AC Power
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AC Power. AC Power. 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. P avg = V I cos .

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AC Power

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

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.

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

the power becomes:

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

Average Power

Normally 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


the average power can be expressed as                       

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.

RLC 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.

Single-phase System

The Sinusoidal voltage

v(t) = Vm sin wt


Vm = the amplitude of the sinusoid

w = the angular frequency in radian/s

t = time

Single phase system

A more general expression for the sinusoid (as shown in the figure):

v(t) = Vm sin (wt + q)

whereqis the phase angle

Single-phase System

Single phase system1
Single-phase System figure):

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

Single phase system2
Single-phase System figure):

Apparent Power, Reactive Power and Power Factor

The 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.

Single phase system3
Single-phase System figure):

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

The complex power:

Generation of three phase
Generation of Three-phase figure):

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 phase1
Generation of Three-phase figure):

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.

Generation of three phase2
Generation of Three-phase figure):

The instantaneous e.m.f. generated in phase R, Y and B:

vR= VRsin wt

vY= VY sin (wt -120o)

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

Generation of three phase3

Generation of Three-phase

VR leads VY, which in turn leads VB

This sequence is produced when the rotor rotates in

the counterclockwise direction

Generation of three phase4
Generation of Three-phase figure):

(b) RBY or negative sequence

VR leads VB, which in turn leads VY

This sequence is produced when the rotor rotates in

the clockwise direction

Star Connection figure):

Three wire system

Wye connection
Wye Connection figure):

Line-to-neutral voltages:

# Reference: VRN

# Positive sequence

Delta Connection figure):

Line-to-line currents:

# Reference: IRY

# Positive sequence.

Vector diagram figure):

  • 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


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)

SYSTEM figure):

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)

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

  • Single phase, two wire, 240 V, up to 12 kVA max demand

  • Three phase, four wire, 415 V, up to 45 kVA max demand

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

  • demand

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

office blocks, etc

  • Low Voltage

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


  • High Voltage and Extra High Voltage

  • Three phase, three wires, 6,600 and 11,000 V for load of 1, 500 kVA

  • max demand and above, whichever voltage is available

  • Three phase, three wires, 22,000 and 33,000 V for load of 5,000 kVA

  • max demand and above, whichever voltage is available

  • Three phase, three wires, 66,000 V, 132,000 V and 275,000 for

  • exceptionally large load of above 20 MVA max demand

Standby Supply commercial,

Standby generator(s) to be used by the consumer in his premises, in

accordance 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.

Beban commercial,

Berubah setiap masa, hari, minggu dan bulan.

Beban mempengaruhi penjanaan tenaga.

Penjanaan tenaga berdasarkan permintaan beban yang lepas.

Lengkuk beban berubah dalam sehari.