| 1. |
- Klintberg, Anton, 1989, et al.
(författare)
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Statistical modeling of OCV curves for aged battery cells
- 2017
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 50:1, s. 2164-2168
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Konferensbidrag (refereegranskat)abstract
- Today it is standard to use equivalent circuit models to describe the dynamic behavior of Li-ion batteries. The parameters and the states of the model are often estimated with model-based approaches which require accurate Open Circuit Voltage (OCV) curves to relate OCV to State of Charge (SoC). However, batteries are inevitably subjected to aging with the consequence that the OCV-curve is changing with time. In this paper we propose a method for modeling the changes of the OCV-curve based on statistical information rather than from electrochemistry. The proposed model has only one free parameter to update, namely capacity based SoH. From laboratory experimental data it is demonstrated that the proposed model can significantly reduce the average deviation from an aged OCV-curve compared to keeping the OCV-curve from the beginning of life. Furthermore, the potential of the method in an estimation context is illustrated by using it together with an Extended Kalman Filter (EKF) for estimation of SoC. Both the maximum and root mean square errors are significantly reduced compared to when the OCV-curve at beginning of life is used.
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| 2. |
- Fridholm, Björn, et al.
(författare)
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Estimating power capability of aged lithium-ion batteries in presence of communication delays
- 2018
-
Ingår i: Journal of Power Sources. - : Elsevier BV. - 0378-7753. ; 383, s. 24-33
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Tidskriftsartikel (refereegranskat)abstract
- Efficient control of electrified powertrains requires accurate estimation of the power capability of the battery for the next few seconds into the future. When implemented in a vehicle, the power estimation is part of a control loop that may contain several networked controllers which introduces time delays that may jeopardize stability. In this article, we present and evaluate an adaptive power estimation method that robustly can handle uncertain health status and time delays. A theoretical analysis shows that stability of the closed loop system can be lost if the resistance of the model is under-estimated. Stability can, however, be restored by filtering the estimated power at the expense of slightly reduced bandwidth of the signal. The adaptive algorithm is experimentally validated in lab tests using an aged lithium-ion cell subject to a high power load profile in temperatures from −20 to +25 °C. The upper voltage limit was set to 4.15 V and the lower voltage limit to 2.6 V, where significant non-linearities are occurring and the validity of the model is limited. After an initial transient when the model parameters are adapted, the prediction accuracy is within ±2% of the actually available power.
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| 3. |
- Klintberg, Anton, 1989, et al.
(författare)
-
Adaption of 2-D look-up tables applied to OCV-curves for aged battery cells
- 2018
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In online automotive applications it is common to use lookup tables, or maps, to model nonlinearities in component models that are to be valid over large operating ranges. If the component characteristics change with ageing 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 operating 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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| 4. |
- Klintberg, Anton, 1989, et al.
(författare)
-
Cramér-Rao Lower Bounds for Battery Estimation
- 2016
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Ingår i: Reglermöte.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- To secure safety, reliability and performance of an electri- fied vehicle, it is important to monitor the State of Charge (SoC) of its battery. Today, there are no sensors that can measure SoC directly. Instead, it is usually estimated with an algorithmic filter. Since batteries are nonlinear, all feasible filters are only able to approximate the posterior densities which, in other words, means that their perfor- mances will be more or less suboptimal (Särkkä, 2013).To be able to evaluate the performance of a filter, it is of great value to know how well a parameter or a state can be estimated. It can then be decided if it is worth spending time on tuning the filter, or implementing a more advanced filter. Furthermore, analyzing the achievable accuracy can be a way to better understand the application.One suitable measure for benchmarking the performance is the Cramér-Rao Lower Bound (CRLB), which is a lower bound on the Mean Square Error (MSE) of any estimator.In this paper we adopt a method to numerically determine the posterior CRLBs with a Monte Carlo-based algorithm. The posterior CRLBs are calculated for combined esti- mation of the states and the parameters of a commonly used equivalent circuit model. It is investigated how the posterior CRLBs depend on the amplitude and the fre- quency of the current. Furthermore, the posterior CRLBs are computed for a commercially available lithium- ion battery using data from laboratory experiments, and the results are compared to the MSEs of an Extended Kalman Filter (EKF). It is shown that the MSEs of the EKF are close to the posterior CRLBs, which means that the EKF seems to be a good observer for this application.
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| 5. |
- Klintberg, Anton, 1989, et al.
(författare)
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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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Ingår i: Control Engineering Practice. - : Elsevier BV. - 0967-0661. ; 84, s. 230-237
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Tidskriftsartikel (refereegranskat)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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| 6. |
- Klintberg, Anton, 1989, et al.
(författare)
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Theoretical bounds on the accuracy of state and parameter estimation for batteries
- 2017
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Ingår i: American Control Conference. - 0743-1619. ; , s. 4035-4041
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Konferensbidrag (refereegranskat)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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| 7. |
- Zou, Changfu, 1987, et al.
(författare)
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Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control
- 2018
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Ingår i: Journal of Power Sources. - : Elsevier BV. - 0378-7753. ; 396, s. 580-589
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Tidskriftsartikel (refereegranskat)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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