Power factor compensation with lossless linear filters is equivalent to (weighted) power equalization and a new cyclo-dissipativity characterization

Recently, it has been established that the problem of power factor compensation for nonlinear loads with non-sinusoidal source voltage can be recast in terms of the property of cyclo-dissipativity. Using this framework the classical capacitor and inductor compensators can be interpreted in terms of energy equalization. Unfortunately, the supply rate is a function of the load, which is usually unknown, styming the applicability of this result for compensator synthesis. The purpose of this brief note is to extend this approach in three directions. First, power factor compensation is shown to be equivalent to a new cyclo-dissipativity condition, whose supply rate is now function of the compensator. Second, we consider general lossless linear filters as compensators and show that the power factor is improved if and only if a certain equalization condition between the weighted powers of inductors and capacitors of the load is ensured. Finally, we exhibit the gap between the ideal compensator, e.g., the one that achieves unitary power factor, and the aforementioned equalization condition. This result naturally leads to the formulation of a problem of optimization of the compensator topology and its parameters.