Problem 10.2

Problem 10.2. Capacity and dispatch optimization in a network with a CO2 constraint.

We build on Problem 10.1 (d), i.e. we optimise F endogenously.

For (a)-(c), always calculate the following values:

• Total system costs (in bn EUR)

• Average electricity price (in EUR/MWh); number/share of hours with a price below 2 EUR/MWh

• Congestion rent

• Utilisation of transmission lines (in % of cap.)

• Total generation per technology (in TWh)

• CO2 price (in EUR/tCO2)

a) Set up a network as in 10.1d) and add a CO2 constraint of 2.5 MtCO2/year.

b) The load distribution between Denmark and Portugal is approx. 1:1.5. Assume that both countries have national targets of 1 MtCO2/year and 1.5 MtCO2/year.

c) Assume the CO2 limits from b, but that the transmission capacities is limited to 1 GW (still endougenously optimised).

d) Change the global CO2 limit to 0.25, 0.5, 1, 1.5, 2 MtCO2/year, and plot the total system costs against the CO2 limit.

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

Prerequisites: handling technology data and costs

We maintain a database (PyPSA/technology-data) which collects assumptions and projections for energy system technologies (such as costs, efficiencies, lifetimes, etc.) for given years, which we can load into a pandas.DataFrame. This requires some pre-processing to load (e.g. converting units, setting defaults, re-arranging dimensions):

year = 2030
url = f"https://raw.githubusercontent.com/PyPSA/technology-data/master/outputs/costs_{year}.csv"
costs = pd.read_csv(url, index_col=[0, 1])

costs.loc[costs.unit.str.contains("/kW"), "value"] *= 1e3
costs.unit = costs.unit.str.replace("/kW", "/MW")

defaults = {
    "FOM": 0,
    "VOM": 0,
    "efficiency": 1,
    "fuel": 0,
    "investment": 0,
    "lifetime": 25,
    "CO2 intensity": 0,
    "discount rate": 0.07,
}
costs = costs.value.unstack().fillna(defaults)

costs.at["OCGT", "fuel"] = costs.at["gas", "fuel"]
costs.at["OCGT", "CO2 intensity"] = costs.at["gas", "CO2 intensity"]
costs.at["CCGT", "CO2 intensity"] = costs.at["gas", "CO2 intensity"]

Let’s also write a small utility function that calculates the annuity to annualise investment costs. The formula is

\[ a(r, n) = \frac{r}{1-(1+r)^{-n}} \]

where \(r\) is the discount rate and \(n\) is the lifetime.

def annuity(r, n):
    return r / (1.0 - 1.0 / (1.0 + r) ** n)

annuity(0.07, 20)

0.09439292574325567

Based on this, we can calculate the marginal generation costs (€/MWh):

costs["marginal_cost"] = costs["VOM"] + costs["fuel"] / costs["efficiency"]

and the annualised investment costs (capital_cost in PyPSA terms, €/MW/a):

annuity = costs.apply(lambda x: annuity(x["discount rate"], x["lifetime"]), axis=1)

costs["capital_cost"] = (annuity + costs["FOM"] / 100) * costs["investment"]

We can now read the capital and marginal cost of onshore wind, solar and OCGT

costs.at["onwind", "capital_cost"] #EUR/MW/a

np.float64(101644.12332388277)

costs.at["solar", "capital_cost"] #EUR/MW/a

np.float64(51346.82981964593)

costs.at["OCGT", "capital_cost"] #EUR/MW/a

np.float64(47718.67056370105)

costs.at["OCGT", "marginal_cost"] #EUR/MWh

np.float64(64.6839512195122)

Retrieving time series data

In this example, wind data from https://zenodo.org/record/3253876#.XSiVOEdS8l0 and solar PV data from https://zenodo.org/record/2613651#.X0kbhDVS-uV is used. The data is downloaded in csv format and saved in the ‘data’ folder. The Pandas package is used as a convenient way of managing the datasets.

For convenience, the column including date information is converted into Datetime and set as index

data_solar = pd.read_csv('data/pv_optimal.csv',sep=';')
data_solar.index = pd.DatetimeIndex(data_solar['utc_time'])

data_wind = pd.read_csv('data/onshore_wind_1979-2017.csv',sep=';')
data_wind.index = pd.DatetimeIndex(data_wind['utc_time'])

data_el = pd.read_csv('data/electricity_demand.csv',sep=';')
data_el.index = pd.DatetimeIndex(data_el['utc_time'])

The data format can now be analyzed using the .head() function to show the first lines of the data set

data_solar.head()

	utc_time	AUT	BEL	BGR	BIH	CHE	CYP	CZE	DEU	DNK	...	MLT	NLD	NOR	POL	PRT	ROU	SRB	SVK	SVN	SWE
utc_time
1979-01-01 00:00:00+00:00	1979-01-01T00:00:00Z	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1979-01-01 01:00:00+00:00	1979-01-01T01:00:00Z	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1979-01-01 02:00:00+00:00	1979-01-01T02:00:00Z	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1979-01-01 03:00:00+00:00	1979-01-01T03:00:00Z	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1979-01-01 04:00:00+00:00	1979-01-01T04:00:00Z	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

5 rows × 33 columns

We will use timeseries for Portugal and Denmark in this excercise

countries = ['PRT', 'DNK']
coordinates = {'PRT': (38.74, -9.15), 'DNK': (55.67, 12.57)}

a. Add CO2 constraint, F endogenous.

For building the model, we start again by initialising an empty network, adding the snapshots, and the electricity buses.

n = pypsa.Network()
hours_in_2015 = pd.date_range('2015-01-01 00:00Z',
                              '2015-12-31 23:00Z',
                              freq='h')

n.set_snapshots(hours_in_2015.values)

for country in countries:
    n.add("Bus",
          country,
          y = coordinates[country][0],
          x = coordinates[country][1],
          carrier="AC"
          )

carriers = [
    "onwind",
    "solar",
    "OCGT",
]

n.madd(
    "Carrier",
    carriers,
    color=["dodgerblue", "gold", "indianred",],
    co2_emissions=[costs.at[c, "CO2 intensity"] for c in carriers],
)

/tmp/ipykernel_3054/68125439.py:7: DeprecatedWarning: madd is deprecated as of 0.31 and will be removed in 1.0. Use `n.add` as a drop-in replacement instead.
  n.madd(

Index(['onwind', 'solar', 'OCGT'], dtype='object')

# add load to the buses
for country in countries:
    n.add("Load",
        f"{country} load",
        bus=country,
        p_set=data_el[country].values,
        carrier = "AC")

for country in countries:
    n.add(
        "Generator",
        f"{country} OCGT",
        bus=country,
        carrier="OCGT",
        capital_cost=costs.at["OCGT", "capital_cost"],
        marginal_cost=costs.at["OCGT", "marginal_cost"],
        efficiency=costs.at["OCGT", "efficiency"],
        p_nom_extendable=True,
    )   
    CF_wind = data_wind[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
    n.add("Generator",
        f"{country} onwind",
        bus=country,
        carrier="onwind",
        capital_cost=costs.at["onwind", "capital_cost"],
        marginal_cost=costs.at["onwind", "marginal_cost"],
        p_max_pu=CF_wind.values,
        efficiency=costs.at["onwind", "efficiency"],
        p_nom_extendable=True,
    )
    CF_solar = data_solar[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
    n.add("Generator",
        f"{country} solar",
        bus=country,
        carrier="solar",
        capital_cost=costs.at["solar", "capital_cost"],
        marginal_cost=costs.at["solar", "marginal_cost"],
        p_max_pu=CF_solar.values,
        efficiency=costs.at["solar", "efficiency"],
        p_nom_extendable=True,
    )

Endogenous optimisation of AC line capacity (starting at 0 GW).

n.add(
    "Line",
    "PRT-DNK",
    bus0="PRT",
    bus1="DNK",
    s_nom = 0,
    x = 1,
    r = 1,
    capital_cost = costs.at["HVAC overhead", "capital_cost"] * 2477,
    s_nom_extendable = True,
)

Index(['PRT-DNK'], dtype='object')

Add global CO2 limit of 2.5 MtCO2/year.

n.add(
    "GlobalConstraint",
    "CO2Limit",
    carrier_attribute="co2_emissions",
    sense="<=",
    constant=2500000, #2.5MtCO2
)

Index(['CO2Limit'], dtype='object')

n.plot(bus_sizes=1, margin=1)

/tmp/ipykernel_3054/2753408878.py:1: DeprecatedWarning: plot is deprecated. Use `n.plot.map()` as a drop-in replacement instead.
  n.plot(bus_sizes=1, margin=1)

{'nodes': {'Bus': <matplotlib.collections.PatchCollection at 0x7efd46b01f90>},
 'branches': {'Line': <matplotlib.collections.LineCollection at 0x7efd46f1bd50>},
 'flows': {}}

n.optimize(solver_name="gurobi")

WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='Load')

WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='Line')

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='Bus')

INFO:linopy.model: Solve problem using Gurobi solver

INFO:linopy.io:Writing objective.

Writing constraints.:   0%|          | 0/10 [00:00<?, ?it/s]

Writing constraints.:  50%|█████     | 5/10 [00:00<00:00, 32.29it/s]

Writing constraints.:  90%|█████████ | 9/10 [00:00<00:00, 13.99it/s]

Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 16.23it/s]

Writing continuous variables.:   0%|          | 0/4 [00:00<?, ?it/s]

Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 39.00it/s]

Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 38.58it/s]

INFO:linopy.io: Writing time: 0.8s

Restricted license - for non-production use only - expires 2026-11-23

INFO:gurobipy:Restricted license - for non-production use only - expires 2026-11-23

Read LP format model from file /tmp/linopy-problem-2g1mj_wn.lp

INFO:gurobipy:Read LP format model from file /tmp/linopy-problem-2g1mj_wn.lp

Reading time = 0.18 seconds

INFO:gurobipy:Reading time = 0.18 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - "Ubuntu 24.04.2 LTS")

INFO:gurobipy:Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - "Ubuntu 24.04.2 LTS")

INFO:gurobipy:

CPU model: AMD EPYC 7763 64-Core Processor, instruction set [SSE2|AVX|AVX2]

INFO:gurobipy:CPU model: AMD EPYC 7763 64-Core Processor, instruction set [SSE2|AVX|AVX2]

Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

INFO:gurobipy:Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

INFO:gurobipy:

---------------------------------------------------------------------------
GurobiError                               Traceback (most recent call last)
Cell In[23], line 1
----> 1 n.optimize(solver_name="gurobi")

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/pypsa/optimization/optimize.py:633, in OptimizationAccessor.__call__(self, *args, **kwargs)
    631 @wraps(optimize)
    632 def __call__(self, *args: Any, **kwargs: Any) -> Any:
--> 633     return optimize(self.n, *args, **kwargs)

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/pypsa/optimization/optimize.py:605, in optimize(n, snapshots, multi_investment_periods, transmission_losses, linearized_unit_commitment, model_kwargs, extra_functionality, assign_all_duals, solver_name, solver_options, compute_infeasibilities, **kwargs)
    603 if extra_functionality:
    604     extra_functionality(n, sns)
--> 605 status, condition = m.solve(solver_name=solver_name, **solver_options, **kwargs)
    607 if status == "ok":
    608     assign_solution(n)

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/linopy/model.py:1206, in Model.solve(self, solver_name, io_api, explicit_coordinate_names, problem_fn, solution_fn, log_fn, basis_fn, warmstart_fn, keep_files, env, sanitize_zeros, sanitize_infinities, slice_size, remote, progress, **solver_options)
   1198             explicit_coordinate_names = False
   1199         problem_fn = self.to_file(
   1200             to_path(problem_fn),
   1201             io_api=io_api,
   (...)   1204             progress=progress,
   1205         )
-> 1206         result = solver.solve_problem_from_file(
   1207             problem_fn=to_path(problem_fn),
   1208             solution_fn=to_path(solution_fn),
   1209             log_fn=to_path(log_fn),
   1210             warmstart_fn=to_path(warmstart_fn),
   1211             basis_fn=to_path(basis_fn),
   1212             env=env,
   1213         )
   1215 finally:
   1216     for fn in (problem_fn, solution_fn):

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/linopy/solvers.py:1039, in Gurobi.solve_problem_from_file(self, problem_fn, solution_fn, log_fn, warmstart_fn, basis_fn, env)
   1035     env_ = env
   1037 m = gurobipy.read(problem_fn_, env=env_)
-> 1039 return self._solve(
   1040     m,
   1041     solution_fn=solution_fn,
   1042     log_fn=log_fn,
   1043     warmstart_fn=warmstart_fn,
   1044     basis_fn=basis_fn,
   1045     io_api=io_api,
   1046     sense=sense,
   1047 )

File /opt/hostedtoolcache/Python/3.11.12/x64/lib/python3.11/site-packages/linopy/solvers.py:1113, in Gurobi._solve(self, m, solution_fn, log_fn, warmstart_fn, basis_fn, io_api, sense)
   1111 if warmstart_fn is not None:
   1112     m.read(path_to_string(warmstart_fn))
-> 1113 m.optimize()
   1115 if basis_fn is not None:
   1116     try:

File src/gurobipy/_model.pyx:903, in gurobipy._model.Model.optimize()

GurobiError: Model too large for size-limited license; visit https://gurobi.com/unrestricted for more information

# Total system costs
n.objective/1e9

7.847091424204098

# Average electricity price
n.buses_t.marginal_price.mean()

Bus
PRT    126.774772
DNK    123.115762
dtype: float64

# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()

Bus
PRT    6803
DNK    6863
dtype: int64

# Share of hours with almost zero price
(n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count())/len(n.snapshots)

Bus
PRT    0.776598
DNK    0.783447
dtype: float64

# Congestion rent
((n.buses_t.marginal_price["PRT"] - n.buses_t.marginal_price["DNK"]) * n.lines_t.p0["PRT-DNK"]).sum()

np.float64(-412486852.2807891)

# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt

Line
PRT-DNK    0.629114
dtype: float64

# Total generation
n.generators_t.p.sum(axis=0).groupby([n.generators.bus, n.generators.carrier]).sum().div(1e6).round(1)

bus  carrier
DNK  OCGT        4.3
     onwind     14.5
     solar       2.0
PRT  OCGT        0.9
     onwind     46.9
     solar      13.2
dtype: float64

n.generators.efficiency

Generator
PRT OCGT      0.41
PRT onwind    1.00
PRT solar     1.00
DNK OCGT      0.41
DNK onwind    1.00
DNK solar     1.00
Name: efficiency, dtype: float64

# Total CO2 emissions
n.generators_t.p.sum(axis=0).groupby([n.generators.carrier]).sum()["OCGT"] * (costs.at["OCGT", "CO2 intensity"] / costs.at["OCGT", "efficiency"])

np.float64(2500000.00000152)

# CO2 price
n.global_constraints

attribute	type	investment_period	carrier_attribute	sense	constant	mu
GlobalConstraint
CO2Limit	primary_energy	NaN	co2_emissions	<=	2500000.0	-981.629031

b. National CO2 limits, F endogenous.

n = pypsa.Network()
hours_in_2015 = pd.date_range('2015-01-01 00:00Z',
                              '2015-12-31 23:00Z',
                              freq='h')

n.set_snapshots(hours_in_2015.values)

for country in countries:
    n.add("Bus",
          country,
          y = coordinates[country][0],
          x = coordinates[country][1],
          carrier="AC"
          )

carriers = [
    "onwind",
    "solar",
    "OCGT",
]

n.madd(
    "Carrier",
    carriers,
    color=["dodgerblue", "gold", "indianred",],
    co2_emissions=[costs.at[c, "CO2 intensity"] for c in carriers],
)
# add load to the bus
for country in countries:
    n.add("Load",
        f"{country} load",
        bus=country,
        p_set=data_el[country].values,
        carrier = "AC")
for country in countries:
    n.add(
        "Generator",
        f"{country} OCGT",
        bus=country,
        carrier="OCGT",
        capital_cost=costs.at["OCGT", "capital_cost"],
        marginal_cost=costs.at["OCGT", "marginal_cost"],
        efficiency=costs.at["OCGT", "efficiency"],
        p_nom_extendable=True,
    )   
    CF_wind = data_wind[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
    n.add("Generator",
        f"{country} onwind",
        bus=country,
        carrier="onwind",
        capital_cost=costs.at["onwind", "capital_cost"],
        marginal_cost=costs.at["onwind", "marginal_cost"],
        p_max_pu=CF_wind.values,
        efficiency=costs.at["onwind", "efficiency"],
        p_nom_extendable=True,
    )
    CF_solar = data_solar[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
    n.add("Generator",
        f"{country} solar",
        bus=country,
        carrier="solar",
        capital_cost=costs.at["solar", "capital_cost"],
        marginal_cost=costs.at["solar", "marginal_cost"],
        p_max_pu=CF_solar.values,
        efficiency=costs.at["solar", "efficiency"],
        p_nom_extendable=True,
    )
n.add(
    "Line",
    "PRT-DNK",
    bus0="PRT",
    bus1="DNK",
    s_nom = 0,
    x = 1,
    r = 1,
    capital_cost = costs.at["HVAC overhead", "capital_cost"] * 2477,
    s_nom_extendable = True,
)

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})

Add national CO2 limits of 1 MtCO2/year for Denmark and 1.5 MtCO2/year for Portugal. Use the hint from the problem description for the code.

n.optimize.create_model()
co2_emission_factor = (costs.at["OCGT", "CO2 intensity"] / costs.at["OCGT", "efficiency"])
n.model.add_constraints(
(n.model.variables["Generator-p"].sum("snapshot") * [co2_emission_factor,0,0,co2_emission_factor,0,0]).groupby(n.generators.bus.to_xarray()).sum(),
    "<=",
    [1000000,1500000],
    name="CO2Limit"
)

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)

Constraint `CO2Limit` (bus: 2):
-------------------------------
[DNK]: +0.4829 Generator-p[2015-01-01 00:00:00, DNK OCGT] + 0 Generator-p[2015-01-01 00:00:00, DNK onwind] + 0 Generator-p[2015-01-01 00:00:00, DNK solar] ... +0.4829 Generator-p[2015-12-31 23:00:00, DNK OCGT] + 0 Generator-p[2015-12-31 23:00:00, DNK onwind] + 0 Generator-p[2015-12-31 23:00:00, DNK solar] ≤ 1000000.0
[PRT]: +0.4829 Generator-p[2015-01-01 00:00:00, PRT OCGT] + 0 Generator-p[2015-01-01 00:00:00, PRT onwind] + 0 Generator-p[2015-01-01 00:00:00, PRT solar] ... +0.4829 Generator-p[2015-12-31 23:00:00, PRT OCGT] + 0 Generator-p[2015-12-31 23:00:00, PRT onwind] + 0 Generator-p[2015-12-31 23:00:00, PRT solar] ≤ 1500000.0

Use hint from the problem description.

n.optimize.solve_model(solver_name="gurobi")

INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 38.61it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 91.28it/s]
INFO:linopy.io: Writing time: 0.34s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-m3kr3kmu.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-m3kr3kmu.lp

Reading time = 0.12 seconds

INFO:gurobipy:Reading time = 0.12 seconds

obj: 140169 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140169 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140169 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140169 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0x8f4082ce

INFO:gurobipy:Model fingerprint: 0x8f4082ce

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 2e+06]

INFO:gurobipy:  RHS range        [2e+03, 2e+06]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70107 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70107 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.270e+05

INFO:gurobipy: AA' NZ     : 2.270e+05

 Factor NZ  : 8.885e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.885e+05 (roughly 50 MB of memory)

 Factor Ops : 1.178e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.178e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   4.22687050e+11  0.00000000e+00  1.26e+09 0.00e+00  1.90e+08     0s

INFO:gurobipy:   0   4.22687050e+11  0.00000000e+00  1.26e+09 0.00e+00  1.90e+08     0s

   1   4.90288192e+11 -9.52973816e+10  2.47e+08 2.23e+02  4.62e+07     0s

INFO:gurobipy:   1   4.90288192e+11 -9.52973816e+10  2.47e+08 2.23e+02  4.62e+07     0s

   2   3.68025619e+11 -1.10031293e+11  1.35e+07 1.70e+00  4.16e+06     0s

INFO:gurobipy:   2   3.68025619e+11 -1.10031293e+11  1.35e+07 1.70e+00  4.16e+06     0s

   3   6.25070764e+10 -3.55890244e+10  1.49e+06 2.36e-09  7.15e+05     0s

INFO:gurobipy:   3   6.25070764e+10 -3.55890244e+10  1.49e+06 2.36e-09  7.15e+05     0s

   4   3.94367930e+10 -1.90579737e+10  8.61e+05 8.73e-10  4.16e+05     0s

INFO:gurobipy:   4   3.94367930e+10 -1.90579737e+10  8.61e+05 8.73e-10  4.16e+05     0s

   5   2.93408898e+10 -1.42914113e+10  5.95e+05 5.24e-10  3.07e+05     0s

INFO:gurobipy:   5   2.93408898e+10 -1.42914113e+10  5.95e+05 5.24e-10  3.07e+05     0s

   6   2.35119955e+10 -9.51457735e+09  4.41e+05 9.90e-10  2.30e+05     0s

INFO:gurobipy:   6   2.35119955e+10 -9.51457735e+09  4.41e+05 9.90e-10  2.30e+05     0s

   7   1.79605788e+10 -3.31826418e+09  3.00e+05 1.75e-10  1.47e+05     0s

INFO:gurobipy:   7   1.79605788e+10 -3.31826418e+09  3.00e+05 1.75e-10  1.47e+05     0s

   8   1.38816008e+10 -9.70796913e+07  1.99e+05 2.62e-10  9.61e+04     0s

INFO:gurobipy:   8   1.38816008e+10 -9.70796913e+07  1.99e+05 2.62e-10  9.61e+04     0s

   9   1.20573576e+10  7.52858379e+08  1.52e+05 1.60e-10  7.76e+04     0s

INFO:gurobipy:   9   1.20573576e+10  7.52858379e+08  1.52e+05 1.60e-10  7.76e+04     0s

  10   1.17211670e+10  1.16006953e+09  1.42e+05 4.66e-10  7.24e+04     0s

INFO:gurobipy:  10   1.17211670e+10  1.16006953e+09  1.42e+05 4.66e-10  7.24e+04     0s

  11   1.10283102e+10  3.12477349e+09  1.24e+05 9.60e-10  5.42e+04     0s

INFO:gurobipy:  11   1.10283102e+10  3.12477349e+09  1.24e+05 9.60e-10  5.42e+04     0s

  12   1.03576993e+10  4.10629529e+09  1.05e+05 1.16e-10  4.29e+04     0s

INFO:gurobipy:  12   1.03576993e+10  4.10629529e+09  1.05e+05 1.16e-10  4.29e+04     0s

  13   9.64387635e+09  4.74351205e+09  8.38e+04 3.20e-10  3.36e+04     0s

INFO:gurobipy:  13   9.64387635e+09  4.74351205e+09  8.38e+04 3.20e-10  3.36e+04     0s

  14   9.46687735e+09  5.07032132e+09  7.84e+04 9.31e-10  3.02e+04     0s

INFO:gurobipy:  14   9.46687735e+09  5.07032132e+09  7.84e+04 9.31e-10  3.02e+04     0s

  15   9.27846728e+09  5.59116180e+09  6.82e+04 2.33e-10  2.53e+04     0s

INFO:gurobipy:  15   9.27846728e+09  5.59116180e+09  6.82e+04 2.33e-10  2.53e+04     0s

  16   8.88778551e+09  5.82291364e+09  5.26e+04 9.31e-10  2.10e+04     0s

INFO:gurobipy:  16   8.88778551e+09  5.82291364e+09  5.26e+04 9.31e-10  2.10e+04     0s

  17   8.57481178e+09  6.00150203e+09  3.88e+04 5.82e-10  1.76e+04     0s

INFO:gurobipy:  17   8.57481178e+09  6.00150203e+09  3.88e+04 5.82e-10  1.76e+04     0s

  18   8.49108031e+09  6.12319302e+09  3.51e+04 4.95e-10  1.62e+04     0s

INFO:gurobipy:  18   8.49108031e+09  6.12319302e+09  3.51e+04 4.95e-10  1.62e+04     0s

  19   8.40165307e+09  6.24855400e+09  3.07e+04 3.20e-10  1.47e+04     0s

INFO:gurobipy:  19   8.40165307e+09  6.24855400e+09  3.07e+04 3.20e-10  1.47e+04     0s

  20   8.30562001e+09  6.61654176e+09  2.57e+04 2.62e-10  1.16e+04     0s

INFO:gurobipy:  20   8.30562001e+09  6.61654176e+09  2.57e+04 2.62e-10  1.16e+04     0s

  21   8.23620308e+09  6.69051639e+09  2.19e+04 8.44e-10  1.06e+04     1s

INFO:gurobipy:  21   8.23620308e+09  6.69051639e+09  2.19e+04 8.44e-10  1.06e+04     1s

  22   8.14246062e+09  7.00230551e+09  1.72e+04 4.07e-10  7.80e+03     1s

INFO:gurobipy:  22   8.14246062e+09  7.00230551e+09  1.72e+04 4.07e-10  7.80e+03     1s

  23   8.10863664e+09  7.09088892e+09  1.55e+04 9.31e-10  6.96e+03     1s

INFO:gurobipy:  23   8.10863664e+09  7.09088892e+09  1.55e+04 9.31e-10  6.96e+03     1s

  24   8.07383512e+09  7.15995037e+09  1.39e+04 1.02e-10  6.25e+03     1s

INFO:gurobipy:  24   8.07383512e+09  7.15995037e+09  1.39e+04 1.02e-10  6.25e+03     1s

  25   8.04599284e+09  7.20276314e+09  1.24e+04 1.31e-10  5.76e+03     1s

INFO:gurobipy:  25   8.04599284e+09  7.20276314e+09  1.24e+04 1.31e-10  5.76e+03     1s

  26   8.03457672e+09  7.23105147e+09  1.17e+04 5.82e-10  5.49e+03     1s

INFO:gurobipy:  26   8.03457672e+09  7.23105147e+09  1.17e+04 5.82e-10  5.49e+03     1s

