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, v0.11.0) 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/v0.11.0/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.add(
"Carrier",
carriers,
color=["dodgerblue", "gold", "indianred",],
co2_emissions=[costs.at[c, "CO2 intensity"] for c in carriers],
)
# 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,
)
Add global CO2 limit of 2.5 MtCO2/year.
n.add(
"GlobalConstraint",
"CO2Limit",
carrier_attribute="co2_emissions",
sense="<=",
constant=2500000, #2.5MtCO2
)
n.plot(bus_sizes=1, margin=1)
{'nodes': {'Bus': <matplotlib.collections.PatchCollection at 0x38b6034d0>},
'branches': {'Line': <matplotlib.collections.LineCollection at 0x38b603610>},
'flows': {}}
n.optimize(solver_name="gurobi")
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 32.75it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 217.36it/s]
INFO:linopy.io: Writing time: 0.29s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-1ptt6vks.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-1ptt6vks.lp
Reading time = 0.22 seconds
INFO:gurobipy:Reading time = 0.22 seconds
obj: 140168 rows, 61327 columns, 271592 nonzeros
INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros
Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0xcf8c11b5
INFO:gurobipy:Model fingerprint: 0xcf8c11b5
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.45s
INFO:gurobipy:Presolve time: 0.45s
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 1s
INFO:gurobipy: 0 5.26765238e+11 0.00000000e+00 3.15e+09 0.00e+00 2.37e+08 1s
1 6.10890823e+11 -9.68985986e+10 6.22e+08 2.23e+02 5.77e+07 1s
INFO:gurobipy: 1 6.10890823e+11 -9.68985986e+10 6.22e+08 2.23e+02 5.77e+07 1s
2 4.48041353e+11 -1.16553990e+11 2.10e+07 2.18e+00 4.69e+06 1s
INFO:gurobipy: 2 4.48041353e+11 -1.16553990e+11 2.10e+07 2.18e+00 4.69e+06 1s
3 7.65399378e+10 -4.00780552e+10 2.31e+06 2.20e-01 8.36e+05 1s
INFO:gurobipy: 3 7.65399378e+10 -4.00780552e+10 2.31e+06 2.20e-01 8.36e+05 1s
4 4.80401967e+10 -2.02946431e+10 1.34e+06 9.60e-10 4.79e+05 1s
INFO:gurobipy: 4 4.80401967e+10 -2.02946431e+10 1.34e+06 9.60e-10 4.79e+05 1s
5 3.30337282e+10 -1.48679559e+10 8.49e+05 6.98e-10 3.32e+05 1s
INFO:gurobipy: 5 3.30337282e+10 -1.48679559e+10 8.49e+05 6.98e-10 3.32e+05 1s
6 2.62029598e+10 -1.03994074e+10 6.29e+05 6.11e-10 2.52e+05 1s
INFO:gurobipy: 6 2.62029598e+10 -1.03994074e+10 6.29e+05 6.11e-10 2.52e+05 1s
7 1.86494975e+10 -4.85299148e+09 3.91e+05 2.62e-10 1.61e+05 1s
INFO:gurobipy: 7 1.86494975e+10 -4.85299148e+09 3.91e+05 2.62e-10 1.61e+05 1s
8 1.45438364e+10 -1.29932145e+09 2.70e+05 3.06e-10 1.08e+05 1s
INFO:gurobipy: 8 1.45438364e+10 -1.29932145e+09 2.70e+05 3.06e-10 1.08e+05 1s
9 1.38103617e+10 -7.49157545e+08 2.46e+05 4.95e-10 9.93e+04 1s
INFO:gurobipy: 9 1.38103617e+10 -7.49157545e+08 2.46e+05 4.95e-10 9.93e+04 1s
10 1.32724454e+10 4.39294294e+08 2.26e+05 6.11e-10 8.75e+04 1s
INFO:gurobipy: 10 1.32724454e+10 4.39294294e+08 2.26e+05 6.11e-10 8.75e+04 1s
11 1.12681179e+10 2.45514877e+09 1.63e+05 9.46e-11 6.00e+04 1s
INFO:gurobipy: 11 1.12681179e+10 2.45514877e+09 1.63e+05 9.46e-11 6.00e+04 1s
12 1.09140516e+10 2.92356088e+09 1.52e+05 4.07e-10 5.44e+04 1s
INFO:gurobipy: 12 1.09140516e+10 2.92356088e+09 1.52e+05 4.07e-10 5.44e+04 1s
13 1.04382174e+10 3.30912657e+09 1.37e+05 5.53e-10 4.85e+04 1s
INFO:gurobipy: 13 1.04382174e+10 3.30912657e+09 1.37e+05 5.53e-10 4.85e+04 1s
14 1.01625762e+10 3.56596622e+09 1.26e+05 6.40e-10 4.49e+04 1s
INFO:gurobipy: 14 1.01625762e+10 3.56596622e+09 1.26e+05 6.40e-10 4.49e+04 1s
15 9.52948858e+09 4.21270707e+09 1.03e+05 8.44e-10 3.62e+04 1s
INFO:gurobipy: 15 9.52948858e+09 4.21270707e+09 1.03e+05 8.44e-10 3.62e+04 1s
16 9.26362538e+09 4.95394175e+09 9.05e+04 1.75e-10 2.93e+04 1s
INFO:gurobipy: 16 9.26362538e+09 4.95394175e+09 9.05e+04 1.75e-10 2.93e+04 1s
17 9.13196092e+09 5.22918629e+09 8.45e+04 4.95e-10 2.66e+04 1s
INFO:gurobipy: 17 9.13196092e+09 5.22918629e+09 8.45e+04 4.95e-10 2.66e+04 1s
18 8.82313808e+09 5.41896103e+09 6.89e+04 6.55e-10 2.32e+04 1s
INFO:gurobipy: 18 8.82313808e+09 5.41896103e+09 6.89e+04 6.55e-10 2.32e+04 1s
19 8.65924562e+09 5.55432626e+09 5.89e+04 8.73e-11 2.11e+04 1s
INFO:gurobipy: 19 8.65924562e+09 5.55432626e+09 5.89e+04 8.73e-11 2.11e+04 1s
20 8.49397810e+09 6.07105532e+09 4.90e+04 7.86e-10 1.65e+04 1s
INFO:gurobipy: 20 8.49397810e+09 6.07105532e+09 4.90e+04 7.86e-10 1.65e+04 1s
21 8.40323974e+09 6.20150879e+09 4.40e+04 1.54e-09 1.50e+04 1s
INFO:gurobipy: 21 8.40323974e+09 6.20150879e+09 4.40e+04 1.54e-09 1.50e+04 1s
22 8.30222493e+09 6.31498984e+09 3.84e+04 5.24e-10 1.35e+04 1s
INFO:gurobipy: 22 8.30222493e+09 6.31498984e+09 3.84e+04 5.24e-10 1.35e+04 1s
23 8.26649916e+09 6.38087684e+09 3.49e+04 2.91e-10 1.28e+04 1s
INFO:gurobipy: 23 8.26649916e+09 6.38087684e+09 3.49e+04 2.91e-10 1.28e+04 1s
24 8.22390988e+09 6.54457323e+09 3.22e+04 4.95e-10 1.14e+04 1s
INFO:gurobipy: 24 8.22390988e+09 6.54457323e+09 3.22e+04 4.95e-10 1.14e+04 1s
25 8.17599646e+09 6.64143869e+09 2.89e+04 2.33e-10 1.04e+04 1s
INFO:gurobipy: 25 8.17599646e+09 6.64143869e+09 2.89e+04 2.33e-10 1.04e+04 1s
26 8.15739438e+09 6.76253791e+09 2.77e+04 3.49e-10 9.48e+03 1s
INFO:gurobipy: 26 8.15739438e+09 6.76253791e+09 2.77e+04 3.49e-10 9.48e+03 1s
27 8.08927947e+09 6.86831869e+09 2.29e+04 6.40e-10 8.30e+03 1s
INFO:gurobipy: 27 8.08927947e+09 6.86831869e+09 2.29e+04 6.40e-10 8.30e+03 1s
28 8.06594186e+09 6.92560759e+09 2.11e+04 6.69e-10 7.75e+03 1s
INFO:gurobipy: 28 8.06594186e+09 6.92560759e+09 2.11e+04 6.69e-10 7.75e+03 1s
29 8.03682206e+09 7.00890060e+09 1.87e+04 4.00e-11 6.98e+03 1s
INFO:gurobipy: 29 8.03682206e+09 7.00890060e+09 1.87e+04 4.00e-11 6.98e+03 1s
30 8.01985692e+09 7.05543159e+09 1.64e+04 6.69e-10 6.55e+03 1s
INFO:gurobipy: 30 8.01985692e+09 7.05543159e+09 1.64e+04 6.69e-10 6.55e+03 1s
31 7.98958400e+09 7.12347378e+09 1.28e+04 2.33e-10 5.87e+03 1s
INFO:gurobipy: 31 7.98958400e+09 7.12347378e+09 1.28e+04 2.33e-10 5.87e+03 1s
32 7.95874226e+09 7.23703268e+09 9.59e+03 3.78e-10 4.89e+03 2s
INFO:gurobipy: 32 7.95874226e+09 7.23703268e+09 9.59e+03 3.78e-10 4.89e+03 2s
33 7.94493370e+09 7.30566827e+09 8.53e+03 8.73e-11 4.33e+03 2s
INFO:gurobipy: 33 7.94493370e+09 7.30566827e+09 8.53e+03 8.73e-11 4.33e+03 2s
34 7.93608045e+09 7.34715634e+09 7.90e+03 1.31e-10 3.99e+03 2s
INFO:gurobipy: 34 7.93608045e+09 7.34715634e+09 7.90e+03 1.31e-10 3.99e+03 2s
35 7.93262336e+09 7.36521865e+09 7.62e+03 2.33e-10 3.84e+03 2s
INFO:gurobipy: 35 7.93262336e+09 7.36521865e+09 7.62e+03 2.33e-10 3.84e+03 2s
36 7.92080197e+09 7.44399114e+09 6.61e+03 7.28e-10 3.23e+03 2s
INFO:gurobipy: 36 7.92080197e+09 7.44399114e+09 6.61e+03 7.28e-10 3.23e+03 2s
37 7.91375483e+09 7.49836500e+09 6.02e+03 2.33e-10 2.82e+03 2s
INFO:gurobipy: 37 7.91375483e+09 7.49836500e+09 6.02e+03 2.33e-10 2.82e+03 2s
38 7.90702839e+09 7.52027521e+09 5.44e+03 8.44e-10 2.62e+03 2s
INFO:gurobipy: 38 7.90702839e+09 7.52027521e+09 5.44e+03 8.44e-10 2.62e+03 2s
39 7.89625971e+09 7.53904197e+09 4.37e+03 2.04e-10 2.42e+03 2s
INFO:gurobipy: 39 7.89625971e+09 7.53904197e+09 4.37e+03 2.04e-10 2.42e+03 2s
40 7.89085593e+09 7.56984622e+09 3.79e+03 3.20e-10 2.17e+03 2s
INFO:gurobipy: 40 7.89085593e+09 7.56984622e+09 3.79e+03 3.20e-10 2.17e+03 2s
41 7.88092023e+09 7.59964684e+09 2.72e+03 1.16e-10 1.90e+03 2s
INFO:gurobipy: 41 7.88092023e+09 7.59964684e+09 2.72e+03 1.16e-10 1.90e+03 2s
42 7.87711253e+09 7.61843549e+09 2.40e+03 2.91e-10 1.75e+03 2s
INFO:gurobipy: 42 7.87711253e+09 7.61843549e+09 2.40e+03 2.91e-10 1.75e+03 2s
43 7.87498033e+09 7.63676267e+09 2.15e+03 3.78e-10 1.61e+03 2s
INFO:gurobipy: 43 7.87498033e+09 7.63676267e+09 2.15e+03 3.78e-10 1.61e+03 2s
44 7.86927998e+09 7.67163453e+09 1.70e+03 3.78e-10 1.33e+03 2s
INFO:gurobipy: 44 7.86927998e+09 7.67163453e+09 1.70e+03 3.78e-10 1.33e+03 2s
45 7.86490384e+09 7.68662082e+09 1.23e+03 1.75e-10 1.20e+03 2s
INFO:gurobipy: 45 7.86490384e+09 7.68662082e+09 1.23e+03 1.75e-10 1.20e+03 2s
46 7.86219547e+09 7.71679392e+09 1.00e+03 6.40e-10 9.81e+02 2s
INFO:gurobipy: 46 7.86219547e+09 7.71679392e+09 1.00e+03 6.40e-10 9.81e+02 2s
47 7.86008375e+09 7.73031407e+09 8.45e+02 3.78e-10 8.75e+02 2s
INFO:gurobipy: 47 7.86008375e+09 7.73031407e+09 8.45e+02 3.78e-10 8.75e+02 2s
48 7.85887615e+09 7.73397533e+09 7.59e+02 4.37e-10 8.42e+02 2s
INFO:gurobipy: 48 7.85887615e+09 7.73397533e+09 7.59e+02 4.37e-10 8.42e+02 2s
49 7.85691075e+09 7.74654850e+09 5.99e+02 3.78e-10 7.44e+02 2s
INFO:gurobipy: 49 7.85691075e+09 7.74654850e+09 5.99e+02 3.78e-10 7.44e+02 2s
50 7.85667993e+09 7.75186239e+09 5.81e+02 7.28e-10 7.07e+02 2s
INFO:gurobipy: 50 7.85667993e+09 7.75186239e+09 5.81e+02 7.28e-10 7.07e+02 2s
51 7.85562967e+09 7.76259402e+09 5.07e+02 4.95e-10 6.27e+02 2s
INFO:gurobipy: 51 7.85562967e+09 7.76259402e+09 5.07e+02 4.95e-10 6.27e+02 2s
52 7.85475612e+09 7.76992715e+09 4.47e+02 9.28e-10 5.72e+02 2s
INFO:gurobipy: 52 7.85475612e+09 7.76992715e+09 4.47e+02 9.28e-10 5.72e+02 2s
53 7.85409753e+09 7.77270987e+09 3.97e+02 1.38e-09 5.49e+02 2s
INFO:gurobipy: 53 7.85409753e+09 7.77270987e+09 3.97e+02 1.38e-09 5.49e+02 2s
54 7.85330524e+09 7.77657650e+09 3.38e+02 1.82e-09 5.17e+02 2s
INFO:gurobipy: 54 7.85330524e+09 7.77657650e+09 3.38e+02 1.82e-09 5.17e+02 2s
55 7.85261938e+09 7.78129618e+09 2.92e+02 4.36e-09 4.80e+02 2s
INFO:gurobipy: 55 7.85261938e+09 7.78129618e+09 2.92e+02 4.36e-09 4.80e+02 2s
56 7.85141038e+09 7.78812469e+09 1.94e+02 3.71e-09 4.26e+02 2s
INFO:gurobipy: 56 7.85141038e+09 7.78812469e+09 1.94e+02 3.71e-09 4.26e+02 2s
57 7.85125030e+09 7.79393338e+09 1.82e+02 5.66e-09 3.86e+02 2s
INFO:gurobipy: 57 7.85125030e+09 7.79393338e+09 1.82e+02 5.66e-09 3.86e+02 2s
58 7.85046873e+09 7.79784536e+09 1.43e+02 7.44e-09 3.54e+02 2s
INFO:gurobipy: 58 7.85046873e+09 7.79784536e+09 1.43e+02 7.44e-09 3.54e+02 2s
59 7.85010575e+09 7.80210811e+09 1.24e+02 8.75e-09 3.23e+02 2s
INFO:gurobipy: 59 7.85010575e+09 7.80210811e+09 1.24e+02 8.75e-09 3.23e+02 2s
60 7.84935326e+09 7.80621305e+09 7.91e+01 8.63e-09 2.90e+02 2s
INFO:gurobipy: 60 7.84935326e+09 7.80621305e+09 7.91e+01 8.63e-09 2.90e+02 2s
61 7.84912298e+09 7.81141873e+09 7.26e+01 1.34e-08 2.54e+02 3s
INFO:gurobipy: 61 7.84912298e+09 7.81141873e+09 7.26e+01 1.34e-08 2.54e+02 3s
62 7.84897276e+09 7.81829320e+09 5.81e+01 1.42e-08 2.06e+02 3s
INFO:gurobipy: 62 7.84897276e+09 7.81829320e+09 5.81e+01 1.42e-08 2.06e+02 3s
63 7.84794091e+09 7.82103224e+09 4.92e+00 1.46e-08 1.81e+02 3s
INFO:gurobipy: 63 7.84794091e+09 7.82103224e+09 4.92e+00 1.46e-08 1.81e+02 3s
64 7.84782990e+09 7.82235752e+09 4.08e+00 1.41e-08 1.71e+02 3s
INFO:gurobipy: 64 7.84782990e+09 7.82235752e+09 4.08e+00 1.41e-08 1.71e+02 3s
65 7.84756191e+09 7.82624525e+09 6.60e-01 1.12e-08 1.43e+02 3s
INFO:gurobipy: 65 7.84756191e+09 7.82624525e+09 6.60e-01 1.12e-08 1.43e+02 3s
66 7.84747160e+09 7.82787978e+09 5.39e-01 1.10e-08 1.32e+02 3s
INFO:gurobipy: 66 7.84747160e+09 7.82787978e+09 5.39e-01 1.10e-08 1.32e+02 3s
67 7.84741751e+09 7.82872468e+09 4.72e-01 1.06e-08 1.26e+02 3s
INFO:gurobipy: 67 7.84741751e+09 7.82872468e+09 4.72e-01 1.06e-08 1.26e+02 3s
68 7.84741248e+09 7.82932813e+09 4.39e-01 1.07e-08 1.22e+02 3s
INFO:gurobipy: 68 7.84741248e+09 7.82932813e+09 4.39e-01 1.07e-08 1.22e+02 3s
69 7.84739946e+09 7.83122560e+09 3.81e-01 9.40e-09 1.09e+02 3s
INFO:gurobipy: 69 7.84739946e+09 7.83122560e+09 3.81e-01 9.40e-09 1.09e+02 3s
70 7.84735700e+09 7.83188437e+09 3.45e-01 9.50e-09 1.04e+02 3s
INFO:gurobipy: 70 7.84735700e+09 7.83188437e+09 3.45e-01 9.50e-09 1.04e+02 3s
71 7.84733047e+09 7.83470298e+09 2.75e-01 7.48e-09 8.49e+01 3s
INFO:gurobipy: 71 7.84733047e+09 7.83470298e+09 2.75e-01 7.48e-09 8.49e+01 3s
72 7.84732820e+09 7.83927511e+09 2.08e-01 5.96e-09 5.41e+01 3s
INFO:gurobipy: 72 7.84732820e+09 7.83927511e+09 2.08e-01 5.96e-09 5.41e+01 3s
73 7.84722252e+09 7.84004495e+09 7.40e-02 5.18e-09 4.82e+01 3s
INFO:gurobipy: 73 7.84722252e+09 7.84004495e+09 7.40e-02 5.18e-09 4.82e+01 3s
74 7.84720150e+09 7.84365462e+09 5.92e-02 2.41e-09 2.38e+01 3s
INFO:gurobipy: 74 7.84720150e+09 7.84365462e+09 5.92e-02 2.41e-09 2.38e+01 3s
75 7.84717043e+09 7.84399030e+09 3.26e-02 2.48e-09 2.14e+01 3s
INFO:gurobipy: 75 7.84717043e+09 7.84399030e+09 3.26e-02 2.48e-09 2.14e+01 3s
76 7.84715457e+09 7.84462755e+09 2.50e-02 1.95e-09 1.70e+01 3s
INFO:gurobipy: 76 7.84715457e+09 7.84462755e+09 2.50e-02 1.95e-09 1.70e+01 3s
77 7.84715302e+09 7.84512416e+09 2.43e-02 2.01e-09 1.36e+01 3s
INFO:gurobipy: 77 7.84715302e+09 7.84512416e+09 2.43e-02 2.01e-09 1.36e+01 3s
78 7.84714586e+09 7.84550866e+09 2.10e-02 1.25e-09 1.10e+01 3s
INFO:gurobipy: 78 7.84714586e+09 7.84550866e+09 2.10e-02 1.25e-09 1.10e+01 3s
79 7.84711442e+09 7.84581456e+09 5.00e-04 9.31e-10 8.74e+00 3s
INFO:gurobipy: 79 7.84711442e+09 7.84581456e+09 5.00e-04 9.31e-10 8.74e+00 3s
80 7.84709546e+09 7.84706359e+09 3.13e-05 1.89e-10 2.14e-01 3s
INFO:gurobipy: 80 7.84709546e+09 7.84706359e+09 3.13e-05 1.89e-10 2.14e-01 3s
81 7.84709147e+09 7.84709123e+09 2.78e-07 7.86e-10 1.60e-03 3s
INFO:gurobipy: 81 7.84709147e+09 7.84709123e+09 2.78e-07 7.86e-10 1.60e-03 3s
82 7.84709142e+09 7.84709142e+09 2.19e-07 9.81e-09 6.73e-09 3s
INFO:gurobipy: 82 7.84709142e+09 7.84709142e+09 2.19e-07 9.81e-09 6.73e-09 3s
INFO:gurobipy:
Barrier solved model in 82 iterations and 3.34 seconds (2.31 work units)
INFO:gurobipy:Barrier solved model in 82 iterations and 3.34 seconds (2.31 work units)
Optimal objective 7.84709142e+09
INFO:gurobipy:Optimal objective 7.84709142e+09
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
52 DPushes remaining with DInf 0.0000000e+00 3s
INFO:gurobipy: 52 DPushes remaining with DInf 0.0000000e+00 3s
0 DPushes remaining with DInf 0.0000000e+00 3s
INFO:gurobipy: 0 DPushes remaining with DInf 0.0000000e+00 3s
Warning: Markowitz tolerance tightened to 0.5
INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.5
INFO:gurobipy:
8572 PPushes remaining with PInf 0.0000000e+00 3s
INFO:gurobipy: 8572 PPushes remaining with PInf 0.0000000e+00 3s
0 PPushes remaining with PInf 0.0000000e+00 4s
INFO:gurobipy: 0 PPushes remaining with PInf 0.0000000e+00 4s
INFO:gurobipy:
Push phase complete: Pinf 0.0000000e+00, Dinf 2.2241642e-09 4s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 2.2241642e-09 4s
INFO:gurobipy:
Crossover time: 0.56 seconds (1.28 work units)
INFO:gurobipy:Crossover time: 0.56 seconds (1.28 work units)
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
8627 7.8470914e+09 0.000000e+00 0.000000e+00 4s
INFO:gurobipy: 8627 7.8470914e+09 0.000000e+00 0.000000e+00 4s
INFO:gurobipy:
Solved in 8627 iterations and 4.03 seconds (3.69 work units)
INFO:gurobipy:Solved in 8627 iterations and 4.03 seconds (3.69 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
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.
