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 × Vph × Iph
× Cos(θ)
Or
= √3×(√3 Vph) × Iph × Cos(θ)
= √3 VL × IL × Cos(θ)
× 10-3 kw ...... [ ∵ in star connection,VL = √3
Vph and IL= Ip and θ = angle between phase current and phase
voltage]
Similarly,
Total
reactive power,Q = √3 VL × IL × Sin(θ) × 10-3 kVAR
So, the total apparant power or complex power of the star connection is obviously
S= √P2+Q2
= √3 VL × IL VA
