The potential coil having high resistance is connected across the load and carries the current proportional to the potential difference across the load. The current coil having low resistance is connected in series with the load.

The

**measurement of power in three phase circuit**can be carried out using the following methods:

- One wattmeter method
- Two wattmeter method
- Three wattmeter method.

# Three Wattmeter Method

The power measurement in three phase, three wire circuit is carried out by this method. The connection is shown in the figure. As the neutral wire is common to the three phases, each wattmeter reads power in its own phase, and the total power is given by the sum of the readings of three wattmeters.

Total power of load circuit, P_{3-φ }= W_{1} + W_{2} + W_{3}

In the case of delta connected circuits, power measurement by three wattmeter method is very difficult because phase coils of load are required to be broken for inserting the current coils of wattmeter.

# One Wattmeter Method of Power Measurement

In a balanced 3-wire, 3-phase load circuit the power in each phase is equal and, therefore, the total power of the circuit can be determined by multiplying the power measured in any one phase. Hence, the power measurement in three phase, three wire circuits can be carried out by using the one wattmeter only.

But this method has the disadvantage that **even a slight degree of unbalance in the loading, produces a large error in the measurement**.

# Measurement of Power by Two Wattmeter Method

**The power measurement in three phase, three wire load circuits usually carried out using this method.**

The current coils of two wattmeters are inserted in any two lines and the potential coil is connected from its own current coil to the line without the current coil.

It can be proved that the sum of the power measured by two wattmeter W_{1} and W_{2} is equal to the total instantaneous power absorbed by the load. But in actual practice wattmeters read the average power because of the inertia of their moving system.

The **two wattmeter** method of *power measurement in three phase circuits* is suitable for every type of three phase circuit weather circuit is balanced or unbalanced and star connected or delta connected.

## Variation in Wattmeter Reading Power Factor (lagging)

In two wattmeter method, readings of both wattmeters depend on power factor of load. Effect of different power factors on wattmeter readings is as under:

**When φ = 0 ^{o}** i.e., cos φ = 1

Both the wattmeters will give an equal and positive reading.

Therefore, P

_{3-φ }= W

_{1}+ W

_{2}

**When φ = 60**i.e., cos φ = 0.5

^{o}In this case, one wattmeter shows a zero deflection and the other one shows a positive reading.

Therefore, P

_{3-φ }= W

_{1}

**When 90**i.e., 0 < cos φ < 0.5

^{o}> φ > 60^{o}**In this case, one wattmeter will give a positive reading and another wattmeter will give a negative reading (down scale reading).**

To obtain a positive reading on W

To obtain a positive reading on W

_{2}, it is necessary to reverse either the potential coil or current coil connection. All readings taken after reversal of connection are to be taken negative.Therefore, P

_{3-φ}= W

_{1}– W

_{2}

**When φ = 90**i.e., cos φ = 0

^{o}Both the wattmeters will give equal and opposite reading.

Therefore, P

_{3-φ}= W

_{1}+ W

_{2}= 0

## Effect of Leading Power Factor on Wattmeter Readings

The effect of leading power factor is that the readings of two wattmeters are interchanged. Now wattmeter W_{2} has become the higher reading wattmeter. All other discussions remain the same as for the lagging power factor.

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