Question

What is the power in 3-phase supply system? 

Answer 1

In a single-phase system power ‘P’ = V_Ph * _IPh * cosϕ watts. 

In 3-ϕ system power ‘P’ = 3 * V_Ph * I_Ph * cosϕ watts. 

In Star connection, I_L = I_Ph and V_Ph = V_L/√3. Substituting the value of I_Ph and V_Ph in the above 3-ϕ power equation, 

P = 3 * V_Ph * I_Ph * cosϕ watts. 

P = 3 * V_L/√3 * I_L * cosϕ watts. 

P = √3 * V_L * I_L * cosϕ watts. 

In Delta connection, V_L = V_Ph and I_Ph = I_L/√3. Substituting the value of I_Ph and V_Ph in the above 3-ϕ power equation, 

P = 3 * V_Ph * I_Ph * cosϕ watts. 

P = 3 * V_L* I_L/√3 * cosϕ watts. 

P = √3 * V_L * I_L * cosϕ watts.

So that the power in three phase supply system whether star connected or delta connected is same and power P = √3 * V_L * I_L * cosϕ watts.

So cosϕ = P/ √3 * V_L * I_L .