Discussion on equivalent circuit model of lithium ion battery
In order to develop the battery management system, two kinds of models are needed, which are control algorithm model and controlled object model.The controlled objects involved in BMS include single battery, contactor, thermal management device, VCU, obcm, charging pile, etc., and the battery model which characterizes the external characteristics of the battery is the most complex and important in the modeling process of the controlled object.
On the one hand, accurate battery model is helpful to verify the control algorithm efficiently and conveniently. On the other hand, the application of battery model can predict the real-time state of battery external characteristics, which is the basis of Kalman filter algorithm.
1. What are the battery models?
Mechanism modeling: the mathematical model is established according to the physical formula, chemical reaction principle and other theoretical derivation.
Experimental modeling: the controlled object is regarded as a "black box", and the change law of the characteristic parameters of the target object is recorded to build the model.
Hybrid modeling: a model that combines mechanism modeling and experimental modeling.
Battery is a highly complex nonlinear electrochemical energy storage device. On the one hand, it is difficult to describe the internal interaction and reaction in the control process by accurate formula. On the other hand, it requires a lot of data input and learning to fully use the experimental data modeling (such as neural network). So hybrid modeling is more common. Electrochemical model, thermodynamic model, coupling model, equivalent circuit model and so on can be used in mechanism modeling. In contrast, the equivalent circuit model does not need to have an in-depth analysis of the electrochemical reaction inside the battery. It describes the open circuit voltage, DC internal resistance and polarization internal resistance of the battery through the circuit, so as to realize the characterization of the external characteristics of the battery.
The cell polarization is mainly composed of ohmic polarization, electrochemical polarization and concentration polarization. The ohmic polarization is caused by the internal resistance of the battery formed by electrode materials, conductive materials and connection impedance. The electrochemical polarization is caused by the electrochemical reaction, and the concentration polarization is caused by the consumption rate of reactants on the electrode surface greater than the replenishment rate. Generally speaking, the corresponding rate ohmic polarization > electrochemical polarization > concentration polarization.
In the equivalent circuit model, ohmic polarization can be characterized by resistance, concentration polarization and electrochemical polarization can not be characterized separately. The sum of them can only be represented by one or more order RC circuits, which makes the polarization effect close to the actual situation.
2. Typical battery model
Rint model
Rint model, also known as internal resistance model, is a relatively simple model designed by Idaho National Laboratory. It includes ideal voltage source UOC and internal resistance R. Because the polarization characteristics of the battery are not considered in the model, the accuracy of the model is low.
The battery terminal voltage UL = UOC - (RO * il).
Thevenin model
The battery terminal voltage UL = UOC - (RO * il) - up.
PNGV model
In September 1993, the U.S. Automobile Research Council (uscar) announced the partnership for new generation of vehicles, The standard equivalent circuit model of PNGV was proposed in the PNGV Battery Test Manual published in 2001, and the standard method for parameter identification of the model was proposed in the FreedomCAR Battery Test Manual published in 2003.
Based on Thevenin's PNGV model, the influence of load current on OCV of battery is considered. In this model, UOC is used to represent the ideal open circuit voltage of the battery, CB is the battery capacitance (representing the OCV change caused by the load current IL), RO is the ohmic internal resistance of the battery (the load current passed is IL), RP is the polarization internal resistance (the polarization current passing is IP), and CP is the polarization capacitance (representing the polarization voltage up change caused by the load current IL).
In order to make the curve fitted by the model match the real voltage curve better, a group of RC circuits are added in the improved PNGV model, which can achieve better matching degree in the curve fitting process.
The battery terminal voltage UL = UOC - (RO * il) - up1-up2-ub.
In order to more comprehensively express the external characteristics of the battery, we can continue to optimize on the basis of the above typical battery model, such as self discharge factors, hysteresis characteristics and so on, which will inevitably increase the complexity of the model and identification difficulty. For model selection and Optimization in specific application, the typical model can be used for parameter identification, and then targeted improvement can be made according to the difference between the model and the actual situation.