  27   8.02939494e+09  7.28075316e+09  1.15e+04 0.00e+00  5.12e+03     1s

INFO:gurobipy:  27   8.02939494e+09  7.28075316e+09  1.15e+04 0.00e+00  5.12e+03     1s

  28   7.99707169e+09  7.33866458e+09  9.18e+03 0.00e+00  4.50e+03     1s

INFO:gurobipy:  28   7.99707169e+09  7.33866458e+09  9.18e+03 0.00e+00  4.50e+03     1s

  29   7.97399394e+09  7.42076690e+09  7.93e+03 1.16e-10  3.78e+03     1s

INFO:gurobipy:  29   7.97399394e+09  7.42076690e+09  7.93e+03 1.16e-10  3.78e+03     1s

  30   7.95708928e+09  7.45365040e+09  6.95e+03 6.98e-10  3.44e+03     1s

INFO:gurobipy:  30   7.95708928e+09  7.45365040e+09  6.95e+03 6.98e-10  3.44e+03     1s

  31   7.94385375e+09  7.52495702e+09  6.13e+03 3.20e-10  2.86e+03     1s

INFO:gurobipy:  31   7.94385375e+09  7.52495702e+09  6.13e+03 3.20e-10  2.86e+03     1s

  32   7.93106549e+09  7.54303948e+09  5.36e+03 2.04e-10  2.65e+03     1s

INFO:gurobipy:  32   7.93106549e+09  7.54303948e+09  5.36e+03 2.04e-10  2.65e+03     1s

  33   7.91815204e+09  7.57406296e+09  4.56e+03 6.98e-10  2.35e+03     1s

INFO:gurobipy:  33   7.91815204e+09  7.57406296e+09  4.56e+03 6.98e-10  2.35e+03     1s

  34   7.91368145e+09  7.60416310e+09  4.19e+03 3.78e-10  2.11e+03     1s

INFO:gurobipy:  34   7.91368145e+09  7.60416310e+09  4.19e+03 3.78e-10  2.11e+03     1s

  35   7.90119741e+09  7.63082788e+09  3.30e+03 9.02e-10  1.84e+03     1s

INFO:gurobipy:  35   7.90119741e+09  7.63082788e+09  3.30e+03 9.02e-10  1.84e+03     1s

  36   7.89107282e+09  7.64918681e+09  2.70e+03 4.07e-10  1.65e+03     1s

INFO:gurobipy:  36   7.89107282e+09  7.64918681e+09  2.70e+03 4.07e-10  1.65e+03     1s

  37   7.88167030e+09  7.67136922e+09  1.99e+03 7.46e-11  1.43e+03     1s

INFO:gurobipy:  37   7.88167030e+09  7.67136922e+09  1.99e+03 7.46e-11  1.43e+03     1s

  38   7.87817050e+09  7.68664083e+09  1.74e+03 1.08e-09  1.30e+03     1s

INFO:gurobipy:  38   7.87817050e+09  7.68664083e+09  1.74e+03 1.08e-09  1.30e+03     1s

  39   7.87338554e+09  7.70242176e+09  1.44e+03 3.20e-10  1.16e+03     1s

INFO:gurobipy:  39   7.87338554e+09  7.70242176e+09  1.44e+03 3.20e-10  1.16e+03     1s

  40   7.86504710e+09  7.73880915e+09  9.17e+02 4.37e-10  8.55e+02     1s

INFO:gurobipy:  40   7.86504710e+09  7.73880915e+09  9.17e+02 4.37e-10  8.55e+02     1s

  41   7.86136506e+09  7.75410198e+09  6.85e+02 1.16e-10  7.26e+02     1s

INFO:gurobipy:  41   7.86136506e+09  7.75410198e+09  6.85e+02 1.16e-10  7.26e+02     1s

  42   7.85836252e+09  7.76340787e+09  5.28e+02 8.44e-10  6.42e+02     1s

INFO:gurobipy:  42   7.85836252e+09  7.76340787e+09  5.28e+02 8.44e-10  6.42e+02     1s

  43   7.85708174e+09  7.77159874e+09  4.61e+02 3.78e-10  5.78e+02     1s

INFO:gurobipy:  43   7.85708174e+09  7.77159874e+09  4.61e+02 3.78e-10  5.78e+02     1s

  44   7.85622013e+09  7.77935754e+09  4.15e+02 1.02e-09  5.19e+02     1s

INFO:gurobipy:  44   7.85622013e+09  7.77935754e+09  4.15e+02 1.02e-09  5.19e+02     1s

  45   7.85542778e+09  7.78407010e+09  3.72e+02 5.24e-10  4.82e+02     1s

INFO:gurobipy:  45   7.85542778e+09  7.78407010e+09  3.72e+02 5.24e-10  4.82e+02     1s

  46   7.85452813e+09  7.78735445e+09  3.25e+02 4.07e-10  4.54e+02     1s

INFO:gurobipy:  46   7.85452813e+09  7.78735445e+09  3.25e+02 4.07e-10  4.54e+02     1s

  47   7.85390975e+09  7.79229725e+09  2.94e+02 2.62e-10  4.16e+02     1s

INFO:gurobipy:  47   7.85390975e+09  7.79229725e+09  2.94e+02 2.62e-10  4.16e+02     1s

  48   7.85350401e+09  7.79582702e+09  2.73e+02 4.07e-10  3.90e+02     1s

INFO:gurobipy:  48   7.85350401e+09  7.79582702e+09  2.73e+02 4.07e-10  3.90e+02     1s

  49   7.85304180e+09  7.79742066e+09  2.49e+02 7.57e-10  3.76e+02     1s

INFO:gurobipy:  49   7.85304180e+09  7.79742066e+09  2.49e+02 7.57e-10  3.76e+02     1s

  50   7.85197024e+09  7.80249496e+09  2.00e+02 4.95e-10  3.34e+02     1s

INFO:gurobipy:  50   7.85197024e+09  7.80249496e+09  2.00e+02 4.95e-10  3.34e+02     1s

  51   7.85156153e+09  7.80675314e+09  1.80e+02 6.66e-10  3.02e+02     1s

INFO:gurobipy:  51   7.85156153e+09  7.80675314e+09  1.80e+02 6.66e-10  3.02e+02     1s

  52   7.85045436e+09  7.80925104e+09  1.34e+02 1.01e-09  2.78e+02     1s

INFO:gurobipy:  52   7.85045436e+09  7.80925104e+09  1.34e+02 1.01e-09  2.78e+02     1s

  53   7.84977374e+09  7.81292637e+09  9.86e+01 2.06e-09  2.48e+02     1s

INFO:gurobipy:  53   7.84977374e+09  7.81292637e+09  9.86e+01 2.06e-09  2.48e+02     1s

  54   7.84966032e+09  7.81660376e+09  9.24e+01 2.72e-09  2.23e+02     1s

INFO:gurobipy:  54   7.84966032e+09  7.81660376e+09  9.24e+01 2.72e-09  2.23e+02     1s

  55   7.84939407e+09  7.82284794e+09  8.26e+01 3.52e-09  1.79e+02     1s

INFO:gurobipy:  55   7.84939407e+09  7.82284794e+09  8.26e+01 3.52e-09  1.79e+02     1s

  56   7.84914811e+09  7.82812337e+09  7.33e+01 3.61e-09  1.42e+02     1s

INFO:gurobipy:  56   7.84914811e+09  7.82812337e+09  7.33e+01 3.61e-09  1.42e+02     1s

  57   7.84849761e+09  7.83061073e+09  4.34e+01 3.37e-09  1.20e+02     1s

INFO:gurobipy:  57   7.84849761e+09  7.83061073e+09  4.34e+01 3.37e-09  1.20e+02     1s

  58   7.84835285e+09  7.83211728e+09  3.67e+01 3.28e-09  1.09e+02     1s

INFO:gurobipy:  58   7.84835285e+09  7.83211728e+09  3.67e+01 3.28e-09  1.09e+02     1s

  59   7.84820241e+09  7.83289540e+09  3.24e+01 3.66e-09  1.03e+02     1s

INFO:gurobipy:  59   7.84820241e+09  7.83289540e+09  3.24e+01 3.66e-09  1.03e+02     1s

  60   7.84807438e+09  7.83442807e+09  2.88e+01 3.64e-09  9.19e+01     1s

INFO:gurobipy:  60   7.84807438e+09  7.83442807e+09  2.88e+01 3.64e-09  9.19e+01     1s

  61   7.84790371e+09  7.83637490e+09  2.28e+01 3.70e-09  7.76e+01     1s

INFO:gurobipy:  61   7.84790371e+09  7.83637490e+09  2.28e+01 3.70e-09  7.76e+01     1s

  62   7.84729506e+09  7.84143319e+09  1.27e+00 2.24e-09  3.94e+01     1s

INFO:gurobipy:  62   7.84729506e+09  7.84143319e+09  1.27e+00 2.24e-09  3.94e+01     1s

  63   7.84720208e+09  7.84371708e+09  5.96e-01 2.03e-09  2.34e+01     1s

INFO:gurobipy:  63   7.84720208e+09  7.84371708e+09  5.96e-01 2.03e-09  2.34e+01     1s

  64   7.84713870e+09  7.84389615e+09  1.97e-01 1.88e-09  2.18e+01     1s

INFO:gurobipy:  64   7.84713870e+09  7.84389615e+09  1.97e-01 1.88e-09  2.18e+01     1s

  65   7.84712850e+09  7.84598907e+09  8.90e-02 3.71e-10  7.65e+00     1s

INFO:gurobipy:  65   7.84712850e+09  7.84598907e+09  8.90e-02 3.71e-10  7.65e+00     1s

  66   7.84710573e+09  7.84631077e+09  1.90e-02 3.78e-10  5.34e+00     1s

INFO:gurobipy:  66   7.84710573e+09  7.84631077e+09  1.90e-02 3.78e-10  5.34e+00     1s

  67   7.84709645e+09  7.84694184e+09  4.61e-03 6.40e-10  1.04e+00     1s

INFO:gurobipy:  67   7.84709645e+09  7.84694184e+09  4.61e-03 6.40e-10  1.04e+00     1s

  68   7.84709165e+09  7.84706339e+09  5.92e-05 1.06e-10  1.90e-01     1s

INFO:gurobipy:  68   7.84709165e+09  7.84706339e+09  5.92e-05 1.06e-10  1.90e-01     1s

  69   7.84709149e+09  7.84709089e+09  1.17e-06 3.03e-09  4.08e-03     1s

INFO:gurobipy:  69   7.84709149e+09  7.84709089e+09  1.17e-06 3.03e-09  4.08e-03     1s

  70   7.84709142e+09  7.84709142e+09  1.61e-08 1.00e-08  1.89e-08     1s

INFO:gurobipy:  70   7.84709142e+09  7.84709142e+09  1.61e-08 1.00e-08  1.89e-08     1s

  71   7.84709142e+09  7.84709142e+09  4.89e-07 9.84e-09  7.29e-12     1s

INFO:gurobipy:  71   7.84709142e+09  7.84709142e+09  4.89e-07 9.84e-09  7.29e-12     1s

INFO:gurobipy:

Barrier solved model in 71 iterations and 1.24 seconds (2.03 work units)

INFO:gurobipy:Barrier solved model in 71 iterations and 1.24 seconds (2.03 work units)

Optimal objective 7.84709142e+09

INFO:gurobipy:Optimal objective 7.84709142e+09

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      51 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:      51 DPushes remaining with DInf 0.0000000e+00                 1s

       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 1s

Warning: Markowitz tolerance tightened to 0.25

INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.25

INFO:gurobipy:

    8562 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:    8562 PPushes remaining with PInf 0.0000000e+00                 1s

       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 5.0723592e-09      2s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 5.0723592e-09      2s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8616    7.8470914e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:    8616    7.8470914e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:

Solved in 8616 iterations and 1.57 seconds (3.31 work units)

INFO:gurobipy:Solved in 8616 iterations and 1.57 seconds (3.31 work units)

Optimal objective  7.847091424e+09

INFO:gurobipy:Optimal objective  7.847091424e+09
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140169 duals
Objective: 7.85e+09
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper, CO2Limit were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)

('ok', 'optimal')

# Total system costs
n.objective/1e9

7.847091424204208

# Average electricity price
n.buses_t.marginal_price.mean()

Bus
PRT    126.774772
DNK    123.115762
dtype: float64

# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()

Bus
PRT    6803
DNK    6863
dtype: int64

# Share of hours with almost zero price
(n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count())/len(n.snapshots)

Bus
PRT    0.776598
DNK    0.783447
dtype: float64

# Congestion rent
((n.buses_t.marginal_price["PRT"] - n.buses_t.marginal_price["DNK"]) * n.lines_t.p0["PRT-DNK"]).sum()

np.float64(-412486852.28078794)

# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt

Line
PRT-DNK    0.628392
dtype: float64

# Total generation
n.generators_t.p.sum(axis=0).groupby([n.generators.bus, n.generators.carrier]).sum().div(1e6).round(1)

bus  carrier
DNK  OCGT        2.1
     onwind     14.5
     solar       2.0
PRT  OCGT        3.1
     onwind     46.9
     solar      13.2
dtype: float64

n.generators.efficiency

Generator
PRT OCGT      0.41
PRT onwind    1.00
PRT solar     1.00
DNK OCGT      0.41
DNK onwind    1.00
DNK solar     1.00
Name: efficiency, dtype: float64

# Total CO2 emissions
n.generators_t.p.sum(axis=0).groupby([n.generators.carrier]).sum()["OCGT"] * (costs.at["OCGT", "CO2 intensity"] / costs.at["OCGT", "efficiency"])

np.float64(2500000.000001519)

Use hint from the problem description.

n.model.dual

<xarray.Dataset> Size: 1MB
Dimensions:                    (Generator-ext: 6, Line-ext: 1, snapshot: 8760,
                                Bus: 2, bus: 2)
Coordinates:
  * Generator-ext              (Generator-ext) object 48B 'PRT OCGT' ... 'DNK...
  * Line-ext                   (Line-ext) object 8B 'PRT-DNK'
  * snapshot                   (snapshot) datetime64[ns] 70kB 2015-01-01 ... ...
  * Bus                        (Bus) object 16B 'PRT' 'DNK'
  * bus                        (bus) object 16B 'DNK' 'PRT'
Data variables:
    Generator-ext-p_nom-lower  (Generator-ext) float64 48B 0.0 0.0 ... 0.0 0.0
    Generator-ext-p_nom-upper  (Generator-ext) float64 48B nan nan ... nan nan
    Line-ext-s_nom-lower       (Line-ext) float64 8B 0.0
    Line-ext-s_nom-upper       (Line-ext) float64 8B nan
    Generator-ext-p-lower      (snapshot, Generator-ext) float64 420kB 537.3 ...
    Generator-ext-p-upper      (snapshot, Generator-ext) float64 420kB 0.0 .....
    Line-ext-s-lower           (snapshot, Line-ext) float64 70kB 0.0 0.0 ... 0.0
    Line-ext-s-upper           (snapshot, Line-ext) float64 70kB 0.0 0.0 ... 0.0
    Bus-nodal_balance          (Bus, snapshot) float64 140kB 1.429 ... 1.429
    CO2Limit                   (bus) float64 16B -981.6 -981.6

xarray.Dataset

• Dimensions:
  • Generator-ext: 6
  • Line-ext: 1
  • snapshot: 8760
  • Bus: 2
  • bus: 2
• Coordinates: (5)
  • Generator-ext
    (Generator-ext)
    object
    'PRT OCGT' ... 'DNK solar'

    array(['PRT OCGT', 'PRT onwind', 'PRT solar', 'DNK OCGT', 'DNK onwind',
           'DNK solar'], dtype=object)

  • Line-ext
    (Line-ext)
    object
    'PRT-DNK'

    array(['PRT-DNK'], dtype=object)

  • snapshot
    (snapshot)
    datetime64[ns]
    2015-01-01 ... 2015-12-31T23:00:00

    array(['2015-01-01T00:00:00.000000000', '2015-01-01T01:00:00.000000000',
           '2015-01-01T02:00:00.000000000', ..., '2015-12-31T21:00:00.000000000',
           '2015-12-31T22:00:00.000000000', '2015-12-31T23:00:00.000000000'],
          shape=(8760,), dtype='datetime64[ns]')

  • Bus
    (Bus)
    object
    'PRT' 'DNK'

    array(['PRT', 'DNK'], dtype=object)

  • bus
    (bus)
    object
    'DNK' 'PRT'

    array(['DNK', 'PRT'], dtype=object)

• Data variables: (10)
  • Generator-ext-p_nom-lower
    (Generator-ext)
    float64
    0.0 0.0 0.0 0.0 0.0 0.0

    array([0., 0., 0., 0., 0., 0.])

  • Generator-ext-p_nom-upper
    (Generator-ext)
    float64
    nan nan nan nan nan nan

    array([nan, nan, nan, nan, nan, nan])

  • Line-ext-s_nom-lower
    (Line-ext)
    float64
    0.0

    array([0.])

  • Line-ext-s_nom-upper
    (Line-ext)
    float64
    nan

    array([nan])

  • Generator-ext-p-lower
    (snapshot, Generator-ext)
    float64
    537.3 0.0 0.0 ... 537.3 0.0 0.0

    array([[537.31034687,   0.        ,   0.        , 537.31034687,
              0.        ,   0.        ],
           [537.31034687,   0.        ,   0.        , 537.31034687,
              0.        ,   0.        ],
           [537.31034687,   0.        ,   0.        , 537.31034687,
              0.        ,   0.        ],
           ...,
           [ -0.        ,   0.        ,   0.        ,   0.        ,
              0.        ,   0.        ],
           [  0.        ,   0.        ,   0.        ,  -0.        ,
              0.        ,   0.        ],
           [537.31034687,   0.        ,   0.        , 537.31034687,
              0.        ,   0.        ]], shape=(8760, 6))

  • Generator-ext-p-upper
    (snapshot, Generator-ext)
    float64
    0.0 0.0 -1.418 ... 0.0 0.0 -1.418

    array([[   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           ...,
           [   0.        , -537.31034687, -538.72834687,    0.        ,
            -537.31034687, -538.72834687],
           [   0.        , -537.31034687, -538.72834687,    0.        ,
            -537.31034687, -538.72834687],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ]], shape=(8760, 6))

  • Line-ext-s-lower
    (snapshot, Line-ext)
    float64
    0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0

    array([[0.],
           [0.],
           [0.],
           ...,
           [0.],
           [0.],
           [0.]], shape=(8760, 1))

  • Line-ext-s-upper
    (snapshot, Line-ext)
    float64
    0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0

    array([[0.],
           [0.],
           [0.],
           ...,
           [0.],
           [0.],
           [0.]], shape=(8760, 1))

  • Bus-nodal_balance
    (Bus, snapshot)
    float64
    1.429 1.429 1.429 ... 538.7 1.429

    array([[  1.4286    ,   1.4286    ,   1.4286    , ..., 538.73894687,
            538.73894687,   1.4286    ],
           [  1.4286    ,   1.4286    ,   1.4286    , ..., 538.73894687,
            538.73894687,   1.4286    ]], shape=(2, 8760))

  • CO2Limit
    (bus)
    float64
    -981.6 -981.6

    array([-981.62903139, -981.62903139])

• Indexes: (5)
  • Generator-ext
    PandasIndex

    PandasIndex(Index(['PRT OCGT', 'PRT onwind', 'PRT solar', 'DNK OCGT', 'DNK onwind',
           'DNK solar'],
          dtype='object', name='Generator-ext'))

  • Line-ext
    PandasIndex

    PandasIndex(Index(['PRT-DNK'], dtype='object', name='Line-ext'))

  • snapshot
    PandasIndex

    PandasIndex(DatetimeIndex(['2015-01-01 00:00:00', '2015-01-01 01:00:00',
                   '2015-01-01 02:00:00', '2015-01-01 03:00:00',
                   '2015-01-01 04:00:00', '2015-01-01 05:00:00',
                   '2015-01-01 06:00:00', '2015-01-01 07:00:00',
                   '2015-01-01 08:00:00', '2015-01-01 09:00:00',
                   ...
                   '2015-12-31 14:00:00', '2015-12-31 15:00:00',
                   '2015-12-31 16:00:00', '2015-12-31 17:00:00',
                   '2015-12-31 18:00:00', '2015-12-31 19:00:00',
                   '2015-12-31 20:00:00', '2015-12-31 21:00:00',
                   '2015-12-31 22:00:00', '2015-12-31 23:00:00'],
                  dtype='datetime64[ns]', name='snapshot', length=8760, freq=None))

  • Bus
    PandasIndex

    PandasIndex(Index(['PRT', 'DNK'], dtype='object', name='Bus'))

  • bus
    PandasIndex

    PandasIndex(Index(['DNK', 'PRT'], dtype='object', name='bus'))

• Attributes: (0)

c. National targets, transmission capacity limited to 1 GW, F endogenous.

n = pypsa.Network()
hours_in_2015 = pd.date_range('2015-01-01 00:00Z',
                              '2015-12-31 23:00Z',
                              freq='h')

n.set_snapshots(hours_in_2015.values)

for country in countries:
    n.add("Bus",
          country,
          y = coordinates[country][0],
          x = coordinates[country][1],
          carrier="AC"
          )

carriers = [
    "onwind",
    "solar",
    "OCGT",
]

n.madd(
    "Carrier",
    carriers,
    color=["dodgerblue", "gold", "indianred",],
    co2_emissions=[costs.at[c, "CO2 intensity"] for c in carriers],
)
# add load to the bus
for country in countries:
    n.add("Load",
        f"{country} load",
        bus=country,
        p_set=data_el[country].values,
        carrier = "AC")
for country in countries:
    n.add(
        "Generator",
        f"{country} OCGT",
        bus=country,
        carrier="OCGT",
        capital_cost=costs.at["OCGT", "capital_cost"],
        marginal_cost=costs.at["OCGT", "marginal_cost"],
        efficiency=costs.at["OCGT", "efficiency"],
        p_nom_extendable=True,
    )   
    CF_wind = data_wind[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
    n.add("Generator",
        f"{country} onwind",
        bus=country,
        carrier="onwind",
        capital_cost=costs.at["onwind", "capital_cost"],
        marginal_cost=costs.at["onwind", "marginal_cost"],
        p_max_pu=CF_wind.values,
        efficiency=costs.at["onwind", "efficiency"],
        p_nom_extendable=True,
    )
    CF_solar = data_solar[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
    n.add("Generator",
        f"{country} solar",
        bus=country,
        carrier="solar",
        capital_cost=costs.at["solar", "capital_cost"],
        marginal_cost=costs.at["solar", "marginal_cost"],
        p_max_pu=CF_solar.values,
        efficiency=costs.at["solar", "efficiency"],
        p_nom_extendable=True,
    )
n.add(
    "Line",
    "PRT-DNK",
    bus0="PRT",
    bus1="DNK",
    s_nom = 0,
    x = 1,
    r = 1,
    capital_cost = costs.at["HVAC overhead", "capital_cost"] * 2477,
    s_nom_max = 1000,
    s_nom_extendable = True,
)

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})

n.optimize.create_model()
co2_emission_factor = (costs.at["OCGT", "CO2 intensity"] / costs.at["OCGT", "efficiency"])
n.model.add_constraints(
(n.model.variables["Generator-p"].sum("snapshot") * [co2_emission_factor,0,0,co2_emission_factor,0,0]).groupby(n.generators.bus.to_xarray()).sum(),
    "<=",
    [1000000,1500000],
    name="CO2Limit"
)

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)

Constraint `CO2Limit` (bus: 2):
-------------------------------
[DNK]: +0.4829 Generator-p[2015-01-01 00:00:00, DNK OCGT] + 0 Generator-p[2015-01-01 00:00:00, DNK onwind] + 0 Generator-p[2015-01-01 00:00:00, DNK solar] ... +0.4829 Generator-p[2015-12-31 23:00:00, DNK OCGT] + 0 Generator-p[2015-12-31 23:00:00, DNK onwind] + 0 Generator-p[2015-12-31 23:00:00, DNK solar] ≤ 1000000.0
[PRT]: +0.4829 Generator-p[2015-01-01 00:00:00, PRT OCGT] + 0 Generator-p[2015-01-01 00:00:00, PRT onwind] + 0 Generator-p[2015-01-01 00:00:00, PRT solar] ... +0.4829 Generator-p[2015-12-31 23:00:00, PRT OCGT] + 0 Generator-p[2015-12-31 23:00:00, PRT onwind] + 0 Generator-p[2015-12-31 23:00:00, PRT solar] ≤ 1500000.0

n.optimize.solve_model(solver_name="gurobi")

INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 39.26it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 92.24it/s]
INFO:linopy.io: Writing time: 0.33s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-o115yw2j.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-o115yw2j.lp

Reading time = 0.12 seconds

INFO:gurobipy:Reading time = 0.12 seconds

obj: 140170 rows, 61327 columns, 271593 nonzeros

INFO:gurobipy:obj: 140170 rows, 61327 columns, 271593 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140170 rows, 61327 columns and 271593 nonzeros

INFO:gurobipy:Optimize a model with 140170 rows, 61327 columns and 271593 nonzeros

Model fingerprint: 0x30650741

INFO:gurobipy:Model fingerprint: 0x30650741

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [1e+03, 2e+06]

INFO:gurobipy:  RHS range        [1e+03, 2e+06]

Presolve removed 70063 rows and 17495 columns

INFO:gurobipy:Presolve removed 70063 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70107 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70107 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.270e+05

INFO:gurobipy: AA' NZ     : 2.270e+05

 Factor NZ  : 8.885e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.885e+05 (roughly 50 MB of memory)

 Factor Ops : 1.178e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.178e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   4.16796336e+11  3.96572113e+09  1.25e+09 3.08e+01  6.50e+08     0s

INFO:gurobipy:   0   4.16796336e+11  3.96572113e+09  1.25e+09 3.08e+01  6.50e+08     0s

   1   4.33859625e+11 -3.86300379e+11  1.07e+09 5.26e+02  3.17e+08     0s

INFO:gurobipy:   1   4.33859625e+11 -3.86300379e+11  1.07e+09 5.26e+02  3.17e+08     0s

