Battery Degradation
Battery performance reducing is known as battery degradation. Battery degradation can occur over time or with battery use.
The performance of a battery is defined by the parameters of power (MW), capacity (MWh) and efficiency (%).
energypylinear does not model battery degradation within a single simulation. Parameters like capacity or efficiency are held constant across a simulation.
Degradation can be handled by splitting up the battery lifetime into multiple simulations, with different parameters used in different simulations.
Modelling a Single Year in Monthly Chunks
To handle battery degradation over a year, we will split the year into 12 months and run a simulation for each month:
import numpy as np
import pandas as pd
import energypylinear as epl
np.random.seed(42)
days = 35
dataset = pd.DataFrame({
"timestamp": pd.date_range("2021-01-01", periods=days * 24, freq="h"),
"prices": np.random.normal(-1000, 1000, days * 24) + 100
})
battery_params = {
"power_mw": 4,
"capacity_mwh": 10,
"efficiency_pct": 0.9,
"freq_mins": 60
}
results = []
objs = []
for month, group in dataset.groupby(dataset['timestamp'].dt.month):
print(f"Month {month}")
battery = epl.Battery(electricity_prices=group['prices'], **battery_params)
simulation = battery.optimize(verbose=3)
results.append(simulation.results)
objs.append(simulation.status.objective)
year = pd.concat(results)
assert year.shape[0] == days * 24
account = epl.get_accounts(year, verbose=3)
np.testing.assert_allclose(account.profit, -1 * sum(objs))
print(account)
The results above do not include any battery degradation - battery parameters are the same at the start of each month.
Modelling Degradation
To model degradation, we need to take a view on how our battery parameters change over time.
For our simulation, we will model:
- battery power decays by 0.1 MW for each 150 MWh of battery charge,
- battery capacity decays by 0.1 MWh for each 150 MWh of battery charge,
- battery efficiency decays by 0.1% over 30 days.
def get_battery_params(cumulative_charge_mwh: float = 0, cumulative_days: float = 0) -> dict:
"""Get degraded battery parameters based on usage and time."""
power_decay_mw_per_mwh = 0.1 / 150
capacity_decay_mwh_per_mwh = 0.1 / 150
efficiency_decay_pct_per_day = 0.1 / 30
return {
"power_mw": 4 - power_decay_mw_per_mwh * cumulative_charge_mwh,
"capacity_mwh": 10 - capacity_decay_mwh_per_mwh * cumulative_charge_mwh,
"efficiency_pct": 0.9 - efficiency_decay_pct_per_day * cumulative_days,
"freq_mins": 60
}
For a fresh battery, our battery parameters are:
For a battery that has been charged with 300 MWh over 60 days, our battery parameters are:
Modelling a Single Year in Monthly Chunks with Degradation
We can include our battery degradation model in our simulation by keeping track of our battery usage and updating the battery parameters at the start of each month:
import collections
results = []
cumulative = collections.defaultdict(float)
for month, group in dataset.groupby(dataset['timestamp'].dt.month):
battery_params = get_battery_params(
cumulative_charge_mwh=cumulative['charge_mwh'],
cumulative_days=cumulative['days']
)
print(f"Month: {month}, Battery Params: {battery_params}")
battery = epl.Battery(electricity_prices=group['prices'], **battery_params)
simulation = battery.optimize(verbose=3)
results.append(simulation.results)
cumulative['charge_mwh'] += simulation.results['battery-electric_charge_mwh'].sum()
cumulative['days'] += group.shape[0] / 24
year = pd.concat(results)
assert year.shape[0] == days * 24
account = epl.get_accounts(year, verbose=3)
print(account)
Month: 1, Battery Params: {'power_mw': 4.0, 'capacity_mwh': 10.0, 'efficiency_pct': 0.9, 'freq_mins': 60}
Month: 2, Battery Params: {'power_mw': 3.0663703705399996, 'capacity_mwh': 9.06637037054, 'efficiency_pct': 0.7966666666666666, 'freq_mins': 60}
<Accounts profit=2460059.00 emissions=16.9273>
Full Example
import collections
import numpy as np
import pandas as pd
import energypylinear as epl
def get_battery_params(cumulative_charge_mwh: float = 0, cumulative_days: float = 0) -> dict:
"""Get degraded battery parameters based on usage and time."""
power_decay_mw_per_mwh = 0.1 / 150
capacity_decay_mwh_per_mwh = 0.1 / 150
efficiency_decay_pct_per_day = 0.1 / 30
return {
"power_mw": 4 - power_decay_mw_per_mwh * cumulative_charge_mwh,
"capacity_mwh": 10 - capacity_decay_mwh_per_mwh * cumulative_charge_mwh,
"efficiency_pct": 0.9 - efficiency_decay_pct_per_day * cumulative_days,
"freq_mins": 60
}
np.random.seed(42)
days = 35
dataset = pd.DataFrame({
"timestamp": pd.date_range("2021-01-01", periods=days * 24, freq="h"),
"prices": np.random.normal(-1000, 1000, days * 24) + 100
})
results = []
cumulative = collections.defaultdict(float)
for month, group in dataset.groupby(dataset['timestamp'].dt.month):
battery_params = get_battery_params(
cumulative_charge_mwh=cumulative['charge_mwh'],
cumulative_days=cumulative['days']
)
print(f"Month: {month}, Battery Params: {battery_params}")
battery = epl.Battery(electricity_prices=group['prices'], **battery_params)
simulation = battery.optimize(verbose=3)
results.append(simulation.results)
cumulative['charge_mwh'] += simulation.results['battery-electric_charge_mwh'].sum()
cumulative['days'] += group.shape[0] / 24
year = pd.concat(results)
assert year.shape[0] == days * 24
account = epl.get_accounts(year, verbose=3)
print(account)