Yang2017 Model

pybamm/CITATIONS.txt

@@ -347,3 +347,17 @@ doi={10.1149/2.0661810jes}
   publisher = {Elsevier Science (USA)},
   doi = {10.1006/jcph.2002.7041},
 }
+
+
+@article{Yang2017,
+  author = {Yang, Xiao-Guang and Leng, Yungjun and Zhang, Guangsheng
+            and Ge, Shanhai and Wang, Chao-Yang},
+  title = {Modeling of lithium plating induced aging of lithium-ion batteries: 
+  Transion from linear to nonlinear aging},
+  journal = {Power Sources},
+  volume = {360},
+  pages = {28--40},
+  year = {2017},
+  publisher = {Elsevier},
+  url = https://doi.org/10.1016/j.jpowsour.2017.05.110
+}

pybamm/expression_tree/symbol.py

@@ -610,8 +610,8 @@ def diff(self, variable):
             return pybamm.Scalar(0)
 
     def _diff(self, variable):
-        """Default behaviour for differentiation, overriden by Binary and Unary Operators
-        """
+        """Default behaviour for differentiation, overriden by Binary
+        and Unary Operators"""
         raise NotImplementedError
 
     def jac(self, variable, known_jacs=None, clear_domain=True):

pybamm/input/parameters/lithium-ion/cells/Yang2017/parameters.csv

@@ -0,0 +1,34 @@
+Name [units],Value,Reference,Notes,,
+# Empty rows and rows starting with ‘#’ will be ignored,,,,,
+,,,,,
+# Macroscale geometry,,,,,
+Negative current collector thickness [m],2.50E-05,Scott Moura FastDFN,no info from Peyman MPM,,`
+Negative electrode thickness [m],4.87E-05,Yang 2017,,,
+Separator thickness [m],2.50E-05,Yang 2017,,,
+Positive electrode thickness [m],4.75E-05,Yang 2017,,,
+Positive current collector thickness [m],2.50E-05,Scott Moura FastDFN,no info from Peyman MPM,,
+Electrode height [m],1,KOKAM SLPB78205130H,Not needed for 1D,,
+Electrode width [m],0.205,KOKAM SLPB78205130H,Not needed for 1D,,
+Cell cooling surface area [m2],0.41,,pouch,,
+Cell volume [m3],3.92E-05,,pouch,,
+,,,,,
+# Current collector properties ,,,,,
+Negative current collector conductivity [S.m-1],59600000,LIONSIMBA,carbon,,
+Positive current collector conductivity [S.m-1],35500000,LIONSIMBA,aluminium,,
+,,,,,
+# Density,,,,,
+Negative current collector density [kg.m-3],8954,,,,
+Positive current collector density [kg.m-3],2707,,,,
+,,,,,
+# Specific heat capacity,,,,,
+Negative current collector specific heat capacity [J.kg-1.K-1],385,,,,
+Positive current collector specific heat capacity [J.kg-1.K-1],897,,,,
+,,,,,
+# Thermal conductivity,,,,,
+Negative current collector thermal conductivity [W.m-1.K-1],401,,,,
+Positive current collector thermal conductivity [W.m-1.K-1],237,,,,
+,,,,,
+# Electrical,,,,,
+Nominal cell capacity [A.h],12.4,Yang2017,,,
+Typical current [A],12.4,,1C current,,
+Current function [A],12.4,default current function,,,

pybamm/input/parameters/lithium-ion/lithium_platings/yang2017_Li_plating/README.md

@@ -0,0 +1,11 @@
+# SEI parameters
+
+Some example parameters for SEI growth from the papers:
+
+> Ramadass, P., Haran, B., Gomadam, P. M., White, R., & Popov, B. N. (2004). Development of first principles capacity fade model for Li-ion cells. Journal of the Electrochemical Society, 151(2), A196-A203.
+> Ploehn, H. J., Ramadass, P., & White, R. E. (2004). Solvent diffusion model for aging of lithium-ion battery cells. Journal of The Electrochemical Society, 151(3), A456-A462.
+> Single, F., Latz, A., & Horstmann, B. (2018). Identifying the mechanism of continued growth of the solid–electrolyte interphase. ChemSusChem, 11(12), 1950-1955.
+> Safari, M., Morcrette, M., Teyssot, A., & Delacour, C. (2009). Multimodal Physics-Based Aging Model for Life Prediction of Li-Ion Batteries. Journal of The Electrochemical Society, 156(3), 
+> Yang, X., Leng, Y., Zhang, G., Ge, S., Wang, C. (2017). Modeling of lithium plating induced aging of lithium-ion batteries: Transition from linear to nonlinear aging. Journal of Power Sources, 360, 28-40.
+
+Note: this parameter set does not claim to be representative of the true parameter values. Instead these are parameter values that were used to fit SEI models to observed experimental data in the referenced papers.

