Three Phase A.C. Circuit

IntroductionWhen 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

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          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

          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. 

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

One Wattmeter Methord

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 .

Three Wattmeter Methord

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 .

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 .

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

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 .

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 )

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 .