79 lines
1.9 KiB
Python
79 lines
1.9 KiB
Python
from matplotlib import pyplot as plot
|
|
import numpy as np
|
|
|
|
|
|
class Params:
|
|
def __init__(self, alpha, beta):
|
|
self.alpha = alpha
|
|
self.beta = beta
|
|
|
|
|
|
def bas(soc: float):
|
|
return 0.05, 25
|
|
|
|
|
|
# from:
|
|
# "Experimental Analysis and Modeling of
|
|
# Temperature Dependence of Lithium-Ion Battery
|
|
# Direct Current Resistance for Power Capability Prediction",
|
|
# Linfeng Zheng et al., University of Technology Sydney, Australia
|
|
# URL:
|
|
# https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://opus.lib.uts.edu.au/rest/bitstreams/80b07f8a-db41-4cdc-b645-dbe5c0bf2446/retrieve&ved=2ahUKEwi4teeEzv2LAxVVxgIHHZwIF1IQFnoECBkQAQ&usg=AOvVaw30hTrXeAXEETJDmB7-0rze
|
|
def model_bat_dcr(temperature: float, soc: float, p: Params):
|
|
rb, tb = bas(soc)
|
|
tb = 25
|
|
tb2 = tb*tb
|
|
|
|
_t = temperature
|
|
t2 = temperature*temperature
|
|
return rb * np.exp(p.alpha*(t2 - tb2) + p.beta*(_t - tb))
|
|
|
|
|
|
def main() -> None:
|
|
temps = [0, 5, 10, 20, 25, 40]
|
|
pl = 10000
|
|
il = 100
|
|
ul = 100
|
|
rl = ul/il
|
|
p_ = np.linspace(0, 20000, 100)
|
|
i_ = p_/ul
|
|
|
|
bat_params = Params(alpha=0.0007545, beta=-0.07033)
|
|
rt_ = []
|
|
for t in temps:
|
|
rt_.append(model_bat_dcr(t, 100, bat_params))
|
|
|
|
plot.figure()
|
|
plot.plot(temps, rt_)
|
|
r, t = bas(100)
|
|
plot.title(f"DCR vs temperature (Base DCR={r}@{t}°C)")
|
|
plot.xlabel("Temperature [°C]")
|
|
plot.ylabel("R [Ohm]")
|
|
plot.grid()
|
|
|
|
titles = [
|
|
"Battery power loss vs internal battery resistance (DCR)",
|
|
"Batter power consumption vs internal battery resistance (DCR)"
|
|
]
|
|
for sp, name, title in zip([0, 1], ["P_loss [kW]", "P_batt [kW]"], titles):
|
|
plot.figure()
|
|
legs = []
|
|
plot.grid()
|
|
for temp in temps:
|
|
dcr = model_bat_dcr(temp, 100, bat_params)
|
|
pi_ = (dcr * i_ * i_) + sp*p_
|
|
x = p_/1000
|
|
y = pi_/1000
|
|
legs.append(f"temp={temp} °C")
|
|
plot.plot(x, y)
|
|
plot.xlabel("P_demand [kW]")
|
|
|
|
plot.title(title)
|
|
plot.legend(legs)
|
|
plot.ylabel(name)
|
|
|
|
plot.show()
|
|
|
|
if __name__ == '__main__':
|
|
main()
|