From 12818f16ff9fa6631a7317d1d25a95ac3f6858ee Mon Sep 17 00:00:00 2001
From: Valentin Sulzer <valentinsulzer@hotmail.com>
Date: Fri, 24 Mar 2023 14:25:19 -0400
Subject: [PATCH] add new esoh variables from dVdQ paper

---
 pybamm/CITATIONS.txt                          |  7 +++++++
 .../lithium_ion/electrode_soh.py              | 21 +++++++++++++++++++
 2 files changed, 28 insertions(+)

diff --git a/pybamm/CITATIONS.txt b/pybamm/CITATIONS.txt
index 1bf09106ec..546f91f0a1 100644
--- a/pybamm/CITATIONS.txt
+++ b/pybamm/CITATIONS.txt
@@ -526,6 +526,13 @@
   doi = {10.1006/jcph.2002.7041},
 }
 
+@article{Weng2023,
+  title={Differential voltage analysis for battery manufacturing process control},
+  author={Weng, Andrew and Siegel, Jason B and Stefanopoulou, Anna},
+  journal={arXiv preprint arXiv:2303.07088},
+  year={2023}
+}
+
 @article{Xu2019,
   title={Evolution of Dead Lithium Growth in Lithium Metal Batteries: Experimentally Validated Model of the Apparent Capacity Loss},
   author={Xu, Shanshan and Chen, Kuan-Hung and Dasgupta, Neil P and Siegel, Jason B and Stefanopoulou, Anna G},
diff --git a/pybamm/models/full_battery_models/lithium_ion/electrode_soh.py b/pybamm/models/full_battery_models/lithium_ion/electrode_soh.py
index a94b0c11eb..f56dbc77a1 100644
--- a/pybamm/models/full_battery_models/lithium_ion/electrode_soh.py
+++ b/pybamm/models/full_battery_models/lithium_ion/electrode_soh.py
@@ -11,6 +11,7 @@ class _ElectrodeSOH(pybamm.BaseModel):
     """Model to calculate electrode-specific SOH, from [1]_.
     This model is mainly for internal use, to calculate summary variables in a
     simulation.
+    Some of the output variables are defined in [2]_.
 
     .. math::
         Q_{Li} = y_{100}Q_p + x_{100}Q_n,
@@ -34,6 +35,7 @@ def __init__(
         self, param=None, solve_for=None, known_value="cyclable lithium capacity"
     ):
         pybamm.citations.register("Mohtat2019")
+        pybamm.citations.register("Weng2023")
         name = "ElectrodeSOH model"
         super().__init__(name)
 
@@ -80,6 +82,7 @@ def __init__(
             self.initial_conditions[x_100] = pybamm.Scalar(0.9)
 
         # These variables are defined in all cases
+        Acc_cm2 = param.A_cc * 1e4
         self.variables = {
             "x_100": x_100,
             "y_100": y_100,
@@ -90,6 +93,18 @@ def __init__(
             "n_Li": Q_Li * 3600 / param.F,
             "Q_n": Q_n,
             "Q_p": Q_p,
+            "Cyclable lithium capacity [A.h]": Q_Li,
+            "Negative electrode capacity [A.h]": Q_n,
+            "Positive electrode capacity [A.h]": Q_p,
+            "Cyclable lithium capacity [mA.h.cm-2]": Q_Li * 1e3 / Acc_cm2,
+            "Negative electrode capacity [mA.h.cm-2]": Q_n * 1e3 / Acc_cm2,
+            "Positive electrode capacity [mA.h.cm-2]": Q_p * 1e3 / Acc_cm2,
+            # eq 33 of Weng2023
+            "Formation capacity loss [A.h]": Q_p - Q_Li,
+            "Formation capacity loss [mA.h.cm-2]": (Q_p - Q_Li) * 1e3 / Acc_cm2,
+            # eq 26 of Weng2024
+            "Negative positive ratio": Q_n / Q_p,
+            "NPR": Q_n / Q_p,
         }
 
         # Define variables and equations for 0% state of charge
@@ -113,10 +128,14 @@ def __init__(
             self.initial_conditions[var] = pybamm.Scalar(0.1)
 
             # These variables are only defined if x_0 is solved for
+            # eq 27 of Weng2023
+            Q_n_excess = Q_n * (1 - x_100)
+            NPR_practical = 1 + Q_n_excess / Q
             self.variables.update(
                 {
                     "Q": Q,
                     "Capacity [A.h]": Q,
+                    "Capacity [mA.h.cm-2]": Q * 1e3 / Acc_cm2,
                     "x_0": x_0,
                     "y_0": y_0,
                     "Un(x_0)": Un_0,
@@ -128,6 +147,8 @@ def __init__(
                     "Q_p * (y_0 - y_100)": Q_p * (y_0 - y_100),
                     "Negative electrode excess capacity ratio": Q_n / Q,
                     "Positive electrode excess capacity ratio": Q_p / Q,
+                    "Practical negative positive ratio": NPR_practical,
+                    "Practical NPR": NPR_practical,
                 }
             )