Merge pull request #2777 from abillscmu/batt-carnot

Method to calculate theoretical efficiency

Author: valentinsulzer

CHANGELOG.md

@@ -29,6 +29,7 @@
 - Added an option for using a banded jacobian and sundials banded solvers for the IDAKLU solve ([#2677](https://github.com/pybamm-team/PyBaMM/pull/2677))
 - The "particle size" option can now be a tuple to allow different behaviour in each electrode ([#2672](https://github.com/pybamm-team/PyBaMM/pull/2672)).
 - Added temperature control to experiment class. ([#2518](https://github.com/pybamm-team/PyBaMM/pull/2518))
+- Added method to calculate maximum theoretical energy. ([#2777](https://github.com/pybamm-team/PyBaMM/pull/2777))
 
 ## Bug fixes
 

pybamm/models/full_battery_models/lithium_ion/electrode_soh.py

@@ -557,3 +557,47 @@ def get_min_max_stoichiometries(
     """
     esoh_solver = ElectrodeSOHSolver(parameter_values, param, known_value)
     return esoh_solver.get_min_max_stoichiometries()
+
+
+def calculate_theoretical_energy(
+    parameter_values, initial_soc=1.0, final_soc=0.0, points=100
+):
+    """
+    Calculate maximum energy possible from a cell given OCV, initial soc, and final soc
+    given voltage limits, open-circuit potentials, etc defined by parameter_values
+
+    Parameters
+    ----------
+    parameter_values : :class:`pybamm.ParameterValues`
+        The parameter values class that will be used for the simulation.
+    initial_soc : float
+        The soc at begining of discharge, default 1.0
+    final_soc : float
+        The soc at end of discharge, default 1.0
+    points : int
+        The number of points at which to calculate voltage.
+
+    Returns
+    -------
+    E
+        The total energy of the cell in Wh
+    """
+    # Get initial and final stoichiometric values.
+    n_i, p_i = get_initial_stoichiometries(initial_soc, parameter_values)
+    n_f, p_f = get_initial_stoichiometries(final_soc, parameter_values)
+    n_vals = np.linspace(n_i, n_f, num=points)
+    p_vals = np.linspace(p_i, p_f, num=points)
+    # Calculate OCV at each stoichiometry
+    param = pybamm.LithiumIonParameters()
+    T = param.T_amb(0)
+    Vs = np.empty(n_vals.shape)
+    for i in range(n_vals.size):
+        Vs[i] = parameter_values.evaluate(
+            param.p.prim.U(p_vals[i], T)
+        ) - parameter_values.evaluate(param.n.prim.U(n_vals[i], T))
+    # Calculate dQ
+    Q_p = parameter_values.evaluate(param.p.prim.Q_init) * (p_f - p_i)
+    dQ = Q_p / (points - 1)
+    # Integrate and convert to W-h
+    E = np.trapz(Vs, dx=dQ)
+    return E

tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_electrode_soh.py

@@ -143,6 +143,25 @@ def test_known_solution(self):
         self.assertAlmostEqual(sol["Uw(x_0)"].data[0], V_min, places=5)
 
 
+class TestCalculateTheoreticalEnergy(unittest.TestCase):
+    def test_efficiency(self):
+        model = pybamm.lithium_ion.DFN(options={"calculate discharge energy": "true"})
+        parameter_values = pybamm.ParameterValues("Chen2020")
+        sim = pybamm.Simulation(model, parameter_values=parameter_values)
+        sol = sim.solve([0, 3600], initial_soc=1.0)
+        discharge_energy = sol["Discharge energy [W.h]"].entries[-1]
+        theoretical_energy = (
+            pybamm.lithium_ion.electrode_soh.calculate_theoretical_energy(
+                parameter_values
+            )
+        )
+        # Real energy should be less than discharge energy,
+        #  and both should be greater than 0
+        self.assertLess(discharge_energy, theoretical_energy)
+        self.assertLess(0, discharge_energy)
+        self.assertLess(0, theoretical_energy)
+
+
 class TestGetInitialSOC(unittest.TestCase):
     def test_initial_soc(self):
         param = pybamm.LithiumIonParameters()