Analysis and Development of a method for state of charge estimation of batteries based on Kalman filters
Análise e Desenvolvimento de um método de estimação de estado de carga de baterias baseado em Filtros de Kalman
Results
The main requirements of the dissertation were the development a BMS function to estimate the state of charge (SOC) of each cell of a battery. The algorithm should be able to be implemented in real time and the intention is using the battery in an EV.
After defining the main requirements was done a theoretical study on the batteries, BMS and estimation methods of SOC. Many estimation methods require the use a battery model , so the same theme was also studied.
Based on the content studied and requirements, including the fact that the battery have a non-linear behavior, was chosen as the method of estimation the Kalman filter Extended (EKF). The literature suggests that this method is that it leads to smaller estimation errors.
The algorithm requires the use of a battery model. Was therefore used for this purpose, an electric model deduced from the diffusion model. From the nonlinear equations that describe the model, was constructed the state space model. After was done the parameterization and initialization of variables related to the electrical model and the filter design. Unlike what happens in Kalman filter(KF), in extended Kalman filter (EKF), these initialization and parameterization are both very important and must be close to the true values. Bad parameterizations and initializations can lead the divergence of the filter.
The EKF algorithm, built in Matlab, was tested with different current profiles. The results obtained proved the proper functioning of the filter for continuous current and pulsed currents. It was also found that by using this estimation method has a lower mean relative error of the estimation using the electric model isolated. However, the algorithm was stopped before being taken estimation for all data relating to the practical test. EKF model starts to diverge when very small amounts of SOC are achieved.
In order to optimize the algorithm, and to avoid this behavior, it was amended considering the variation of link resistence as a function of discharge current. This variation in the case of the EKF, makes a reduction of the mean relative error between the estimated voltage and the measured voltage, as was intended. The filter converges for all values tested.
Comparing the results obtained in the dissertation with results obtained by other authors It is noted that the developed model gives the better SOC estimation once that the estimation mean relative error is lower.
We can also conclude, after using NEDC tests data, the estimation algorithm developed is robust and the maximum error obtained was 0.5890%.
The statistical study, made for three practical tests, demonstrates that good results are no coincidence since for both the filter has a good performance and a good estimation results.
Based on this finding and attending to the concept of the EKF itself is expected that is possible to implement this algorithm to estimate SOC of batteries in real time.
Future work
Although the objectives of the dissertation have been met, the developed algorithm can be improved.
Batteries lose part of their capacity each discharge cycle, this phenomenon is given the name of aging. In order to more accurately predict the SOC of the battery is necessary to take into account this phenomenon. From the same state-space model can be developed in a future dual extended Kalman filter, to estimate both the SOC and refresh the series resistance of the battery.
Since it is possible to implement the algorithm developed in time can also be adapted to be implemented in a microcontroller. Note that along this implementation it is necessary to develop a system for acquiring accurate because the accuracy of the measurements of the terminal voltage and current are the main parameters that influence the filter.