Modeling of Electrolytic Capacitors Based on Fractional Order Elements
Fractional Order Calculation, Constant Phase Element (CPE),
Fractional Order Capacitor (FOC), Equivalent Series Resistance (ESR).
Power converters are essential for the operation of modern electronic systems, with the DC-Link bus being particularly relevant for signal filtering and stabilization. However, the electrolytic capacitors used in these buses represent one of the most vulnerable points, accounting for up to 30% of converter failures. Condition monitoring (CM) focused on equivalent series resistance (ESR) and capacitance is vital for predictive maintenance, but traditional integer-order models fail to capture the memory, dissipation, and frequency dispersion effects intrinsic to real components. To overcome these limitations, this dissertation proposes the development and validation of a robust method for near-online identification of electrolytic capacitor parameters using Fractional Order Calculus (FOC), representing the component as a Constant Phase Element (CPE) or Fractional Order Capacitor (FOC). The methodology adopts the design of a recursive parallel RC network with compensation elements to approximate fractional behavior. To validate the proposed model, computer simulations and experimental bench tests were performed on a two-stage (Boost and VSI) three-phase photovoltaic (PV) system. Through the injection of harmonic signals in the 2.5 kHz to 5.0 kHz range and the use of the Fast Fourier Transform (FFT), the capacitor parameters were estimated. The experimentally obtained results showed that the average error of the estimated ESR in relation to the FOC model was less than 5%, validating the accuracy, robustness, and applicability of the proposed methodology for improving fault diagnosis systems in power electronics.