Battery State of Charge Estimation Using

Battery State of Charge Estimation by Using a Combination of Coulomb Counting and Dynamic Model With Adjusted Gain Asep Nugroho1 , Estiko Rijanto1, F.Danang Wijaya2, Prapto Nugroho2 1 Research Center of Electrical Power and Mechatronic Indonesian Institute of Sciences Bandung, Indonesia 1 [email protected] 2 Dept. of Electrical Engineering and Information Technology Gadjah Mada University Yogyakarta, Indonesia

Abstract— Majority of electric vehicles depend on batteries that require a Battery Management System (BMS). Increasing accuracy of State of charge (SoC) estimation was crucial. The uncomplicated method for SoC estimation is Coulomb Counting (CC), however it has drawback in information of previous SoC initial value and tolerate with error propagation. Dynamic model equipped with integral controller can increase accuracy of the CC method. In this paper adjusted gain of the integral controller is proposed to further improve performance of SOC estimation. The Li-ion battery was modelled using first order RC battery model. Least square method is used to determine parameter of battery model. The simulation results show that the combination of CC and dynamic model with fixed integral gain could increase accuracy of the CC algorithm approximately to 87%, and the mixed algorithm with adjusted integral gain could further increase it to around 89%. Keywords— state of charge, coulomb counting, battery model, integral controller, adjusted gain.

INTRODUCTION Decreasing oil consumption has been a concern for reducing the green house effect. Electric and hybrid vehicles utilization is one of the solution to solve the problem. Challenge in this area is related to batteries utilization. Most batteries require battery management system (BMS). One of the important key issues in BMS design is the accuracy of state of charge (SoC) estimation [1]. SoC of Li-ion batteries shows strong nonlinearity. A mistake in SoC measurement within BMS can yield misidentification of overcharge and overdischarge conditions of the battery [2]. Estimating SoC based on current sense is known as Coulomb Counting (CC) method. This method is simple and popular for SoC estimation where prior knowledge of initial SoC is needed, but it suffers from error propagation [3].

Non linearity behaviour in battery could be estimated by neural networks, fuzzy logic, and so forth which behave as learning machine. These methods have exquisite performance to persue nonlinear functions. However, the large computational resources was needed to learning process; thus, it is not appropriate be used in online applications [4][5]. Stepwise model whose parameter values are optimized by using Particle Swarm Optimization (PSO) has also been used to predict battery SoC [6]. Open-circuit voltage (OCV) method is more proper than CC. However, it can not be purposed in real-time applications because relaxation is required in to estimating the SoC [7]. Estimation using battery models are powerful to approximate nonlinear behaviour of battery. This idea is conducted by entering gauged battery signals to battery model. Afterwards, the terminal voltage of battery is calculated by taken measurement signal into account parameters as well as current and old states of battery. In order to keep the estimation updated, gaps among values derived from calculation and measurements are then inputted into an observer [7][8]. Some models apply said approach are Luenberger's [8][9], Kalman Filter [8][10] and also that of slidingmode's [11][12]. A mixed algorithm between CC and model based method has been proposed and analyzed [13][14][15][16][17]. This paper proposes adjusted gain feature which is used in SoC estimation based on the mixed CC and model based method. The algorithm is optimized by variation of integral gain in lessen to the magnitude of gaps between the measured and the estimated of battery voltage. In our research, we used simulation test for validating the algorithm. Randomize discharge simulation data which was generated by simulation software was used in examining the algorithm performance. The paper is constructed like following : In Section II a brief depiction of first order RC battery model and its parameter identification are presented: a battery model which

is needed by the PI observer because it needs to predict the battery terminal voltage. In Section III the SoC estimation algorithms is described. Finally some conclusion are given in Section IV. BATTERY MODEL Single polarization RC battery model was used in our research. The model could be represented by circuit equivalent which is illustrated in Fig. 1 [13].: The voltage source (VOCV) is modelled as OCV which is an SoC function. Internal resistance is denoted as R0. The resistance R1 and capacitor C1 are adopted as dynamic behavior. The battery model can be written as (Laplace) :   R1 EL  U L  Vocv   I L ( s )  R0   1  R C ( s ) 1 1   EL ( s ) R0  R1  R0 R1C1 ( s ) G(s)   I L ( s) 1  R1C1 ( s ) K  K (s) 3 G(s)  2 1  K (s) 1

where, a1 

T  2 R1C1 T  2 R1C1

a2 

R0T  R1T  2 R0 R1C1 T  2 R1C1

a2 

R0T  R1T  2 R0 R1C1 T  2 R1C1

EL (k )  Vocv (k )  U L (k )

In order to determine parameter values, pulse discharge experiment was conducted through computer simulation. Discharge current, battery terminal voltage and SoC were recorded illustrated in Fig. 2 . Battery capacity (Cn) is 27.4 Ah. The discharged current pulse is 1.76 A in the period of 45 minutes. This discharged current pulse corresponds to around 0.05 Cn.

(1)

Using Tustin transform Eq.1 can be rewritten as follows [14]: a  a (z 1 ) E G (z 1 )  2 3 1  L 1  a (z ) IL 1 EL (k )  a EL (z 1 )  a I L  a I L (z 1 ) 1 2 3 EL (k )  a EL (k  1)  a I L (k )  a I L (k  1) 1 2 3

(2)

Fig. 1. Single polarization RC battery model.

