**DOI :**

**10.17577/IJERTV9IS050639**

**Open Access****Authors :**Rakshitha. R, Dr. Usha Surendra**Paper ID :**IJERTV9IS050639**Volume & Issue :**Volume 09, Issue 05 (May 2020)**Published (First Online):**30-05-2020**ISSN (Online) :**2278-0181**Publisher Name :**IJERT**License:**This work is licensed under a Creative Commons Attribution 4.0 International License

#### Integration of Coulomb Counting Method in Battery Management System for Electric Vehicle

Rakshitha. R

Phd Scholar, Christ University;

Assistant Professor RVITM

Dr. Usha Surendra

Professor EEE Department

Christ university

Abstract : The coulomb counting (CC) approach is widely

used in SOC estimation due to its simplicity and low

calculation cost. However, in practical applications, the lack

of error correction ability limits its accuracy due to the

measured noise in the practical occasion. To address the issue,

an improved CC (ICC) approach based on numerical

iteration is proposed in this paper. In the proposed approach,

a battery model based on a 2nd-order, RC circuit is first

formulated to determine the SOC-OCV curve, R-OCV curve,

and inner parameters. In the model, the slow dynamic and

fast dynamic voltages are described separately, and are

utilized for battery state assessment. Then, the SOC will be

estimated by the CC approach at the unsteady state but

through a numerical iteration approach at steady state.

Consequently, the accumulative SOC error from the CC

approach will be corrected when the numerical iteration

approach is applied.

INDEX TERMS: Improved coulomb counting (ICC), state of

charge (SOC), accumulative error correction, numerical

iteration, error accumulation rate.

I. INTRODUCTION:

To cut fossil energy consumption and mitigate the

greenhouse effect, electric vehicle (EV) has been widely

concerned. Battery system, as the energy provider in the

EV, requires a battery management system (BMS) to

ensure its safe operation [1]. Both over-charging and overdischarging

will reduce the lifespan of the battery system

or even lead to serious security accidents. Therefore,

monitoring the state of charge (SOC), which is defined as

the percentage of residual charge, has become one of the

key tasks of the BMS. However, due to the complex

electro-chemical behavior in a battery, estimating the exact

SOC for a battery is extremely difficult in practice. Hence,

the only available way is to perform an estimation of the

SOC based on the measurable external parameters of the

battery, such as current and voltage [2], [3]. The Coulomb

Counting (CC) approach and open-circuit voltage (OCV)

approach are the conventional methods to estimate SOC

[4]. Ideally, CC approach could obtain relatively accurate

SOC. However, in practice, there will be a large

accumulated error due to the unavoidable measured noise

and the lack of error correction ability. An enhanced CC

approach has been proposed to improve the SOC accuracy,

but the error is impossible to be eliminated fundamentally

[5]. As to the OCV method, the relationship curve between

SOC and battery OCV is usually applied for SOC

estimation. Nevertheless, the OCV can be unavailable

online due to the internal resistance and polarization

phenomena of the battery

Model-based SOC estimation algorithms are another hot

topic for SOC estimation [11]–[33]. In these algorithms,

OCV is calculated based on the battery model, and then the

SOC values obtained by OCV and CC are fused together

using a weight coefficient. Compared with CC, error

elimination ability is obtained. In general, model-based

algorithms, such as EKF, UKF and H infinite filters [11],

perform high accuracy and excellent stability if the battery

model is ideal. However, model error can hardly be

avoided in practice due to the complex chemical reaction in

the battery and the noise [3], [12], even through numerous

models have been proposed [13]–[24], such as the nth

Thevenin model [13], multi-time scale model [14]–[16]
and real-time updated model [17], [18]. To decrease the

influence caused by model error, many information

processing technologies are developed. The adaptive EKF

can update the process and measured noise covariance in

real-time [25]–[27]. The wavelet analysis technology has

been employed to preprocess the measured data, which

contain strong noise [28]. Algorithms using multiple filters

and information fusion technologies have also been

presented to improve the accuracy [29]–[33]. In these

algorithms, more factors such as state of health (SOH) and

models differences are considered. However, additional

technologies result in the increase of calculation cost and

implementation difficulty [9], [28]. In order to solve the

contradiction between SOC accuracy and calculation cost,

the ICC approach based on numerical iteration is proposed,

where the battery model based on a 2nd-order RC circuit is

built firstly with SOC-OCV curve, R-OCV curve and inner

parameters identified offline. Then, the SOC is estimated

by the CC approach in the unsteady state of the battery but

by a numerical iteration approach in the steady state.

