BatterySimulatorBLAST/lfp_gr_SonyMurata3Ah_2018.py

271 lines
12 KiB
Python

# Paul Gasper, NREL
import numpy as np
from functions.extract_stressors import extract_stressors
from functions.state_functions import update_power_B_state, update_sigmoid_state
import scipy.stats as stats
# EXPERIMENTAL AGING DATA SUMMARY:
# Aging test matrix varied temperature and state-of-charge for calendar aging, and
# varied depth-of-discharge, average state-of-charge, and C-rates for cycle aging.
# There is NO LOW TEMPERATURE cycling aging data, i.e., no lithium-plating induced by
# kinetic limitations on cell performance; CYCLING WAS ONLY DONE AT 25 CELSIUS AND 45 CELSIUS,
# so any model predictions at low temperature cannot incorporate low temperature degradation modes.
# Discharge capacity
# 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 average state-of-charge during a cycle, depth-of-discharge, and average of the
# charge and discharge C-rates.
# MODEL LIMITATIONS
# There is no influence of TEMPERATURE on CYCLING DEGRADATION RATE due to limited data. This is
# NOT PHYSICALLY REALISTIC AND IS BASED ON LIMITED DATA.
class Lfp_Gr_SonyMurata3Ah_Battery:
# Model predicting the degradation of Sony-Murata 3 Ah LFP-Gr cylindrical cells.
# Data is from Technical University of Munich, reported in studies led by Maik Naumann.
# Capacity model identification was conducted at NREL. Resistance model is from Naumann et al.
# Naumann et al used an interative fitting procedure, but it was found that lower model error could be
# achieved by simply reoptimizing all resistance growth parameters to the entire data set.
# Calendar aging data source: https://doi.org/10.1016/j.est.2018.01.019
# Cycle aging data source: https://doi.org/10.1016/j.jpowsour.2019.227666
# Model identification source: https://doi.org/10.1149/1945-7111/ac86a8
# Degradation rate is a function of the aging stressors, i.e., ambient temperature and use.
# The state of the battery is updated throughout the lifetime of the cell.
# Performance metrics are capacity and DC resistance. These metrics change as a function of the
# cell's current degradation state, as well as the ambient temperature. The model predicts time and
# cycling dependent degradation. Cycling dependent degradation includes a break-in mechanism as well
# as long term cycling fade; the break-in mechanism strongly influenced results of the accelerated
# aging test, but is not expected to have much influence on real-world applications.
# Parameters to modify to change fade rates:
# q1_b0: rate of capacity loss due to calendar degradation
# q5_b0: rate of capacity loss due to cycling degradation
# k_ref_r_cal: rate of resistance growth due to calendar degradation
# A_r_cyc: rate of resistance growth due to cycling degradation
def __init__(self):
# States: Internal states of the battery model
self.states = {
'qLoss_LLI_t': np.array([0]),
'qLoss_LLI_EFC': np.array([0]),
'qLoss_BreakIn_EFC': np.array([1e-10]),
'rGain_LLI_t': np.array([0]),
'rGain_LLI_EFC': np.array([0]),
}
# Outputs: Battery properties derived from state values
self.outputs = {
'q': np.array([1]),
'q_LLI_t': np.array([1]),
'q_LLI_EFC': np.array([1]),
'q_BreakIn_EFC': np.array([1]),
'r': np.array([1]),
'r_LLI_t': np.array([1]),
'r_LLI_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]),
'Ua': np.array([np.nan]),
'dod': np.array([np.nan]),
'Crate': np.array([np.nan]),
}
# Rates: History of stressor-dependent degradation rates
self.rates = {
'q1': np.array([np.nan]),
'q3': np.array([np.nan]),
'q5': np.array([np.nan]),
'q7': np.array([np.nan]),
'r_kcal': np.array([np.nan]),
'r_kcyc': np.array([np.nan]),
}
# Nominal capacity
@property
def _cap(self):
return 3
# Define life model parameters
@property
def _params_life(self):
return {
# Capacity fade parameters
'q2': 0.000130510034211874,
'q1_b0': 0.989687151293590, # CHANGE to modify calendar degradation rate
'q1_b1': -2881067.56019324,
'q1_b2': 8742.06309157261,
'q3_b0': 0.000332850281062177,
'q3_b1': 734553185711.369,
'q3_b2': -2.82161575620780e-06,
