Problem 10.1#
Problem 10.1. Capacity and dispatch optimization in a network.
We build on the models described in Problems 3 and 9, however we add Denmark as a second node. Optimize the capacity and dispatch of solar PV, onshore wind, and Open Cycle Gas Turbine (OCGT) generators to supply the inelastic electricity demand throughout one year. To do this, take the time series for the wind and solar capacity factors for Portugal and Denmark in 2015 obtained from https://zenodo.org/record/3253876#.XSiVOEdS8l0 and https://zenodo.org/record/2613651#.X0kbhDVS-uV (select the file ‘pvoptimal.csv’) and the electricity demand from martavp/integrated-energy-grids. Assume that methane gas emits 0.198 tCO2 per MWh of thermal energy contained in the gas. We assume the distance between the two nodes is 2477 km, the distance between Copenhagen and Lisbon.
For all of the following subproblems, 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)
Total CO2 emissions (in MtCO2)
a) Set up a network with two nodes and connect them with an overhead AC line (however, keep the capacity at 0 GW, and it cannot be extended).
b) Now assume the AC line connecting Portugal and Denmark has a capacity of 1 GW.
c) Now assume the AC line connecting Portugal and Denmark has a capacity of 10 GW.
d) Optimise the AC line capacity endogenously (assume it starts at 0 GW capacity).
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. Capacity and dispatch optimisation in a network, F = 0 GW#
For building the model, we start again by initialising an empty network, adding the snapshots, and the electricity buses per country.
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.
# 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")
Add generators to the buses.
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,
)
Add an overhead AC line between the buses with 0 MW capacity.
n.add(
"Line",
"PRT-DNK",
bus0="PRT",
bus1="DNK",
s_nom = 0,
x = 1,
r = 1,
)
n.plot(bus_sizes=1, margin=1)
{'nodes': {'Bus': <matplotlib.collections.PatchCollection at 0x32c454550>},
'branches': {'Line': <matplotlib.collections.LineCollection at 0x32c454690>},
'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%|██████████| 6/6 [00:00<00:00, 38.87it/s]
Writing continuous variables.: 100%|██████████| 3/3 [00:00<00:00, 331.85it/s]
INFO:linopy.io: Writing time: 0.37s
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-jl6xrpb2.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-jl6xrpb2.lp
Reading time = 0.13 seconds
INFO:gurobipy:Reading time = 0.13 seconds
obj: 140166 rows, 61326 columns, 236551 nonzeros
INFO:gurobipy:obj: 140166 rows, 61326 columns, 236551 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 140166 rows, 61326 columns and 236551 nonzeros (Min)
INFO:gurobipy:Optimize a model with 140166 rows, 61326 columns and 236551 nonzeros (Min)
Model fingerprint: 0x2610728d
