ESTIMATION OF STATE OF CHARGE OF LITHIUM-ION BATTERY BASED ON PHOTOVOLTAIC GENERATION ENERGY STORAGE SYSTEM

Original scientific paper The fast and accurate estimation of state of charge (SOC) of lithium-ion battery is one of the key technologies of battery management system. In view of this nonlinear dynamic system of lithium battery, through the test and analysis of lithium-ion battery hysteresis characteristics, the second-order RC hysteresis model is established, and the cubature Kalman filter algorithm is used to estimate the battery state of charge in this report. The experiment results show that the battery model can essentially predict the dynamic hysteresis voltage behavior of the lithium-ion battery and cubature Kalman Filtering algorithm can maintain high accuracy in the estimation process.


Introduction
With environmental protection and energy saving issues increasing, prominent, lithium ion battery, due to its high energy density, high working voltage, long cycle life, no pollution, light weight, and small self-discharge [1], takes on a more significant role in the field of energy storage batteries.To take full advantage of the dynamic performance of the battery system and prevent battery overcharge, a battery management system is needed.
Reliable cell model is the premise condition of SOC accurate estimates.The accuracy of the model affects the precision of SOC estimation.Hysteretic characteristics are one of the basic characteristics of lithium ion batteries.It refers to the fact that OCV of battery during the charge process does not match the OCV of the discharge process.In order to improve the precision of the equivalent model of a lithium-ion battery, hysteretic characteristics must be taken into account.
In recent publications several SOC estimation algorithms such as the open circuit voltage (OCV) method, Ampere-Hour integral method and Kalman filter (KF) method are presented [2÷5].The OCV method [2] needs a long rest time, so it cannot be utilized in real time applications.The Ampere-Hour integral algorithm however is the most simple and convenient one, but it requires a prior knowledge of initial SOC and suffers from accumulated errors from noise and measurement.KF method is proposed to solve the above problem in recent years, but it is only suitable for linear system [4].The Extended Kalman Filter (EKF) [5] is a nonlinear method of the KF, which has been used particularly for systems with nonlinear dynamic models.
This paper proposes a model based on hysteretic characteristics [6] of lithium-ion battery, and uses Cubature Kalman Filter (CKF) algorithm [7] to estimate the SOC, which greatly reduces the model error and the algorithm error.The next part is experiment analysis of battery hysteresis characteristics and its influence.In part III, we propose a high-precision battery hysteresis model which takes the hysteresis effect into consideration.Part IV introduces the volume Kalman filtering algorithm in the SOC estimation.In part V, the hysteresis model is verified by experiments and CKF method is used to estimate the accuracy of SOC.Part VI summarizes the article.

Experiment analyses of Lithium ion battery hysteretic characteristics
The test of the hysteretic characteristics during the charge and discharge process has been done to show how the hysteretic characteristics affect the SOC estimation.The LP2770102AC lithium-ion battery, which is a lithium iron phosphate battery that can be used in portable high power devices, grid stabilization energy storage, and electric vehicles, has been chosen.Its capacity is 12,5 Ah and nominal voltage is 3,3 V.A Digatron MCT 30-05-40 cell cycler was used to test.The battery temperature should be kept at 20 ± 2 °C.The battery voltage is assumed to keep stable value after standing for 1 hour in the charging and discharging test process [8].

The major loop of the hysteretic characteristics
The major loop of the hysteretic characteristics is the OCV-SOC characteristic curve in one complete battery SOC cycle [9].Fig. 1 shows the testing process.The process of charging and discharging time is about 53 hours, and sampling time is 1 second.It can be seen the OCV changes greatly when the SOC < 10 % and SOC>90 %.
The major loop of the hysteretic characteristics curve and the difference curve can be drawn with the data in Fig. 1.As shown in Fig. 2, it can be seen the charging OCV is always above the discharging OCV in the same SOC.

The minor loop of the hysteresis characteristics
In practical applications of lithium-ion batteries, such as electric vehicle, lithium-ion battery is mainly working under the partial charge and discharge cycles [11].Therefore minor loop of the hysteresis characteristics which is the battery OCV-SOC curve under local SOC cycle must be under considered in the battery SOC estimation [12].Fig. 4 shows the voltage and current curves in testing process.
Fig. 4 shows the minor loop of the hysteresis characteristics curve.As shown in Fig. 5, Black arrows represent the changing direction of SOC.
Experimental results show the following conclusion: 1) Hysteresis characteristic is a bunch of curve.
2) It is a history function of charging-discharging process.
3) It is a function of rest time.4) The OCV-SOC curve of minor loop of hysteretic characteristics is always under the charging and discharging OCV-SOC curves of the major loop.5) When the current changes direction, the SOC-OCV trajectory also changes direction and successive approach to the major loop curves with the same direction [13,14].

The influence of hysteretic characteristics to SOC estimation
SOC estimation error caused by the hysteresis characteristics is: .% 100 By exchanging the axes of Fig. 2(a) and make a difference, the curve of SOC-OCV and SOC error curve are as shown in Fig. 6.
As can be seen from the Fig. characteristics is 32,6 % (OCV = 3,3 V), which means estimating the SOC with the average of charging and discharging OCV-SOC curve will cause a big error.Battery SOC is sensitive to the change of the OCV especially in range of 10 % to 90 %.Very small OCV fluctuations are likely to cause a big SOC estimation error.Therefore the hysteresis characteristics must be taken into account.

