Electric Vehicles¶

In this example, a battery electric vehicle (BEV) is driven 100 km in the morning and 100 km in the evening, to simulate commuting, and charged during the day by a solar panel at the driver's place of work. The size of the panel is computed by the optimisation.

The BEV has a battery of size 100 kWh and an electricity consumption of 0.18 kWh/km.

This example will use units of kW and kWh, unlike the PyPSA defaults. This is unproblematic as long as no power flow simulations are performed.

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import matplotlib.pyplot as plt
import pandas as pd

import pypsa

import matplotlib.pyplot as plt import pandas as pd import pypsa

As time index, we use a 24 hour period.

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index = pd.date_range("2016-01-01 00:00", "2016-01-01 23:00", freq="h")

index = pd.date_range("2016-01-01 00:00", "2016-01-01 23:00", freq="h")

The consumption pattern in kW of the BEV is defined as follows

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bev_usage = pd.Series([0] * 7 + [9] * 2 + [0] * 8 + [9] * 2 + [0] * 5, index)

bev_usage = pd.Series([0] * 7 + [9] * 2 + [0] * 8 + [9] * 2 + [0] * 5, index)

The capacity factor profile of the solar panel in per-unit of capacity is given by:

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pv_pu = pd.Series(
    [0.0] * 7
    + [0.2, 0.4, 0.6, 0.75, 0.85, 0.9, 0.85, 0.75, 0.6, 0.4, 0.2, 0.1]
    + [0.0] * 5,
    index,
)

pv_pu = pd.Series( [0.0] * 7 + [0.2, 0.4, 0.6, 0.75, 0.85, 0.9, 0.85, 0.75, 0.6, 0.4, 0.2, 0.1] + [0.0] * 5, index, )

The availability of charging - i.e. only when parked at office - is constrained as follows:

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charger_p_max_pu = pd.Series(0, index=index)
charger_p_max_pu["2016-01-01 09:00":"2016-01-01 16:00"] = 1

charger_p_max_pu = pd.Series(0, index=index) charger_p_max_pu["2016-01-01 09:00":"2016-01-01 16:00"] = 1

Together, this gives:

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df = pd.concat({"BEV": bev_usage, "PV": pv_pu, "Charger": charger_p_max_pu}, axis=1)
df.plot.area(subplots=True);

df = pd.concat({"BEV": bev_usage, "PV": pv_pu, "Charger": charger_p_max_pu}, axis=1) df.plot.area(subplots=True);

Now initialise the network and add the relevant components. Then optimise:

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n = pypsa.Network()
n.set_snapshots(index)

n.add("Bus", "place of work")

n.add("Bus", "car battery")

n.add(
    "Generator",
    "PV panel",
    bus="place of work",
    p_nom_extendable=True,
    p_max_pu=pv_pu,
    capital_cost=1000,  # dummy cost value
)

n.add("Load", "driving", bus="car battery", p_set=bev_usage)

n.add(
    "Link",
    "charger",
    bus0="place of work",
    bus1="car battery",
    p_nom=120,
    p_max_pu=charger_p_max_pu,
    efficiency=0.9,
)

n.add("Store", "battery", bus="car battery", e_cyclic=True, e_nom=100);

n = pypsa.Network() n.set_snapshots(index) n.add("Bus", "place of work") n.add("Bus", "car battery") n.add( "Generator", "PV panel", bus="place of work", p_nom_extendable=True, p_max_pu=pv_pu, capital_cost=1000, # dummy cost value ) n.add("Load", "driving", bus="car battery", p_set=bev_usage) n.add( "Link", "charger", bus0="place of work", bus1="car battery", p_nom=120, p_max_pu=charger_p_max_pu, efficiency=0.9, ) n.add("Store", "battery", bus="car battery", e_cyclic=True, e_nom=100);

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n.optimize()
print("Objective:", n.objective)

n.optimize() print("Objective:", n.objective)

The optimal panel size in kW is:

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n.generators.p_nom_opt["PV panel"]

n.generators.p_nom_opt["PV panel"]

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n.generators_t.p.plot.area()

n.generators_t.p.plot.area()

The battery operation is optimised to follow:

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df = pd.DataFrame({attr: n.stores_t[attr]["battery"] for attr in ["p", "e"]})
df.plot(grid=True, ylim=(-10, 40))
plt.legend(labels=["Energy output", "State of charge"])

df = pd.DataFrame({attr: n.stores_t[attr]["battery"] for attr in ["p", "e"]}) df.plot(grid=True, ylim=(-10, 40)) plt.legend(labels=["Energy output", "State of charge"])

The losses in kWh per pay are:

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(n.generators_t.p.loc[:, "PV panel"].sum() - n.loads_t.p.loc[:, "driving"].sum())

(n.generators_t.p.loc[:, "PV panel"].sum() - n.loads_t.p.loc[:, "driving"].sum())

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n.links_t.p0.plot.area()

n.links_t.p0.plot.area()