INFO:gurobipy:Model fingerprint: 0x2610728d
Model has 52566 linear objective coefficients
INFO:gurobipy:Model has 52566 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, 9e+03]
INFO:gurobipy: RHS range [2e+03, 9e+03]
Presolve removed 87556 rows and 26230 columns
INFO:gurobipy:Presolve removed 87556 rows and 26230 columns
Presolve time: 0.07s
INFO:gurobipy:Presolve time: 0.07s
Presolved: 52610 rows, 35096 columns, 114005 nonzeros
INFO:gurobipy:Presolved: 52610 rows, 35096 columns, 114005 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: 0.00s
INFO:gurobipy:Ordering time: 0.00s
INFO:gurobipy:
Barrier statistics:
INFO:gurobipy:Barrier statistics:
Dense cols : 6
INFO:gurobipy: Dense cols : 6
AA' NZ : 7.892e+04
INFO:gurobipy: AA' NZ : 7.892e+04
Factor NZ : 2.544e+05 (roughly 40 MB of memory)
INFO:gurobipy: Factor NZ : 2.544e+05 (roughly 40 MB of memory)
Factor Ops : 1.325e+06 (less than 1 second per iteration)
INFO:gurobipy: Factor Ops : 1.325e+06 (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 5.46588478e+10 -3.70662960e+11 1.16e+05 2.03e-13 1.53e+08 0s
INFO:gurobipy: 0 5.46588478e+10 -3.70662960e+11 1.16e+05 2.03e-13 1.53e+08 0s
1 1.00173309e+11 -4.81775490e+11 1.43e+04 6.38e+02 2.77e+07 0s
INFO:gurobipy: 1 1.00173309e+11 -4.81775490e+11 1.43e+04 6.38e+02 2.77e+07 0s
2 9.16553033e+10 -1.97469164e+11 5.68e-10 1.21e+00 2.58e+06 0s
INFO:gurobipy: 2 9.16553033e+10 -1.97469164e+11 5.68e-10 1.21e+00 2.58e+06 0s
3 1.94386009e+10 -1.92838349e+10 6.55e-11 1.22e-09 3.41e+05 0s
INFO:gurobipy: 3 1.94386009e+10 -1.92838349e+10 6.55e-11 1.22e-09 3.41e+05 0s
4 9.84672045e+09 -5.33198343e+09 1.86e-11 7.86e-10 1.33e+05 0s
INFO:gurobipy: 4 9.84672045e+09 -5.33198343e+09 1.86e-11 7.86e-10 1.33e+05 0s
5 8.59508822e+09 -7.62629932e+08 1.46e-11 5.82e-10 8.22e+04 0s
INFO:gurobipy: 5 8.59508822e+09 -7.62629932e+08 1.46e-11 5.82e-10 8.22e+04 0s
6 7.64223940e+09 1.51736846e+09 7.31e-10 5.82e-10 5.38e+04 0s
INFO:gurobipy: 6 7.64223940e+09 1.51736846e+09 7.31e-10 5.82e-10 5.38e+04 0s
7 6.54100664e+09 2.94577551e+09 3.64e-10 1.46e-10 3.16e+04 0s
INFO:gurobipy: 7 6.54100664e+09 2.94577551e+09 3.64e-10 1.46e-10 3.16e+04 0s
8 5.93920735e+09 3.69895466e+09 2.56e-10 2.62e-10 1.97e+04 0s
INFO:gurobipy: 8 5.93920735e+09 3.69895466e+09 2.56e-10 2.62e-10 1.97e+04 0s
9 5.66701376e+09 4.57644617e+09 1.78e-10 1.46e-10 9.57e+03 0s
INFO:gurobipy: 9 5.66701376e+09 4.57644617e+09 1.78e-10 1.46e-10 9.57e+03 0s
10 5.50945025e+09 4.85752354e+09 3.57e-10 3.20e-10 5.72e+03 0s
INFO:gurobipy: 10 5.50945025e+09 4.85752354e+09 3.57e-10 3.20e-10 5.72e+03 0s
11 5.40620944e+09 4.98268432e+09 5.02e-10 7.28e-10 3.72e+03 0s
INFO:gurobipy: 11 5.40620944e+09 4.98268432e+09 5.02e-10 7.28e-10 3.72e+03 0s
12 5.35580066e+09 5.00777396e+09 1.08e-09 6.11e-10 3.05e+03 0s
INFO:gurobipy: 12 5.35580066e+09 5.00777396e+09 1.08e-09 6.11e-10 3.05e+03 0s