   2   6.82459931e+11 -4.93428969e+11  9.64e+07 2.77e+01  3.40e+07     0s

INFO:gurobipy:   2   6.82459931e+11 -4.93428969e+11  9.64e+07 2.77e+01  3.40e+07     0s

   3   2.02172001e+11 -3.29667454e+11  1.44e+07 2.45e-08  6.43e+06     0s

INFO:gurobipy:   3   2.02172001e+11 -3.29667454e+11  1.44e+07 2.45e-08  6.43e+06     0s

   4   1.04938166e+11 -1.59534340e+11  6.47e+06 0.00e+00  2.70e+06     0s

INFO:gurobipy:   4   1.04938166e+11 -1.59534340e+11  6.47e+06 0.00e+00  2.70e+06     0s

   5   6.63016417e+10 -1.01908244e+11  3.62e+06 3.22e-10  1.54e+06     0s

INFO:gurobipy:   5   6.63016417e+10 -1.01908244e+11  3.62e+06 3.22e-10  1.54e+06     0s

   6   4.73562899e+10 -6.95327020e+10  2.31e+06 2.42e-09  1.00e+06     0s

INFO:gurobipy:   6   4.73562899e+10 -6.95327020e+10  2.31e+06 2.42e-09  1.00e+06     0s

   7   3.53804981e+10 -5.45341229e+10  1.49e+06 0.00e+00  7.26e+05     0s

INFO:gurobipy:   7   3.53804981e+10 -5.45341229e+10  1.49e+06 0.00e+00  7.26e+05     0s

   8   2.94478025e+10 -1.92589726e+10  1.14e+06 0.00e+00  3.87e+05     0s

INFO:gurobipy:   8   2.94478025e+10 -1.92589726e+10  1.14e+06 0.00e+00  3.87e+05     0s

   9   2.43310354e+10 -1.38359442e+10  8.71e+05 0.00e+00  2.97e+05     0s

INFO:gurobipy:   9   2.43310354e+10 -1.38359442e+10  8.71e+05 0.00e+00  2.97e+05     0s

  10   2.09459071e+10 -9.44969710e+09  6.68e+05 0.00e+00  2.32e+05     0s

INFO:gurobipy:  10   2.09459071e+10 -9.44969710e+09  6.68e+05 0.00e+00  2.32e+05     0s

  11   1.84657795e+10 -4.00446027e+09  5.20e+05 0.00e+00  1.70e+05     0s

INFO:gurobipy:  11   1.84657795e+10 -4.00446027e+09  5.20e+05 0.00e+00  1.70e+05     0s

  12   1.72643963e+10 -2.54506389e+09  4.52e+05 0.00e+00  1.49e+05     0s

INFO:gurobipy:  12   1.72643963e+10 -2.54506389e+09  4.52e+05 0.00e+00  1.49e+05     0s

  13   1.60600199e+10  1.16341321e+09  3.90e+05 0.00e+00  1.12e+05     0s

INFO:gurobipy:  13   1.60600199e+10  1.16341321e+09  3.90e+05 0.00e+00  1.12e+05     0s

  14   1.48552717e+10  2.91872678e+09  3.25e+05 0.00e+00  8.91e+04     0s

INFO:gurobipy:  14   1.48552717e+10  2.91872678e+09  3.25e+05 0.00e+00  8.91e+04     0s

  15   1.37047729e+10  4.51160287e+09  2.62e+05 0.00e+00  6.84e+04     0s

INFO:gurobipy:  15   1.37047729e+10  4.51160287e+09  2.62e+05 0.00e+00  6.84e+04     0s

  16   1.29555584e+10  5.50916522e+09  2.28e+05 3.09e-11  5.54e+04     0s

INFO:gurobipy:  16   1.29555584e+10  5.50916522e+09  2.28e+05 3.09e-11  5.54e+04     0s

  17   1.23644061e+10  6.24017524e+09  1.96e+05 0.00e+00  4.56e+04     0s

INFO:gurobipy:  17   1.23644061e+10  6.24017524e+09  1.96e+05 0.00e+00  4.56e+04     0s

  18   1.20994616e+10  6.78336543e+09  1.80e+05 0.00e+00  3.96e+04     0s

INFO:gurobipy:  18   1.20994616e+10  6.78336543e+09  1.80e+05 0.00e+00  3.96e+04     0s

  19   1.15139646e+10  7.09713423e+09  1.51e+05 0.00e+00  3.29e+04     0s

INFO:gurobipy:  19   1.15139646e+10  7.09713423e+09  1.51e+05 0.00e+00  3.29e+04     0s

  20   1.14178547e+10  7.33413150e+09  1.45e+05 4.38e-10  3.04e+04     0s

INFO:gurobipy:  20   1.14178547e+10  7.33413150e+09  1.45e+05 4.38e-10  3.04e+04     0s

  21   1.12511235e+10  7.65658400e+09  1.35e+05 0.00e+00  2.69e+04     1s

INFO:gurobipy:  21   1.12511235e+10  7.65658400e+09  1.35e+05 0.00e+00  2.69e+04     1s

  22   1.09161301e+10  7.79084464e+09  1.13e+05 0.00e+00  2.33e+04     1s

INFO:gurobipy:  22   1.09161301e+10  7.79084464e+09  1.13e+05 0.00e+00  2.33e+04     1s

  23   1.06563250e+10  7.94564584e+09  9.58e+04 0.00e+00  2.01e+04     1s

INFO:gurobipy:  23   1.06563250e+10  7.94564584e+09  9.58e+04 0.00e+00  2.01e+04     1s

  24   1.05715977e+10  8.15196507e+09  8.83e+04 0.00e+00  1.80e+04     1s

INFO:gurobipy:  24   1.05715977e+10  8.15196507e+09  8.83e+04 0.00e+00  1.80e+04     1s

  25   1.03740039e+10  8.41478937e+09  7.24e+04 5.26e-10  1.45e+04     1s

INFO:gurobipy:  25   1.03740039e+10  8.41478937e+09  7.24e+04 5.26e-10  1.45e+04     1s

  26   1.02838823e+10  8.47790654e+09  6.62e+04 0.00e+00  1.34e+04     1s

INFO:gurobipy:  26   1.02838823e+10  8.47790654e+09  6.62e+04 0.00e+00  1.34e+04     1s

  27   1.01442529e+10  8.69801447e+09  5.55e+04 0.00e+00  1.07e+04     1s

INFO:gurobipy:  27   1.01442529e+10  8.69801447e+09  5.55e+04 0.00e+00  1.07e+04     1s

  28   9.98147267e+09  8.77817300e+09  4.15e+04 0.00e+00  8.83e+03     1s

INFO:gurobipy:  28   9.98147267e+09  8.77817300e+09  4.15e+04 0.00e+00  8.83e+03     1s

  29   9.90571958e+09  8.95403293e+09  3.44e+04 0.00e+00  7.00e+03     1s

INFO:gurobipy:  29   9.90571958e+09  8.95403293e+09  3.44e+04 0.00e+00  7.00e+03     1s

  30   9.82102678e+09  9.04851817e+09  2.74e+04 0.00e+00  5.67e+03     1s

INFO:gurobipy:  30   9.82102678e+09  9.04851817e+09  2.74e+04 0.00e+00  5.67e+03     1s

  31   9.75697300e+09  9.13797882e+09  2.20e+04 0.00e+00  4.54e+03     1s

INFO:gurobipy:  31   9.75697300e+09  9.13797882e+09  2.20e+04 0.00e+00  4.54e+03     1s

  32   9.70417966e+09  9.19398498e+09  1.69e+04 0.00e+00  3.72e+03     1s

INFO:gurobipy:  32   9.70417966e+09  9.19398498e+09  1.69e+04 0.00e+00  3.72e+03     1s

  33   9.66272538e+09  9.24979490e+09  1.36e+04 5.55e-10  3.00e+03     1s

INFO:gurobipy:  33   9.66272538e+09  9.24979490e+09  1.36e+04 5.55e-10  3.00e+03     1s

  34   9.63786069e+09  9.31942352e+09  1.15e+04 0.00e+00  2.33e+03     1s

INFO:gurobipy:  34   9.63786069e+09  9.31942352e+09  1.15e+04 0.00e+00  2.33e+03     1s

  35   9.62407470e+09  9.34416949e+09  1.04e+04 0.00e+00  2.05e+03     1s

INFO:gurobipy:  35   9.62407470e+09  9.34416949e+09  1.04e+04 0.00e+00  2.05e+03     1s

  36   9.61269250e+09  9.36834811e+09  9.51e+03 0.00e+00  1.80e+03     1s

INFO:gurobipy:  36   9.61269250e+09  9.36834811e+09  9.51e+03 0.00e+00  1.80e+03     1s

  37   9.60072802e+09  9.38454401e+09  8.55e+03 0.00e+00  1.59e+03     1s

INFO:gurobipy:  37   9.60072802e+09  9.38454401e+09  8.55e+03 0.00e+00  1.59e+03     1s

  38   9.58553714e+09  9.39583971e+09  7.25e+03 0.00e+00  1.39e+03     1s

INFO:gurobipy:  38   9.58553714e+09  9.39583971e+09  7.25e+03 0.00e+00  1.39e+03     1s

  39   9.56481102e+09  9.42362315e+09  5.33e+03 0.00e+00  1.04e+03     1s

INFO:gurobipy:  39   9.56481102e+09  9.42362315e+09  5.33e+03 0.00e+00  1.04e+03     1s

  40   9.55678779e+09  9.42858138e+09  4.64e+03 4.09e-10  9.37e+02     1s

INFO:gurobipy:  40   9.55678779e+09  9.42858138e+09  4.64e+03 4.09e-10  9.37e+02     1s

  41   9.55156734e+09  9.43655899e+09  4.23e+03 6.71e-10  8.42e+02     1s

INFO:gurobipy:  41   9.55156734e+09  9.43655899e+09  4.23e+03 6.71e-10  8.42e+02     1s

  42   9.54303992e+09  9.45298030e+09  3.49e+03 0.00e+00  6.62e+02     1s

INFO:gurobipy:  42   9.54303992e+09  9.45298030e+09  3.49e+03 0.00e+00  6.62e+02     1s

  43   9.54077589e+09  9.45737502e+09  3.29e+03 0.00e+00  6.14e+02     1s

INFO:gurobipy:  43   9.54077589e+09  9.45737502e+09  3.29e+03 0.00e+00  6.14e+02     1s

  44   9.53115993e+09  9.46602847e+09  2.48e+03 0.00e+00  4.78e+02     1s

INFO:gurobipy:  44   9.53115993e+09  9.46602847e+09  2.48e+03 0.00e+00  4.78e+02     1s

  45   9.52251215e+09  9.47192746e+09  1.72e+03 0.00e+00  3.67e+02     1s

INFO:gurobipy:  45   9.52251215e+09  9.47192746e+09  1.72e+03 0.00e+00  3.67e+02     1s

  46   9.51547222e+09  9.48432789e+09  1.09e+03 0.00e+00  2.27e+02     1s

INFO:gurobipy:  46   9.51547222e+09  9.48432789e+09  1.09e+03 0.00e+00  2.27e+02     1s

  47   9.51400679e+09  9.48734390e+09  9.82e+02 1.20e-09  1.95e+02     1s

INFO:gurobipy:  47   9.51400679e+09  9.48734390e+09  9.82e+02 1.20e-09  1.95e+02     1s

  48   9.51177968e+09  9.48886719e+09  7.92e+02 0.00e+00  1.67e+02     1s

INFO:gurobipy:  48   9.51177968e+09  9.48886719e+09  7.92e+02 0.00e+00  1.67e+02     1s

  49   9.51106285e+09  9.49099691e+09  7.30e+02 0.00e+00  1.47e+02     1s

INFO:gurobipy:  49   9.51106285e+09  9.49099691e+09  7.30e+02 0.00e+00  1.47e+02     1s

  50   9.51051283e+09  9.49324912e+09  6.88e+02 0.00e+00  1.27e+02     1s

INFO:gurobipy:  50   9.51051283e+09  9.49324912e+09  6.88e+02 0.00e+00  1.27e+02     1s

  51   9.50867694e+09  9.49553693e+09  5.46e+02 0.00e+00  9.70e+01     1s

INFO:gurobipy:  51   9.50867694e+09  9.49553693e+09  5.46e+02 0.00e+00  9.70e+01     1s

  52   9.50598401e+09  9.50015619e+09  3.17e+02 0.00e+00  4.42e+01     1s

INFO:gurobipy:  52   9.50598401e+09  9.50015619e+09  3.17e+02 0.00e+00  4.42e+01     1s

  53   9.50539920e+09  9.50079164e+09  2.67e+02 0.00e+00  3.52e+01     1s

INFO:gurobipy:  53   9.50539920e+09  9.50079164e+09  2.67e+02 0.00e+00  3.52e+01     1s

  54   9.50451517e+09  9.50093184e+09  1.91e+02 0.00e+00  2.71e+01     1s

INFO:gurobipy:  54   9.50451517e+09  9.50093184e+09  1.91e+02 0.00e+00  2.71e+01     1s

  55   9.50350051e+09  9.50115981e+09  1.04e+02 0.00e+00  1.74e+01     1s

INFO:gurobipy:  55   9.50350051e+09  9.50115981e+09  1.04e+02 0.00e+00  1.74e+01     1s

  56   9.50309124e+09  9.50153494e+09  6.93e+01 0.00e+00  1.16e+01     1s

INFO:gurobipy:  56   9.50309124e+09  9.50153494e+09  6.93e+01 0.00e+00  1.16e+01     1s

  57   9.50274034e+09  9.50172822e+09  4.18e+01 0.00e+00  7.47e+00     1s

INFO:gurobipy:  57   9.50274034e+09  9.50172822e+09  4.18e+01 0.00e+00  7.47e+00     1s

  58   9.50254034e+09  9.50180038e+09  2.47e+01 0.00e+00  5.37e+00     1s

INFO:gurobipy:  58   9.50254034e+09  9.50180038e+09  2.47e+01 0.00e+00  5.37e+00     1s

  59   9.50242890e+09  9.50194703e+09  1.59e+01 0.00e+00  3.49e+00     1s

INFO:gurobipy:  59   9.50242890e+09  9.50194703e+09  1.59e+01 0.00e+00  3.49e+00     1s

  60   9.50224286e+09  9.50197715e+09  9.79e-01 0.00e+00  1.80e+00     1s

INFO:gurobipy:  60   9.50224286e+09  9.50197715e+09  9.79e-01 0.00e+00  1.80e+00     1s

  61   9.50223209e+09  9.50202913e+09  4.17e-01 0.00e+00  1.37e+00     1s

INFO:gurobipy:  61   9.50223209e+09  9.50202913e+09  4.17e-01 0.00e+00  1.37e+00     1s

  62   9.50222771e+09  9.50216070e+09  1.79e-01 1.95e-09  4.53e-01     1s

INFO:gurobipy:  62   9.50222771e+09  9.50216070e+09  1.79e-01 1.95e-09  4.53e-01     1s

  63   9.50222336e+09  9.50221686e+09  3.50e-02 3.40e-08  4.42e-02     1s

INFO:gurobipy:  63   9.50222336e+09  9.50221686e+09  3.50e-02 3.40e-08  4.42e-02     1s

  64   9.50222194e+09  9.50222182e+09  1.66e-03 1.37e-08  7.89e-04     1s

INFO:gurobipy:  64   9.50222194e+09  9.50222182e+09  1.66e-03 1.37e-08  7.89e-04     1s

  65   9.50222185e+09  9.50222185e+09  8.00e-06 3.53e-08  9.46e-08     1s

INFO:gurobipy:  65   9.50222185e+09  9.50222185e+09  8.00e-06 3.53e-08  9.46e-08     1s

  66   9.50222185e+09  9.50222185e+09  3.81e-07 6.21e-08  1.00e-13     1s

INFO:gurobipy:  66   9.50222185e+09  9.50222185e+09  3.81e-07 6.21e-08  1.00e-13     1s

INFO:gurobipy:

Barrier solved model in 66 iterations and 1.18 seconds (1.90 work units)

INFO:gurobipy:Barrier solved model in 66 iterations and 1.18 seconds (1.90 work units)

Optimal objective 9.50222185e+09

INFO:gurobipy:Optimal objective 9.50222185e+09

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      34 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:      34 DPushes remaining with DInf 0.0000000e+00                 1s

       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:

    5716 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:    5716 PPushes remaining with PInf 0.0000000e+00                 1s

       0 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 3.7555221e-09      1s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 3.7555221e-09      1s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    5753    9.5022219e+09   0.000000e+00   0.000000e+00      1s

INFO:gurobipy:    5753    9.5022219e+09   0.000000e+00   0.000000e+00      1s

INFO:gurobipy:

Solved in 5753 iterations and 1.44 seconds (2.87 work units)

INFO:gurobipy:Solved in 5753 iterations and 1.44 seconds (2.87 work units)

Optimal objective  9.502221855e+09

INFO:gurobipy:Optimal objective  9.502221855e+09
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140170 duals
Objective: 9.50e+09
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper, CO2Limit were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)

('ok', 'optimal')

# Total system costs
n.objective/1e9

9.502221854584588

# Average electricity price
n.buses_t.marginal_price.mean()

Bus
PRT    179.515992
DNK    209.775581
dtype: float64

# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()

Bus
PRT    7053
DNK    6799
dtype: int64

# Share of hours with almost zero price
(n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count())/len(n.snapshots)

Bus
PRT    0.805137
DNK    0.776142
dtype: float64

# Congestion rent
((n.buses_t.marginal_price["PRT"] - n.buses_t.marginal_price["DNK"]) * n.lines_t.p0["PRT-DNK"]).sum()

np.float64(-1884193551.7485387)

# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt

Line
PRT-DNK    0.871409
dtype: float64

# Total generation
n.generators_t.p.sum(axis=0).groupby([n.generators.bus, n.generators.carrier]).sum().div(1e6).round(1)

bus  carrier
DNK  OCGT        2.1
     onwind     18.0
     solar       8.2
PRT  OCGT        3.1
     onwind     37.0
     solar      13.4
dtype: float64

n.generators.efficiency

Generator
PRT OCGT      0.41
PRT onwind    1.00
PRT solar     1.00
DNK OCGT      0.41
DNK onwind    1.00
DNK solar     1.00
Name: efficiency, dtype: float64

# Total CO2 emissions
n.generators_t.p.sum(axis=0).groupby([n.generators.carrier]).sum()["OCGT"] * (costs.at["OCGT", "CO2 intensity"] / costs.at["OCGT", "efficiency"])

np.float64(2500000.0000015204)

n.model.dual

<xarray.Dataset> Size: 1MB
Dimensions:                    (Generator-ext: 6, Line-ext: 1, snapshot: 8760,
                                Bus: 2, bus: 2)
Coordinates:
  * Generator-ext              (Generator-ext) object 48B 'PRT OCGT' ... 'DNK...
  * Line-ext                   (Line-ext) object 8B 'PRT-DNK'
  * snapshot                   (snapshot) datetime64[ns] 70kB 2015-01-01 ... ...
  * Bus                        (Bus) object 16B 'PRT' 'DNK'
  * bus                        (bus) object 16B 'DNK' 'PRT'
Data variables:
    Generator-ext-p_nom-lower  (Generator-ext) float64 48B 0.0 0.0 ... 0.0 0.0
    Generator-ext-p_nom-upper  (Generator-ext) float64 48B nan nan ... nan nan
    Line-ext-s_nom-lower       (Line-ext) float64 8B 0.0
    Line-ext-s_nom-upper       (Line-ext) float64 8B -1.78e+06
    Generator-ext-p-lower      (snapshot, Generator-ext) float64 420kB 886.7 ...
    Generator-ext-p-upper      (snapshot, Generator-ext) float64 420kB 0.0 .....
    Line-ext-s-lower           (snapshot, Line-ext) float64 70kB 0.0 0.0 ... 0.0
    Line-ext-s-upper           (snapshot, Line-ext) float64 70kB 0.0 0.0 ... 0.0
    Bus-nodal_balance          (Bus, snapshot) float64 140kB 1.429 ... 1.429
    CO2Limit                   (bus) float64 16B -1.755e+03 -1.705e+03

xarray.Dataset

• Dimensions:
  • Generator-ext: 6
  • Line-ext: 1
  • snapshot: 8760
  • Bus: 2
  • bus: 2
• Coordinates: (5)
  • Generator-ext
    (Generator-ext)
    object
    'PRT OCGT' ... 'DNK solar'

    array(['PRT OCGT', 'PRT onwind', 'PRT solar', 'DNK OCGT', 'DNK onwind',
           'DNK solar'], dtype=object)

  • Line-ext
    (Line-ext)
    object
    'PRT-DNK'

    array(['PRT-DNK'], dtype=object)

  • snapshot
    (snapshot)
    datetime64[ns]
    2015-01-01 ... 2015-12-31T23:00:00

    array(['2015-01-01T00:00:00.000000000', '2015-01-01T01:00:00.000000000',
           '2015-01-01T02:00:00.000000000', ..., '2015-12-31T21:00:00.000000000',
           '2015-12-31T22:00:00.000000000', '2015-12-31T23:00:00.000000000'],
          shape=(8760,), dtype='datetime64[ns]')

  • Bus
    (Bus)
    object
    'PRT' 'DNK'

    array(['PRT', 'DNK'], dtype=object)

  • bus
    (bus)
    object
    'DNK' 'PRT'

    array(['DNK', 'PRT'], dtype=object)

• Data variables: (10)
  • Generator-ext-p_nom-lower
    (Generator-ext)
    float64
    0.0 0.0 0.0 0.0 0.0 0.0

    array([0., 0., 0., 0., 0., 0.])

  • Generator-ext-p_nom-upper
    (Generator-ext)
    float64
    nan nan nan nan nan nan

    array([nan, nan, nan, nan, nan, nan])

  • Line-ext-s_nom-lower
    (Line-ext)
    float64
    0.0

    array([0.])

  • Line-ext-s_nom-upper
    (Line-ext)
    float64
    -1.78e+06

    array([-1780141.03945753])

  • Generator-ext-p-lower
    (snapshot, Generator-ext)
    float64
    886.7 0.0 0.0 ... 910.8 0.0 0.0

    array([[886.70652194,   0.        ,   0.        , 910.79768644,
              0.        ,   0.        ],
           [886.70652194,   0.        ,   0.        , 910.79768644,
              0.        ,   0.        ],
           [886.70652194,   0.        ,   0.        , 910.79768644,
              0.        ,   0.        ],
           ...,
           [  0.        ,   0.        ,   0.        ,  24.0911645 ,
              0.        ,   0.        ],
           [886.70652194,   0.        ,   0.        , 910.79768644,
              0.        ,   0.        ],
           [886.70652194,   0.        ,   0.        , 910.79768644,
              0.        ,   0.        ]], shape=(8760, 6))

  • Generator-ext-p-upper
    (snapshot, Generator-ext)
    float64
    0.0 0.0 -1.418 ... 0.0 0.0 -1.418

    array([[   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           ...,
           [   0.        , -886.70652194, -888.12452194,    0.        ,
            -886.70652194, -888.12452194],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ],
           [   0.        ,    0.        ,   -1.418     ,    0.        ,
               0.        ,   -1.418     ]], shape=(8760, 6))

  • Line-ext-s-lower
    (snapshot, Line-ext)
    float64
    0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0

    array([[0.],
           [0.],
           [0.],
           ...,
           [0.],
           [0.],
           [0.]], shape=(8760, 1))

  • Line-ext-s-upper
    (snapshot, Line-ext)
    float64
    0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0

    array([[0.],
           [0.],
           [0.],
           ...,
           [0.],
           [0.],
           [0.]], shape=(8760, 1))

  • Bus-nodal_balance
    (Bus, snapshot)
    float64
    1.429 1.429 1.429 ... 1.429 1.429

    array([[  1.4286    ,   1.4286    ,   1.4286    , ..., 888.13512194,
              1.4286    ,   1.4286    ],
           [  1.4286    ,   1.4286    ,   1.4286    , ..., 888.13512194,
              1.4286    ,   1.4286    ]], shape=(2, 8760))

  • CO2Limit
    (bus)
    float64
    -1.755e+03 -1.705e+03

    array([-1755.01190626, -1705.1261616 ])

• Indexes: (5)
  • Generator-ext
    PandasIndex

    PandasIndex(Index(['PRT OCGT', 'PRT onwind', 'PRT solar', 'DNK OCGT', 'DNK onwind',
           'DNK solar'],
          dtype='object', name='Generator-ext'))

  • Line-ext
    PandasIndex

    PandasIndex(Index(['PRT-DNK'], dtype='object', name='Line-ext'))

  • snapshot
    PandasIndex

    PandasIndex(DatetimeIndex(['2015-01-01 00:00:00', '2015-01-01 01:00:00',
                   '2015-01-01 02:00:00', '2015-01-01 03:00:00',
                   '2015-01-01 04:00:00', '2015-01-01 05:00:00',
                   '2015-01-01 06:00:00', '2015-01-01 07:00:00',
                   '2015-01-01 08:00:00', '2015-01-01 09:00:00',
                   ...
                   '2015-12-31 14:00:00', '2015-12-31 15:00:00',
                   '2015-12-31 16:00:00', '2015-12-31 17:00:00',
                   '2015-12-31 18:00:00', '2015-12-31 19:00:00',
                   '2015-12-31 20:00:00', '2015-12-31 21:00:00',
                   '2015-12-31 22:00:00', '2015-12-31 23:00:00'],
                  dtype='datetime64[ns]', name='snapshot', length=8760, freq=None))

  • Bus
    PandasIndex

    PandasIndex(Index(['PRT', 'DNK'], dtype='object', name='Bus'))

  • bus
    PandasIndex

    PandasIndex(Index(['DNK', 'PRT'], dtype='object', name='bus'))

