Power in 3 Phase Star Connection || Electrical Circuit || Bangla 

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Power in Star Connection :
In a three phase AC circuit, the total True or Active power is the sum of the three phase power. Or the sum of the all three phase powers is the Total Active or True Power.
Hence, total active or true power in a three phase AC system;
Total True or Active Power = 3 Phase Power
Or
P = 3 x VPH x IPH x CosФ ….. Eq … (1)
We know that the values of Phase Current and Phase Voltage in Star Connection;
IL = IPH
VPH = VL /√3 ….. (From VL = √3 VPH)
Putting these values in power eq……. (1)
P = 3 x (VL/√3) x IL x CosФ …….…. (VPH = VL /√3)
P = √3 x√3 x (VL/√3) x IL x CosФ ….… {3 = √3x√3}
P = √3 x VL x IL x CosФ
Hence proved;
Power in Star Connection,
P = 3 x VPH x IPH x CosФ or
P = √3 x VL x IL x CosФ
Similarly,
Total Reactive Power = Q = √3 x VL x IL x SinФ
Where Cos Φ = Power factor = the phase angle between Phase Voltage and Phase Current and not between Line current and line voltage.
Also, the total apparent power of the three phases;
Total Apparent Power = S = √3 x VL x IL
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