# The Identify of Dynamic Model and the Self

The Identify of Dynamic Model and
the Self-tuning Prediction of SOC for EV Battery
Runjin Ma, Li Sun, Hongfan Tian
North China University of Technology, Beijing 10041, PRC
Tel: 86-10-68839054, Fax: 86-10-68875846
[email protected], [email protected] ,
Abstract:
This paper gives a dynamic model and its parameters for EV batteries' discharging process based on
system identifying approach. On the great lot data from the experiment on three different kind
batteries usually used in the light-weight electric vehicle, the paper shows the relationship between the
parameters and the SOC of battery. The easy tested characteristic voltage, △U(10), is used to predict
the SOC of EV battery.
Keywords: battery model , Bicycle, State of charge,
Introduction
Electric bicycle comes to play an important role in the progress of low pollution motorization in the
China. In the mainland of China, about 271,000 pieces of electric bicycle were sold in the 2000
contrast to 15,000 pieces in 1997. The most types of battery used in the electric bicycle sold in the
China is lead-acid battery, and few of them are Ni-MH and Ni-Ca battery due to the high price. The
disadvantages of the lead acid battery are the short running distance for one charge and short lifetime.
This paper builds a dynamic model for batteries used in the electric bicycle. By a great deal
experimentation and the parameter identify arithmetic, this paper shows the relationship between the
model parameter and the SOC of battery. Future more, the characteristic voltage △U(10) is used to
adjust the prediction of SOC. The temperature influence and battery parameter change will also be
discussed in the paper.
Discharge experimentation for electric bicycle battery
Fig.1 shows the test beach for the electric bicycle battery discharging experimentation. The sample
interval is chosen as 1/4 second by experience.
Let U0 be the voltage of battery without load and Ua be the voltage of battery with the load Ra. Since
the battery has the inner impedance Z0, we have
△U = U0 — Ua
The curve of △U and its mathematics model
The inner impedance of battery Z0, has a very good relationship with the state of battery especially the
state of charge. Figure 2 shows the voltage curve of battery with the load Ra. The test time was lasted
30 seconds. From the enlarged curve (Fig.3) we could find that △U has three components:
△U = △U1 + △U2 + △U3
△U1 , the biggest part in the three components, is square wave. △U2 , the middle one in the three
components, is exponent curve. It is means that there is capacitate reactance in the battery. △U3 , the
smallest in the three components, is linear. It is means that the voltage-drop at inner residence of
battery is without stable state. The voltage of battery will keep down in the discharge process until
SOC exhaust.
△U1 could be obtained directly from sampling data and two other components might be get by least
square method. The experiment shows that the inner impedance of battery could been described by the
equivalent circuit in figure 4 and the transfer function in figure 5. Theλin the figure 4 and figure 5
reflect the attenuation coefficient of △U3, and T is the time constant of △U2 .
Least Square Estimate for Model Parameter of Battery
Using the bi-input - single output CAR model we have
y(k) = a *y(k-1) + b0 *u(k-1)+b1 *u(k-2) + c *(k-k0) + ε(k)
Here the sampling input series { u(k) } is measurable. While the switch K is on，u(k) = Uo . While
switch K is off, u(k) = 0. { y(k) } , measurable output series, is the sampling data of (△U2 + △U3).
(k-k0) is used as an other measurable input for identify the attenuation coefficient λ.
k0 represent the time when K is switch on. {(k)} is the un-measurable random disturbance which
mainly come from the model deviation and measure disturbance. The model could also be express in
vector equation:
y (k )   k    (k )
T
where
 Tk  [a, b0 , b1 , c]
 Tk  [ y(k  1), u (k  1), u (k  2), (k  k0 )]
The object criterion is chosen as
N
J  [ y (k )   Tk  ]2
k 1
We could obtain the parameter  based on least square method with the minimizing J . Figure 6 shows
the result of estimated parameters.
The batteries used in the tests were 12Ah lead-acid batteries. The discharging current were chosen at
0.25C, 0.5C and 1C which represent the typical working states of electric bicycle: smooth road riding,
opposing wind or sloping riding, starting.
The analysis of model parameter
From the estimated parameter a , b0 , b1 , c and discharging current I a together with △U1
which could be get directly from sampling data, we could calculate the parameters of
equivalent circuit in figure 4.
 Tk  [a, b0 , b1 , c]
△U2 = ( b0+b1)/ (1—a)
R0-1 = △U 1 /
(v )
Ia
( Ohm)
R0-2 = △U 2 / I a
(Ohm)
T = -T0 / ln(a)
(Ohm)
λ= c * 4 * 60
(V/Min)
From the model and the experiments data we could have:
1. △U1 and
R0-1 have the very complex relationship with discharging state. (Fig. 7)
2. T and R0-2 fall when the discharging quantity increase. This characteristic could be used to
determine the state of charge for battery (Fig.7,Fig.8).
3. The attenuation coefficientλ, which reflect the increase speed of △U3, increase slowly at the
begin of discharging process and enhance rapidly while deep discharging. (Fig.9)
4. Since it is complex to gain T 、R0-2 and λ, we introduce a parameter, the characteristic voltage
△U(10) which is easier to be measured and has a very good mutuality to the T 、R0-2 and λ. The
△U(10)is the difference of voltage while beginning of discharge and the voltage at 10 seconds in the
discharging process. The △U(10), a useful and easier to be measured parameter, could be used to
determined the SOC of battery. Figure 10 shows the relationship between △U(10) and SOC of
battery.
5. Figure 11 shows the relations between △U(10) and the riding distance of electric bicycle. It is
showed that △U(10) could be used to forecast the remaining range of electric bicycle and the SOC of
battery.
6. Figure 12 shows the relation between △U(10) and SOC at different temperature. It is necessary to
modify the △U(10) forecast result since the state of battery is varied to the temperature.
7. The experiments showed that the △U(10) forecast method is also suitable for Ni-MH and Ni-Ca
battery. The △U’s three components of the different kind battery have different value and different
ratio. The △U2 of Ni-MH and Ni-Ca battery are much smaller than the lead-acid battery.
8. The SOC indicators in the electric bicycle are usually by the means of end voltage or ammeter. It is
effective to use the characteristic voltage △U(10) to adjust the result gained by tradition methods.
The influence of cycle times and temperature on battery states should be considered to increase
forecast precision.
Reference:
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System, evs17,2000
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[4] Morio Kayano, etc: Battery SOC and Distance to Empty Meter of the Honda EV Plus, EVS-14,1997
[5] Johansson, Arne O. Battery module diagnostics based on the IEC/TC 69 load profile,EVS-14,1997
[6] D. Heinemann, etc: A New Design of a Battery Management System Including a Range Forecast,
EVS-14,1997
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[10] Pritpal Singh and Sangeetha Damodar,
Fuzzy Logic-Based Determination of Pb-Acid Battery SOC by
Impedance Interrogation Methods, evs-17,2000
Figure 1. The test circuit
Figure 2. The voltage curve of battery
while the switch K is on at t0
Figure 3 The enlarged curve of Fig.2
Figure 4. The equivalent circuit of battery
Figure 5. The transfer function of battery
Figure 6. The result of estimated parameters.
Figure 7. The relation between R0-1 and the battery's state of discharge.
Figure 8. The relation between time constant T and battery's state of discharge
Figure 9. The relations between attenuation coefficientλ and battery's state of discharge
Figure 10. The relation between △U(10) and battery's state of discharge
Figure 11. The relation between △U(10) and remained riding range
Figure 12. The relation between △U(10) and battery's state of discharge at different temperature

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