• Attributes: (0)

d. CO2 limits 0.25, 0.5, 1, 1.5, 2, 2.5 MtCO2/year, F endogenous

n1, n2, n3, n4, n5, n6 = [pypsa.Network() for _ in range(6)]
for emission, n in zip([250000, 500000, 1000000, 1500000, 2000000, 2500000], [n1,n2,n3,n4,n5,n6]):
    hours_in_2015 = pd.date_range('2015-01-01 00:00Z',
                                '2015-12-31 23:00Z',
                                freq='h')

    n.set_snapshots(hours_in_2015.values)

    for country in countries:
        n.add("Bus",
            country,
            y = coordinates[country][0],
            x = coordinates[country][1],
            carrier="AC"
            )

    carriers = [
        "onwind",
        "solar",
        "OCGT",
    ]

    n.madd(
        "Carrier",
        carriers,
        color=["dodgerblue", "gold", "indianred",],
        co2_emissions=[costs.at[c, "CO2 intensity"] for c in carriers],
    )
    # add load to the bus
    for country in countries:
        n.add("Load",
            f"{country} load",
            bus=country,
            p_set=data_el[country].values,
            carrier = "AC")
    for country in countries:
        n.add(
            "Generator",
            f"{country} OCGT",
            bus=country,
            carrier="OCGT",
            capital_cost=costs.at["OCGT", "capital_cost"],
            marginal_cost=costs.at["OCGT", "marginal_cost"],
            efficiency=costs.at["OCGT", "efficiency"],
            p_nom_extendable=True,
        )   
        CF_wind = data_wind[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
        n.add("Generator",
            f"{country} onwind",
            bus=country,
            carrier="onwind",
            capital_cost=costs.at["onwind", "capital_cost"],
            marginal_cost=costs.at["onwind", "marginal_cost"],
            p_max_pu=CF_wind.values,
            efficiency=costs.at["onwind", "efficiency"],
            p_nom_extendable=True,
        )
        CF_solar = data_solar[country][[hour.strftime("%Y-%m-%dT%H:%M:%SZ") for hour in n.snapshots]]
        n.add("Generator",
            f"{country} solar",
            bus=country,
            carrier="solar",
            capital_cost=costs.at["solar", "capital_cost"],
            marginal_cost=costs.at["solar", "marginal_cost"],
            p_max_pu=CF_solar.values,
            efficiency=costs.at["solar", "efficiency"],
            p_nom_extendable=True,
        )
    n.add(
        "Line",
        "PRT-DNK",
        bus0="PRT",
        bus1="DNK",
        s_nom = 0,
        x = 1,
        r = 1,
        capital_cost = costs.at["HVAC overhead", "capital_cost"] * 2477,
        s_nom_extendable = True,
    )
    n.add(
        "GlobalConstraint",
        "CO2Limit",
        carrier_attribute="co2_emissions",
        sense="<=",
        constant=emission, 
    )
    n.optimize(solver_name="gurobi")

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/components.py:323: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise an error in a future version of pandas. Value '[]' has dtype incompatible with float64, please explicitly cast to a compatible dtype first.
  attrs.loc[bool_b, "default"] = attrs.loc[bool_b].isin({True, "True"})
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)
INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 38.55it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 91.83it/s]
INFO:linopy.io: Writing time: 0.34s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-qon_4xie.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-qon_4xie.lp

Reading time = 0.12 seconds

INFO:gurobipy:Reading time = 0.12 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0x122577b2

INFO:gurobipy:Model fingerprint: 0x122577b2

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 2e+05]

INFO:gurobipy:  RHS range        [2e+03, 2e+05]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.182e+05

INFO:gurobipy: AA' NZ     : 2.182e+05

 Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

 Factor Ops : 1.008e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.008e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   1.81179319e+11  0.00000000e+00  1.07e+09 0.00e+00  8.05e+07     0s

INFO:gurobipy:   0   1.81179319e+11  0.00000000e+00  1.07e+09 0.00e+00  8.05e+07     0s

   1   2.10986413e+11 -8.60652604e+10  1.93e+08 2.20e+02  1.92e+07     0s

INFO:gurobipy:   1   2.10986413e+11 -8.60652604e+10  1.93e+08 2.20e+02  1.92e+07     0s

   2   1.51850835e+11 -7.09714767e+10  6.92e+06 1.08e+00  1.72e+06     0s

INFO:gurobipy:   2   1.51850835e+11 -7.09714767e+10  6.92e+06 1.08e+00  1.72e+06     0s

   3   5.40297885e+10 -1.21107184e+10  1.95e+06 4.95e-10  4.81e+05     0s

INFO:gurobipy:   3   5.40297885e+10 -1.21107184e+10  1.95e+06 4.95e-10  4.81e+05     0s

   4   3.89140611e+10 -4.52566441e+09  1.32e+06 6.98e-10  3.13e+05     0s

INFO:gurobipy:   4   3.89140611e+10 -4.52566441e+09  1.32e+06 6.98e-10  3.13e+05     0s

   5   3.16419219e+10 -2.50148685e+09  1.01e+06 4.07e-10  2.45e+05     0s

INFO:gurobipy:   5   3.16419219e+10 -2.50148685e+09  1.01e+06 4.07e-10  2.45e+05     0s

   6   2.76616278e+10 -4.13884538e+08  8.27e+05 4.66e-10  2.01e+05     0s

INFO:gurobipy:   6   2.76616278e+10 -4.13884538e+08  8.27e+05 4.66e-10  2.01e+05     0s

   7   2.28844778e+10  2.29643676e+09  6.20e+05 3.78e-10  1.48e+05     0s

INFO:gurobipy:   7   2.28844778e+10  2.29643676e+09  6.20e+05 3.78e-10  1.48e+05     0s

   8   2.10493492e+10  3.57495332e+09  5.39e+05 6.11e-10  1.26e+05     0s

INFO:gurobipy:   8   2.10493492e+10  3.57495332e+09  5.39e+05 6.11e-10  1.26e+05     0s

   9   1.94595775e+10  4.88497499e+09  4.63e+05 3.78e-10  1.06e+05     0s

INFO:gurobipy:   9   1.94595775e+10  4.88497499e+09  4.63e+05 3.78e-10  1.06e+05     0s

  10   1.79167807e+10  5.76456531e+09  3.87e+05 3.78e-10  8.90e+04     0s

INFO:gurobipy:  10   1.79167807e+10  5.76456531e+09  3.87e+05 3.78e-10  8.90e+04     0s

  11   1.72539808e+10  6.32980349e+09  3.25e+05 3.78e-10  7.99e+04     0s

INFO:gurobipy:  11   1.72539808e+10  6.32980349e+09  3.25e+05 3.78e-10  7.99e+04     0s

  12   1.68423458e+10  6.83208026e+09  3.00e+05 2.91e-10  7.36e+04     0s

INFO:gurobipy:  12   1.68423458e+10  6.83208026e+09  3.00e+05 2.91e-10  7.36e+04     0s

  13   1.63886229e+10  7.57420272e+09  2.70e+05 8.73e-10  6.54e+04     0s

INFO:gurobipy:  13   1.63886229e+10  7.57420272e+09  2.70e+05 8.73e-10  6.54e+04     0s

  14   1.61519836e+10  7.87593182e+09  2.37e+05 1.16e-09  6.12e+04     0s

INFO:gurobipy:  14   1.61519836e+10  7.87593182e+09  2.37e+05 1.16e-09  6.12e+04     0s

  15   1.60159396e+10  8.35006430e+09  2.27e+05 5.53e-10  5.71e+04     0s

INFO:gurobipy:  15   1.60159396e+10  8.35006430e+09  2.27e+05 5.53e-10  5.71e+04     0s

  16   1.58231903e+10  8.85060545e+09  2.11e+05 9.60e-10  5.23e+04     0s

INFO:gurobipy:  16   1.58231903e+10  8.85060545e+09  2.11e+05 9.60e-10  5.23e+04     0s

  17   1.57071007e+10  9.03219224e+09  1.92e+05 9.31e-10  4.99e+04     0s

INFO:gurobipy:  17   1.57071007e+10  9.03219224e+09  1.92e+05 9.31e-10  4.99e+04     0s

  18   1.55959125e+10  9.78647037e+09  1.68e+05 8.73e-10  4.39e+04     0s

INFO:gurobipy:  18   1.55959125e+10  9.78647037e+09  1.68e+05 8.73e-10  4.39e+04     0s

  19   1.55682597e+10  9.91327483e+09  1.53e+05 5.09e-11  4.25e+04     0s

INFO:gurobipy:  19   1.55682597e+10  9.91327483e+09  1.53e+05 5.09e-11  4.25e+04     0s

  20   1.54407398e+10  1.09630186e+10  1.30e+05 9.02e-10  3.44e+04     0s

INFO:gurobipy:  20   1.54407398e+10  1.09630186e+10  1.30e+05 9.02e-10  3.44e+04     0s

  21   1.53324828e+10  1.16018946e+10  1.16e+05 3.78e-10  2.92e+04     0s

INFO:gurobipy:  21   1.53324828e+10  1.16018946e+10  1.16e+05 3.78e-10  2.92e+04     0s

  22   1.52711000e+10  1.19603658e+10  1.07e+05 6.11e-10  2.63e+04     1s

INFO:gurobipy:  22   1.52711000e+10  1.19603658e+10  1.07e+05 6.11e-10  2.63e+04     1s

  23   1.52376182e+10  1.21147408e+10  9.85e+04 1.02e-10  2.48e+04     1s

INFO:gurobipy:  23   1.52376182e+10  1.21147408e+10  9.85e+04 1.02e-10  2.48e+04     1s

  24   1.52711047e+10  1.24309618e+10  8.19e+04 4.66e-10  2.23e+04     1s

INFO:gurobipy:  24   1.52711047e+10  1.24309618e+10  8.19e+04 4.66e-10  2.23e+04     1s

  25   1.52858403e+10  1.25265967e+10  7.87e+04 4.66e-10  2.17e+04     1s

INFO:gurobipy:  25   1.52858403e+10  1.25265967e+10  7.87e+04 4.66e-10  2.17e+04     1s

  26   1.52609863e+10  1.28950662e+10  7.27e+04 2.04e-10  1.89e+04     1s

INFO:gurobipy:  26   1.52609863e+10  1.28950662e+10  7.27e+04 2.04e-10  1.89e+04     1s

  27   1.52284786e+10  1.30206857e+10  6.48e+04 1.08e-09  1.75e+04     1s

INFO:gurobipy:  27   1.52284786e+10  1.30206857e+10  6.48e+04 1.08e-09  1.75e+04     1s

  28   1.52414743e+10  1.31530316e+10  5.95e+04 3.64e-11  1.65e+04     1s

INFO:gurobipy:  28   1.52414743e+10  1.31530316e+10  5.95e+04 3.64e-11  1.65e+04     1s

  29   1.52233206e+10  1.32501634e+10  5.34e+04 6.40e-10  1.55e+04     1s

INFO:gurobipy:  29   1.52233206e+10  1.32501634e+10  5.34e+04 6.40e-10  1.55e+04     1s

  30   1.52203971e+10  1.33098488e+10  5.16e+04 6.11e-10  1.50e+04     1s

INFO:gurobipy:  30   1.52203971e+10  1.33098488e+10  5.16e+04 6.11e-10  1.50e+04     1s

  31   1.52291134e+10  1.35107503e+10  4.98e+04 1.02e-10  1.37e+04     1s

INFO:gurobipy:  31   1.52291134e+10  1.35107503e+10  4.98e+04 1.02e-10  1.37e+04     1s

  32   1.52199897e+10  1.36275145e+10  4.53e+04 5.82e-10  1.27e+04     1s

INFO:gurobipy:  32   1.52199897e+10  1.36275145e+10  4.53e+04 5.82e-10  1.27e+04     1s

  33   1.52296940e+10  1.38578738e+10  4.27e+04 1.75e-10  1.11e+04     1s

INFO:gurobipy:  33   1.52296940e+10  1.38578738e+10  4.27e+04 1.75e-10  1.11e+04     1s

  34   1.52387163e+10  1.39453197e+10  3.13e+04 6.18e-11  1.01e+04     1s

INFO:gurobipy:  34   1.52387163e+10  1.39453197e+10  3.13e+04 6.18e-11  1.01e+04     1s

  35   1.52410638e+10  1.40323584e+10  2.79e+04 6.40e-10  9.38e+03     1s

INFO:gurobipy:  35   1.52410638e+10  1.40323584e+10  2.79e+04 6.40e-10  9.38e+03     1s

  36   1.52467633e+10  1.41610248e+10  2.34e+04 6.40e-10  8.36e+03     1s

INFO:gurobipy:  36   1.52467633e+10  1.41610248e+10  2.34e+04 6.40e-10  8.36e+03     1s

  37   1.52478682e+10  1.42104839e+10  2.15e+04 1.46e-10  7.96e+03     1s

INFO:gurobipy:  37   1.52478682e+10  1.42104839e+10  2.15e+04 1.46e-10  7.96e+03     1s

  38   1.52486509e+10  1.42688505e+10  2.08e+04 2.04e-10  7.54e+03     1s

INFO:gurobipy:  38   1.52486509e+10  1.42688505e+10  2.08e+04 2.04e-10  7.54e+03     1s

  39   1.52536937e+10  1.42954813e+10  1.95e+04 2.76e-10  7.34e+03     1s

INFO:gurobipy:  39   1.52536937e+10  1.42954813e+10  1.95e+04 2.76e-10  7.34e+03     1s

  40   1.52516539e+10  1.44601912e+10  1.75e+04 3.49e-10  6.14e+03     1s

INFO:gurobipy:  40   1.52516539e+10  1.44601912e+10  1.75e+04 3.49e-10  6.14e+03     1s

  41   1.52514063e+10  1.46037367e+10  1.59e+04 5.82e-10  5.11e+03     1s

INFO:gurobipy:  41   1.52514063e+10  1.46037367e+10  1.59e+04 5.82e-10  5.11e+03     1s

  42   1.52602843e+10  1.46523771e+10  1.24e+04 1.75e-10  4.68e+03     1s

INFO:gurobipy:  42   1.52602843e+10  1.46523771e+10  1.24e+04 1.75e-10  4.68e+03     1s

  43   1.52673295e+10  1.47351295e+10  1.05e+04 3.17e-10  4.08e+03     1s

INFO:gurobipy:  43   1.52673295e+10  1.47351295e+10  1.05e+04 3.17e-10  4.08e+03     1s

  44   1.52753616e+10  1.48131042e+10  7.40e+03 1.89e-10  3.46e+03     1s

INFO:gurobipy:  44   1.52753616e+10  1.48131042e+10  7.40e+03 1.89e-10  3.46e+03     1s

  45   1.52853404e+10  1.48837590e+10  3.99e+03 1.52e-09  2.89e+03     1s

INFO:gurobipy:  45   1.52853404e+10  1.48837590e+10  3.99e+03 1.52e-09  2.89e+03     1s

  46   1.52858179e+10  1.49209286e+10  3.80e+03 2.18e-09  2.64e+03     1s

INFO:gurobipy:  46   1.52858179e+10  1.49209286e+10  3.80e+03 2.18e-09  2.64e+03     1s

  47   1.52861300e+10  1.50316841e+10  3.18e+03 4.38e-09  1.87e+03     1s

INFO:gurobipy:  47   1.52861300e+10  1.50316841e+10  3.18e+03 4.38e-09  1.87e+03     1s

  48   1.52875943e+10  1.51515028e+10  1.94e+03 4.32e-09  1.01e+03     1s

INFO:gurobipy:  48   1.52875943e+10  1.51515028e+10  1.94e+03 4.32e-09  1.01e+03     1s

  49   1.52872460e+10  1.51951904e+10  1.33e+03 3.29e-09  6.85e+02     1s

INFO:gurobipy:  49   1.52872460e+10  1.51951904e+10  1.33e+03 3.29e-09  6.85e+02     1s

  50   1.52865282e+10  1.52326056e+10  8.22e+02 2.76e-09  4.04e+02     1s

INFO:gurobipy:  50   1.52865282e+10  1.52326056e+10  8.22e+02 2.76e-09  4.04e+02     1s

  51   1.52858547e+10  1.52458855e+10  5.25e+02 2.08e-09  2.95e+02     1s

INFO:gurobipy:  51   1.52858547e+10  1.52458855e+10  5.25e+02 2.08e-09  2.95e+02     1s

  52   1.52851061e+10  1.52514803e+10  2.65e+02 1.54e-09  2.39e+02     1s

INFO:gurobipy:  52   1.52851061e+10  1.52514803e+10  2.65e+02 1.54e-09  2.39e+02     1s

  53   1.52850062e+10  1.52587536e+10  2.29e+02 1.52e-09  1.88e+02     1s

INFO:gurobipy:  53   1.52850062e+10  1.52587536e+10  2.29e+02 1.52e-09  1.88e+02     1s

  54   1.52843775e+10  1.52781573e+10  5.68e+01 1.01e-09  4.47e+01     1s

INFO:gurobipy:  54   1.52843775e+10  1.52781573e+10  5.68e+01 1.01e-09  4.47e+01     1s

  55   1.52838894e+10  1.52834354e+10  7.15e+00 1.46e-10  3.41e+00     1s

INFO:gurobipy:  55   1.52838894e+10  1.52834354e+10  7.15e+00 1.46e-10  3.41e+00     1s

  56   1.52838120e+10  1.52837561e+10  1.38e+00 8.15e-10  4.45e-01     1s

INFO:gurobipy:  56   1.52838120e+10  1.52837561e+10  1.38e+00 8.15e-10  4.45e-01     1s

  57   1.52837941e+10  1.52837896e+10  9.84e-02 2.04e-10  3.51e-02     1s

INFO:gurobipy:  57   1.52837941e+10  1.52837896e+10  9.84e-02 2.04e-10  3.51e-02     1s

  58   1.52837926e+10  1.52837926e+10  5.77e-07 9.02e-10  7.81e-06     1s

INFO:gurobipy:  58   1.52837926e+10  1.52837926e+10  5.77e-07 9.02e-10  7.81e-06     1s

  59   1.52837926e+10  1.52837926e+10  6.15e-09 2.12e-09  3.02e-10     1s

INFO:gurobipy:  59   1.52837926e+10  1.52837926e+10  6.15e-09 2.12e-09  3.02e-10     1s

INFO:gurobipy:

Barrier solved model in 59 iterations and 0.99 seconds (1.73 work units)

INFO:gurobipy:Barrier solved model in 59 iterations and 0.99 seconds (1.73 work units)

Optimal objective 1.52837926e+10

INFO:gurobipy:Optimal objective 1.52837926e+10

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      27 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:      27 DPushes remaining with DInf 0.0000000e+00                 1s

       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:

    8742 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:    8742 PPushes remaining with PInf 0.0000000e+00                 1s

       0 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 2.1383512e-09      1s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 2.1383512e-09      1s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8772    1.5283793e+10   0.000000e+00   0.000000e+00      1s

INFO:gurobipy:    8772    1.5283793e+10   0.000000e+00   0.000000e+00      1s

INFO:gurobipy:

Solved in 8772 iterations and 1.09 seconds (1.94 work units)

INFO:gurobipy:Solved in 8772 iterations and 1.09 seconds (1.94 work units)

Optimal objective  1.528379259e+10

INFO:gurobipy:Optimal objective  1.528379259e+10
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140168 duals
Objective: 1.53e+10
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)
INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 39.12it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 90.74it/s]
INFO:linopy.io: Writing time: 0.34s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-azu4qglv.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-azu4qglv.lp

Reading time = 0.12 seconds

INFO:gurobipy:Reading time = 0.12 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0x1a72cd45

INFO:gurobipy:Model fingerprint: 0x1a72cd45

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 5e+05]

INFO:gurobipy:  RHS range        [2e+03, 5e+05]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.182e+05

INFO:gurobipy: AA' NZ     : 2.182e+05

 Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

 Factor Ops : 1.008e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.008e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   2.52804117e+11  0.00000000e+00  1.50e+09 0.00e+00  1.13e+08     0s

INFO:gurobipy:   0   2.52804117e+11  0.00000000e+00  1.50e+09 0.00e+00  1.13e+08     0s

   1   2.93802075e+11 -9.01086111e+10  2.82e+08 2.21e+02  2.71e+07     0s

INFO:gurobipy:   1   2.93802075e+11 -9.01086111e+10  2.82e+08 2.21e+02  2.71e+07     0s

   2   2.11894628e+11 -8.73218685e+10  1.13e+07 1.66e+00  2.41e+06     0s

INFO:gurobipy:   2   2.11894628e+11 -8.73218685e+10  1.13e+07 1.66e+00  2.41e+06     0s

   3   5.91579593e+10 -1.50671637e+10  2.30e+06 2.33e-10  5.43e+05     0s

INFO:gurobipy:   3   5.91579593e+10 -1.50671637e+10  2.30e+06 2.33e-10  5.43e+05     0s

   4   4.35885622e+10 -1.19762945e+10  1.60e+06 7.57e-10  4.02e+05     0s

INFO:gurobipy:   4   4.35885622e+10 -1.19762945e+10  1.60e+06 7.57e-10  4.02e+05     0s

   5   3.73338795e+10 -8.53132089e+09  1.32e+06 3.78e-10  3.30e+05     0s

INFO:gurobipy:   5   3.73338795e+10 -8.53132089e+09  1.32e+06 3.78e-10  3.30e+05     0s

   6   3.28662366e+10 -5.21363458e+09  1.12e+06 3.93e-10  2.72e+05     0s

INFO:gurobipy:   6   3.28662366e+10 -5.21363458e+09  1.12e+06 3.93e-10  2.72e+05     0s

   7   2.69587102e+10 -1.50128930e+09  8.66e+05 1.75e-10  2.03e+05     0s

INFO:gurobipy:   7   2.69587102e+10 -1.50128930e+09  8.66e+05 1.75e-10  2.03e+05     0s

   8   2.16391077e+10  1.13540429e+09  6.18e+05 4.66e-10  1.46e+05     0s

INFO:gurobipy:   8   2.16391077e+10  1.13540429e+09  6.18e+05 4.66e-10  1.46e+05     0s

   9   1.87291512e+10  1.87186884e+09  4.79e+05 3.49e-10  1.19e+05     0s

INFO:gurobipy:   9   1.87291512e+10  1.87186884e+09  4.79e+05 3.49e-10  1.19e+05     0s

  10   1.78193616e+10  2.62402717e+09  4.29e+05 6.55e-11  1.08e+05     0s

INFO:gurobipy:  10   1.78193616e+10  2.62402717e+09  4.29e+05 6.55e-11  1.08e+05     0s

  11   1.66746820e+10  4.26528899e+09  3.73e+05 2.91e-11  8.85e+04     0s

INFO:gurobipy:  11   1.66746820e+10  4.26528899e+09  3.73e+05 2.91e-11  8.85e+04     0s

  12   1.57459814e+10  4.83791031e+09  3.23e+05 8.73e-11  7.78e+04     0s

INFO:gurobipy:  12   1.57459814e+10  4.83791031e+09  3.23e+05 8.73e-11  7.78e+04     0s

  13   1.53301001e+10  5.43521735e+09  2.99e+05 1.75e-10  7.08e+04     0s

INFO:gurobipy:  13   1.53301001e+10  5.43521735e+09  2.99e+05 1.75e-10  7.08e+04     0s

  14   1.49019594e+10  5.85792692e+09  2.69e+05 1.09e-10  6.48e+04     0s

INFO:gurobipy:  14   1.49019594e+10  5.85792692e+09  2.69e+05 1.09e-10  6.48e+04     0s

  15   1.45578580e+10  6.91825158e+09  2.44e+05 1.46e-10  5.53e+04     0s

INFO:gurobipy:  15   1.45578580e+10  6.91825158e+09  2.44e+05 1.46e-10  5.53e+04     0s

  16   1.40963985e+10  7.11403180e+09  2.14e+05 1.60e-10  5.04e+04     0s

INFO:gurobipy:  16   1.40963985e+10  7.11403180e+09  2.14e+05 1.60e-10  5.04e+04     0s

  17   1.39300945e+10  7.42667365e+09  2.03e+05 1.46e-10  4.71e+04     0s

INFO:gurobipy:  17   1.39300945e+10  7.42667365e+09  2.03e+05 1.46e-10  4.71e+04     0s

  18   1.37795329e+10  7.58492844e+09  1.91e+05 2.62e-10  4.49e+04     0s

INFO:gurobipy:  18   1.37795329e+10  7.58492844e+09  1.91e+05 2.62e-10  4.49e+04     0s

  19   1.36650379e+10  7.82615603e+09  1.80e+05 0.00e+00  4.23e+04     0s

INFO:gurobipy:  19   1.36650379e+10  7.82615603e+09  1.80e+05 0.00e+00  4.23e+04     0s

  20   1.35788001e+10  7.99253889e+09  1.73e+05 1.46e-10  4.05e+04     0s

INFO:gurobipy:  20   1.35788001e+10  7.99253889e+09  1.73e+05 1.46e-10  4.05e+04     0s

  21   1.35155931e+10  8.12940465e+09  1.67e+05 2.76e-10  3.91e+04     0s

INFO:gurobipy:  21   1.35155931e+10  8.12940465e+09  1.67e+05 2.76e-10  3.91e+04     0s

  22   1.33878452e+10  8.38281970e+09  1.56e+05 0.00e+00  3.65e+04     1s

INFO:gurobipy:  22   1.33878452e+10  8.38281970e+09  1.56e+05 0.00e+00  3.65e+04     1s

  23   1.33751823e+10  8.53131938e+09  1.55e+05 3.78e-10  3.54e+04     1s

INFO:gurobipy:  23   1.33751823e+10  8.53131938e+09  1.55e+05 3.78e-10  3.54e+04     1s

  24   1.33016947e+10  8.61998054e+09  1.47e+05 3.06e-10  3.42e+04     1s

INFO:gurobipy:  24   1.33016947e+10  8.61998054e+09  1.47e+05 3.06e-10  3.42e+04     1s

  25   1.31282318e+10  8.79589138e+09  1.31e+05 3.78e-10  3.16e+04     1s

INFO:gurobipy:  25   1.31282318e+10  8.79589138e+09  1.31e+05 3.78e-10  3.16e+04     1s

  26   1.30879159e+10  9.03792620e+09  1.23e+05 4.66e-10  2.96e+04     1s

INFO:gurobipy:  26   1.30879159e+10  9.03792620e+09  1.23e+05 4.66e-10  2.96e+04     1s

  27   1.30012950e+10  9.31079862e+09  1.12e+05 1.42e-10  2.70e+04     1s

INFO:gurobipy:  27   1.30012950e+10  9.31079862e+09  1.12e+05 1.42e-10  2.70e+04     1s