Consequently, the accumulated SOC error from the CC

approach can be corrected through the numerical iteration

approach. Furthermore, a compensation coefficient is

employed into CC approach to reduce the error

accumulation rate. Hence, the proposed ICC approach

could make full use of the advantage of conventional CC in

the calculation rate and the numerical iteration approach in

error correction.

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II. METHODOLOGY:

MODEL AND OFF-LINE PARAMETER

IDENTIFICATION OF LITHIUM-ION BATTERY A.

BATTERY MODEL

The nth-order Thevenin model is widely used for SOC

estimation because of its relatively high accuracy and

computation efficiency compared with other models [1].

Increasing the order of the Thevenin model will improve

the model accuracy further. However, higher order result in

additional calculation cost [17]. In the paper, a 2nd-order

RC model as shown in Fig. 1 is employed to estimate the

dynamic characteristics of the battery. The voltage source

UOCV represents the battery OCV. ro is the internal ohmic

resistance. The parallel RC network consists of rp1 and cp1

is aimed to model the fast dynamic voltage of the battery.

Similarly, the parallel RC network consists of rp2 and cp2

is aimed to model the slow dynamic performance. Up1 and

Up2 represent the polarization voltages across the two RC

networks, respectively. Uo and I are the terminal voltage

and load current, respectively. The electrical behavior of

the battery can be expressed as follows.

where, k denotes the present step, k-1 denotes the previous

step. T denotes the sampling period, QN denotes the

maximum available capacity of the battery, and τ1 and τ2

are the time constants of the RC networks. The time

constants denote the response rates of Up1 and Up2,

respectively. A higher constant means a longer time for the

polarization voltage to reach balance, for a given constant

load current

B. OFF-LINE PARAMETERS IDENTIFICATION To

verify the performance of the proposed algorithm, an

18650 Li-ion battery with the nominal capacity of 3Ah and

rated voltage of 3.6V was modeled. The parameter

identification tests were performed on a rek-8511

programmable electronic load, where the measuring

accuracy of voltage and current is 0.03%-0.05%. Then, the

data were processed in Matlab. Different from the

identification process in [2], the lumped resistance R,

which is the sum of ro, rp1 and rp2, was identified

independently. In practice, temperature and aging both

have effect on battery performance. Hence, the tests were

implemented under room temperature. Considering limited

charging process in the test, the influence of aging on the

battery performance is negligible.

1) IDENTIFICATION OF SOC-OCV CURVE:

The hybrid pulse power characterization (HPPC) test with

one hour interval and 5% SOC each time was carried out

[27]. Due to the employment of accuracy measuring

equipment, the SOC could be calculated accurately based

on measured data, and accuracy OCV could also be

accurately measured after a long rest of the battery. The

SOC-OCV relationship curve fitted by a 5-order

polynomial is shown in Fig. 2.

2) DENTIFICATION OF R-OCV CURVE In the paper,

the R-OCV curve will be utilized in the numerical iteration

approach, which will be discussed in Section III. Hence,

the identification accuracy of R is critical to identify the

OCV.

Generally, the lumped resistance R defined in (5) can be

calculated through the identification ofro,rp1 and rp2,

respectively. However, the curve fitting errors of ro, rp1

and rp2 will decrease the accuracy of R. Therefore, the

constant current discharg (CCD) test was carried out to

obtain better accuracy. During the CCD test, the battery

was discharged from 100% to 10% with the discharging

current of 0.8A. Consequently, the discharging process

would last more than three hours. As the Li-ion battery can

reach its steady state after only a few minutes [14]–[16],

the transient process into steady state can be neglected

compared with the whole discharging process. After the

dynamic voltage enters steady state, following equation

could be expressed as:

where, I(k) and Uo(k) are measured based on accurate

measuring instrument. Hence, SOC(k) could be obtained

through the CC approach. UOCV (k) could be calculated

using the SOC-OCV curve discussed in previous Part.