13 5.33709085e+09 5.03544563e+09 1.41e-09 1.25e-09 2.65e+03 0s
INFO:gurobipy: 13 5.33709085e+09 5.03544563e+09 1.41e-09 1.25e-09 2.65e+03 0s
14 5.30901486e+09 5.06530513e+09 1.18e-09 3.20e-10 2.14e+03 0s
INFO:gurobipy: 14 5.30901486e+09 5.06530513e+09 1.18e-09 3.20e-10 2.14e+03 0s
15 5.25487020e+09 5.08419974e+09 7.79e-10 4.07e-10 1.50e+03 0s
INFO:gurobipy: 15 5.25487020e+09 5.08419974e+09 7.79e-10 4.07e-10 1.50e+03 0s
16 5.22365376e+09 5.12498354e+09 8.97e-10 8.44e-10 8.66e+02 0s
INFO:gurobipy: 16 5.22365376e+09 5.12498354e+09 8.97e-10 8.44e-10 8.66e+02 0s
17 5.21148387e+09 5.12887466e+09 6.69e-10 4.07e-10 7.25e+02 0s
INFO:gurobipy: 17 5.21148387e+09 5.12887466e+09 6.69e-10 4.07e-10 7.25e+02 0s
18 5.19905794e+09 5.13388242e+09 2.95e-09 7.28e-10 5.72e+02 0s
INFO:gurobipy: 18 5.19905794e+09 5.13388242e+09 2.95e-09 7.28e-10 5.72e+02 0s
19 5.19204502e+09 5.14006580e+09 2.32e-09 1.75e-10 4.56e+02 0s
INFO:gurobipy: 19 5.19204502e+09 5.14006580e+09 2.32e-09 1.75e-10 4.56e+02 0s
20 5.18227131e+09 5.14874185e+09 2.49e-09 2.33e-10 2.94e+02 0s
INFO:gurobipy: 20 5.18227131e+09 5.14874185e+09 2.49e-09 2.33e-10 2.94e+02 0s
21 5.17815390e+09 5.15693791e+09 2.13e-09 6.11e-10 1.86e+02 0s
INFO:gurobipy: 21 5.17815390e+09 5.15693791e+09 2.13e-09 6.11e-10 1.86e+02 0s
22 5.17620616e+09 5.15824492e+09 1.85e-09 2.62e-10 1.58e+02 0s
INFO:gurobipy: 22 5.17620616e+09 5.15824492e+09 1.85e-09 2.62e-10 1.58e+02 0s
23 5.17359874e+09 5.16016182e+09 4.01e-09 2.33e-10 1.18e+02 0s
INFO:gurobipy: 23 5.17359874e+09 5.16016182e+09 4.01e-09 2.33e-10 1.18e+02 0s
24 5.17267149e+09 5.16362224e+09 2.55e-09 4.95e-10 7.94e+01 0s
INFO:gurobipy: 24 5.17267149e+09 5.16362224e+09 2.55e-09 4.95e-10 7.94e+01 0s
25 5.17184861e+09 5.16517941e+09 3.13e-09 6.40e-10 5.85e+01 0s
INFO:gurobipy: 25 5.17184861e+09 5.16517941e+09 3.13e-09 6.40e-10 5.85e+01 0s
26 5.17127805e+09 5.16559370e+09 4.23e-09 1.05e-09 4.99e+01 1s
INFO:gurobipy: 26 5.17127805e+09 5.16559370e+09 4.23e-09 1.05e-09 4.99e+01 1s
27 5.17056184e+09 5.16635355e+09 1.77e-08 4.07e-10 3.69e+01 1s
INFO:gurobipy: 27 5.17056184e+09 5.16635355e+09 1.77e-08 4.07e-10 3.69e+01 1s
28 5.17025817e+09 5.16730735e+09 2.15e-08 3.78e-10 2.59e+01 1s
INFO:gurobipy: 28 5.17025817e+09 5.16730735e+09 2.15e-08 3.78e-10 2.59e+01 1s
29 5.17010663e+09 5.16790043e+09 1.36e-08 3.78e-10 1.94e+01 1s
INFO:gurobipy: 29 5.17010663e+09 5.16790043e+09 1.36e-08 3.78e-10 1.94e+01 1s
30 5.17001154e+09 5.16801237e+09 1.13e-08 1.19e-09 1.75e+01 1s
INFO:gurobipy: 30 5.17001154e+09 5.16801237e+09 1.13e-08 1.19e-09 1.75e+01 1s
31 5.16989172e+09 5.16836397e+09 9.36e-09 5.09e-11 1.34e+01 1s
INFO:gurobipy: 31 5.16989172e+09 5.16836397e+09 9.36e-09 5.09e-11 1.34e+01 1s
32 5.16979485e+09 5.16863584e+09 6.59e-08 4.66e-10 1.02e+01 1s
INFO:gurobipy: 32 5.16979485e+09 5.16863584e+09 6.59e-08 4.66e-10 1.02e+01 1s
33 5.16967184e+09 5.16884093e+09 4.48e-08 1.19e-09 7.29e+00 1s
