Smart Grid and Renewable Energy, 2012, 3, 51-55 Published Online February 2012 ( 51
The SOC Estimation of Power Li-Ion Battery Based on
ANFIS Model*
Tiezhou Wu, Mingyue Wang, Qing Xiao, Xieyang Wang
School of Electrical & Electronic Engineering, Hubei University of Technology, Wuhan, China.
Received September 5th, 2011; revised October 11th, 2011; accepted October 18th, 2011
On basis of traditional battery performance model, paper analyzed the advantage and disadvantage of SOC estimation
methods, introduced Adaptive Neuro-Fuzzy Inference Systems which integrated artificial neural network and fuzzy
logic have predicted SOC o f b attery. It’s a battery resid u al capacity model with more generalization ab ility, adaptab ility
and high precision. By analyzing the battery charge and discharge process, the key parameters of SOC are determined
and the experimental model is modified in MATLAB platform.Experimental results show that the difference of SOC
prediction and actual SOC is below 3%. The model can reflect the characteristics curve of th e battery. SOC estimation
algorithm can meet the requirements for precision. The results have a high practical value.
Keywords: State of Charge; ANFIS; Estimation Method; Li-Ion Battery
1. Introduction
Battery is an energy source for electric vehicles. In order
to make sure the good performance of the battery pack
and extend it’s life, it is necessary to make good control
and management for the battery pack. Li-ion battery has
the advantages of high voltage, high energy, long cycle
life, low self-discharge, no memory effect, no pollution
etc [1]. So it gradually replaces the others in electric ve-
hicles and hybrid electric vehicle.
In the light of the battery voltage, current, temperature
and other real-time online measurement, the online and
real-time estimation about the SOC is possible. The value
of SOC directly reflects the state of the battery, it is ap-
propriate to tell the different performances between the
various cells in the battery pack by the different SOC
value of each cell, and the balanced charge can be
operated according the different performances. The final
aim is to extend the battery life, limit the maximum
discharge current and predict the driving range of electric
vehicles etc [2]. There is much improved room in the
application of battery SOC online and real-time estima-
tion method. It is impossible to meet the actual require-
ments as the error of estimation more than 8% [3]. To
improve the accuracy of SOC online and real-time esti-
mation, intensive study is necessary in measurements
method, the battery model and estimation method.
2. Traditional SOC Estimation Method
SOC show that the percentage of remaining capacity in
marker capacity [4], and that is defined as the rate of
remaining and the ratio capacity. The range is from 0%
to 100%:
SOC 100%
 (1)
Here, Qn is the total battery power; Qt is the remaining
battery capacity at the time of t, and formula can be
expressed as following:
QQ itt
Here, Q0 is the initial capacity of the battery,
define the change of the battery capacity from
the time of 0 to t.
Originally, some relatively simple algorithm was pro-
posed, such as: integrate the current in amperes-time
method [5], open circuit voltage method by means of
OCV and SOC correspondence relationship and etc [6].
Then, the modified algorithm of these methods appeared,
which added some or all amendments of the temperature,
charge and discharge rate, charge and discharge effi-
ciency. There are some advanced methods to be put for-
*This work was supported by natural science foundation of Hubei prov-
ince (research on soc estimation method and equalizing charging o
lithium-ion battery for HEV. No. ZRY1530). Author: Tiezhou Wu
(1966-), male, associate professor, mater tutor, Research direction:
signal analysis and system integration.
Copyright © 2012 SciRes. SGRE
The SOC Estimation of Power Li-Ion Battery Based on ANFIS Model
ward as well, such as: fuzzy control algorithm, neural
network algorithm [7], Kalman filter algorithm [8], and
the newly emerged impedance spectroscopy method and
C. Ehret’s linear models method.
Although people pay a lot of effort to research this
problem, the result is unsatisfactory. The mainly reason
is that the battery’s highly nonlinear. Various methods
exist their shortcomings, such as: amperes-time method
have error accumulation; open circuit voltage method is
not suitable for current frequent fluctuation during driv-
ing; fuzzy control depend on engineering experience;
neural networks rely on the choice of sample [9]; Kalman
filtering depend on accurate battery and calculation com-
plexity; impedance spectroscopy method requires addi-
tional function generator, increase costs; linear model
method is only suitable for low current situation etc [10].
At present, generally combine the several algorithms to
estimate SOC [11].
