Worked examples

WORKED EXAMPLES

THREE PHASE POWER MEASUREMENT

By 2 wattmeter method

Case (a): Balanced star connected loads.COM

Example 13 Determine the power and power factor if the two wattmeters read (i) 1000 w each, both positive (ii) 1000 w each of opposite sign.

Solution: Case (i):

W₁ = 1000 watts

W₂ = 1000 watts

This power factor may be lead or lag. As the load is not specified, (inductive or capacitive) we can not identify the nature of power factor.

Example 14 The power input to a 2000 V, 50 HZ, 36 motor running on full load at an efficiency of 90% is measured by two wattmeters which indicate 300KW and 100KW respectively. Calculate i) Input, ii) Power factor, iii) Line current, iv) H.P. output.

Solution:

W₁ = 300 KW

W₂ = 100 KW

i) Total input power = W₁ + W₂ = 400 KW = 400 × 10³ W

ii) The motor is assumed to be Induction motor. Hence the power factor is lagging in nature.

Example 15 In a balanced 34 system, the power is measured by two-wattmeter method and the ratio of two wattmeter readings is 2: 1. Determine the power factor of the system.

Solution: Data: W₂ / W₁ = 1/2 = r  (say)

We know that for lagging power factor,

Example 16 A balanced delta connected load takes a line current of 15A when connected to a balanced 3 phase 400 V system. A wattmeter with its current coil in one line and potential coil between the two remaining lines read 2000 W. Describe the load impedance.

Solution : For this type of connection, the wattmeter indicates reactive power. Hence the given power must be in VAR and not watts.

Watt meter reading

Example 17 Three identical coils each having a resistance of 202 and a reactance of 202 are connected in i) star ii) delta across 440 V, 3 phase supply. Calculate for each case, line current and reading in each of the wattmeters connected to measure power.

Solution: