Measurement of Power

MEASUREMENT OF POWER

Power the rate of doing work. In the electrical system, the unit of power is "watt". In DC system the power is given by the product of voltage and current.

 P = V*I (DC Circuit).

This power can be calculated by using voltmeter and ammeter or by a wattmeter.

In a AC circuit the instantaneous power is given by p=vi, where p, v, i are the average instantaneous values of power, voltage and current respectively. We can prove that the power over a cycle is given by,

P = VI cos ϕ (AC circuit)

Where,

P = average power

V = voltage.

I = current

cos ϕ = Power factor of the load.

Thus, we should know the power factor of the load, in AC circuit to calculate the power. So, a wattmeter is used which takes the power factor of the load also into account.

In ac circuit the power is measured by using voltmeter, ammeter and a power factor meter or mostly using a wattmeter. Wattmeter comes under the group of indicating instruments.

Classification of Wattmeters

Wattmeters are mainly classified into three groups namely,

1. Dynamometer type

2. Induction type

3. Electrostatic type wattmeters

Dynamometer type wattmeter

Dynamometer type wattmeters are sub‒divided into two groups:

(i) Pivoted coil direct indicating wattmeters.

(ii) Suspended tension wattmeters.

Measurement of power in three phase power by using two watt meter method

Using two wattmeter method, the power measured by the two wattmeters i.e. the sum of the two wattmeter readings is equal to root 3 times of the phase voltage and line voltage (√3V_LI_Lcos ϕ) which is the actual power consumed in a 3 phase balanced load. The connection diagram of a 3 phase balanced load connected as Star Connection is shown below.

The load is considered as an inductive load. The three voltages V_RN, V_YN and V_BN, are displaced by an angle of 120 degrees electrical as shown in the phasor diagram. The phase current lag behind their respective phase voltages by an angle ϕ. Now, the current flowing through the current coil of the Wattmeter, W₁ will be given as

W₁ = I_R

Potential difference across the pressure or potential coil of the Wattmeter, W₁ will be

To obtain the value of V_YB, reverse the phasor V_BN and add it to the phasor V_YN as shown in the phasor diagram. The phase difference between V_RB and I_R is (30° – ϕ).

Therefore, the power measured by the Wattmeter, W₁is

W₁ = V_RBI_R COS (30° ‒ ϕ)

Current through the current coil of the Wattmeter, W₂ is given as

W₂ = I_Y

Potential different across the wattmeter, W₂ is

The phase difference V_YB and I_Y is (30°+ϕ).

Therefore, the power measured by the Wattmeter, W₂ is given by the equation shown below.

W₂ = V_YBI_Y cos (30°+ϕ)

Since, the load is in balanced condition, hence,

I_R=I_Y=I_B=I_L and

V_RY= V_YB= V_BR=V_L

Therefore, the wattmeter readings will be

W₁ = V_LI_L cos (30° − ϕ) and

W₂ = V_L I_L cos (30° + ϕ)

Now, the sum of two wattmeter readings will be given as

W₁+ W₂ = V_LI_L cos (30°‒ϕ) + V_LI_L cos (30° + ϕ)

W₁+ W₂ = V_LI_L [ cos (30°‒ϕ) + cos (30° + ϕ) ] or

W₁+ W₂ = V_LI_L [cos 30° cos ϕ + sin 30° sin ϕ + cos 30° cos ϕ  ‒ sin 30° sin ϕ ] or

W₁+ W₂ = V_LI_L (2cos 30° cos ϕ ) or

W₁+ W₂ = V_LI_L (2 √3/2 cosϕ)

W₁+ W₂ = √3V_LI_Lcosϕ

W₁+ W₂ = P

The above equation (1) gives the total power absorbed by a 3 phase balanced load.

Thus, the sum of the readings of the two Wattmeters is equal to the power absorbed in a 3 phase balanced load.

Circuit diagram