Lfp parameters

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Features
 
+-   Added parameter set for an A123 LFP cell ([#1209](https://github.com/pybamm-team/PyBaMM/pull/1209))
 -   Added variables related to equivalent circuit models ([#1204](https://github.com/pybamm-team/PyBaMM/pull/1204))
 -   Added an example script to check conservation of lithium ([#1186](https://github.com/pybamm-team/PyBaMM/pull/1186))
 -   Added `erf` and `erfc` functions ([#1184](https://github.com/pybamm-team/PyBaMM/pull/1184))

examples/scripts/compare_spectral_volume.py

@@ -8,8 +8,10 @@
 
 # load model
 # don't use new_copy
-models = [pybamm.lithium_ion.DFN(name="Finite Volume"),
-          pybamm.lithium_ion.DFN(name="Spectral Volume")]
+models = [
+    pybamm.lithium_ion.DFN(name="Finite Volume"),
+    pybamm.lithium_ion.DFN(name="Spectral Volume"),
+]
 
 # create geometry
 geometries = [m.default_geometry for m in models]
@@ -24,32 +26,31 @@
 var = pybamm.standard_spatial_vars
 var_pts = {var.x_n: 1, var.x_s: 1, var.x_p: 1, var.r_n: 1, var.r_p: 1}
 # the Finite Volume method also works on spectral meshes
-meshes = [pybamm.Mesh(
-    geometry,
-    {
-        "negative particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "positive particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "negative electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "separator": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "positive electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "current collector": pybamm.SubMesh0D,
-    },
-    var_pts) for geometry in geometries]
+meshes = [
+    pybamm.Mesh(
+        geometry,
+        {
+            "negative particle": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "positive particle": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "negative electrode": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "separator": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "positive electrode": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "current collector": pybamm.SubMesh0D,
+        },
+        var_pts,
+    )
+    for geometry in geometries
+]
 
 # discretise model
 disc_fv = pybamm.Discretisation(meshes[0], models[0].default_spatial_methods)
@@ -61,8 +62,8 @@
         "negative electrode": pybamm.SpectralVolume(order=order),
         "separator": pybamm.SpectralVolume(order=order),
         "positive electrode": pybamm.SpectralVolume(order=order),
-        "current collector": pybamm.ZeroDimensionalSpatialMethod()
-    }
+        "current collector": pybamm.ZeroDimensionalSpatialMethod(),
+    },
 )
 
 disc_fv.process_model(models[0])

pybamm/CITATIONS.txt

@@ -78,12 +78,15 @@ year={2019},
 publisher={The Electrochemical Society}
 }
 
-@article{Mohtat2020,
-author = {Mohtat, Peyman and Siegel, Jason B and Stefanopoulou, Anna G},
-title = {{High C-rate Differential Expansion and Voltage Model for Li-ion Batteries}},
-journal = {Submitted for publication},
-year = {2019},
-publisher={ECSarXiv}
+@article{mohtat2020differential,
+  title={Differential Expansion and Voltage Model for Li-ion Batteries at Practical Charging Rates},
+  author={Mohtat, Peyman and Lee, Suhak and Sulzer, Valentin and Siegel, Jason B and Stefanopoulou, Anna G},
+  journal={Journal of The Electrochemical Society},
+  volume={167},
+  number={11},
+  pages={110561},
+  year={2020},
+  publisher={IOP Publishing}
 }
 
 @article{scikits-odes,
@@ -204,3 +207,25 @@ primaryClass={physics.app-ph},
   year={2005},
   publisher={IOP Publishing}
 }
+
+@article{lain2019design,
+  title={Design Strategies for High Power vs. High Energy Lithium Ion Cells},
+  author={Lain, Michael J and Brandon, James and Kendrick, Emma},
+  journal={Batteries},
+  volume={5},
+  number={4},
+  pages={64},
+  year={2019},
+  publisher={Multidisciplinary Digital Publishing Institute}
+}
+
+@article{prada2013simplified,
+  title={A simplified electrochemical and thermal aging model of LiFePO4-graphite Li-ion batteries: power and capacity fade simulations},
+  author={Prada, Eric and Di Domenico, D and Creff, Y and Bernard, J and Sauvant-Moynot, Val{\'e}rie and Huet, Fran{\c{c}}ois},
+  journal={Journal of The Electrochemical Society},
+  volume={160},
+  number={4},
+  pages={A616},
+  year={2013},
+  publisher={IOP Publishing}
+}

pybamm/expression_tree/operations/evaluate.py

@@ -9,10 +9,12 @@
 
 import numbers
 from platform import system
+
 if system() != "Windows":
     import jax
 
     from jax.config import config
+
     config.update("jax_enable_x64", True)
 
