Elements of Electrical Engineering

1. Three Phase A.C. Circuit

2. Introduction
When a generator produces A.C. in a single circuit ,
the resulting emf causes the current to vary
periodically over a cycle . In the course of one cycle
the voltage & current reach zero twice .
Such a circuit is referred to as a single phase circuit &
the resulting current in this circuit is called as only a
single current alternates at different intervals of time .
1 cycle 1 cycle
e i

3. Three phase power transmission has become the
standard for power distribution.
Three phase power generation and distribution is advantageous
over single phase power distribution.
Three phase power distribution requires lesser amount
of copper or aluminum for transferring the same amount of
power as compared to single phase power
The size of a three phase motor is smaller than that of
a single phase motor of the same rating.
Three phase motors are self starting as they can produce
a rotatingmagnetic field. The single phase motor requires a
special starting winding as it produces only a pulsating magnetic
field.
Advantage of 3 phase over Single
Phase

4. In single phase motors, the power transferred in
motors is a function of the instantaneous current which is
constantly varying. Hence, single phase motors are more
prone to vibrations. In three phase motors, however, the
power transferred is uniform through out the cycle and
hence vibrations are greatly reduced.
The ripple factor of rectified DC produced
from three phase power is less than the DC produced
from single phase supply.
Three phase motors have better power factor regulation.
Motors above 10HP are usually three phase.
Three phase generators are smaller in size
than single phase generatorsas winding phase can be
more efficiently used.

5. Power is measured in the electrical circuits using a
wattmeter . A single phase wattmeter consists of two
coils ; namely the current coil and the pressure coil .
The current coil is connected in series with the line
and thus carries the line current . The pressure coil is
connected in parallel with the line . The wattmeter
reading gives the power per phase .
Power measurement in the 3- phase system depends
upon whether the load connected across it is
balanced or unbalanced and whether it is in star or
delta . Power in the three – phase circuits is
measured using the following methods :
Measurement of power in 3-
phase

6. One Wattmeter Methord

7. In this method , a single wattmeter is used . It’s
current coil is connected in one line and the pressure
coil is connected between that line and the neutral .
The wattmeter gives the value of the power per
phase .
Total power = 3 * Power per phase
= 3 * wattmeter reading
The one wattmeter methord is used for
power measurement in the 3 – phase .

8. Three Wattmeter Methord

9. Like in the one wattmeter methord , where the
wattmeter is connected in one phase , in the three
wattmeter method , it is connected in all 3-Phases.
However , there is one difficulty in this type of
connection . Sometimes it is not possible to have
access of the neutral point in the star connection .
Fig shows the power measurement using 3-
wattmeter methord for a delta connected load .

10. However , it is not easy to make the connection into
the phases of a delta connected load .
The total power measured in either of the above two
methods = W1 + W2 + W3 .
The 3 – Wattmeter method can be used for star &
delta connected unbalanced loads .

11. This method is commonly used for the power
measurement in the 3 – phase circuits .
Here, as the name suggests , only two wattmeter are
used . The current coils of the two wattmeter's are
connected in series on any two lines and the third
line on which no wattmeter is connected .
The two wattmeter is used for the power
measurement in the 3 – phase system , irrespective
of whether the load is balanced or unbalanced , star
or delta connected .
Two Wattmeter Methord

13. Let VRN , VYN and VBN be the phase voltages across
the three loads and iR , iY and iB be the phase
currents respectively .
Thus the total instantaneous power in the load = VRN
iR + VYN iY + VBN iB
To find the power measured by the wattmeter's W1
and W2 .
The instantaneous value of the current flowing
through the current coil of wattmeter W1 = iR .
The instantaneous voltage across the pressure coil of
W1 = eRB .

14. But, eRB = VRN - VBN .
The instantaneous power measured by wattmeter
W1 = iR . (eRB) = iR (VRN – VBN )
Similarly , the instantaneous power measured by
wattmeter W1 = iY .
The instantaneous voltage across the pressure coil of
W2 = eYB .
But eYB = VYN – VBN
The instantaneous power measurement by wattmeter
W2 = iY eYB = iY (VYN – VBN )

15. W1 + W2 = iR (VRN – VBN ) + iY (VYN – VBN )
= iR VRN + iY VYN (iR + iY)
But in the star connection , applying kirchoff’s Current law
at the junction . We get ,
 iR + iB+ iY = 0
 iY + iR = - iB .
Putting the value of ( iY + iR = - iB ) in the equation of W1
+ W2 = The total instantaneous power .