Let us consider a resistive load R is connected across the secondary of transformer whose impedance is r+jX, so in calculation of the power factor of the supply (here in this case it is the secondary of the transformer ), Will the supply power factor be : cos theta = R+r/Z or will it be r/Z only ? Does supply power factor of the system has anything to do with load impedance ?
The power factor measured at the input side of a transformer is mostly determined by the load. Unless the load is very small, the effect of the impedance of the transformer itself is almost negligible.
The power factor measured at the primary of the transformer is the result of applying the source voltage to the combined impedance of the transformer equivalent circuit and the load.
The power factor at the secondary of the transformer is determined only by the load circuit. If the load changes, the power factor changes according to the change in the components of the load circuit that are responsible for the change in load.
See the equivalent circuit of a transformer:
For the usual mains transformer, copper losses R_p and R_s' and stray inductance L_sigma_p and L_sigma_s' are so low they are negligible aside from secondary short circuit condition.
What means your load impedance Z_l is in parallel to iron losses R_Fe and L_µ, the main inductance of the transformer.
Again, for the usual mains transformer, R_Fe and L_µ are so high their influence on primary current is negligible for any condition but secondary open.