 
@@ -95,30 +97,35 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
             dummy_eval_left = symbol.children[0].evaluate_for_shape()
             dummy_eval_right = symbol.children[1].evaluate_for_shape()
             if not to_dense and scipy.sparse.issparse(dummy_eval_left):
-                symbol_str = "{0}.multiply({1})"\
-                    .format(children_vars[0], children_vars[1])
+                symbol_str = "{0}.multiply({1})".format(
+                    children_vars[0], children_vars[1]
+                )
             elif not to_dense and scipy.sparse.issparse(dummy_eval_right):
-                symbol_str = "{1}.multiply({0})"\
-                    .format(children_vars[0], children_vars[1])
+                symbol_str = "{1}.multiply({0})".format(
+                    children_vars[0], children_vars[1]
+                )
             else:
                 symbol_str = "{0} * {1}".format(children_vars[0], children_vars[1])
         elif isinstance(symbol, pybamm.Division):
             dummy_eval_left = symbol.children[0].evaluate_for_shape()
             if not to_dense and scipy.sparse.issparse(dummy_eval_left):
-                symbol_str = "{0}.multiply(1/{1})"\
-                    .format(children_vars[0], children_vars[1])
+                symbol_str = "{0}.multiply(1/{1})".format(
+                    children_vars[0], children_vars[1]
+                )
             else:
                 symbol_str = "{0} / {1}".format(children_vars[0], children_vars[1])
 
         elif isinstance(symbol, pybamm.Inner):
             dummy_eval_left = symbol.children[0].evaluate_for_shape()
             dummy_eval_right = symbol.children[1].evaluate_for_shape()
             if not to_dense and scipy.sparse.issparse(dummy_eval_left):
-                symbol_str = "{0}.multiply({1})"\
-                    .format(children_vars[0], children_vars[1])
+                symbol_str = "{0}.multiply({1})".format(
+                    children_vars[0], children_vars[1]
+                )
             elif not to_dense and scipy.sparse.issparse(dummy_eval_right):
-                symbol_str = "{1}.multiply({0})"\
-                    .format(children_vars[0], children_vars[1])
+                symbol_str = "{1}.multiply({0})".format(
+                    children_vars[0], children_vars[1]
+                )
             else:
                 symbol_str = "{0} * {1}".format(children_vars[0], children_vars[1])
 
@@ -294,18 +301,20 @@ def __init__(self, symbol):
         # extract constants in generated function
         for i, symbol_id in enumerate(constants.keys()):
             const_name = id_to_python_variable(symbol_id, True)
-            python_str = '{} = constants[{}]\n'.format(const_name, i) + python_str
+            python_str = "{} = constants[{}]\n".format(const_name, i) + python_str
 
         # constants passed in as an ordered dict, convert to list
         self._constants = list(constants.values())
 
         # indent code
-        python_str = '   ' + python_str
-        python_str = python_str.replace('\n', '\n   ')
+        python_str = "   " + python_str
+        python_str = python_str.replace("\n", "\n   ")
 
         # add function def to first line
-        python_str = 'def evaluate(constants, t=None, y=None, '\
-            'y_dot=None, inputs=None, known_evals=None):\n' + python_str
+        python_str = (
+            "def evaluate(constants, t=None, y=None, "
+            "y_dot=None, inputs=None, known_evals=None):\n" + python_str
+        )
 
         # calculate the final variable that will output the result of calling `evaluate`
         # on `symbol`
@@ -315,21 +324,18 @@ def __init__(self, symbol):
 
         # add return line
         if symbol.is_constant() and isinstance(result_value, numbers.Number):
-            python_str = python_str + '\n   return ' + str(result_value)
+            python_str = python_str + "\n   return " + str(result_value)
         else:
-            python_str = python_str + '\n   return ' + result_var
+            python_str = python_str + "\n   return " + result_var
 
         # store a copy of examine_jaxpr
-        python_str = python_str + \
-            '\nself._evaluate = evaluate'
+        python_str = python_str + "\nself._evaluate = evaluate"
 
         self._python_str = python_str
         self._symbol = symbol
 
         # compile and run the generated python code,
-        compiled_function = compile(
-            python_str, result_var, "exec"
-        )
+        compiled_function = compile(python_str, result_var, "exec")
         exec(compiled_function)
 
     def evaluate(self, t=None, y=None, y_dot=None, inputs=None, known_evals=None):
@@ -377,7 +383,7 @@ def __init__(self, symbol):
         constants, python_str = pybamm.to_python(symbol, debug=False, to_dense=True)
 
         # replace numpy function calls to jax numpy calls
-        python_str = python_str.replace('np.', 'jax.numpy.')
+        python_str = python_str.replace("np.", "jax.numpy.")
 
