Content uploaded by Shunli Wang
Author content
All content in this area was uploaded by Shunli Wang on Jun 23, 2020
Content may be subject to copyright.
西西西西西西
•A Novel Parameter Identification of
Lithium-ion Battery Based on Fractional
Equivalent Model
Reporter 西 He mingfang
Report time: December 13,
2019
西西西西西西
catalogue
Fractional circuit model
1
2
3
Parameter Identification of
fractional order model
Definition of Fractional Calculus
西西西西西西
1.Definition of Fractional Calculus
Fractional calculus in a narrow sense mainly includes
fractional differentiation and fractional integration. It can be
considered that fractional calculus extends the number of
differentiation or integration in traditional calculus from
positive integer domain to the whole real number domain.
A sign of continuous integral-differential operator is introduced
and defined as follows 西
Where a is the order of the fractional
operator, which changes in the real
number field, and t0 and t are the
boundaries of the operation.
西西西西西西
1. Definition of Fractional Calculus
Fractional calculus includes three definitions: GL definition, RL and
Caputo definition. The only discrete form of fractional calculus can be
obtained by GL definition, as shown in the following formula.
In this formula, t0 is defaulted to 0, h is the sampling interval, a is the number
of fractional operators, and are Newton binomial coefficients, the specific
equation is as follows:
Similarly, in order to extend Newton binomial domain from integer domain
to whole real domain, gamma function is introduced, and its conversion
relation is as follows
西西西西西西
2. Fractional equivalent circuit model
As mentioned earlier, the fractional equivalent circuit model of lithium-
ion battery can be obtained from the typical impedance spectrum curve
of lithium-ion battery, as shown in the figure.
EIS ：Fractional circuit model ：
西西西西西西
2. Fractional order circuit model
The constant phase angle element CPE1
impedance expression is shown below 西
Since lithium battery hardly works in ultra-
low frequency state, the function of warbuge
element can be ignored, so KVL equation of
circuit can be expressed as follows:
For RC parallel circuit:
Integer RC circuit: Fractional order RC circuit
西西西西西西
2. Fractional order circuit model
According to the GL definition of fractional calculus mentioned above:
UCPE and its discrete form can be get as follows:
and KCL equation of fractional RC loop mentioned above,
In order to simplify the calculation, the recurrence formula of Newton binomial is
introduced as follows
西西西西西西
3.parameter identification
Particle swarm optimization algorithm is used to identify the parameters of
fractional equivalent circuit model. The flow of particle swarm
optimization algorithm is shown in the following figure.
The algorithm has four parameters to be
identified:
The fitness function is as follows.
Um(k) is the actual battery output voltage 西
is the output voltage of the model
According to the principle of short-term memory, if the data length is
shortened and N=2 or N=3. When N=2, the model output voltage is as
follows
1
min(e) ( ( ) ( , ))
n
m m
j
J U k U k
�
�
( ) ( )
1 0 1
( ) ( 1) ( ) ( ) ( 1)
p p p p p
a a
m m
p p p p p p
R C TR RR C
U k w U k R I k w I k
R C T R C T R C T
�
西西西西西西
According to the discrete equation of appeal, the optimal particle swarm optimization
algorithm can be used to identify the model parameters, and the identification results
are as follows:
西西西西西西
Thanks!