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Electrochemical Nickel-Metal Hydride

Electrochemical model of a nickel-metal hydride battery

 

Description

Variables

Connections

Basic Parameters

Basic Thermal Parameters

Extended Parameters

References

Description

The Nickel-Metal Hydride component is a model of a nickel-metal hydride battery based on a planar electrode approximation. The mass-balance of active materials, the kinetics of electrochemical reactions, internal resistance, and the energy balance of the cell are incorporated. See [1].

There are two main redox reactions at the positive and negative electrodes: the reaction of the nickel active material at the positive electrode and the reaction of the metal hydride material at the negative electrode.  Besides that, Ni-MH cells are also known to have side reactions which cause gases to form inside the cell casing. The most significant side reactions are the oxygen evolution reaction at the positive electrode and the oxygen reduction reaction at the negative electrode. The main and side chemical reactions are described by the following equations:

Positive nickel electrode:

Negative metal hydride electrode:

Governing Equations

Butler-Volmer's equation describes the kinetics of reactions for both positive and negative electrodes:

where

  

 are the electrical potentials in the positive and negative electrodes,

  

 is the equilibrium potential of reaction  at the standard conditions,

  

 is the exchange current density of reaction ,

  

 is limiting current density of the oxygen reduction reaction, and

  

 are the pressure and reference pressure of oxygen in the cell.

The exchange current densities vary with the nickel hydroxide concentration ( + ) in the nickel active material, and the hydrogen concentration in metal hydride material ( ) and are described by the following equations.

The open-circuit potential curves based on the Nernst equation are utilized:

The charge and mass balances on the electrodes are given by

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, .

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  and  become available and are used in the heat equation

where  is the heat generated in each cell, including chemical reactions and ohmic resistive losses,  is the heat flow out of each cell, and  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 , , , , and  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  given by

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  sets the minimum allowable state-of-charge; if the battery is discharged past this level, the simulation is terminated and an error message is raised. This prevents the battery model from reaching non-physical conditions. A similar effect occurs if the battery is fully charged so that the state of charge reaches one.

The parameter  assigns the initial state-of charge of the battery.

Capacity

The capacity of a cell can either be a fixed value, , or be controlled via an input signal, , if the use capacity input box is checked.

Resistance

The resistance of each cell can either be a fixed value, , or be controlled via an input signal, , if the use cell resistance input box is checked.

Variables

Name

Units

Description

Modelica ID

Internal temperature of battery

Tcell

Current into battery

i

Voltage across battery

v

Connections

Name

Type

Description

Modelica ID

Electrical

Positive pin

p

Electrical

Negative pin

n

Real output

State of charge [0..1]

SOC

Real input

Sets capacity of cell, in ampere hours; available when use capacity input is true

Cin

Real input

Sets resistance of cell, in Ohms; available when use resistance input is true

Rin

Real output

Temperature of cell, in Kelvin; available with convection heat model

Tout

Thermal

Thermal connection; available with external port heat model

heatPort

Basic Parameters

Name

Default

Units

Description

Modelica ID

 

Number of cells, connected in series

ncell

Capacity of cell, in ampere-hours

C

 

Initial state-of-charge [0..1]

SOC0

 

Minimum allowable state-of-charge

SOCmin

Internal resistance of one cell; available if use cell resistance input is not enabled

Rcell

Basic Thermal Parameters

Name

Default

Units

Description

Modelica ID

Constant cell temperature; used with isothermal heat model

Tiso

Specific heat capacity of cell

cp

Mass of one cell

mcell

Surface coefficient of heat transfer; used with convection heat model

h

Surface area of one cell; used with convection heat model

Acell

Ambient temperature; used with convection heat model

Tamb

Extended Parameters

Name

Default

Units

Description

Modelica ID

Activation energy of reaction 1

Ea1

Activation energy of reaction 2

Ea2

Activation energy of reaction 3

Ea3

Activation energy of reaction 4

Ea4

Loading of nickel active material

LMH

Loading of metal hydroxide material

LNiOH2

Apparent open-circuit potential of the redox reaction of nickel active material at standard conditions during the whole range charge process

U1c

Apparent open-circuit potential of the redox reaction of nickel active material at standard conditions during the whole range discharge process

U1d

Equilibrium potential of reaction 2 at standard condition

U2

Equilibrium potential of reaction 3 at standard condition

U3

Equilibrium potential of reaction 4 at standard condition

U4

Specific surface area of negative electrode

aneg

Specific surface area of positive electrode

apos

Maximum concentration of nickel hydroxide in nickel active material

cHmax

Reference concentration of nickel hydroxide in nickel active material

cHref

Maximum concentration of hydrogen in metal hydride material

cMHmax

Reference concentration of hydrogen in metal hydride material

cMHref

Concentration of KOH electrolyte

ce

Reference concentration of KOH electrolyte

ceref

Temperature coefficient of reaction 1, from Wang (2000) Thermal-Electrochemical Modeling of Battery Systems

dU1dT

Temperature coefficient of reaction 2, from Wang (2000) Thermal-Electrochemical Modeling of Battery Systems

dU2dT

Temperature coefficient of reaction 3, from Wang (2000) Thermal-Electrochemical Modeling of Battery Systems

dU3dT

Temperature coefficient of reaction 4, from Wang (2000) Thermal-Electrochemical Modeling of Battery Systems

dU4dT

Exchange current density of reaction 1 at reference reactant concentrations

i01ref

Exchange current density of reaction 2 at reference reactant concentrations

i02ref

Exchange current density of reaction 3 at reference reactant concentrations

i03ref

Exchange current density of reaction 4 at reference reactant concentrations

i04ref

Thickness of negative electrode

lneg

Thickness of positive electrode

lpos

Reference oxygen pressure in cell

pO2ref

Density of metal hydride

rhoMH

Density of nickel active material

rhoNiOH2

Gas volume in cell

Vgas

Volume of cell

VolCell

References

  

[1] Wu, B., Mohammed, M., Brigham, D., Elder, R., and White, R.E., A non-isothermal model of a nickel-metal hydride cell, Journal of Power Sources, 101 (2001) pp. 149-157.

  

[2] Dao, T.S. and McPhee, J., Dynamic modeling of electrochemical systems using linear graph theory, Journal of Power Sources, No. 196, pp.10442-10454, 2011.

See Also

Battery Library Overview

 


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