Running parameter sweep

In this tutorial we will compare the effect that parameter values have on cell performance.

Lets start with loading some pre-defined cell parameters and cycling protocols.

julia

using BattMo, GLMakie

cell_parameters = load_cell_parameters(; from_default_set = "Chen2020")
cycling_protocol = load_cycling_protocol(; from_default_set = "CCDischarge")

model_setup = LithiumIonBattery()

LithiumIonBattery("Setup object for a P2D lithium-ion model", {
    "RampUp" => "Sinusoidal"
    "Metadata" =>     {
        "Description" => "Default model settings for a P2D simulation including a current ramp up, excluding current collectors and SEI effects."
        "Title" => "P2D"
    }
    "TransportInSolid" => "FullDiffusion"
    "ModelFramework" => "P2D"
}, true)

Sweeping through reaction rates

First lets see the effect that the reaction rate of the negative electrode has on cell performance. To do this, we simply loop through a list of parameter values, carry a simulation for each value, store the outputs, and compare the voltage curves for every output. We use the logarithm of the reaction rates to change their values by orders of magnitude.

julia

log_rate_start = -3.0
log_rate_stop = -13.0

outputs_rate = []
for r in range(log_rate_start, log_rate_stop, length = 10)
	cell_parameters["NegativeElectrode"]["ActiveMaterial"]["ReactionRateConstant"] = 10^r
	sim = Simulation(model_setup, cell_parameters, cycling_protocol)
	result = solve(sim; config_kwargs = (; end_report = false))
	push!(outputs_rate, (r = r, output = result))  # store r together with output
end

✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps
✔️ Validation of CellParameters passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of CyclingProtocol passed: No issues found.
──────────────────────────────────────────────────
✔️ Validation of SimulationSettings passed: No issues found.
──────────────────────────────────────────────────
Jutul: Simulating 2 hours, 12 minutes as 163 report steps

Now, plot the discharge curves for each reaction rate:

julia

using Printf
fig = Figure()
ax = Axis(fig[1, 1], ylabel = "Voltage / V", xlabel = "Time / s", title = "Discharge curve")

for data in outputs_rate
	local t = [state[:Control][:Controller].time for state in data.output[:states]]
	local E = [state[:Control][:Phi][1] for state in data.output[:states]]
	lines!(ax, t, E, label = @sprintf("%.1e", 10^data.r))
end

fig[1, 2] = Legend(fig, ax, "Reaction rate", framevisible = false)

Sweeping reaction rates result in interesting behavior of the cells voltage and capacity. High reaction rates have negligible influence on the cell voltage curve. However, values below 1e-10 result in a noticeable difference on the curves and the cell's capacity. This observations might be attributed to the interplay between Li+ diffusion and reaction processes. For high reaction rates, the limiting Li+ transport step might be diffusing Li+ from/to the electrodes. However, below a threshold value, the reaction kinetics becomes the bottleneck step in Li+ transport, thus contributing significantly to the cell's overpotential.

Sweeping through diffusion coefficients

Lets now see the effect that the diffusion coefficient of the positive electrode has on cell performance. We first set the reaction rate to the original value in the parameter set, and then follow the same procedure as above.

julia

cell_parameters["NegativeElectrode"]["ActiveMaterial"]["ReactionRateConstant"] = 1.0e-13

log_D_start = -10.0
log_D_stop = -15.0

outputs_diff = []

for d in range(log_D_start, log_D_stop, length = 10)
	cell_parameters["PositiveElectrode"]["ActiveMaterial"]["DiffusionCoefficient"] = 10^d
	sim = Simulation(model_setup, cell_parameters, cycling_protocol)
	result = solve(sim; config_kwargs = (; end_report = false))
	push!(outputs_diff, (d = d, output = result))  # store r together with output
end

fig1 = Figure()
ax1 = Axis(fig1[1, 1], ylabel = "Voltage / V", xlabel = "Time / s", title = "Discharge curve")

for data in outputs_diff
	if length(data.output[:states]) > 0 #if simulation is successful
		local t = [state[:Control][:Controller].time for state in data.output[:states]]
		local E = [state[:Control][:Phi][1] for state in data.output[:states]]
		lines!(ax1, t, E, label = @sprintf("%.1e", 10^data.d))
	end
end

fig1[1, 2] = Legend(fig1, ax1, "Diffusion Coefficient", framevisible = false)

Diffusion coefficients, just as reaction rates, have also a non-linear effect on the cells voltage and capacity. Diffusion coefficients down to 5e-14 have negligible influence on the cell voltage curve. However, as the coefficients fall below 5e-14 they start to influence the curves and the cell's capacity in a noticeable way. The effect becomes more pronounced at lower values. As with reaction rates, these observations might originate from the interplay between Li+ diffusion and reaction processes, where the cell's overpotential responds to the transport limiting step.

Example on GitHub

If you would like to run this example yourself, it can be downloaded from the BattMo.jl GitHub repository as a script.

This page was generated using Literate.jl.

Running parameter sweep ​

Sweeping through reaction rates ​

Sweeping through diffusion coefficients ​

Example on GitHub ​

Running parameter sweep

Sweeping through reaction rates

Sweeping through diffusion coefficients

Example on GitHub