3. ANFIS’s Theorem and Structure
3.1. Combination the Fuzzy Technology and
Neural Network
Single neural network, just a black box system, is lacking
of performance that could not provide the heuristic
knowledge for the SOC’s predication of battery. There-
fore, It is not appropriate to express the knowledge based
on the rules and not good to make use of the existing
experience and knowledge. These drawbacks will in-
crease the network’s training time. A single fuzzy pre-
dictive can simply realize the learning heuristic knowl-
edge but can’t get the accurate result. Because the per-
formance of self-learning and adaptive capacity is weak,
it is difficult to form automatically and adjust the fuzzy
rules of membersh ip function local extremism. Combina-
tion of both can get the exact value at any conditions, and
meanwhile can also understand the estimation process,
can get the advantage of neural network and fuzzy sys-
In the fuzzy control system, fuzzy reasoning is a map
to the relationship of input-output. Input as the premise
(the error E, the change rate of E and other fuzzy vol-
ume), makes the non-fuzziness control output. Since
neurons can map any function relationships, it also can
be used to make the fuzzy inference come true. In addi-
tion, the neural network can realize fuzziness and non-
fuzziness. So that the neural network can represent all
fuzzy control.we call this fuzzy control which is based on
neural network. It has many advantages, such as com-
puting and the number of knowledge experience are in-
dependent; allowed to contain a small amount of error
experience (because it can be automatically excluded in
the study)and can be parallel, distributed computing etc.
Thus this fuzzy neural network, neural network-based
fuzzy control, was used in hybrid electric vehicle energy
management system [12].
3.2. ANFIS’s Construction
Artificial Neuro-Fuzzy Inference Systems [13] is exten-
sively used in the field of modeling, decision-making,
signal processing and control. Here, the structure of
ANFIS and its learning rule would be introduced.
Assuming that the fuzzy neural network has two inputs
x and y, one output z.
For the first-order Sugeno fuzzy model [14], the fol-
lowing rules:
Rule 1: If x is 1
and y is , then
11 11
px qyr
Rule 2: If x is 2
and y is , then
22 22
px qy r
The corresponding equivalent ANFIS model structure
shown in Figure 1, the same floor node here has the
same function.
Layer 1: 1
and 1 are input variables fuzzy sets, This
layer node activation function on behalf of the member-
ship function of fuzzy variables, the output represents
fuzzy result called membership, one of the node transfer
function can be expressed as:
1, ixi
Ofx (3)
1, 2i
1, 2
Of y
Commonly the Gaussian function is used as the activa-
tion function.
Layer 2: multiply any two memberships which get by
the fuzzy, so the output represents fuzzy rules or applica-
ble degree of intensity.
2,ii xiyi
1, 2i
Layer 3: normalize each rule’s apply degree:
3, 12
 (6) 1, 2i
Layer 4: calculate each rule’s conclusion:
ii i
 (7) 1, 2i
Layer 5: Calculate the output of all rules and that the
Figure 1. Equivalent ANFIS structure.
Copyright © 2012 SciRes. SGRE
The SOC Estimation of Power Li-Ion Battery Based on ANFIS Model 53
output of the system output:
112 2
zwzwz (8)
i, i, i are unknown, through the algorithm train-
ing, ANFIS can get them at a specified target to achieve
the purpose of fuzzy modeling.
p q r
4. SOC Estimation Based on ANFIS
4.1. SOC Estimation Model Based on ANFIS
Hybrid operation process is very complicated. During the
working process, the battery’s SOC would be affected by
many factors, such as: environmental temperature, initial
voltage, battery resistance, working hours, and etc. The
car will meet all kinds of problems in running, such as
acceleration, climbing, cold, heat, rain, etc, as the battery
power source is also influence by these conditions. Of
course, the ideal neural network model is the more
comprehensive input the better the output of the mapping,
the more close to the actual conditions. However, many
input data rely on a variety of instruments and sensors to
get. More input data requires more costs, in light of this
point and with the prerequisite of getting satisfied result,
less input is good for result, which does not only reduce
the difficulty of dealing with the problem, but also
reduce costs.
In this paper, three inputs variables are available—the
voltage V, current I, and cells surface temperature T,
SOC’s remaining battery charge percentage of capacity
as only one output valu e is predicted, as shown in Figure
2. It is very difficult to realize the mapping from the
three-dimensional space to one-dimensional by means of
traditional method. For overcoming this problem, the
appearance of development of fuzzy logic method is .to
come with the tide of fashion. Through a large number of
typical test data, the curve to extract some of the rules
with regularity, that is human “work experience”, and
then use the fuzzy logic of the “reasoning” to achieve
this “experience”, it often can achieve better results. The
design makes full use of fuzzy logic reasoning is simple,
strong robustness and accuracy of neural network sys-
tems, and because neural network system for the three-
Figure 2. Adaptive fuzzy neural network prediction SOC
values model diagram.
input single-output system, making the hidden nodes is
greatly reduced, easy to implement.
