BatterySimulatorBLAST/nmc811_grSi_LGMJ1_4Ah_2020.py

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2023-04-08 06:05:55 +09:00
# Paul Gasper, NREL
# This model is fit to LG MJ1 cell aging data reported as part of the EU EVERLASTING battery project, report D2.3
# https://everlasting-project.eu/wp-content/uploads/2020/03/EVERLASTING_D2.3_final_20200228.pdf
# Cell tests were reported in early 2020, so likely 2018 or 2019 LG MJ1 cells.
import numpy as np
from functions.extract_stressors import extract_stressors
from functions.state_functions import update_power_state
# EXPERIMENTAL AGING DATA SUMMARY:
# Calendar aging varied SOC (10%, 70%, 90%) and temperature.
# Cycle aging varied temperature and C-rates; all DOD is 80% (10%-90%). NO ACCELERATED FADE OBSERVED.
# Relative discharge capacity is reported from measurements recorded at 25 Celsius and C/20 rate.
# MODEL SENSITIVITY
# The model predicts degradation rate versus time as a function of temperature and average
# state-of-charge and degradation rate versus equivalent full cycles (charge-throughput) as
# a function of C-rate, temperature, and depth-of-discharge (DOD dependence is assumed to be linear, no aging data)
# MODEL LIMITATIONS
# Cycle degradation predictions WILL NOT PREDICT KNEE-POINT due to limited data.
# OPERATION AT HIGH DOD PREDCTIONS ARE LIKELY INACCURATE (it is unclear what voltage window corresponds to SOCs defined in the test data).
# NMC811 is known to degrade quickly at voltages above 4.1 V.
class Nmc811_GrSi_LGMJ1_4Ah_Battery:
def __init__(self):
# States: Internal states of the battery model
self.states = {
'qLoss_t': np.array([0]),
'qLoss_EFC': np.array([0]),
}
# Outputs: Battery properties derived from state values
self.outputs = {
'q': np.array([1]),
'q_t': np.array([1]),
'q_EFC': np.array([1]),
}
# Stressors: History of stressors on the battery
self.stressors = {
'delta_t_days': np.array([np.nan]),
't_days': np.array([0]),
'delta_efc': np.array([np.nan]),
'efc': np.array([0]),
'TdegK': np.array([np.nan]),
'soc': np.array([np.nan]),
'dod': np.array([np.nan]),
'Crate': np.array([np.nan]),
}
# Rates: History of stressor-dependent degradation rates
self.rates = {
'k_cal': np.array([np.nan]),
'k_cyc': np.array([np.nan]),
}
# Nominal capacity
@property
def _cap(self):
return 3.5
# Define life model parameters
@property
def _params_life(self):
return {
# Capacity fade parameters
'qcal_A': 0.0353,
'qcal_B': -1.03e+03,
'qcal_C': 57.7,
'qcal_p': 0.743,
'qcyc_A': 1.77e-07,
'qcyc_B': 8.08e-13,
'qcyc_C': 2.21e-07,
'qcyc_D': 2.25e+03,
'qcyc_E': 1.14e+04,
'qcyc_p': 0.695,
}
# Battery model
def update_battery_state(self, t_secs, soc, T_celsius):
# Update the battery states, based both on the degradation state as well as the battery performance
# at the ambient temperature, T_celsius
# Inputs:
# t_secs (ndarry): vector of the time in seconds since beginning of life for the soc_timeseries data points
# soc (ndarry): vector of the state-of-charge of the battery at each t_sec
# T_celsius (ndarray): the temperature of the battery during this time period, in Celsius units.
# Check some input types:
if not isinstance(t_secs, np.ndarray):
raise TypeError('Input "t_secs" must be a numpy.ndarray')
if not isinstance(soc, np.ndarray):
raise TypeError('Input "soc" must be a numpy.ndarray')
if not isinstance(T_celsius, np.ndarray):
raise TypeError('Input "T_celsius" must be a numpy.ndarray')
if not (len(t_secs) == len(soc) and len(t_secs) == len(T_celsius)):
raise ValueError('All input timeseries must be the same length')
self.__update_states(t_secs, soc, T_celsius)
self.__update_outputs()
def __update_states(self, t_secs, soc, T_celsius):
# Update the battery states, based both on the degradation state as well as the battery performance
# at the ambient temperature, T_celsius
# Inputs:
# t_secs (ndarry): vector of the time in seconds since beginning of life for the soc_timeseries data points
# soc (ndarry): vector of the state-of-charge of the battery at each t_sec
# T_celsius (ndarray): the temperature of the battery during this time period, in Celsius units.
# Extract stressors
delta_t_secs = t_secs[-1] - t_secs[0]
delta_t_days, delta_efc, TdegK, soc, Ua, dod, Crate, cycles = extract_stressors(t_secs, soc, T_celsius)
# Grab parameters
p = self._params_life
# Calculate the degradation coefficients
k_cal = p['qcal_A'] * np.exp(p['qcal_B']/TdegK) * np.exp(p['qcal_C']*soc/TdegK)
k_cyc = (
(p['qcyc_A'] + p['qcyc_B']*Crate + p['qcyc_C']*dod)
* (np.exp(p['qcyc_D']/TdegK) + np.exp(-p['qcyc_E']/TdegK))
)
# Calculate time based average of each rate
k_cal = np.trapz(k_cal, x=t_secs) / delta_t_secs
k_cyc = np.trapz(k_cyc, x=t_secs) / delta_t_secs
# Calculate incremental state changes
states = self.states
# Capacity
dq_t = update_power_state(states['qLoss_t'][-1], delta_t_days, k_cal, p['qcal_p'])
dq_EFC = update_power_state(states['qLoss_EFC'][-1], delta_efc, k_cyc, p['qcyc_p'])
# Accumulate and store states
dx = np.array([dq_t, dq_EFC])
for k, v in zip(states.keys(), dx):
x = self.states[k][-1] + v
self.states[k] = np.append(self.states[k], x)
# Store stressors
t_days = self.stressors['t_days'][-1] + delta_t_days
efc = self.stressors['efc'][-1] + delta_efc
stressors = np.array([delta_t_days, t_days, delta_efc, efc, np.mean(TdegK), np.mean(soc), dod, Crate])
for k, v in zip(self.stressors.keys(), stressors):
self.stressors[k] = np.append(self.stressors[k], v)
# Store rates
rates = np.array([k_cal, k_cyc])
for k, v in zip(self.rates.keys(), rates):
self.rates[k] = np.append(self.rates[k], v)
def __update_outputs(self):
# Calculate outputs, based on current battery state
states = self.states
# Capacity
q_t = 1 - states['qLoss_t'][-1]
q_EFC = 1 - states['qLoss_EFC'][-1]
q = 1 - states['qLoss_t'][-1] - states['qLoss_EFC'][-1]
# Assemble output
out = np.array([q, q_t, q_EFC])
# Store results
for k, v in zip(list(self.outputs.keys()), out):
self.outputs[k] = np.append(self.outputs[k], v)