3-Phase AC Circuit

Introduction Three phase system is a part of a

poly phase system.The different circuits in polyphase system operate at same frequency, but their voltage and currents are out of phase from one other.

In poly phase many number of phase are displaced from each other with appropriate angle of electrical degree.

Thus, an ac system having a group of poly phasers having equal voltage & frequency arregement with equal phase angle difference between adjacent phases is called a polyphase system.By considering many advantages of three phase system over single phase for bulk power handling, for all practical purpose, three phase system is universally employed for generation , transmission& distribution of electrical power. In addition to that the reason for immense popularity of three phase appartus are that (a) more efficiency (b) less material required for given capicity (c) less cost for same capacity than single-phase equipment.

Agvantages of 3-phase system over 1-phase

(1)Higher power/weight ratio of alternators. A three phase alternator is smaller and lighter that a single phase alternator of the same power output. Hence, it is also cheaper.

(2)A three phase transmission system requires less copper or aluminium to transmit the same quantity of power of a specific distance than a single phase system.

(3)Three phase motors are self-starting due to the rotating magnetic field induced by the three phases. On the other hand, a single phase motor is not self starting, it requires a capacitor and an auxilliary winding.

(4)In Single phase systems, the instanteous power(power delivered at any instant) is not constant and is sinusoidal. This results in vibrations in single phase motors.In a three phase power system, though, the instanteous power is always the same.

(5)Three phase motors have better power factor compared to single phase motors.

(6)Three phase supply can be rectified into dc supply with a lesser ripple factor

Generation of Three Phase Voltage

3-Phase Generator

In 3-phase the armature windings ar displace 120 degree electrical apart. Hence , voltages induced displacementt between different three phases. So in general except two-phase system, electrical displacement between different phases in 360/n, where n is the number of phases or windings.In figure 2-poles & 3-phase stationary armature are shown in figure.The field winding is on rotating part known as rotor & armature winding is on stationary part known as stator of 3-phase a.c. generator or alternator.

It has thre armature coils displaced 120 degree apart from each other.For clock wise rotation of poles, it is found that the e.m.f. induced in conductor for coil is maximum when pole axis lies. The emf is in conductor for coil would be maximum when the N-S liesss . Thus we can say , the induced emf is conductor reaches its maximum value 120 degree later than the maximum value value in conductor. In same manner the maximum emf will induced in conductor , 120 degree later than that or 240 degree later than that in.

When the rotor is rotated in clockwise direction st constant angular velocity w rad/sec, a sinusoidal voltage is generated across each coil & thre emf are 120 degree out of phase with one onother as shown in below wave. As three coils under 90 with same velocity of field coil mounted on rotor.Frequency & amplitude of emfs are equal.

Wave Form of 3-Phase

Phase Sequence of 3-Phase System

A three phase system of voltages (or currents) has a sequence (or order) in which the phases reach a particular position (for example peak value). This is the natural sequence of the supply. According to usual notation, we would call the sequence R-Y-B or A-B-C. If we consider a balanced system of voltages (or currents) they will have only the natural sequence, and there will no other components present. However, Fortescue has formulated that any unbalanced system can be split up into a series of balanced systems. [This is like saying that any force can be broken up into its components along the x-axis, y-axis and z-axis. The advantage of such a decomposition is in the analysis of more than one quantity]

In the case of unbalanced three phase system, such as shown in figure 14, the unbalanced system can be split up into 3 components: (i) a balanced system having the same phase sequence as the unbalanced system, (ii) a balanced system having the opposite phase sequence to the unbalanced system (rotation of phasors is always anticlockwise whether they are in the same sequence or opposite, so that it is the order of the phases that changes, and not the direction of rotation), and (iii) a balanced system of inphase quantities.

R

YB

≡

PositiveSequence

R1

B1 Y1

NegativeSequence

R2

B2

Y2

Decomposition of unbalanced three phase

R0,Y0,B0

ZeroSequence

In any three phase system, the phase quantities R, Y and B (or A, B and C) may be

expressed as the phasor sum of:a set of balanced positive phase sequence

quantities A1, B1 and C1(phase sequence a-b-c : same phase sequence

as originalunbalanced quantities),a set of balanced negative phase sequence

currents A2, B2 and C2(phase sequence a-c-b: opposite phase sequence

to originalunbalanced quantities),a set of identical zero

phase sequence currents A0, B0 and C0

Regrouping

Interconnection of Three Phase

The interconnection generally made out following methods:

(1) Star or Wye Connection(2) Mesh or Delta Connction

(1) Star or Wye Connection

In this kind of interconnection, the starting ends or finishing ends (Similar ends) of three coils are connected together to form the neutral point. Or

Star Connection is obtained by connecting together similar ends of the three coils, either “Starting” or “finishing”. The other ends are joined to the line wires. The common point is called the neutral or Star Point, which is represented by N. (As shown in fig 1)

Star Connection is also called Three Phase 4 wires (3-Phase, 4-Wires) system.

Line Voltages and Phase Voltages in Star Connection

 if VR = VY = VB = VPH, thenVRY = 2 x VPH x Cos (60°/2) = 2 x VPH x Cos 30° = 2 x VPH x (√3/2) …… Since Cos 30° =

√3/2 = √3 VPHSimilarly,VYB = VY – VB = √3 VPHAndVBR = VB – VR = √3 VPHHence, it is proved that VRY = VYB = VBR is

line voltages VL in Star Connection, Therefore, in Star Connection;

VL = √3 VPH or VL = √3 EPH

(2) Mesh or Delta Connection

In this system of interconnection, the starting ends of the three phases or coils are connected to the finishing ends of the coil. Or the starting end of the first coil is connected to the finishing end of the second coil and so on (for all three coils) and it looks like a closed mesh or circuit as shown in fig (1).

In more clear words, all three coils are connected in series to form a close mesh or circuit. Three wires are taken out from three junctions and the all outgoing currents from junction assumed to be positive.

In Delta connection, the three windings interconnection looks like a short circuit, but this is not true, if the system is balanced, then the value of the algebraic sum of all voltages around the mesh is zero.

When a terminal is open, then there is no chance of flowing currents with basic frequency around the closed mesh.

 Line Currents and Phase Currents in Delta Connection

Current in Line 1= I1 = IR – IB

Current in Line 2 =I2 = IY – IR

Current in Line 3 =I3 = IB – IY

Masurement of Power In 3-Phase Circuit

There following methods(1) Three Wattmeters Method(2) Two Wattmeters Method

(1) Three Wattmeters Method

(2) Two Wattmeters Method