'q3_b3': -3284991315.45121,
'q3_b4': 0.00127227593657290,
'q8': 0.00303553871631028,
'q9': 1.43752162947637,
'q7_b0': 0.582258029148225,
'q7_soc_skew': 0.0583128906965484,
'q7_soc_width': 0.208738181522897,
'q7_dod_skew': -3.80744333129564,
'q7_dod_width': 1.16126260428210,
'q7_dod_growth': 25.4130804598602,
'q6': 1.12847759334355,
'q5_b0': -6.81260579372875e-06, # CHANGE to modify cycling degradation rate
'q5_b1': 2.59615973160844e-05,
'q5_b2': 2.11559710307295e-06,
# Resistance growth parameters
'k_ref_r_cal': 3.4194e-10, # CHANGE to modify calendar degradation rate
'Ea_r_cal': 71827,
'C_r_cal': -3.3903,
'D_r_cal': 1.5604,
'A_r_cyc': -0.002, # CHANGE to modify cycling degradation rate
'B_r_cyc': 0.0021,
'C_r_cyc': 6.8477,
'D_r_cyc': 0.91882
}
# 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
q1 = np.abs(
p['q1_b0']
* np.exp(p['q1_b1']*(1/(TdegK**2))*(Ua**0.5))
* np.exp(p['q1_b2']*(1/TdegK)*(Ua**0.5))
)
q3 = np.abs(
p['q3_b0']
* np.exp(p['q3_b1']*(1/(TdegK**4))*(Ua**(1/3)))
* np.exp(p['q3_b2']*(TdegK**3)*(Ua**(1/4)))
* np.exp(p['q3_b3']*(1/(TdegK**3))*(Ua**(1/3)))
* np.exp(p['q3_b4']*(TdegK**2)*(Ua**(1/4)))
)
q5 = np.abs(
p['q5_b0']
+ p['q5_b1']*dod
+ p['q5_b2']*np.exp((dod**2)*(Crate**3))
)
q7 = np.abs(
p['q7_b0']
* skewnormpdf(soc, p['q7_soc_skew'], p['q7_soc_width'])
* skewnormpdf(dod, p['q7_dod_skew'], p['q7_dod_width'])
* sigmoid(dod, 1, p['q7_dod_growth'], 1)
)
k_temp_r_cal = (
p['k_ref_r_cal']
* np.exp((-p['Ea_r_cal'] / 8.3144) * (1/TdegK - 1/298.15))
)
k_soc_r_cal = p['C_r_cal'] * (soc - 0.5)**3 + p['D_r_cal']
k_Crate_r_cyc = p['A_r_cyc'] * Crate + p['B_r_cyc']
k_dod_r_cyc = p['C_r_cyc']* (dod - 0.5)**3 + p['D_r_cyc']
# Calculate time based average of each rate
q1 = np.trapz(q1, x=t_secs) / delta_t_secs
q3 = np.trapz(q3, x=t_secs) / delta_t_secs
#q5 = np.trapz(q5, x=t_secs) / delta_t_secs # no time varying inputs
q7 = np.trapz(q7, x=t_secs) / delta_t_secs # no time varying inputs
k_temp_r_cal = np.trapz(k_temp_r_cal, x=t_secs) / delta_t_secs
k_soc_r_cal = np.trapz(k_soc_r_cal, x=t_secs) / delta_t_secs # no time varying inputs
#k_Crate_r_cyc = np.trapz(k_Crate_r_cyc, x=t_secs) / delta_t_secs # no time varying inputs
#k_dod_r_cyc = np.trapz(k_dod_r_cyc, x=t_secs) / delta_t_secs # no time varying inputs
# Calculate incremental state changes
states = self.states
# Capacity
dq_LLI_t = update_sigmoid_state(states['qLoss_LLI_t'][-1], delta_t_days, q1, p['q2'], q3)
dq_LLI_EFC = update_power_B_state(states['qLoss_LLI_EFC'][-1], delta_efc, q5, p['q6'])
if delta_efc / delta_t_days > 2: # only evalaute if more than 2 full cycles per day
dq_BreakIn_EFC = update_sigmoid_state(states['qLoss_BreakIn_EFC'][-1], delta_efc, q7, p['q8'], p['q9'])
else:
dq_BreakIn_EFC = 0
# Resistance
dr_LLI_t = k_temp_r_cal * k_soc_r_cal * delta_t_secs
dr_LLI_EFC = k_Crate_r_cyc * k_dod_r_cyc * delta_efc / 100
# Accumulate and store states
dx = np.array([dq_LLI_t, dq_LLI_EFC, dq_BreakIn_EFC, dr_LLI_t, dr_LLI_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), np.mean(Ua), 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([q1, q3, q5, q7, k_temp_r_cal * k_soc_r_cal, k_Crate_r_cyc * k_dod_r_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
p = self._params_life
# Capacity
q_LLI_t = 1 - states['qLoss_LLI_t'][-1]
q_LLI_EFC = 1 - states['qLoss_LLI_EFC'][-1]
q_BreakIn_EFC = 1 - states['qLoss_BreakIn_EFC'][-1]
q = 1 - states['qLoss_LLI_t'][-1] - states['qLoss_LLI_EFC'][-1] - states['qLoss_BreakIn_EFC'][-1]
# Resistance
r_LLI_t = 1 + states['rGain_LLI_t'][-1]
r_LLI_EFC = 1 + states['rGain_LLI_EFC'][-1]
r = 1 + states['rGain_LLI_t'][-1] + states['rGain_LLI_EFC'][-1]
# Assemble output
out = np.array([q, q_LLI_t, q_LLI_EFC, q_BreakIn_EFC, r, r_LLI_t, r_LLI_EFC])
# Store results
for k, v in zip(list(self.outputs.keys()), out):
self.outputs[k] = np.append(self.outputs[k], v)
def sigmoid(x, alpha, beta, gamma):
return 2*alpha*(1/2 - 1/(1 + np.exp((beta*x)**gamma)))
def skewnormpdf(x, skew, width):
x_prime = (x-0.5)/width
return 2 * stats.norm.pdf(x_prime) * stats.norm.cdf(skew * (x_prime))