Study on Battery Fast Charge and Discharge Model and Its Parameters

In order to study the battery performance, putting forward a kind of two order RC equivalent circuit model , measuring static and transient data by HPPC test, fitting the relationship between open circuit voltage and state of charge (SOC), analyzing system identification of the dynamic parameters with MATLAB tool. Finally, by comparing the simulation data with the test data, the model is correct and feasible.


INTRODUCTION
Because of environmental pollution needs, electric vehicles aroused more attention for energy saving and environmental protection.With the popularization of electric vehicles, the battery charging and discharging technology is especially important.The battery model is the key factor of charge and discharge of the battery.After defining model parameters through system identification, it can simulater charge-discharge and reflect the real performance status of battery, so as to study the battery capacity, circulation service life, self discharge rate and (SOC) etc [1,2].

SELECTING MODEL
Modeling of the battery system mainly includes electrochemical model, artificial intelligence model and equivalent circuit model [3].Establishment of model required high accuracy, little calculation work and achieving easily parameters.Therefore, an intuitive and accurate equivalent mathematical model was presented on the basis of the two order RC equivalent circuit model [4], as shown in Fig.Based on circuit diagram, ordinary differential equation of the mathematical model were built: In equation
The Hybrid Pulse in Power Characterization (HPPC) of "Freedom CAD battery test manual" was used to complete charge and discharge test [5].The HPPC can test dynamic power by pulse charge and discharge test system.The discharge test system adopted in the experiment: First, charging to full SOC using three stage constant current-constant voltage method and then holding for one hour at 25°C temperatures.
Second, discharging 10% (0.7Ah) of battery capacity by 1C(7A) and then holding for one hour, SOC was 0.9.Third, discharging for 10 seconds by 2C(14A) and then holding for 40 seconds, charging for 10 seconds by 1.5C(10.5A)and then holding for 10 seconds.This process is shown in Fig. (2).
Fourth, repeating the steps second and third, each process released 10% battery capacity and respectively SOC was 0.8, 0.7,... 0.1 to the end of the test.
The HPPC charging process was similar to the discharging process.Beginning Charging process after discharging to the cut-off voltage and holding four one hour, then replace 'discharging' to 'charging' in the second.The following study would revolve mainly around the discharge process.

SYSTEM PARAMETERS IDENTIFICATION
Some unknown parameters of dynamic mathematical model in Fig. (1) were not certain because of SOC, the temperature of the environment and the cycle life of the battery.But considering the influence of SOC in a stable environment temperature and for several days.

The Relationship Between the Open Circuit Voltage and SOC
When there is no current through the battery, the potential difference between two poles is the open circuit voltage (OCV).
After the HPPC test, the battery was in holding state for one hour and the current was zero, then the polarization voltage would be gradually eliminated and the terminal voltage continued to rise.

Chen et al.
Rs when pulse current began discharging at ten seconds.
Similarly the voltage was also caused by resistance Rs when pulse current discharge completed.Due to the impact of discharge process, the values of and were not same. ( In Fig. (4), there was holding stage after pulse discharging for 20 to 60 seconds and the current in the circuit is zero.and circuits were zero input.We had = In equation 4, and were voltages when discharging instantly.
The least Square Fit was applied to calibrate and using pulse current discharge curve by equation 5 and MATLAB toolbox.Then and could be obtained from = and = .
Parameter identification of the battery model resulted as shown in Table 1, the parameters , , , and depended upon SOC.

MODEL VERIFING
In order to verify the parameter identification, building the simulation model in Matlab/Simulink, As shown in Fig. (5).
According to the Simulink model in Fig. (5), using constant current discharge to simulate and compare with experimental datas.The curve of test discharge was the same as simulation curve under the same discharge rate of battery.This showed that mathematical model could be fitted well to the the actual operation of the battery and the identification method was feasible.

CONCLUSION
Putting forward more intuitive and accurate circuit model of battery and completing system parameters identification based on the mathematical model now.Through MATLAB (1).In Fig. (1), left side of the circuit was on behalf of battery capacity, state of charge (SOC) and the operation time of battery; right side of it was transient state.The controlled voltage source was characterized with the nonlinear relationship between the SOC and the open circuit voltage.was the open circuit voltage.was the ohmic resistance, standing for loss energy for long time, and could consider to infinity because of little impact by self discharge.was capacity of the battery.was charge or discharge current.
Fig. (3) showed the voltage curve after holding for one hour.
in 20 to 60 seconds by MATLAB toolbox.In Fig. (4), because of holding one hour before, and circuits were zero state response during pulse current discharge in 10 to 20 seconds.At this time, =
the simulation datas and the experimental datas and verifying the correctness of the model to be applied to estimate SOC.