4. Real-time implementation of the Li-Ion battery SOC estimators on MATLAB/SIMULINK platform: Results comparison

For comparison purpose, we represent on the same graph the SOC estimates of all three real-time nonlinear estimators (UKF, PF, and NOE) versus EMC SOC true value and ADVISOR MATLAB SOC estimate, as are revealed in Figures 7, 10 and 13. The simulation results in Figure 16 disclose a precious information about the convergence of all three proposed estimators to Li-Ion EMC SOC true values for the proposed Li-Ion battery EMC. Furthermore, a useful benchmark is built in terms of the statistics errors between the states estimates and the corresponding model states values, such as root mean square error (RMSE), mean square error (MSE) and mean absolute error (MAE), defined in [6]. They are very easy to be computed in MATLAB R2017a, and the results are shown in Table 1. The MSE is a measure of how close the estimates values fit to model "true" values. The squaring is done so negative values do not cancel positive values. The smaller the MSE, the closer the fit of the estimates values is to the model "true" values. The RMSE is just the square root of the MSE [6].

UKF and PF estimators. Consequently, for this kind of applications the EMC-NOE SOC

Table 1. Statistics on SOC estimation performance of the proposed nonlinear estimators UKF, PF and NOE - Benchmark.

Figure 16. EMC SOCs and output terminal voltages versus EMC, EMC-UKF, EMC-PF, and EMC-NOE estimated values

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MAE MSE RMSE MAE MSE RMSE MAE MSE RMSE 0.0915 26.1030 0.1380 0.0572 4.9724 0.0602 0.0247 2.4584 0.0424

The main contribution of this research paper is the design and implementation in real time of a three robust nonlinear estimators, namely UKF, PF and NOE, capable to estimate with high accuracy and robustness the Li-Ion battery SOC based on a simple battery 2R EMC without disturbance uncertainties. The simulation results obtained in a real-time MATLAB simulation environment reveal that amongst all three proposed nonlinear SOC estimators the EMC NOE is a most suitable alternative to SOC UKF and PF estimators for this kind of application. The number of tuning parameters for SOC EMC NOE is much smaller than for UKF and PF estimators. The proposed SOC EMC NOE proves its effectiveness in terms of implementation

estimator is the most suitable estimator compare to UKF and PF estimators.

UKF estimator PF estimator NOE

5. Conclusions

during UDDS cycle current profile test.

RMSE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P<sup>i</sup>¼<sup>N</sup> <sup>i</sup>¼<sup>1</sup> xestð Þ�<sup>i</sup> xmodel ð Þ ð Þ<sup>i</sup> <sup>2</sup> N r <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffi MSE <sup>p</sup> The RMSE is probably the most easily interpreted statistic, since it has the same units as the model states. Similar as MSE, lower RMSE the state estimates fit better the model states, i.e. battery SOC and the battery polarization voltages. The MAE statistic is helpful to determine the accuracy of the Li-Ion battery EMC-UKF, EMC-PF and EMC-NOE SOC estimates with respect to the "true" model values. It is usually similar in magnitude to RMSE, but slightly smaller, and has the same units as the model states data set. MAE ¼ P<sup>i</sup>¼<sup>N</sup> <sup>i</sup>¼<sup>1</sup> <sup>j</sup>xestð Þ�<sup>i</sup> xmodel ð Þ ð Þj <sup>i</sup> <sup>N</sup> The statistics of errors from benchmark reveal that EMC nonlinear observer estimator (EMC-NOE) outperforms in terms of all statistics (RMSE, MSE, MAE) the Estimation Techniques for State of Charge in Battery Management Systems on Board of Hybrid Electric Vehicles… http://dx.doi.org/10.5772/intechopen.76230 79

Figure 16. EMC SOCs and output terminal voltages versus EMC, EMC-UKF, EMC-PF, and EMC-NOE estimated values during UDDS cycle current profile test.


Table 1. Statistics on SOC estimation performance of the proposed nonlinear estimators UKF, PF and NOE - Benchmark.

UKF and PF estimators. Consequently, for this kind of applications the EMC-NOE SOC estimator is the most suitable estimator compare to UKF and PF estimators.

#### 5. Conclusions

4. Real-time implementation of the Li-Ion battery SOC estimators on

For comparison purpose, we represent on the same graph the SOC estimates of all three real-time nonlinear estimators (UKF, PF, and NOE) versus EMC SOC true value and ADVISOR MATLAB SOC estimate, as are revealed in Figures 7, 10 and 13. The simulation results in Figure 16 disclose a precious information about the convergence of all three proposed estimators to Li-Ion EMC SOC true values for the proposed Li-Ion battery EMC. Furthermore, a useful benchmark is built in terms of the statistics errors between the states estimates and the corresponding model states values, such as root mean square error (RMSE), mean square error (MSE) and mean absolute error (MAE), defined in [6]. They are very easy to be computed in MATLAB R2017a, and the results are shown in Table 1. The MSE is a measure of how close the estimates values fit to model "true" values. The squaring is done so negative values do not cancel positive values. The smaller the MSE, the closer the fit of the estimates values is to the model "true" values. The RMSE

Figure 15. The robustness of Li-Ion EMC-NOE estimator to the changes in internal battery resistance for an UDDS cycle

tistic, since it has the same units as the model states. Similar as MSE, lower RMSE the state estimates fit better the model states, i.e. battery SOC and the battery polarization voltages. The MAE statistic is helpful to determine the accuracy of the Li-Ion battery EMC-UKF, EMC-PF and EMC-NOE SOC estimates with respect to the "true" model values. It is usually similar in magnitude to RMSE, but slightly smaller, and has the same units as the model states data set.

observer estimator (EMC-NOE) outperforms in terms of all statistics (RMSE, MSE, MAE) the

<sup>N</sup> The statistics of errors from benchmark reveal that EMC nonlinear

<sup>p</sup> The RMSE is probably the most easily interpreted sta-

MATLAB/SIMULINK platform: Results comparison

<sup>¼</sup> ffiffiffiffiffiffiffiffiffiffi MSE

is just the square root of the MSE [6].

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>i</sup>¼<sup>1</sup> <sup>j</sup>xestð Þ�<sup>i</sup> xmodel ð Þ ð Þj <sup>i</sup>

<sup>i</sup>¼<sup>1</sup> xestð Þ�<sup>i</sup> xmodel ð Þ ð Þ<sup>i</sup> <sup>2</sup> N

P<sup>i</sup>¼<sup>N</sup>

r

current profile test.

78 New Trends in Electrical Vehicle Powertrains

P<sup>i</sup>¼<sup>N</sup>

RMSE ¼

MAE ¼

The main contribution of this research paper is the design and implementation in real time of a three robust nonlinear estimators, namely UKF, PF and NOE, capable to estimate with high accuracy and robustness the Li-Ion battery SOC based on a simple battery 2R EMC without disturbance uncertainties. The simulation results obtained in a real-time MATLAB simulation environment reveal that amongst all three proposed nonlinear SOC estimators the EMC NOE is a most suitable alternative to SOC UKF and PF estimators for this kind of application. The number of tuning parameters for SOC EMC NOE is much smaller than for UKF and PF estimators. The proposed SOC EMC NOE proves its effectiveness in terms of implementation simplicity, Li-Ion battery SOC estimation accuracy and robustness. Therefore, it can be considered as one of the most suitable nonlinear estimator, and a feasible alternative to UKF and PF estimators.

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