# THREE PHASE POWER MEASUREMENT USING TWO WATTMETERS

OBJECTIVES:

• To measure the total power consumed in a balanced three phase star / delta connected load by using two wattmeters.
• To calculate the power factor of the load connected to the three phase system.

THEORY:

A wattmeter consists of two coils: a low resistance current coil which is connected in series with the line carrying the current, and a high resistance  potential coil which is connected across the two points whose potential difference is to be measured. Thus, a wattmeter shows a reading which is propoprtional to the product of the current through its current coil, the potential drop across its voltage coil and the cosine of the angle between this voltage and the current.

In order to measure the power consumed in a three phase ac circuit (whether wye or delta) by two wattmeters, the current coils of the wattmeters are inserted in series in any of the two lines and the potential coils are shorted and connected to the third line.

1. Wye or star connection

Let the phase voltages be V1=V2=V3=VP, the line-to-line voltage be VL, phase currents be IP and line currents be IL. For a star connection, the phase and line voltages are realated as $$V_L=\sqrt{3V_p}$$……..(1)

and the phase and line currents are related as

$$I_L=I_p$$………..(2)

If the power factor of the load is cos θ, then, the power measured by wattmeter W1 is ILVLcos(30o-θ).  Similarly, the power measured by wattmeter W2 is ILVLcos(30o+θ). Adding the two readings, $$W_1+W_2=\sqrt{3V_LI_Lcos\theta}….(3)$$

similarly,

$$W_1-W_2=V_LI_Lsin\theta……(4)$$

therefore  $$tan\theta=\sqrt3\frac{(W_1-W_2)}{W_1+W_2}…….(5)$$

or  $$cos\theta=cos(tan^{-1}\sqrt3\frac{W_1-W_2}{W_1+W_2})—–(6)$$

ii. Delta connection:

Let the phase voltages be V1=V2=V3=VP, the line-to-line voltage be VL, phase currents be IP and line currents be IL. For a delta connection, the phase and line voltages are related as $$V_L=V_P…..(7)$$

and the phase and line currents are related as  $$I_L=\sqrt3I_P……(8)$$

If the power factor of the load is cos θ, then, the power measured by wattmeter W1 is ILVLcos(30o-θ).  Similarly, the power measured by wattmeter W2 is ILVLcos(30o+θ). Adding the two readings,

$$W_1+W_2=\sqrt3V_LI_Lcos\theta…..(9)$$

similary

$$W_1-W_2=V_LI_L sin\theta……(10)$$

therefore  $$tan\theta=\sqrt3\frac{(W_1-W2)}{W_1+W_2}…..(11)$$

or $$cos\theta=cos(tan^{-1}\sqrt3\frac{(W_1-W_2)}{W_1+W_2})…(12)$$

CIRCUIT DIAGRAMS:

APPARATUS USED:

 Sl. No. Name of the apparatus used Quantity Maker’s Name Range / rating of the apparatus

PROCEDURE:

• The connections are made as shown in the circuit diagram (1 or 2).
• The supply is switched on and the variac is gradually increased to a fixed value.
• The voltmeter and wattmeter readings are noted down.
• The above steps are again repeated with different values of variac voltage or different values of load current.
• Finally the variac is brought to zero and the supply is switched off.

EXPERIMENTAL DATA TABLE:

 Sl. No. VRY (VL) in volts VYB (VL) in volts VBR (VL) in volts IR (IL) in amps IY (IL) in amps IB (IL) in amps P1 (W1) in watts P2 (W2) in watts Total Power P1+P2= W1 + W2 (in watts) Power  component = 3 VphIph (in watts) Power Factor   (cos θ)

PHYSICAL CHARACTERISTICS:

• Plot the phasor diagram

CONCLUSION:

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