INFO:gurobipy: 33 5.16967184e+09 5.16884093e+09 4.48e-08 1.19e-09 7.29e+00 1s
34 5.16958491e+09 5.16905182e+09 3.07e-08 6.40e-10 4.68e+00 1s
INFO:gurobipy: 34 5.16958491e+09 5.16905182e+09 3.07e-08 6.40e-10 4.68e+00 1s
35 5.16954503e+09 5.16926968e+09 1.07e-07 8.73e-10 2.42e+00 1s
INFO:gurobipy: 35 5.16954503e+09 5.16926968e+09 1.07e-07 8.73e-10 2.42e+00 1s
36 5.16953946e+09 5.16928524e+09 2.36e-07 6.11e-10 2.23e+00 1s
INFO:gurobipy: 36 5.16953946e+09 5.16928524e+09 2.36e-07 6.11e-10 2.23e+00 1s
37 5.16951416e+09 5.16938251e+09 2.02e-07 7.57e-10 1.16e+00 1s
INFO:gurobipy: 37 5.16951416e+09 5.16938251e+09 2.02e-07 7.57e-10 1.16e+00 1s
38 5.16949557e+09 5.16946137e+09 1.40e-07 1.66e-09 3.00e-01 1s
INFO:gurobipy: 38 5.16949557e+09 5.16946137e+09 1.40e-07 1.66e-09 3.00e-01 1s
39 5.16948777e+09 5.16947239e+09 3.91e-07 7.57e-10 1.35e-01 1s
INFO:gurobipy: 39 5.16948777e+09 5.16947239e+09 3.91e-07 7.57e-10 1.35e-01 1s
40 5.16948404e+09 5.16947345e+09 2.70e-07 4.07e-10 9.29e-02 1s
INFO:gurobipy: 40 5.16948404e+09 5.16947345e+09 2.70e-07 4.07e-10 9.29e-02 1s
41 5.16947621e+09 5.16947534e+09 1.19e-08 4.07e-10 7.65e-03 1s
INFO:gurobipy: 41 5.16947621e+09 5.16947534e+09 1.19e-08 4.07e-10 7.65e-03 1s
42 5.16947582e+09 5.16947582e+09 2.36e-10 2.27e-09 4.25e-05 1s
INFO:gurobipy: 42 5.16947582e+09 5.16947582e+09 2.36e-10 2.27e-09 4.25e-05 1s
43 5.16947582e+09 5.16947582e+09 7.37e-11 1.48e-09 1.35e-10 1s
INFO:gurobipy: 43 5.16947582e+09 5.16947582e+09 7.37e-11 1.48e-09 1.35e-10 1s
INFO:gurobipy:
Barrier solved model in 43 iterations and 0.92 seconds (0.81 work units)
INFO:gurobipy:Barrier solved model in 43 iterations and 0.92 seconds (0.81 work units)
Optimal objective 5.16947582e+09
INFO:gurobipy:Optimal objective 5.16947582e+09
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
35 DPushes remaining with DInf 0.0000000e+00 1s
INFO:gurobipy: 35 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:
1 PPushes remaining with PInf 0.0000000e+00 1s
INFO:gurobipy: 1 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 1.1724562e-09 1s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.1724562e-09 1s
INFO:gurobipy:
Crossover time: 0.07 seconds (0.03 work units)
INFO:gurobipy:Crossover time: 0.07 seconds (0.03 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
39 5.1694758e+09 0.000000e+00 0.000000e+00 1s
INFO:gurobipy: 39 5.1694758e+09 0.000000e+00 0.000000e+00 1s
INFO:gurobipy:
Solved in 39 iterations and 1.05 seconds (0.89 work units)
INFO:gurobipy:Solved in 39 iterations and 1.05 seconds (0.89 work units)
Optimal objective 5.169475822e+09
INFO:gurobipy:Optimal objective 5.169475822e+09
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 61326 primals, 140166 duals
Objective: 5.17e+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-fix-s-lower, Line-fix-s-upper were not assigned to the network.
