A cyclo-dissipativity characterization of power factor compensation of nonlinear loads under nonsinusoidal conditions
Résumé
Recently, it has been established that power factor (PF) improvement for nonlinear loads with nonsinusoidal source voltage is equivalent to imposing the property of cyclodissipativity to the source terminals. Using this framework, the classical capacitor and inductor compensators were interpreted in terms of energy equalization. The purpose of this brief note is to extend this approach in three directions. In the result reported in the literature, the supply rate is a function of the load, which is usually unknown, stymieing the applicability of the technique for compensator synthesis. Our first contribution is a new cyclodissipativity condition, which is also equivalent to PF improvement, but whose supply rate is now function of the compensator. Second, we consider general lossless linear compensators, instead of only capacitive or inductive compensators. As a result, we show that the PF 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, namely the one that achieves unitary PF, and the aforementioned equalization condition. This result naturally leads to the formulation of a problem of optimization of the parameters of the compensator.