# Parameter Observer Useable for the Condition Monitoring of a Capacitor
## 1 Introduction  
Electolytic capacitors are characterized by high electrical capacity/volume ratio, low internal resistance, and last but not least, their low price. These features are of great importance for various applications in the field of short-term electricity storage [1]. However, capacitors are vulnerable devices, responsible for numerous failures [2; 3; 4]. The high frequency of failures caused by electrolytic capacitors imposes the requirement of monitoring their equivalent parameters, mainly the capacitance (C) decreasing and the equivalent serial resistance (ESR) increasing, as part of condition monitoring. Much electronic equipment in the aerospace, medical, military or energy domains requires high reliability [5], and, consequently, fault diagnosis or maintenance based on monitoring the ESR and the capacitance of electrolytic capacitors [6; 7; 8] to ensure that they operate within the required degradation model [9]. There are more recent studies on the operational safety of equipment, in particular of power converters, from several perspectives. A wide range of analysis and decision-making techniques are used for this purpose, nowadays reaching the use of machine learning techniques [10; 11; 12]. Specific interfaces and algorithms, suitable for interaction with converters, are required for their application. Article [13] considers an ESR monitoring scheme without a current sensor, based on the calculation of the parameter's values from the measurement of the AC component of the output voltage at precise times of the output switching cycle. In [14] a method of ESR monitoring is proposed based on the jump of the output voltage and the measurement of the ripple voltage output and inductor current. A model-free predictive control strategy, for the online estimation of the ESR and capacitance,aimed at the continuous evaluation of the electrolytic capacitor condition is discussed in [4]. The capacitor current and output voltage acquisitions are required. The design of electronic circuits involving electrolytic capacitors uses different conceptual electrical models of capacitors, more or less simplified, and equivalent electrical parameters [5; 15; 16]. Simple models, type R-C, are widely used in modelling the circuits in which the capacitors are embedded, particularly in DC-DC converters [17]. In practice, C and ESR, the main parameters of electrolytic capacitors, vary substantially depending on the operating mode (voltage waveform, working frequency and temperature), but also due to the irreversible aging phenomenon [18]. During the transient phenomena, characteristic of electric charging-discharging cycles, there is a reversible variation in the values of the main parameters of the electrolytic capacitors. In [19] this behaviour is highlighted for a capacitor discharging process. A comprehensive and topical synthesis regarding monitoring dc-link capacitors in power converters is presented in [7]. It highlights the equivalent conceptual schemes and estimation principles used. From the perspective of our research, we note the equivalent scheme R-C, used when the equivalent series inductance is negligible, as well as the principle of the model-based estimation in the non-periodic discharging profile variant. It is also worth noting the study in [20], which addresses the monitoring of the output capacitor and the inductor of a boost converter, considering for the capacitor an equivalent R-C model. The authors of [8] propose a method of online monitoring of the ESR and C of the output capacitor of a buck converter based on the analysis of the transient voltage regimes at the terminals of the output capacitor. In the same vein, [6] presents a condition-monitoring procedure for dc-link capacitors of AC-DC-AC power converters based on a variable electrical network capable of estimating the equivalent C and the equivalent ESR of the dc-link capacitor. No current sensor was used in either study, and no external signal was injected.