Degradation Modeling and Reliability Assessment of Capacitors

Abstract

The degradation of capacitors under accelerated stress conditions occur in a monotonic and non-linear fashion. Several efforts have been made to model the degradation behavior of capacitor considering either physics-of-failure models or statistical models and subsequently estimate its reliability and lifetime parameters. But most of these models fail to reflect the physical properties of the degradation path, which varies according to several intrinsic and extrinsic factors. These factors introduce random and temporal uncertainty among the population of capacitors. The gamma stochastic process can model both type of uncertainties among the population of capacitors. In this paper, we model the capacitor degradation by non-homogeneous gamma stochastic process in which both the model parameters (shape and scale) are dependent on stress variables. The model parameters are estimated using the maximum likelihood estimation approach.

Impact of cell spreading on second‐life of lithium‐ion batteries

“…An approximated cumulative distribution function (CDF) of time‐to‐failure for threshold is given by where and is the initial degradation value. [ 19 ]…”

“…These characteristics make gamma stochastic models suitable to describe degradation phenomena when the degradation increments depend only on the age of the product. [18] NHGP was used by Gupta et al [19] to model the degradation of capacitors. Their three-parameter NHGP [19] is suitable for any degradation process exhibiting monotonic, non-linear, and unidirectional behaviours, being capable of modelling temporal and sampling uncertainties.…”

“…[18] NHGP was used by Gupta et al [19] to model the degradation of capacitors. Their three-parameter NHGP [19] is suitable for any degradation process exhibiting monotonic, non-linear, and unidirectional behaviours, being capable of modelling temporal and sampling uncertainties. [20] The expression for the NHGP distribution is as follows:…”

“…where ω b ¼ ωÀx 0 b and x 0 is the initial degradation value. [19] Galatro et al [11] used NHGP to predict the capacity fade as a measurement of SOH, or time-to-failure for any battery architecture, fitting these distributions to individual degradation trajectories of cells in a dataset, as well as obtaining an overall NHGP assumed to be representative of the degradation trajectories of an entire module or battery pack. In the next section, we describe the steps required to estimate the capacity fade of lithium-ion batteries employing NHGP.…”

“…NHGP was used by Gupta et al [ 19 ] to model the degradation of capacitors. Their three‐parameter NHGP [ 19 ] is suitable for any degradation process exhibiting monotonic, non‐linear, and unidirectional behaviours, being capable of modelling temporal and sampling uncertainties. [ 20 ] The expression for the NHGP distribution is as follows: where is the gamma function for the shape parameter , is a scale parameter, and is a threshold parameter, which is a monotonic increasing function of time.…”