  28   1.29725577e+10  9.42520317e+09  1.04e+05 4.07e-10  2.59e+04     1s

INFO:gurobipy:  28   1.29725577e+10  9.42520317e+09  1.04e+05 4.07e-10  2.59e+04     1s

  29   1.29733223e+10  9.60307788e+09  9.62e+04 5.24e-10  2.46e+04     1s

INFO:gurobipy:  29   1.29733223e+10  9.60307788e+09  9.62e+04 5.24e-10  2.46e+04     1s

  30   1.29393598e+10  9.91099428e+09  8.82e+04 4.37e-10  2.21e+04     1s

INFO:gurobipy:  30   1.29393598e+10  9.91099428e+09  8.82e+04 4.37e-10  2.21e+04     1s

  31   1.29109338e+10  1.00569710e+10  8.11e+04 6.69e-10  2.08e+04     1s

INFO:gurobipy:  31   1.29109338e+10  1.00569710e+10  8.11e+04 6.69e-10  2.08e+04     1s

  32   1.28771193e+10  1.02594868e+10  7.23e+04 2.33e-10  1.91e+04     1s

INFO:gurobipy:  32   1.28771193e+10  1.02594868e+10  7.23e+04 2.33e-10  1.91e+04     1s

  33   1.28725112e+10  1.03795458e+10  6.52e+04 2.62e-10  1.81e+04     1s

INFO:gurobipy:  33   1.28725112e+10  1.03795458e+10  6.52e+04 2.62e-10  1.81e+04     1s

  34   1.28668288e+10  1.04709808e+10  6.32e+04 4.95e-10  1.74e+04     1s

INFO:gurobipy:  34   1.28668288e+10  1.04709808e+10  6.32e+04 4.95e-10  1.74e+04     1s

  35   1.28780494e+10  1.05906498e+10  6.02e+04 2.62e-10  1.66e+04     1s

INFO:gurobipy:  35   1.28780494e+10  1.05906498e+10  6.02e+04 2.62e-10  1.66e+04     1s

  36   1.28752101e+10  1.07154698e+10  5.32e+04 3.78e-10  1.56e+04     1s

INFO:gurobipy:  36   1.28752101e+10  1.07154698e+10  5.32e+04 3.78e-10  1.56e+04     1s

  37   1.28395305e+10  1.09193464e+10  4.43e+04 2.04e-10  1.39e+04     1s

INFO:gurobipy:  37   1.28395305e+10  1.09193464e+10  4.43e+04 2.04e-10  1.39e+04     1s

  38   1.28326668e+10  1.11098416e+10  4.20e+04 3.49e-10  1.25e+04     1s

INFO:gurobipy:  38   1.28326668e+10  1.11098416e+10  4.20e+04 3.49e-10  1.25e+04     1s

  39   1.28163744e+10  1.11587939e+10  3.86e+04 4.37e-10  1.20e+04     1s

INFO:gurobipy:  39   1.28163744e+10  1.11587939e+10  3.86e+04 4.37e-10  1.20e+04     1s

  40   1.28139604e+10  1.13153348e+10  3.28e+04 1.75e-10  1.08e+04     1s

INFO:gurobipy:  40   1.28139604e+10  1.13153348e+10  3.28e+04 1.75e-10  1.08e+04     1s

  41   1.28048745e+10  1.14691979e+10  3.02e+04 4.37e-10  9.66e+03     1s

INFO:gurobipy:  41   1.28048745e+10  1.14691979e+10  3.02e+04 4.37e-10  9.66e+03     1s

  42   1.27884772e+10  1.15981418e+10  2.73e+04 2.33e-10  8.62e+03     1s

INFO:gurobipy:  42   1.27884772e+10  1.15981418e+10  2.73e+04 2.33e-10  8.62e+03     1s

  43   1.27948884e+10  1.16771734e+10  2.59e+04 2.62e-10  8.10e+03     1s

INFO:gurobipy:  43   1.27948884e+10  1.16771734e+10  2.59e+04 2.62e-10  8.10e+03     1s

  44   1.27842182e+10  1.17672956e+10  2.19e+04 2.55e-11  7.34e+03     1s

INFO:gurobipy:  44   1.27842182e+10  1.17672956e+10  2.19e+04 2.55e-11  7.34e+03     1s

  45   1.27787641e+10  1.18006072e+10  1.95e+04 3.78e-10  7.02e+03     1s

INFO:gurobipy:  45   1.27787641e+10  1.18006072e+10  1.95e+04 3.78e-10  7.02e+03     1s

  46   1.27749705e+10  1.19075960e+10  1.78e+04 9.90e-10  6.24e+03     1s

INFO:gurobipy:  46   1.27749705e+10  1.19075960e+10  1.78e+04 9.90e-10  6.24e+03     1s

  47   1.27741210e+10  1.19380220e+10  1.40e+04 2.91e-10  5.94e+03     1s

INFO:gurobipy:  47   1.27741210e+10  1.19380220e+10  1.40e+04 2.91e-10  5.94e+03     1s

  48   1.27739539e+10  1.20193511e+10  1.35e+04 5.93e-10  5.38e+03     1s

INFO:gurobipy:  48   1.27739539e+10  1.20193511e+10  1.35e+04 5.93e-10  5.38e+03     1s

  49   1.27758328e+10  1.20763192e+10  1.17e+04 4.95e-10  4.98e+03     1s

INFO:gurobipy:  49   1.27758328e+10  1.20763192e+10  1.17e+04 4.95e-10  4.98e+03     1s

  50   1.27767353e+10  1.21756397e+10  8.77e+03 3.89e-10  4.25e+03     1s

INFO:gurobipy:  50   1.27767353e+10  1.21756397e+10  8.77e+03 3.89e-10  4.25e+03     1s

  51   1.27776114e+10  1.22151202e+10  8.21e+03 6.11e-10  3.97e+03     1s

INFO:gurobipy:  51   1.27776114e+10  1.22151202e+10  8.21e+03 6.11e-10  3.97e+03     1s

  52   1.27771803e+10  1.23003420e+10  7.09e+03 7.09e-10  3.37e+03     1s

INFO:gurobipy:  52   1.27771803e+10  1.23003420e+10  7.09e+03 7.09e-10  3.37e+03     1s

  53   1.27675373e+10  1.23117556e+10  3.13e+03 3.45e-09  3.14e+03     1s

INFO:gurobipy:  53   1.27675373e+10  1.23117556e+10  3.13e+03 3.45e-09  3.14e+03     1s

  54   1.27668260e+10  1.24371382e+10  2.77e+03 2.26e-08  2.28e+03     1s

INFO:gurobipy:  54   1.27668260e+10  1.24371382e+10  2.77e+03 2.26e-08  2.28e+03     1s

  55   1.27637905e+10  1.24794778e+10  8.81e+02 2.18e-08  1.93e+03     1s

INFO:gurobipy:  55   1.27637905e+10  1.24794778e+10  8.81e+02 2.18e-08  1.93e+03     1s

  56   1.27624910e+10  1.25028935e+10  6.85e+02 2.95e-08  1.76e+03     1s

INFO:gurobipy:  56   1.27624910e+10  1.25028935e+10  6.85e+02 2.95e-08  1.76e+03     1s

  57   1.27621921e+10  1.25286295e+10  6.21e+02 3.27e-08  1.59e+03     1s

INFO:gurobipy:  57   1.27621921e+10  1.25286295e+10  6.21e+02 3.27e-08  1.59e+03     1s

  58   1.27613442e+10  1.25603716e+10  4.89e+02 2.76e-08  1.36e+03     1s

INFO:gurobipy:  58   1.27613442e+10  1.25603716e+10  4.89e+02 2.76e-08  1.36e+03     1s

  59   1.27576876e+10  1.25743644e+10  2.69e+02 2.77e-08  1.24e+03     1s

INFO:gurobipy:  59   1.27576876e+10  1.25743644e+10  2.69e+02 2.77e-08  1.24e+03     1s

  60   1.27570926e+10  1.26008141e+10  1.92e+02 2.98e-08  1.06e+03     1s

INFO:gurobipy:  60   1.27570926e+10  1.26008141e+10  1.92e+02 2.98e-08  1.06e+03     1s

  61   1.27563013e+10  1.26125943e+10  1.75e+02 3.61e-08  9.71e+02     1s

INFO:gurobipy:  61   1.27563013e+10  1.26125943e+10  1.75e+02 3.61e-08  9.71e+02     1s

  62   1.27554242e+10  1.26567606e+10  1.25e+02 3.97e-08  6.66e+02     1s

INFO:gurobipy:  62   1.27554242e+10  1.26567606e+10  1.25e+02 3.97e-08  6.66e+02     1s

  63   1.27546199e+10  1.26596487e+10  1.06e+02 3.96e-08  6.41e+02     1s

INFO:gurobipy:  63   1.27546199e+10  1.26596487e+10  1.06e+02 3.96e-08  6.41e+02     1s

  64   1.27542022e+10  1.26692697e+10  9.76e+01 3.14e-08  5.73e+02     1s

INFO:gurobipy:  64   1.27542022e+10  1.26692697e+10  9.76e+01 3.14e-08  5.73e+02     1s

  65   1.27539715e+10  1.26707294e+10  9.10e+01 3.07e-08  5.62e+02     1s

INFO:gurobipy:  65   1.27539715e+10  1.26707294e+10  9.10e+01 3.07e-08  5.62e+02     1s

  66   1.27532791e+10  1.26986106e+10  7.28e+01 2.73e-08  3.69e+02     1s

INFO:gurobipy:  66   1.27532791e+10  1.26986106e+10  7.28e+01 2.73e-08  3.69e+02     1s

  67   1.27526374e+10  1.27086766e+10  5.54e+01 2.21e-08  2.97e+02     1s

INFO:gurobipy:  67   1.27526374e+10  1.27086766e+10  5.54e+01 2.21e-08  2.97e+02     1s

  68   1.27515542e+10  1.27412351e+10  2.78e+01 5.89e-09  7.00e+01     1s

INFO:gurobipy:  68   1.27515542e+10  1.27412351e+10  2.78e+01 5.89e-09  7.00e+01     1s

  69   1.27508427e+10  1.27476781e+10  1.40e+01 1.64e-09  2.16e+01     1s

INFO:gurobipy:  69   1.27508427e+10  1.27476781e+10  1.40e+01 1.64e-09  2.16e+01     1s

  70   1.27506720e+10  1.27477060e+10  1.11e+01 1.54e-09  2.02e+01     1s

INFO:gurobipy:  70   1.27506720e+10  1.27477060e+10  1.11e+01 1.54e-09  2.02e+01     1s

  71   1.27502520e+10  1.27483512e+10  3.88e+00 1.37e-09  1.29e+01     1s

INFO:gurobipy:  71   1.27502520e+10  1.27483512e+10  3.88e+00 1.37e-09  1.29e+01     1s

  72   1.27500955e+10  1.27498266e+10  1.30e+00 3.97e-10  1.84e+00     1s

INFO:gurobipy:  72   1.27500955e+10  1.27498266e+10  1.30e+00 3.97e-10  1.84e+00     1s

  73   1.27500176e+10  1.27499933e+10  2.30e-01 5.24e-10  1.69e-01     1s

INFO:gurobipy:  73   1.27500176e+10  1.27499933e+10  2.30e-01 5.24e-10  1.69e-01     1s

  74   1.27500031e+10  1.27500002e+10  3.53e-02 1.19e-09  2.01e-02     1s

INFO:gurobipy:  74   1.27500031e+10  1.27500002e+10  3.53e-02 1.19e-09  2.01e-02     1s

  75   1.27500004e+10  1.27500004e+10  8.19e-05 4.67e-09  1.32e-04     1s

INFO:gurobipy:  75   1.27500004e+10  1.27500004e+10  8.19e-05 4.67e-09  1.32e-04     1s

  76   1.27500004e+10  1.27500004e+10  4.22e-08 2.44e-09  3.19e-10     1s

INFO:gurobipy:  76   1.27500004e+10  1.27500004e+10  4.22e-08 2.44e-09  3.19e-10     1s

INFO:gurobipy:

Barrier solved model in 76 iterations and 1.30 seconds (2.13 work units)

INFO:gurobipy:Barrier solved model in 76 iterations and 1.30 seconds (2.13 work units)

Optimal objective 1.27500004e+10

INFO:gurobipy:Optimal objective 1.27500004e+10

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      38 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:      38 DPushes remaining with DInf 0.0000000e+00                 1s

       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 1s

Warning: Markowitz tolerance tightened to 0.25

INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.25

INFO:gurobipy:

    8727 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:    8727 PPushes remaining with PInf 0.0000000e+00                 1s

       0 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 2.1215878e-09      1s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 2.1215878e-09      1s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8768    1.2750000e+10   0.000000e+00   0.000000e+00      1s

INFO:gurobipy:    8768    1.2750000e+10   0.000000e+00   0.000000e+00      1s

INFO:gurobipy:

Solved in 8768 iterations and 1.43 seconds (2.45 work units)

INFO:gurobipy:Solved in 8768 iterations and 1.43 seconds (2.45 work units)

Optimal objective  1.275000036e+10

INFO:gurobipy:Optimal objective  1.275000036e+10
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140168 duals
Objective: 1.28e+10
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)
INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 38.70it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 89.06it/s]
INFO:linopy.io: Writing time: 0.34s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-_4ei__yq.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-_4ei__yq.lp

Reading time = 0.12 seconds

INFO:gurobipy:Reading time = 0.12 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0xa59b640e

INFO:gurobipy:Model fingerprint: 0xa59b640e

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 1e+06]

INFO:gurobipy:  RHS range        [2e+03, 1e+06]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.182e+05

INFO:gurobipy: AA' NZ     : 2.182e+05

 Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

 Factor Ops : 1.008e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.008e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   3.50708435e+11  0.00000000e+00  2.09e+09 0.00e+00  1.57e+08     0s

INFO:gurobipy:   0   3.50708435e+11  0.00000000e+00  2.09e+09 0.00e+00  1.57e+08     0s

   1   4.07043306e+11 -9.33032559e+10  4.03e+08 2.22e+02  3.80e+07     0s

INFO:gurobipy:   1   4.07043306e+11 -9.33032559e+10  4.03e+08 2.22e+02  3.80e+07     0s

   2   2.99386027e+11 -1.01221685e+11  3.54e+07 1.73e+00  3.82e+06     0s

INFO:gurobipy:   2   2.99386027e+11 -1.01221685e+11  3.54e+07 1.73e+00  3.82e+06     0s

   3   5.92104792e+10 -2.89317892e+10  4.86e+06 5.24e-10  6.84e+05     0s

INFO:gurobipy:   3   5.92104792e+10 -2.89317892e+10  4.86e+06 5.24e-10  6.84e+05     0s

   4   4.41014312e+10 -1.64330203e+10  3.46e+06 3.78e-10  4.60e+05     0s

INFO:gurobipy:   4   4.41014312e+10 -1.64330203e+10  3.46e+06 3.78e-10  4.60e+05     0s

   5   3.42571357e+10 -1.26675316e+10  2.54e+06 2.33e-10  3.51e+05     0s

INFO:gurobipy:   5   3.42571357e+10 -1.26675316e+10  2.54e+06 2.33e-10  3.51e+05     0s

   6   2.85278566e+10 -9.37358328e+09  1.99e+06 1.93e-10  2.81e+05     0s

INFO:gurobipy:   6   2.85278566e+10 -9.37358328e+09  1.99e+06 1.93e-10  2.81e+05     0s

   7   2.30804507e+10 -3.26236792e+09  1.52e+06 7.86e-10  1.93e+05     0s

INFO:gurobipy:   7   2.30804507e+10 -3.26236792e+09  1.52e+06 7.86e-10  1.93e+05     0s

   8   1.83868456e+10 -2.17774306e+08  1.07e+06 7.57e-10  1.36e+05     0s

INFO:gurobipy:   8   1.83868456e+10 -2.17774306e+08  1.07e+06 7.57e-10  1.36e+05     0s

   9   1.55917572e+10  2.64601414e+09  8.04e+05 6.40e-10  9.45e+04     0s

INFO:gurobipy:   9   1.55917572e+10  2.64601414e+09  8.04e+05 6.40e-10  9.45e+04     0s

  10   1.43825154e+10  3.34151270e+09  6.79e+05 6.69e-10  8.05e+04     0s

INFO:gurobipy:  10   1.43825154e+10  3.34151270e+09  6.79e+05 6.69e-10  8.05e+04     0s

  11   1.36626539e+10  3.81080814e+09  5.82e+05 5.38e-10  7.16e+04     0s

INFO:gurobipy:  11   1.36626539e+10  3.81080814e+09  5.82e+05 5.38e-10  7.16e+04     0s

  12   1.32676379e+10  4.81591115e+09  5.41e+05 8.73e-11  6.18e+04     0s

INFO:gurobipy:  12   1.32676379e+10  4.81591115e+09  5.41e+05 8.73e-11  6.18e+04     0s

  13   1.27308208e+10  5.16330208e+09  4.81e+05 6.40e-10  5.53e+04     0s

INFO:gurobipy:  13   1.27308208e+10  5.16330208e+09  4.81e+05 6.40e-10  5.53e+04     0s

  14   1.23773675e+10  5.45268075e+09  4.29e+05 3.49e-10  5.06e+04     0s

INFO:gurobipy:  14   1.23773675e+10  5.45268075e+09  4.29e+05 3.49e-10  5.06e+04     0s

  15   1.19706944e+10  6.05637507e+09  3.81e+05 6.11e-10  4.34e+04     0s

INFO:gurobipy:  15   1.19706944e+10  6.05637507e+09  3.81e+05 6.11e-10  4.34e+04     0s

  16   1.17802952e+10  6.26626808e+09  3.56e+05 2.33e-10  4.04e+04     0s

INFO:gurobipy:  16   1.17802952e+10  6.26626808e+09  3.56e+05 2.33e-10  4.04e+04     0s

  17   1.15219337e+10  6.50096115e+09  3.19e+05 2.91e-10  3.68e+04     0s

INFO:gurobipy:  17   1.15219337e+10  6.50096115e+09  3.19e+05 2.91e-10  3.68e+04     0s

  18   1.14138671e+10  6.67901926e+09  2.95e+05 4.66e-10  3.47e+04     0s

INFO:gurobipy:  18   1.14138671e+10  6.67901926e+09  2.95e+05 4.66e-10  3.47e+04     0s

  19   1.13081349e+10  6.93841806e+09  2.78e+05 3.06e-10  3.21e+04     1s

INFO:gurobipy:  19   1.13081349e+10  6.93841806e+09  2.78e+05 3.06e-10  3.21e+04     1s

  20   1.11683145e+10  7.22367414e+09  2.52e+05 3.20e-10  2.90e+04     1s

INFO:gurobipy:  20   1.11683145e+10  7.22367414e+09  2.52e+05 3.20e-10  2.90e+04     1s

  21   1.10456207e+10  7.44410096e+09  2.26e+05 1.16e-10  2.64e+04     1s

INFO:gurobipy:  21   1.10456207e+10  7.44410096e+09  2.26e+05 1.16e-10  2.64e+04     1s

  22   1.10153051e+10  7.57630915e+09  2.15e+05 7.64e-11  2.52e+04     1s

INFO:gurobipy:  22   1.10153051e+10  7.57630915e+09  2.15e+05 7.64e-11  2.52e+04     1s

  23   1.09119121e+10  7.82389420e+09  1.91e+05 3.78e-10  2.27e+04     1s

INFO:gurobipy:  23   1.09119121e+10  7.82389420e+09  1.91e+05 3.78e-10  2.27e+04     1s

  24   1.08440067e+10  7.99115321e+09  1.74e+05 6.40e-10  2.09e+04     1s

INFO:gurobipy:  24   1.08440067e+10  7.99115321e+09  1.74e+05 6.40e-10  2.09e+04     1s

  25   1.08112314e+10  8.12926248e+09  1.58e+05 6.11e-10  1.96e+04     1s

INFO:gurobipy:  25   1.08112314e+10  8.12926248e+09  1.58e+05 6.11e-10  1.96e+04     1s

  26   1.07898020e+10  8.27208295e+09  1.43e+05 3.06e-10  1.84e+04     1s

INFO:gurobipy:  26   1.07898020e+10  8.27208295e+09  1.43e+05 3.06e-10  1.84e+04     1s

  27   1.07074459e+10  8.73634403e+09  1.12e+05 7.86e-10  1.44e+04     1s

INFO:gurobipy:  27   1.07074459e+10  8.73634403e+09  1.12e+05 7.86e-10  1.44e+04     1s

  28   1.06612913e+10  8.85557958e+09  9.96e+04 7.57e-10  1.32e+04     1s

INFO:gurobipy:  28   1.06612913e+10  8.85557958e+09  9.96e+04 7.57e-10  1.32e+04     1s

  29   1.06249292e+10  8.94215574e+09  9.09e+04 3.78e-10  1.23e+04     1s

INFO:gurobipy:  29   1.06249292e+10  8.94215574e+09  9.09e+04 3.78e-10  1.23e+04     1s

  30   1.05975879e+10  9.10759787e+09  8.36e+04 1.16e-10  1.09e+04     1s

INFO:gurobipy:  30   1.05975879e+10  9.10759787e+09  8.36e+04 1.16e-10  1.09e+04     1s

  31   1.05683069e+10  9.19165447e+09  7.49e+04 3.78e-10  1.00e+04     1s

INFO:gurobipy:  31   1.05683069e+10  9.19165447e+09  7.49e+04 3.78e-10  1.00e+04     1s

  32   1.05382689e+10  9.24958371e+09  6.56e+04 2.62e-10  9.36e+03     1s

INFO:gurobipy:  32   1.05382689e+10  9.24958371e+09  6.56e+04 2.62e-10  9.36e+03     1s

  33   1.05415617e+10  9.28427283e+09  6.17e+04 7.86e-10  9.10e+03     1s

INFO:gurobipy:  33   1.05415617e+10  9.28427283e+09  6.17e+04 7.86e-10  9.10e+03     1s

  34   1.05203940e+10  9.42002128e+09  5.38e+04 7.82e-10  7.97e+03     1s

INFO:gurobipy:  34   1.05203940e+10  9.42002128e+09  5.38e+04 7.82e-10  7.97e+03     1s

  35   1.05041585e+10  9.52732808e+09  4.82e+04 6.58e-10  7.08e+03     1s

INFO:gurobipy:  35   1.05041585e+10  9.52732808e+09  4.82e+04 6.58e-10  7.08e+03     1s

  36   1.04927204e+10  9.56557349e+09  4.37e+04 3.89e-10  6.70e+03     1s

INFO:gurobipy:  36   1.04927204e+10  9.56557349e+09  4.37e+04 3.89e-10  6.70e+03     1s

  37   1.04837237e+10  9.61319174e+09  3.87e+04 9.02e-10  6.27e+03     1s

INFO:gurobipy:  37   1.04837237e+10  9.61319174e+09  3.87e+04 9.02e-10  6.27e+03     1s

  38   1.04738540e+10  9.71846351e+09  3.26e+04 2.27e-09  5.43e+03     1s

INFO:gurobipy:  38   1.04738540e+10  9.71846351e+09  3.26e+04 2.27e-09  5.43e+03     1s

  39   1.04657783e+10  9.75752287e+09  2.97e+04 2.17e-09  5.08e+03     1s

INFO:gurobipy:  39   1.04657783e+10  9.75752287e+09  2.97e+04 2.17e-09  5.08e+03     1s

  40   1.04596821e+10  9.78916271e+09  2.78e+04 1.13e-09  4.81e+03     1s

INFO:gurobipy:  40   1.04596821e+10  9.78916271e+09  2.78e+04 1.13e-09  4.81e+03     1s

  41   1.04616258e+10  9.81666468e+09  2.44e+04 9.79e-10  4.60e+03     1s

INFO:gurobipy:  41   1.04616258e+10  9.81666468e+09  2.44e+04 9.79e-10  4.60e+03     1s

  42   1.04526980e+10  9.89728312e+09  2.06e+04 1.42e-09  3.96e+03     1s

INFO:gurobipy:  42   1.04526980e+10  9.89728312e+09  2.06e+04 1.42e-09  3.96e+03     1s

  43   1.04485025e+10  9.90550666e+09  1.90e+04 1.26e-09  3.86e+03     1s

INFO:gurobipy:  43   1.04485025e+10  9.90550666e+09  1.90e+04 1.26e-09  3.86e+03     1s

  44   1.04463646e+10  9.98421007e+09  1.63e+04 7.02e-10  3.28e+03     1s

INFO:gurobipy:  44   1.04463646e+10  9.98421007e+09  1.63e+04 7.02e-10  3.28e+03     1s

  45   1.04364430e+10  1.00111313e+10  1.32e+04 1.12e-09  3.00e+03     1s

INFO:gurobipy:  45   1.04364430e+10  1.00111313e+10  1.32e+04 1.12e-09  3.00e+03     1s

  46   1.04326378e+10  1.00238696e+10  1.19e+04 7.68e-10  2.88e+03     1s

INFO:gurobipy:  46   1.04326378e+10  1.00238696e+10  1.19e+04 7.68e-10  2.88e+03     1s

  47   1.04312043e+10  1.00669773e+10  9.68e+03 2.50e-09  2.55e+03     1s

INFO:gurobipy:  47   1.04312043e+10  1.00669773e+10  9.68e+03 2.50e-09  2.55e+03     1s

  48   1.04262261e+10  1.00969518e+10  8.28e+03 5.58e-08  2.30e+03     1s

INFO:gurobipy:  48   1.04262261e+10  1.00969518e+10  8.28e+03 5.58e-08  2.30e+03     1s

  49   1.04205867e+10  1.01582781e+10  6.53e+03 1.11e-07  1.84e+03     1s

INFO:gurobipy:  49   1.04205867e+10  1.01582781e+10  6.53e+03 1.11e-07  1.84e+03     1s

  50   1.04178315e+10  1.01971515e+10  5.01e+03 1.11e-07  1.54e+03     1s

INFO:gurobipy:  50   1.04178315e+10  1.01971515e+10  5.01e+03 1.11e-07  1.54e+03     1s

