The purpose of this paper is to bring the attention of the control community some of the aspects of the practically important, and mathematically challenging, power factor compensation problem. Our main contribution is identifying the key role played by cyclo-dissipativity in the solution of the problem. Namely, we prove that a necessary condition for a (shunt) compensator to improve the power transfer is that the load satisfies a given cyclo-dissipativity property, which naturally leads to a formulation of the compensation problem as one of cyclo-dissipasivation. Cyclo-dissipativity systems exhibit a net absorption of (abstract) energy only along closed paths, while a dissipative system cannot create energy for all trajectories, henceforth, this concept generalizes the one of passivation