Power in a Star Connection | Three Phase Power

It is assumed that you know the basics of a star connected network and how we reach to the below shown phasor diagram. If not, It is strongly recommended to go through Relationship between Line and Phase Voltages and Currents in Star Connection .  In the case shown let it be a balanced load with impedances  Z ( lagging load) carrying phase current (same as line current for star connection)  lagging phase voltage by an angle θ degree.

Since line voltages in a star connection leads their respective phase voltages by 30 degrees. Therefore, the angle between a line voltage and corresponding line current is  (30+ θ)  degrees. In with any Ac circuit, this star configuration will also have real, reactive and apparant power.

Total Active or Real power in a Star Connection :-

The total real power in the circuit is the sum of the individual three phase powers.  

Therefore,                                

       Total active power,P = 3 × individual phase power

                                       = 3 × V_ph × I_ph × Cos(θ)       

                             Or      = √3×(√3 V_ph) × I_ph × Cos(θ)         

                                       = √3 V_L × I_L × Cos(θ) × 10^-3  kw                           ......   [ ∵ in star connection,V_L = √3 V_ph  and   I_L= I_p   and θ = angle between phase current and phase voltage]

Similarly,                                  

       Total reactive power,Q = √3 V_L × I_L × Sin(θ) × 10^-3  kVAR

So, the total apparant power or complex power of the star connection is obviously

S= √P²+Q²

   ⁼ √3 V_L × I_L   VA