/240 V) is 3-phase four wire.The low voltage system is a mixture of overhead lines and under ground cables.

The high voltage and extra high voltage system is 3-phase three wire Configuration. Overhead line and under ground cable system are used.

Supply Method (two types of premises)Supply Method (two types of premises)

1. Single consumer such as private dwelling house, workshop, factory, etc

a. Single phase, two wire, 240 V, up to 12 kVA max demandb. Three phase, four wire, 415 V, up to 45 kVA max demandc. Three phase, four wire, C. T. metered 415 V, up to 1,500 kVA max demand

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2. Multi tenanted premises, such as high rises flats, commercial, office blocks, etc

- Low Voltage

a. Three phase, three wires, 6,600 and 11,000 V for load of 1, 500 kVA max demand and above, whichever voltage is available

b. Three phase, three wires, 22,000 and 33,000 V for load of 5,000 kVA max demand and above, whichever voltage is available

c. Three phase, three wires, 66,000 V, 132,000 V and 275,000 for exceptionally large load of above 20 MVA max demand

Three phase, four wire, C.T. metered 415 V, up to 1,500 kVA maxdemand

- High Voltage and Extra High Voltage

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Standby Supply

Standby generator(s) to be used by the consumer in his premises, inaccordance with the relevant by-laws, may be provided by the consumer

The generator(s) shall remain a separate system from the TNB’s Distribution system and should be certified and registered by Suruhanjaya Tenaga (formerly JBE)

This may be used in place of the TNB’s supply source through a suitable,Approved change over facility under emergency conditions.

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Beban

Berubah setiap masa, hari, minggu dan bulan.

Beban mempengaruhi penjanaan tenaga.

Penjanaan tenaga berdasarkan permintaan beban yang lepas.

Lengkuk beban berubah dalam sehari.

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AC Power