Then, R(k) could be solved through (6). The relationship

between OCV and R is shown in Fig.3. Obviously, the

OCV-R curve in Fig. 3 shows strong nonlinearity. Thus it

requires extremely high order polynomial to fit the curve.

To simplify, the OCV-R curve is decomposed into seven

linear segments according to the inflection points in the

OCV-R curve. The simplified curve is expressed as the

following equations:

3) IDENTIFICATION OF INNER PARAMETERS:

The other inner parameters are identified based on HPPC

test as well. Cooperating with the voltage response

expressions [2], [28], cp1, cp2ro,rp1 and rp2 can be

obtained through curve fitting method.

III. REAL-TIME STATE OF CHARGE

ESTIMATION USING THE IMPROVED COULOMB

COUNTING APPROACH A. STATE JUDGMENT

STRATEGY FOR THE BATTERY

The principle of conventional CC approach is shown in

(13). Due to the measured noise in I(k), an increasing

accumulative error will be introduced into the SOC.

Generally, if the battery model is precise, model-based

SOC estimation approaches, such as EKF and UKF,

perform well without accumulative error. However, the

accuracy of the model will be reduced at the unsteady state

of a battery and model-based SOC estimation approaches

have heavy calculation [16], [19], [34]. Hence, in the

proposed approach, CC approach is still employed at

unsteady state, and numerical iteration based on battery

model is proposed to correct the SOC value at steady state.

Before the proposed approach is implemented, whether the

battery has been steady should be assessed. As mentioned

previously, at the steady state of a battery, the current

flowing through the capacitors of the RC circuits in the

model are negligible. That is to say, it can be assumed that

the measured current I only goes through rp1 and rp2.

Therefore, following criterion could be formulated:

where, s1 and s2 are defined as the steady coefficients,

reflecting the divergence degree of the dynamic voltages

from steady state. In practice, the criterion can hardly be

achieved due to the complex operation condition of EVs.

To address the issue, a looser criterion is employed. This

criterion denotes that if Up1 and Up2 approximate to the

steady state in an adjacent time domain, their mean values

will also close to the steady state. Namely, the battery is in

quasi-steady state. The restrictions for the mean values are

aimed to eliminate the misjudgment caused by the

oscillation in I(k).

B. OCV ESTIMATION USING NUMERICAL

ITERATION A simple iteration algorithm is employed for

OCV estimation and then the SOC could be estimated

directly through SOCOCV curve. Corresponding principle

can be illustrated by (16)-(19).

The equation to be solved needs to be deformed into (16)

firstly, where 8(x) is named as iterative function. Further,

corresponding iteration structure can be discretized as (17),

where xl is the solution of the lth iteration and will be taken

as the input variable of the next iteration. If xl+1 satisfies

equation (18) after infinite iterations, it is treated as x ∗ ,

named the fixed point of 8(x), which is the approximate

solution of x. In practice, infinite iteration is unnecessary,

and xl satisfying equation is sufficient. ε is a pretty small

value, which is set according to the required accuracy.

Assuming that the battery is in steady state at k, following

iteration function can be obtained

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Corresponding iteration structure is shown in (21). UOCV l

is the solution of the lth iteration, and UOCV l+1 is the

solution of the (l+1)th iteration. With iteration going on,

UOCV l+1 will converge to a certain value, which is the

solution of UOCV (k). It is notable that, the initial value of

UOCV 1 should be within the OCV range of the battery

C. COMPENSATION COEFICIENT TO PREVENT

ERROR ACCUMULATION IN CC APPROACH

Assuming that numeral iteration happens at ki . Then, the

accumulative SOC error Ei during each time interval can

be calculated by following equation

where, SOC(ki) is the precise SOC estimated by numerical

iteration. SOC(ki −1) is the last SOC value got by CC,

which contains the SOC error accumulated during [ki−1

+1, ki −1]. Therefore, the error accumulation rate α can be

estimated by following equation.

DESIGN OF ALGORITHMS USED:Algorithms used

for SOC and SOH Estimation are:

1. coulomb counting,OCV

2. kalman filter

3. Internal Resistance and Impedance Measurement

Method.

