电动汽车SOC估计方法研究

power battery based on EKF

Tiezhou Wu

1. Huazhong University of Science & Technology;

2. Hubei University of

Technology

1. Department of Control science & Engineering;

2. Department of Electrical & Electronic Engineering

WuHan, China Wtz315@163.com

Xueguang Chen

1.Huazhong University of Science & Technology 1. Department of Control science & Engineering

WuHan, China

xgchen9@mail.hust.edu.cn

Fangzhen Xia

2. Department of Electrical & Electronic Engineering

WuHan, China 842980035@qq.com

Jianfeng Xiang

2. Department of Electrical & Electronic Engineering

WuHan, China freefall_xjf@163.com

Abstract: Accurate estimation of power battery SOC （state of charge ）is the basis of HEV power control strategy. SOC estimation algorithm has a significant impact on the accuracy of SOC estimation. This paper described the basic concept of SOC, discussed the significance of SOC estimation algorithm, difficulties and the main factors affecting SOC estimation, proposed a hybrid battery SOC estimation method with combination of extended Kalman filtering algorithm and improved Ampere Hour(AH) Method based on analyzing existed algorithms. Experimental results show that the hybrid SOC estimation method can meet the accuracy requirement of HEV SOC estimation excellently and is superior to the individual EKF method .

Keywords: Ampere Hour Method ；EKF ；SOC ；Estimation Algorithm

CLC number: ：TP17 WM ：A

I.

I NTRUDUCTION

In the procedure of using power battery, battery capacity is affected by many uncertain factors, and the accuracy of SOC estimation affects HEV energy distribution directly, which also affects battery lifetime [1]. So it’s a problem to make accurate estimation of the current battery capacity state by measurable battery parameters. The value of Battery SOC is defined as a ratio [2] of the remained battery capacity with respect to total battery capacity. For the batteries in dynamic system, SOC is defined [3] as equation (1).

∫−=t d n

Q i i

SOC t SOC 0

)()0()(ττη (1)

Here, SOC (0) is the initial state of batteries; i(t) is the current through batteries from time t to 0.

At present, SOC estimation methods in the world are mainly AH method and the open circuit voltage, but both of them have deficiencies. The most problem of AH method is that it requires determining initial value [4] of SOC and its estimation errors is very large in practical applications. The open circuit voltage method requires batteries standing by

when measured, and that the time standing by should be not too long or too short [5]. Therefore these two methods are not suitable for SOC estimations of HEV vehicles.

In order to minimize the SOC estimation error of HEV batteries, this paper proposed a hybrid SOC estimation strategy with combination of extended Kalman algorithm and AH method to improve the accuracy of battery SOC estimation.

II.

E XTENDED K ALMAN

F ILTER P RINCIPLE

2.1 Linear Kalman filter

The discrete model of the random signals to be estimated [4] is equation (2),

)

()()1()(k w k Bu k Ax k x ++−= (2) The observation equation is equation (3)

)()()()(k v k Du k Cx k y ++= (3)

Here,)(k x is system state at time k, A 、B are system parameters, )(k w is system process noise; )(k y is measured value at time k, C 、D are parameters of measurement system. This paper assumes that D = 0, )(k v is

system measurement noise.

Figure 1.Diagram of linear Kalman filter The principle of Kalman filter can be expressed in figure 1. When )(k u is sent into the measurement system model and system state model, the predictive value )1|(−k k x and measured value )(k y will be derived. The gain )(k G is changed according to the difference between )1|(−k k x

978-1-4244-6255-1/11/$26.00 ©2011 Crown

and )(k y . Then, change )|(k k x by )1|(−k k x 、)(k y , and )(k G to bring )|(k k x closer to actual value )(k x eventually.

Linear Kalman filtering flow chart is shown in figure 2.

Figure 2. Kalman filter auto-regssive algorithm

Here,

)1|(−k k x is the predicted outcome with the optimal predictive value at last moment. )1|1(−−k k x is the optimal prediction at last moment; )|(k k x is the optimal prediction at time t; )1|(−k k P is corresponding covariance of )1|(−k k x , )1|1(−−k k P is the corresponding covariance of )1|1(−−k k x ; )(k G is the

Kalman gain at time k; )(k y is the observations at time k; E is unit matrix.

2.2 Extended Kalman Filte r

Extended Kalman filter is formed by linearization of the nonlinear system with Kalman filter [6]. Battery system is also nonlinear system [7]. The state equation and measurement equation of nonlinear system is equation (4), (5):

)())(),1(()(k w k u k x f k x +−= (4)

)())(),(()(k v k u k x g k y += (5)

Here,)(k w ，)(k v is Gaussian white noise , w Q , v Q are their covariances, ))(),((k u k x f is state transition function of a nonlinear system, ))(),((k u k x g is measurement functions of a nonlinear system.

