In what condition,we can have \$P_{\Delta}=P_{Y}\$,not \$P_Y=\frac{1}{3}P_{\Delta} \$
So in what condition,we can have \$P_Δ=P_Y\$


In a star connected load, the phase current is the line current. 
In a delta connected load, the line current is \$\sqrt3\$ times greater than that for a star load using the same limb impedances. 


So if you want a star load to match a delta load in terms of power (VA), each limb of the star has to have an impedance that is \$\sqrt3\$ times lower than each limb of the delta load. This will then make the phase current (also line current) \$\sqrt3\$ times bigger and therefore matches the delta load line current.