What is the power in 3-phase supply system?

1 Answer

Answer :

In a single-phase system power ‘P’ = VPh * IPh * cosϕ watts.
 In 3-ϕ system power ‘P’ = 3 * VPh * IPh * cosϕ watts.
In Star connection, IL = IPh and VPh = VL/√3. Substituting the value of IPh and VPh
in the above 3-ϕ power equation,
 P = 3 * VPh * IPh * cosϕ watts.
 P = 3 * VL/√3 * IL * cosϕ watts.
 P = √3 * VL * IL * cosϕ watts.

In Delta connection, VL = VPh and IPh = IL/√3. Substituting the value of IPh and VPh
in the above 3-ϕ power equation,
 P = 3 * VPh * IPh * cosϕ watts.
 P = 3 * VL* IL/√3 * cosϕ watts.
 P = √3 * VL * IL * cosϕ watts.
So that the power in three phase supply system whether star connected or delta
connected is same and power P = √3 * VL * IL * cosϕ watts.
So cosϕ = P/ √3 * VL * IL .

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