Innovative Applied Energy (IAPE 2019)
14-15 March, 2019
Oxford City, United Kingdom
On the Dynamics and Operational
Performance Analysis of Lead-Acid
Battery Interfaced to Electrical Grid
Mohammad S. Widyan, Associate Professor
Electrical Engineering Department
The Hashemite University
JORDAN
1
CONTENT
General Overview of Lead-Acid Battery
System Under Study
System Mathematical Model
Numerical Simulation Results
Conclusions
2
General Overview of Lead-Acid Batteries
The main advantages of Lead-Acid battery compared with
other types are:
1) the most cost competitor.
2) very low internal resistance.
3) the highest overcharge tolerance.
4) good self-discharge rate.
5) thermally stable.
6) well known nonlinear dynamical
mathematical model.
7) well known electrical equivalent circuit.
* However, it has the disadvantages of low cycle life and
toxicity nature .
3
Configuration of the System Under Study and
Equivalent Electrical Circuit of Lead-Acid Battery
4
Nonlinear Dynamical Mathematical Model
* Lead-Acid Battery
The nonlinear dynamical mathematical model of the Lead-Acid
Battery can be summarized as:
di1
1
 im  i1
dt
dQe
 im
dt
(   a )
d
C
 Ps 
dt
R
RC Low-Pass Filter
The nonlinear dynamical mathematical model of RC low
pass filter in dq stationary reference frame can be
summarized as:
didF
L
 V ph sin   RF idF  s LiqF  vdC
dt
L
diqF
dt
 V ph cos   RF iqF   s LidF  vqC
dvdC
CF
 idF  id  s CF vqC
dt
CF
dvqC
dt
 iqF  iq   s C F vdC
6
Transmission Line (Underground Cable)
The dynamical model of the underground cable can
be summarized in dq stationary reference frame
did
LL
 vdC  RL id  s LL iq
dt
LL
diq
dt
 vqC  RL iq   s LL id  Vinf
7
Further Equations of Lead-Acid Battery



Qe (t )
SOC  1  



K
C
1


 C o*
   f




 
 
 
 
 Qe (t ) 
DOC  1  

C
(
I
,

)


avg
Em  Emo  K E (275   )(1  SOC )
Ro  Roo [1  Ao (1  SOC )]
R1   R10 ln( DOC )
R2  R20
e[ A2 1(1 SOC )]
1 e
 A2 2im 
 * 
 I 
8
Numerical Simulations
Response of the system (a) injected current, (b) battery state-ofcharge, (c) injected active power and (d) injected reactive power
following step reduction in the infinite bus voltage by 6%
9
Response of the system (a) battery internal resistance, (b) battery
terminal voltage, (c) inverter terminal voltage and (d) battery
efficiency following step reduction in the infinite bus voltage by
10
6%
11
Conclusions
1) Response of the system (a) battery internal resistance, (b)
battery terminal voltage, (c) inverter terminal voltage and (d)
battery efficiency following step reduction in the infinite bus
voltage by 6%
2) The study is carried out based on the complete nonlinear
dynamical mathematical model of all system components
including the electrochemical interaction of the battery.
.
3) All parameters of the system decrease as function of time
except the efficiency of the battery which can be justified by
the fact the output current from the battery decreases and
therefore the copper losses inside the battery decreases.
12
4) The response of the system after step change in the value of
the infinite bus voltage is investigated. The system goes shortly
into transient state directly after the step change for about 11s. It,
then, settles down to stable steady-state behaviour.
5) Starting from fully charged battery, the battery can feed the
electrical grid effectively with active and reactive power for about
40 hours.
6) The efficiency of the battery ranges from about 94.8% to about
96.7%.
7) As a general conclusion, Lead-Acid battery characterized by
the most cost effective among all other battery types, can be
effectively interfaced to electrical grid.
13
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