Nowadays, considering the time-varying nature of harmonic sources is a significant trend in the power quality studies. In this research, the optimum sizing of multiple-steps passive LC compensator for maximum power factor and minimum transmission loss for non-linear loads under time-varying conditions of background harmonic voltages, system impedance, and load impedance, is determined. The source harmonic voltages are varying in time independently of each other. The equivalent system impedance is given by varying the Thevenin impedance over a finite period. The functioning of the concerned LC filter is explained through a representative case study. Simulation results illustrate the viability of the suggested approach. © 2016 IEEE.