4. Neural Network

5. Support Vector Machine

6. Sliding Mode Observer

7. Fault Diagnostic Methods

8. fuzzy logic

9. incremental capacity analysis (ICA) method ,

10. Gaussian process regression method,

11. Bayesian network,

12. particle filter method,

13. Thevenin model.

State of charge (SOC) is a relative measure of the amount

of energy stored in a battery, defined as the ratio between

the amount of charge extractable from the cell at a specific

point in time and the total capacity. Accurate state-ofcharge

estimation is important because battery

management systems (BMSs) use the SOC estimate to

inform the user of the expected usage until the next

recharge, keep the battery within the safe operating

window, implement control strategies, and ultimately

improve battery life.

Traditional approaches to state-of-charge estimation, such

as open-circuit voltage (OCV) measurement and current

integration (coulomb counting), can be reasonably accurate

for cell chemistries with a significant OCV variation

throughout the SOC range, as long as the current

measurement is accurate. However, estimating the state of

charge for battery chemistries that exhibit a flat OCV-SOC

discharge signature, such as lithium iron phosphate (LFP),

is challenging. Kalman filtering is a promising alternative

approach that circumvents these challenges with a slightly

higher computational effort. Such observers typically

include a nonlinear battery model, which uses the current

and voltage measured from the cell as inputs, as well as a

recursive algorithm that calculates the internal states of the

system, including state of charge.

However, estimating the SOC for modern battery

chemistries that have flat OCVSOC discharge signatures

requires a different approach. Extended Kalman filtering

(EKF) is one such approach that has been shown to provide

accurate results for a reasonable computational effort.

1. Coulomb Counting Method.

The Coulomb counting method is associated with

monitoring the input and the output current continuously.

Since capacity is the integral of current with respect to

time, by measuring the input and the output current, change

in capacity or capacity degradation of a battery can be

measuredeasily.Inthismethod,SoHiscalculatedbydividingm

easured capacity (after discharging the battery to 0% SoC

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value) to its

ratedcapacity.Itisanextensivelyusedmethodbyresearchersfor

itssimplicity.But,theaccuracyofthismethodisnotveryhigh.

Therefore, to improve its accuracy, for example, Ng et al.

proposed a smart coulomb counting method to estimate

both SoC and SoH accurately. Similarly, an adaptive

neurofuzzy inference system (ANFIS) was modeled in the

paper [51]. It considered the cell’s nonlinear characteristics

to get the relationship between SoC and open circuit

voltage (OCV) at different temperatures. During the

estimation of SoC, at some random OCV and temperature

,modelingofcellcharacteristicswasdonebyANFIS.Theassess

mentwas done on the cell level instead of the pack level for

better precision.

The coulomb counting method, also known as ampere hour

counting and current integration, is the most common

technique for calculating the SOC. This method employs

battery current readings mathematically integrated over the

usage period to calculate SOC values given by

where SOC(t0) is the initial SOC, Crated is the rated

capacity, Ib is the battery current, and Iloss is the current

consumed by the loss reactions. The coulomb counting

method then calculates the remaining capacity simply by

accumulating the charge transferred in or out of the battery.

The accuracy of this method resorts primarily to a precise

measurement of the battery current and accurate estimation

of the initial SOC. With a preknown capacity, which might

be memorized or initially estimated by the operating

conditions, the SOC of a battery can be calculated by

integrating the charging and discharging currents over the

operating periods. However, the releasable charge is

always less than the stored charge in the charging and

discharging cycle. In other words, there are losses during

charging and discharging. These losses, in addition with

the self discharging, cause accumulating errors. For more

precise SOC estimation, these factors should be taken into

account. In addition, the SOC should be recalibrated on a

regular basis and the declination of the releasable capacity

should be considered for more precise estimation.

Enhanced Coulomb Counting Algorithm:In order to

overcome the shortcomings of the coulomb counting

method and to improve its estimation accuracy, an

enhanced coulomb counting algorithm has been proposed

for estimating the SOC and SOH parameters of Li-ion

batteries. The initial SOC is obtained from the loaded

voltages (charging and discharging) or the open circuit

voltages. The losses are compensated by considering the

charging and discharging efficiencies. With dynamic

recalibration on the maximum releasable capacity of an

operating battery, the SOH of the battery is evaluated at the

same time. This in turn leads to a more precise SOC

estimation.