Linear models
As shown in Fig. 7, linear model regards the battery as a large capacitor C, and U oc represents capacitor voltage.Meanwhile, a small resistor R 0 is cascaded with the capacitor.The resistor is called the battery's "internal resistor" and changes with the ambient temperature and the life of batteries [18].

Relaxation model
This battery model takes relaxation characteristic [19] into consideration.Relaxation characteristic is the phenomenon of battery OCV slow return to equilibrium after a period of time charging or discharging, which can be expressed by a series of RC networks.The more RC networks, the closer to true OCV.Compared with linear model, it uses controllable voltage source instead of large capacitor to represent electromotive force, and the voltage is a function of SOC.Fig. 8 the relaxation model.

Hysteresis model
Hysteresis model is the battery model that takes hysteresis characteristic into consideration.
The basic idea to describe the hysteresis characteristics of this paper is to propose a mathematical model that successively approaches the upper curve OCV Charge when the cell is charging and approach the lower one OCV Discharge when it discharges [20].The following models are chosen after many times comparison: The second order RC hysteresis equivalent circuit model is chosen by considering model precision, complexity and chosen LiFePO4.The model is shown in Fig. 10.
In order to verify the accuracy of the models, results are shown in Fig. 9.Even if the demonstrated hysteresis model is very simple, the OCV can be simulated accurately with deviations of less than 2 mV.
In order to improve the precision of model, the recursive least squares method is used to estimate the above parameters of the equivalent circuit model.The estimation results based on a pulse discharge data are shown in Fig. 11.

SOC estimation of lithium-ion battery based on the hysteresis model
There are two disadvantages in the process of EKF state estimation: 1) When the high-order Taylor expansion term of nonlinear function cannot be ignored, linearization will produce bigger system error, and even make the filter unstable.
2) Jacobin matrix is needed to calculate at each filter cycle, and this will greatly increase the computational complexity of filtering estimation.  (6  This paper uses another kind of Kalman filter nonlinear method -Cubature Kalman Filter (CKF) [18] to estimate lithium-ion battery SOC.It uses the same weight cubature points to approximate posterior distribution of optimal state [19,20].CKF is suitable to solve nonlinear state estimation problems from low dimension to high dimension, and its estimation precision can reach second order Taylor precision at least.

Result validations
The lithium-ion battery hysteresis model and CKF algorithm are verified with two DST conditions, which are charging condition and discharging conditions respectively.Both of two DST conditions have 5 testing cycles, in which every testing cycle consists of 14 steps.Fig. 12 shows the terminal voltage and current of lithium ion battery of two DST conditions.

Model validation
Fig. 13 shows the estimation value of lithium-ion battery terminal voltage and estimation error of equivalent model with and without considered hysteretic characteristics.The results of the two conditions can be found by utilized battery current and voltage data in the hysteresis models shown in Fig. 10.order RC hysteresis model can track the dynamic characteristics of lithium-ion battery more accurately even in the condition of the severe changes of current.

Algorithm verification
The experiment results are shown in Fig. 14 by Using CKF to estimate the battery SOC.All the truth value of SOC is based on an ampere-hour integral method.Fig. 14(c) shows that SOC estimation errors are less than 2 % and 5 % respectively, which explains CKF algorithm can accurately estimate the battery SOC even if model error is considerable.It can accurately track the actual value of SOC, which shows CKF has good robustness.
In order to compare the speed of CKF and EKF converging to the true value with wrong initial value, initial SOC of charging and discharge conditions is set to 0,4 and 0,6 respectively.As shown in Fog. 15, CKF converges to true SOC faster than EKF, and has better dynamic interference resistance as well.

Figure 1 Figure 2
Figure 1 Voltage and current curve of hysteresis major loop

Figure 3
Figure 3 Hysteresis major loop characteristics with different rest time

Figure 4 Figure 5
Figure 4 Voltage and current curve of hysteresis minor loop

3
Lithium-ion battery equivalent circuit models Considering the accuracy, complexity and the requirements of different precision comprehensively, the battery model can be divided into linear model, static model and hysteresis model [15÷17].

6
(a) SOC-OCV curve (b) SOC error curve Figure The influence of hysteretic characteristics

Figure 7
Figure 7 Equivalent circuit of liner model

Figure 8
Figure 8 Equivalent circuit of rest model

Figure 9 Figure 10
Figure 9 Estimate curve of hysteresis characteristics

Figure 11
Figure 11 Parameters identification curve

Figure 12
Terminal voltage and current in DST conditions (a) True voltage and estimated voltage (b) Local amplification of true voltage and estimated voltage (c) Estimation error of voltage Figure 13 The results of model validation in DST conditions (a) True SOC and estimated SOC (b) The error of SOC estimation Figure 14 The results of algorithm validation in DST condition (a) True SOC and estimated SOC (b) Local amplification of true SOC and estimated SOC Figure 15 The results of algorithm validation in DST condition with wrong initial conditionAs shown in Fig.13(c), the terminal voltage estimation error is within 0,02 V when considering hysteresis characteristics.This means that the second- ) is obtained.Wher τ e is coulomb efficiency.τ e is rated capacity of the battery; T is