# ELECTRICAL ENGINEERING-THREE PHASE A.C. CIRCUITS (PART ONE)

1.Introduction
Generation, transmission and heavy-power
utilisation of A.C. electric energy almost invariably involve a type of
system or circuit called a polyphase system or polyphase circuit. In
such a system, each voltage source consists of a group of voltages
having relative magnitudes and phase angles. Thus, am-phase system will
employ voltage sources which, conventionally, consist of m voltages
substantially equal in magnitude and successively displaced by a phase
angle of 360° I m.
A 3-phase system will employ voltage sources which, conventionally,
consist of three voltages substantially equal in magnitude and
displaced by phase angles of 120°. Because it possesses definite
economic and operating advantages, the 3-phase system is by far the most
common, and consequently emphasis is placed on 3-phase circuits.
2.Advantages of Poly phase Systems

The advantages of polyphase systems over single-phase systems are:
1. A polyphase transmission line requires less conductor material
than a single-phase line for transmitting  the same amount power at the
same voltage.

2. For a given frame size a polyphase machine gives a higher output
than a single-phase machine For example, output of a 3-phase motor is
1.5 times the output of single-phase motor of same size

3. Polyphase motors have a uniform torque where most of the single-phase motors have a pulsating  torque.

4. Polyphase induction motors are self-starting and are more
efficient. On the other hand single phase induction motors are not
self-starting and are less efficient.

5. Per unit of output, the polyphase machine is very much cheaper.

6. Power factor of a single-phase motor is lower than that of polyphase motor of the same

7. Rotating field can be set up by passing polyphase current through stationary coils.

8. Parallel operation of polyphase alternators is simple as compared
to that of single-phase  alternators because of pulsating reaction in
single-phase alternator.

It has been found that the above advantages are best realized in the
case of three-phase systems. Consequently, the electric power is
generated and transmitted in the form of three-phase system

3.Generation of Three-phase Voltages
Let us consider an elementary 3-phase 2-pole generator as shown in
Fig: 1. On the armature are three coils, ll’, mm’, and nn’ whose axes
are displaced 120° in space from each other.

When the field is excited and rotated, voltages will be generated in
the three phases in accordance with Faraday’s law. If the field
structure is so designed that the flux is distributed sinusoidally over
the poles, the flux linking any phase will vary sinusoidally with time
and sinusoidal voltages will be induced in three-phases. These three
waves will be displaced 120 electrical degrees (Fig. 2) in time as a
result of the phases being displaced

120° in space. The corresponding phasor diagram is shown in Fig. 3.
The equations of the instantaneous values of the three voltages (given
by Fig. 2) are:

e l’ l  = E max .. sin wt
e m ‘m = E max. sin (wt- 120°)
e n ‘n = E max. sin (wt – 240°)

The sum of the above three e.m.fs. is always zero as shown below :

Resultant instantaneous e.m.f.
= e l’ l + e m’ m + e n’ n
= E max. sin wt+ E max. sin (wt- 120°) + E max. sin ( wt – 240°)
= E max. [sin rot + (sin wt cos 120° – cos wt sin 120° + sin wt cos 240° – cos wt sin 240°)]

= E max. [sin rot+ (- sin wt cos 60° – cos rot sin 60° – sin wt cos 60° + cos wt sin 60°)]

= E max. (sin rot – 2 sin wt cos 60°)
= E max. (sin rot- sin wt) = 0.
4.PHASE SEQUENCE AND NUMBERING OF PHASES
By phase sequence is meant the order in which the three phases attain their peak or maximum,

In the generation of three-phase e.m.fs. in Fig. 2 clockwise rotation
of the field system in Fig. 1 was assumed. This assumption made the
e.m.f. of phase ‘m‘ lag behind that of ‘l‘ by 1200 and in a similar way, made that of ‘n‘ lag behind that of ‘m‘ by 120° (or that of l by 240°). Hence, the order in which the e.m.fs. of phases l, m and n attain their maximum value is Imn. It is called the phase order or phase sequence l → m → n. If now the rotation offield structure of Fig. 1 is reversed i.e. made
counter-clockwise, then the order in which three phases would attain
their corresponding maximum voltages would also be reversed. The phase
sequencewould become l → n → m. This means that e.m.f. of phase ‘n’ would now lag behind that of phase ‘l‘ by 120° instead of 240° as in the previous case.

The phase sequence of the voltages applied to a load, in general, is
determined by the order in which the 3-phase lines are connected. The phase sequence can be reversed by interchanging any pair of lines . (In the case of an induction motor, reversal of sequence results in the reversed direction of motor rotation).

The three-phases may be numbered l, m, n or 1, 2, 3 or they may be given three colours(as is customary).

The colours used commercially are red, yellow (or sometimes white) and blue. In this case sequence is RYE.
Evidently in any three-phase system, there two possible sequences, in
which three coils or phase voltages may pass through their maximum
value i.e., red → yellow → blue (RYE) or red → blue → yellow (RBY).
By convention:
RYE ….. taken as positive.
RBY ….. taken as negative.

5. INTER-CONNECTION OF THREE PHASES

Each coil of three phases has two terminals [one ‘start’ (S) and another ‘finish’ (F)]and if
individual phase is connected to a separate load circuit, as shown in Fig. 4, we get a non-interlinked

3-phasesystem. In such a system each circuit will require two conductors, therefore, 6 conductors
all. This makes the whole system complicated and expensive. Hence the three phases are gene
interconnected which results in substantial saving of copper.

The general method of inter-connections are:
1. Star or Wye (Y) connection.
2. Mesh or delta (∆) connection.

TO BE CONTINUOUS……….