4.2. SOC Estimates to Realize Based on ANFIS
4.2.1. Collect Da ta, Analyze and Crea te D at a Se ts an d
Test Data Sets
At 22˚C - 27˚C ambient temperature of the laboratory,
we do constant flow duration discharge test for a manu-
facturer 3.3 V - 10.5 Ah LiFePO4 batteries SLFP-PT30,
at the condition of 0.48 C, 0.95 C, 1.43 C (i.e. 5 A, 10 A,
15 A). According to the relevant information of manu-
facturer to take 0.48 C, 0.95 C, 1.43 C constant current
battery discharge continued to discharge termination
voltage is 3.18 V, 3.24 V, 3. 2 8 V.
The following is the fitting curve in the condition of
different discharge current and battery voltage discharge
time. It is shown in Figure 3.
It can be seen from the curves that the voltage’s down-
ward trend under the condition of large discharge current
is faster than then the relatively small one.
4.2.2. Determination the ANFIS Network Structure
In order to make use of MATLAB fuzzy toolbox anfis
simulation of the data collected, we choose the function
of genfisl inside. Function genfisl through the way of
grid partition to given data set to generate a fuzzy
inference system, which can be used in conjunction with
the function anfis. By function genfisl generated the
fuzzy inference system input and output membership
function curves are to ensure that cover the entire input
and output space evenly divided on the basis of its input
and output membership functio ns of the type an d number
specified in the use, you can also use short provincial
Provide Training data and test data: With the different
discharge rate of the voltage, current, SOC and time
series. The odd items were regarded as the training data,
and the even items as the authentication data.
4.2.3. Determination the Type of Input and Output
Membership Functi on
Usually, ANFIS network could provide 8 variable pa-
Figure 3. Different discharge current-voltage measurements.
Copyright © 2012 SciRes. SGRE
The SOC Estimation of Power Li-Ion Battery Based on ANFIS Model
Copyright © 2012 SciRes. SGRE
rameters of the function type MF. In the current paper,
the Gaussian membership function (Gaussmf) is applica-
tion [15]. Since ANFIS is a Sugeno type fuzzy system, so
there are two output variables membership functions,
namely: constant and linear functions. In this paper, con-
stant, that the first order Sugeno fuzzy system.
problem of the error function, using steepest descent for
nonlinear programming method, in accordance with the
error function of the negative gradient direction to mod-
ify the weights, so it existence the disadvantage of low
learning efficiency, slow convergence, and vulnerable
Local minimum state, relatively poor network generali-
zation ability.
4.2.4. Divination Inpu t Variable Space The following is a BP network, ANFIS model com-
parison in predicted remaining battery capacity.
First determine the maximum and minimum input vari-
ables: then order the collected data to obtain the mini-
mum and maximum input variables; finally, establish
three fuzzy sets for each input variable, the correspond-
ing generated results are high, low, medium membership
functions, the input space is the input variables corre-
sponding to the product of the membership. The output
value from correspo nding is between 0 and 1.
Figure 4 shows the compared curve between predic-
tive value and measured one of the remaining capacity of
8 A constant discharge.
Figure 5 shows the remaining capacity under the 20A
constant discharge predicted and measured values of the
contrast curve.
According to the Figures 4 and 5, under the experi-
mental condition, compared the SOC’s predictive value
and actual one, the majority of relative error could be
controlled within 5%. What’s more, the predictive effect
of ANFIS model is better and the error could be con-
trolled within 3%, which would not only meet the re-
quirements of industrial applications, but is suitable to
apply for the actual predictive research. And from the
view of training steps and training time, ANFIS model to
predict SOC is more efficient, ideal for real-time predic-
5. Experimental Validation and Analysis
The selection of training data may give unreliable results
bring some factors as before mentioned, This addition
not only requires some pre-work on the availability of
data, training process and the final result of model check-
ing is also very important. In general, the result model
test procedure is used for training those who do not use
as the input/output data, to compare the model is or not
trained to a very good match and predict these data.
The essence of BP algorithm is to solve the minimum
Figure 4. 8 A constant current discharge of the predictive value of SOC compared with the real.
Figure 5. 20 A constant current discharge of the predictive value of SOC compared with the real.
The SOC Estimation of Power Li-Ion Battery Based on ANFIS Model 55
6. Conclusion
Based on the analysis of the traditional state of charge
(SOC) estimation method, the current paper proposed a
battery residual capacity model, featured with more gen-
eralization ability, adaptability and high precision. By
analyzing the battery charge and discharge process, it is
to determine the key parameters of SOC and then modify
the experimental model in MATLAB platform. Through
BP network prediction with comparison of experimental
simulation of SOC values, indicating that the ANFIS has
strong ability of adaptation and generalization, this me-
thod reduces the estimation error of SOC to less than 3%,
it can be used for intelligent monitoring system in hybrid
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