Diagnostic of Supercapacitors based on State Estimation through Extended Kalman Filter

This thesis aimed to analyze the supercapacitor behavior to verify the possibility of the estimation of its internal parameters for diagnostic purposes. The target has been reached firstly by a theoretical analysis which showed that the crucial parameters for diagnostic purposes are the voltage of the non-linear capacitance, since it gives a measure of the stored charge, and the parasitic resistance which limits the maximum allowable current and influences losses. Secondly it has been verified when a supercapacitor parameters are observable and finally an extended Kalman filter to obtain such parameters has been set up. The Thesis demonstrated that a supercapacitor can be modelled by a 2-branch Double-Layer capacitor including a non-linear capacitance, it is observable thanks to the fact that such SC can be characterized by a parabola in the state space region in which the observability is not guaranteed. It has been shown that this curve usually does not cross the normal operating region corresponding to a part of the first quadrant of the state space plane. Then the internal parameters have been estimated by an Extended Kalman Filter , or EKF . A windowed-EKF , or wEKF , has been used for learning the EKF behavior, when it has to engage with measured the output y with respect to pre-configured time ranges. The main parameter to be estimated has been identified in the voltage of the non-linear capacitance since it gives a measure of the stored charge and of the parasitic resistance. The goal of diagnostics is reached since a very low error between the real and estimated values of the voltage on the non-linear capacitance has been obtained. The assessed method can be operated on-line: during the lifecycle of a SC , some values could differ from rated ones; so that, a possible SC degradation can be detected. In this case the SC replacement can be programmed with benefits for operators and equipment.