pybamm/input/parameters/lithium-ion/lithium_platings/yang2017_Li_plating/parameters.csv

@@ -0,0 +1,8 @@
+Name [units],Value,Reference,Notes
+,,,
+,,,
+# Lithium plating parameters,,,
+Lithium metal partial molar volume [m3.mol-1],1.30E-05,Yang2017,
+Lithium plating kinetic rate constant [m.s-1],1.00E+00,,Not required for Yang2017
+Exchange-current density for plating [A.m-2],[function]plating_exchange_current_density_OKane2020,,
+Initial plated lithium concentration [mol.m-3],0.00E+00,,

pybamm/input/parameters/lithium-ion/lithium_platings/yang2017_Li_plating/plating_exchange_current_density_OKane2020.py

@@ -0,0 +1,26 @@
+from pybamm import Scalar
+
+
+def plating_exchange_current_density_OKane2020(c_e, c_Li, T):
+    """
+    Exchange-current density for Li plating reaction [A.m-2].
+    References
+    ----------
+    .. [1] O’Kane, Simon EJ, Ian D. Campbell, Mohamed WJ Marzook, Gregory J. Offer, and
+    Monica Marinescu. "Physical origin of the differential voltage minimum associated
+    with lithium plating in Li-ion batteries." Journal of The Electrochemical Society
+    167, no. 9 (2020): 090540.
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_Li : :class:`pybamm.Symbol`
+        Plated lithium concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+    return Scalar(0.001)

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/README.md

@@ -0,0 +1,12 @@
+# Graphite negative electrode parameters
+
+Parameters for a graphite negative electrode, from the papers:
+
+> Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of a lithium-ion battery I. determination of parameters." Journal of the Electrochemical Society 162.9 (2015): A1836-A1848.
+
+>Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of a lithium-ion battery II. Model validation." Journal of The Electrochemical Society 162.9 (2015): A1849-A1857.
+
+The fits to data for the electrode and electrolyte properties are those provided
+by Dr. Simon O’Kane in the paper:
+
+> Richardson, Giles, et. al. "Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation." Electrochemica Acta 339 (2020): 135862

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/graphite_diffusivity_Ecker2015.py

@@ -0,0 +1,37 @@
+from pybamm import exp, constants
+
+
+def graphite_diffusivity_Ecker2015(sto, T):
+    """
+    Graphite diffusivity as a function of stochiometry [1, 2, 3].
+
+    References
+    ----------
+     .. [1] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery i. determination of parameters." Journal of the
+    Electrochemical Society 162.9 (2015): A1836-A1848.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery ii. model validation." Journal of The Electrochemical
+    Society 162.9 (2015): A1849-A1857.
+    .. [3] Richardson, Giles, et. al. "Generalised single particle models for
+    high-rate operation of graded lithium-ion electrodes: Systematic derivation
+    and validation." Electrochemica Acta 339 (2020): 135862
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+
+    D_ref = 8.4e-13 * exp(-11.3 * sto) + 8.2e-15
+    E_D_s = 3.03e4
+    arrhenius = exp(-E_D_s / (constants.R * T)) * exp(E_D_s / (constants.R * 296))
+
+    return D_ref * arrhenius

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/graphite_electrolyte_exchange_current_density_Ecker2015.py