SOC estimation process of filter EKF is divided into the following steps:

1）Firstly, establish dynamic model of battery according to the requirement of EKF, i.e. establish the battery's state equation and measurement equation (corresponding with equation(4)(5);

2）Linearize ))(),((k u k x f and ))(),((k u k x g in state and measurement equations of model [9], i.e., Taylor series expansion, and then find the parameters A 、B 、C 、D etc. corresponding with equation (2) (3);

3）Use linear Kalman filter to estimate SOC.

III. A N I MPROVED AH E STIMATION OF SOC

3.1 AH Principles

Ampere Hour method (AH) method is a basic method of measuring SOC [10]; its formula is equation (6),

∫−×+−=k

k dt t i k SOC k SOC 1)(1η (6)

By accurately measuring the current through batteries from time 1−k to k , the integral value of the current

∫−k

k dt t i 1)( in this period of time can be calculated. The current batteries SOC value can be obtained with correction of charge efficiency or discharge rate (η) and the initial state of batteries (Assume the charge current direction positive and discharge current direction negative). This method is the only accurate way to calculate battery SOC currently. After the battery discharge completely at a discharge rate (generally the discharge rate η＝1), the integral of current value in the process of discharge, i.e. the initial battery SOC value is gained.

3.2 Improved AH Estimation of SOC

AH method in equation (6) does not consider self-recovery effect in the charge-discharge process, which makes the calculation error accelerate with time. So this paper improves an AH method (illustrating with charge procedure). The self-recovery factor and dynamic restoration part of power which is calculated based on the factor is added to the SOC estimation of charge process to improve the Accuracy of AH method.

If 12ηη> then

%100/)(×∫Δ+×+=Δ+Q c t

t t dt t I t SOC t t SOC η

%100/)1122(××Δ×−×Δ×+Q t I t I ηη (7)

The second item to the right side of the equation means the actual part of charge into the battery; the third means the dynamically recovered power during battery charge process.

If 12ηη≤ then

%

100/)(×∫Δ+×+=Δ+Q c t

t t dt t I t SOC t t SOC η(8)

c η、)(t I are the charge rate an

d th

e current between

time t and t t Δ+; 1η，1I ，2η，2I are respectively the

charging rate and current at time t, the charging rate and current at the time t t Δ+.

IV. SOC E STIMATION B ASED ON EKF-AH

AH method is a more accurate one to estimate the battery SOC currently. It is restricted in the application mainly because the initial value of SOC is usually unknown, which causes greater estimation error. But AH method has nothing to do with battery equivalent model. EKF is able to be convergent to the model values fast, but the error because of model

inaccuracy can not be corrected. Therefore, the accuracy of SOC estimation can be improved further with combination of EKF and AH method.

The algorithm combining EKF and AH method is described as following,

Step 1: Before SOC estimation, compare the SOC estimated by EKF with SOC measured by open circuit voltage based on the battery model to identify model error.

Step 2: Initialization, k=0，SOC1=25%，SOC2=25%； Step 3: From time tk to tk+1, choose SOC1 for initial value to obtain new SOC1 value by Kalman filtering. At the same time, correct the results by the model error to get the actual SOC1.

Step 4: From time tk+1 to tk+2, select corrected SOC1 at time tk+1 as initial value, calculate battery SOC2 value at time tk+2 with AH method, output the result. Kalman method also estimates battery SOC1 value at time tk+2. SOC1 is obtained by correcting the result according to model error.

Step 5：k=k+1，Back to Step 3.

V.

E XPERIMENT RESULTS

In order to verify EKF-AH method, we make comparative experiments with EKF and EKF-AH method estimating SOC and OCV-SOC at 0℃、25℃、and 50℃. As is shown in figure 3,4,5.

290

3003103203303403503603703803904000

10

20

30

40

5060

70

80

90

100

SOC%

v o l t a g e (V )

Figure 3. Comparison of SOC and OCV-SOC estimation with EKF and

EKF-AH at 0℃

300

3103203303403503603703803904000

10

20

30

40

5060

70

80

90

100

SOC%

v o l t a g e (V )

Figure 4. Comparison of SOC and OCV-SOC estimation with EKF and

EKF-AH at 25℃

300

3103203303403503603703803904000

10

20

30

40

5060

70

80

90

100

SOC%

v o l t a g e (V )

Figure 5. Comparison of SOC and OCV-SOC estimation with EKF and

EKF-AH at 50℃

The above experiment results show that the SOC estimation with the EKF-AH is more accurate than with EKF alone.

VI. C ONCLUSION

The SOC of power battery is one of the key parameters of hybrid vehicle power distribution control. Therefore, accurate estimation of SOC is an important job in the battery hybrid vehicle research and development. This paper studied the battery SOC estimation method with EKF filter and the improved AH method, and then proposed EKF-AH to estimate SOC. Experiment data show that the EKF-AH-based SOC estimation algorithm can meet the SOC estimation accuracy of HEV excellently. Its performance is superior to the EKF method alone. However, the algorithm based on EKF is strong dependent on the model and further optimization of the model is the future work to be done.

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