| 1. |
- Ekström, Henrik, et al.
(author)
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Comparison of lumped diffusion models for voltage prediction of a lithium-ion battery cell during dynamic loads
- 2018
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In: Journal of Power Sources. - : Elsevier. - 0378-7753 .- 1873-2755. ; 402, s. 296-300
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Journal article (peer-reviewed)abstract
- Three different time-dependent lumped battery models are presented, using a limited set of only either three or four fitting parameters. The models all include one linear (resistive), one non-linear (kinetic) and one time-dependent element, the latter describing the diffusive processes in the battery. The voltage predictive capabilities of the models versus experimental dynamic load data for a plug-in hybrid vehicle battery are compared. It is shown that models based on a diffusion equation in an idealized particle perform similarly to a model based on an RC (resistive-capacitor) pair. In addition, by exchanging the RC element by a diffusion equation in an idealized particle it is also shown that it is possible to reduce the number of needed fitting parameters by one.
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| 2. |
- Klintberg, Anton, 1989, et al.
(author)
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Kalman filter for adaptive learning of two-dimensional look-up tables applied to OCV-curves for aged battery cells
- 2019
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In: Control Engineering Practice. - : Elsevier BV. - 0967-0661. ; 84, s. 230-237
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Journal article (peer-reviewed)abstract
- In online automotive applications it is common to use look-up tables, or maps, to describe nonlinearities in component models that are to be valid over large operating ranges. If the component characteristics change with aging or wear, these look-up tables must be updated online. For 2-D look-up tables, the existing methods in the literature only adapt the observable parameters in the look-up table, which means that parameters in operation points that have not been visited for a long time may be far from their true values. In this work, correlations between different operating points are used to also update non-observable parameters of the look-up table. The method is applied to Open Circuit Voltage (OCV) curves for aged battery cells. From laboratory experimental data it is demonstrated that the proposed method can significantly reduce the average deviation from an aged OCV-curve compared to keeping the OCV-curve from the beginning of the cell's life, both for observable and non-observable parameters.
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| 3. |
- Klintberg, Anton, 1989, et al.
(author)
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Theoretical bounds on the accuracy of state and parameter estimation for batteries
- 2017
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In: American Control Conference. - 0743-1619. ; , s. 4035-4041
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Conference paper (peer-reviewed)abstract
- Today it is standard to use equivalent circuit models to describe the dynamic behavior of Li-ion vehicle batteries. The parameters and states change with operating point and are therefore continuously estimated using bayesian observers, though without knowing to what degree the performance can be improved. Posterior Cramér-Rao Lower Bounds (CRLBs) can be used to theoretically quantify the optimal accuracy of bayesian estimators. In this paper we apply this to a second-order nonlinear equivalent-circuit model of a lithium-ion battery. It is shown, by numerical calculations, how the posterior Cramér-Rao Lower Bounds depend on the amplitude and frequency of the current, and on the slope of the Open Circuit Voltage (OCV) curve. Furthermore, it is investigated how much the accuracy is reduced in combined estimation of the states and the resistance compared to when the resistance is perfectly known. More importantly, it is also shown that the Mean Square Errors (MSE) of an Extended Kalman Filter (EKF) are close to the posterior CRLBs, which means that, under the investigated circumstances, it is not possible to significantly reduce the MSEs by replacing the EKF by any other observer.
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| 4. |
- Wik, Torsten, 1968, et al.
(author)
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Implementation and robustness of an analytically based battery state of power
- 2015
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In: Journal of Power Sources. - : Elsevier BV. - 0378-7753 .- 1873-2755. ; 287, s. 448-457
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Journal article (peer-reviewed)abstract
- Today it is common practice to use simplified equivalent circuit models for predicting the short term behaviour of the voltage and current during charging and discharging battery cells. If the circuit parameters are assumed to be unchanged the response for a given open circuit voltage (OCV) will be the solution to a linear ordinary differential equation. This means that for given voltage limits the maximum charge and discharge powers can be analytically derived. In advanced battery management units, such as those used for hybrid electric vehicles, it is central to know how much that can be charged or discharged within a certain range of time, which is one definition of state of power (SoP). Using the linearizing assumption we derive a method for an adaptive estimation of the state of power based on incremental analysis. The method is easy to implement and have two tuning parameters that are straightforward to relate to. Using frequency analysis the method is analytically proven to have very strong robustness properties. The risk of exceeding voltage limits by effectively applying the maximum charge or discharge currents is marginal in spite of large circuit parameter errors, unmodelled hysteresis, unknown OCV and static nonlinearities.
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| 5. |
- Zou, Changfu, 1987, et al.
(author)
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Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control
- 2018
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In: Journal of Power Sources. - : Elsevier BV. - 0378-7753. ; 396, s. 580-589
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Journal article (peer-reviewed)abstract
- Technical challenges facing determination of battery available power arise from its complicated nonlinear dynamics, input and output constraints, and inaccessible internal states. Available solutions often resorted to open-loop prediction with simplified battery models or linear control algorithms. To resolve these challenges simultaneously, this paper formulates an economic nonlinear model predictive control to forecast a battery's state-of-power. This algorithm is built upon a high-fidelity model that captures nonlinear coupled electrical and thermal dynamics of a lithium-ion battery. Constraints imposed on current, voltage, temperature, and state-of-charge are then taken into account in a systematic fashion. Illustrative results from several different tests over a wide range of conditions demonstrate that the proposed approach is capable of accurately predicting the power capability with the error less than 0.2% while protecting the battery from undesirable reactions. Furthermore, the effects of temperature constraints, prediction horizon, and model accuracy are quantitatively examined. The proposed power prediction algorithm is general and then can be equally applicable to different lithium-ion batteries and cell chemistries where proper mathematical models exist.
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