Hi Bahdir,
I believe the effect is real and can't be 'solved'. When the loads are purely resitive, the current and voltage are exactly in phase. With a resistive+reactive load, the current and voltage are no longer exactly in phase. The age-old mnemonic ELI the ICE man says that for an inductor, current lags voltage. Accordingly, in the lower plot you can see the current peaks all occur later than in the upper plot.
When you change the loads all of a sudden, there will be some transients involved in shifting the phases from the old values to the new. The transients die down due to the resistances in the circuit and you end up with a steady state, different from the original steady state.
