Note

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Multi Investment Optimization

In the following, we show how PyPSA can deal with multi-investment optimization, also known as multi-horizon optimization.

Here, the total set of snapshots is divided into investment periods. For the model, this translates into multi-indexed snapshots with the first level being the investment period and the second level the according time steps. In each investment period new asset may be added to the system. On the other hand assets may only operate as long as allowed by their lifetime.

In contrast to the ordinary optimisation, the following concepts have to be taken into account.

  1. investment_periods - pypsa.Network attribute. This is the set of periods which specify when new assets may be built. In the current implementation, these have to be the same as the first level values in the snapshots attribute.

  2. investment_period_weightings - pypsa.Network attribute. These specify the weighting of each period in the objective function.

  3. build_year - general component attribute. A single asset may only be built when the build year is smaller or equal to the current investment period. For example, assets with a build year 2029 are considered in the investment period 2030, but not in the period 2025.

  4. lifetime - general component attribute. An asset is only considered in an investment period if present at the beginning of an investment period. For example, an asset with build year 2029 and lifetime 30 is considered in the investment period 2055 but not in the period 2060.

In the following, we set up a three node network with generators, lines and storages and run a optimisation covering the time span from 2020 to 2050 and each decade is one investment period.

[1]:
import pypsa
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

We set up the network with investment periods and snapshots.

[2]:
n = pypsa.Network()
years = [2020, 2030, 2040, 2050]
freq = "24"

snapshots = pd.DatetimeIndex([])
for year in years:
    period = pd.date_range(
        start="{}-01-01 00:00".format(year),
        freq="{}H".format(freq),
        periods=8760 / float(freq),
    )
    snapshots = snapshots.append(period)

# convert to multiindex and assign to network
n.snapshots = pd.MultiIndex.from_arrays([snapshots.year, snapshots])
n.investment_periods = years

n.snapshot_weightings
[2]:
objective stores generators
period timestep
2020 2020-01-01 1.0 1.0 1.0
2020-01-02 1.0 1.0 1.0
2020-01-03 1.0 1.0 1.0
2020-01-04 1.0 1.0 1.0
2020-01-05 1.0 1.0 1.0
... ... ... ... ...
2050 2050-12-27 1.0 1.0 1.0
2050-12-28 1.0 1.0 1.0
2050-12-29 1.0 1.0 1.0
2050-12-30 1.0 1.0 1.0
2050-12-31 1.0 1.0 1.0

1460 rows × 3 columns

[3]:
n.investment_periods
[3]:
Int64Index([2020, 2030, 2040, 2050], dtype='int64')

Set the years and objective weighting per investment period. For the objective weighting, we consider a discount rate defined by

\[D(t) = \dfrac{1}{(1+r)^t}\]

where \(r\) is the discount rate. For each period we sum up all discounts rates of the corresponding years which gives us the effective objective weighting.

[4]:
n.investment_period_weightings["years"] = list(np.diff(years)) + [10]

r = 0.01
T = 0
for period, nyears in n.investment_period_weightings.years.items():
    discounts = [(1 / (1 + r) ** t) for t in range(T, T + nyears)]
    n.investment_period_weightings.at[period, "objective"] = sum(discounts)
    T += nyears
n.investment_period_weightings
[4]:
objective years
2020 9.566018 10
2030 8.659991 10
2040 7.839777 10
2050 7.097248 10

Add the components

[5]:
for i in range(3):
    n.add("Bus", "bus {}".format(i))

# add three lines in a ring
n.add(
    "Line",
    "line 0->1",
    bus0="bus 0",
    bus1="bus 1",
)

n.add(
    "Line",
    "line 1->2",
    bus0="bus 1",
    bus1="bus 2",
    capital_cost=10,
    build_year=2030,
)

n.add(
    "Line",
    "line 2->0",
    bus0="bus 2",
    bus1="bus 0",
)

n.lines["x"] = 0.0001
n.lines["s_nom_extendable"] = True
[6]:
n.lines
[6]:
attribute bus0 bus1 type x r g b s_nom s_nom_extendable s_nom_min ... v_ang_min v_ang_max sub_network x_pu r_pu g_pu b_pu x_pu_eff r_pu_eff s_nom_opt
Line
line 0->1 bus 0 bus 1 0.0001 0.0 0.0 0.0 0.0 True 0.0 ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0
line 1->2 bus 1 bus 2 0.0001 0.0 0.0 0.0 0.0 True 0.0 ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0
line 2->0 bus 2 bus 0 0.0001 0.0 0.0 0.0 0.0 True 0.0 ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0

3 rows × 29 columns

[7]:
# add some generators
p_nom_max = pd.Series(
    (np.random.uniform() for sn in range(len(n.snapshots))),
    index=n.snapshots,
    name="generator ext 2020",
)

# renewable (can operate 2020, 2030)
n.add(
    "Generator",
    "generator ext 0 2020",
    bus="bus 0",
    p_nom=50,
    build_year=2020,
    lifetime=20,
    marginal_cost=2,
    capital_cost=1,
    p_max_pu=p_nom_max,
    carrier="solar",
    p_nom_extendable=True,
)

