In this paper literature review of different types of battery models are given. These battery models having various characteristics are discussed and these models also described. In this paper, important parameters of battery like state of health(SOH), state of charge(SOC), run time etc. which affect the performance of battery. This paper gives the brief information of battery models. Moreover merits and demerits of these battery models are summarized.
1- Introduction
Battery is used to store energy basically its convert chemical energy into electrical energy or vice versa. This property of battery is very useful in power system. It has used everywhere for availability of energy. Some of its main applications are grown in last decade of year, these are:
‘ Battery is in Electrical vehicle[1].
‘ For the energy storage in plant we use Battery Energy Storage Plants. In this we compensate the flow active or reactive power.
‘ Batteries are used in Uninterrupted Power Supplies.
There are many parameters related to battery modeling like internal resistance, discharge type and discharge mode. Internal resistance consisting of Self-discharge Resistance, Resistances for Charge and Discharge and Overcharge and Over-discharge Resistance. In discharge type one is Continuous Discharging in which battery gives the energy to load without any rest and other is intermittent discharging gives the energy to load for a period due to which voltage recovery take place cause increase in voltage. Discharge mode is consisting of constant load, constant current, constant power and rate of charge/discharge. High rate of charge/discharge decrease the battery life. A controlling method is used to avoid deep discharging of battery as well as reduce the charging and discharging cycle of battery[1]. It will improve the state of health of battery. Self-discharge, battery storage capacity, over voltage and internal resistance represents behaviour battery parameters[2] and a model explain non-linear characteristics of battery in terms of state of charge[3].
2. Different Types of Battery Model
There are many techniques of battery modelling are present. Few of them are mentioned here with their merits and demerits are given below:
A. Simple Battery Model
It is the most common model of the battery. This model is having a terminal voltage and internal resistance of battery which is equivalent to constant internal resistance ESR with open circuit voltage . It is consisting of ideal battery which having unlimited power is assumed shown in fig. 1:
Fig. 1: Circuit of the simple Battery model
At fully charged condition, the terminal voltage is obtained from open circuit measurement. ESR can be obtained by connecting a load and by measuring the voltage and current across the load. This model seems very simple but it is does not depend upon the state of charge (SOC), changes in internal resistance ESR due to temperature and electrolyte concentration. This model never is used for monitoring of battery in Electric vehicle. It is applicable in specific circuit simulation where power is assume to be unlimited[1].
B. Modified Battery Model
It is the improve model of simple battery model. In this model, the disadvantages of above model was considered and make a propagate model. Here battery internal resistance ESR changes according to changes occur in state of charge over the time. A common formula is set and given as:
(1)
At fully charged condition, internal resistance of battery was calculated and
(2)
Where, is 10 hour battery capacity(Ah) at reference temperature ( it may be change according to battery age). S is changes from 0 when battery is completely discharge or 1 when battery is completely charge. The Coefficient k is function of discharge rate of battery and it is calculated by , and basis which can be determined by curve given by manufacture[3].
C. Thevenin Based Electrical Model
This model is consisting of ideal no load battery voltage , capacitance C occur due to capacitance of parallel plate[3], internal resistance and over voltage resistance occur due to the contact resistance of plate to electrolyte shown in fig 2:
Fig. 2: Thevenin Battery Model
The drawbacks of Thevenin based electrical model are that all elements are considered to be constant but they are not constant[4].
D. Resistive Thevenin Battery Model
This model is having some assumptions these are:
‘ constant current is drawn during discharging
‘ constant electrolytic resistance during discharging
‘ porous materials are used for electrode
Resistive Thevenin battery model is given by[4]:
Fig. 3: Resistive Thevenin Battery Model
In this model, two internal resistances battery and are used for charging and discharging. Two diode are used out of which only one forward biased and other one in reverse biased at a time. It depends upon the process of charging or discharging.
E. Modified Thevenin Equivalent Battery Model
Charging and discharging dynamic equation of this model is given as:
(3)
(4)
Where,
(5)
Fig. 5: Modified Thevenin equivalent battery Model
This model is modified resistive thevenin battery model, c is the polarization capacitance.
Battery current is determined when =0 then = [5].