('ok', 'optimal')
# Total system costs
n.objective/1e9
7.8470914242010945
# Average electricity price
n.buses_t.marginal_price.mean()
name
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()
name
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)
name
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(-412486852.28237)
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK 0.630284
dtype: float64
n.lines.s_nom_opt
name
PRT-DNK 3964.218097
Name: s_nom_opt, 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
name
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(2500000.0000000084)
# CO2 price
n.global_constraints
| type | investment_period | bus | carrier_attribute | sense | constant | mu | |
|---|---|---|---|---|---|---|---|
| name | |||||||
| 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.add(
"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,
)
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"])
# Create emission factors for each generator (indexed by generator name)
import xarray as xr
emission_factors = xr.DataArray(
[co2_emission_factor, 0, 0, co2_emission_factor, 0, 0],
dims=["name"],
coords={"name": n.generators.index}
)
# Calculate total emissions: sum over snapshots, multiply by emission factors
total_generation = n.model.variables["Generator-p"].sum("snapshot")
emissions = total_generation * emission_factors
# Group by bus and sum
emissions_per_bus = emissions.groupby(n.generators.bus.to_xarray()).sum()
# Create CO2 limits for each bus
co2_limits = xr.DataArray(
[1000000, 1500000],
dims=["bus"],
coords={"bus": ["PRT", "DNK"]}
)
# Add constraint
n.model.add_constraints(
emissions_per_bus,
"<=",
co2_limits,
name="CO2Limit"
)
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
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
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 49.92it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 317.21it/s]
INFO:linopy.io: Writing time: 0.19s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-tft8zhxx.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-tft8zhxx.lp
Reading time = 0.15 seconds
INFO:gurobipy:Reading time = 0.15 seconds
obj: 140169 rows, 61327 columns, 271592 nonzeros
INFO:gurobipy:obj: 140169 rows, 61327 columns, 271592 nonzeros
Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140169 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0xd765481b
INFO:gurobipy:Model fingerprint: 0xd765481b
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.25s
INFO:gurobipy:Presolve time: 0.25s
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 1.78e-09 7.15e+05 0s
INFO:gurobipy: 3 6.25070764e+10 -3.55890244e+10 1.49e+06 1.78e-09 7.15e+05 0s
4 3.94367930e+10 -1.90579737e+10 8.64e+05 2.91e-10 4.16e+05 0s
INFO:gurobipy: 4 3.94367930e+10 -1.90579737e+10 8.64e+05 2.91e-10 4.16e+05 0s
5 2.93408898e+10 -1.42914113e+10 5.97e+05 3.49e-10 3.07e+05 1s
INFO:gurobipy: 5 2.93408898e+10 -1.42914113e+10 5.97e+05 3.49e-10 3.07e+05 1s
6 2.35119955e+10 -9.51457735e+09 4.43e+05 2.18e-10 2.30e+05 1s
INFO:gurobipy: 6 2.35119955e+10 -9.51457735e+09 4.43e+05 2.18e-10 2.30e+05 1s
7 1.79605788e+10 -3.31826418e+09 3.02e+05 2.04e-10 1.47e+05 1s
INFO:gurobipy: 7 1.79605788e+10 -3.31826418e+09 3.02e+05 2.04e-10 1.47e+05 1s
8 1.38816008e+10 -9.70796908e+07 2.00e+05 2.91e-10 9.61e+04 1s
INFO:gurobipy: 8 1.38816008e+10 -9.70796908e+07 2.00e+05 2.91e-10 9.61e+04 1s
9 1.20573576e+10 7.52858379e+08 1.53e+05 8.44e-10 7.76e+04 1s
INFO:gurobipy: 9 1.20573576e+10 7.52858379e+08 1.53e+05 8.44e-10 7.76e+04 1s
10 1.17211670e+10 1.16006953e+09 1.43e+05 3.82e-11 7.24e+04 1s
INFO:gurobipy: 10 1.17211670e+10 1.16006953e+09 1.43e+05 3.82e-11 7.24e+04 1s
11 1.10283102e+10 3.12477349e+09 1.25e+05 1.14e-09 5.42e+04 1s
INFO:gurobipy: 11 1.10283102e+10 3.12477349e+09 1.25e+05 1.14e-09 5.42e+04 1s
12 1.03576993e+10 4.10629529e+09 1.06e+05 9.09e-11 4.29e+04 1s
INFO:gurobipy: 12 1.03576993e+10 4.10629529e+09 1.06e+05 9.09e-11 4.29e+04 1s
13 9.64387635e+09 4.74351205e+09 8.41e+04 5.82e-10 3.36e+04 1s
INFO:gurobipy: 13 9.64387635e+09 4.74351205e+09 8.41e+04 5.82e-10 3.36e+04 1s
14 9.46687735e+09 5.07032132e+09 7.87e+04 1.60e-09 3.02e+04 1s
INFO:gurobipy: 14 9.46687735e+09 5.07032132e+09 7.87e+04 1.60e-09 3.02e+04 1s
15 9.27846728e+09 5.59116180e+09 6.85e+04 4.66e-10 2.53e+04 1s
INFO:gurobipy: 15 9.27846728e+09 5.59116180e+09 6.85e+04 4.66e-10 2.53e+04 1s
16 8.88778551e+09 5.82291364e+09 5.28e+04 5.53e-10 2.10e+04 1s
INFO:gurobipy: 16 8.88778551e+09 5.82291364e+09 5.28e+04 5.53e-10 2.10e+04 1s
17 8.57481178e+09 6.00150203e+09 3.90e+04 3.78e-10 1.76e+04 1s
INFO:gurobipy: 17 8.57481178e+09 6.00150203e+09 3.90e+04 3.78e-10 1.76e+04 1s
18 8.49108031e+09 6.12319302e+09 3.52e+04 4.66e-10 1.62e+04 1s
INFO:gurobipy: 18 8.49108031e+09 6.12319302e+09 3.52e+04 4.66e-10 1.62e+04 1s
19 8.40165307e+09 6.24855400e+09 3.08e+04 9.02e-10 1.47e+04 1s
INFO:gurobipy: 19 8.40165307e+09 6.24855400e+09 3.08e+04 9.02e-10 1.47e+04 1s
20 8.30562001e+09 6.61654176e+09 2.58e+04 4.07e-10 1.16e+04 1s
INFO:gurobipy: 20 8.30562001e+09 6.61654176e+09 2.58e+04 4.07e-10 1.16e+04 1s
21 8.23620308e+09 6.69051639e+09 2.20e+04 5.53e-10 1.06e+04 1s
INFO:gurobipy: 21 8.23620308e+09 6.69051639e+09 2.20e+04 5.53e-10 1.06e+04 1s
22 8.14246062e+09 7.00230551e+09 1.72e+04 6.40e-10 7.80e+03 1s
INFO:gurobipy: 22 8.14246062e+09 7.00230551e+09 1.72e+04 6.40e-10 7.80e+03 1s
23 8.10863664e+09 7.09088892e+09 1.56e+04 1.31e-10 6.96e+03 1s
INFO:gurobipy: 23 8.10863664e+09 7.09088892e+09 1.56e+04 1.31e-10 6.96e+03 1s
24 8.07383512e+09 7.15995037e+09 1.39e+04 4.37e-10 6.25e+03 1s
INFO:gurobipy: 24 8.07383512e+09 7.15995037e+09 1.39e+04 4.37e-10 6.25e+03 1s
25 8.04599284e+09 7.20276314e+09 1.24e+04 6.98e-10 5.76e+03 1s
INFO:gurobipy: 25 8.04599284e+09 7.20276314e+09 1.24e+04 6.98e-10 5.76e+03 1s
26 8.03457672e+09 7.23105147e+09 1.18e+04 6.55e-11 5.49e+03 1s
INFO:gurobipy: 26 8.03457672e+09 7.23105147e+09 1.18e+04 6.55e-11 5.49e+03 1s
27 8.02939494e+09 7.28075316e+09 1.15e+04 2.47e-10 5.12e+03 1s
INFO:gurobipy: 27 8.02939494e+09 7.28075316e+09 1.15e+04 2.47e-10 5.12e+03 1s
28 7.99707169e+09 7.33866458e+09 9.22e+03 5.53e-10 4.50e+03 1s
INFO:gurobipy: 28 7.99707169e+09 7.33866458e+09 9.22e+03 5.53e-10 4.50e+03 1s
29 7.97399394e+09 7.42076690e+09 7.96e+03 2.91e-10 3.78e+03 1s
INFO:gurobipy: 29 7.97399394e+09 7.42076690e+09 7.96e+03 2.91e-10 3.78e+03 1s
30 7.95708928e+09 7.45365040e+09 6.97e+03 2.91e-10 3.44e+03 1s
INFO:gurobipy: 30 7.95708928e+09 7.45365040e+09 6.97e+03 2.91e-10 3.44e+03 1s
31 7.94385375e+09 7.52495702e+09 6.15e+03 4.95e-10 2.86e+03 1s
INFO:gurobipy: 31 7.94385375e+09 7.52495702e+09 6.15e+03 4.95e-10 2.86e+03 1s
32 7.93106549e+09 7.54303948e+09 5.38e+03 5.82e-11 2.65e+03 1s
INFO:gurobipy: 32 7.93106549e+09 7.54303948e+09 5.38e+03 5.82e-11 2.65e+03 1s
33 7.91815204e+09 7.57406296e+09 4.57e+03 2.91e-11 2.35e+03 1s
INFO:gurobipy: 33 7.91815204e+09 7.57406296e+09 4.57e+03 2.91e-11 2.35e+03 1s
34 7.91368145e+09 7.60416310e+09 4.20e+03 8.73e-11 2.11e+03 1s
INFO:gurobipy: 34 7.91368145e+09 7.60416310e+09 4.20e+03 8.73e-11 2.11e+03 1s
35 7.90119741e+09 7.63082788e+09 3.31e+03 5.24e-10 1.84e+03 1s
INFO:gurobipy: 35 7.90119741e+09 7.63082788e+09 3.31e+03 5.24e-10 1.84e+03 1s
36 7.89107282e+09 7.64918681e+09 2.71e+03 7.86e-10 1.65e+03 1s
INFO:gurobipy: 36 7.89107282e+09 7.64918681e+09 2.71e+03 7.86e-10 1.65e+03 1s
37 7.88167031e+09 7.67136922e+09 1.99e+03 6.98e-10 1.43e+03 1s
INFO:gurobipy: 37 7.88167031e+09 7.67136922e+09 1.99e+03 6.98e-10 1.43e+03 1s
38 7.87817052e+09 7.68664078e+09 1.75e+03 2.91e-10 1.30e+03 1s
INFO:gurobipy: 38 7.87817052e+09 7.68664078e+09 1.75e+03 2.91e-10 1.30e+03 1s
39 7.87338555e+09 7.70242169e+09 1.45e+03 4.95e-10 1.16e+03 1s
INFO:gurobipy: 39 7.87338555e+09 7.70242169e+09 1.45e+03 4.95e-10 1.16e+03 1s
40 7.86504712e+09 7.73880912e+09 9.20e+02 4.07e-10 8.55e+02 1s
INFO:gurobipy: 40 7.86504712e+09 7.73880912e+09 9.20e+02 4.07e-10 8.55e+02 1s
41 7.86136531e+09 7.75410219e+09 6.88e+02 2.62e-10 7.26e+02 1s
INFO:gurobipy: 41 7.86136531e+09 7.75410219e+09 6.88e+02 2.62e-10 7.26e+02 1s
42 7.85836264e+09 7.76340807e+09 5.30e+02 5.82e-10 6.42e+02 1s
INFO:gurobipy: 42 7.85836264e+09 7.76340807e+09 5.30e+02 5.82e-10 6.42e+02 1s
43 7.85708183e+09 7.77159907e+09 4.63e+02 2.33e-10 5.78e+02 1s
INFO:gurobipy: 43 7.85708183e+09 7.77159907e+09 4.63e+02 2.33e-10 5.78e+02 1s
44 7.85622019e+09 7.77935776e+09 4.16e+02 4.07e-10 5.19e+02 1s
INFO:gurobipy: 44 7.85622019e+09 7.77935776e+09 4.16e+02 4.07e-10 5.19e+02 1s
45 7.85542784e+09 7.78406996e+09 3.74e+02 3.49e-10 4.82e+02 2s
INFO:gurobipy: 45 7.85542784e+09 7.78406996e+09 3.74e+02 3.49e-10 4.82e+02 2s
46 7.85452898e+09 7.78735456e+09 3.26e+02 1.37e-09 4.54e+02 2s
INFO:gurobipy: 46 7.85452898e+09 7.78735456e+09 3.26e+02 1.37e-09 4.54e+02 2s
47 7.85390984e+09 7.79230033e+09 2.95e+02 1.31e-10 4.16e+02 2s
INFO:gurobipy: 47 7.85390984e+09 7.79230033e+09 2.95e+02 1.31e-10 4.16e+02 2s
48 7.85350250e+09 7.79583789e+09 2.74e+02 3.20e-10 3.89e+02 2s
INFO:gurobipy: 48 7.85350250e+09 7.79583789e+09 2.74e+02 3.20e-10 3.89e+02 2s
49 7.85303881e+09 7.79739639e+09 2.50e+02 1.93e-10 3.76e+02 2s
INFO:gurobipy: 49 7.85303881e+09 7.79739639e+09 2.50e+02 1.93e-10 3.76e+02 2s
50 7.85196053e+09 7.80237548e+09 2.00e+02 4.37e-10 3.35e+02 2s
INFO:gurobipy: 50 7.85196053e+09 7.80237548e+09 2.00e+02 4.37e-10 3.35e+02 2s
51 7.85155258e+09 7.80670677e+09 1.80e+02 5.57e-10 3.03e+02 2s
INFO:gurobipy: 51 7.85155258e+09 7.80670677e+09 1.80e+02 5.57e-10 3.03e+02 2s
52 7.85045868e+09 7.80930010e+09 1.36e+02 9.71e-10 2.77e+02 2s
INFO:gurobipy: 52 7.85045868e+09 7.80930010e+09 1.36e+02 9.71e-10 2.77e+02 2s
53 7.85025540e+09 7.81062001e+09 1.26e+02 1.11e-09 2.67e+02 2s
INFO:gurobipy: 53 7.85025540e+09 7.81062001e+09 1.26e+02 1.11e-09 2.67e+02 2s
54 7.85007534e+09 7.81442547e+09 1.19e+02 1.95e-09 2.40e+02 2s
INFO:gurobipy: 54 7.85007534e+09 7.81442547e+09 1.19e+02 1.95e-09 2.40e+02 2s
55 7.84992684e+09 7.81741083e+09 1.12e+02 1.84e-09 2.19e+02 2s
INFO:gurobipy: 55 7.84992684e+09 7.81741083e+09 1.12e+02 1.84e-09 2.19e+02 2s
56 7.84962031e+09 7.81780488e+09 9.97e+01 2.07e-09 2.14e+02 2s
INFO:gurobipy: 56 7.84962031e+09 7.81780488e+09 9.97e+01 2.07e-09 2.14e+02 2s
57 7.84955526e+09 7.82416190e+09 9.61e+01 1.90e-09 1.71e+02 2s
INFO:gurobipy: 57 7.84955526e+09 7.82416190e+09 9.61e+01 1.90e-09 1.71e+02 2s
58 7.84785763e+09 7.82521177e+09 1.14e+01 1.76e-09 1.52e+02 2s
INFO:gurobipy: 58 7.84785763e+09 7.82521177e+09 1.14e+01 1.76e-09 1.52e+02 2s
59 7.84779737e+09 7.82641813e+09 1.05e+01 2.84e-09 1.44e+02 2s
INFO:gurobipy: 59 7.84779737e+09 7.82641813e+09 1.05e+01 2.84e-09 1.44e+02 2s
60 7.84772831e+09 7.82809565e+09 9.63e+00 2.85e-09 1.32e+02 2s
INFO:gurobipy: 60 7.84772831e+09 7.82809565e+09 9.63e+00 2.85e-09 1.32e+02 2s
61 7.84764588e+09 7.83061776e+09 7.77e+00 2.74e-09 1.14e+02 2s
INFO:gurobipy: 61 7.84764588e+09 7.83061776e+09 7.77e+00 2.74e-09 1.14e+02 2s
62 7.84764013e+09 7.83110809e+09 7.67e+00 2.72e-09 1.11e+02 2s
INFO:gurobipy: 62 7.84764013e+09 7.83110809e+09 7.67e+00 2.72e-09 1.11e+02 2s
63 7.84761760e+09 7.83158918e+09 7.33e+00 2.76e-09 1.08e+02 2s
INFO:gurobipy: 63 7.84761760e+09 7.83158918e+09 7.33e+00 2.76e-09 1.08e+02 2s
64 7.84748641e+09 7.83205048e+09 5.88e+00 2.85e-09 1.04e+02 2s
INFO:gurobipy: 64 7.84748641e+09 7.83205048e+09 5.88e+00 2.85e-09 1.04e+02 2s
65 7.84745232e+09 7.83446921e+09 5.19e+00 1.19e-09 8.72e+01 2s
INFO:gurobipy: 65 7.84745232e+09 7.83446921e+09 5.19e+00 1.19e-09 8.72e+01 2s
66 7.84743621e+09 7.83666753e+09 4.63e+00 1.67e-09 7.24e+01 2s
INFO:gurobipy: 66 7.84743621e+09 7.83666753e+09 4.63e+00 1.67e-09 7.24e+01 2s
67 7.84736526e+09 7.83768497e+09 3.45e+00 1.67e-09 6.50e+01 2s
INFO:gurobipy: 67 7.84736526e+09 7.83768497e+09 3.45e+00 1.67e-09 6.50e+01 2s
68 7.84730967e+09 7.84176654e+09 1.88e+00 1.03e-09 3.72e+01 2s
INFO:gurobipy: 68 7.84730967e+09 7.84176654e+09 1.88e+00 1.03e-09 3.72e+01 2s
69 7.84722873e+09 7.84423798e+09 9.01e-01 2.20e-09 2.01e+01 2s
INFO:gurobipy: 69 7.84722873e+09 7.84423798e+09 9.01e-01 2.20e-09 2.01e+01 2s
70 7.84717271e+09 7.84482962e+09 4.31e-01 1.62e-09 1.57e+01 2s
INFO:gurobipy: 70 7.84717271e+09 7.84482962e+09 4.31e-01 1.62e-09 1.57e+01 2s
71 7.84713967e+09 7.84496009e+09 2.37e-01 1.65e-09 1.46e+01 2s
INFO:gurobipy: 71 7.84713967e+09 7.84496009e+09 2.37e-01 1.65e-09 1.46e+01 2s
72 7.84713282e+09 7.84566184e+09 1.99e-01 1.52e-09 9.88e+00 2s
INFO:gurobipy: 72 7.84713282e+09 7.84566184e+09 1.99e-01 1.52e-09 9.88e+00 2s
73 7.84709368e+09 7.84696565e+09 7.06e-05 8.73e-10 8.60e-01 2s
INFO:gurobipy: 73 7.84709368e+09 7.84696565e+09 7.06e-05 8.73e-10 8.60e-01 2s
74 7.84709161e+09 7.84709079e+09 6.40e-06 3.19e-09 5.47e-03 2s
INFO:gurobipy: 74 7.84709161e+09 7.84709079e+09 6.40e-06 3.19e-09 5.47e-03 2s
75 7.84709142e+09 7.84709142e+09 3.37e-07 2.66e-09 8.48e-07 2s
INFO:gurobipy: 75 7.84709142e+09 7.84709142e+09 3.37e-07 2.66e-09 8.48e-07 2s
76 7.84709142e+09 7.84709142e+09 4.47e-07 2.40e-09 2.83e-10 2s
INFO:gurobipy: 76 7.84709142e+09 7.84709142e+09 4.47e-07 2.40e-09 2.83e-10 2s
INFO:gurobipy:
Barrier solved model in 76 iterations and 2.20 seconds (2.18 work units)
INFO:gurobipy:Barrier solved model in 76 iterations and 2.20 seconds (2.18 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:
8562 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 8562 PPushes remaining with PInf 0.0000000e+00 2s
0 PPushes remaining with PInf 0.0000000e+00 3s
INFO:gurobipy: 0 PPushes remaining with PInf 0.0000000e+00 3s
INFO:gurobipy:
Push phase complete: Pinf 0.0000000e+00, Dinf 2.8288003e-09 3s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 2.8288003e-09 3s
INFO:gurobipy:
Crossover time: 0.48 seconds (1.21 work units)
INFO:gurobipy:Crossover time: 0.48 seconds (1.21 work units)
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 3s
INFO:gurobipy: 8616 7.8470914e+09 0.000000e+00 0.000000e+00 3s
INFO:gurobipy:
Solved in 8616 iterations and 2.82 seconds (3.48 work units)
INFO:gurobipy:Solved in 8616 iterations and 2.82 seconds (3.48 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
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.
('ok', 'optimal')
# Total system costs
n.objective/1e9
7.847091424201071
# Average electricity price
n.buses_t.marginal_price.mean()
name
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()
name
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)
name
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(-412486852.2823695)
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK 0.628202
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
name
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(2500000.0000000023)
Use hint from the problem description.
n.model.dual
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.13/site-packages/linopy/common.py:459: UserWarning:
Coordinates across variables not equal. Perform outer join.
<xarray.Dataset> Size: 3MB
Dimensions: (name: 9, snapshot: 8760, bus: 2)
Coordinates:
* name (name) object 72B 'DNK' 'DNK OCGT' ... 'PRT-DNK'
* snapshot (snapshot) datetime64[ns] 70kB 2015-01-01 ... ...
