Hysteresis ESOH (#5163)

* hyst

* more progress

* asdf

* passing tests

* test

* wrap main

* working but not numerically

* fix

* wrap

* fix error?

* fix direction issue

* add direction to mohtat test

* fix notebook

* add initial state setting

* fix hysteresis

* reduce calls to _get_lithiation_delithiation

* update docs

---------

Co-authored-by: Robert Timms <[email protected]>
Co-authored-by: rtimms <[email protected]>

Author: aabills

src/pybamm/input/parameters/lithium_ion/Chen2020_composite.py

@@ -82,7 +82,7 @@ def silicon_ocp_lithiation_Mark2016(sto):
         + p6 * sto**2
         + p7 * sto
         + p8
-    )
+    ) + 1e-4 * (1 / sto + 1 / (sto - 1))
     return U_lithiation
 
 
@@ -205,7 +205,7 @@ def nmc_LGM50_ocp_Chen2020(sto):
         - 0.0428 * np.tanh(18.5138 * (sto - 0.5542))
         - 17.7326 * np.tanh(15.7890 * (sto - 0.3117))
         + 17.5842 * np.tanh(15.9308 * (sto - 0.3120))
-    )
+    ) + 1e-4 * (1 / sto + 1 / (sto - 1))
 
     return u_eq
 

src/pybamm/models/full_battery_models/equivalent_circuit/initial_state.py

@@ -6,6 +6,7 @@
 def set_initial_state(
     initial_value,
     parameter_values,
+    direction=None,
     param=None,
     inplace=True,
     options=None,