Fig. 2. Pulse discharging simulation data

SOC ESTIMATION ALGORITHM Fig. 5 displays scheme of SoC estimation algorithm with adjusted gain value. This algorithm is developed based on the mixed algorithm previously proposed by other researchers [16][17]. Firstly, the current and voltage are measured. The current is integrated using CC method to obtain the estimated SoC (labeled SoC ˆ in Fig. 4). The value of SoC ˆ is fed into an OCV-SoC Function Block to generate Open Circuit Voltage (OCV). The relationship is non linear as demonstrated in figure 3. The battery model could be associated as the control

Fig. 3. Relationship OCV and SoC

. Rest time of 135 minutes is provided after every discharge current pulse. The terminal voltage during rest time is used to decide SoC and OCV connections which is illustrated in Fig. 3. The data was used to determine a1 , a 2 , and a 3 which are shown in Table I. In this research linear least square method was chosen for parameter identification [15]. Fig. 4 illustrates the battery model in Simulink block which is developed based on Eq.2. TABLE I.

RESULT OF PARAMETER IDENTIFICATION

a1

-0.954400

a2

0.009761

a3

-0.009280

system control system work floor. The input variable is SoC , whereas the controlled output is estimation of terminal voltage. Terminal voltage measured became the reference output. A simple integral controller is added to correct SoC. Aim of this paper is to providing an algorithm to adjust integral gain based on the value of error. The proposed gain adjustment algorithm is given in the following equation.  Ts  (k)  {K 0  ( K1  e(k) )}    e(k)   z 1 

(3)

It can be noted that a pure CC algorithm can be realized by setting the integral gain value being zero ( K 0 = K1 = 0). While a mixed algorithm which incorporates CC and model based method is realized by selecting a fixed integral gain value ( K1 =0). To confirm the performance of the proposed algorithm proposed some simulations have been carried out under different accuracy of SoC initial preset values. The battery cell is discharged in random current values as shown in Fig. 6. The mean discharge current value is around 28 A. The maximum and minimum discharge currents are 45.7A and 6.8 A, respectively.

Fig. 4. Battery dynamic model in Simulink block Fig. 5. Mixed SoC estimation algorithm with adjusted gain.

Fig. 9 shows simulation results when SoC initial preset value is around 0.68 which is far from the real initial value of 1.0. It can be noticed that the pure CC algorithm significantly suffers from the error in initial value. Both the mixed algorithm and the mixed algorithm with adjusted gain could compensate the SoC initial value error.

Fig. 6. Random discharge current for performance validation.

Fig. 7 shows simulation results when SoC initial preset value is around 0.98 which is quite close to the real initial value of 1.0. Horizontal line is time in seconds and vertical line is SoC. Real reference SoC is represented using the dotted light brown line, estimated SoC with CC algorithm represented using solid green line, estimated SoC using the mixed CC and model based represented using the blue line, and the solid red line is the estimated SoC based on the proposed algorithm in equation (3). Visually all the algorithms seem to give good SoC prediction capabilities. Fig. 8 shows simulation results when SoC initial preset value is around 0.78 which is rather close to the real initial value of 1.0. It can be noticed that the pure CC algorithm suffers from the SoC initial value error. The mixed algorithm and the proposed mixed algorithm with adjusted gain value are both able to compensate the error. Both of these algorithms provide better performance than the pure CC algorithm.

Fig. 8. SoC estimation in case 2 (estimated initial value of 0.78)



REFERENCE TABLE II.

PERFORMANCE INDICATOR ( IN MEAN SQUARE ERROR)

[1]

CC Algorithm

The mixed algorithm

The mixed algorithm with adjusted gain

[2]

Case 1

0.000386

0.000189

0.000186

[3]

Case 2

0.048233

0.005814

0.005040

Case 3

0.102157

0.013191

0.011063

Simulation Case

TABLE III.

INCREASING ACCURACY ( IN PERCENT)

The mixed algorithm with fixed gain

The mixed algorithm with adjusted gain

(compared to CC)

(compared to CC)

Case 1

51.04%

51.81%

Case 2

87.95%

89.55%

Case 3

87.08%

89.17%

Simulation Case

[4]

[5]

[6]

[7]

[8]

Table II summarizes performance indicator of each algorithm for all the cases investigated above. Mean square error of SoC value is selected as the performance indicator. From this table it is obvious that the mixed algorithm with adjusted gain value provides the best performance for all cases investigated through computer simulation. Table III illustrates about the increasing accuracy of the mixed algorithm with fixed gain and the mixed algorithm with adjusted gain as compared to CC Algorithm.

[9]

[10]

[11]

CONCLUSION An algorithm to estimate SoC of a battery has been proposed based on combination of coulomb counting (CC) method and dynamic model method. The algorithm adjusts the value of integral gain based on the error magnitude between the measured and the estimate of battery terminal voltages.From simulation results under different initial values setting of SoC, it concluded that the proposed algorithm perform better than the coulomb counting method as well as the mixed algorithm having fixed integral gain value. When SoC initial preset value is around 0.68, the combination of CC and dynamic model with fixed integral gain could increase accuracy of CC algorithm approximately to 87%, and the mixed algorithm with adjusted integral gain could further increase it to around 89%. ACKNOWLEDGE The author have given appreciation to Naili Huda for helping me in editing my paper and I would give gratitude to all staff of Indonesian Institute of Sciences for their support in this research.

[12]

[13]

[14]

[15]

[16]

[17]

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