This article advances an analysis and compensator design framework for power-factor compensation based on cyclodissipativity. Although the framework applies to general polyphase unbalanced circuits, this paper have focused on the problem of power factor compensation with LTI capacitors or inductors of single-phase loads. The full power of the approach are expected to become evident for polyphase unbalanced loads with possibly nonlinear lossless compensators, where the existing solutions are far from satisfactory. The main obstacle appears to be the lack of knowledge about the load, a piece of information that is essential for a successful design