F. Dynamic Battery Model
This battery model is development for lead-acid traction battery and given by:
(6)
Where, is battery terminal voltage, is the terminal resistance of battery, SOC is the state of charge, is the discharge current, k is polarization constant equal to .1 ohm[6]. The modification of this model is used to account for the non-linear characteristic of both open circuit voltage[7] and the internal resistance represented by the component.
G. Fourth Order Dynamic Model
The Fourth order dynamic model is given as[7]:
Fig. 6: Circuit of Fourth-order Dynamic model
This battery model is consisting of two parts:
‘ current is flowing through (electrolyte reaction), (Ohmic effect) and its associated leakage capacitance and (waste of energy) and it is associated with leakage capacitance
‘ current flowing through (self discharge).
This model has few demerits are mentions below:
‘ Due to higher order system it takes longer time for computation
‘ lots of empirical data is required it becomes complicated
H. Run Time Based Model
This model consisting of three categories[3]. The information of terminal voltage and SOC is given in the first part here represent SOC of battery and represent internal resistance of battery. Second part deals with the transient behaviour of the battery through and . Third part deals with , and where which represent voltage loss, self-discharge resistance and capacity of battery.
This model has good accuracy for predicting dc response and run time of battery. Run time model shown in fig.
Fig. 7:Run Time Based Model
I. Over-Current Battery Model
The over current battery model is given by:
Fig. 8: Circuit of Over-current Battery Model
is the battery current having variable current source, it is explain by the Peukert relationship and given as:
(7)
is the battery voltage having variable voltage source, it is explain by Nernstian relationship and given as:
(8)
R represents the internal resistance of battery consists of , and . resistance is grid resistance and it is constant, is electrolyte resistance and equal to , is of plate surface sulfation resistance and equal to . is the capacitance[8].
J. Battery Model From Manufacture Data
In this model, combining the algebraic equations with manufacturers data to obtaining the following parameters[9]:
‘ discharge current function of battery
‘ SOC function of discharge voltage
‘ SOC function in terms of battery internal resistance
‘ adjusting model parameters for Variable multipliers for increasing discharge current
Battery current and discharge current relationship given by Peukerts equation:
(9)
Where, is battery current in amp, C is battery capacity, p and K is Peukerts parameters.
Peukerts parameters are determined from capacity vs. discharge current curve given by the manufactures[10]. Soc in terms of discharge voltage is determined from terminal voltage and discharge curve. Manufacture data sheet also gives the information of battery internal resistance in terms of SOC.
K. Accurately Estimating Soc And Soh Calculations For Adaptive Modeling
SOH defines the state of health of battery which estimated the degradation of battery parameters due aging and comparing with standard value[11]. These entire models give the little importance to SOC and SOH. Comparing these parameters using Kalman filter technique.
The equation of this model given by using state-space representation technique:
(10)
(11)
And
(12)
. Fig. 9: SOC and SOH Evaluating Adaptive Battery Model Circuit
Fig.9 transform into fig using star delta transformation. The equations are given as:
(13)
(14)
(15)
Fig. 10: Adaptive Battery Model of Delta Transformed Circuit
L. Predicting Battery Run-Time and I-V Characteristics
This model is consisting two parts one is battery lifetime in which , and and other part is V-I characteristics in which and gives the transient response, and [L].
Fig.11: Battery Model Predicting Both Run-time and characteristic
This modified model is used for predicting battery Run-time and I-V characteristic but this model is not suitable for transient response occurred due to short duration load. This model is used in Li-ion, NiMH, and lead-acid batteries for predicting SOC, terminal voltage, and power losses. Accurate determination of battery in this model, discharge capacity is a function of the discharge rate i(t) , temperature and cycle number it also include rate factor . SOC and is given by equation as:
(16)
(17)
(18)
The modified Battery Model for Predicting both Run-time and I-V characteristic is given as below:
Fig. 12: Modified Battery Model for Predicting both Run-time and I-V characteristic
Conclusions
This paper summarized the literature about the types of battery models. Among these models, the adaptive model is more suitable for EVs, and this battery model can be employed in battery monitoring algorithms for the online estimation of state of charge, predicted time to run, etc for many applications.