MaplesoftBattery

EquivCircuit.OTCtable $—$ One time-constant table-based equivalent-circuit model of a battery

Description

The EquivCircuit.OTCtable component is an equivalent-circuit model of a generic battery. The open-circuit voltage depends on the state-of-charge (SoC) and, optionally, the temperature of the cell, based on an interpolation table. The transient response is modeled by an SoC-dependent resistor-capacitor network.

 Open Circuit Cell Voltage The open-circuit cell voltage (${V}_{\mathrm{oc}}$) is dependent on the state-of-charge and, optionally, the cell temperature. If the Use temperature boolean parameter is false, then ${V}_{\mathrm{oc}}$ depends only on the state-of-charge, using interpolation of the 1D Table parameter; otherwise ${V}_{\mathrm{oc}}$ depends on SoC and the cell temperature, using interpolation of the the 2D Table parameter. The Data Source parameter selects whether the interpolation table is defined inline, as an attachment, or as an external file. The first column of the 1D Table is the state-of-charge (SoC), which varies from 0 (fully discharged) to 1 (fully charged). A selected column of the table contains the open-circuit voltage data corresponding to the SoC in column 1. If Data Source is inline, the selected column is the second column, otherwise it is the value of the Column parameter. The Skip rows parameter specifies the number of rows, starting with the first, to skip to get to the actual data. The first column of the 2D Table is the SoC. The first row of the 2D Table is the temperature in degrees Celsius. The bulk of the content of the table specifies ${V}_{\mathrm{oc}}$ at the corresponding SoC and temperature.

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, ${T}_{\mathrm{iso}}$.
 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 ${m}_{\mathrm{cell}}$ and ${c}_{p}$ become available and are used in the heat equation ${m}_{\mathrm{cell}}{c}_{p}\frac{\mathrm{d}{T}_{\mathrm{cell}}}{\mathrm{d}t}={P}_{\mathrm{cell}}-{Q}_{\mathrm{cell}}$ ${Q}_{\mathrm{flow}}={n}_{\mathrm{cell}}{Q}_{\mathrm{cell}}$ ${P}_{\mathrm{cell}}={i}_{\mathrm{cell}}\left({v}_{\mathrm{cell}}-{v}_{\mathrm{oc}}\right)$ where ${P}_{\mathrm{cell}}$ is the heat generated in each cell, including chemical reactions and ohmic resistive losses, ${Q}_{\mathrm{cell}}$ is the heat flow out of each cell, and ${Q}_{\mathrm{flow}}$ 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 ${m}_{\mathrm{cell}}$, ${c}_{p}$, ${A}_{\mathrm{cell}}$, $h$, and ${T}_{\mathrm{amb}}$ 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 ${Q}_{\mathrm{cell}}$ given by ${Q}_{\mathrm{cell}}=h{A}_{\mathrm{cell}}\left({T}_{\mathrm{cell}}-{T}_{\mathrm{amb}}\right)$
 Capacity The capacity of the battery 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

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 ${N}_{\mathrm{cell}}$ $1$ Number of cells, connected in series Ncell ${R}_{\mathrm{cell}}$ $0.005$ $\mathrm{\Omega }$ 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

Basic Thermal Parameters

 Name Default Units Description Modelica ID ${T}_{\mathrm{iso}}$ $298.15$ $K$ Constant cell temperature; used with isothermal heat model Tiso ${c}_{p}$ $750$ $\frac{J}{\mathrm{kg}K}$ Specific heat capacity of cell cp ${m}_{\mathrm{cell}}$ $0.014$ $\mathrm{kg}$ Mass of one cell mcell $h$ $100$ $\frac{W}{{m}^{2}K}$ Surface coefficient of heat transfer; used with convection heat model h ${A}_{\mathrm{cell}}$ $0.0014$ ${m}^{2}$ Surface area of one cell; used with convection heat model Acell ${T}_{\mathrm{amb}}$ $298.15$ $K$ Ambient temperature; used with convection heat model Tamb

Voc Parameters

 Name Units Description Modelica ID Use temperature True means use the 2D table VocUseTemp Data Source Selects whether the table is inline, an attachment, or a file VocDataSource Data Name of file or attachment VocData Table 1D Inline 1D interpolation table VocTable1D Table 2D Inline 2D interpolation table VocTable2D Column Specifies data column; used with 1D attachment/file VocColumn Skip rows Specifies rows to skip; used with 1D attachment/file VocSkipRows

General Parameters

 Name Default Units Description Modelica ID ${R}_{\mathrm{out}}$ $\mathrm{\Omega }$ 1D interpolation table for series resistance Rout ${R}_{\mathrm{tc}}$ $\mathrm{\Omega }$ 1D interpolation table for time-constant resistance Rtc ${T}_{\mathrm{tc}}$ $s$ 1D interpolation table for time-constant duration Ttc

A 1D interpolation table is a two-column Matrix. The first column is the state-of-charge, sorted, with low value (0) first. The second column is the corresponding parameter value at that state-of-charge.

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.