Battery Electric Vehicle Charging

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.

NB: this example will use units of kW and kWh, unlike the PyPSA defaults

[1]:

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

[2]:

# use 24 hour period for consideration
index = pd.date_range("2016-01-01 00:00","2016-01-01 23:00", freq="H")

# consumption pattern of BEV
bev_usage = pd.Series([0.]*7 + [9.]*2 + [0.]*8 + [9.]*2 + [0.]*5, index)

# solar PV panel generation per unit of capacity
pv_pu = pd.Series([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.]*5, index)

# availability of charging - i.e. only when parked at office
charger_p_max_pu = pd.Series(0, index=index)
charger_p_max_pu["2016-01-01 09:00":"2016-01-01 16:00"] = 1.

[3]:

df = pd.concat({'BEV': bev_usage, 'PV': pv_pu, 'Charger': charger_p_max_pu}, axis=1)
df.plot.area(subplots=True, figsize=(10,7))
plt.tight_layout()

../_images/examples_battery-electric-vehicle-charging_3_0.png

Initialize the network

[4]:

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

network.add("Bus",
            "place of work",
            carrier="AC")

network.add("Bus",
            "battery",
            carrier="Li-ion")

network.add("Generator",
            "PV panel",
            bus="place of work",
            p_nom_extendable=True,
            p_max_pu=pv_pu,
            capital_cost=1000.)

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

network.add("Link",
            "charger",
            bus0="place of work",
            bus1="battery",
            p_nom=120,  #super-charger with 120 kW
            p_max_pu=charger_p_max_pu,
            efficiency=0.9)


network.add("Store",
            "battery storage",
            bus="battery",
            e_cyclic=True,
            e_nom=100.)

[5]:

network.lopf()
print("Objective:",network.objective)

INFO:pypsa.opf:Performed preliminary steps
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
INFO:pypsa.opf:Solving model using glpk
INFO:pypsa.opf:Optimization successful

# ==========================================================
# = Solver Results                                         =
# ==========================================================
# ----------------------------------------------------------
#   Problem Information
# ----------------------------------------------------------
Problem:
- Name: unknown
  Lower bound: 7017.54385964912
  Upper bound: 7017.54385964912
  Number of objectives: 1
  Number of constraints: 169
  Number of variables: 98
  Number of nonzeros: 277
  Sense: minimize
# ----------------------------------------------------------
#   Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
  Termination condition: optimal
  Statistics:
    Branch and bound:
      Number of bounded subproblems: 0
      Number of created subproblems: 0
  Error rc: 0
  Time: 0.0032958984375
# ----------------------------------------------------------
#   Solution Information
# ----------------------------------------------------------
Solution:
- number of solutions: 0
  number of solutions displayed: 0
Objective: 7017.54385964912

/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.19.1/lib/python3.10/site-packages/pypsa/opf.py:1293: FutureWarning: Using the level keyword in DataFrame and Series aggregations is deprecated and will be removed in a future version. Use groupby instead. df.sum(level=1) should use df.groupby(level=1).sum().
  pd.concat({c.name:

The optimal panel size in kW is

[6]:

network.generators.p_nom_opt["PV panel"]

[6]:

7.01754385964912

[7]:

network.generators_t.p.plot.area(figsize = (9,4))
plt.tight_layout()

../_images/examples_battery-electric-vehicle-charging_9_0.png

[8]:

df = pd.DataFrame({attr: network.stores_t[attr]["battery storage"] for attr in ["p","e"]})
df.plot(grid=True, figsize = (10,5))
plt.legend(labels=['Energy output', 'State of charge'])
plt.tight_layout()

../_images/examples_battery-electric-vehicle-charging_10_0.png

The losses in kWh per pay are:

[9]:

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

[9]:

3.9999999999999716

[10]:

network.links_t.p0.plot.area(figsize = (9,5))
plt.tight_layout()

../_images/examples_battery-electric-vehicle-charging_13_0.png