@@ -0,0 +1,48 @@
+from pybamm import exp, constants, Parameter
+
+
+def graphite_electrolyte_exchange_current_density_Ecker2015(c_e, c_s_surf, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in
+    EC:DMC.
+
+    References
+    ----------
+    .. [1] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery i. determination of parameters." Journal of the
+    Electrochemical Society 162.9 (2015): A1836-A1848.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery ii. model validation." Journal of The Electrochemical
+    Society 162.9 (2015): A1849-A1857.
+    .. [3] Richardson, Giles, et. al. "Generalised single particle models for
+    high-rate operation of graded lithium-ion electrodes: Systematic derivation
+    and validation." Electrochemica Acta 339 (2020): 135862
+
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_s_surf : :class:`pybamm.Symbol`
+        Particle concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+
+    k_ref = 1.995 * 1e-10
+
+    # multiply by Faraday's constant to get correct units
+    m_ref = constants.F * k_ref  # (A/m2)(mol/m3)**1.5 - includes ref concentrations
+    E_r = 53400
+
+    arrhenius = exp(-E_r / (constants.R * T)) * exp(E_r / (constants.R * 296.15))
+
+    c_n_max = Parameter("Maximum concentration in negative electrode [mol.m-3]")
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_n_max - c_s_surf) ** 0.5
+    )

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/graphite_ocp_Ecker2015.csv

@@ -0,0 +1,41 @@
+0.0015151515151514694, 1.4325153374233128
+0.0060606060606061, 0.8619631901840491
+0.010606060606060619, 0.7914110429447854
+0.016666666666666607, 0.6595092024539877
+0.021212121212121238, 0.5797546012269938
+0.022727272727272707, 0.5245398773006136
+0.030303030303030276, 0.4754601226993864
+0.039393939393939315, 0.4141104294478526
+0.045454545454545414, 0.3680981595092023
+0.05303030303030298, 0.3312883435582821
+0.06666666666666665, 0.28220858895705514
+0.07878787878787874, 0.24846625766871155
+0.08939393939393936, 0.2239263803680982
+0.10151515151515145, 0.22085889570552153
+0.12727272727272732, 0.21165644171779152
+0.14242424242424245, 0.2024539877300613
+0.15909090909090917, 0.19938650306748462
+0.17727272727272725, 0.19325153374233128
+0.19393939393939397, 0.18404907975460127
+0.21363636363636362, 0.1809815950920246
+0.23333333333333328, 0.17177914110429437
+0.25757575757575757, 0.16564417177914104
+0.2787878787878788, 0.16257668711656437
+0.303030303030303, 0.15337423312883436
+0.32878787878787885, 0.14110429447852746
+0.35151515151515156, 0.13496932515337412
+0.3712121212121211, 0.13190184049079745
+0.39242424242424234, 0.128834355828221
+0.5681818181818183, 0.1257668711656441
+0.5878787878787879, 0.12269938650306744
+0.6060606060606062, 0.1165644171779141
+0.6272727272727272, 0.10122699386503076
+0.6545454545454545, 0.0950920245398772
+0.6742424242424243, 0.0950920245398772
+0.6939393939393939, 0.08895705521472386
+0.7181818181818183, 0.08895705521472386
+0.7393939393939393, 0.08588957055214719
+0.8909090909090911, 0.08282208588957074
+0.956060606060606, 0.08272208588957074
+0.9772727272727273, 0.07975460122699385
+1, 0.07055214723926384

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/graphite_ocp_Ecker2015_function.py

@@ -0,0 +1,62 @@
+from pybamm import exp, tanh
+
+
+def graphite_ocp_Ecker2015_function(sto):
+    """
+    Graphite OCP as a function of stochiometry [1, 2, 3].
+
+    References
+    ----------
+     .. [1] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery i. determination of parameters." Journal of the
+    Electrochemical Society 162.9 (2015): A1836-A1848.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery ii. model validation." Journal of The Electrochemical
+    Society 162.9 (2015): A1849-A1857.
+    .. [3] Richardson, Giles, et. al. "Generalised single particle models for
+    high-rate operation of graded lithium-ion electrodes: Systematic derivation
+    and validation." Electrochemica Acta 339 (2020): 135862
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Open circuit potential
+    """
+
+    # Graphite negative electrode from Ecker, Kabitz, Laresgoiti et al.
+    # Analytical fit (WebPlotDigitizer + gnuplot)
+    a = 0.716502
+    b = 369.028
+    c = 0.12193
+    d = 35.6478
+    e = 0.0530947
+    g = 0.0169644
+    h = 27.1365
+    i = 0.312832
+    j = 0.0199313
+    k = 28.5697
+    m = 0.614221
+    n = 0.931153
+    o = 36.328
+    p = 1.10743
+    q = 0.140031
+    r = 0.0189193
+    s = 21.1967
+    t = 0.196176
+
+    u_eq = (
+        a * exp(-b * sto)
+        + c * exp(-d * (sto - e))
+        - r * tanh(s * (sto - t))
+        - g * tanh(h * (sto - i))
+        - j * tanh(k * (sto - m))
+        - n * exp(o * (sto - p))
+        + q
+    )
+
+    return u_eq

