Core

LiionBatteryModels core, allows access to the following submodules:

• SenthilModel
• AshwiniModel

Implementation of reduced order model for a lithium ion cell with uniform reaction rate approximation.

For model details refer here.

Volume averaged solid concentration

Fields

• c₁ₙ: Solid phase concentration in active material spheres in negative electrode.
• c₁ₚ: Solid phase concentration in active material spheres in positive electrode.

Interfacial electrolyte concentration

Fields

• c₂ᵢₙ: Interfacial electrolyte concentration in negative electrode.
• c₂ᵢₚ: Interfacial electrolyte concentration in positive electrode.

Interfacial flux

Fields

• q₂ᵢₙ: Interfacial flux in negative electrode.
• q₂ᵢₚ: Interfacial flux in positive electrode.

Radially averaged solid concentration

Fields

• c₁ₙᵣ: Solid phase concentration in active material spheres in negative electrode.
• c₁ₚᵣ: Solid phase concentration in active material spheres in positive electrode.

State of Charge in negative electrode

State of Charge in positive electrode

Open circuit potential in negative electrode

Open circuit potential in positive electrode

Cell voltage across the battery

Overall electrolyte concentration function

Average electrolyte concentration in negative electrode

Average electrolyte concentration in positive electrode

Average electrolyte concentration in separator

Electrloyte concentration in negative electrode

Electrloyte concentration in positive electrode

Electrloyte concentration in separator

Surface solid phase concentration in negative electrode

Surface solid phase concentration in positive electrode

Local surface reaction rate in negative electrode

Over-potential in negative electrode

Local surface reaction rate in positive electrode

Over-potential in positive electrode

Electrloyte conductivity

Electrloyte conductivity in negative electrode

Electrloyte conductivity in positive electrode

Electrloyte conductivity in separator

Simultaneous ODE solver based on the Runge-Kutta 4ᵗʰ order method.

Overall solid potential function

Solid potential in negative electrode

Solid potential in positive electrode

Overall electrolyte potential function

Interfacial potential at negative electrode

Interfacial potential at positive electrode

Electrloyte potential in negative electrode

Electrloyte potential in positive electrode

Electrloyte potential in separator

Solid diffusivity in negative electrode

Solid diffusivity in positive electrode

Electrolyte diffusivity of material

Effective electrolyte diffusivity in the negative electrode

Effective electrolyte diffusivity in the positive electrode

Effective electrolyte diffusivity in the separator

Faraday's constant

Total cell thickness

Universal gas constant

System Temperature (in K)

Specific surface area of active material in negative electrode

Specific surface area of active material in positive electrode

Bruggeman factor

Initial solid phase concentrations in negative electrode

Maximum solid phase concentrations in negative electrode

Initial solid phase concentrations in positive electrode

Maximum solid phase concentrations in positive electrode

Initial electrolyte concentration

Surface reaction rate constants in negative electrode

Surface reaction rate constants in positive electrode

Thickness of negative electrode

Thickness of positive electrode

Thickness of negative separator

Radii of active material spheres in negative electrode

Radii of active material sphere in positive electrode

Electrloyte transference number

Parameter constant at separator interface of the negative electrode

Parameter constant at separator interface of the positive electrode

Active material fraction in negative electrode

Active material fraction in positive electrode

Active material fraction in separator

Electrloyte volume fraction in negative electrode

Electrloyte volume fraction in positive electrode

Electrloyte volume fraction in separator

Implementation of a closed form reduced order electrochemical model for Lithium-Ion Cells.

For model details refer here.

State of Charge in negative electrode

State of Charge in positive electrode

Open circuit potential in negative electrode

Open circuit potential in positive electrode

Cell voltage across the battery

Average solid phase concentration in positive electode

Gradient of average solid phase concentration in positive electode

Overall electrolyte concentration function

Average electrolyte concentration in negative electrode

Average electrolyte concentration in positive electrode

Average electrolyte concentration in separator

Interfacial electrolyte concentration in negative electrode

Interfacial electrolyte concentration in positive electrode

Electrolyte concentration in the middle of battery

Electrloyte concentration in negative electrode [68]

• Parameters:
  • x: position in -ve electrode.
  • n0: params[1]
  • n2: params[2]
  • n3: params[3]

Electrolyte concentration @ x=0 in negative electrode

Electrloyte concentration in positive electrode [69]

• Parameters:
  • x: position in +ve electrode.
  • p0: params[1]
  • p2: params[2]
  • p3: params[3]

Electrolyte concentration @ x = L in positive electrode.

Electrloyte concentration in separator [70]

• Parameters:
  • x: position in the separator.
  • s0: params[1]
  • s1: params[2]
  • s2: params[3]

Surface solid phase concentration in negative electrode

Electrolyte diffusivity of material

Electrolyte diffusivity in negative electrode

Electrolyte diffusivity in positive electrode

Electrolyte diffusivity in separator

Average surface reaction rate in negative electrode

Average surface reaction rate in positive electrode

Local surface reaction rate in negative electrode

Over-potential in negative electrode

Local surface reaction rate in positive electrode

Over-potential in positive electrode

Electrloyte conductivity [Ref45 - 25]

Effective Electrloyte conductivity in negative electrode

Electrloyte conductivity in positive electrode

Electrloyte conductivity in separator

param_solver

The key function to get all the parameters required to solve for c₂ at a given timestep in the timeseries.

Returns the 16 parameters: n₀(t), n₁(t), n₂(t), n₃(t), p₀(t), p₁(t), p₂(t), p₃(t), s₀(t), s₁(t), s₂(t), <c₂>ₙ, <c₂>ₚ , <c₂>ₛ, c₂|ₓ₌₀ and c₂|ₓ₌ₗ in this order

Params:

- I: The current at the timestep.
- Δt: The span of the timestep.
- c₂ₙₚ: The previous average concentration in negative electrode
- c₂ₛₚ: The The previous average concentration in separator
- c₂ₚₚ: The previous average concentration in positive electrode
- c₂ₙ₀ₚ: The previous concentration in negative electrode @ x=0
- c₂ₚₗₚ: The previous average concentration in positive electrode @x=L
- jn_0: The reaction rate @x=0
- jp_l: The reaction rate @x=L

Overall solid potential function

Solid potential in negative electrode

Solid potential in positive electrode

Overall electrolyte potential function

Interfacial potential at negative electrode

Interfacial potential at positive electrode

Electrolyte potential in negative electrode

Electrolyte potential in positive electrode

Electrolyte potential in separator

Solid diffusivity in negative electrode

Solid diffusivity in positive electrode

Faraday's constant

Total cell thickness

Universal gas constant

System Temperature (in K)

Specific surface area of active material in negative electrode

Specific surface area of active material in positive electrode

Bruggeman factor in negative electrode

Bruggeman factor in positive electrode

Bruggeman factor in separator

Initial solid phase concentrations in negative electrode

Maximum solid phase concentrations in negative electrode

Initial solid phase concentrations in positive electrode

Maximum solid phase concentrations in positive electrode

Initial electrolyte concentration

Electronic conductivity in negative electode

Electronic conductivity in positive electode

Thickness of negative electrode

Thickness of positive electrode

Thickness of separator

Radii of active material spheres in negative electrode

Radii of active material spheres in positive electrode

Transferennce number of Li ion species dissolved in liquid

Cathodic transfer coefficient

Anodic transfer coefficient

Effective electronic conductivity in negative electode

Effective electronic conductivity in positive electode

Active material fraction in negative electrode

Active material fraction in positive electrode

Volume fraction in negative electrode

Volume fraction in positive electrode

Volume fraction in separator