CR1620 battery

　　Research on CR1620 battery pack degradation model

　　Lithium-ion batteries are widely used in electric vehicles. The life of the battery pack will directly affect the use and maintenance costs of electric vehicles. Therefore, the study of the degradation mechanism of the battery pack is particularly important. During the use of the battery pack, the decline of the single cells, the uneven charge and discharge of the single cells in the battery pack, and the uneven temperature distribution in the battery pack will all cause the capacity of the battery pack to continue to decline, thus affecting the battery. The prediction of battery decline is much more difficult and complex than the prediction of single battery decline. Therefore, most of the current decline mechanism research and decay model research are focused on single lithium-ion batteries. We need A bridge can connect the degradation pattern of the battery pack with the degradation pattern of the single cell, thereby achieving accurate prediction of battery pack degradation.

　　Chin-Yao Chang and others from Ohio State University in the United States developed a battery pack degradation prediction method based on a probabilistic method, which takes into account the accuracy and complexity of calculations. In this model, the differences between single cells due to manufacturing and different use temperatures can be measured to obtain the decay model parameters, and then the probabilistic method is used to synthesize the decay model of the single cell into the decay model of the battery pack. , this model can be used to predict the degradation of the plug-in hybrid electric vehicle PHEV battery pack. It is worth mentioning that this model also includes the most serious situation of the degradation of a certain battery in the battery pack. In general, , this method has the following three major characteristics

　　1) Use probabilistic methods to extend the degradation model of single cells to battery packs.

　　2) The model can also determine a semi-empirical model in situations where measurements can be made (such as PHEV).

　　3) Identify the most degraded battery in the battery pack.

　　Background introduction

　　Before starting to introduce the battery pack degradation model developed by Chin-YaoChang, we first make a brief summary of the existing battery degradation models. First of all, for batteries, battery decline will mainly cause the battery's capacity to decrease and its internal resistance to increase. Therefore, for the decline of a single battery, we mainly focus on the two parameters Xc (the battery's capacity decline ratio) and Xr ( The ratio of the increase in internal resistance of the battery), these two parameters can be calculated using the following formula

　　In the above formula, Ti is the internal temperature of the battery, Vi is the voltage of the battery, Ii is the battery current, ai is a parameter of the battery's decay model, which is related to the difference between single cells, and Zi is related to the cumulative use time of a battery. parameters, also called pressure parameters.

　　Battery packs are generally composed of single cells connected in series and parallel. Batteries connected in parallel are generally considered to be one "big battery" because the voltage and current of each battery cannot be measured individually. Therefore, The actual battery pack can be simplified into a model consisting of many "big batteries" connected in series, as shown in the figure below.

　　Therefore, under ideal circumstances, if the degradation of each single cell in the battery pack can be accurately known and there is no uncertainty in the battery pack usage time parameter Zi, then the Xc and Xr of the battery pack can be calculated directly. However, in fact, due to the large differences between single cells, the degradation parameter ai of each battery is difficult to accurately measure. Therefore, we need to develop a method to estimate the degradation model parameters of the battery pack.

　　Application of parameter online estimation in single battery

　　Chin-YaoChang research shows that small errors in the degradation model parameters will lead to huge errors between the model prediction results and the actual structure. Therefore, estimating the battery pack degradation model parameters can significantly improve the prediction accuracy of the model. The degradation of a single battery mainly depends on factors such as battery temperature, cumulative charge and discharge capacity, minimum SoC, charge rate, charge depletion state time and charge retention time. These parameters can be calculated by the following formula.

　　In order to verify the impact of the model parameters on the prediction results, Chin-YaoChang randomly generated 100 model parameters that deviated within 5% from the ordinary values. Therefore, 100 models were generated. The prediction results of the model were compared with the experimental values and The predicted values of the common model are compared, and the experimental results are shown in the figure below. Judging from the results, in long-term prediction, errors caused by small errors in model parameters (within 5%) gradually increase during the battery cycle, resulting in distortion of model predictions. Therefore, it is necessary to conduct sensitivity analysis on the model parameters. The sensitivity analysis is carried out using the digital perturbation method, as shown in the following formula, where a is the decay model parameter, a is the perturbation, and Sen is the sensitivity measure.

　　The figure below shows the sensitivity of the model to different parameters. As can be seen from the figure, the model has the highest sensitivity to the two parameters y and a3, so these two parameters have a great impact on the accuracy of model prediction.

　　From the above analysis, we can know that accurately estimating model parameters is of great significance to improving the accuracy of model prediction. In order to improve the accuracy of online prediction, Chin-YaoChang used four methods to estimate model parameters online. : 1) Extended Kalman filter EKF, 2) Lossless Kalman filter UKF, 3) Particle filter PF, 4) Extended Kalman particle filter EKPF. Four methods are used to estimate the model parameters, and then the results of using these parameters to predict single cell degradation are shown in the figure below. As can be seen from the figure, the experiment is divided into two parts. The first part is from 0 to 17.6kAh. This part of the data is used to estimate the model parameters. The second part is from 17.6 to 22.4kAh. The estimated parameters are used to estimate the single cell. Decay is predicted. Judging from the results, after estimating the model parameters through several methods, the root mean square difference between the model prediction results and the experimental results is significantly smaller than the prediction results of the original model, which shows that the use of online model parameter estimation can significantly improve the model. The accuracy of the forecast.

　　Earlier we introduced the battery life prediction model developed by Chin-YaoChang, so how to extend this model to battery packs? What are the difficulties in battery pack prediction? The biggest obstacle to promoting from single cells to battery packs is that each battery is unique and each battery will have differences, so that each battery has unique attenuation characteristics, making the battery pack no longer a single battery. Simple superposition becomes a complex system. Therefore, Chin-YaoChang et al. used probabilistic methods to extend the single battery degradation model to battery pack life prediction.

　　Application of parameter prediction method in battery pack

　　From the above analysis, we can see that online estimation of parameters can significantly improve the accuracy of single cell degradation model prediction, so Chin-YaoChang tried to extend this method to battery packs. The battery pack is composed of single cells connected in series and parallel, so the probabilistic method can be used to integrate the degradation model of the single cell into the degradation model of the battery pack. First, we simplify the battery pack into the following form, that is, all parallel batteries are regarded as a "big battery". In this battery pack, the voltage and temperature of the individual cells are measurable, and the current of the battery pack can also be measured.

　　Most current studies on SoC estimation treat the capacity of the battery pack as a fixed constant. Since the capacity of lithium-ion batteries declines very slowly, this assumption is basically valid. However, in Chin-YaoChang's research, the battery pack capacity is a variable that changes with time, so the existing SoC estimation model needs to be extended to make the SoC change with time. By predicting the existing SoC model, Chin -YaoChang got the following dual SoC-timing models.

　　The superscript in this model is a time-related parameter, h is a constant describing the relationship between SoC and Voc, which can be obtained from the OCV-SoC curve, Wx and Wy are Gaussian white noise, and the model is a linear system , so it is suitable to use linear Kalman filtering. Through Kalman filtering, the SoC and capacity of the battery pack can be estimated efficiently. The SoC and capacity estimation of the battery pack can be calculated by the following formula

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