         # convert all numpy constants to device vectors
         for symbol_id in constants:
@@ -387,18 +393,20 @@ def __init__(self, symbol):
         # extract constants in generated function
         for i, symbol_id in enumerate(constants.keys()):
             const_name = id_to_python_variable(symbol_id, True)
-            python_str = '{} = constants[{}]\n'.format(const_name, i) + python_str
+            python_str = "{} = constants[{}]\n".format(const_name, i) + python_str
 
         # constants passed in as an ordered dict, convert to list
         self._constants = list(constants.values())
 
         # indent code
-        python_str = '   ' + python_str
-        python_str = python_str.replace('\n', '\n   ')
+        python_str = "   " + python_str
+        python_str = python_str.replace("\n", "\n   ")
 
         # add function def to first line
-        python_str = 'def evaluate_jax(constants, t=None, y=None, '\
-            'y_dot=None, inputs=None, known_evals=None):\n' + python_str
+        python_str = (
+            "def evaluate_jax(constants, t=None, y=None, "
+            "y_dot=None, inputs=None, known_evals=None):\n" + python_str
+        )
 
         # calculate the final variable that will output the result of calling `evaluate`
         # on `symbol`
@@ -408,18 +416,15 @@ def __init__(self, symbol):
 
         # add return line
         if symbol.is_constant() and isinstance(result_value, numbers.Number):
-            python_str = python_str + '\n   return ' + str(result_value)
+            python_str = python_str + "\n   return " + str(result_value)
         else:
-            python_str = python_str + '\n   return ' + result_var
+            python_str = python_str + "\n   return " + result_var
 
         # store a copy of examine_jaxpr
-        python_str = python_str + \
-            '\nself._evaluate_jax = evaluate_jax'
+        python_str = python_str + "\nself._evaluate_jax = evaluate_jax"
 
         # compile and run the generated python code,
-        compiled_function = compile(
-            python_str, result_var, "exec"
-        )
+        compiled_function = compile(python_str, result_var, "exec")
         exec(compiled_function)
 
         self._jit_evaluate = jax.jit(self._evaluate_jax, static_argnums=(0, 4, 5))

pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_electrolyte_exchange_current_density_kashkooli2017.py

@@ -0,0 +1,37 @@
+from pybamm import exp, constants, Parameter
+
+
+def LFP_electrolyte_exchange_current_density_kashkooli2017(c_e, c_s_surf, T):  # , 1
+    """
+    Exchange-current density for Butler-Volmer reactions between LFP and electrolyte
+
+    References
+    ----------
+    .. [1] Kashkooli, A. G., Amirfazli, A., Farhad, S., Lee, D. U., Felicelli, S., Park,
+    H. W., ... & Chen, Z. (2017). Representative volume element model of lithium-ion
+    battery electrodes based on X-ray nano-tomography. Journal of Applied
+    Electrochemistry, 47(3), 281-293.
+
+    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]
+    """
+
+    m_ref = 6 * 10 ** (-7)  # (A/m2)(mol/m3)**1.5 - includes ref concentrations
+    E_r = 39570
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+    c_p_max = Parameter("Maximum concentration in positive electrode [mol.m-3]")
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_p_max - c_s_surf) ** 0.5
+    )

pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_ocp_ashfar2017.py

@@ -0,0 +1,24 @@
+from pybamm import exp
+
+
+def LFP_ocp_ashfar2017(sto):
+    """
+    Open-circuit potential for LFP
+
+    References
+    ----------
+    .. [1] Afshar, S., Morris, K., & Khajepour, A. (2017). Efficient electrochemical
+    model for lithium-ion cells. arXiv preprint arXiv:1709.03970.
+
+    Parameters
+    ----------
+    sto : :class:`pybamm.Symbol`
+       Stochiometry of material (li-fraction)
+
+    """
+
+    c1 = -150 * sto
+    c2 = -30 * (1 - sto)
+    k = 3.4077 - 0.020269 * sto + 0.5 * exp(c1) - 0.9 * exp(c2)
+
+    return k

pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/README.md

@@ -0,0 +1,7 @@
+# Lithium Cobalt Oxide cathode parameters
+
+Parameters for an LFP cathode, from the paper
+
+> Prada, E., Di Domenico, D., Creff, Y., Bernard, J., Sauvant-Moynot, V., & Huet, F. (2013). A simplified electrochemical and thermal aging model of LiFePO4-graphite Li-ion batteries: power and capacity fade simulations. [Journal of The Electrochemical Society](https://doi.org/10.1149/2.053304jes), 160(4), A616.
+
+and references therein. The functions used for OCP and exchange-current density are from separate references (documented within the functions), to provide better fit to data