  51   1.04138687e+10  1.02061918e+10  4.23e+03 1.23e-07  1.44e+03     1s

INFO:gurobipy:  51   1.04138687e+10  1.02061918e+10  4.23e+03 1.23e-07  1.44e+03     1s

  52   1.04132611e+10  1.02449128e+10  4.04e+03 1.30e-07  1.18e+03     1s

INFO:gurobipy:  52   1.04132611e+10  1.02449128e+10  4.04e+03 1.30e-07  1.18e+03     1s

  53   1.04091808e+10  1.02578034e+10  2.65e+03 1.35e-07  1.05e+03     1s

INFO:gurobipy:  53   1.04091808e+10  1.02578034e+10  2.65e+03 1.35e-07  1.05e+03     1s

  54   1.04080443e+10  1.02670692e+10  2.45e+03 1.40e-07  9.75e+02     1s

INFO:gurobipy:  54   1.04080443e+10  1.02670692e+10  2.45e+03 1.40e-07  9.75e+02     1s

  55   1.04069426e+10  1.02716120e+10  2.24e+03 1.43e-07  9.34e+02     1s

INFO:gurobipy:  55   1.04069426e+10  1.02716120e+10  2.24e+03 1.43e-07  9.34e+02     1s

  56   1.04047114e+10  1.02838879e+10  1.86e+03 1.46e-07  8.33e+02     1s

INFO:gurobipy:  56   1.04047114e+10  1.02838879e+10  1.86e+03 1.46e-07  8.33e+02     1s

  57   1.04045479e+10  1.02986342e+10  1.71e+03 1.23e-07  7.31e+02     1s

INFO:gurobipy:  57   1.04045479e+10  1.02986342e+10  1.71e+03 1.23e-07  7.31e+02     1s

  58   1.04014381e+10  1.03040135e+10  9.20e+02 1.18e-07  6.65e+02     1s

INFO:gurobipy:  58   1.04014381e+10  1.03040135e+10  9.20e+02 1.18e-07  6.65e+02     1s

  59   1.04010024e+10  1.03178177e+10  8.67e+02 1.23e-07  5.69e+02     1s

INFO:gurobipy:  59   1.04010024e+10  1.03178177e+10  8.67e+02 1.23e-07  5.69e+02     1s

  60   1.04006201e+10  1.03235661e+10  7.94e+02 1.15e-07  5.27e+02     1s

INFO:gurobipy:  60   1.04006201e+10  1.03235661e+10  7.94e+02 1.15e-07  5.27e+02     1s

  61   1.04001346e+10  1.03303912e+10  6.82e+02 9.87e-08  4.76e+02     1s

INFO:gurobipy:  61   1.04001346e+10  1.03303912e+10  6.82e+02 9.87e-08  4.76e+02     1s

  62   1.03999904e+10  1.03325577e+10  6.57e+02 9.60e-08  4.60e+02     1s

INFO:gurobipy:  62   1.03999904e+10  1.03325577e+10  6.57e+02 9.60e-08  4.60e+02     1s

  63   1.03998450e+10  1.03339678e+10  6.41e+02 9.52e-08  4.50e+02     1s

INFO:gurobipy:  63   1.03998450e+10  1.03339678e+10  6.41e+02 9.52e-08  4.50e+02     1s

  64   1.03997102e+10  1.03360813e+10  6.22e+02 9.41e-08  4.34e+02     1s

INFO:gurobipy:  64   1.03997102e+10  1.03360813e+10  6.22e+02 9.41e-08  4.34e+02     1s

  65   1.03990893e+10  1.03451687e+10  5.45e+02 8.97e-08  3.68e+02     1s

INFO:gurobipy:  65   1.03990893e+10  1.03451687e+10  5.45e+02 8.97e-08  3.68e+02     1s

  66   1.03992361e+10  1.03505104e+10  4.94e+02 8.15e-08  3.33e+02     1s

INFO:gurobipy:  66   1.03992361e+10  1.03505104e+10  4.94e+02 8.15e-08  3.33e+02     1s

  67   1.03980612e+10  1.03527557e+10  3.76e+02 7.86e-08  3.09e+02     1s

INFO:gurobipy:  67   1.03980612e+10  1.03527557e+10  3.76e+02 7.86e-08  3.09e+02     1s

  68   1.03977508e+10  1.03560788e+10  3.22e+02 7.34e-08  2.84e+02     1s

INFO:gurobipy:  68   1.03977508e+10  1.03560788e+10  3.22e+02 7.34e-08  2.84e+02     1s

  69   1.03975912e+10  1.03573667e+10  3.02e+02 7.05e-08  2.74e+02     1s

INFO:gurobipy:  69   1.03975912e+10  1.03573667e+10  3.02e+02 7.05e-08  2.74e+02     1s

  70   1.03973345e+10  1.03715036e+10  2.61e+02 4.48e-08  1.77e+02     1s

INFO:gurobipy:  70   1.03973345e+10  1.03715036e+10  2.61e+02 4.48e-08  1.77e+02     1s

  71   1.03959212e+10  1.03814144e+10  1.76e+01 2.55e-08  9.76e+01     1s

INFO:gurobipy:  71   1.03959212e+10  1.03814144e+10  1.76e+01 2.55e-08  9.76e+01     1s

  72   1.03958897e+10  1.03821838e+10  1.63e+01 2.41e-08  9.22e+01     1s

INFO:gurobipy:  72   1.03958897e+10  1.03821838e+10  1.63e+01 2.41e-08  9.22e+01     1s

  73   1.03958267e+10  1.03846154e+10  1.36e+01 1.94e-08  7.55e+01     1s

INFO:gurobipy:  73   1.03958267e+10  1.03846154e+10  1.36e+01 1.94e-08  7.55e+01     1s

  74   1.03956698e+10  1.03920361e+10  4.43e+00 5.87e-09  2.45e+01     1s

INFO:gurobipy:  74   1.03956698e+10  1.03920361e+10  4.43e+00 5.87e-09  2.45e+01     1s

  75   1.03955235e+10  1.03950956e+10  7.01e-01 4.58e-10  2.88e+00     1s

INFO:gurobipy:  75   1.03955235e+10  1.03950956e+10  7.01e-01 4.58e-10  2.88e+00     1s

  76   1.03954847e+10  1.03954327e+10  6.52e-03 6.98e-10  3.49e-01     1s

INFO:gurobipy:  76   1.03954847e+10  1.03954327e+10  6.52e-03 6.98e-10  3.49e-01     1s

  77   1.03954835e+10  1.03954832e+10  8.17e-07 9.82e-11  1.97e-03     1s

INFO:gurobipy:  77   1.03954835e+10  1.03954832e+10  8.17e-07 9.82e-11  1.97e-03     1s

  78   1.03954834e+10  1.03954834e+10  7.28e-12 1.32e-08  1.82e-08     1s

INFO:gurobipy:  78   1.03954834e+10  1.03954834e+10  7.28e-12 1.32e-08  1.82e-08     1s

  79   1.03954834e+10  1.03954834e+10  1.68e-08 1.38e-08  2.50e-12     1s

INFO:gurobipy:  79   1.03954834e+10  1.03954834e+10  1.68e-08 1.38e-08  2.50e-12     1s

INFO:gurobipy:

Barrier solved model in 79 iterations and 1.42 seconds (2.20 work units)

INFO:gurobipy:Barrier solved model in 79 iterations and 1.42 seconds (2.20 work units)

Optimal objective 1.03954834e+10

INFO:gurobipy:Optimal objective 1.03954834e+10

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      51 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:      51 DPushes remaining with DInf 0.0000000e+00                 1s

       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:

    8693 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:    8693 PPushes remaining with PInf 0.0000000e+00                 1s

       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 2.9825902e-09      2s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 2.9825902e-09      2s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8747    1.0395483e+10   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:    8747    1.0395483e+10   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:

Solved in 8747 iterations and 1.60 seconds (2.72 work units)

INFO:gurobipy:Solved in 8747 iterations and 1.60 seconds (2.72 work units)

Optimal objective  1.039548341e+10

INFO:gurobipy:Optimal objective  1.039548341e+10
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140168 duals
Objective: 1.04e+10
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)
INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 38.67it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 89.79it/s]
INFO:linopy.io: Writing time: 0.34s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-5wg2roq4.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-5wg2roq4.lp

Reading time = 0.15 seconds

INFO:gurobipy:Reading time = 0.15 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0x0ba17c00

INFO:gurobipy:Model fingerprint: 0x0ba17c00

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 2e+06]

INFO:gurobipy:  RHS range        [2e+03, 2e+06]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.182e+05

INFO:gurobipy: AA' NZ     : 2.182e+05

 Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

 Factor Ops : 1.008e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.008e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   4.22179212e+11  0.00000000e+00  2.52e+09 0.00e+00  1.89e+08     0s

INFO:gurobipy:   0   4.22179212e+11  0.00000000e+00  2.52e+09 0.00e+00  1.89e+08     0s

   1   4.89752024e+11 -9.49274621e+10  4.92e+08 2.22e+02  4.60e+07     0s

INFO:gurobipy:   1   4.89752024e+11 -9.49274621e+10  4.92e+08 2.22e+02  4.60e+07     0s

   2   3.68451266e+11 -1.08374085e+11  3.36e+07 1.81e+00  4.35e+06     0s

INFO:gurobipy:   2   3.68451266e+11 -1.08374085e+11  3.36e+07 1.81e+00  4.35e+06     0s

   3   6.87293074e+10 -3.77406728e+10  3.59e+06 4.15e-02  7.91e+05     0s

INFO:gurobipy:   3   6.87293074e+10 -3.77406728e+10  3.59e+06 4.15e-02  7.91e+05     0s

   4   4.28243545e+10 -1.90123493e+10  2.08e+06 1.40e-09  4.47e+05     0s

INFO:gurobipy:   4   4.28243545e+10 -1.90123493e+10  2.08e+06 1.40e-09  4.47e+05     0s

   5   3.30103082e+10 -1.31404206e+10  1.50e+06 1.31e-10  3.29e+05     0s

INFO:gurobipy:   5   3.30103082e+10 -1.31404206e+10  1.50e+06 1.31e-10  3.29e+05     0s

   6   2.73838707e+10 -8.49879025e+09  1.17e+06 7.86e-10  2.54e+05     0s

INFO:gurobipy:   6   2.73838707e+10 -8.49879025e+09  1.17e+06 7.86e-10  2.54e+05     0s

   7   2.09502659e+10 -3.25076392e+09  7.99e+05 1.37e-09  1.69e+05     0s

INFO:gurobipy:   7   2.09502659e+10 -3.25076392e+09  7.99e+05 1.37e-09  1.69e+05     0s

   8   1.59435254e+10 -9.47053265e+08  5.07e+05 9.90e-10  1.17e+05     0s

INFO:gurobipy:   8   1.59435254e+10 -9.47053265e+08  5.07e+05 9.90e-10  1.17e+05     0s

   9   1.41574253e+10  1.63207841e+09  4.07e+05 1.14e-09  8.70e+04     0s

INFO:gurobipy:   9   1.41574253e+10  1.63207841e+09  4.07e+05 1.14e-09  8.70e+04     0s

  10   1.29235530e+10  2.44705989e+09  3.38e+05 2.47e-10  7.27e+04     0s

INFO:gurobipy:  10   1.29235530e+10  2.44705989e+09  3.38e+05 2.47e-10  7.27e+04     0s

  11   1.21702066e+10  2.97857892e+09  2.90e+05 4.95e-10  6.37e+04     0s

INFO:gurobipy:  11   1.21702066e+10  2.97857892e+09  2.90e+05 4.95e-10  6.37e+04     0s

  12   1.19102659e+10  3.22293291e+09  2.70e+05 6.98e-10  6.02e+04     0s

INFO:gurobipy:  12   1.19102659e+10  3.22293291e+09  2.70e+05 6.98e-10  6.02e+04     0s

  13   1.12543533e+10  4.63308398e+09  2.28e+05 7.28e-10  4.60e+04     0s

INFO:gurobipy:  13   1.12543533e+10  4.63308398e+09  2.28e+05 7.28e-10  4.60e+04     0s

  14   1.10854714e+10  4.79987223e+09  2.14e+05 5.82e-10  4.37e+04     0s

INFO:gurobipy:  14   1.10854714e+10  4.79987223e+09  2.14e+05 5.82e-10  4.37e+04     0s

  15   1.09019403e+10  5.11529135e+09  2.02e+05 1.37e-09  4.02e+04     0s

INFO:gurobipy:  15   1.09019403e+10  5.11529135e+09  2.02e+05 1.37e-09  4.02e+04     0s

  16   1.04781491e+10  5.37417034e+09  1.71e+05 6.69e-10  3.54e+04     0s

INFO:gurobipy:  16   1.04781491e+10  5.37417034e+09  1.71e+05 6.69e-10  3.54e+04     0s

  17   1.02110054e+10  5.64570859e+09  1.48e+05 7.28e-10  3.17e+04     0s

INFO:gurobipy:  17   1.02110054e+10  5.64570859e+09  1.48e+05 7.28e-10  3.17e+04     0s

  18   1.01837926e+10  5.97932535e+09  1.45e+05 1.31e-09  2.92e+04     0s

INFO:gurobipy:  18   1.01837926e+10  5.97932535e+09  1.45e+05 1.31e-09  2.92e+04     0s

  19   1.00091614e+10  6.29934115e+09  1.27e+05 7.86e-10  2.58e+04     0s

INFO:gurobipy:  19   1.00091614e+10  6.29934115e+09  1.27e+05 7.86e-10  2.58e+04     0s

  20   9.85781927e+09  6.46669280e+09  1.10e+05 4.37e-10  2.35e+04     0s

INFO:gurobipy:  20   9.85781927e+09  6.46669280e+09  1.10e+05 4.37e-10  2.35e+04     0s

  21   9.78624928e+09  6.65665482e+09  1.02e+05 1.75e-10  2.17e+04     1s

INFO:gurobipy:  21   9.78624928e+09  6.65665482e+09  1.02e+05 1.75e-10  2.17e+04     1s

  22   9.71142015e+09  6.77953897e+09  9.22e+04 9.60e-10  2.03e+04     1s

INFO:gurobipy:  22   9.71142015e+09  6.77953897e+09  9.22e+04 9.60e-10  2.03e+04     1s

  23   9.64648165e+09  6.91910853e+09  8.31e+04 1.02e-09  1.89e+04     1s

INFO:gurobipy:  23   9.64648165e+09  6.91910853e+09  8.31e+04 1.02e-09  1.89e+04     1s

  24   9.59477560e+09  7.07112261e+09  7.01e+04 4.73e-11  1.74e+04     1s

INFO:gurobipy:  24   9.59477560e+09  7.07112261e+09  7.01e+04 4.73e-11  1.74e+04     1s

  25   9.54664796e+09  7.42722128e+09  6.42e+04 3.49e-10  1.47e+04     1s

INFO:gurobipy:  25   9.54664796e+09  7.42722128e+09  6.42e+04 3.49e-10  1.47e+04     1s

  26   9.50335624e+09  7.56212660e+09  5.84e+04 3.49e-10  1.34e+04     1s

INFO:gurobipy:  26   9.50335624e+09  7.56212660e+09  5.84e+04 3.49e-10  1.34e+04     1s

  27   9.46514595e+09  7.62381176e+09  5.30e+04 4.66e-10  1.27e+04     1s

INFO:gurobipy:  27   9.46514595e+09  7.62381176e+09  5.30e+04 4.66e-10  1.27e+04     1s

  28   9.45767048e+09  7.68959094e+09  4.77e+04 4.95e-10  1.22e+04     1s

INFO:gurobipy:  28   9.45767048e+09  7.68959094e+09  4.77e+04 4.95e-10  1.22e+04     1s

  29   9.39430392e+09  7.84134315e+09  3.82e+04 1.16e-10  1.07e+04     1s

INFO:gurobipy:  29   9.39430392e+09  7.84134315e+09  3.82e+04 1.16e-10  1.07e+04     1s

  30   9.39897237e+09  7.90348694e+09  3.46e+04 4.07e-10  1.03e+04     1s

INFO:gurobipy:  30   9.39897237e+09  7.90348694e+09  3.46e+04 4.07e-10  1.03e+04     1s

  31   9.35759377e+09  7.99869112e+09  2.94e+04 2.33e-10  9.33e+03     1s

INFO:gurobipy:  31   9.35759377e+09  7.99869112e+09  2.94e+04 2.33e-10  9.33e+03     1s

  32   9.32925998e+09  8.10818000e+09  2.58e+04 1.14e-09  8.38e+03     1s

INFO:gurobipy:  32   9.32925998e+09  8.10818000e+09  2.58e+04 1.14e-09  8.38e+03     1s

  33   9.31514861e+09  8.19628682e+09  2.38e+04 6.40e-10  7.68e+03     1s

INFO:gurobipy:  33   9.31514861e+09  8.19628682e+09  2.38e+04 6.40e-10  7.68e+03     1s

  34   9.30794733e+09  8.23521456e+09  2.26e+04 5.53e-10  7.36e+03     1s

INFO:gurobipy:  34   9.30794733e+09  8.23521456e+09  2.26e+04 5.53e-10  7.36e+03     1s

  35   9.28713758e+09  8.27444922e+09  1.93e+04 8.44e-10  6.93e+03     1s

INFO:gurobipy:  35   9.28713758e+09  8.27444922e+09  1.93e+04 8.44e-10  6.93e+03     1s

  36   9.28283609e+09  8.30914089e+09  1.59e+04 4.95e-10  6.65e+03     1s

INFO:gurobipy:  36   9.28283609e+09  8.30914089e+09  1.59e+04 4.95e-10  6.65e+03     1s

  37   9.26506506e+09  8.44909858e+09  1.38e+04 8.44e-10  5.58e+03     1s

INFO:gurobipy:  37   9.26506506e+09  8.44909858e+09  1.38e+04 8.44e-10  5.58e+03     1s

  38   9.25628858e+09  8.51197196e+09  1.25e+04 2.91e-11  5.09e+03     1s

INFO:gurobipy:  38   9.25628858e+09  8.51197196e+09  1.25e+04 2.91e-11  5.09e+03     1s

  39   9.24699203e+09  8.53459147e+09  1.09e+04 4.95e-10  4.86e+03     1s

INFO:gurobipy:  39   9.24699203e+09  8.53459147e+09  1.09e+04 4.95e-10  4.86e+03     1s

  40   9.24605943e+09  8.59574237e+09  9.96e+03 6.69e-10  4.44e+03     1s

INFO:gurobipy:  40   9.24605943e+09  8.59574237e+09  9.96e+03 6.69e-10  4.44e+03     1s

  41   9.23618783e+09  8.62362604e+09  8.77e+03 8.73e-11  4.18e+03     1s

INFO:gurobipy:  41   9.23618783e+09  8.62362604e+09  8.77e+03 8.73e-11  4.18e+03     1s

  42   9.22799063e+09  8.68848399e+09  7.72e+03 4.07e-10  3.68e+03     1s

INFO:gurobipy:  42   9.22799063e+09  8.68848399e+09  7.72e+03 4.07e-10  3.68e+03     1s

  43   9.22304810e+09  8.71346475e+09  6.98e+03 8.15e-10  3.47e+03     1s

INFO:gurobipy:  43   9.22304810e+09  8.71346475e+09  6.98e+03 8.15e-10  3.47e+03     1s

  44   9.22042812e+09  8.72595948e+09  6.23e+03 1.75e-10  3.36e+03     1s

INFO:gurobipy:  44   9.22042812e+09  8.72595948e+09  6.23e+03 1.75e-10  3.36e+03     1s

  45   9.21437167e+09  8.74963779e+09  5.35e+03 7.28e-12  3.16e+03     1s

INFO:gurobipy:  45   9.21437167e+09  8.74963779e+09  5.35e+03 7.28e-12  3.16e+03     1s

  46   9.21376519e+09  8.76591996e+09  4.85e+03 1.75e-10  3.04e+03     1s

INFO:gurobipy:  46   9.21376519e+09  8.76591996e+09  4.85e+03 1.75e-10  3.04e+03     1s

  47   9.20970551e+09  8.80336346e+09  4.30e+03 9.60e-10  2.76e+03     1s

INFO:gurobipy:  47   9.20970551e+09  8.80336346e+09  4.30e+03 9.60e-10  2.76e+03     1s

  48   9.20632109e+09  8.85003681e+09  3.73e+03 8.15e-10  2.42e+03     1s

INFO:gurobipy:  48   9.20632109e+09  8.85003681e+09  3.73e+03 8.15e-10  2.42e+03     1s

  49   9.20255629e+09  8.86137978e+09  3.16e+03 3.49e-10  2.31e+03     1s

INFO:gurobipy:  49   9.20255629e+09  8.86137978e+09  3.16e+03 3.49e-10  2.31e+03     1s

  50   9.19994989e+09  8.88028581e+09  2.80e+03 5.53e-10  2.17e+03     1s

INFO:gurobipy:  50   9.19994989e+09  8.88028581e+09  2.80e+03 5.53e-10  2.17e+03     1s

  51   9.19974118e+09  8.88829171e+09  2.74e+03 5.24e-10  2.11e+03     1s

INFO:gurobipy:  51   9.19974118e+09  8.88829171e+09  2.74e+03 5.24e-10  2.11e+03     1s

  52   9.19951527e+09  8.89655092e+09  2.70e+03 7.28e-10  2.05e+03     1s

INFO:gurobipy:  52   9.19951527e+09  8.89655092e+09  2.70e+03 7.28e-10  2.05e+03     1s

  53   9.19918107e+09  8.90812758e+09  2.65e+03 7.57e-10  1.97e+03     1s

INFO:gurobipy:  53   9.19918107e+09  8.90812758e+09  2.65e+03 7.57e-10  1.97e+03     1s

  54   9.19747618e+09  8.92931465e+09  2.44e+03 7.86e-10  1.82e+03     1s

INFO:gurobipy:  54   9.19747618e+09  8.92931465e+09  2.44e+03 7.86e-10  1.82e+03     1s

  55   9.19599611e+09  8.94557133e+09  2.24e+03 4.37e-10  1.70e+03     1s

INFO:gurobipy:  55   9.19599611e+09  8.94557133e+09  2.24e+03 4.37e-10  1.70e+03     1s

  56   9.19347290e+09  8.96148797e+09  1.97e+03 5.24e-10  1.57e+03     1s

INFO:gurobipy:  56   9.19347290e+09  8.96148797e+09  1.97e+03 5.24e-10  1.57e+03     1s

  57   9.19326310e+09  8.96693692e+09  1.90e+03 2.91e-10  1.53e+03     1s

INFO:gurobipy:  57   9.19326310e+09  8.96693692e+09  1.90e+03 2.91e-10  1.53e+03     1s

  58   9.19155297e+09  8.98063570e+09  1.46e+03 8.44e-10  1.43e+03     1s

INFO:gurobipy:  58   9.19155297e+09  8.98063570e+09  1.46e+03 8.44e-10  1.43e+03     1s

  59   9.19024912e+09  8.99126002e+09  1.31e+03 1.03e-09  1.35e+03     1s

INFO:gurobipy:  59   9.19024912e+09  8.99126002e+09  1.31e+03 1.03e-09  1.35e+03     1s

  60   9.18876372e+09  9.01755320e+09  1.15e+03 2.07e-09  1.16e+03     1s

INFO:gurobipy:  60   9.18876372e+09  9.01755320e+09  1.15e+03 2.07e-09  1.16e+03     1s

  61   9.18723703e+09  9.04883747e+09  9.70e+02 5.30e-09  9.36e+02     1s

INFO:gurobipy:  61   9.18723703e+09  9.04883747e+09  9.70e+02 5.30e-09  9.36e+02     1s

  62   9.18510837e+09  9.05345724e+09  6.60e+02 5.04e-09  8.89e+02     1s

INFO:gurobipy:  62   9.18510837e+09  9.05345724e+09  6.60e+02 5.04e-09  8.89e+02     1s

  63   9.18490403e+09  9.05879667e+09  6.35e+02 4.72e-09  8.52e+02     1s

INFO:gurobipy:  63   9.18490403e+09  9.05879667e+09  6.35e+02 4.72e-09  8.52e+02     1s

  64   9.18476082e+09  9.07007171e+09  6.19e+02 5.32e-09  7.75e+02     1s

INFO:gurobipy:  64   9.18476082e+09  9.07007171e+09  6.19e+02 5.32e-09  7.75e+02     1s

  65   9.18396812e+09  9.07671477e+09  5.22e+02 5.54e-09  7.24e+02     1s

INFO:gurobipy:  65   9.18396812e+09  9.07671477e+09  5.22e+02 5.54e-09  7.24e+02     1s

  66   9.18328263e+09  9.08332280e+09  4.54e+02 6.18e-09  6.75e+02     1s

INFO:gurobipy:  66   9.18328263e+09  9.08332280e+09  4.54e+02 6.18e-09  6.75e+02     1s

  67   9.18276667e+09  9.09119027e+09  4.12e+02 6.30e-09  6.18e+02     1s

INFO:gurobipy:  67   9.18276667e+09  9.09119027e+09  4.12e+02 6.30e-09  6.18e+02     1s

  68   9.18232804e+09  9.09714497e+09  3.66e+02 6.09e-09  5.75e+02     1s

INFO:gurobipy:  68   9.18232804e+09  9.09714497e+09  3.66e+02 6.09e-09  5.75e+02     1s

  69   9.18197510e+09  9.10131692e+09  3.39e+02 6.77e-09  5.44e+02     1s

INFO:gurobipy:  69   9.18197510e+09  9.10131692e+09  3.39e+02 6.77e-09  5.44e+02     1s

  70   9.18177006e+09  9.10416958e+09  3.22e+02 6.71e-09  5.24e+02     1s

INFO:gurobipy:  70   9.18177006e+09  9.10416958e+09  3.22e+02 6.71e-09  5.24e+02     1s

  71   9.18138679e+09  9.10998198e+09  2.89e+02 6.80e-09  4.82e+02     1s

INFO:gurobipy:  71   9.18138679e+09  9.10998198e+09  2.89e+02 6.80e-09  4.82e+02     1s

