Equivalent-circuit model of a lead-acid battery

Important: The Lead Acid battery model has been deprecated.

Description

The EquivCircuit.LeadAcid component is an equivalent-circuit model of a lead-acid battery; see the following figure.

${R}_{0}=\mathrm{expoly}\left({R}_{\mathrm{out}},\mathrm{soc}\right)$

${R}_{1}=\mathrm{expoly}\left({R}_{\mathrm{tc1}},\mathrm{soc}\right)$

${R}_{2}=\mathrm{expoly}\left({R}_{\mathrm{tc2}},\mathrm{soc}\right)$

${R}_{1}{C}_{1}=\mathrm{expoly}\left({T}_{\mathrm{tc1}},\mathrm{soc}\right)$

${R}_{2}{C}_{2}=\mathrm{expoly}\left({T}_{\mathrm{tc2}},\mathrm{soc}\right)$

 Capacity The capacity of a cell can either be a fixed value, $\mathrm{CA}$, or be controlled via an input signal, ${C}_{\mathrm{in}}$, if the use capacity input box is checked.
 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 ${\mathrm{SOC}}_{\mathrm{min}}$ 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 ${\mathrm{SOC}}_{0}$ assigns the initial state-of charge of the battery.

Connections

 Name Type Description Modelica ID $p$ Electrical Positive pin p $n$ Electrical Negative pin n $\mathrm{soc}$ Real output State of charge [0..1] soc ${C}_{\mathrm{in}}$ Real input Sets capacity of cell, in ampere hours; available when use capacity input is true Cin ${R}_{\mathrm{in}}$ Real input Sets resistance of cell, in ohms; available when use cell resistance input is true Rin

Variables

 Name Units Description Modelica ID ${T}_{\mathrm{cell}}$ $K$ Internal temperature of battery Tcell $i$ $A$ Current into battery i $v$ $V$ Voltage across battery v

Basic Parameters

 Name Default Units Description Modelica ID ${N}_{\mathrm{cell}}$ $1$ Number of cells, connected in series Ncell $\mathrm{CA}$ $1$ $\mathrm{A·h}$ Capacity of cell; available when use capacity input is false C ${\mathrm{SOC}}_{0}$ $1$ Initial state-of-charge [0..1] SOC0 ${\mathrm{SOC}}_{\mathrm{min}}$ $0.02$ Minimum allowable state-of-charge SOCmin ${R}_{\mathrm{cell}}$ $0.005$ $\mathrm{\Omega }$ Fixed cell resistance, if use cell resistance input is false Rcell allow overcharge false True allows simulation to continue with $1<\mathrm{SoC}$ allow_overcharge allow overdischarge false True allows simulation to continue with $\mathrm{SoC}<{\mathrm{SoC}}_{\mathrm{min}}$ allow_overdischarge use capacity input false True allows enables the ${C}_{\mathrm{in}}$ input port useCapacityInput use cell resistance input false True allows enables the ${R}_{\mathrm{in}}$ input port useResistInput

Circuit Parameters

 Name Default Units Description Modelica ID ${R}_{\mathrm{out}}$ $\mathrm{\Omega }$ expoly array for series resistance Rseries ${R}_{\mathrm{tc1}}$ $\mathrm{\Omega }$ expoly array for short time-constant resistance Rtc1 ${T}_{\mathrm{tc1}}$ $s$ expoly array for short time-constant duration Ttc1 ${R}_{\mathrm{tc2}}$ $\mathrm{\Omega }$ expoly array for short time-constant resistance Rtc2 ${T}_{\mathrm{tc2}}$ $s$ expoly array for short time-constant duration Ttc2

An exponential-polynomial (expoly) is a polynomial with an exponential term included. Its coefficients are given by a one-dimensional array, $k$, such that $ⅇxpoly\left(k,\mathrm{soc}\right)={k}_{1}ⅇxp\left({k}_{2}\mathrm{soc}\right)+{k}_{3}+{k}_{4}\mathrm{soc}+{k}_{5}{\mathrm{soc}}^{2}+\cdots$.

References

 [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.