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Two state of charge estimation methods using fractional order extended and unscented Kalman filter and a nonlinear variable fractional order battery model are implemented. Both, battery model and Kalman filters are evaluated and compared using measurements of an actual lithium-ion polymer battery cell. The observability of the battery model and the influence of an initialization function on the estimation algorithms is investigated.

Abstract-This paper is about the decentralization and distribution of a Kalman filter for fractional order systems. A fractional order discrete state space for a global system is introduced and divided into different submodules. The distribution of the model and of the state estimation algorithm into submodules leads to small and scalable units, which do not need a central processing node. Each submodule performs its computation locally. All information required by other nodes is communicated between the nodes directly. Finally, an example is given to compare the fractional Kalman filter (FKF) for the overall system with the distributed and decentralized fractional Kalman filter (DDFKF).

This paper considers a fractional modelbased identification method with the objective to determine the aging of a battery cell. The method avoids lumped approximations of the fractional operator. Moreover with this approach it is possible to identify physically motivated battery cell parameters. The basic idea is to transfer the derivatives from the measurements to the so called modulating functions. With the help of simulations a robust behavior against measurement noise is shown. It is possible to use the method for online battery identification. Zusammenfassung:In diesem Artikel wird eine fraktionale modellbasierte Identifikationsmethode vorgestellt. Diese liefert einen Beitrag zur Altersdiagnose von Batteriezellen. Vorteilhaft ist, dass die sonst frühe Approximation des fraktionalen Operators entfällt und dass mit ihr physikalisch motivierte Parameter identifiziert werden können. Die Kernidee des Verfahrens ist, Ableitungen der Messgröẞen auf sogenannte Modulationsfunktionen zu über-tragen. Anhand von Simulationen konnte gezeigt werden, dass das Verfahren robust gegenüber Messrauschen ist. Die Methode ist aus den genannten Gründen für eine online Identifikation einer Batteriezelle geeignet.

This paper presents a distributed Kalman filter algorithm for cascaded systems of fractional order. Certain conditions are introduced under which a division of a fractional system into cascaded subsystems is possible. A functional distribution of a large scale system and of the state estimation algorithm leads to smaller and scalable nodes with reduced memory and computational effort. Since each subsystem performs its calculations locally, a central processing node is not needed. All data which are required by subsequent nodes are communicated to them unidirectionally. Also a comparison between the Fractional Kalman Filter (FKF) and the Cascaded Fractional Kalman Filter (CFKF) is given by an example.

In this paper, a cascaded fractional Kalman filter for state of charge and branch current estimation of largescale battery systems is proposed. As a centralized approach for the estimation of a large-scale system is costly in terms of effort and time, a partition into smaller and, therefore, simpler subsystems is applied. Since the overall system is divided into smaller units, a local computation is allowed and complexity reduced. In these distributed systems, usually, the subsystems communicate with each other to exchange relevant data. Using a model based on mesh currents, we receive a cascaded system structure which results in a hierarchical arrangement of all subsystems. This concludes in a one-directional information flow and, therefore, reduces the overall communication effort. Using this proposed approach, it is not only possible to estimate the states of each branch locally but also to calculate the branch currents when the total current is known. Finally, a practical test with real measurement data is presented.

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