  72   9.18084753e+09  9.11379556e+09  2.39e+02 6.57e-09  4.52e+02     1s

INFO:gurobipy:  72   9.18084753e+09  9.11379556e+09  2.39e+02 6.57e-09  4.52e+02     1s

  73   9.18047739e+09  9.11680379e+09  2.03e+02 6.46e-09  4.29e+02     1s

INFO:gurobipy:  73   9.18047739e+09  9.11680379e+09  2.03e+02 6.46e-09  4.29e+02     1s

  74   9.18031126e+09  9.11989256e+09  1.89e+02 6.33e-09  4.07e+02     1s

INFO:gurobipy:  74   9.18031126e+09  9.11989256e+09  1.89e+02 6.33e-09  4.07e+02     1s

  75   9.18026338e+09  9.13072006e+09  1.87e+02 7.87e-09  3.34e+02     1s

INFO:gurobipy:  75   9.18026338e+09  9.13072006e+09  1.87e+02 7.87e-09  3.34e+02     1s

  76   9.17978496e+09  9.13586263e+09  1.47e+02 7.28e-09  2.96e+02     1s

INFO:gurobipy:  76   9.17978496e+09  9.13586263e+09  1.47e+02 7.28e-09  2.96e+02     1s

  77   9.17936702e+09  9.14722832e+09  1.09e+02 5.19e-09  2.17e+02     1s

INFO:gurobipy:  77   9.17936702e+09  9.14722832e+09  1.09e+02 5.19e-09  2.17e+02     1s

  78   9.17871808e+09  9.15240557e+09  6.08e+01 4.26e-09  1.77e+02     1s

INFO:gurobipy:  78   9.17871808e+09  9.15240557e+09  6.08e+01 4.26e-09  1.77e+02     1s

  79   9.17845543e+09  9.15322215e+09  4.46e+01 4.27e-09  1.70e+02     1s

INFO:gurobipy:  79   9.17845543e+09  9.15322215e+09  4.46e+01 4.27e-09  1.70e+02     1s

  80   9.17833444e+09  9.15926941e+09  3.61e+01 3.14e-09  1.28e+02     1s

INFO:gurobipy:  80   9.17833444e+09  9.15926941e+09  3.61e+01 3.14e-09  1.28e+02     1s

  81   9.17806581e+09  9.16184172e+09  1.86e+01 3.04e-09  1.09e+02     1s

INFO:gurobipy:  81   9.17806581e+09  9.16184172e+09  1.86e+01 3.04e-09  1.09e+02     1s

  82   9.17803395e+09  9.16465780e+09  1.67e+01 2.39e-09  9.00e+01     1s

INFO:gurobipy:  82   9.17803395e+09  9.16465780e+09  1.67e+01 2.39e-09  9.00e+01     1s

  83   9.17794152e+09  9.16703721e+09  1.30e+01 1.68e-09  7.34e+01     1s

INFO:gurobipy:  83   9.17794152e+09  9.16703721e+09  1.30e+01 1.68e-09  7.34e+01     1s

  84   9.17777946e+09  9.16962908e+09  4.71e+00 1.40e-09  5.48e+01     1s

INFO:gurobipy:  84   9.17777946e+09  9.16962908e+09  4.71e+00 1.40e-09  5.48e+01     1s

  85   9.17759051e+09  9.17320068e+09  8.55e-01 1.30e-09  2.95e+01     1s

INFO:gurobipy:  85   9.17759051e+09  9.17320068e+09  8.55e-01 1.30e-09  2.95e+01     1s

  86   9.17752855e+09  9.17708174e+09  1.59e-02 1.02e-09  3.00e+00     2s

INFO:gurobipy:  86   9.17752855e+09  9.17708174e+09  1.59e-02 1.02e-09  3.00e+00     2s

  87   9.17752328e+09  9.17744959e+09  1.08e-02 6.55e-10  4.95e-01     2s

INFO:gurobipy:  87   9.17752328e+09  9.17744959e+09  1.08e-02 6.55e-10  4.95e-01     2s

  88   9.17751917e+09  9.17750615e+09  7.51e-03 2.55e-10  8.75e-02     2s

INFO:gurobipy:  88   9.17751917e+09  9.17750615e+09  7.51e-03 2.55e-10  8.75e-02     2s

  89   9.17751229e+09  9.17750891e+09  1.84e-03 1.93e-10  2.27e-02     2s

INFO:gurobipy:  89   9.17751229e+09  9.17750891e+09  1.84e-03 1.93e-10  2.27e-02     2s

  90   9.17751005e+09  9.17750987e+09  1.21e-04 1.46e-09  1.20e-03     2s

INFO:gurobipy:  90   9.17751005e+09  9.17750987e+09  1.21e-04 1.46e-09  1.20e-03     2s

  91   9.17750988e+09  9.17750988e+09  8.88e-07 3.68e-09  1.47e-07     2s

INFO:gurobipy:  91   9.17750988e+09  9.17750988e+09  8.88e-07 3.68e-09  1.47e-07     2s

  92   9.17750988e+09  9.17750988e+09  7.05e-07 3.67e-09  4.71e-12     2s

INFO:gurobipy:  92   9.17750988e+09  9.17750988e+09  7.05e-07 3.67e-09  4.71e-12     2s

INFO:gurobipy:

Barrier solved model in 92 iterations and 1.62 seconds (2.52 work units)

INFO:gurobipy:Barrier solved model in 92 iterations and 1.62 seconds (2.52 work units)

Optimal objective 9.17750988e+09

INFO:gurobipy:Optimal objective 9.17750988e+09

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      51 DPushes remaining with DInf 0.0000000e+00                 2s

INFO:gurobipy:      51 DPushes remaining with DInf 0.0000000e+00                 2s

       0 DPushes remaining with DInf 0.0000000e+00                 2s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 2s

INFO:gurobipy:

    8648 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:    8648 PPushes remaining with PInf 0.0000000e+00                 2s

       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 2.6689891e-09      2s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 2.6689891e-09      2s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8702    9.1775099e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:    8702    9.1775099e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:

Solved in 8702 iterations and 1.82 seconds (3.29 work units)

INFO:gurobipy:Solved in 8702 iterations and 1.82 seconds (3.29 work units)

Optimal objective  9.177509876e+09

INFO:gurobipy:Optimal objective  9.177509876e+09
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140168 duals
Objective: 9.18e+09
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)
INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 37.30it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 84.17it/s]
INFO:linopy.io: Writing time: 0.35s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-h682qoky.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-h682qoky.lp

Reading time = 0.13 seconds

INFO:gurobipy:Reading time = 0.13 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0x8c43a66e

INFO:gurobipy:Model fingerprint: 0x8c43a66e

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 2e+06]

INFO:gurobipy:  RHS range        [2e+03, 2e+06]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.182e+05

INFO:gurobipy: AA' NZ     : 2.182e+05

 Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

 Factor Ops : 1.008e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.008e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   4.79289564e+11  0.00000000e+00  2.87e+09 0.00e+00  2.15e+08     0s

INFO:gurobipy:   0   4.79289564e+11  0.00000000e+00  2.87e+09 0.00e+00  2.15e+08     0s

   1   5.55880715e+11 -9.60342820e+10  5.63e+08 2.22e+02  5.23e+07     0s

INFO:gurobipy:   1   5.55880715e+11 -9.60342820e+10  5.63e+08 2.22e+02  5.23e+07     0s

   2   4.16146785e+11 -1.13081126e+11  2.79e+07 2.01e+00  4.60e+06     0s

INFO:gurobipy:   2   4.16146785e+11 -1.13081126e+11  2.79e+07 2.01e+00  4.60e+06     0s

   3   7.32220671e+10 -3.73037490e+10  3.02e+06 5.93e-02  8.05e+05     0s

INFO:gurobipy:   3   7.32220671e+10 -3.73037490e+10  3.02e+06 5.93e-02  8.05e+05     0s

   4   4.67808481e+10 -2.19477626e+10  1.80e+06 5.53e-10  4.89e+05     0s

INFO:gurobipy:   4   4.67808481e+10 -2.19477626e+10  1.80e+06 5.53e-10  4.89e+05     0s

   5   3.49912389e+10 -1.55687457e+10  1.26e+06 3.49e-10  3.56e+05     0s

INFO:gurobipy:   5   3.49912389e+10 -1.55687457e+10  1.26e+06 3.49e-10  3.56e+05     0s

   6   2.72746493e+10 -1.07945360e+10  9.14e+05 3.78e-10  2.65e+05     0s

INFO:gurobipy:   6   2.72746493e+10 -1.07945360e+10  9.14e+05 3.78e-10  2.65e+05     0s

   7   2.07818241e+10 -6.07610889e+09  6.29e+05 5.24e-10  1.86e+05     0s

INFO:gurobipy:   7   2.07818241e+10 -6.07610889e+09  6.29e+05 5.24e-10  1.86e+05     0s

   8   1.56388253e+10 -2.89829517e+09  4.01e+05 5.53e-10  1.28e+05     0s

INFO:gurobipy:   8   1.56388253e+10 -2.89829517e+09  4.01e+05 5.53e-10  1.28e+05     0s

   9   1.37642839e+10 -1.92501816e+08  3.21e+05 7.86e-10  9.58e+04     0s

INFO:gurobipy:   9   1.37642839e+10 -1.92501816e+08  3.21e+05 7.86e-10  9.58e+04     0s

  10   1.20986773e+10  1.79747168e+09  2.48e+05 1.35e-10  7.07e+04     0s

INFO:gurobipy:  10   1.20986773e+10  1.79747168e+09  2.48e+05 1.35e-10  7.07e+04     0s

  11   1.12647187e+10  2.62113592e+09  2.08e+05 2.76e-10  5.93e+04     0s

INFO:gurobipy:  11   1.12647187e+10  2.62113592e+09  2.08e+05 2.76e-10  5.93e+04     0s

  12   1.09993556e+10  3.13153417e+09  1.96e+05 6.98e-10  5.39e+04     0s

INFO:gurobipy:  12   1.09993556e+10  3.13153417e+09  1.96e+05 6.98e-10  5.39e+04     0s

  13   1.06629742e+10  3.65451191e+09  1.80e+05 6.37e-11  4.81e+04     0s

INFO:gurobipy:  13   1.06629742e+10  3.65451191e+09  1.80e+05 6.37e-11  4.81e+04     0s

  14   1.05419143e+10  3.84369778e+09  1.73e+05 1.16e-09  4.59e+04     0s

INFO:gurobipy:  14   1.05419143e+10  3.84369778e+09  1.73e+05 1.16e-09  4.59e+04     0s

  15   9.84848354e+09  4.63099031e+09  1.35e+05 5.82e-10  3.58e+04     0s

INFO:gurobipy:  15   9.84848354e+09  4.63099031e+09  1.35e+05 5.82e-10  3.58e+04     0s

  16   9.74957497e+09  5.01115391e+09  1.27e+05 5.24e-10  3.25e+04     0s

INFO:gurobipy:  16   9.74957497e+09  5.01115391e+09  1.27e+05 5.24e-10  3.25e+04     0s

  17   9.58403115e+09  5.30079226e+09  1.17e+05 6.40e-10  2.94e+04     0s

INFO:gurobipy:  17   9.58403115e+09  5.30079226e+09  1.17e+05 6.40e-10  2.94e+04     0s

  18   9.43643230e+09  5.73120854e+09  1.03e+05 8.44e-10  2.54e+04     0s

INFO:gurobipy:  18   9.43643230e+09  5.73120854e+09  1.03e+05 8.44e-10  2.54e+04     0s

  19   9.23756510e+09  5.97517632e+09  8.84e+04 1.13e-10  2.24e+04     1s

INFO:gurobipy:  19   9.23756510e+09  5.97517632e+09  8.84e+04 1.13e-10  2.24e+04     1s

  20   9.17759905e+09  6.06403846e+09  8.32e+04 2.33e-10  2.13e+04     1s

INFO:gurobipy:  20   9.17759905e+09  6.06403846e+09  8.32e+04 2.33e-10  2.13e+04     1s

  21   9.03446459e+09  6.37625806e+09  7.21e+04 4.24e-03  1.82e+04     1s

INFO:gurobipy:  21   9.03446459e+09  6.37625806e+09  7.21e+04 4.24e-03  1.82e+04     1s

  22   8.96749467e+09  6.67420096e+09  6.51e+04 1.75e-10  1.57e+04     1s

INFO:gurobipy:  22   8.96749467e+09  6.67420096e+09  6.51e+04 1.75e-10  1.57e+04     1s

  23   8.87235390e+09  6.81910768e+09  5.51e+04 5.82e-10  1.41e+04     1s

INFO:gurobipy:  23   8.87235390e+09  6.81910768e+09  5.51e+04 5.82e-10  1.41e+04     1s

  24   8.79653172e+09  6.92938916e+09  4.67e+04 2.33e-10  1.28e+04     1s

INFO:gurobipy:  24   8.79653172e+09  6.92938916e+09  4.67e+04 2.33e-10  1.28e+04     1s

  25   8.75482211e+09  7.13402061e+09  4.29e+04 5.53e-10  1.11e+04     1s

INFO:gurobipy:  25   8.75482211e+09  7.13402061e+09  4.29e+04 5.53e-10  1.11e+04     1s

  26   8.73030838e+09  7.18065837e+09  4.04e+04 2.22e-10  1.06e+04     1s

INFO:gurobipy:  26   8.73030838e+09  7.18065837e+09  4.04e+04 2.22e-10  1.06e+04     1s

  27   8.68513000e+09  7.35837448e+09  3.44e+04 1.46e-10  9.09e+03     1s

INFO:gurobipy:  27   8.68513000e+09  7.35837448e+09  3.44e+04 1.46e-10  9.09e+03     1s

  28   8.63357276e+09  7.50106948e+09  2.94e+04 6.40e-10  7.76e+03     1s

INFO:gurobipy:  28   8.63357276e+09  7.50106948e+09  2.94e+04 6.40e-10  7.76e+03     1s

  29   8.60673412e+09  7.56416622e+09  2.67e+04 1.05e-09  7.14e+03     1s

INFO:gurobipy:  29   8.60673412e+09  7.56416622e+09  2.67e+04 1.05e-09  7.14e+03     1s

  30   8.58029420e+09  7.62670097e+09  2.38e+04 4.07e-10  6.53e+03     1s

INFO:gurobipy:  30   8.58029420e+09  7.62670097e+09  2.38e+04 4.07e-10  6.53e+03     1s

  31   8.55898227e+09  7.72479866e+09  2.14e+04 7.28e-10  5.71e+03     1s

INFO:gurobipy:  31   8.55898227e+09  7.72479866e+09  2.14e+04 7.28e-10  5.71e+03     1s

  32   8.55258782e+09  7.74561495e+09  2.05e+04 3.78e-10  5.52e+03     1s

INFO:gurobipy:  32   8.55258782e+09  7.74561495e+09  2.05e+04 3.78e-10  5.52e+03     1s

  33   8.53045117e+09  7.78804975e+09  1.73e+04 1.46e-10  5.07e+03     1s

INFO:gurobipy:  33   8.53045117e+09  7.78804975e+09  1.73e+04 1.46e-10  5.07e+03     1s

  34   8.51263679e+09  7.89632298e+09  1.43e+04 8.44e-10  4.21e+03     1s

INFO:gurobipy:  34   8.51263679e+09  7.89632298e+09  1.43e+04 8.44e-10  4.21e+03     1s

  35   8.50021112e+09  7.98943341e+09  1.28e+04 4.37e-10  3.50e+03     1s

INFO:gurobipy:  35   8.50021112e+09  7.98943341e+09  1.28e+04 4.37e-10  3.50e+03     1s

  36   8.48875893e+09  8.01490308e+09  1.11e+04 4.95e-10  3.24e+03     1s

INFO:gurobipy:  36   8.48875893e+09  8.01490308e+09  1.11e+04 4.95e-10  3.24e+03     1s

  37   8.47584911e+09  8.03177595e+09  9.55e+03 2.47e-10  3.03e+03     1s

INFO:gurobipy:  37   8.47584911e+09  8.03177595e+09  9.55e+03 2.47e-10  3.03e+03     1s

  38   8.47019001e+09  8.05327545e+09  8.64e+03 7.57e-10  2.84e+03     1s

INFO:gurobipy:  38   8.47019001e+09  8.05327545e+09  8.64e+03 7.57e-10  2.84e+03     1s

  39   8.46226164e+09  8.07275028e+09  7.38e+03 1.82e-12  2.65e+03     1s

INFO:gurobipy:  39   8.46226164e+09  8.07275028e+09  7.38e+03 1.82e-12  2.65e+03     1s

  40   8.45597232e+09  8.12317726e+09  6.57e+03 4.95e-10  2.27e+03     1s

INFO:gurobipy:  40   8.45597232e+09  8.12317726e+09  6.57e+03 4.95e-10  2.27e+03     1s

  41   8.44990465e+09  8.14035372e+09  5.71e+03 2.04e-10  2.11e+03     1s

INFO:gurobipy:  41   8.44990465e+09  8.14035372e+09  5.71e+03 2.04e-10  2.11e+03     1s

  42   8.44817253e+09  8.15104739e+09  5.49e+03 0.00e+00  2.02e+03     1s

INFO:gurobipy:  42   8.44817253e+09  8.15104739e+09  5.49e+03 0.00e+00  2.02e+03     1s

  43   8.44441124e+09  8.17701669e+09  4.99e+03 3.20e-10  1.82e+03     1s

INFO:gurobipy:  43   8.44441124e+09  8.17701669e+09  4.99e+03 3.20e-10  1.82e+03     1s

  44   8.44077697e+09  8.20297588e+09  4.51e+03 3.78e-10  1.62e+03     1s

INFO:gurobipy:  44   8.44077697e+09  8.20297588e+09  4.51e+03 3.78e-10  1.62e+03     1s

  45   8.44010931e+09  8.21119300e+09  4.42e+03 1.16e-10  1.56e+03     1s

INFO:gurobipy:  45   8.44010931e+09  8.21119300e+09  4.42e+03 1.16e-10  1.56e+03     1s

  46   8.43716914e+09  8.22130835e+09  3.97e+03 3.78e-10  1.47e+03     1s

INFO:gurobipy:  46   8.43716914e+09  8.22130835e+09  3.97e+03 3.78e-10  1.47e+03     1s

  47   8.43370769e+09  8.24780341e+09  3.54e+03 4.66e-10  1.27e+03     1s

INFO:gurobipy:  47   8.43370769e+09  8.24780341e+09  3.54e+03 4.66e-10  1.27e+03     1s

  48   8.43056262e+09  8.26266072e+09  3.14e+03 4.66e-10  1.14e+03     1s

INFO:gurobipy:  48   8.43056262e+09  8.26266072e+09  3.14e+03 4.66e-10  1.14e+03     1s

  49   8.42764200e+09  8.26865002e+09  2.71e+03 3.78e-10  1.08e+03     1s

INFO:gurobipy:  49   8.42764200e+09  8.26865002e+09  2.71e+03 3.78e-10  1.08e+03     1s

  50   8.42352379e+09  8.28147171e+09  2.18e+03 4.95e-10  9.65e+02     1s

INFO:gurobipy:  50   8.42352379e+09  8.28147171e+09  2.18e+03 4.95e-10  9.65e+02     1s

  51   8.42158522e+09  8.29159176e+09  1.85e+03 2.04e-10  8.83e+02     1s

INFO:gurobipy:  51   8.42158522e+09  8.29159176e+09  1.85e+03 2.04e-10  8.83e+02     1s

  52   8.42057649e+09  8.29722383e+09  1.72e+03 8.73e-11  8.37e+02     1s

INFO:gurobipy:  52   8.42057649e+09  8.29722383e+09  1.72e+03 8.73e-11  8.37e+02     1s

  53   8.41891905e+09  8.30295688e+09  1.52e+03 8.15e-10  7.87e+02     1s

INFO:gurobipy:  53   8.41891905e+09  8.30295688e+09  1.52e+03 8.15e-10  7.87e+02     1s

  54   8.41732803e+09  8.31773235e+09  1.27e+03 1.46e-10  6.76e+02     1s

INFO:gurobipy:  54   8.41732803e+09  8.31773235e+09  1.27e+03 1.46e-10  6.76e+02     1s

  55   8.41680398e+09  8.32321350e+09  1.20e+03 6.91e-11  6.35e+02     1s

INFO:gurobipy:  55   8.41680398e+09  8.32321350e+09  1.20e+03 6.91e-11  6.35e+02     1s

  56   8.41573638e+09  8.32767545e+09  1.05e+03 2.91e-10  5.97e+02     1s

INFO:gurobipy:  56   8.41573638e+09  8.32767545e+09  1.05e+03 2.91e-10  5.97e+02     1s

  57   8.41358632e+09  8.34944731e+09  7.58e+02 6.04e-10  4.35e+02     1s

INFO:gurobipy:  57   8.41358632e+09  8.34944731e+09  7.58e+02 6.04e-10  4.35e+02     1s

  58   8.41058569e+09  8.35315312e+09  4.32e+02 8.80e-10  3.88e+02     1s

INFO:gurobipy:  58   8.41058569e+09  8.35315312e+09  4.32e+02 8.80e-10  3.88e+02     1s

  59   8.41005669e+09  8.35922775e+09  3.68e+02 7.17e-10  3.43e+02     1s

INFO:gurobipy:  59   8.41005669e+09  8.35922775e+09  3.68e+02 7.17e-10  3.43e+02     1s

  60   8.40843849e+09  8.37121903e+09  1.92e+02 3.38e-10  2.51e+02     1s

INFO:gurobipy:  60   8.40843849e+09  8.37121903e+09  1.92e+02 3.38e-10  2.51e+02     1s

  61   8.40773401e+09  8.38065015e+09  1.27e+02 9.39e-10  1.83e+02     1s

INFO:gurobipy:  61   8.40773401e+09  8.38065015e+09  1.27e+02 9.39e-10  1.83e+02     1s

  62   8.40724683e+09  8.38330475e+09  8.62e+01 7.53e-10  1.61e+02     1s

INFO:gurobipy:  62   8.40724683e+09  8.38330475e+09  8.62e+01 7.53e-10  1.61e+02     1s

  63   8.40691893e+09  8.38988826e+09  5.84e+01 4.91e-10  1.15e+02     1s

INFO:gurobipy:  63   8.40691893e+09  8.38988826e+09  5.84e+01 4.91e-10  1.15e+02     1s

  64   8.40647106e+09  8.39155962e+09  2.95e+01 6.88e-10  1.00e+02     1s

INFO:gurobipy:  64   8.40647106e+09  8.39155962e+09  2.95e+01 6.88e-10  1.00e+02     1s

  65   8.40630358e+09  8.39617627e+09  1.77e+01 5.64e-10  6.81e+01     1s

INFO:gurobipy:  65   8.40630358e+09  8.39617627e+09  1.77e+01 5.64e-10  6.81e+01     1s

  66   8.40618724e+09  8.39710217e+09  1.19e+01 1.15e-09  6.11e+01     1s

INFO:gurobipy:  66   8.40618724e+09  8.39710217e+09  1.19e+01 1.15e-09  6.11e+01     1s

  67   8.40602163e+09  8.40056018e+09  1.58e+00 6.69e-10  3.67e+01     1s

INFO:gurobipy:  67   8.40602163e+09  8.40056018e+09  1.58e+00 6.69e-10  3.67e+01     1s

  68   8.40595783e+09  8.40181291e+09  6.33e-01 6.69e-10  2.79e+01     1s

INFO:gurobipy:  68   8.40595783e+09  8.40181291e+09  6.33e-01 6.69e-10  2.79e+01     1s

  69   8.40592344e+09  8.40374327e+09  1.53e-01 1.78e-09  1.47e+01     1s

INFO:gurobipy:  69   8.40592344e+09  8.40374327e+09  1.53e-01 1.78e-09  1.47e+01     1s

  70   8.40590871e+09  8.40560159e+09  2.37e-02 5.36e-09  2.06e+00     1s

INFO:gurobipy:  70   8.40590871e+09  8.40560159e+09  2.37e-02 5.36e-09  2.06e+00     1s

  71   8.40589143e+09  8.40583765e+09  5.15e-03 1.78e-09  3.61e-01     1s

INFO:gurobipy:  71   8.40589143e+09  8.40583765e+09  5.15e-03 1.78e-09  3.61e-01     1s

  72   8.40588648e+09  8.40588084e+09  9.11e-05 6.55e-10  3.79e-02     1s

INFO:gurobipy:  72   8.40588648e+09  8.40588084e+09  9.11e-05 6.55e-10  3.79e-02     1s

  73   8.40588625e+09  8.40588565e+09  5.46e-08 2.91e-10  4.05e-03     1s

INFO:gurobipy:  73   8.40588625e+09  8.40588565e+09  5.46e-08 2.91e-10  4.05e-03     1s

  74   8.40588625e+09  8.40588618e+09  1.09e-11 1.31e-09  4.19e-04     1s

INFO:gurobipy:  74   8.40588625e+09  8.40588618e+09  1.09e-11 1.31e-09  4.19e-04     1s

  75   8.40588625e+09  8.40588625e+09  1.76e-07 4.91e-09  5.11e-07     1s

INFO:gurobipy:  75   8.40588625e+09  8.40588625e+09  1.76e-07 4.91e-09  5.11e-07     1s

  76   8.40588625e+09  8.40588625e+09  8.55e-07 4.74e-09  1.55e-10     1s

INFO:gurobipy:  76   8.40588625e+09  8.40588625e+09  8.55e-07 4.74e-09  1.55e-10     1s

INFO:gurobipy:

Barrier solved model in 76 iterations and 1.36 seconds (2.15 work units)

INFO:gurobipy:Barrier solved model in 76 iterations and 1.36 seconds (2.15 work units)

Optimal objective 8.40588625e+09

INFO:gurobipy:Optimal objective 8.40588625e+09

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      51 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:      51 DPushes remaining with DInf 0.0000000e+00                 1s

       0 DPushes remaining with DInf 0.0000000e+00                 1s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 1s

Warning: Markowitz tolerance tightened to 0.5

INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.5

INFO:gurobipy:

    8604 PPushes remaining with PInf 0.0000000e+00                 1s

INFO:gurobipy:    8604 PPushes remaining with PInf 0.0000000e+00                 1s

       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 2.7327664e-09      2s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 2.7327664e-09      2s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8658    8.4058862e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:    8658    8.4058862e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:

Solved in 8658 iterations and 1.63 seconds (3.21 work units)

INFO:gurobipy:Solved in 8658 iterations and 1.63 seconds (3.21 work units)

Optimal objective  8.405886246e+09

INFO:gurobipy:Optimal objective  8.405886246e+09
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140168 duals
Objective: 8.41e+09
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/constraints.py:531: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(n.loads.bus, axis=1)
INFO:linopy.model: Solve problem using Gurobi solver

Set parameter Username

INFO:gurobipy:Set parameter Username

Set parameter LicenseID to value 2609678

INFO:gurobipy:Set parameter LicenseID to value 2609678

Academic license - for non-commercial use only - expires 2026-01-14

INFO:gurobipy:Academic license - for non-commercial use only - expires 2026-01-14
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 10/10 [00:00<00:00, 38.51it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 86.75it/s]
INFO:linopy.io: Writing time: 0.34s

Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-ns47mtua.lp

INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-ns47mtua.lp

Reading time = 0.13 seconds

INFO:gurobipy:Reading time = 0.13 seconds

obj: 140168 rows, 61327 columns, 271592 nonzeros

INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros

Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[arm] - Darwin 24.3.0 24D81)

INFO:gurobipy:

CPU model: Apple M3

INFO:gurobipy:CPU model: Apple M3

Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

INFO:gurobipy:

Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros

Model fingerprint: 0x8e828acd

INFO:gurobipy:Model fingerprint: 0x8e828acd

Coefficient statistics:

INFO:gurobipy:Coefficient statistics:

  Matrix range     [1e-03, 1e+00]

INFO:gurobipy:  Matrix range     [1e-03, 1e+00]

  Objective range  [1e-02, 1e+05]

INFO:gurobipy:  Objective range  [1e-02, 1e+05]

  Bounds range     [0e+00, 0e+00]

INFO:gurobipy:  Bounds range     [0e+00, 0e+00]

  RHS range        [2e+03, 2e+06]

INFO:gurobipy:  RHS range        [2e+03, 2e+06]

Presolve removed 70062 rows and 17495 columns

INFO:gurobipy:Presolve removed 70062 rows and 17495 columns

Presolve time: 0.15s

INFO:gurobipy:Presolve time: 0.15s

Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:Presolved: 70106 rows, 43832 columns, 209475 nonzeros

INFO:gurobipy:

Concurrent LP optimizer: primal simplex, dual simplex, and barrier

INFO:gurobipy:Concurrent LP optimizer: primal simplex, dual simplex, and barrier

Showing barrier log only...