* bus (bus) object 16B 'DNK' 'PRT'
Data variables:
Generator-ext-p_nom-lower (name) float64 72B nan 0.0 0.0 ... 0.0 0.0 nan
Line-ext-s_nom-lower (name) float64 72B nan nan nan ... nan nan 0.0
Generator-ext-p-lower (snapshot, name) float64 631kB nan 537.3 ... nan
Generator-ext-p-upper (snapshot, name) float64 631kB nan 0.0 ... nan
Line-ext-s-lower (snapshot, name) float64 631kB nan nan ... 0.0
Line-ext-s-upper (snapshot, name) float64 631kB nan nan ... 0.0
Bus-nodal_balance (name, snapshot) float64 631kB 1.429 ... nan
CO2Limit (bus) float64 16B -981.6 -981.6c. 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.add(
"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,
)
n.optimize.create_model()
co2_emission_factor = (costs.at["OCGT", "CO2 intensity"] / costs.at["OCGT", "efficiency"])
# Create emission factors for each generator (indexed by generator name)
emission_factors = xr.DataArray(
[co2_emission_factor, 0, 0, co2_emission_factor, 0, 0],
dims=["name"],
coords={"name": n.generators.index}
)
# Calculate total emissions: sum over snapshots, multiply by emission factors
total_generation = n.model.variables["Generator-p"].sum("snapshot")
emissions = total_generation * emission_factors
# Group by bus and sum
emissions_per_bus = emissions.groupby(n.generators.bus.to_xarray()).sum()
# Create CO2 limits for each bus
co2_limits = xr.DataArray(
[1000000, 1500000],
dims=["bus"],
coords={"bus": ["PRT", "DNK"]}
)
# Add constraint
n.model.add_constraints(
emissions_per_bus,
"<=",
co2_limits,
name="CO2Limit"
)
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
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
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 9/9 [00:00<00:00, 50.35it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 375.23it/s]
INFO:linopy.io: Writing time: 0.21s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-ek1ioa1a.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-ek1ioa1a.lp
Reading time = 0.15 seconds
INFO:gurobipy:Reading time = 0.15 seconds
obj: 140170 rows, 61327 columns, 271593 nonzeros
INFO:gurobipy:obj: 140170 rows, 61327 columns, 271593 nonzeros
Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140170 rows, 61327 columns and 271593 nonzeros (Min)
Model fingerprint: 0x68f63895
INFO:gurobipy:Model fingerprint: 0x68f63895
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.18s
INFO:gurobipy:Presolve time: 0.18s
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 1.45e+07 9.80e-10 6.43e+06 0s
INFO:gurobipy: 3 2.02172001e+11 -3.29667454e+11 1.45e+07 9.80e-10 6.43e+06 0s
4 1.04938166e+11 -1.59534340e+11 6.47e+06 7.50e-09 2.70e+06 0s
INFO:gurobipy: 4 1.04938166e+11 -1.59534340e+11 6.47e+06 7.50e-09 2.70e+06 0s
5 6.63016417e+10 -1.01908244e+11 3.63e+06 1.01e-08 1.54e+06 0s
INFO:gurobipy: 5 6.63016417e+10 -1.01908244e+11 3.63e+06 1.01e-08 1.54e+06 0s
6 4.73562899e+10 -6.95327020e+10 2.31e+06 0.00e+00 1.00e+06 0s
INFO:gurobipy: 6 4.73562899e+10 -6.95327020e+10 2.31e+06 0.00e+00 1.00e+06 0s
7 3.53804981e+10 -5.45341229e+10 1.49e+06 3.08e-09 7.26e+05 0s
INFO:gurobipy: 7 3.53804981e+10 -5.45341229e+10 1.49e+06 3.08e-09 7.26e+05 0s
8 2.94478025e+10 -1.92589726e+10 1.14e+06 0.00e+00 3.87e+05 1s
INFO:gurobipy: 8 2.94478025e+10 -1.92589726e+10 1.14e+06 0.00e+00 3.87e+05 1s
9 2.43310354e+10 -1.38359442e+10 8.72e+05 1.10e-09 2.97e+05 1s
INFO:gurobipy: 9 2.43310354e+10 -1.38359442e+10 8.72e+05 1.10e-09 2.97e+05 1s
10 2.09459071e+10 -9.44969710e+09 6.68e+05 1.21e-09 2.32e+05 1s
INFO:gurobipy: 10 2.09459071e+10 -9.44969710e+09 6.68e+05 1.21e-09 2.32e+05 1s
11 1.84657795e+10 -4.00446027e+09 5.20e+05 3.98e-10 1.70e+05 1s
INFO:gurobipy: 11 1.84657795e+10 -4.00446027e+09 5.20e+05 3.98e-10 1.70e+05 1s
12 1.72643963e+10 -2.54506389e+09 4.52e+05 0.00e+00 1.49e+05 1s
INFO:gurobipy: 12 1.72643963e+10 -2.54506389e+09 4.52e+05 0.00e+00 1.49e+05 1s
13 1.60600199e+10 1.16341321e+09 3.90e+05 2.09e-09 1.12e+05 1s
INFO:gurobipy: 13 1.60600199e+10 1.16341321e+09 3.90e+05 2.09e-09 1.12e+05 1s
14 1.48552717e+10 2.91872678e+09 3.26e+05 2.82e-10 8.91e+04 1s
INFO:gurobipy: 14 1.48552717e+10 2.91872678e+09 3.26e+05 2.82e-10 8.91e+04 1s
15 1.37047729e+10 4.51160288e+09 2.63e+05 0.00e+00 6.84e+04 1s
INFO:gurobipy: 15 1.37047729e+10 4.51160288e+09 2.63e+05 0.00e+00 6.84e+04 1s
16 1.29555584e+10 5.50916522e+09 2.28e+05 0.00e+00 5.54e+04 1s
INFO:gurobipy: 16 1.29555584e+10 5.50916522e+09 2.28e+05 0.00e+00 5.54e+04 1s
17 1.23644061e+10 6.24017524e+09 1.96e+05 0.00e+00 4.56e+04 1s
INFO:gurobipy: 17 1.23644061e+10 6.24017524e+09 1.96e+05 0.00e+00 4.56e+04 1s
18 1.20994616e+10 6.78336543e+09 1.80e+05 0.00e+00 3.96e+04 1s
INFO:gurobipy: 18 1.20994616e+10 6.78336543e+09 1.80e+05 0.00e+00 3.96e+04 1s
19 1.15139646e+10 7.09713423e+09 1.51e+05 1.88e-09 3.29e+04 1s
INFO:gurobipy: 19 1.15139646e+10 7.09713423e+09 1.51e+05 1.88e-09 3.29e+04 1s
20 1.14178547e+10 7.33413150e+09 1.45e+05 0.00e+00 3.04e+04 1s
INFO:gurobipy: 20 1.14178547e+10 7.33413150e+09 1.45e+05 0.00e+00 3.04e+04 1s
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 1.14e+05 0.00e+00 2.33e+04 1s
INFO:gurobipy: 22 1.09161301e+10 7.79084464e+09 1.14e+05 0.00e+00 2.33e+04 1s
23 1.06563250e+10 7.94564584e+09 9.59e+04 1.10e-09 2.01e+04 1s
INFO:gurobipy: 23 1.06563250e+10 7.94564584e+09 9.59e+04 1.10e-09 2.01e+04 1s
24 1.05715977e+10 8.15196507e+09 8.83e+04 6.31e-10 1.80e+04 1s
INFO:gurobipy: 24 1.05715977e+10 8.15196507e+09 8.83e+04 6.31e-10 1.80e+04 1s
25 1.03740039e+10 8.41478937e+09 7.25e+04 0.00e+00 1.45e+04 1s
INFO:gurobipy: 25 1.03740039e+10 8.41478937e+09 7.25e+04 0.00e+00 1.45e+04 1s
26 1.02838823e+10 8.47790654e+09 6.63e+04 1.66e-10 1.34e+04 1s
INFO:gurobipy: 26 1.02838823e+10 8.47790654e+09 6.63e+04 1.66e-10 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 9.98147266e+09 8.77817300e+09 4.15e+04 0.00e+00 8.83e+03 1s
INFO:gurobipy: 28 9.98147266e+09 8.77817300e+09 4.15e+04 0.00e+00 8.83e+03 1s
29 9.90571958e+09 8.95403293e+09 3.44e+04 1.16e-09 7.00e+03 1s
INFO:gurobipy: 29 9.90571958e+09 8.95403293e+09 3.44e+04 1.16e-09 7.00e+03 1s
30 9.82102678e+09 9.04851816e+09 2.74e+04 0.00e+00 5.67e+03 1s
INFO:gurobipy: 30 9.82102678e+09 9.04851816e+09 2.74e+04 0.00e+00 5.67e+03 1s
31 9.75697301e+09 9.13797882e+09 2.20e+04 0.00e+00 4.54e+03 1s
INFO:gurobipy: 31 9.75697301e+09 9.13797882e+09 2.20e+04 0.00e+00 4.54e+03 1s
32 9.70417961e+09 9.19398498e+09 1.69e+04 1.71e-09 3.72e+03 1s
INFO:gurobipy: 32 9.70417961e+09 9.19398498e+09 1.69e+04 1.71e-09 3.72e+03 1s
33 9.66272544e+09 9.24979489e+09 1.36e+04 3.40e-10 3.00e+03 1s
INFO:gurobipy: 33 9.66272544e+09 9.24979489e+09 1.36e+04 3.40e-10 3.00e+03 1s
34 9.63786075e+09 9.31942351e+09 1.15e+04 2.82e-10 2.33e+03 1s
INFO:gurobipy: 34 9.63786075e+09 9.31942351e+09 1.15e+04 2.82e-10 2.33e+03 1s
35 9.62407479e+09 9.34416929e+09 1.04e+04 6.02e-10 2.05e+03 1s
INFO:gurobipy: 35 9.62407479e+09 9.34416929e+09 1.04e+04 6.02e-10 2.05e+03 1s
36 9.61269259e+09 9.36834780e+09 9.52e+03 6.31e-10 1.80e+03 1s
INFO:gurobipy: 36 9.61269259e+09 9.36834780e+09 9.52e+03 6.31e-10 1.80e+03 1s
37 9.60072796e+09 9.38454386e+09 8.55e+03 0.00e+00 1.59e+03 1s
INFO:gurobipy: 37 9.60072796e+09 9.38454386e+09 8.55e+03 0.00e+00 1.59e+03 1s
38 9.58553692e+09 9.39583960e+09 7.25e+03 0.00e+00 1.39e+03 1s
INFO:gurobipy: 38 9.58553692e+09 9.39583960e+09 7.25e+03 0.00e+00 1.39e+03 1s
39 9.56481028e+09 9.42362323e+09 5.33e+03 0.00e+00 1.04e+03 1s
INFO:gurobipy: 39 9.56481028e+09 9.42362323e+09 5.33e+03 0.00e+00 1.04e+03 1s
40 9.55678673e+09 9.42858187e+09 4.64e+03 0.00e+00 9.37e+02 1s
INFO:gurobipy: 40 9.55678673e+09 9.42858187e+09 4.64e+03 0.00e+00 9.37e+02 1s
41 9.55156602e+09 9.43655904e+09 4.23e+03 0.00e+00 8.42e+02 1s
INFO:gurobipy: 41 9.55156602e+09 9.43655904e+09 4.23e+03 0.00e+00 8.42e+02 1s
42 9.54303900e+09 9.45297674e+09 3.49e+03 1.39e-09 6.62e+02 1s
INFO:gurobipy: 42 9.54303900e+09 9.45297674e+09 3.49e+03 1.39e-09 6.62e+02 1s
43 9.54077474e+09 9.45737313e+09 3.29e+03 0.00e+00 6.14e+02 1s
INFO:gurobipy: 43 9.54077474e+09 9.45737313e+09 3.29e+03 0.00e+00 6.14e+02 1s
44 9.53115853e+09 9.46602498e+09 2.49e+03 0.00e+00 4.78e+02 1s
INFO:gurobipy: 44 9.53115853e+09 9.46602498e+09 2.49e+03 0.00e+00 4.78e+02 1s
45 9.52251051e+09 9.47192417e+09 1.72e+03 8.35e-10 3.67e+02 1s
INFO:gurobipy: 45 9.52251051e+09 9.47192417e+09 1.72e+03 8.35e-10 3.67e+02 1s
46 9.51547167e+09 9.48432118e+09 1.09e+03 0.00e+00 2.27e+02 1s
INFO:gurobipy: 46 9.51547167e+09 9.48432118e+09 1.09e+03 0.00e+00 2.27e+02 1s
47 9.51400824e+09 9.48733442e+09 9.83e+02 1.94e-09 1.95e+02 1s
INFO:gurobipy: 47 9.51400824e+09 9.48733442e+09 9.83e+02 1.94e-09 1.95e+02 1s
48 9.51177827e+09 9.48887616e+09 7.92e+02 0.00e+00 1.67e+02 1s
INFO:gurobipy: 48 9.51177827e+09 9.48887616e+09 7.92e+02 0.00e+00 1.67e+02 1s
49 9.51106889e+09 9.49098806e+09 7.31e+02 0.00e+00 1.47e+02 2s
INFO:gurobipy: 49 9.51106889e+09 9.49098806e+09 7.31e+02 0.00e+00 1.47e+02 2s
50 9.51052317e+09 9.49324136e+09 6.89e+02 0.00e+00 1.27e+02 2s
INFO:gurobipy: 50 9.51052317e+09 9.49324136e+09 6.89e+02 0.00e+00 1.27e+02 2s
51 9.50870293e+09 9.49552830e+09 5.48e+02 0.00e+00 9.73e+01 2s
INFO:gurobipy: 51 9.50870293e+09 9.49552830e+09 5.48e+02 0.00e+00 9.73e+01 2s
52 9.50599490e+09 9.50014593e+09 3.18e+02 0.00e+00 4.44e+01 2s
INFO:gurobipy: 52 9.50599490e+09 9.50014593e+09 3.18e+02 0.00e+00 4.44e+01 2s
53 9.50540487e+09 9.50079354e+09 2.68e+02 0.00e+00 3.53e+01 2s
INFO:gurobipy: 53 9.50540487e+09 9.50079354e+09 2.68e+02 0.00e+00 3.53e+01 2s
54 9.50452375e+09 9.50093377e+09 1.92e+02 0.00e+00 2.72e+01 2s
INFO:gurobipy: 54 9.50452375e+09 9.50093377e+09 1.92e+02 0.00e+00 2.72e+01 2s
55 9.50350674e+09 9.50116064e+09 1.05e+02 0.00e+00 1.74e+01 2s
INFO:gurobipy: 55 9.50350674e+09 9.50116064e+09 1.05e+02 0.00e+00 1.74e+01 2s
56 9.50309277e+09 9.50153836e+09 6.95e+01 0.00e+00 1.16e+01 2s
INFO:gurobipy: 56 9.50309277e+09 9.50153836e+09 6.95e+01 0.00e+00 1.16e+01 2s
57 9.50274003e+09 9.50172460e+09 4.18e+01 0.00e+00 7.49e+00 2s
INFO:gurobipy: 57 9.50274003e+09 9.50172460e+09 4.18e+01 0.00e+00 7.49e+00 2s
58 9.50259508e+09 9.50179427e+09 2.95e+01 0.00e+00 5.85e+00 2s
INFO:gurobipy: 58 9.50259508e+09 9.50179427e+09 2.95e+01 0.00e+00 5.85e+00 2s
59 9.50251266e+09 9.50195261e+09 2.21e+01 0.00e+00 4.11e+00 2s
INFO:gurobipy: 59 9.50251266e+09 9.50195261e+09 2.21e+01 0.00e+00 4.11e+00 2s
60 9.50229382e+09 9.50212040e+09 5.35e+00 0.00e+00 1.25e+00 2s
INFO:gurobipy: 60 9.50229382e+09 9.50212040e+09 5.35e+00 0.00e+00 1.25e+00 2s
61 9.50223805e+09 9.50219375e+09 1.13e+00 0.00e+00 3.16e-01 2s
INFO:gurobipy: 61 9.50223805e+09 9.50219375e+09 1.13e+00 0.00e+00 3.16e-01 2s
62 9.50222233e+09 9.50221981e+09 2.25e-02 7.57e-10 1.72e-02 2s
INFO:gurobipy: 62 9.50222233e+09 9.50221981e+09 2.25e-02 7.57e-10 1.72e-02 2s
63 9.50222186e+09 9.50222184e+09 7.54e-05 4.39e-09 1.10e-04 2s
INFO:gurobipy: 63 9.50222186e+09 9.50222184e+09 7.54e-05 4.39e-09 1.10e-04 2s
64 9.50222185e+09 9.50222185e+09 2.31e-07 4.93e-09 1.14e-10 2s
INFO:gurobipy: 64 9.50222185e+09 9.50222185e+09 2.31e-07 4.93e-09 1.14e-10 2s
INFO:gurobipy:
Barrier solved model in 64 iterations and 1.74 seconds (1.89 work units)
INFO:gurobipy:Barrier solved model in 64 iterations and 1.74 seconds (1.89 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 2s
INFO:gurobipy: 34 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 0.25
INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.25
INFO:gurobipy:
5716 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 5716 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 3.5827636e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 3.5827636e-09 2s
INFO:gurobipy:
Crossover time: 0.33 seconds (0.87 work units)
INFO:gurobipy:Crossover time: 0.33 seconds (0.87 work units)
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 2s
INFO:gurobipy: 5753 9.5022219e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy:
Solved in 5753 iterations and 2.12 seconds (2.86 work units)
INFO:gurobipy:Solved in 5753 iterations and 2.12 seconds (2.86 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
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.
('ok', 'optimal')
# Total system costs
n.objective/1e9
9.502221854579842
# Average electricity price
n.buses_t.marginal_price.mean()
name
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()
name
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)
name
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(-1884193551.7469282)
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK 0.871805
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
name
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(2500000.000000002)
n.model.dual
/opt/homebrew/Caskroom/miniforge/base/envs/integrated-energy-grids/lib/python3.13/site-packages/linopy/common.py:459: UserWarning:
Coordinates across variables not equal. Perform outer join.
<xarray.Dataset> Size: 3MB
Dimensions: (name: 9, snapshot: 8760, bus: 2)
Coordinates:
* name (name) object 72B 'DNK' 'DNK OCGT' ... 'PRT-DNK'
* snapshot (snapshot) datetime64[ns] 70kB 2015-01-01 ... ...
* bus (bus) object 16B 'DNK' 'PRT'
Data variables:
Generator-ext-p_nom-lower (name) float64 72B nan 0.0 0.0 ... 0.0 0.0 nan
Line-ext-s_nom-lower (name) float64 72B nan nan nan ... nan nan 0.0
Line-ext-s_nom-upper (name) float64 72B nan nan nan ... nan -1.78e+06
Generator-ext-p-lower (snapshot, name) float64 631kB nan 910.8 ... nan
Generator-ext-p-upper (snapshot, name) float64 631kB nan 0.0 ... nan
Line-ext-s-lower (snapshot, name) float64 631kB nan nan ... 0.0
Line-ext-s-upper (snapshot, name) float64 631kB nan nan ... 0.0
Bus-nodal_balance (name, snapshot) float64 631kB 1.429 ... nan
CO2Limit (bus) float64 16B -1.755e+03 -1.705e+03d. 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.add(
"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")
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 69.43it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 475.50it/s]
INFO:linopy.io: Writing time: 0.13s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-qhwa5lj2.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-qhwa5lj2.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 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0xc84ef539
INFO:gurobipy:Model fingerprint: 0xc84ef539
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.16s
INFO:gurobipy:Presolve time: 0.16s
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 1.25e-09 4.81e+05 0s
INFO:gurobipy: 3 5.40297885e+10 -1.21107184e+10 1.95e+06 1.25e-09 4.81e+05 0s
4 3.89140611e+10 -4.52566441e+09 1.32e+06 8.15e-10 3.13e+05 0s
INFO:gurobipy: 4 3.89140611e+10 -4.52566441e+09 1.32e+06 8.15e-10 3.13e+05 0s
5 3.16419219e+10 -2.50148685e+09 1.01e+06 1.11e-09 2.45e+05 0s
INFO:gurobipy: 5 3.16419219e+10 -2.50148685e+09 1.01e+06 1.11e-09 2.45e+05 0s
6 2.76616278e+10 -4.13884538e+08 8.28e+05 5.24e-10 2.01e+05 0s
INFO:gurobipy: 6 2.76616278e+10 -4.13884538e+08 8.28e+05 5.24e-10 2.01e+05 0s
7 2.28844778e+10 2.29643676e+09 6.21e+05 6.40e-10 1.48e+05 0s
INFO:gurobipy: 7 2.28844778e+10 2.29643676e+09 6.21e+05 6.40e-10 1.48e+05 0s
8 2.10493492e+10 3.57495332e+09 5.39e+05 3.49e-10 1.26e+05 0s
INFO:gurobipy: 8 2.10493492e+10 3.57495332e+09 5.39e+05 3.49e-10 1.26e+05 0s
9 1.94595775e+10 4.88497499e+09 4.63e+05 1.05e-09 1.06e+05 0s
INFO:gurobipy: 9 1.94595775e+10 4.88497499e+09 4.63e+05 1.05e-09 1.06e+05 0s
10 1.79167807e+10 5.76456531e+09 3.87e+05 2.62e-10 8.90e+04 0s
INFO:gurobipy: 10 1.79167807e+10 5.76456531e+09 3.87e+05 2.62e-10 8.90e+04 0s
11 1.72539808e+10 6.32980349e+09 3.25e+05 2.33e-10 7.99e+04 0s
INFO:gurobipy: 11 1.72539808e+10 6.32980349e+09 3.25e+05 2.33e-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 1.75e-10 6.54e+04 0s
INFO:gurobipy: 13 1.63886229e+10 7.57420272e+09 2.70e+05 1.75e-10 6.54e+04 0s
14 1.61519836e+10 7.87593182e+09 2.37e+05 1.46e-10 6.12e+04 0s
INFO:gurobipy: 14 1.61519836e+10 7.87593182e+09 2.37e+05 1.46e-10 6.12e+04 0s
15 1.60159396e+10 8.35006429e+09 2.27e+05 2.91e-10 5.71e+04 0s
INFO:gurobipy: 15 1.60159396e+10 8.35006429e+09 2.27e+05 2.91e-10 5.71e+04 0s
16 1.58231902e+10 8.85060571e+09 2.11e+05 3.78e-10 5.23e+04 0s
INFO:gurobipy: 16 1.58231902e+10 8.85060571e+09 2.11e+05 3.78e-10 5.23e+04 0s
17 1.57071004e+10 9.03219407e+09 1.92e+05 4.66e-10 4.99e+04 1s
INFO:gurobipy: 17 1.57071004e+10 9.03219407e+09 1.92e+05 4.66e-10 4.99e+04 1s
18 1.55959123e+10 9.78646568e+09 1.68e+05 2.62e-10 4.39e+04 1s
INFO:gurobipy: 18 1.55959123e+10 9.78646568e+09 1.68e+05 2.62e-10 4.39e+04 1s
19 1.55682624e+10 9.91326085e+09 1.53e+05 4.07e-10 4.25e+04 1s
INFO:gurobipy: 19 1.55682624e+10 9.91326085e+09 1.53e+05 4.07e-10 4.25e+04 1s
20 1.54407391e+10 1.09630757e+10 1.30e+05 1.31e-10 3.44e+04 1s
INFO:gurobipy: 20 1.54407391e+10 1.09630757e+10 1.30e+05 1.31e-10 3.44e+04 1s
21 1.53324798e+10 1.16019355e+10 1.17e+05 5.53e-10 2.92e+04 1s
INFO:gurobipy: 21 1.53324798e+10 1.16019355e+10 1.17e+05 5.53e-10 2.92e+04 1s
22 1.52711027e+10 1.19604135e+10 1.07e+05 3.49e-10 2.63e+04 1s
INFO:gurobipy: 22 1.52711027e+10 1.19604135e+10 1.07e+05 3.49e-10 2.63e+04 1s
23 1.52376129e+10 1.21147674e+10 9.85e+04 4.07e-10 2.48e+04 1s
INFO:gurobipy: 23 1.52376129e+10 1.21147674e+10 9.85e+04 4.07e-10 2.48e+04 1s
24 1.52710994e+10 1.24309894e+10 8.19e+04 3.49e-10 2.23e+04 1s
INFO:gurobipy: 24 1.52710994e+10 1.24309894e+10 8.19e+04 3.49e-10 2.23e+04 1s
25 1.52858243e+10 1.25265660e+10 7.87e+04 4.37e-10 2.17e+04 1s
INFO:gurobipy: 25 1.52858243e+10 1.25265660e+10 7.87e+04 4.37e-10 2.17e+04 1s
26 1.52610058e+10 1.28950471e+10 7.27e+04 6.98e-10 1.89e+04 1s
INFO:gurobipy: 26 1.52610058e+10 1.28950471e+10 7.27e+04 6.98e-10 1.89e+04 1s
27 1.52284617e+10 1.30206636e+10 6.48e+04 6.98e-10 1.75e+04 1s
INFO:gurobipy: 27 1.52284617e+10 1.30206636e+10 6.48e+04 6.98e-10 1.75e+04 1s
28 1.52415021e+10 1.31530402e+10 5.95e+04 2.33e-10 1.65e+04 1s
INFO:gurobipy: 28 1.52415021e+10 1.31530402e+10 5.95e+04 2.33e-10 1.65e+04 1s
29 1.52233679e+10 1.32502817e+10 5.34e+04 3.78e-10 1.55e+04 1s
INFO:gurobipy: 29 1.52233679e+10 1.32502817e+10 5.34e+04 3.78e-10 1.55e+04 1s
30 1.52204471e+10 1.33100232e+10 5.16e+04 7.28e-10 1.50e+04 1s
INFO:gurobipy: 30 1.52204471e+10 1.33100232e+10 5.16e+04 7.28e-10 1.50e+04 1s
31 1.52291626e+10 1.35112333e+10 4.98e+04 4.95e-10 1.37e+04 1s
INFO:gurobipy: 31 1.52291626e+10 1.35112333e+10 4.98e+04 4.95e-10 1.37e+04 1s
32 1.52201612e+10 1.36281181e+10 4.53e+04 1.16e-10 1.27e+04 1s
INFO:gurobipy: 32 1.52201612e+10 1.36281181e+10 4.53e+04 1.16e-10 1.27e+04 1s
33 1.52297896e+10 1.38587976e+10 4.27e+04 6.91e-11 1.11e+04 1s
INFO:gurobipy: 33 1.52297896e+10 1.38587976e+10 4.27e+04 6.91e-11 1.11e+04 1s
34 1.52388447e+10 1.39460703e+10 3.13e+04 5.82e-11 1.01e+04 1s
INFO:gurobipy: 34 1.52388447e+10 1.39460703e+10 3.13e+04 5.82e-11 1.01e+04 1s
35 1.52412184e+10 1.40327543e+10 2.79e+04 4.73e-11 9.38e+03 1s
INFO:gurobipy: 35 1.52412184e+10 1.40327543e+10 2.79e+04 4.73e-11 9.38e+03 1s
36 1.52468445e+10 1.41618835e+10 2.34e+04 2.33e-10 8.35e+03 1s
INFO:gurobipy: 36 1.52468445e+10 1.41618835e+10 2.34e+04 2.33e-10 8.35e+03 1s
37 1.52480268e+10 1.42112442e+10 2.14e+04 6.40e-10 7.95e+03 1s
INFO:gurobipy: 37 1.52480268e+10 1.42112442e+10 2.14e+04 6.40e-10 7.95e+03 1s
38 1.52489216e+10 1.42637425e+10 2.06e+04 1.75e-10 7.57e+03 1s
INFO:gurobipy: 38 1.52489216e+10 1.42637425e+10 2.06e+04 1.75e-10 7.57e+03 1s
39 1.52513363e+10 1.43007284e+10 1.94e+04 1.89e-10 7.29e+03 1s
INFO:gurobipy: 39 1.52513363e+10 1.43007284e+10 1.94e+04 1.89e-10 7.29e+03 1s
40 1.52507721e+10 1.44313763e+10 1.82e+04 5.82e-10 6.36e+03 1s
INFO:gurobipy: 40 1.52507721e+10 1.44313763e+10 1.82e+04 5.82e-10 6.36e+03 1s
41 1.52508098e+10 1.44769971e+10 1.66e+04 3.49e-10 5.99e+03 1s
INFO:gurobipy: 41 1.52508098e+10 1.44769971e+10 1.66e+04 3.49e-10 5.99e+03 1s
42 1.52592532e+10 1.45676343e+10 1.33e+04 6.11e-10 5.28e+03 1s
INFO:gurobipy: 42 1.52592532e+10 1.45676343e+10 1.33e+04 6.11e-10 5.28e+03 1s
43 1.52642877e+10 1.45848808e+10 1.11e+04 1.02e-09 5.09e+03 1s
INFO:gurobipy: 43 1.52642877e+10 1.45848808e+10 1.11e+04 1.02e-09 5.09e+03 1s
44 1.52704837e+10 1.46649035e+10 9.39e+03 3.49e-10 4.52e+03 1s
INFO:gurobipy: 44 1.52704837e+10 1.46649035e+10 9.39e+03 3.49e-10 4.52e+03 1s
45 1.52732242e+10 1.48301619e+10 8.44e+03 3.24e-10 3.38e+03 1s
INFO:gurobipy: 45 1.52732242e+10 1.48301619e+10 8.44e+03 3.24e-10 3.38e+03 1s
46 1.52786787e+10 1.48452751e+10 5.72e+03 1.15e-09 3.19e+03 1s
INFO:gurobipy: 46 1.52786787e+10 1.48452751e+10 5.72e+03 1.15e-09 3.19e+03 1s
47 1.52806996e+10 1.49366115e+10 5.01e+03 1.78e-09 2.55e+03 1s
INFO:gurobipy: 47 1.52806996e+10 1.49366115e+10 5.01e+03 1.78e-09 2.55e+03 1s
48 1.52850617e+10 1.50566330e+10 3.05e+03 2.68e-09 1.69e+03 1s
INFO:gurobipy: 48 1.52850617e+10 1.50566330e+10 3.05e+03 2.68e-09 1.69e+03 1s
49 1.52865486e+10 1.50871929e+10 2.11e+03 2.72e-09 1.44e+03 1s
INFO:gurobipy: 49 1.52865486e+10 1.50871929e+10 2.11e+03 2.72e-09 1.44e+03 1s
50 1.52873582e+10 1.52260266e+10 1.09e+03 2.22e-09 4.67e+02 1s
INFO:gurobipy: 50 1.52873582e+10 1.52260266e+10 1.09e+03 2.22e-09 4.67e+02 1s
51 1.52864332e+10 1.52617329e+10 7.17e+02 9.39e-10 2.02e+02 1s
INFO:gurobipy: 51 1.52864332e+10 1.52617329e+10 7.17e+02 9.39e-10 2.02e+02 1s
52 1.52845396e+10 1.52744618e+10 1.23e+02 1.28e-09 7.39e+01 1s
INFO:gurobipy: 52 1.52845396e+10 1.52744618e+10 1.23e+02 1.28e-09 7.39e+01 1s
53 1.52841484e+10 1.52809600e+10 5.28e+01 6.69e-10 2.41e+01 1s
INFO:gurobipy: 53 1.52841484e+10 1.52809600e+10 5.28e+01 6.69e-10 2.41e+01 1s
54 1.52838757e+10 1.52832271e+10 1.13e+01 7.28e-10 4.93e+00 1s
INFO:gurobipy: 54 1.52838757e+10 1.52832271e+10 1.13e+01 7.28e-10 4.93e+00 1s
55 1.52838079e+10 1.52837363e+10 1.99e+00 7.57e-10 5.82e-01 1s
INFO:gurobipy: 55 1.52838079e+10 1.52837363e+10 1.99e+00 7.57e-10 5.82e-01 1s
56 1.52837939e+10 1.52837914e+10 1.53e-01 4.95e-10 2.48e-02 1s
INFO:gurobipy: 56 1.52837939e+10 1.52837914e+10 1.53e-01 4.95e-10 2.48e-02 1s
57 1.52837926e+10 1.52837926e+10 2.94e-05 6.82e-09 1.99e-05 1s
INFO:gurobipy: 57 1.52837926e+10 1.52837926e+10 2.94e-05 6.82e-09 1.99e-05 1s
58 1.52837926e+10 1.52837926e+10 2.59e-08 2.15e-08 3.86e-08 1s
INFO:gurobipy: 58 1.52837926e+10 1.52837926e+10 2.59e-08 2.15e-08 3.86e-08 1s
59 1.52837926e+10 1.52837926e+10 5.12e-08 1.69e-08 6.22e-11 1s
INFO:gurobipy: 59 1.52837926e+10 1.52837926e+10 5.12e-08 1.69e-08 6.22e-11 1s
INFO:gurobipy:
Barrier solved model in 59 iterations and 1.13 seconds (1.75 work units)
INFO:gurobipy:Barrier solved model in 59 iterations and 1.13 seconds (1.75 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 1.6376782e-09 1s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.6376782e-09 1s
INFO:gurobipy:
Crossover time: 0.08 seconds (0.17 work units)
INFO:gurobipy:Crossover time: 0.08 seconds (0.17 work units)
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 1.25 seconds (1.96 work units)
INFO:gurobipy:Solved in 8772 iterations and 1.25 seconds (1.96 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
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.
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 70.80it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 434.22it/s]
INFO:linopy.io: Writing time: 0.13s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-86lg08db.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-86lg08db.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 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0x046e0b75
INFO:gurobipy:Model fingerprint: 0x046e0b75
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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 9.60e-10 5.43e+05 0s
INFO:gurobipy: 3 5.91579593e+10 -1.50671637e+10 2.30e+06 9.60e-10 5.43e+05 0s
4 4.35885622e+10 -1.19762945e+10 1.60e+06 9.90e-10 4.02e+05 0s
INFO:gurobipy: 4 4.35885622e+10 -1.19762945e+10 1.60e+06 9.90e-10 4.02e+05 0s
5 3.73338795e+10 -8.53132089e+09 1.32e+06 2.62e-10 3.30e+05 0s
INFO:gurobipy: 5 3.73338795e+10 -8.53132089e+09 1.32e+06 2.62e-10 3.30e+05 0s
6 3.28662366e+10 -5.21363458e+09 1.12e+06 4.66e-10 2.72e+05 0s
INFO:gurobipy: 6 3.28662366e+10 -5.21363458e+09 1.12e+06 4.66e-10 2.72e+05 0s
7 2.69587102e+10 -1.50128930e+09 8.66e+05 9.90e-10 2.03e+05 0s
INFO:gurobipy: 7 2.69587102e+10 -1.50128930e+09 8.66e+05 9.90e-10 2.03e+05 0s
8 2.16391077e+10 1.13540429e+09 6.18e+05 3.35e-10 1.46e+05 0s
INFO:gurobipy: 8 2.16391077e+10 1.13540429e+09 6.18e+05 3.35e-10 1.46e+05 0s
9 1.87291512e+10 1.87186884e+09 4.79e+05 3.64e-10 1.19e+05 0s
INFO:gurobipy: 9 1.87291512e+10 1.87186884e+09 4.79e+05 3.64e-10 1.19e+05 0s
10 1.78193616e+10 2.62402717e+09 4.29e+05 2.91e-10 1.08e+05 0s
INFO:gurobipy: 10 1.78193616e+10 2.62402717e+09 4.29e+05 2.91e-10 1.08e+05 0s
11 1.66746820e+10 4.26528899e+09 3.73e+05 3.78e-10 8.85e+04 0s
INFO:gurobipy: 11 1.66746820e+10 4.26528899e+09 3.73e+05 3.78e-10 8.85e+04 0s
12 1.57459814e+10 4.83791031e+09 3.23e+05 2.91e-10 7.78e+04 0s
INFO:gurobipy: 12 1.57459814e+10 4.83791031e+09 3.23e+05 2.91e-10 7.78e+04 0s
13 1.53301001e+10 5.43521735e+09 2.99e+05 9.02e-10 7.08e+04 0s
INFO:gurobipy: 13 1.53301001e+10 5.43521735e+09 2.99e+05 9.02e-10 7.08e+04 0s
14 1.49019594e+10 5.85792692e+09 2.69e+05 9.31e-10 6.48e+04 0s
INFO:gurobipy: 14 1.49019594e+10 5.85792692e+09 2.69e+05 9.31e-10 6.48e+04 0s
15 1.45578580e+10 6.91825158e+09 2.44e+05 4.66e-10 5.53e+04 0s
INFO:gurobipy: 15 1.45578580e+10 6.91825158e+09 2.44e+05 4.66e-10 5.53e+04 0s
16 1.40963985e+10 7.11403180e+09 2.14e+05 2.33e-10 5.04e+04 0s
INFO:gurobipy: 16 1.40963985e+10 7.11403180e+09 2.14e+05 2.33e-10 5.04e+04 0s
17 1.39300945e+10 7.42667365e+09 2.03e+05 5.53e-10 4.71e+04 0s
INFO:gurobipy: 17 1.39300945e+10 7.42667365e+09 2.03e+05 5.53e-10 4.71e+04 0s
18 1.37795329e+10 7.58492844e+09 1.91e+05 3.49e-10 4.49e+04 0s
INFO:gurobipy: 18 1.37795329e+10 7.58492844e+09 1.91e+05 3.49e-10 4.49e+04 0s
19 1.36650379e+10 7.82615603e+09 1.80e+05 4.37e-10 4.23e+04 1s
INFO:gurobipy: 19 1.36650379e+10 7.82615603e+09 1.80e+05 4.37e-10 4.23e+04 1s
20 1.35788001e+10 7.99253889e+09 1.73e+05 2.47e-10 4.05e+04 1s
INFO:gurobipy: 20 1.35788001e+10 7.99253889e+09 1.73e+05 2.47e-10 4.05e+04 1s
21 1.35155931e+10 8.12940465e+09 1.67e+05 4.66e-10 3.91e+04 1s
INFO:gurobipy: 21 1.35155931e+10 8.12940465e+09 1.67e+05 4.66e-10 3.91e+04 1s
22 1.33878452e+10 8.38281970e+09 1.56e+05 1.02e-10 3.65e+04 1s
INFO:gurobipy: 22 1.33878452e+10 8.38281970e+09 1.56e+05 1.02e-10 3.65e+04 1s
23 1.33751823e+10 8.53131938e+09 1.55e+05 6.11e-10 3.54e+04 1s
INFO:gurobipy: 23 1.33751823e+10 8.53131938e+09 1.55e+05 6.11e-10 3.54e+04 1s
24 1.33016947e+10 8.61998054e+09 1.47e+05 4.07e-10 3.42e+04 1s
INFO:gurobipy: 24 1.33016947e+10 8.61998054e+09 1.47e+05 4.07e-10 3.42e+04 1s
25 1.31282318e+10 8.79589138e+09 1.31e+05 5.24e-10 3.16e+04 1s
INFO:gurobipy: 25 1.31282318e+10 8.79589138e+09 1.31e+05 5.24e-10 3.16e+04 1s
26 1.30879159e+10 9.03792620e+09 1.23e+05 5.24e-10 2.96e+04 1s
INFO:gurobipy: 26 1.30879159e+10 9.03792620e+09 1.23e+05 5.24e-10 2.96e+04 1s
27 1.30012950e+10 9.31079862e+09 1.12e+05 2.91e-10 2.70e+04 1s
INFO:gurobipy: 27 1.30012950e+10 9.31079862e+09 1.12e+05 2.91e-10 2.70e+04 1s
28 1.29725577e+10 9.42520317e+09 1.04e+05 4.95e-10 2.59e+04 1s
INFO:gurobipy: 28 1.29725577e+10 9.42520317e+09 1.04e+05 4.95e-10 2.59e+04 1s
29 1.29733223e+10 9.60307788e+09 9.62e+04 1.16e-10 2.46e+04 1s
INFO:gurobipy: 29 1.29733223e+10 9.60307788e+09 9.62e+04 1.16e-10 2.46e+04 1s
30 1.29393598e+10 9.91099428e+09 8.82e+04 6.69e-10 2.21e+04 1s
INFO:gurobipy: 30 1.29393598e+10 9.91099428e+09 8.82e+04 6.69e-10 2.21e+04 1s
31 1.29109338e+10 1.00569710e+10 8.11e+04 4.66e-10 2.08e+04 1s
INFO:gurobipy: 31 1.29109338e+10 1.00569710e+10 8.11e+04 4.66e-10 2.08e+04 1s
32 1.28771193e+10 1.02594868e+10 7.23e+04 2.62e-10 1.91e+04 1s
INFO:gurobipy: 32 1.28771193e+10 1.02594868e+10 7.23e+04 2.62e-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 7.86e-10 1.74e+04 1s
INFO:gurobipy: 34 1.28668288e+10 1.04709808e+10 6.32e+04 7.86e-10 1.74e+04 1s
35 1.28780494e+10 1.05906499e+10 6.02e+04 4.95e-10 1.66e+04 1s
INFO:gurobipy: 35 1.28780494e+10 1.05906499e+10 6.02e+04 4.95e-10 1.66e+04 1s
36 1.28752101e+10 1.07154699e+10 5.33e+04 7.86e-10 1.56e+04 1s
INFO:gurobipy: 36 1.28752101e+10 1.07154699e+10 5.33e+04 7.86e-10 1.56e+04 1s
37 1.28395305e+10 1.09193464e+10 4.43e+04 5.24e-10 1.39e+04 1s
INFO:gurobipy: 37 1.28395305e+10 1.09193464e+10 4.43e+04 5.24e-10 1.39e+04 1s
38 1.28326668e+10 1.11098415e+10 4.20e+04 1.46e-10 1.25e+04 1s
INFO:gurobipy: 38 1.28326668e+10 1.11098415e+10 4.20e+04 1.46e-10 1.25e+04 1s
39 1.28163744e+10 1.11587939e+10 3.86e+04 7.28e-11 1.20e+04 1s
INFO:gurobipy: 39 1.28163744e+10 1.11587939e+10 3.86e+04 7.28e-11 1.20e+04 1s
40 1.28139604e+10 1.13153349e+10 3.28e+04 2.33e-10 1.08e+04 1s
INFO:gurobipy: 40 1.28139604e+10 1.13153349e+10 3.28e+04 2.33e-10 1.08e+04 1s
41 1.28048745e+10 1.14691978e+10 3.02e+04 8.15e-10 9.66e+03 1s
INFO:gurobipy: 41 1.28048745e+10 1.14691978e+10 3.02e+04 8.15e-10 9.66e+03 1s
42 1.27884773e+10 1.15981418e+10 2.73e+04 4.66e-10 8.62e+03 1s
INFO:gurobipy: 42 1.27884773e+10 1.15981418e+10 2.73e+04 4.66e-10 8.62e+03 1s
43 1.27948884e+10 1.16771735e+10 2.59e+04 4.37e-11 8.10e+03 1s
INFO:gurobipy: 43 1.27948884e+10 1.16771735e+10 2.59e+04 4.37e-11 8.10e+03 1s
44 1.27842182e+10 1.17672943e+10 2.19e+04 5.82e-11 7.34e+03 1s
INFO:gurobipy: 44 1.27842182e+10 1.17672943e+10 2.19e+04 5.82e-11 7.34e+03 1s
45 1.27787646e+10 1.18006088e+10 1.95e+04 3.49e-10 7.02e+03 1s
INFO:gurobipy: 45 1.27787646e+10 1.18006088e+10 1.95e+04 3.49e-10 7.02e+03 1s
46 1.27749705e+10 1.19075930e+10 1.78e+04 2.91e-10 6.24e+03 1s
INFO:gurobipy: 46 1.27749705e+10 1.19075930e+10 1.78e+04 2.91e-10 6.24e+03 1s
47 1.27741264e+10 1.19380085e+10 1.40e+04 3.78e-10 5.94e+03 1s
INFO:gurobipy: 47 1.27741264e+10 1.19380085e+10 1.40e+04 3.78e-10 5.94e+03 1s
48 1.27739584e+10 1.20193153e+10 1.35e+04 2.36e-10 5.38e+03 1s
INFO:gurobipy: 48 1.27739584e+10 1.20193153e+10 1.35e+04 2.36e-10 5.38e+03 1s
49 1.27758206e+10 1.20765943e+10 1.17e+04 4.33e-10 4.97e+03 1s
INFO:gurobipy: 49 1.27758206e+10 1.20765943e+10 1.17e+04 4.33e-10 4.97e+03 1s
50 1.27767054e+10 1.21766778e+10 8.77e+03 4.95e-10 4.24e+03 1s
INFO:gurobipy: 50 1.27767054e+10 1.21766778e+10 8.77e+03 4.95e-10 4.24e+03 1s
51 1.27776157e+10 1.22165644e+10 8.20e+03 9.50e-10 3.96e+03 1s
INFO:gurobipy: 51 1.27776157e+10 1.22165644e+10 8.20e+03 9.50e-10 3.96e+03 1s
52 1.27771340e+10 1.23010475e+10 7.07e+03 1.10e-09 3.37e+03 1s
INFO:gurobipy: 52 1.27771340e+10 1.23010475e+10 7.07e+03 1.10e-09 3.37e+03 1s
53 1.27676079e+10 1.23126818e+10 3.17e+03 3.77e-09 3.13e+03 1s
INFO:gurobipy: 53 1.27676079e+10 1.23126818e+10 3.17e+03 3.77e-09 3.13e+03 1s
54 1.27668489e+10 1.24365769e+10 2.82e+03 2.30e-08 2.29e+03 1s
INFO:gurobipy: 54 1.27668489e+10 1.24365769e+10 2.82e+03 2.30e-08 2.29e+03 1s
55 1.27638306e+10 1.24805972e+10 7.81e+02 2.17e-08 1.92e+03 1s
INFO:gurobipy: 55 1.27638306e+10 1.24805972e+10 7.81e+02 2.17e-08 1.92e+03 1s
56 1.27630431e+10 1.25102569e+10 7.00e+02 3.79e-08 1.72e+03 1s
INFO:gurobipy: 56 1.27630431e+10 1.25102569e+10 7.00e+02 3.79e-08 1.72e+03 1s
57 1.27598853e+10 1.25259154e+10 4.64e+02 3.97e-08 1.58e+03 1s
INFO:gurobipy: 57 1.27598853e+10 1.25259154e+10 4.64e+02 3.97e-08 1.58e+03 1s
58 1.27580907e+10 1.25601373e+10 2.40e+02 3.43e-08 1.34e+03 1s
INFO:gurobipy: 58 1.27580907e+10 1.25601373e+10 2.40e+02 3.43e-08 1.34e+03 1s
59 1.27559913e+10 1.25684112e+10 1.44e+02 3.55e-08 1.26e+03 1s
INFO:gurobipy: 59 1.27559913e+10 1.25684112e+10 1.44e+02 3.55e-08 1.26e+03 1s
60 1.27552043e+10 1.25951791e+10 9.95e+01 3.10e-08 1.08e+03 1s
INFO:gurobipy: 60 1.27552043e+10 1.25951791e+10 9.95e+01 3.10e-08 1.08e+03 1s
61 1.27549711e+10 1.25980639e+10 9.33e+01 3.04e-08 1.06e+03 1s
INFO:gurobipy: 61 1.27549711e+10 1.25980639e+10 9.33e+01 3.04e-08 1.06e+03 1s
62 1.27546960e+10 1.26002296e+10 8.71e+01 3.11e-08 1.04e+03 1s
INFO:gurobipy: 62 1.27546960e+10 1.26002296e+10 8.71e+01 3.11e-08 1.04e+03 1s
63 1.27545353e+10 1.26141125e+10 8.39e+01 3.09e-08 9.46e+02 1s
INFO:gurobipy: 63 1.27545353e+10 1.26141125e+10 8.39e+01 3.09e-08 9.46e+02 1s
64 1.27541231e+10 1.26408040e+10 6.93e+01 3.31e-08 7.64e+02 1s
INFO:gurobipy: 64 1.27541231e+10 1.26408040e+10 6.93e+01 3.31e-08 7.64e+02 1s
65 1.27536728e+10 1.26493455e+10 6.31e+01 2.88e-08 7.03e+02 1s
INFO:gurobipy: 65 1.27536728e+10 1.26493455e+10 6.31e+01 2.88e-08 7.03e+02 1s
66 1.27532454e+10 1.26665210e+10 5.47e+01 3.22e-08 5.85e+02 1s
INFO:gurobipy: 66 1.27532454e+10 1.26665210e+10 5.47e+01 3.22e-08 5.85e+02 1s
67 1.27532182e+10 1.26739257e+10 5.07e+01 2.96e-08 5.34e+02 1s
INFO:gurobipy: 67 1.27532182e+10 1.26739257e+10 5.07e+01 2.96e-08 5.34e+02 1s
68 1.27526991e+10 1.26747676e+10 4.43e+01 2.92e-08 5.25e+02 1s
INFO:gurobipy: 68 1.27526991e+10 1.26747676e+10 4.43e+01 2.92e-08 5.25e+02 1s
69 1.27526705e+10 1.26801463e+10 4.29e+01 2.70e-08 4.89e+02 1s
INFO:gurobipy: 69 1.27526705e+10 1.26801463e+10 4.29e+01 2.70e-08 4.89e+02 1s
70 1.27521443e+10 1.26889429e+10 3.14e+01 2.41e-08 4.26e+02 1s
INFO:gurobipy: 70 1.27521443e+10 1.26889429e+10 3.14e+01 2.41e-08 4.26e+02 1s
71 1.27515666e+10 1.26982335e+10 1.99e+01 2.08e-08 3.59e+02 1s
INFO:gurobipy: 71 1.27515666e+10 1.26982335e+10 1.99e+01 2.08e-08 3.59e+02 1s
72 1.27513693e+10 1.27202237e+10 1.67e+01 1.21e-08 2.10e+02 1s
INFO:gurobipy: 72 1.27513693e+10 1.27202237e+10 1.67e+01 1.21e-08 2.10e+02 1s
73 1.27503688e+10 1.27433617e+10 1.33e+00 2.68e-09 4.72e+01 1s
INFO:gurobipy: 73 1.27503688e+10 1.27433617e+10 1.33e+00 2.68e-09 4.72e+01 1s
74 1.27502103e+10 1.27442628e+10 6.67e-01 2.19e-09 4.00e+01 1s
INFO:gurobipy: 74 1.27502103e+10 1.27442628e+10 6.67e-01 2.19e-09 4.00e+01 1s
75 1.27500586e+10 1.27489507e+10 1.03e-01 8.66e-10 7.45e+00 1s
INFO:gurobipy: 75 1.27500586e+10 1.27489507e+10 1.03e-01 8.66e-10 7.45e+00 1s
76 1.27500104e+10 1.27498702e+10 1.50e-02 8.44e-10 9.43e-01 1s
INFO:gurobipy: 76 1.27500104e+10 1.27498702e+10 1.50e-02 8.44e-10 9.43e-01 1s
77 1.27500008e+10 1.27499872e+10 2.95e-04 1.11e-09 9.17e-02 1s
INFO:gurobipy: 77 1.27500008e+10 1.27499872e+10 2.95e-04 1.11e-09 9.17e-02 1s
78 1.27500004e+10 1.27500004e+10 8.01e-07 1.22e-09 2.62e-05 1s
INFO:gurobipy: 78 1.27500004e+10 1.27500004e+10 8.01e-07 1.22e-09 2.62e-05 1s
79 1.27500004e+10 1.27500004e+10 3.06e-07 2.01e-09 1.87e-10 1s
INFO:gurobipy: 79 1.27500004e+10 1.27500004e+10 3.06e-07 2.01e-09 1.87e-10 1s
INFO:gurobipy:
Barrier solved model in 79 iterations and 1.44 seconds (2.23 work units)
INFO:gurobipy:Barrier solved model in 79 iterations and 1.44 seconds (2.23 work units)
Optimal objective 1.27500004e+10
INFO:gurobipy:Optimal objective 1.27500004e+10
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
37 DPushes remaining with DInf 0.0000000e+00 1s
INFO:gurobipy: 37 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 2s
INFO:gurobipy: 0 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy:
Push phase complete: Pinf 0.0000000e+00, Dinf 2.3406661e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 2.3406661e-09 2s
INFO:gurobipy:
Crossover time: 0.12 seconds (0.27 work units)
INFO:gurobipy:Crossover time: 0.12 seconds (0.27 work units)
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
8767 1.2750000e+10 0.000000e+00 0.000000e+00 2s
INFO:gurobipy: 8767 1.2750000e+10 0.000000e+00 0.000000e+00 2s
INFO:gurobipy:
Solved in 8767 iterations and 1.60 seconds (2.54 work units)
INFO:gurobipy:Solved in 8767 iterations and 1.60 seconds (2.54 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
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.
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 66.87it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 410.10it/s]
INFO:linopy.io: Writing time: 0.14s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-rrwf2mkb.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-rrwf2mkb.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 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0x018ce841
INFO:gurobipy:Model fingerprint: 0x018ce841
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.17s
INFO:gurobipy:Presolve time: 0.17s
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 6.11e-10 6.84e+05 0s
INFO:gurobipy: 3 5.92104792e+10 -2.89317892e+10 4.86e+06 6.11e-10 6.84e+05 0s
4 4.41014312e+10 -1.64330203e+10 3.46e+06 2.76e-10 4.60e+05 0s
INFO:gurobipy: 4 4.41014312e+10 -1.64330203e+10 3.46e+06 2.76e-10 4.60e+05 0s
5 3.42571357e+10 -1.26675316e+10 2.54e+06 5.53e-10 3.51e+05 0s
INFO:gurobipy: 5 3.42571357e+10 -1.26675316e+10 2.54e+06 5.53e-10 3.51e+05 0s
6 2.85278566e+10 -9.37358328e+09 1.99e+06 1.16e-10 2.81e+05 0s
INFO:gurobipy: 6 2.85278566e+10 -9.37358328e+09 1.99e+06 1.16e-10 2.81e+05 0s
7 2.30804507e+10 -3.26236792e+09 1.52e+06 1.20e-10 1.93e+05 0s
INFO:gurobipy: 7 2.30804507e+10 -3.26236792e+09 1.52e+06 1.20e-10 1.93e+05 0s
8 1.83868456e+10 -2.17774306e+08 1.07e+06 3.09e-11 1.36e+05 0s
INFO:gurobipy: 8 1.83868456e+10 -2.17774306e+08 1.07e+06 3.09e-11 1.36e+05 0s
9 1.55917572e+10 2.64601414e+09 8.04e+05 3.20e-10 9.45e+04 0s
INFO:gurobipy: 9 1.55917572e+10 2.64601414e+09 8.04e+05 3.20e-10 9.45e+04 0s
10 1.43825154e+10 3.34151270e+09 6.79e+05 2.62e-10 8.05e+04 0s
INFO:gurobipy: 10 1.43825154e+10 3.34151270e+09 6.79e+05 2.62e-10 8.05e+04 0s
11 1.36626539e+10 3.81080814e+09 5.82e+05 1.75e-10 7.16e+04 0s
INFO:gurobipy: 11 1.36626539e+10 3.81080814e+09 5.82e+05 1.75e-10 7.16e+04 0s
12 1.32676379e+10 4.81591115e+09 5.41e+05 4.95e-10 6.18e+04 0s
INFO:gurobipy: 12 1.32676379e+10 4.81591115e+09 5.41e+05 4.95e-10 6.18e+04 0s
13 1.27308208e+10 5.16330208e+09 4.81e+05 2.33e-10 5.53e+04 0s
INFO:gurobipy: 13 1.27308208e+10 5.16330208e+09 4.81e+05 2.33e-10 5.53e+04 0s
14 1.23773675e+10 5.45268075e+09 4.29e+05 4.66e-10 5.06e+04 1s
INFO:gurobipy: 14 1.23773675e+10 5.45268075e+09 4.29e+05 4.66e-10 5.06e+04 1s
15 1.19706944e+10 6.05637507e+09 3.81e+05 4.95e-10 4.34e+04 1s
INFO:gurobipy: 15 1.19706944e+10 6.05637507e+09 3.81e+05 4.95e-10 4.34e+04 1s
16 1.17802952e+10 6.26626808e+09 3.56e+05 4.00e-11 4.04e+04 1s
INFO:gurobipy: 16 1.17802952e+10 6.26626808e+09 3.56e+05 4.00e-11 4.04e+04 1s
17 1.15219337e+10 6.50096115e+09 3.19e+05 5.24e-10 3.68e+04 1s
INFO:gurobipy: 17 1.15219337e+10 6.50096115e+09 3.19e+05 5.24e-10 3.68e+04 1s
18 1.14138671e+10 6.67901926e+09 2.95e+05 4.22e-10 3.47e+04 1s
INFO:gurobipy: 18 1.14138671e+10 6.67901926e+09 2.95e+05 4.22e-10 3.47e+04 1s
19 1.13081349e+10 6.93841806e+09 2.78e+05 2.47e-10 3.21e+04 1s
INFO:gurobipy: 19 1.13081349e+10 6.93841806e+09 2.78e+05 2.47e-10 3.21e+04 1s
20 1.11683145e+10 7.22367414e+09 2.52e+05 2.91e-10 2.90e+04 1s
INFO:gurobipy: 20 1.11683145e+10 7.22367414e+09 2.52e+05 2.91e-10 2.90e+04 1s
21 1.10456207e+10 7.44410096e+09 2.26e+05 2.91e-10 2.64e+04 1s
INFO:gurobipy: 21 1.10456207e+10 7.44410096e+09 2.26e+05 2.91e-10 2.64e+04 1s
22 1.10153051e+10 7.57630915e+09 2.15e+05 1.89e-10 2.52e+04 1s
INFO:gurobipy: 22 1.10153051e+10 7.57630915e+09 2.15e+05 1.89e-10 2.52e+04 1s
23 1.09119121e+10 7.82389419e+09 1.91e+05 1.11e-09 2.27e+04 1s
INFO:gurobipy: 23 1.09119121e+10 7.82389419e+09 1.91e+05 1.11e-09 2.27e+04 1s
24 1.08440067e+10 7.99115321e+09 1.74e+05 3.49e-10 2.09e+04 1s
INFO:gurobipy: 24 1.08440067e+10 7.99115321e+09 1.74e+05 3.49e-10 2.09e+04 1s
25 1.08112314e+10 8.12926248e+09 1.58e+05 7.57e-10 1.96e+04 1s
INFO:gurobipy: 25 1.08112314e+10 8.12926248e+09 1.58e+05 7.57e-10 1.96e+04 1s
26 1.07898020e+10 8.27208295e+09 1.43e+05 5.24e-10 1.84e+04 1s
INFO:gurobipy: 26 1.07898020e+10 8.27208295e+09 1.43e+05 5.24e-10 1.84e+04 1s
27 1.07074459e+10 8.73634402e+09 1.12e+05 1.05e-09 1.44e+04 1s
INFO:gurobipy: 27 1.07074459e+10 8.73634402e+09 1.12e+05 1.05e-09 1.44e+04 1s
28 1.06612913e+10 8.85557958e+09 9.96e+04 1.02e-10 1.32e+04 1s
INFO:gurobipy: 28 1.06612913e+10 8.85557958e+09 9.96e+04 1.02e-10 1.32e+04 1s
29 1.06249292e+10 8.94215573e+09 9.09e+04 1.46e-10 1.23e+04 1s
INFO:gurobipy: 29 1.06249292e+10 8.94215573e+09 9.09e+04 1.46e-10 1.23e+04 1s
30 1.05975879e+10 9.10759787e+09 8.36e+04 8.73e-10 1.09e+04 1s
INFO:gurobipy: 30 1.05975879e+10 9.10759787e+09 8.36e+04 8.73e-10 1.09e+04 1s
31 1.05683069e+10 9.19165447e+09 7.49e+04 6.98e-10 1.00e+04 1s
INFO:gurobipy: 31 1.05683069e+10 9.19165447e+09 7.49e+04 6.98e-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 6.11e-10 9.10e+03 1s
INFO:gurobipy: 33 1.05415617e+10 9.28427283e+09 6.17e+04 6.11e-10 9.10e+03 1s
34 1.05203940e+10 9.42002127e+09 5.38e+04 5.75e-10 7.97e+03 1s
INFO:gurobipy: 34 1.05203940e+10 9.42002127e+09 5.38e+04 5.75e-10 7.97e+03 1s
35 1.05041585e+10 9.52732807e+09 4.82e+04 4.26e-10 7.08e+03 1s
INFO:gurobipy: 35 1.05041585e+10 9.52732807e+09 4.82e+04 4.26e-10 7.08e+03 1s
36 1.04927204e+10 9.56557349e+09 4.37e+04 1.22e-09 6.70e+03 1s
INFO:gurobipy: 36 1.04927204e+10 9.56557349e+09 4.37e+04 1.22e-09 6.70e+03 1s
37 1.04837237e+10 9.61319174e+09 3.87e+04 2.47e-10 6.27e+03 1s
INFO:gurobipy: 37 1.04837237e+10 9.61319174e+09 3.87e+04 2.47e-10 6.27e+03 1s
38 1.04738540e+10 9.71846355e+09 3.26e+04 1.75e-09 5.43e+03 1s
INFO:gurobipy: 38 1.04738540e+10 9.71846355e+09 3.26e+04 1.75e-09 5.43e+03 1s
39 1.04657783e+10 9.75752289e+09 2.97e+04 1.53e-09 5.08e+03 1s
INFO:gurobipy: 39 1.04657783e+10 9.75752289e+09 2.97e+04 1.53e-09 5.08e+03 1s
40 1.04596821e+10 9.78916272e+09 2.78e+04 8.84e-10 4.81e+03 1s
INFO:gurobipy: 40 1.04596821e+10 9.78916272e+09 2.78e+04 8.84e-10 4.81e+03 1s
41 1.04616258e+10 9.81666469e+09 2.44e+04 1.11e-09 4.60e+03 1s
INFO:gurobipy: 41 1.04616258e+10 9.81666469e+09 2.44e+04 1.11e-09 4.60e+03 1s
42 1.04526980e+10 9.89728303e+09 2.06e+04 1.23e-09 3.96e+03 1s
INFO:gurobipy: 42 1.04526980e+10 9.89728303e+09 2.06e+04 1.23e-09 3.96e+03 1s
43 1.04485024e+10 9.90550635e+09 1.90e+04 9.28e-10 3.86e+03 1s
INFO:gurobipy: 43 1.04485024e+10 9.90550635e+09 1.90e+04 9.28e-10 3.86e+03 1s
44 1.04463647e+10 9.98420995e+09 1.63e+04 7.68e-10 3.28e+03 1s
INFO:gurobipy: 44 1.04463647e+10 9.98420995e+09 1.63e+04 7.68e-10 3.28e+03 1s
45 1.04364431e+10 1.00111314e+10 1.32e+04 1.15e-09 3.00e+03 1s
INFO:gurobipy: 45 1.04364431e+10 1.00111314e+10 1.32e+04 1.15e-09 3.00e+03 1s
46 1.04326379e+10 1.00238692e+10 1.19e+04 1.34e-09 2.88e+03 1s
INFO:gurobipy: 46 1.04326379e+10 1.00238692e+10 1.19e+04 1.34e-09 2.88e+03 1s
47 1.04312042e+10 1.00669791e+10 9.68e+03 3.03e-09 2.55e+03 1s
INFO:gurobipy: 47 1.04312042e+10 1.00669791e+10 9.68e+03 3.03e-09 2.55e+03 1s
48 1.04262315e+10 1.00969640e+10 8.28e+03 5.70e-08 2.30e+03 1s
INFO:gurobipy: 48 1.04262315e+10 1.00969640e+10 8.28e+03 5.70e-08 2.30e+03 1s
49 1.04205881e+10 1.01583767e+10 6.53e+03 1.07e-07 1.83e+03 1s
INFO:gurobipy: 49 1.04205881e+10 1.01583767e+10 6.53e+03 1.07e-07 1.83e+03 1s
50 1.04178333e+10 1.01972262e+10 5.01e+03 1.10e-07 1.54e+03 1s
INFO:gurobipy: 50 1.04178333e+10 1.01972262e+10 5.01e+03 1.10e-07 1.54e+03 1s
51 1.04138718e+10 1.02062456e+10 4.23e+03 1.21e-07 1.44e+03 1s
INFO:gurobipy: 51 1.04138718e+10 1.02062456e+10 4.23e+03 1.21e-07 1.44e+03 1s
52 1.04132624e+10 1.02449418e+10 4.05e+03 1.27e-07 1.18e+03 1s
INFO:gurobipy: 52 1.04132624e+10 1.02449418e+10 4.05e+03 1.27e-07 1.18e+03 1s
53 1.04091774e+10 1.02576949e+10 2.66e+03 1.31e-07 1.05e+03 1s
INFO:gurobipy: 53 1.04091774e+10 1.02576949e+10 2.66e+03 1.31e-07 1.05e+03 1s
54 1.04080459e+10 1.02668121e+10 2.45e+03 1.37e-07 9.77e+02 1s
INFO:gurobipy: 54 1.04080459e+10 1.02668121e+10 2.45e+03 1.37e-07 9.77e+02 1s
55 1.04068890e+10 1.02713919e+10 2.24e+03 1.41e-07 9.36e+02 1s
INFO:gurobipy: 55 1.04068890e+10 1.02713919e+10 2.24e+03 1.41e-07 9.36e+02 1s
56 1.04047215e+10 1.02831038e+10 1.87e+03 1.45e-07 8.38e+02 1s
INFO:gurobipy: 56 1.04047215e+10 1.02831038e+10 1.87e+03 1.45e-07 8.38e+02 1s
57 1.04045403e+10 1.02983510e+10 1.69e+03 1.22e-07 7.33e+02 1s
INFO:gurobipy: 57 1.04045403e+10 1.02983510e+10 1.69e+03 1.22e-07 7.33e+02 1s
58 1.04021333e+10 1.03028306e+10 1.10e+03 1.18e-07 6.80e+02 1s
INFO:gurobipy: 58 1.04021333e+10 1.03028306e+10 1.10e+03 1.18e-07 6.80e+02 1s
59 1.04016609e+10 1.03165743e+10 1.04e+03 1.16e-07 5.83e+02 1s
INFO:gurobipy: 59 1.04016609e+10 1.03165743e+10 1.04e+03 1.16e-07 5.83e+02 1s
60 1.04006028e+10 1.03280057e+10 8.43e+02 1.01e-07 4.97e+02 1s
INFO:gurobipy: 60 1.04006028e+10 1.03280057e+10 8.43e+02 1.01e-07 4.97e+02 1s
61 1.04003845e+10 1.03390887e+10 7.93e+02 8.46e-08 4.21e+02 1s
INFO:gurobipy: 61 1.04003845e+10 1.03390887e+10 7.93e+02 8.46e-08 4.21e+02 1s
62 1.03998864e+10 1.03413529e+10 6.91e+02 8.31e-08 4.01e+02 1s
INFO:gurobipy: 62 1.03998864e+10 1.03413529e+10 6.91e+02 8.31e-08 4.01e+02 1s
63 1.03991326e+10 1.03457039e+10 5.76e+02 7.74e-08 3.65e+02 1s
INFO:gurobipy: 63 1.03991326e+10 1.03457039e+10 5.76e+02 7.74e-08 3.65e+02 1s
64 1.03988793e+10 1.03497782e+10 5.30e+02 7.11e-08 3.36e+02 1s
INFO:gurobipy: 64 1.03988793e+10 1.03497782e+10 5.30e+02 7.11e-08 3.36e+02 1s
65 1.03984990e+10 1.03513956e+10 4.71e+02 6.87e-08 3.22e+02 1s
INFO:gurobipy: 65 1.03984990e+10 1.03513956e+10 4.71e+02 6.87e-08 3.22e+02 1s
66 1.03984498e+10 1.03549836e+10 4.43e+02 6.17e-08 2.97e+02 1s
INFO:gurobipy: 66 1.03984498e+10 1.03549836e+10 4.43e+02 6.17e-08 2.97e+02 1s
67 1.03983183e+10 1.03577072e+10 4.13e+02 5.87e-08 2.78e+02 1s
INFO:gurobipy: 67 1.03983183e+10 1.03577072e+10 4.13e+02 5.87e-08 2.78e+02 1s
68 1.03979297e+10 1.03623798e+10 3.38e+02 5.32e-08 2.43e+02 1s
INFO:gurobipy: 68 1.03979297e+10 1.03623798e+10 3.38e+02 5.32e-08 2.43e+02 1s
69 1.03968430e+10 1.03727682e+10 1.25e+02 3.53e-08 1.63e+02 1s
INFO:gurobipy: 69 1.03968430e+10 1.03727682e+10 1.25e+02 3.53e-08 1.63e+02 1s
70 1.03965779e+10 1.03902555e+10 1.01e+02 8.26e-09 4.36e+01 1s
INFO:gurobipy: 70 1.03965779e+10 1.03902555e+10 1.01e+02 8.26e-09 4.36e+01 1s
71 1.03960805e+10 1.03929226e+10 5.16e+01 5.61e-09 2.18e+01 1s
INFO:gurobipy: 71 1.03960805e+10 1.03929226e+10 5.16e+01 5.61e-09 2.18e+01 1s
72 1.03956986e+10 1.03947963e+10 1.72e+01 2.37e-09 6.26e+00 1s
INFO:gurobipy: 72 1.03956986e+10 1.03947963e+10 1.72e+01 2.37e-09 6.26e+00 1s
73 1.03956043e+10 1.03953694e+10 9.48e+00 1.13e-09 1.69e+00 1s
INFO:gurobipy: 73 1.03956043e+10 1.03953694e+10 9.48e+00 1.13e-09 1.69e+00 1s
74 1.03954985e+10 1.03954126e+10 1.11e+00 6.18e-10 5.89e-01 1s
INFO:gurobipy: 74 1.03954985e+10 1.03954126e+10 1.11e+00 6.18e-10 5.89e-01 1s
75 1.03954864e+10 1.03954627e+10 1.83e-01 2.58e-08 1.61e-01 1s
INFO:gurobipy: 75 1.03954864e+10 1.03954627e+10 1.83e-01 2.58e-08 1.61e-01 1s
76 1.03954835e+10 1.03954817e+10 1.90e-03 1.46e-08 1.23e-02 1s
INFO:gurobipy: 76 1.03954835e+10 1.03954817e+10 1.90e-03 1.46e-08 1.23e-02 1s
77 1.03954834e+10 1.03954834e+10 6.78e-07 0.00e+00 6.60e-05 1s
INFO:gurobipy: 77 1.03954834e+10 1.03954834e+10 6.78e-07 0.00e+00 6.60e-05 1s
78 1.03954834e+10 1.03954834e+10 5.38e-07 1.25e-09 1.51e-10 1s
INFO:gurobipy: 78 1.03954834e+10 1.03954834e+10 5.38e-07 1.25e-09 1.51e-10 1s
INFO:gurobipy:
Barrier solved model in 78 iterations and 1.47 seconds (2.19 work units)
INFO:gurobipy:Barrier solved model in 78 iterations and 1.47 seconds (2.19 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 2s
INFO:gurobipy: 0 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy:
8693 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 8693 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 2.3532234e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 2.3532234e-09 2s
INFO:gurobipy:
Crossover time: 0.31 seconds (0.46 work units)
INFO:gurobipy:Crossover time: 0.31 seconds (0.46 work units)
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 1.99 seconds (2.71 work units)
INFO:gurobipy:Solved in 8747 iterations and 1.99 seconds (2.71 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
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.
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 72.43it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 492.29it/s]
INFO:linopy.io: Writing time: 0.13s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-r5c1a9by.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-r5c1a9by.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 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0x0c1c6aa6
INFO:gurobipy:Model fingerprint: 0x0c1c6aa6
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.16s
INFO:gurobipy:Presolve time: 0.16s
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 1.25e-09 4.47e+05 0s
INFO:gurobipy: 4 4.28243545e+10 -1.90123493e+10 2.08e+06 1.25e-09 4.47e+05 0s
5 3.30103082e+10 -1.31404206e+10 1.50e+06 2.07e-09 3.29e+05 0s
INFO:gurobipy: 5 3.30103082e+10 -1.31404206e+10 1.50e+06 2.07e-09 3.29e+05 0s
6 2.73838707e+10 -8.49879025e+09 1.17e+06 1.31e-09 2.54e+05 0s
INFO:gurobipy: 6 2.73838707e+10 -8.49879025e+09 1.17e+06 1.31e-09 2.54e+05 0s
7 2.09502659e+10 -3.25076392e+09 7.99e+05 3.49e-10 1.69e+05 0s
INFO:gurobipy: 7 2.09502659e+10 -3.25076392e+09 7.99e+05 3.49e-10 1.69e+05 0s
8 1.59435254e+10 -9.47053265e+08 5.07e+05 1.16e-10 1.17e+05 0s
INFO:gurobipy: 8 1.59435254e+10 -9.47053265e+08 5.07e+05 1.16e-10 1.17e+05 0s
9 1.41574253e+10 1.63207841e+09 4.07e+05 7.28e-10 8.70e+04 0s
INFO:gurobipy: 9 1.41574253e+10 1.63207841e+09 4.07e+05 7.28e-10 8.70e+04 0s
10 1.29235530e+10 2.44705989e+09 3.38e+05 1.08e-09 7.27e+04 0s
INFO:gurobipy: 10 1.29235530e+10 2.44705989e+09 3.38e+05 1.08e-09 7.27e+04 0s
11 1.21702066e+10 2.97857892e+09 2.90e+05 5.82e-10 6.37e+04 0s
INFO:gurobipy: 11 1.21702066e+10 2.97857892e+09 2.90e+05 5.82e-10 6.37e+04 0s
12 1.19102659e+10 3.22293291e+09 2.70e+05 6.40e-10 6.02e+04 0s
INFO:gurobipy: 12 1.19102659e+10 3.22293291e+09 2.70e+05 6.40e-10 6.02e+04 0s
13 1.12543533e+10 4.63308398e+09 2.28e+05 1.16e-10 4.60e+04 0s
INFO:gurobipy: 13 1.12543533e+10 4.63308398e+09 2.28e+05 1.16e-10 4.60e+04 0s
14 1.10854714e+10 4.79987223e+09 2.14e+05 2.18e-10 4.37e+04 0s
INFO:gurobipy: 14 1.10854714e+10 4.79987223e+09 2.14e+05 2.18e-10 4.37e+04 0s
15 1.09019403e+10 5.11529135e+09 2.02e+05 7.86e-10 4.02e+04 0s
INFO:gurobipy: 15 1.09019403e+10 5.11529135e+09 2.02e+05 7.86e-10 4.02e+04 0s
16 1.04781491e+10 5.37417034e+09 1.71e+05 5.82e-10 3.54e+04 0s
INFO:gurobipy: 16 1.04781491e+10 5.37417034e+09 1.71e+05 5.82e-10 3.54e+04 0s
17 1.02110054e+10 5.64570859e+09 1.48e+05 9.02e-10 3.17e+04 0s
INFO:gurobipy: 17 1.02110054e+10 5.64570859e+09 1.48e+05 9.02e-10 3.17e+04 0s
18 1.01837926e+10 5.97932535e+09 1.45e+05 7.28e-10 2.92e+04 1s
INFO:gurobipy: 18 1.01837926e+10 5.97932535e+09 1.45e+05 7.28e-10 2.92e+04 1s
19 1.00091614e+10 6.29934114e+09 1.27e+05 6.69e-10 2.58e+04 1s
INFO:gurobipy: 19 1.00091614e+10 6.29934114e+09 1.27e+05 6.69e-10 2.58e+04 1s
20 9.85781927e+09 6.46669279e+09 1.10e+05 9.02e-10 2.35e+04 1s
INFO:gurobipy: 20 9.85781927e+09 6.46669279e+09 1.10e+05 9.02e-10 2.35e+04 1s
21 9.78624928e+09 6.65665480e+09 1.02e+05 9.31e-10 2.17e+04 1s
INFO:gurobipy: 21 9.78624928e+09 6.65665480e+09 1.02e+05 9.31e-10 2.17e+04 1s
22 9.71142016e+09 6.77953897e+09 9.22e+04 7.57e-10 2.03e+04 1s
INFO:gurobipy: 22 9.71142016e+09 6.77953897e+09 9.22e+04 7.57e-10 2.03e+04 1s
23 9.64648165e+09 6.91910853e+09 8.31e+04 6.69e-10 1.89e+04 1s
INFO:gurobipy: 23 9.64648165e+09 6.91910853e+09 8.31e+04 6.69e-10 1.89e+04 1s
24 9.59477560e+09 7.07112257e+09 7.01e+04 2.91e-10 1.74e+04 1s
INFO:gurobipy: 24 9.59477560e+09 7.07112257e+09 7.01e+04 2.91e-10 1.74e+04 1s
25 9.54664797e+09 7.42722121e+09 6.42e+04 9.60e-10 1.47e+04 1s
INFO:gurobipy: 25 9.54664797e+09 7.42722121e+09 6.42e+04 9.60e-10 1.47e+04 1s
26 9.50335625e+09 7.56212654e+09 5.84e+04 6.18e-11 1.34e+04 1s
INFO:gurobipy: 26 9.50335625e+09 7.56212654e+09 5.84e+04 6.18e-11 1.34e+04 1s
27 9.46514596e+09 7.62381171e+09 5.30e+04 4.95e-10 1.27e+04 1s
INFO:gurobipy: 27 9.46514596e+09 7.62381171e+09 5.30e+04 4.95e-10 1.27e+04 1s
28 9.45767048e+09 7.68959098e+09 4.77e+04 8.44e-10 1.22e+04 1s
INFO:gurobipy: 28 9.45767048e+09 7.68959098e+09 4.77e+04 8.44e-10 1.22e+04 1s
29 9.39430393e+09 7.84134342e+09 3.82e+04 2.04e-10 1.07e+04 1s
INFO:gurobipy: 29 9.39430393e+09 7.84134342e+09 3.82e+04 2.04e-10 1.07e+04 1s
30 9.39897214e+09 7.90348532e+09 3.46e+04 2.33e-10 1.03e+04 1s
INFO:gurobipy: 30 9.39897214e+09 7.90348532e+09 3.46e+04 2.33e-10 1.03e+04 1s
31 9.35759369e+09 7.99868961e+09 2.94e+04 8.44e-10 9.33e+03 1s
INFO:gurobipy: 31 9.35759369e+09 7.99868961e+09 2.94e+04 8.44e-10 9.33e+03 1s
32 9.32925927e+09 8.10817156e+09 2.58e+04 1.46e-10 8.38e+03 1s
INFO:gurobipy: 32 9.32925927e+09 8.10817156e+09 2.58e+04 1.46e-10 8.38e+03 1s
33 9.31514832e+09 8.19628006e+09 2.38e+04 4.95e-10 7.68e+03 1s
INFO:gurobipy: 33 9.31514832e+09 8.19628006e+09 2.38e+04 4.95e-10 7.68e+03 1s
34 9.30794775e+09 8.23520164e+09 2.27e+04 1.75e-10 7.36e+03 1s
INFO:gurobipy: 34 9.30794775e+09 8.23520164e+09 2.27e+04 1.75e-10 7.36e+03 1s
35 9.28713841e+09 8.27444053e+09 1.93e+04 9.31e-10 6.93e+03 1s
INFO:gurobipy: 35 9.28713841e+09 8.27444053e+09 1.93e+04 9.31e-10 6.93e+03 1s
36 9.28288131e+09 8.30915484e+09 1.59e+04 1.11e-09 6.65e+03 1s
INFO:gurobipy: 36 9.28288131e+09 8.30915484e+09 1.59e+04 1.11e-09 6.65e+03 1s
37 9.26500394e+09 8.44857172e+09 1.38e+04 2.33e-10 5.58e+03 1s
INFO:gurobipy: 37 9.26500394e+09 8.44857172e+09 1.38e+04 2.33e-10 5.58e+03 1s
38 9.25610754e+09 8.51205586e+09 1.25e+04 6.11e-10 5.08e+03 1s
INFO:gurobipy: 38 9.25610754e+09 8.51205586e+09 1.25e+04 6.11e-10 5.08e+03 1s
39 9.24572531e+09 8.53956773e+09 1.06e+04 4.66e-10 4.82e+03 1s
INFO:gurobipy: 39 9.24572531e+09 8.53956773e+09 1.06e+04 4.66e-10 4.82e+03 1s
40 9.24070099e+09 8.59176391e+09 9.43e+03 5.82e-10 4.42e+03 1s
INFO:gurobipy: 40 9.24070099e+09 8.59176391e+09 9.43e+03 5.82e-10 4.42e+03 1s
41 9.23071901e+09 8.64375195e+09 8.21e+03 2.33e-10 4.00e+03 1s
INFO:gurobipy: 41 9.23071901e+09 8.64375195e+09 8.21e+03 2.33e-10 4.00e+03 1s
42 9.22745509e+09 8.67087528e+09 7.68e+03 9.02e-10 3.79e+03 1s
INFO:gurobipy: 42 9.22745509e+09 8.67087528e+09 7.68e+03 9.02e-10 3.79e+03 1s
43 9.22316399e+09 8.71766068e+09 7.11e+03 2.91e-10 3.44e+03 1s
INFO:gurobipy: 43 9.22316399e+09 8.71766068e+09 7.11e+03 2.91e-10 3.44e+03 1s
44 9.21729614e+09 8.73749308e+09 5.77e+03 3.20e-10 3.26e+03 1s
INFO:gurobipy: 44 9.21729614e+09 8.73749308e+09 5.77e+03 3.20e-10 3.26e+03 1s
45 9.21266113e+09 8.75883745e+09 4.94e+03 4.66e-10 3.08e+03 1s
INFO:gurobipy: 45 9.21266113e+09 8.75883745e+09 4.94e+03 4.66e-10 3.08e+03 1s
46 9.20810666e+09 8.77695546e+09 3.97e+03 0.00e+00 2.92e+03 1s
INFO:gurobipy: 46 9.20810666e+09 8.77695546e+09 3.97e+03 0.00e+00 2.92e+03 1s
47 9.20672207e+09 8.78560535e+09 3.70e+03 1.75e-10 2.85e+03 1s
INFO:gurobipy: 47 9.20672207e+09 8.78560535e+09 3.70e+03 1.75e-10 2.85e+03 1s
48 9.20552770e+09 8.81338806e+09 3.40e+03 7.28e-11 2.66e+03 1s
INFO:gurobipy: 48 9.20552770e+09 8.81338806e+09 3.40e+03 7.28e-11 2.66e+03 1s
49 9.20529152e+09 8.83436150e+09 3.22e+03 3.78e-10 2.51e+03 1s
INFO:gurobipy: 49 9.20529152e+09 8.83436150e+09 3.22e+03 3.78e-10 2.51e+03 1s
50 9.20173713e+09 8.87392583e+09 2.79e+03 6.55e-11 2.22e+03 1s
INFO:gurobipy: 50 9.20173713e+09 8.87392583e+09 2.79e+03 6.55e-11 2.22e+03 1s
51 9.19900962e+09 8.89306376e+09 2.50e+03 5.24e-10 2.07e+03 1s
INFO:gurobipy: 51 9.19900962e+09 8.89306376e+09 2.50e+03 5.24e-10 2.07e+03 1s
52 9.19663434e+09 8.92294386e+09 2.13e+03 2.91e-10 1.85e+03 1s
INFO:gurobipy: 52 9.19663434e+09 8.92294386e+09 2.13e+03 2.91e-10 1.85e+03 1s
53 9.19452868e+09 8.94969725e+09 1.85e+03 6.40e-10 1.66e+03 1s
INFO:gurobipy: 53 9.19452868e+09 8.94969725e+09 1.85e+03 6.40e-10 1.66e+03 1s
54 9.19345094e+09 8.95958377e+09 1.71e+03 6.11e-10 1.58e+03 1s
INFO:gurobipy: 54 9.19345094e+09 8.95958377e+09 1.71e+03 6.11e-10 1.58e+03 1s
55 9.19181438e+09 8.97883044e+09 1.51e+03 1.63e-09 1.44e+03 1s
INFO:gurobipy: 55 9.19181438e+09 8.97883044e+09 1.51e+03 1.63e-09 1.44e+03 1s
56 9.19116010e+09 8.98732798e+09 1.43e+03 1.94e-09 1.38e+03 1s
INFO:gurobipy: 56 9.19116010e+09 8.98732798e+09 1.43e+03 1.94e-09 1.38e+03 1s
57 9.19039580e+09 8.99046109e+09 1.34e+03 1.86e-09 1.35e+03 1s
INFO:gurobipy: 57 9.19039580e+09 8.99046109e+09 1.34e+03 1.86e-09 1.35e+03 1s
58 9.18892341e+09 9.02498209e+09 1.14e+03 4.52e-09 1.11e+03 1s
INFO:gurobipy: 58 9.18892341e+09 9.02498209e+09 1.14e+03 4.52e-09 1.11e+03 1s
59 9.18787723e+09 9.03417285e+09 1.01e+03 4.58e-09 1.04e+03 1s
INFO:gurobipy: 59 9.18787723e+09 9.03417285e+09 1.01e+03 4.58e-09 1.04e+03 1s
60 9.18713931e+09 9.04469926e+09 9.19e+02 4.75e-09 9.63e+02 1s
INFO:gurobipy: 60 9.18713931e+09 9.04469926e+09 9.19e+02 4.75e-09 9.63e+02 1s
61 9.18678897e+09 9.05833227e+09 8.79e+02 5.48e-09 8.69e+02 1s
INFO:gurobipy: 61 9.18678897e+09 9.05833227e+09 8.79e+02 5.48e-09 8.69e+02 1s
62 9.18599576e+09 9.06631804e+09 7.76e+02 5.08e-09 8.09e+02 1s
INFO:gurobipy: 62 9.18599576e+09 9.06631804e+09 7.76e+02 5.08e-09 8.09e+02 1s
63 9.18524767e+09 9.07061096e+09 6.84e+02 5.54e-09 7.75e+02 1s
INFO:gurobipy: 63 9.18524767e+09 9.07061096e+09 6.84e+02 5.54e-09 7.75e+02 1s
64 9.18421936e+09 9.08085484e+09 5.81e+02 6.69e-09 6.98e+02 1s
INFO:gurobipy: 64 9.18421936e+09 9.08085484e+09 5.81e+02 6.69e-09 6.98e+02 1s
65 9.18399900e+09 9.08112838e+09 5.58e+02 7.24e-09 6.95e+02 1s
INFO:gurobipy: 65 9.18399900e+09 9.08112838e+09 5.58e+02 7.24e-09 6.95e+02 1s
66 9.18323737e+09 9.09957766e+09 4.81e+02 9.40e-09 5.65e+02 1s
INFO:gurobipy: 66 9.18323737e+09 9.09957766e+09 4.81e+02 9.40e-09 5.65e+02 1s
67 9.18304990e+09 9.10191504e+09 4.59e+02 9.66e-09 5.48e+02 1s
INFO:gurobipy: 67 9.18304990e+09 9.10191504e+09 4.59e+02 9.66e-09 5.48e+02 1s
68 9.18279199e+09 9.10336357e+09 4.32e+02 9.98e-09 5.36e+02 1s
INFO:gurobipy: 68 9.18279199e+09 9.10336357e+09 4.32e+02 9.98e-09 5.36e+02 1s
69 9.18245263e+09 9.10792309e+09 4.00e+02 9.94e-09 5.03e+02 2s
INFO:gurobipy: 69 9.18245263e+09 9.10792309e+09 4.00e+02 9.94e-09 5.03e+02 2s
70 9.18220300e+09 9.11273425e+09 3.78e+02 1.02e-08 4.69e+02 2s
INFO:gurobipy: 70 9.18220300e+09 9.11273425e+09 3.78e+02 1.02e-08 4.69e+02 2s
71 9.18178095e+09 9.12172977e+09 3.30e+02 9.99e-09 4.05e+02 2s
INFO:gurobipy: 71 9.18178095e+09 9.12172977e+09 3.30e+02 9.99e-09 4.05e+02 2s
72 9.18114989e+09 9.12403922e+09 2.82e+02 9.88e-09 3.85e+02 2s
INFO:gurobipy: 72 9.18114989e+09 9.12403922e+09 2.82e+02 9.88e-09 3.85e+02 2s
73 9.18109114e+09 9.12687778e+09 2.72e+02 1.02e-08 3.66e+02 2s
INFO:gurobipy: 73 9.18109114e+09 9.12687778e+09 2.72e+02 1.02e-08 3.66e+02 2s
74 9.18043284e+09 9.13087165e+09 2.16e+02 9.58e-09 3.34e+02 2s
INFO:gurobipy: 74 9.18043284e+09 9.13087165e+09 2.16e+02 9.58e-09 3.34e+02 2s
75 9.18021622e+09 9.14247451e+09 1.87e+02 7.31e-09 2.55e+02 2s
INFO:gurobipy: 75 9.18021622e+09 9.14247451e+09 1.87e+02 7.31e-09 2.55e+02 2s
76 9.17835117e+09 9.15027518e+09 1.87e+01 5.75e-09 1.89e+02 2s
INFO:gurobipy: 76 9.17835117e+09 9.15027518e+09 1.87e+01 5.75e-09 1.89e+02 2s
77 9.17805574e+09 9.15810771e+09 1.00e+01 4.99e-09 1.34e+02 2s
INFO:gurobipy: 77 9.17805574e+09 9.15810771e+09 1.00e+01 4.99e-09 1.34e+02 2s
78 9.17793478e+09 9.15904070e+09 6.82e+00 4.82e-09 1.27e+02 2s
INFO:gurobipy: 78 9.17793478e+09 9.15904070e+09 6.82e+00 4.82e-09 1.27e+02 2s
79 9.17787727e+09 9.16474806e+09 4.95e+00 3.15e-09 8.82e+01 2s
INFO:gurobipy: 79 9.17787727e+09 9.16474806e+09 4.95e+00 3.15e-09 8.82e+01 2s
80 9.17774389e+09 9.16942359e+09 1.71e+00 2.14e-09 5.59e+01 2s
INFO:gurobipy: 80 9.17774389e+09 9.16942359e+09 1.71e+00 2.14e-09 5.59e+01 2s
81 9.17765768e+09 9.17127885e+09 7.97e-01 1.80e-09 4.28e+01 2s
INFO:gurobipy: 81 9.17765768e+09 9.17127885e+09 7.97e-01 1.80e-09 4.28e+01 2s
82 9.17764595e+09 9.17340389e+09 6.99e-01 8.62e-10 2.85e+01 2s
INFO:gurobipy: 82 9.17764595e+09 9.17340389e+09 6.99e-01 8.62e-10 2.85e+01 2s
83 9.17759090e+09 9.17616248e+09 2.80e-01 1.21e-09 9.59e+00 2s
INFO:gurobipy: 83 9.17759090e+09 9.17616248e+09 2.80e-01 1.21e-09 9.59e+00 2s
84 9.17751880e+09 9.17729945e+09 9.75e-03 4.37e-10 1.47e+00 2s
INFO:gurobipy: 84 9.17751880e+09 9.17729945e+09 9.75e-03 4.37e-10 1.47e+00 2s
85 9.17751091e+09 9.17748577e+09 7.48e-04 2.91e-10 1.69e-01 2s
INFO:gurobipy: 85 9.17751091e+09 9.17748577e+09 7.48e-04 2.91e-10 1.69e-01 2s
86 9.17750988e+09 9.17750983e+09 1.90e-05 6.91e-11 3.45e-04 2s
INFO:gurobipy: 86 9.17750988e+09 9.17750983e+09 1.90e-05 6.91e-11 3.45e-04 2s
87 9.17750988e+09 9.17750988e+09 3.41e-08 1.51e-09 5.04e-10 2s
INFO:gurobipy: 87 9.17750988e+09 9.17750988e+09 3.41e-08 1.51e-09 5.04e-10 2s
INFO:gurobipy:
Barrier solved model in 87 iterations and 1.79 seconds (2.40 work units)
INFO:gurobipy:Barrier solved model in 87 iterations and 1.79 seconds (2.40 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
Warning: Markowitz tolerance tightened to 0.5
INFO:gurobipy:Warning: Markowitz tolerance tightened to 0.5
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 1.5196581e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.5196581e-09 2s
INFO:gurobipy:
Crossover time: 0.19 seconds (0.75 work units)
INFO:gurobipy:Crossover time: 0.19 seconds (0.75 work units)
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 2.01 seconds (3.22 work units)
INFO:gurobipy:Solved in 8702 iterations and 2.01 seconds (3.22 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
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.
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 67.62it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 371.09it/s]
INFO:linopy.io: Writing time: 0.14s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-ah9q8k7s.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-ah9q8k7s.lp
Reading time = 0.14 seconds
INFO:gurobipy:Reading time = 0.14 seconds
obj: 140168 rows, 61327 columns, 271592 nonzeros
INFO:gurobipy:obj: 140168 rows, 61327 columns, 271592 nonzeros
Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0x971c7167
INFO:gurobipy:Model fingerprint: 0x971c7167
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.19s
INFO:gurobipy:Presolve time: 0.19s
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 1.72e-09 4.89e+05 0s
INFO:gurobipy: 4 4.67808481e+10 -2.19477626e+10 1.80e+06 1.72e-09 4.89e+05 0s
5 3.49912389e+10 -1.55687457e+10 1.26e+06 1.66e-09 3.56e+05 0s
INFO:gurobipy: 5 3.49912389e+10 -1.55687457e+10 1.26e+06 1.66e-09 3.56e+05 0s
6 2.72746493e+10 -1.07945360e+10 9.16e+05 2.76e-10 2.65e+05 0s
INFO:gurobipy: 6 2.72746493e+10 -1.07945360e+10 9.16e+05 2.76e-10 2.65e+05 0s
7 2.07818241e+10 -6.07610889e+09 6.31e+05 6.11e-10 1.86e+05 0s
INFO:gurobipy: 7 2.07818241e+10 -6.07610889e+09 6.31e+05 6.11e-10 1.86e+05 0s
8 1.56388253e+10 -2.89829517e+09 4.02e+05 4.07e-10 1.28e+05 0s
INFO:gurobipy: 8 1.56388253e+10 -2.89829517e+09 4.02e+05 4.07e-10 1.28e+05 0s
9 1.37642839e+10 -1.92501816e+08 3.22e+05 4.51e-10 9.58e+04 0s
INFO:gurobipy: 9 1.37642839e+10 -1.92501816e+08 3.22e+05 4.51e-10 9.58e+04 0s
10 1.20986773e+10 1.79747168e+09 2.49e+05 5.82e-10 7.07e+04 0s
INFO:gurobipy: 10 1.20986773e+10 1.79747168e+09 2.49e+05 5.82e-10 7.07e+04 0s
11 1.12647187e+10 2.62113592e+09 2.09e+05 2.91e-10 5.93e+04 0s
INFO:gurobipy: 11 1.12647187e+10 2.62113592e+09 2.09e+05 2.91e-10 5.93e+04 0s
12 1.09993556e+10 3.13153417e+09 1.96e+05 6.98e-10 5.39e+04 1s
INFO:gurobipy: 12 1.09993556e+10 3.13153417e+09 1.96e+05 6.98e-10 5.39e+04 1s
13 1.06629742e+10 3.65451191e+09 1.80e+05 2.91e-10 4.81e+04 1s
INFO:gurobipy: 13 1.06629742e+10 3.65451191e+09 1.80e+05 2.91e-10 4.81e+04 1s
14 1.05419143e+10 3.84369778e+09 1.73e+05 2.04e-10 4.59e+04 1s
INFO:gurobipy: 14 1.05419143e+10 3.84369778e+09 1.73e+05 2.04e-10 4.59e+04 1s
15 9.84848354e+09 4.63099031e+09 1.35e+05 7.57e-10 3.58e+04 1s
INFO:gurobipy: 15 9.84848354e+09 4.63099031e+09 1.35e+05 7.57e-10 3.58e+04 1s
16 9.74957497e+09 5.01115391e+09 1.28e+05 6.40e-10 3.25e+04 1s
INFO:gurobipy: 16 9.74957497e+09 5.01115391e+09 1.28e+05 6.40e-10 3.25e+04 1s
17 9.58403115e+09 5.30079226e+09 1.17e+05 1.19e-09 2.94e+04 1s
INFO:gurobipy: 17 9.58403115e+09 5.30079226e+09 1.17e+05 1.19e-09 2.94e+04 1s
18 9.43643230e+09 5.73120854e+09 1.03e+05 3.78e-10 2.54e+04 1s
INFO:gurobipy: 18 9.43643230e+09 5.73120854e+09 1.03e+05 3.78e-10 2.54e+04 1s
19 9.23756510e+09 5.97517632e+09 8.85e+04 3.49e-10 2.24e+04 1s
INFO:gurobipy: 19 9.23756510e+09 5.97517632e+09 8.85e+04 3.49e-10 2.24e+04 1s
20 9.17759905e+09 6.06403846e+09 8.34e+04 3.78e-10 2.13e+04 1s
INFO:gurobipy: 20 9.17759905e+09 6.06403846e+09 8.34e+04 3.78e-10 2.13e+04 1s
21 9.03446459e+09 6.37625806e+09 7.22e+04 4.24e-03 1.82e+04 1s
INFO:gurobipy: 21 9.03446459e+09 6.37625806e+09 7.22e+04 4.24e-03 1.82e+04 1s
22 8.96749467e+09 6.67420096e+09 6.53e+04 7.64e-11 1.57e+04 1s
INFO:gurobipy: 22 8.96749467e+09 6.67420096e+09 6.53e+04 7.64e-11 1.57e+04 1s
23 8.87235390e+09 6.81910768e+09 5.52e+04 1.16e-10 1.41e+04 1s
INFO:gurobipy: 23 8.87235390e+09 6.81910768e+09 5.52e+04 1.16e-10 1.41e+04 1s
24 8.79653172e+09 6.92938917e+09 4.68e+04 6.98e-10 1.28e+04 1s
INFO:gurobipy: 24 8.79653172e+09 6.92938917e+09 4.68e+04 6.98e-10 1.28e+04 1s
25 8.75482211e+09 7.13402061e+09 4.29e+04 2.33e-10 1.11e+04 1s
INFO:gurobipy: 25 8.75482211e+09 7.13402061e+09 4.29e+04 2.33e-10 1.11e+04 1s
26 8.73030838e+09 7.18065837e+09 4.05e+04 3.49e-10 1.06e+04 1s
INFO:gurobipy: 26 8.73030838e+09 7.18065837e+09 4.05e+04 3.49e-10 1.06e+04 1s
27 8.68512999e+09 7.35837448e+09 3.45e+04 5.82e-10 9.09e+03 1s
INFO:gurobipy: 27 8.68512999e+09 7.35837448e+09 3.45e+04 5.82e-10 9.09e+03 1s
28 8.63357276e+09 7.50106948e+09 2.94e+04 1.16e-10 7.76e+03 1s
INFO:gurobipy: 28 8.63357276e+09 7.50106948e+09 2.94e+04 1.16e-10 7.76e+03 1s
29 8.60673412e+09 7.56416622e+09 2.67e+04 3.20e-10 7.14e+03 1s
INFO:gurobipy: 29 8.60673412e+09 7.56416622e+09 2.67e+04 3.20e-10 7.14e+03 1s
30 8.58029420e+09 7.62670097e+09 2.38e+04 6.11e-10 6.53e+03 1s
INFO:gurobipy: 30 8.58029420e+09 7.62670097e+09 2.38e+04 6.11e-10 6.53e+03 1s
31 8.55898227e+09 7.72479866e+09 2.14e+04 2.91e-11 5.71e+03 1s
INFO:gurobipy: 31 8.55898227e+09 7.72479866e+09 2.14e+04 2.91e-11 5.71e+03 1s
32 8.55258782e+09 7.74561495e+09 2.06e+04 1.75e-10 5.52e+03 1s
INFO:gurobipy: 32 8.55258782e+09 7.74561495e+09 2.06e+04 1.75e-10 5.52e+03 1s
33 8.53045117e+09 7.78804975e+09 1.73e+04 0.00e+00 5.07e+03 1s
INFO:gurobipy: 33 8.53045117e+09 7.78804975e+09 1.73e+04 0.00e+00 5.07e+03 1s
34 8.51263679e+09 7.89632298e+09 1.44e+04 3.78e-10 4.21e+03 1s
INFO:gurobipy: 34 8.51263679e+09 7.89632298e+09 1.44e+04 3.78e-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 1.12e+04 6.69e-10 3.24e+03 1s
INFO:gurobipy: 36 8.48875893e+09 8.01490308e+09 1.12e+04 6.69e-10 3.24e+03 1s
37 8.47584911e+09 8.03177595e+09 9.57e+03 8.73e-10 3.03e+03 1s
INFO:gurobipy: 37 8.47584911e+09 8.03177595e+09 9.57e+03 8.73e-10 3.03e+03 1s
38 8.47019001e+09 8.05327545e+09 8.66e+03 8.44e-10 2.84e+03 1s
INFO:gurobipy: 38 8.47019001e+09 8.05327545e+09 8.66e+03 8.44e-10 2.84e+03 1s
39 8.46226166e+09 8.07275028e+09 7.39e+03 2.62e-10 2.65e+03 1s
INFO:gurobipy: 39 8.46226166e+09 8.07275028e+09 7.39e+03 2.62e-10 2.65e+03 1s
40 8.45597232e+09 8.12317725e+09 6.58e+03 8.44e-10 2.27e+03 1s
INFO:gurobipy: 40 8.45597232e+09 8.12317725e+09 6.58e+03 8.44e-10 2.27e+03 1s
41 8.44990465e+09 8.14035370e+09 5.72e+03 5.24e-10 2.11e+03 1s
INFO:gurobipy: 41 8.44990465e+09 8.14035370e+09 5.72e+03 5.24e-10 2.11e+03 1s
42 8.44817253e+09 8.15104741e+09 5.50e+03 6.18e-11 2.02e+03 1s
INFO:gurobipy: 42 8.44817253e+09 8.15104741e+09 5.50e+03 6.18e-11 2.02e+03 1s
43 8.44441124e+09 8.17701661e+09 5.00e+03 2.91e-11 1.82e+03 1s
INFO:gurobipy: 43 8.44441124e+09 8.17701661e+09 5.00e+03 2.91e-11 1.82e+03 1s
44 8.44077696e+09 8.20297596e+09 4.52e+03 1.60e-10 1.62e+03 1s
INFO:gurobipy: 44 8.44077696e+09 8.20297596e+09 4.52e+03 1.60e-10 1.62e+03 1s
45 8.44010931e+09 8.21119306e+09 4.43e+03 2.91e-10 1.56e+03 1s
INFO:gurobipy: 45 8.44010931e+09 8.21119306e+09 4.43e+03 2.91e-10 1.56e+03 1s
46 8.43716847e+09 8.22130836e+09 3.98e+03 3.20e-10 1.47e+03 1s
INFO:gurobipy: 46 8.43716847e+09 8.22130836e+09 3.98e+03 3.20e-10 1.47e+03 1s
47 8.43370737e+09 8.24780490e+09 3.55e+03 4.95e-10 1.27e+03 1s
INFO:gurobipy: 47 8.43370737e+09 8.24780490e+09 3.55e+03 4.95e-10 1.27e+03 1s
48 8.43056273e+09 8.26266160e+09 3.15e+03 3.20e-10 1.14e+03 1s
INFO:gurobipy: 48 8.43056273e+09 8.26266160e+09 3.15e+03 3.20e-10 1.14e+03 1s
49 8.42764179e+09 8.26864909e+09 2.72e+03 6.11e-10 1.08e+03 1s
INFO:gurobipy: 49 8.42764179e+09 8.26864909e+09 2.72e+03 6.11e-10 1.08e+03 1s
50 8.42352376e+09 8.28147266e+09 2.18e+03 6.55e-11 9.65e+02 1s
INFO:gurobipy: 50 8.42352376e+09 8.28147266e+09 2.18e+03 6.55e-11 9.65e+02 1s
51 8.42158390e+09 8.29158312e+09 1.85e+03 4.07e-10 8.83e+02 1s
INFO:gurobipy: 51 8.42158390e+09 8.29158312e+09 1.85e+03 4.07e-10 8.83e+02 1s
52 8.42054978e+09 8.29713944e+09 1.71e+03 2.04e-10 8.38e+02 1s
INFO:gurobipy: 52 8.42054978e+09 8.29713944e+09 1.71e+03 2.04e-10 8.38e+02 1s
53 8.41888140e+09 8.30289402e+09 1.52e+03 1.16e-10 7.87e+02 1s
INFO:gurobipy: 53 8.41888140e+09 8.30289402e+09 1.52e+03 1.16e-10 7.87e+02 1s
54 8.41732541e+09 8.31554342e+09 1.27e+03 1.48e-09 6.90e+02 1s
INFO:gurobipy: 54 8.41732541e+09 8.31554342e+09 1.27e+03 1.48e-09 6.90e+02 1s
55 8.41606328e+09 8.32879047e+09 1.13e+03 4.37e-10 5.92e+02 1s
INFO:gurobipy: 55 8.41606328e+09 8.32879047e+09 1.13e+03 4.37e-10 5.92e+02 1s
56 8.41479787e+09 8.34107880e+09 9.90e+02 6.69e-10 5.00e+02 1s
INFO:gurobipy: 56 8.41479787e+09 8.34107880e+09 9.90e+02 6.69e-10 5.00e+02 1s
57 8.41303498e+09 8.35315327e+09 7.65e+02 6.80e-10 4.06e+02 1s
INFO:gurobipy: 57 8.41303498e+09 8.35315327e+09 7.65e+02 6.80e-10 4.06e+02 1s
58 8.41194961e+09 8.36061657e+09 6.28e+02 7.28e-10 3.48e+02 1s
INFO:gurobipy: 58 8.41194961e+09 8.36061657e+09 6.28e+02 7.28e-10 3.48e+02 1s
59 8.41027628e+09 8.36683233e+09 4.23e+02 3.64e-10 2.94e+02 1s
INFO:gurobipy: 59 8.41027628e+09 8.36683233e+09 4.23e+02 3.64e-10 2.94e+02 1s
60 8.40922701e+09 8.37026374e+09 3.10e+02 1.82e-10 2.63e+02 1s
INFO:gurobipy: 60 8.40922701e+09 8.37026374e+09 3.10e+02 1.82e-10 2.63e+02 1s
61 8.40892840e+09 8.37505508e+09 2.78e+02 2.18e-10 2.29e+02 1s
INFO:gurobipy: 61 8.40892840e+09 8.37505508e+09 2.78e+02 2.18e-10 2.29e+02 1s
62 8.40813913e+09 8.38062064e+09 1.91e+02 5.97e-10 1.86e+02 1s
INFO:gurobipy: 62 8.40813913e+09 8.38062064e+09 1.91e+02 5.97e-10 1.86e+02 1s
63 8.40780840e+09 8.38267962e+09 1.59e+02 3.53e-10 1.70e+02 1s
INFO:gurobipy: 63 8.40780840e+09 8.38267962e+09 1.59e+02 3.53e-10 1.70e+02 1s
64 8.40735787e+09 8.38604782e+09 1.17e+02 5.53e-10 1.44e+02 2s
INFO:gurobipy: 64 8.40735787e+09 8.38604782e+09 1.17e+02 5.53e-10 1.44e+02 2s
65 8.40721501e+09 8.38748105e+09 1.04e+02 4.07e-10 1.33e+02 2s
INFO:gurobipy: 65 8.40721501e+09 8.38748105e+09 1.04e+02 4.07e-10 1.33e+02 2s
66 8.40698306e+09 8.38899605e+09 8.13e+01 1.42e-10 1.21e+02 2s
INFO:gurobipy: 66 8.40698306e+09 8.38899605e+09 8.13e+01 1.42e-10 1.21e+02 2s
67 8.40659883e+09 8.39034677e+09 4.80e+01 6.11e-10 1.09e+02 2s
INFO:gurobipy: 67 8.40659883e+09 8.39034677e+09 4.80e+01 6.11e-10 1.09e+02 2s
68 8.40646289e+09 8.39292618e+09 3.56e+01 1.19e-09 9.11e+01 2s
INFO:gurobipy: 68 8.40646289e+09 8.39292618e+09 3.56e+01 1.19e-09 9.11e+01 2s
69 8.40625938e+09 8.39745334e+09 1.87e+01 1.87e-09 5.93e+01 2s
INFO:gurobipy: 69 8.40625938e+09 8.39745334e+09 1.87e+01 1.87e-09 5.93e+01 2s
70 8.40619819e+09 8.39945251e+09 1.51e+01 1.68e-09 4.54e+01 2s
INFO:gurobipy: 70 8.40619819e+09 8.39945251e+09 1.51e+01 1.68e-09 4.54e+01 2s
71 8.40597237e+09 8.40184172e+09 1.06e+00 1.49e-09 2.78e+01 2s
INFO:gurobipy: 71 8.40597237e+09 8.40184172e+09 1.06e+00 1.49e-09 2.78e+01 2s
72 8.40592191e+09 8.40330612e+09 1.34e-01 9.64e-10 1.76e+01 2s
INFO:gurobipy: 72 8.40592191e+09 8.40330612e+09 1.34e-01 9.64e-10 1.76e+01 2s
73 8.40591133e+09 8.40335728e+09 8.56e-02 9.20e-10 1.72e+01 2s
INFO:gurobipy: 73 8.40591133e+09 8.40335728e+09 8.56e-02 9.20e-10 1.72e+01 2s
74 8.40591217e+09 8.40341094e+09 5.97e-02 8.91e-10 1.68e+01 2s
INFO:gurobipy: 74 8.40591217e+09 8.40341094e+09 5.97e-02 8.91e-10 1.68e+01 2s
75 8.40591647e+09 8.40502370e+09 3.90e-02 1.04e-08 6.00e+00 2s
INFO:gurobipy: 75 8.40591647e+09 8.40502370e+09 3.90e-02 1.04e-08 6.00e+00 2s
76 8.40589638e+09 8.40576984e+09 1.10e-02 3.93e-09 8.50e-01 2s
INFO:gurobipy: 76 8.40589638e+09 8.40576984e+09 1.10e-02 3.93e-09 8.50e-01 2s
77 8.40588663e+09 8.40588302e+09 6.06e-04 5.97e-10 2.42e-02 2s
INFO:gurobipy: 77 8.40588663e+09 8.40588302e+09 6.06e-04 5.97e-10 2.42e-02 2s
78 8.40588625e+09 8.40588608e+09 2.10e-06 2.44e-09 1.17e-03 2s
INFO:gurobipy: 78 8.40588625e+09 8.40588608e+09 2.10e-06 2.44e-09 1.17e-03 2s
79 8.40588625e+09 8.40588625e+09 9.95e-07 3.94e-09 3.24e-06 2s
INFO:gurobipy: 79 8.40588625e+09 8.40588625e+09 9.95e-07 3.94e-09 3.24e-06 2s
80 8.40588625e+09 8.40588625e+09 4.29e-07 9.80e-09 4.26e-09 2s
INFO:gurobipy: 80 8.40588625e+09 8.40588625e+09 4.29e-07 9.80e-09 4.26e-09 2s
INFO:gurobipy:
Barrier solved model in 80 iterations and 1.77 seconds (2.24 work units)
INFO:gurobipy:Barrier solved model in 80 iterations and 1.77 seconds (2.24 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 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:
8604 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 8604 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 1.4626470e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.4626470e-09 2s
INFO:gurobipy:
Crossover time: 0.28 seconds (0.98 work units)
INFO:gurobipy:Crossover time: 0.28 seconds (0.98 work units)
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 2.08 seconds (3.30 work units)
INFO:gurobipy:Solved in 8658 iterations and 2.08 seconds (3.30 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
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.
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['PRT', 'DNK'], dtype='object', name='name')
WARNING:pypsa.consistency:The following loads have carriers which are not defined:
Index(['PRT load', 'DNK load'], dtype='object', name='name')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['PRT-DNK'], dtype='object', name='name')
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 8/8 [00:00<00:00, 67.95it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 455.28it/s]
INFO:linopy.io: Writing time: 0.14s
Set parameter Username
INFO:gurobipy:Set parameter Username
Set parameter LicenseID to value 2767832
INFO:gurobipy:Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20
INFO:gurobipy:Academic license - for non-commercial use only - expires 2027-01-20
Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-4qvcgk0n.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-4qvcgk0n.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 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
INFO:gurobipy:Gurobi Optimizer version 13.0.0 build v13.0.0rc1 (mac64[arm] - Darwin 25.3.0 25D2128)
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 (Min)
INFO:gurobipy:Optimize a model with 140168 rows, 61327 columns and 271592 nonzeros (Min)
Model fingerprint: 0xcf8c11b5
INFO:gurobipy:Model fingerprint: 0xcf8c11b5
Model has 52567 linear objective coefficients
INFO:gurobipy:Model has 52567 linear objective coefficients
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: 0.16s
INFO:gurobipy:Presolve time: 0.16s
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 1.34e+06 9.60e-10 4.79e+05 0s
INFO:gurobipy: 4 4.80401967e+10 -2.02946431e+10 1.34e+06 9.60e-10 4.79e+05 0s
5 3.30337282e+10 -1.48679559e+10 8.49e+05 6.98e-10 3.32e+05 0s
INFO:gurobipy: 5 3.30337282e+10 -1.48679559e+10 8.49e+05 6.98e-10 3.32e+05 0s
6 2.62029598e+10 -1.03994074e+10 6.29e+05 6.11e-10 2.52e+05 0s
INFO:gurobipy: 6 2.62029598e+10 -1.03994074e+10 6.29e+05 6.11e-10 2.52e+05 0s
7 1.86494975e+10 -4.85299148e+09 3.91e+05 2.62e-10 1.61e+05 0s
INFO:gurobipy: 7 1.86494975e+10 -4.85299148e+09 3.91e+05 2.62e-10 1.61e+05 0s
8 1.45438364e+10 -1.29932145e+09 2.70e+05 3.06e-10 1.08e+05 0s
INFO:gurobipy: 8 1.45438364e+10 -1.29932145e+09 2.70e+05 3.06e-10 1.08e+05 0s
9 1.38103617e+10 -7.49157545e+08 2.46e+05 4.95e-10 9.93e+04 0s
INFO:gurobipy: 9 1.38103617e+10 -7.49157545e+08 2.46e+05 4.95e-10 9.93e+04 0s
10 1.32724454e+10 4.39294294e+08 2.26e+05 6.11e-10 8.75e+04 0s
INFO:gurobipy: 10 1.32724454e+10 4.39294294e+08 2.26e+05 6.11e-10 8.75e+04 0s
11 1.12681179e+10 2.45514877e+09 1.63e+05 9.46e-11 6.00e+04 0s
INFO:gurobipy: 11 1.12681179e+10 2.45514877e+09 1.63e+05 9.46e-11 6.00e+04 0s
12 1.09140516e+10 2.92356088e+09 1.52e+05 4.07e-10 5.44e+04 0s
INFO:gurobipy: 12 1.09140516e+10 2.92356088e+09 1.52e+05 4.07e-10 5.44e+04 0s
13 1.04382174e+10 3.30912657e+09 1.37e+05 5.53e-10 4.85e+04 1s
INFO:gurobipy: 13 1.04382174e+10 3.30912657e+09 1.37e+05 5.53e-10 4.85e+04 1s
14 1.01625762e+10 3.56596622e+09 1.26e+05 6.40e-10 4.49e+04 1s
INFO:gurobipy: 14 1.01625762e+10 3.56596622e+09 1.26e+05 6.40e-10 4.49e+04 1s
15 9.52948858e+09 4.21270707e+09 1.03e+05 8.44e-10 3.62e+04 1s
INFO:gurobipy: 15 9.52948858e+09 4.21270707e+09 1.03e+05 8.44e-10 3.62e+04 1s
16 9.26362538e+09 4.95394175e+09 9.05e+04 1.75e-10 2.93e+04 1s
INFO:gurobipy: 16 9.26362538e+09 4.95394175e+09 9.05e+04 1.75e-10 2.93e+04 1s
17 9.13196092e+09 5.22918629e+09 8.45e+04 4.95e-10 2.66e+04 1s
INFO:gurobipy: 17 9.13196092e+09 5.22918629e+09 8.45e+04 4.95e-10 2.66e+04 1s
18 8.82313808e+09 5.41896103e+09 6.89e+04 6.55e-10 2.32e+04 1s
INFO:gurobipy: 18 8.82313808e+09 5.41896103e+09 6.89e+04 6.55e-10 2.32e+04 1s
19 8.65924562e+09 5.55432626e+09 5.89e+04 8.73e-11 2.11e+04 1s
INFO:gurobipy: 19 8.65924562e+09 5.55432626e+09 5.89e+04 8.73e-11 2.11e+04 1s
20 8.49397810e+09 6.07105532e+09 4.90e+04 7.86e-10 1.65e+04 1s
INFO:gurobipy: 20 8.49397810e+09 6.07105532e+09 4.90e+04 7.86e-10 1.65e+04 1s
21 8.40323974e+09 6.20150879e+09 4.40e+04 1.54e-09 1.50e+04 1s
INFO:gurobipy: 21 8.40323974e+09 6.20150879e+09 4.40e+04 1.54e-09 1.50e+04 1s
22 8.30222493e+09 6.31498984e+09 3.84e+04 5.24e-10 1.35e+04 1s
INFO:gurobipy: 22 8.30222493e+09 6.31498984e+09 3.84e+04 5.24e-10 1.35e+04 1s
23 8.26649916e+09 6.38087684e+09 3.49e+04 2.91e-10 1.28e+04 1s
INFO:gurobipy: 23 8.26649916e+09 6.38087684e+09 3.49e+04 2.91e-10 1.28e+04 1s
24 8.22390988e+09 6.54457323e+09 3.22e+04 4.95e-10 1.14e+04 1s
INFO:gurobipy: 24 8.22390988e+09 6.54457323e+09 3.22e+04 4.95e-10 1.14e+04 1s
25 8.17599646e+09 6.64143869e+09 2.89e+04 2.33e-10 1.04e+04 1s
INFO:gurobipy: 25 8.17599646e+09 6.64143869e+09 2.89e+04 2.33e-10 1.04e+04 1s
26 8.15739438e+09 6.76253791e+09 2.77e+04 3.49e-10 9.48e+03 1s
INFO:gurobipy: 26 8.15739438e+09 6.76253791e+09 2.77e+04 3.49e-10 9.48e+03 1s
27 8.08927947e+09 6.86831869e+09 2.29e+04 6.40e-10 8.30e+03 1s
INFO:gurobipy: 27 8.08927947e+09 6.86831869e+09 2.29e+04 6.40e-10 8.30e+03 1s
28 8.06594186e+09 6.92560759e+09 2.11e+04 6.69e-10 7.75e+03 1s
INFO:gurobipy: 28 8.06594186e+09 6.92560759e+09 2.11e+04 6.69e-10 7.75e+03 1s
29 8.03682206e+09 7.00890060e+09 1.87e+04 4.00e-11 6.98e+03 1s
INFO:gurobipy: 29 8.03682206e+09 7.00890060e+09 1.87e+04 4.00e-11 6.98e+03 1s
30 8.01985692e+09 7.05543159e+09 1.64e+04 6.69e-10 6.55e+03 1s
INFO:gurobipy: 30 8.01985692e+09 7.05543159e+09 1.64e+04 6.69e-10 6.55e+03 1s
31 7.98958400e+09 7.12347378e+09 1.28e+04 2.33e-10 5.87e+03 1s
INFO:gurobipy: 31 7.98958400e+09 7.12347378e+09 1.28e+04 2.33e-10 5.87e+03 1s
32 7.95874226e+09 7.23703268e+09 9.59e+03 3.78e-10 4.89e+03 1s
INFO:gurobipy: 32 7.95874226e+09 7.23703268e+09 9.59e+03 3.78e-10 4.89e+03 1s
33 7.94493370e+09 7.30566827e+09 8.53e+03 8.73e-11 4.33e+03 1s
INFO:gurobipy: 33 7.94493370e+09 7.30566827e+09 8.53e+03 8.73e-11 4.33e+03 1s
34 7.93608045e+09 7.34715634e+09 7.90e+03 1.31e-10 3.99e+03 1s
INFO:gurobipy: 34 7.93608045e+09 7.34715634e+09 7.90e+03 1.31e-10 3.99e+03 1s
35 7.93262336e+09 7.36521865e+09 7.62e+03 2.33e-10 3.84e+03 1s
INFO:gurobipy: 35 7.93262336e+09 7.36521865e+09 7.62e+03 2.33e-10 3.84e+03 1s
36 7.92080197e+09 7.44399114e+09 6.61e+03 7.28e-10 3.23e+03 1s
INFO:gurobipy: 36 7.92080197e+09 7.44399114e+09 6.61e+03 7.28e-10 3.23e+03 1s
37 7.91375483e+09 7.49836500e+09 6.02e+03 2.33e-10 2.82e+03 1s
INFO:gurobipy: 37 7.91375483e+09 7.49836500e+09 6.02e+03 2.33e-10 2.82e+03 1s
38 7.90702839e+09 7.52027521e+09 5.44e+03 8.44e-10 2.62e+03 1s
INFO:gurobipy: 38 7.90702839e+09 7.52027521e+09 5.44e+03 8.44e-10 2.62e+03 1s
39 7.89625971e+09 7.53904197e+09 4.37e+03 2.04e-10 2.42e+03 1s
INFO:gurobipy: 39 7.89625971e+09 7.53904197e+09 4.37e+03 2.04e-10 2.42e+03 1s
40 7.89085593e+09 7.56984622e+09 3.79e+03 3.20e-10 2.17e+03 1s
INFO:gurobipy: 40 7.89085593e+09 7.56984622e+09 3.79e+03 3.20e-10 2.17e+03 1s
41 7.88092023e+09 7.59964684e+09 2.72e+03 1.16e-10 1.90e+03 1s
INFO:gurobipy: 41 7.88092023e+09 7.59964684e+09 2.72e+03 1.16e-10 1.90e+03 1s
42 7.87711253e+09 7.61843549e+09 2.40e+03 2.91e-10 1.75e+03 1s
INFO:gurobipy: 42 7.87711253e+09 7.61843549e+09 2.40e+03 2.91e-10 1.75e+03 1s
43 7.87498033e+09 7.63676267e+09 2.15e+03 3.78e-10 1.61e+03 1s
INFO:gurobipy: 43 7.87498033e+09 7.63676267e+09 2.15e+03 3.78e-10 1.61e+03 1s
44 7.86927998e+09 7.67163453e+09 1.70e+03 3.78e-10 1.33e+03 1s
INFO:gurobipy: 44 7.86927998e+09 7.67163453e+09 1.70e+03 3.78e-10 1.33e+03 1s
45 7.86490384e+09 7.68662082e+09 1.23e+03 1.75e-10 1.20e+03 1s
INFO:gurobipy: 45 7.86490384e+09 7.68662082e+09 1.23e+03 1.75e-10 1.20e+03 1s
46 7.86219547e+09 7.71679392e+09 1.00e+03 6.40e-10 9.81e+02 1s
INFO:gurobipy: 46 7.86219547e+09 7.71679392e+09 1.00e+03 6.40e-10 9.81e+02 1s
47 7.86008375e+09 7.73031407e+09 8.45e+02 3.78e-10 8.75e+02 1s
INFO:gurobipy: 47 7.86008375e+09 7.73031407e+09 8.45e+02 3.78e-10 8.75e+02 1s
48 7.85887615e+09 7.73397533e+09 7.59e+02 4.37e-10 8.42e+02 1s
INFO:gurobipy: 48 7.85887615e+09 7.73397533e+09 7.59e+02 4.37e-10 8.42e+02 1s
49 7.85691075e+09 7.74654850e+09 5.99e+02 3.78e-10 7.44e+02 1s
INFO:gurobipy: 49 7.85691075e+09 7.74654850e+09 5.99e+02 3.78e-10 7.44e+02 1s
50 7.85667993e+09 7.75186239e+09 5.81e+02 7.28e-10 7.07e+02 1s
INFO:gurobipy: 50 7.85667993e+09 7.75186239e+09 5.81e+02 7.28e-10 7.07e+02 1s
51 7.85562967e+09 7.76259402e+09 5.07e+02 4.95e-10 6.27e+02 1s
INFO:gurobipy: 51 7.85562967e+09 7.76259402e+09 5.07e+02 4.95e-10 6.27e+02 1s
52 7.85475612e+09 7.76992715e+09 4.47e+02 9.28e-10 5.72e+02 1s
INFO:gurobipy: 52 7.85475612e+09 7.76992715e+09 4.47e+02 9.28e-10 5.72e+02 1s
53 7.85409753e+09 7.77270987e+09 3.97e+02 1.38e-09 5.49e+02 1s
INFO:gurobipy: 53 7.85409753e+09 7.77270987e+09 3.97e+02 1.38e-09 5.49e+02 1s
54 7.85330524e+09 7.77657650e+09 3.38e+02 1.82e-09 5.17e+02 1s
INFO:gurobipy: 54 7.85330524e+09 7.77657650e+09 3.38e+02 1.82e-09 5.17e+02 1s
55 7.85261938e+09 7.78129618e+09 2.92e+02 4.36e-09 4.80e+02 1s
INFO:gurobipy: 55 7.85261938e+09 7.78129618e+09 2.92e+02 4.36e-09 4.80e+02 1s
56 7.85141038e+09 7.78812469e+09 1.94e+02 3.71e-09 4.26e+02 1s
INFO:gurobipy: 56 7.85141038e+09 7.78812469e+09 1.94e+02 3.71e-09 4.26e+02 1s
57 7.85125030e+09 7.79393338e+09 1.82e+02 5.66e-09 3.86e+02 1s
INFO:gurobipy: 57 7.85125030e+09 7.79393338e+09 1.82e+02 5.66e-09 3.86e+02 1s
58 7.85046873e+09 7.79784536e+09 1.43e+02 7.44e-09 3.54e+02 1s
INFO:gurobipy: 58 7.85046873e+09 7.79784536e+09 1.43e+02 7.44e-09 3.54e+02 1s
59 7.85010575e+09 7.80210811e+09 1.24e+02 8.75e-09 3.23e+02 1s
INFO:gurobipy: 59 7.85010575e+09 7.80210811e+09 1.24e+02 8.75e-09 3.23e+02 1s
60 7.84935326e+09 7.80621305e+09 7.91e+01 8.63e-09 2.90e+02 1s
INFO:gurobipy: 60 7.84935326e+09 7.80621305e+09 7.91e+01 8.63e-09 2.90e+02 1s
61 7.84912298e+09 7.81141873e+09 7.26e+01 1.34e-08 2.54e+02 1s
INFO:gurobipy: 61 7.84912298e+09 7.81141873e+09 7.26e+01 1.34e-08 2.54e+02 1s
62 7.84897276e+09 7.81829320e+09 5.81e+01 1.42e-08 2.06e+02 1s
INFO:gurobipy: 62 7.84897276e+09 7.81829320e+09 5.81e+01 1.42e-08 2.06e+02 1s
63 7.84794091e+09 7.82103224e+09 4.92e+00 1.46e-08 1.81e+02 1s
INFO:gurobipy: 63 7.84794091e+09 7.82103224e+09 4.92e+00 1.46e-08 1.81e+02 1s
64 7.84782990e+09 7.82235752e+09 4.08e+00 1.41e-08 1.71e+02 1s
INFO:gurobipy: 64 7.84782990e+09 7.82235752e+09 4.08e+00 1.41e-08 1.71e+02 1s
65 7.84756191e+09 7.82624525e+09 6.60e-01 1.12e-08 1.43e+02 1s
INFO:gurobipy: 65 7.84756191e+09 7.82624525e+09 6.60e-01 1.12e-08 1.43e+02 1s
66 7.84747160e+09 7.82787978e+09 5.39e-01 1.10e-08 1.32e+02 1s
INFO:gurobipy: 66 7.84747160e+09 7.82787978e+09 5.39e-01 1.10e-08 1.32e+02 1s
67 7.84741751e+09 7.82872468e+09 4.72e-01 1.06e-08 1.26e+02 1s
INFO:gurobipy: 67 7.84741751e+09 7.82872468e+09 4.72e-01 1.06e-08 1.26e+02 1s
68 7.84741248e+09 7.82932813e+09 4.39e-01 1.07e-08 1.22e+02 2s
INFO:gurobipy: 68 7.84741248e+09 7.82932813e+09 4.39e-01 1.07e-08 1.22e+02 2s
69 7.84739946e+09 7.83122560e+09 3.81e-01 9.40e-09 1.09e+02 2s
INFO:gurobipy: 69 7.84739946e+09 7.83122560e+09 3.81e-01 9.40e-09 1.09e+02 2s
70 7.84735700e+09 7.83188437e+09 3.45e-01 9.50e-09 1.04e+02 2s
INFO:gurobipy: 70 7.84735700e+09 7.83188437e+09 3.45e-01 9.50e-09 1.04e+02 2s
71 7.84733047e+09 7.83470298e+09 2.75e-01 7.48e-09 8.49e+01 2s
INFO:gurobipy: 71 7.84733047e+09 7.83470298e+09 2.75e-01 7.48e-09 8.49e+01 2s
72 7.84732820e+09 7.83927511e+09 2.08e-01 5.96e-09 5.41e+01 2s
INFO:gurobipy: 72 7.84732820e+09 7.83927511e+09 2.08e-01 5.96e-09 5.41e+01 2s
73 7.84722252e+09 7.84004495e+09 7.40e-02 5.18e-09 4.82e+01 2s
INFO:gurobipy: 73 7.84722252e+09 7.84004495e+09 7.40e-02 5.18e-09 4.82e+01 2s
74 7.84720150e+09 7.84365462e+09 5.92e-02 2.41e-09 2.38e+01 2s
INFO:gurobipy: 74 7.84720150e+09 7.84365462e+09 5.92e-02 2.41e-09 2.38e+01 2s
75 7.84717043e+09 7.84399030e+09 3.26e-02 2.48e-09 2.14e+01 2s
INFO:gurobipy: 75 7.84717043e+09 7.84399030e+09 3.26e-02 2.48e-09 2.14e+01 2s
76 7.84715457e+09 7.84462755e+09 2.50e-02 1.95e-09 1.70e+01 2s
INFO:gurobipy: 76 7.84715457e+09 7.84462755e+09 2.50e-02 1.95e-09 1.70e+01 2s
77 7.84715302e+09 7.84512416e+09 2.43e-02 2.01e-09 1.36e+01 2s
INFO:gurobipy: 77 7.84715302e+09 7.84512416e+09 2.43e-02 2.01e-09 1.36e+01 2s
78 7.84714586e+09 7.84550866e+09 2.10e-02 1.25e-09 1.10e+01 2s
INFO:gurobipy: 78 7.84714586e+09 7.84550866e+09 2.10e-02 1.25e-09 1.10e+01 2s
79 7.84711442e+09 7.84581456e+09 5.00e-04 9.31e-10 8.74e+00 2s
INFO:gurobipy: 79 7.84711442e+09 7.84581456e+09 5.00e-04 9.31e-10 8.74e+00 2s
80 7.84709546e+09 7.84706359e+09 3.13e-05 1.89e-10 2.14e-01 2s
INFO:gurobipy: 80 7.84709546e+09 7.84706359e+09 3.13e-05 1.89e-10 2.14e-01 2s
81 7.84709147e+09 7.84709123e+09 2.78e-07 7.86e-10 1.60e-03 2s
INFO:gurobipy: 81 7.84709147e+09 7.84709123e+09 2.78e-07 7.86e-10 1.60e-03 2s
82 7.84709142e+09 7.84709142e+09 2.19e-07 9.81e-09 6.73e-09 2s
INFO:gurobipy: 82 7.84709142e+09 7.84709142e+09 2.19e-07 9.81e-09 6.73e-09 2s
INFO:gurobipy:
Barrier solved model in 82 iterations and 1.75 seconds (2.31 work units)
INFO:gurobipy:Barrier solved model in 82 iterations and 1.75 seconds (2.31 work units)
Optimal objective 7.84709142e+09
INFO:gurobipy:Optimal objective 7.84709142e+09
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
52 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy: 52 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:
8572 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 8572 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 2.2241642e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 2.2241642e-09 2s
INFO:gurobipy:
Crossover time: 0.34 seconds (1.28 work units)
INFO:gurobipy:Crossover time: 0.34 seconds (1.28 work units)
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
8627 7.8470914e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy: 8627 7.8470914e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy:
Solved in 8627 iterations and 2.13 seconds (3.69 work units)
INFO:gurobipy:Solved in 8627 iterations and 2.13 seconds (3.69 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
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.
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: >