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/measured_graphite_diffusivity_Ecker2015.csv

@@ -0,0 +1,23 @@
+0.04291659469592768,2.5318983605709854e-13
+0.08025337997334403,4.438292394020732e-14
+0.12014956931041065,3.1947426343055446e-14
+0.15796120718295306,2.6077962994674755e-14
+0.19575227382393767,2.255908580891848e-14
+0.2357650334731653,1.16865022242173e-14
+0.27144412034088194,1.2386927328130891e-14
+0.3100288936661386,2.0291954487412547e-14
+0.3484165260222996,3.2604716406478646e-15
+0.3866704453733347,7.640156635519089e-16
+0.4264157790123111,8.417747371928056e-16
+0.4641862744217376,7.717093525037831e-16
+0.5018779134435263,8.837921553351043e-16
+0.5412118224513462,3.109171322297572e-15
+0.5766749113877059,6.062184667385398e-15
+0.6148036890800979,3.595937210129949e-14
+0.6545815938357071,2.0323093806678467e-15
+0.7681399348426814,7.802664217099549e-16
+0.8089429726375879,7.728942922045022e-16
+0.8823034129113143,9.65829674321414e-16
+0.9220864604748132,9.566999594213241e-16
+0.9607500901877076,1.2545776383613633e-15
+0.9976360226401492,1.395684713792463e-14

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/parameters.csv

@@ -0,0 +1,25 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrode properties,,,
+Negative electrode conductivity [S.m-1],14,,
+Maximum concentration in negative electrode [mol.m-3],31920,,
+Measured negative electrode diffusivity [m2.s-1],[data]measured_graphite_diffusivity_Ecker2015,,
+Negative electrode diffusivity [m2.s-1],[function]graphite_diffusivity_Ecker2015,,
+Measured negative electrode OCP [V],[data]graphite_ocp_Ecker2015,,
+Negative electrode OCP [V],[function]graphite_ocp_Ecker2015_function,,
+,,,
+# Microstructure,,,
+Negative electrode porosity,0.32,Yang2017,
+Negative electrode active material volume fraction,0.372403,,
+Negative particle radius [m],1.00E-05,Yang2017,
+Negative electrode Bruggeman coefficient (electrolyte),1.637278934,Solve for permeability factor B=0.162=eps^b,
+Negative electrode Bruggeman coefficient (electrode),0,No Bruggeman correction to the solid conductivity,
+,,,
+# Interfacial reactions,,,
+Negative electrode cation signed stoichiometry,-1,,
+Negative electrode electrons in reaction,1,,
+Negative electrode exchange-current density [A.m-2],[function]graphite_electrolyte_exchange_current_density_Ecker2015,,
+,,,
+# Thermal parameters,,,
+Negative electrode OCP entropic change [V.K-1],0,,

pybamm/input/parameters/lithium-ion/negative_electrodes/graphite_Yang2017/plating_exchange_current_density_OKane2020.py

@@ -0,0 +1,26 @@
+from pybamm import Scalar
+
+
+def plating_exchange_current_density_OKane2020(c_e, c_Li, T):
+    """
+    Exchange-current density for Li plating reaction [A.m-2].
+    References
+    ----------
+    .. [1] O’Kane, Simon EJ, Ian D. Campbell, Mohamed WJ Marzook, Gregory J. Offer, and
+    Monica Marinescu. "Physical origin of the differential voltage minimum associated
+    with lithium plating in Li-ion batteries." Journal of The Electrochemical Society
+    167, no. 9 (2020): 090540.
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_Li : :class:`pybamm.Symbol`
+        Plated lithium concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+    return Scalar(0.001)