# can operate 2040, 2050
n.add(
    "Generator",
    "generator ext 0 2040",
    bus="bus 0",
    p_nom=50,
    build_year=2040,
    lifetime=11,
    marginal_cost=25,
    capital_cost=10,
    carrier="OCGT",
    p_nom_extendable=True,
)

# can operate in 2040
n.add(
    "Generator",
    "generator fix 1 2040",
    bus="bus 1",
    p_nom=50,
    build_year=2040,
    lifetime=10,
    carrier="CCGT",
    marginal_cost=20,
    capital_cost=1,
)

n.generators
[7]:
attribute bus control type p_nom p_nom_extendable p_nom_min p_nom_max p_min_pu p_max_pu p_set ... shut_down_cost min_up_time min_down_time up_time_before down_time_before ramp_limit_up ramp_limit_down ramp_limit_start_up ramp_limit_shut_down p_nom_opt
Generator
generator ext 0 2020 bus 0 PQ 50.0 True 0.0 inf 0.0 1.0 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
generator ext 0 2040 bus 0 PQ 50.0 True 0.0 inf 0.0 1.0 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
generator fix 1 2040 bus 1 PQ 50.0 False 0.0 inf 0.0 1.0 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0

3 rows × 30 columns

[8]:
n.add(
    "StorageUnit",
    "storageunit non-cyclic 2030",
    bus="bus 2",
    p_nom=0,
    capital_cost=2,
    build_year=2030,
    lifetime=21,
    cyclic_state_of_charge=False,
    p_nom_extendable=False,
)

n.add(
    "StorageUnit",
    "storageunit periodic 2020",
    bus="bus 2",
    p_nom=0,
    capital_cost=1,
    build_year=2020,
    lifetime=21,
    cyclic_state_of_charge=True,
    cyclic_state_of_charge_per_period=True,
    p_nom_extendable=True,
)

n.storage_units
[8]:
attribute bus control type p_nom p_nom_extendable p_nom_min p_nom_max p_min_pu p_max_pu p_set ... state_of_charge_initial_per_period state_of_charge_set cyclic_state_of_charge cyclic_state_of_charge_per_period max_hours efficiency_store efficiency_dispatch standing_loss inflow p_nom_opt
StorageUnit
storageunit non-cyclic 2030 bus 2 PQ 0.0 False 0.0 inf -1.0 1.0 0.0 ... False NaN False True 1.0 1.0 1.0 0.0 0.0 0.0
storageunit periodic 2020 bus 2 PQ 0.0 True 0.0 inf -1.0 1.0 0.0 ... False NaN True True 1.0 1.0 1.0 0.0 0.0 0.0

2 rows × 28 columns

Add the load

[9]:
load_var = pd.Series(
    100 * np.random.rand(len(n.snapshots)), index=n.snapshots, name="load"
)
n.add("Load", "load 2", bus="bus 2", p_set=load_var)

load_fix = pd.Series(75, index=n.snapshots, name="load")
n.add("Load", "load 1", bus="bus 1", p_set=load_fix)

Run the optimization

[10]:
n.loads_t.p_set
[10]:
Load load 2 load 1
period timestep
2020 2020-01-01 54.897805 75.0
2020-01-02 94.985932 75.0
2020-01-03 95.808419 75.0
2020-01-04 69.313188 75.0
2020-01-05 71.412629 75.0
... ... ... ...
2050 2050-12-27 27.533763 75.0
2050-12-28 10.388748 75.0
2050-12-29 19.216660 75.0
2050-12-30 15.741111 75.0
2050-12-31 32.412021 75.0

1460 rows × 2 columns

[11]:
n.lopf(pyomo=False, multi_investment_periods=True)
INFO:pypsa.linopf:Perform multi-investment optimization.
INFO:pypsa.linopf:Prepare linear problem
INFO:pypsa.linopf:Total preparation time: 0.7s
INFO:pypsa.linopf:Solve linear problem using Glpk solver
INFO:pypsa.linopf:Optimization successful. Objective value: 1.82e+07
[11]:
('ok', 'optimal')
[12]:
c = "Generator"
df = pd.concat(
    {
        period: n.get_active_assets(c, period) * n.df(c).p_nom_opt
        for period in n.investment_periods
    },
    axis=1,
)
df.T.plot.bar(
    stacked=True,
    edgecolor="white",
    width=1,
    ylabel="Capacity",
    xlabel="Investment Period",
    rot=0,
    figsize=(10, 5),
)
plt.tight_layout()
../_images/examples_multi-investment-optimisation_17_0.png
[13]:
df = n.generators_t.p.sum(level=0).T
df.T.plot.bar(
    stacked=True,
    edgecolor="white",
    width=1,
    ylabel="Generation",
    xlabel="Investment Period",
    rot=0,
    figsize=(10, 5),
)
/tmp/ipykernel_3741/111636765.py:1: 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().
  df = n.generators_t.p.sum(level=0).T
[13]:
<AxesSubplot:xlabel='Investment Period', ylabel='Generation'>
../_images/examples_multi-investment-optimisation_18_2.png
[ ]: