TTCexpoly
Two time-constant expoly-based equivalent-circuit model of a battery
Description
Connections
Variables
Basic Parameters
Basic Thermal Parameters
General Parameters
References
The EquivCircuit.TTCexpoly component is an equivalent-circuit model of a generic battery. The open-circuit voltage depends on the state-of-charge (SoC) based on a polynomial with an exponential term. The transient response is modeled by a pair of SoC-dependent resistor-capacitor networks; see the following figure.
Voc=expolyVoc,soc
R0=expolyRout,soc
R1=expolyRtc1,soc
R2=expolyRtc2,soc
R1C1=expolyTtc1,soc
R2C2=expolyTtc2,soc
Degradation
The gradual decay, with use, of a cell's capacity and increase of its resistance is modeled by enabling the include degradation effects boolean parameter. Enabling this feature adds a state-of-health (soh) output to the model. This signal is 1 when the cell has no decay and 0 when is completely decayed.
The soh output is given by
soh=1−sRs3
where
s is thickness of the solid-electrolyte interface (SEI),
Rs is radius of the particles of active material in the SEI.
The decay of the capacity is
C=Cmaxsoh
C is the effective capacity, and
Cmax is the specified capacity equal to either the parameter CA or the input Cin.
The additional series resistance added to a cell is
Rsei=sκ
with κ a parameter of the model.
The following equations govern the increase in the thickness of the SEI layer (s).
k=Aeexp−EaRT
dsdt={kcM1+ksDdiffρseicharging0otherwise
Thermal Effects
Select the thermal model of the battery from the heat model drop-down list. The available models are: isothermal, external port, and convection.
Isothermal
The isothermal model sets the cell temperature to a constant parameter, Tiso.
External Port
The external port model adds a thermal port to the battery model. The temperature of the heat port is the cell temperature. The parameters mcell and cp become available and are used in the heat equation
mcellcpdTcelldt=Pcell−Qcell
Qflow=ncellQcell
Pcell=icellvcell−voc
where Pcell is the heat generated in each cell, including chemical reactions and ohmic resistive losses, Qcell is the heat flow out of each cell, and Qflow is the heat flow out of the external port.
Convection
The convection model assumes the heat dissipation from each cell is due to uniform convection from the surface to an ambient temperature. The parameters mcell, cp, Acell, h, and Tamb become available, as does an output signal port that gives the cell temperature in Kelvin. The heat equation is the same as the heat equation for the external port, with Qcell given by
Qcell=hAcellTcell−Tamb
Capacity
The capacity of a cell can either be a fixed value, CA, or be controlled via an input signal, Cin, if the use capacity input box is checked.
Resistance
The resistance of a cell can either be a fixed value, Rcell, or be controlled via an input signal, Rin, if the use resistance input box is checked. This resistance is in addition to the resistance of the equivalent circuit.
State of Charge
A signal output, soc, gives the state-of-charge of the battery, with 0 being fully discharged and 1 being fully charged.
The parameter SOCmin sets the minimum allowable state-of-charge; if the battery is discharged past this level, the simulation is either terminated and an error message is raised, or, if the allow overdischarge parameter is true, a warning is generated. A similar effect occurs if the battery is fully charged so that the state of charge reaches one; the simulation is terminated unless allow overcharge is true.
The parameter SOC0 assigns the initial state-of charge of the battery.
Name
Type
Modelica ID
p
Electrical
Positive pin
n
Negative pin
soc
Real output
State of charge [0..1]
Cin
Real input
Sets capacity of cell, in ampere hours; available when use capacity input is true
Rin
Sets resistance of cell, in ohms; available when use cell resistance input is true
Units
Tcell
K
Internal temperature of battery
i
A
Current into battery
v
V
Voltage across battery
Default
Ncell
1
Number of cells, connected in series
CA
A·h
Capacity of cell; available when use capacity input is false
C
SOC0
Initial state-of-charge [0..1]
SOCmin
0.02
Minimum allowable state-of-charge
Rcell
0.005
Ω
Fixed cell resistance, if use cell resistance input is false
allow overcharge
false
True allows simulation to continue with 1<SoC
allow_overcharge
allow overdischarge
True allows simulation to continue with SoC<SoCmin
allow_overdischarge
use capacity input
True allows enables the Cin input port
useCapacityInput
use cell resistance input
True allows enables the Rin input port
useResistInput
Tiso
298.15
Constant cell temperature; used with isothermal heat model
cp
750
JkgK
Specific heat capacity of cell
mcell
0.014
kg
Mass of one cell
h
100
Wm2K
Surface coefficient of heat transfer; used with convection heat model
Acell
0.0014
m2
Surface area of one cell; used with convection heat model
Tamb
Ambient temperature; used with convection heat model
Voc
expoly array for open-circuit voltage
Rout
expoly array for series resistance
Rtc1
expoly array for short time-constant resistance
Ttc1
s
expoly array for short time-constant duration
Rtc2
expoly array for long time-constant resistance
Ttc2
expoly array for long time-constant duration
An exponential-polynomial (expoly) is a polynomial with an exponential term included. Its coefficients are given by a one-dimensional array, k, such that ⅇxpolyk,soc=k1ⅇxpk2soc+k3+k4soc+k5soc2+⋯.
[1] Chen, M. and Rincón-Mora, G.A., Accurate electrical battery model capable of predicting runtime and I-V performance, IEEE Transactions of Energy Conversion, Vol. 21, No. 2, 2006.
See Also
Battery Library Overview
Equivalent Circuit Overview
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