Draw and explain the power triangle for a 3-ϕ lagging load.

The total power in a three phase system is the sum of powers in the three phases. For a balanced load, the power consumed in each load phase is the same. 

Total active power (P) = 3 x power in each phase = 3 Vph Iph cos $\phi $

In a star connected three phase system, 

$V_{ph}=\dfrac{V_L}{\sqrt 3}$

$I_{ph}=I_L$

$P=3\times \dfrac{V_L}{\sqrt 3}\times I_L\times cos\ \phi =\sqrt 3\times V_L\ I_L \ cos\ \phi $

Where,  $\phi $ is the phase difference between phase voltage and corresponding phase current. 

Similarly, total reactive power $Q=3\ V_{ph}\ I_{ph}\ sin\ \phi =\sqrt 3\ V_L\ I_L sin\phi $

Total Apparent Power (S) $=3\ V_{ph}\ I_{ph}=\sqrt 3 \ V_L\ I_L$

The power triangle of a three phase system is as shown in Fig. 1 below;