standards

Measurement of Three Phase Power by Three Wattmeters Method

The circuit diagram is shown below-
three wattmeter method power measurement

Here, it is applied to three phase four wire systems, current coil of all the three wattmeters marked as one, two and three are connected to respective phases marked as one, two and three. Pressure coils of all the three wattmeter are connected to common point at neutral line. Clearly each wattmeter will give reading as product of phase currentand line voltage which is phase power. The resultant sum of all the readings of wattmeter will give the total power of the circuit. Mathematically we can

$P\;=\;P_1\;+\;P_2\;+\;P_3\;=\;V_1I_1\;+\;V_2I_2\;+\;V_3I_3$

Measurement of Three Phase Power by Two Wattmeters Method

In this method we have two types of connections
(a)Star connection of loads
(b)Delta connection of loads.
When the star connected load, the diagram is shown in below-
two wattmeter method star connected of load

two wattmeter method star connected of load

For star connected load clearly the reading of wattmeter one is product phase current andvoltage difference (V2-V3). Similarly the reading of wattmeter two is the product of phasecurrent and the voltage difference (V2-V3). Thus the total power of the circuit is sum of the reading of both the wattmeters. Mathematically we can write

$P\;=\;P_1\;+\;+\;P_2\;=\;I_1(\;V_1\;+\;V_2\;)\;+\;I_2(\;V_2\;-\;V_3\;)$

but we have I1+I2+I3=0,hence putting the value of I1+I2=-I3.

We get total power as V1I1+V2I2+V3I3.

When delta connected load, the diagram is shown in below
two wattmeter method delta connected load

The reading of wattmeter one can be written as

$P_1\;=\;-V_3(\;I_1\;-\;I_3\;)$

and reading of wattmeter two is

$P_2\;=\;-V_2(\;I_2\;-\;I_1\;)$

$Total\;power\;is\;\;P\;=\;P_1\;+\;P_2\;=\;V_2I_2\;+\;V_3I_3\;-\;I_1(\;V_2\;+\;V_3\;)$

but V1+V2+V3=0, hence expression for total power will reduce to V1I1+V2I2+V3I3.

Measurement of Three Phase Power by One Wattmeter Method

Limitation of this method is that it cannot be applied on unbalanced load. So under this condition we have I1=I2=I3=I and V1=V2=V3=V.

Diagram is shown below:

measurement of three phase power using single wattmeter method

One Wattmeter Method

Two switches are given which are marked as 1-3 and 1-2, by closing the switch 1-3 we get reading of wattmeter as
$P_1\;=\;V_{13}I_1\cos (\;30\;-\;\phi \;)\;=\;\sqrt{3}\;\times VI\cos (\;30\;-\;\phi \;)$

Similarly the reading of wattmeter when switch 1-2 is closed is