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**Faculty of Electrical Engineering Universiti Teknologi Malaysia**

Mechanical and Electrical Systems SKAA 2032 Power Supply (AC and DC) Faculty of Electrical Engineering Universiti Teknologi Malaysia

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**Alternating voltage and current**

Electricity is produced by generators at power station. Electricity is then distributed by a vast network of transmission lines called National Grid System. It is easier and cheaper to generate AC than DC. It is more convenient to distribute AC than DC since the voltage can be readily altered using transformer. Whenever DC is needed, devices called rectifiers are used for conversion.

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**Alternating voltage and current**

Rectifier Power socket

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**Generation of Single Phase**

An electric current can be induced in a circuit by a changing magnetic field – Faraday’s Law The direction of the induced current is such that the induced magnetic field always opposes the change in the flux – Len’z Law Direction of current for generator – Fleming’s right hand rule.

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Single phase Single phase electricity is generated by rotating a single turn coil through a magnetic field. The shape of the waveform produced by a generator (i.e. the alternator) is in the form of sine wave. Wires used: Live conductor (yellow) Neutral conductor (blue) Earth conductor (green) –connected from neutral via a protective gear to earth

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Single phase

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**Single phase system A general expression for the sinusoid is given by:**

v(t) = Vm sin (wt + q) where Vm is the amplitude or peak value ω is the angular frequency radian/s given by ω=2πft f is the frequency in hertz (Hz) t is the time in second (s) T is the period in second, given by T=1/f θ is the phase angle in degree

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**The angular frequency in radians/second**

Single phase system The angular frequency in radians/second

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Single phase system 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: cos ωt = sin (ωt + 90o) sin ωt = cos (ωt - 90o)

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**Single phase system (a) v(t) = 12 cos (50t + 10o)**

Example 1.1 Find the amplitude, phase angle, angular frequency, period and frequency of the sinusoidal waveform (a) v(t) = 12 cos (50t + 10o) (b) v(t) = 5 sin (4πt - 60o) (a) (12V, 10o, 50rads/sec, sec., Hz) (a) (5V, -60o, 4π rads/sec, 0.5 sec., 2 Hz)

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Single phase system Sinusoids are easily expressed in terms of phasors. A phasor is a complex number that represents the amplitude and phase of a sinusoid. v(t) = Vm cos (ωt + θ) Time domain Phasor domain Time domain Phasor domain

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**Single phase system Instantaneous and Average Power**

The instantaneous power is the power at any instant of time: p(t) = v(t) i(t) Where v(t) = Vm cos (ωt + θv) i(t) = Im cos (ωt + θi) Using the trigonometric identity, gives

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Single phase system The average power is the average of the instantaneous power over one period.

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Single phase system The effective value is the root mean square (rms) of the periodic signal. The average power in terms of the rms values is given by Where

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Single phase system Example 1.2 An ac voltage of a sinusoidal waveform has a peak value of 300 V. What is the rms value of this voltage? (212.1 V) Example 1.3 What is the peak voltage of 120 V rms? (169.7)

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Single phase system Example 1.4 An alternating current of sinusoidal waveform has a r.m.s value of 10A. What are the peak values of this current over one cycle? (14.14A & A)

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Single phase system Example 1.5 An alternating voltage can be represented by v=141.4 sin 377t. Determine: (a) r.m.s. voltage (b) frequency (c) the instantaneous voltage when t = 3 ms (100V, 60Hz, 127.8V)

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Single phase system 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.

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**Single phase system The complex power:**

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

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**Single phase system True or active power: Watts (W) Apparent power: S**

Q volt·amperes (VA) θv–θi Reactive power: P reactive volt·amperes (var)

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Three phase system

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Three phase system A three-phase electricity is generated when three coils are placed 120° apart, and the whole rotated in a magnetic field. The result is three independent supplies of equal phase voltage - distinguished by 120° phase angle. The convention adopted to identify the phase voltages: R-red, Y-yellow, B-blue. The standard phase sequence is R, Y, B.

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**Generation of Three-phase**

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 through a magnetic field.

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Three phase system Three conductors (lines) to carry the three phase supply, colored red, yellow and blue. A fourth conductors called the neutral, connected through protective device to earth. The three phase system is usually connected using: star connection (sources i.e. alternators) delta connection (transformers, motors and other loads)

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**Generation of Three-phase**

The instantaneous e.m.f. generated in phase R, Y and B: vR = VR sin wt vY = VY sin (wt -120o) vB = VB sin (wt -240o) = VBsin (wt +120o)

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**Generation of Three-phase**

Phase sequences: RYB or positive sequence VR leads VY, which in turn leads VB. This sequence is produced when the rotor rotates in the counterclockwise direction.

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**Generation of Three-phase**

(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.

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Star Connection Three wire system

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Star Connection Four wire system

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**Star Connection of Load**

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Delta Connection

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**Delta Connection of Load**

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**Star Connection Phase voltages (line-to-neutral voltages):**

Line voltages (line-to-line voltages): # Reference: VRN # Positive sequence.

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**Star Connection Line currents, Iline:**

Phase currents are equal to their line currents:

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**Star Connection – Line Voltages**

The two other can be calculated using similar method.

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**Star Connection - Line voltages**

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**Star connection - Vector diagram**

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

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**Star connection - Distribution**

Typical distribution voltage of 415/240V, 3 phase 4 wires system

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**Delta Connection Phase voltages are equal to the line voltages**

# Reference: IRY # Positive sequence.

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Delta Connection R Y B Phase currents:

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**Delta Connection – Line Currents**

The two other can be calculated using similar method.

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**Delta Connection – Line Currents**

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**Delta Connection – Vector Diagram**

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**TNB Supply System Voltage 3 phase, 50 Hz**

The main transmission and substation network are: - 275 kV - 132 kV kV The distribution are: kV kV kV kV 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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**TNB Supply System Supply Method (two types of premises)**

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

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

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Standby Supply Standby generator(s) may be used by the applicant at their premises, subject to compliance with the relevant laws. The generators shall remain a separate system from TNB distribution system and the applicant shall declare to TNB on the safe installation of the generator(s). This may be used in place of TNB’s supply source through a suitable, approved changeover facility. The Energy Commission and other relevant authorities govern the usage of generators and standby supply. 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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