Dynamic analysis of active filters using Chaos theory

Active filters are power electronic devices used to improve the electrical energy quality by providing either the necessary harmonic currents that nonlinear loads demand (current or parallel active filter), or voltage signals to cancel the voltage disturbances added to the 60 Hz sine wave (voltage or series active filter). Due to the switching operation of the active filters, the corresponding equations, based on the equivalent electrical circuits, are nonlinear with time-varying associated parameters. This work searches the feasibility of a dynamic analysis for active filters based on the chaos theory, since this theory yields information about bounded regions having a non-periodic performance. The operation ranges for the active filters before chaos occurring were found under the action of two different controllers (PI control and passivity-based control), justifying the superiority of the latter. A novel methodology is presented, based on the chaos theory and Poincare diagrams, to determine the proper values for the passivity resistors in the passivity-based control, such that an improvement in the demand total distortion (parallel active filter) and the total harmonic distortion (series active filter) was obtained, and hence improving the filter performance and the quality in the electrical supply.