Technical Principle

The releasable capacity (Creleasable), of an operating

battery is the released capacity when it is completely

discharged. Accordingly, the SOC is defined as the

percentage of the releasable capacity relative to the battery

rated capacity (Crated), given by the manufacturer.

A fully charged battery has the maximal releasable capacity

(Cmax), which can be different from the rated capacity. In

general, Cmax is to some extent different from Crated for a

newly used battery and will decline with the used time. It

can be used for evaluating the SOH of a battery.

When a battery is discharging, the depth of discharge

(DOD) can be expressed as the percentage of the capacity

that has been discharged relative to Crated,

where Creleased is the capacity discharged by any amount

of current. With a measured charging and discharging

current (Ib), the difference of the DOD in an operating

period (Ʈ) can be calculated by

where Ib is positive for charging and negative for

discharging. As time elapsed, the DOD is accumulated.

DOD(t) = DOD(t0) + ΔDOD

To improve the accuracy of estimation, the operating

efficiency denoted as ŋ is considered and the DOD

expression becomes,

DOD(t) = DOD(t0) + ηΔDOD

with ŋ equal to ŋc during charging stage and equal to ŋd

during discharging stage. Without considering the

operating efficiency and the battery aging, the SOC can be

expressed as

SOC(t) = 100% – DOD(t)

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Considering the SOH, the SOC is estimated as SOC(t) =

SOH(t) – DOD(t) .

Figure 1 shows the flowchart of the enhanced coulomb

counting algorithm. At the start, the historic data of the

used battery is retrieved from the associated memory.

Without any information for a newly used battery, the SOH

is assumed to be healthy and has a value of 100%, and the

SOC is initially estimated by testing either the open circuit

voltage, or the loaded voltage depending on the starting

conditions. The estimation process is based on monitoring

the battery voltage (Vb) and Ib. The battery operation

mode can be known from the amount and the direction of

the operating current. The DOD is adding up the drained

charge in the discharging mode and counting down with

the accumulated charge into the battery for the charging

mode. After a correction with the charging and discharging

efficiency, a more accurate estimation can be achieved. The

SOC can be then estimated by subtracting the DOD

quantity from the SOH one. When the battery is open

circuited with zero current, the SOC is directly obtained

from the relationship between the OCV and SOC. It is

noted that the SOH can be reevaluated when the battery is

either exhausted or fully charged, and the battery operating

current and voltage are specified by manufacturers. The

battery is exhausted when the loaded voltage (Vb) becomes

less than the lower limit (Vmin) during the discharging. In

this case, the battery can no longer be used and should be

recharged. At the same time, a recalibration to the SOH can

be made by reevaluating the SOH value by the

accumulative DOD at the exhausted state. On the other

hand, the used battery is fully charged if (Vb) reaches the

upper limit (Vmax) and (Ib) declines to the lower limit

(Imin) during charging. A new SOH is obtained by

accumulating the sum of the total charge put into the

battery and is then equal to SOC. In practice, the fully

charged and exhausted states occur occasionally. The

accuracy of the SOH evaluation can be improved when the

battery is frequently fully charged and discharged. finally

simple calculation and the uncomplicated hardware

requirements, the enhanced coulomb counting algorithm

can be easily implemented in all portable devices, as well

as electric vehicles. In addition, the estimation error can be

reduced to 1% at the operating cycle next to the

reevaluation of the SOH.

Figure: Flowchart of the enhanced coulomb counting

algorithm.

Charging and discharging methods of coulomb counting:

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V. CONCLUSION

In the paper, an ICC approach with real-time error

correction ability is proposed. The SOC is estimated online

by the CC approach at unsteady state, leading a much

higher estimation rate. At steady state, numerical iteration

approach can accurately eliminate the accumulated SOC

error of CC approach, leading a much higher accuracy than

traditional CC approach. The numerical iteration approach

is based on a 2ndorder RC circuit model, where its

parameters were identified offline during HPPC and CCD

tests. Hence, the proposed approach could combine the

advantages of CC approach and model-based approach

together. Furthermore, a compensation coefficient α is

employed into the CC approach to reduce the error

accumulation rate. Experimental results suggest that the

SOC error of ICC is effectively limited within 1% and its

calculation cost is 94% lower than that of EKF. Therefore,

it provides beneficial guidance for the real-time SOC

estimation in EVs.

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