Battery Degradation How-To

docs/docs/how-to/battery-degradation.md

@@ -0,0 +1,189 @@
+Battery degradation is where battery performance reduces with time or battery use.
+
+The performance of the battery is defined by the parameters of power (MW), capacity (MWh) and efficiency (%).
+
+`energypylinear` does not model battery degradation within a single simulation - degradation can be handled by splitting up the battery lifetime into multiple 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:
+
+<!--phmdoctest-share-names-->
+```python
+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)
+```
+
+```
+Month 1
+Month 2
+<Accounts profit=2501349.07 emissions=15.7333>
+```
+
+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.
+
+<!--phmdoctest-share-names-->
+```python
+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:
+
+<!--phmdoctest-share-names-->
+```python
+print(get_battery_params())
+```
+
+```
+{'power_mw': 4.0, 'capacity_mwh': 10.0, 'efficiency_pct': 0.9, 'freq_mins': 60}
+```
+
+For a battery that has been charged with 300 MWh over 60 days, our battery parameters are:
+
+<!--phmdoctest-share-names-->
+```python
+print(get_battery_params(cumulative_charge_mwh=300, cumulative_days=60))
+```
+
+```
+{'power_mw': 3.8, 'capacity_mwh': 9.8, 'efficiency_pct': 0.7, 'freq_mins': 60}
+```
+
+## 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:
+
+<!--phmdoctest-share-names-->
+```python
+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
+
+```python
+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)
+```
+
+```
+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>
+```

docs/docs/how-to/price-carbon.md

@@ -1,4 +1,4 @@
-`energypylinear` has the ability to optimize for both price and carbon as optimization objectives.
+`energypylinear` can optimize for both price and carbon as optimization objectives.
 
 This ability comes from two things - an objective function, which can be either for price or carbon, along with accounting of both price and carbon emissions.