INFO:gurobipy:Showing barrier log only...

INFO:gurobipy:

Ordering time: 0.01s

INFO:gurobipy:Ordering time: 0.01s

INFO:gurobipy:

Barrier statistics:

INFO:gurobipy:Barrier statistics:

 Dense cols : 7

INFO:gurobipy: Dense cols : 7

 AA' NZ     : 2.182e+05

INFO:gurobipy: AA' NZ     : 2.182e+05

 Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

INFO:gurobipy: Factor NZ  : 8.184e+05 (roughly 50 MB of memory)

 Factor Ops : 1.008e+07 (less than 1 second per iteration)

INFO:gurobipy: Factor Ops : 1.008e+07 (less than 1 second per iteration)

 Threads    : 6

INFO:gurobipy: Threads    : 6

INFO:gurobipy:

                  Objective                Residual

INFO:gurobipy:                  Objective                Residual

Iter       Primal          Dual         Primal    Dual     Compl     Time

INFO:gurobipy:Iter       Primal          Dual         Primal    Dual     Compl     Time

   0   5.26765238e+11  0.00000000e+00  3.15e+09 0.00e+00  2.37e+08     0s

INFO:gurobipy:   0   5.26765238e+11  0.00000000e+00  3.15e+09 0.00e+00  2.37e+08     0s

   1   6.10890823e+11 -9.68985986e+10  6.22e+08 2.23e+02  5.77e+07     0s

INFO:gurobipy:   1   6.10890823e+11 -9.68985986e+10  6.22e+08 2.23e+02  5.77e+07     0s

   2   4.48041353e+11 -1.16553990e+11  2.10e+07 2.18e+00  4.69e+06     0s

INFO:gurobipy:   2   4.48041353e+11 -1.16553990e+11  2.10e+07 2.18e+00  4.69e+06     0s

   3   7.65399378e+10 -4.00780552e+10  2.31e+06 2.20e-01  8.36e+05     0s

INFO:gurobipy:   3   7.65399378e+10 -4.00780552e+10  2.31e+06 2.20e-01  8.36e+05     0s

   4   4.80401967e+10 -2.02946431e+10  1.33e+06 5.82e-10  4.79e+05     0s

INFO:gurobipy:   4   4.80401967e+10 -2.02946431e+10  1.33e+06 5.82e-10  4.79e+05     0s

   5   3.30337282e+10 -1.48679559e+10  8.43e+05 1.14e-09  3.32e+05     0s

INFO:gurobipy:   5   3.30337282e+10 -1.48679559e+10  8.43e+05 1.14e-09  3.32e+05     0s

   6   2.62029598e+10 -1.03994074e+10  6.24e+05 6.98e-10  2.52e+05     0s

INFO:gurobipy:   6   2.62029598e+10 -1.03994074e+10  6.24e+05 6.98e-10  2.52e+05     0s

   7   1.86494975e+10 -4.85299148e+09  3.87e+05 1.16e-10  1.61e+05     0s

INFO:gurobipy:   7   1.86494975e+10 -4.85299148e+09  3.87e+05 1.16e-10  1.61e+05     0s

   8   1.45438364e+10 -1.29932145e+09  2.68e+05 3.78e-10  1.08e+05     0s

INFO:gurobipy:   8   1.45438364e+10 -1.29932145e+09  2.68e+05 3.78e-10  1.08e+05     0s

   9   1.38103617e+10 -7.49157545e+08  2.43e+05 4.66e-10  9.93e+04     1s

INFO:gurobipy:   9   1.38103617e+10 -7.49157545e+08  2.43e+05 4.66e-10  9.93e+04     1s

  10   1.32724454e+10  4.39294294e+08  2.23e+05 4.37e-11  8.75e+04     1s

INFO:gurobipy:  10   1.32724454e+10  4.39294294e+08  2.23e+05 4.37e-11  8.75e+04     1s

  11   1.12681179e+10  2.45514877e+09  1.62e+05 1.25e-09  6.00e+04     1s

INFO:gurobipy:  11   1.12681179e+10  2.45514877e+09  1.62e+05 1.25e-09  6.00e+04     1s

  12   1.09140516e+10  2.92356088e+09  1.51e+05 6.40e-10  5.44e+04     1s

INFO:gurobipy:  12   1.09140516e+10  2.92356088e+09  1.51e+05 6.40e-10  5.44e+04     1s

  13   1.04382174e+10  3.30912657e+09  1.36e+05 6.40e-10  4.85e+04     1s

INFO:gurobipy:  13   1.04382174e+10  3.30912657e+09  1.36e+05 6.40e-10  4.85e+04     1s

  14   1.01625762e+10  3.56596622e+09  1.25e+05 2.62e-10  4.49e+04     1s

INFO:gurobipy:  14   1.01625762e+10  3.56596622e+09  1.25e+05 2.62e-10  4.49e+04     1s

  15   9.52948858e+09  4.21270707e+09  1.02e+05 8.73e-11  3.62e+04     1s

INFO:gurobipy:  15   9.52948858e+09  4.21270707e+09  1.02e+05 8.73e-11  3.62e+04     1s

  16   9.26362538e+09  4.95394175e+09  8.98e+04 4.73e-11  2.93e+04     1s

INFO:gurobipy:  16   9.26362538e+09  4.95394175e+09  8.98e+04 4.73e-11  2.93e+04     1s

  17   9.13196092e+09  5.22918629e+09  8.39e+04 5.82e-11  2.66e+04     1s

INFO:gurobipy:  17   9.13196092e+09  5.22918629e+09  8.39e+04 5.82e-11  2.66e+04     1s

  18   8.82313808e+09  5.41896103e+09  6.84e+04 6.55e-11  2.32e+04     1s

INFO:gurobipy:  18   8.82313808e+09  5.41896103e+09  6.84e+04 6.55e-11  2.32e+04     1s

  19   8.65924562e+09  5.55432626e+09  5.85e+04 1.46e-11  2.11e+04     1s

INFO:gurobipy:  19   8.65924562e+09  5.55432626e+09  5.85e+04 1.46e-11  2.11e+04     1s

  20   8.49397810e+09  6.07105532e+09  4.87e+04 2.62e-10  1.65e+04     1s

INFO:gurobipy:  20   8.49397810e+09  6.07105532e+09  4.87e+04 2.62e-10  1.65e+04     1s

  21   8.40323974e+09  6.20150879e+09  4.37e+04 1.27e-10  1.50e+04     1s

INFO:gurobipy:  21   8.40323974e+09  6.20150879e+09  4.37e+04 1.27e-10  1.50e+04     1s

  22   8.30222493e+09  6.31498984e+09  3.82e+04 5.82e-11  1.35e+04     1s

INFO:gurobipy:  22   8.30222493e+09  6.31498984e+09  3.82e+04 5.82e-11  1.35e+04     1s

  23   8.26649916e+09  6.38087684e+09  3.47e+04 9.60e-10  1.28e+04     1s

INFO:gurobipy:  23   8.26649916e+09  6.38087684e+09  3.47e+04 9.60e-10  1.28e+04     1s

  24   8.22390988e+09  6.54457323e+09  3.20e+04 2.33e-10  1.14e+04     1s

INFO:gurobipy:  24   8.22390988e+09  6.54457323e+09  3.20e+04 2.33e-10  1.14e+04     1s

  25   8.17599646e+09  6.64143869e+09  2.87e+04 6.55e-11  1.04e+04     1s

INFO:gurobipy:  25   8.17599646e+09  6.64143869e+09  2.87e+04 6.55e-11  1.04e+04     1s

  26   8.15739438e+09  6.76253791e+09  2.75e+04 7.64e-11  9.48e+03     1s

INFO:gurobipy:  26   8.15739438e+09  6.76253791e+09  2.75e+04 7.64e-11  9.48e+03     1s

  27   8.08927947e+09  6.86831869e+09  2.27e+04 3.78e-10  8.30e+03     1s

INFO:gurobipy:  27   8.08927947e+09  6.86831869e+09  2.27e+04 3.78e-10  8.30e+03     1s

  28   8.06594186e+09  6.92560759e+09  2.09e+04 1.02e-10  7.75e+03     1s

INFO:gurobipy:  28   8.06594186e+09  6.92560759e+09  2.09e+04 1.02e-10  7.75e+03     1s

  29   8.03682206e+09  7.00890060e+09  1.86e+04 6.40e-10  6.98e+03     1s

INFO:gurobipy:  29   8.03682206e+09  7.00890060e+09  1.86e+04 6.40e-10  6.98e+03     1s

  30   8.01985692e+09  7.05543158e+09  1.63e+04 3.78e-10  6.55e+03     1s

INFO:gurobipy:  30   8.01985692e+09  7.05543158e+09  1.63e+04 3.78e-10  6.55e+03     1s

  31   7.98958400e+09  7.12347378e+09  1.27e+04 3.06e-10  5.87e+03     1s

INFO:gurobipy:  31   7.98958400e+09  7.12347378e+09  1.27e+04 3.06e-10  5.87e+03     1s

  32   7.95874228e+09  7.23703262e+09  9.53e+03 3.78e-10  4.89e+03     1s

INFO:gurobipy:  32   7.95874228e+09  7.23703262e+09  9.53e+03 3.78e-10  4.89e+03     1s

  33   7.94493370e+09  7.30566823e+09  8.49e+03 1.46e-10  4.33e+03     1s

INFO:gurobipy:  33   7.94493370e+09  7.30566823e+09  8.49e+03 1.46e-10  4.33e+03     1s

  34   7.93608045e+09  7.34715630e+09  7.85e+03 1.75e-10  3.99e+03     1s

INFO:gurobipy:  34   7.93608045e+09  7.34715630e+09  7.85e+03 1.75e-10  3.99e+03     1s

  35   7.93262307e+09  7.36521865e+09  7.57e+03 5.82e-11  3.84e+03     1s

INFO:gurobipy:  35   7.93262307e+09  7.36521865e+09  7.57e+03 5.82e-11  3.84e+03     1s

  36   7.92080215e+09  7.44398679e+09  6.57e+03 1.16e-10  3.23e+03     1s

INFO:gurobipy:  36   7.92080215e+09  7.44398679e+09  6.57e+03 1.16e-10  3.23e+03     1s

  37   7.91375401e+09  7.49836397e+09  5.99e+03 8.44e-10  2.82e+03     1s

INFO:gurobipy:  37   7.91375401e+09  7.49836397e+09  5.99e+03 8.44e-10  2.82e+03     1s

  38   7.90702779e+09  7.52027692e+09  5.41e+03 7.82e-11  2.62e+03     1s

INFO:gurobipy:  38   7.90702779e+09  7.52027692e+09  5.41e+03 7.82e-11  2.62e+03     1s

  39   7.89625964e+09  7.53904525e+09  4.35e+03 2.91e-10  2.42e+03     1s

INFO:gurobipy:  39   7.89625964e+09  7.53904525e+09  4.35e+03 2.91e-10  2.42e+03     1s

  40   7.89085528e+09  7.56984710e+09  3.77e+03 3.20e-10  2.17e+03     1s

INFO:gurobipy:  40   7.89085528e+09  7.56984710e+09  3.77e+03 3.20e-10  2.17e+03     1s

  41   7.88092338e+09  7.59963959e+09  2.71e+03 1.05e-09  1.90e+03     1s

INFO:gurobipy:  41   7.88092338e+09  7.59963959e+09  2.71e+03 1.05e-09  1.90e+03     1s

  42   7.87711235e+09  7.61841939e+09  2.39e+03 5.09e-11  1.75e+03     1s

INFO:gurobipy:  42   7.87711235e+09  7.61841939e+09  2.39e+03 5.09e-11  1.75e+03     1s

  43   7.87497999e+09  7.63676343e+09  2.14e+03 3.64e-10  1.61e+03     1s

INFO:gurobipy:  43   7.87497999e+09  7.63676343e+09  2.14e+03 3.64e-10  1.61e+03     1s

  44   7.86928599e+09  7.67162185e+09  1.70e+03 2.62e-10  1.34e+03     1s

INFO:gurobipy:  44   7.86928599e+09  7.67162185e+09  1.70e+03 2.62e-10  1.34e+03     1s

  45   7.86489633e+09  7.68666057e+09  1.23e+03 5.24e-10  1.20e+03     1s

INFO:gurobipy:  45   7.86489633e+09  7.68666057e+09  1.23e+03 5.24e-10  1.20e+03     1s

  46   7.86220525e+09  7.71691853e+09  9.96e+02 6.40e-10  9.80e+02     1s

INFO:gurobipy:  46   7.86220525e+09  7.71691853e+09  9.96e+02 6.40e-10  9.80e+02     1s

  47   7.86006126e+09  7.73064874e+09  8.39e+02 3.49e-10  8.73e+02     1s

INFO:gurobipy:  47   7.86006126e+09  7.73064874e+09  8.39e+02 3.49e-10  8.73e+02     1s

  48   7.85885829e+09  7.73425401e+09  7.54e+02 7.86e-10  8.40e+02     1s

INFO:gurobipy:  48   7.85885829e+09  7.73425401e+09  7.54e+02 7.86e-10  8.40e+02     1s

  49   7.85690288e+09  7.74659345e+09  5.95e+02 1.46e-10  7.44e+02     1s

INFO:gurobipy:  49   7.85690288e+09  7.74659345e+09  5.95e+02 1.46e-10  7.44e+02     1s

  50   7.85650366e+09  7.75278174e+09  5.64e+02 1.16e-10  6.99e+02     2s

INFO:gurobipy:  50   7.85650366e+09  7.75278174e+09  5.64e+02 1.16e-10  6.99e+02     2s

  51   7.85572912e+09  7.76315051e+09  5.13e+02 6.98e-10  6.24e+02     2s

INFO:gurobipy:  51   7.85572912e+09  7.76315051e+09  5.13e+02 6.98e-10  6.24e+02     2s

  52   7.85485409e+09  7.77093108e+09  4.53e+02 1.32e-09  5.66e+02     2s

INFO:gurobipy:  52   7.85485409e+09  7.77093108e+09  4.53e+02 1.32e-09  5.66e+02     2s

  53   7.85433308e+09  7.77287997e+09  4.09e+02 1.12e-09  5.49e+02     2s

INFO:gurobipy:  53   7.85433308e+09  7.77287997e+09  4.09e+02 1.12e-09  5.49e+02     2s

  54   7.85345680e+09  7.78280902e+09  3.49e+02 2.75e-09  4.76e+02     2s

INFO:gurobipy:  54   7.85345680e+09  7.78280902e+09  3.49e+02 2.75e-09  4.76e+02     2s

  55   7.85283403e+09  7.79826291e+09  3.13e+02 9.63e-09  3.68e+02     2s

INFO:gurobipy:  55   7.85283403e+09  7.79826291e+09  3.13e+02 9.63e-09  3.68e+02     2s

  56   7.85233479e+09  7.79999159e+09  2.79e+02 9.27e-09  3.53e+02     2s

INFO:gurobipy:  56   7.85233479e+09  7.79999159e+09  2.79e+02 9.27e-09  3.53e+02     2s

  57   7.85174784e+09  7.80447595e+09  2.41e+02 1.19e-08  3.19e+02     2s

INFO:gurobipy:  57   7.85174784e+09  7.80447595e+09  2.41e+02 1.19e-08  3.19e+02     2s

  58   7.85120949e+09  7.80819345e+09  2.11e+02 1.22e-08  2.90e+02     2s

INFO:gurobipy:  58   7.85120949e+09  7.80819345e+09  2.11e+02 1.22e-08  2.90e+02     2s

  59   7.85073764e+09  7.81145437e+09  1.83e+02 1.23e-08  2.65e+02     2s

INFO:gurobipy:  59   7.85073764e+09  7.81145437e+09  1.83e+02 1.23e-08  2.65e+02     2s

  60   7.85053184e+09  7.81173190e+09  1.74e+02 1.24e-08  2.61e+02     2s

INFO:gurobipy:  60   7.85053184e+09  7.81173190e+09  1.74e+02 1.24e-08  2.61e+02     2s

  61   7.85034902e+09  7.81970655e+09  1.67e+02 1.75e-08  2.07e+02     2s

INFO:gurobipy:  61   7.85034902e+09  7.81970655e+09  1.67e+02 1.75e-08  2.07e+02     2s

  62   7.84999296e+09  7.82542908e+09  1.49e+02 1.78e-08  1.66e+02     2s

INFO:gurobipy:  62   7.84999296e+09  7.82542908e+09  1.49e+02 1.78e-08  1.66e+02     2s

  63   7.84922994e+09  7.82726197e+09  9.53e+01 1.64e-08  1.48e+02     2s

INFO:gurobipy:  63   7.84922994e+09  7.82726197e+09  9.53e+01 1.64e-08  1.48e+02     2s

  64   7.84896730e+09  7.82818824e+09  8.37e+01 1.60e-08  1.40e+02     2s

INFO:gurobipy:  64   7.84896730e+09  7.82818824e+09  8.37e+01 1.60e-08  1.40e+02     2s

  65   7.84889370e+09  7.82972710e+09  7.74e+01 1.49e-08  1.29e+02     2s

INFO:gurobipy:  65   7.84889370e+09  7.82972710e+09  7.74e+01 1.49e-08  1.29e+02     2s

  66   7.84859002e+09  7.83150269e+09  6.40e+01 1.30e-08  1.15e+02     2s

INFO:gurobipy:  66   7.84859002e+09  7.83150269e+09  6.40e+01 1.30e-08  1.15e+02     2s

  67   7.84833143e+09  7.83206162e+09  5.37e+01 1.28e-08  1.10e+02     2s

INFO:gurobipy:  67   7.84833143e+09  7.83206162e+09  5.37e+01 1.28e-08  1.10e+02     2s

  68   7.84821039e+09  7.83244057e+09  4.34e+01 1.23e-08  1.06e+02     2s

INFO:gurobipy:  68   7.84821039e+09  7.83244057e+09  4.34e+01 1.23e-08  1.06e+02     2s

  69   7.84793974e+09  7.83385912e+09  3.30e+01 1.16e-08  9.48e+01     2s

INFO:gurobipy:  69   7.84793974e+09  7.83385912e+09  3.30e+01 1.16e-08  9.48e+01     2s

  70   7.84782254e+09  7.83516048e+09  2.84e+01 1.55e-08  8.52e+01     2s

INFO:gurobipy:  70   7.84782254e+09  7.83516048e+09  2.84e+01 1.55e-08  8.52e+01     2s

  71   7.84748798e+09  7.83762059e+09  1.24e+01 1.13e-08  6.64e+01     2s

INFO:gurobipy:  71   7.84748798e+09  7.83762059e+09  1.24e+01 1.13e-08  6.64e+01     2s

  72   7.84728046e+09  7.84240527e+09  8.11e-01 4.85e-09  3.28e+01     2s

INFO:gurobipy:  72   7.84728046e+09  7.84240527e+09  8.11e-01 4.85e-09  3.28e+01     2s

  73   7.84719457e+09  7.84266131e+09  3.06e-01 4.86e-09  3.05e+01     2s

INFO:gurobipy:  73   7.84719457e+09  7.84266131e+09  3.06e-01 4.86e-09  3.05e+01     2s

  74   7.84719059e+09  7.84322941e+09  2.84e-01 4.29e-09  2.66e+01     2s

INFO:gurobipy:  74   7.84719059e+09  7.84322941e+09  2.84e-01 4.29e-09  2.66e+01     2s

  75   7.84713853e+09  7.84509838e+09  3.51e-02 2.24e-09  1.37e+01     2s

INFO:gurobipy:  75   7.84713853e+09  7.84509838e+09  3.51e-02 2.24e-09  1.37e+01     2s

  76   7.84710830e+09  7.84521821e+09  9.60e-03 1.94e-09  1.27e+01     2s

INFO:gurobipy:  76   7.84710830e+09  7.84521821e+09  9.60e-03 1.94e-09  1.27e+01     2s

  77   7.84710511e+09  7.84563406e+09  4.57e-05 1.39e-09  9.89e+00     2s

INFO:gurobipy:  77   7.84710511e+09  7.84563406e+09  4.57e-05 1.39e-09  9.89e+00     2s

  78   7.84710756e+09  7.84698801e+09  3.43e-05 2.82e-09  8.03e-01     2s

INFO:gurobipy:  78   7.84710756e+09  7.84698801e+09  3.43e-05 2.82e-09  8.03e-01     2s

  79   7.84709184e+09  7.84708332e+09  2.86e-06 1.25e-09  5.72e-02     2s

INFO:gurobipy:  79   7.84709184e+09  7.84708332e+09  2.86e-06 1.25e-09  5.72e-02     2s

  80   7.84709143e+09  7.84709142e+09  1.84e-10 5.13e-10  5.21e-05     2s

INFO:gurobipy:  80   7.84709143e+09  7.84709142e+09  1.84e-10 5.13e-10  5.21e-05     2s

  81   7.84709142e+09  7.84709142e+09  5.46e-07 1.69e-09  1.31e-10     2s

INFO:gurobipy:  81   7.84709142e+09  7.84709142e+09  5.46e-07 1.69e-09  1.31e-10     2s

INFO:gurobipy:

Barrier solved model in 81 iterations and 2.05 seconds (2.24 work units)

INFO:gurobipy:Barrier solved model in 81 iterations and 2.05 seconds (2.24 work units)

Optimal objective 7.84709142e+09

INFO:gurobipy:Optimal objective 7.84709142e+09

INFO:gurobipy:

Crossover log...

INFO:gurobipy:Crossover log...

INFO:gurobipy:

      51 DPushes remaining with DInf 0.0000000e+00                 2s

INFO:gurobipy:      51 DPushes remaining with DInf 0.0000000e+00                 2s

       0 DPushes remaining with DInf 0.0000000e+00                 2s

INFO:gurobipy:       0 DPushes remaining with DInf 0.0000000e+00                 2s

Warning: Markowitz tolerance tightened to 0.5

INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.5

INFO:gurobipy:

    8563 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:    8563 PPushes remaining with PInf 0.0000000e+00                 2s

       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:       0 PPushes remaining with PInf 0.0000000e+00                 2s

INFO:gurobipy:

  Push phase complete: Pinf 0.0000000e+00, Dinf 3.9947344e-09      2s

INFO:gurobipy:  Push phase complete: Pinf 0.0000000e+00, Dinf 3.9947344e-09      2s

INFO:gurobipy:

INFO:gurobipy:

Solved with barrier

INFO:gurobipy:Solved with barrier

Iteration    Objective       Primal Inf.    Dual Inf.      Time

INFO:gurobipy:Iteration    Objective       Primal Inf.    Dual Inf.      Time

    8617    7.8470914e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:    8617    7.8470914e+09   0.000000e+00   0.000000e+00      2s

INFO:gurobipy:

Solved in 8617 iterations and 2.41 seconds (3.61 work units)

INFO:gurobipy:Solved in 8617 iterations and 2.41 seconds (3.61 work units)

Optimal objective  7.847091424e+09

INFO:gurobipy:Optimal objective  7.847091424e+09
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140168 duals
Objective: 7.85e+09
Solver model: available
Solver message: 2

/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:355: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  n.df(c)[attr + "_opt"].update(df)
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper were not assigned to the network.
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.12/site-packages/pypsa/optimization/optimize.py:473: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
  .groupby(level=0, axis=1)

emission_costs = pd.DataFrame(
    {
        "Total system costs": [
            n1.objective,
            n2.objective,
            n3.objective,
            n4.objective,
            n5.objective,
            n6.objective,
        ],
    }, index = [250000, 500000, 1000000, 1500000, 2000000, 2500000]
)

emission_costs.plot(marker="x")

<Axes: >