('ok', 'optimal')
# Total system costs
n.objective/1e9
5.169475822317724
# Average electricity price
n.buses_t.marginal_price.mean()
name
PRT 61.105150
DNK 59.640202
dtype: float64
# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()
name
PRT 1244
DNK 1452
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 0.142009
DNK 0.165753
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(0.0)
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK NaN
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 16.0
onwind 15.2
solar 1.6
PRT OCGT 27.0
onwind 9.4
solar 12.5
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(20729628.597112704)
b. F = 1 GW#
Repeat the same procedure as in a.
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,
)
Add the overhead AC line between the buses with 1 GW capacity.
n.add(
"Line",
"PRT-DNK",
bus0="PRT",
bus1="DNK",
s_nom = 1000,
x = 1,
r = 1,
)
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%|██████████| 6/6 [00:00<00:00, 22.84it/s]
Writing continuous variables.: 100%|██████████| 3/3 [00:00<00:00, 76.11it/s]
INFO:linopy.io: Writing time: 0.33s
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-avv5tqyp.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-avv5tqyp.lp
Reading time = 0.19 seconds
INFO:gurobipy:Reading time = 0.19 seconds
obj: 140166 rows, 61326 columns, 236551 nonzeros
INFO:gurobipy:obj: 140166 rows, 61326 columns, 236551 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 140166 rows, 61326 columns and 236551 nonzeros (Min)
INFO:gurobipy:Optimize a model with 140166 rows, 61326 columns and 236551 nonzeros (Min)
Model fingerprint: 0xa670afd8
INFO:gurobipy:Model fingerprint: 0xa670afd8
Model has 52566 linear objective coefficients
INFO:gurobipy:Model has 52566 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, 9e+03]
INFO:gurobipy: RHS range [1e+03, 9e+03]
Presolve removed 78821 rows and 8735 columns
INFO:gurobipy:Presolve removed 78821 rows and 8735 columns
Presolve time: 0.12s
INFO:gurobipy:Presolve time: 0.12s
Presolved: 61345 rows, 52591 columns, 148995 nonzeros
INFO:gurobipy:Presolved: 61345 rows, 52591 columns, 148995 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: 0.02s
INFO:gurobipy:Ordering time: 0.02s
INFO:gurobipy:
Barrier statistics:
INFO:gurobipy:Barrier statistics:
Dense cols : 6
INFO:gurobipy: Dense cols : 6
AA' NZ : 9.641e+04
INFO:gurobipy: AA' NZ : 9.641e+04
Factor NZ : 5.642e+05 (roughly 50 MB of memory)
INFO:gurobipy: Factor NZ : 5.642e+05 (roughly 50 MB of memory)
Factor Ops : 5.571e+06 (less than 1 second per iteration)
INFO:gurobipy: Factor Ops : 5.571e+06 (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 3.69032254e+10 -4.67469621e+10 4.54e+04 0.00e+00 1.66e+07 0s
INFO:gurobipy: 0 3.69032254e+10 -4.67469621e+10 4.54e+04 0.00e+00 1.66e+07 0s
1 4.09409335e+10 -1.07093146e+11 3.77e+03 2.18e+02 2.93e+06 0s
INFO:gurobipy: 1 4.09409335e+10 -1.07093146e+11 3.77e+03 2.18e+02 2.93e+06 0s
2 2.55520931e+10 -1.58805991e+10 3.20e-10 6.24e+00 3.13e+05 0s
INFO:gurobipy: 2 2.55520931e+10 -1.58805991e+10 3.20e-10 6.24e+00 3.13e+05 0s
3 1.16019556e+10 -1.03665148e+09 9.00e-11 6.46e-01 8.96e+04 0s
INFO:gurobipy: 3 1.16019556e+10 -1.03665148e+09 9.00e-11 6.46e-01 8.96e+04 0s
4 9.00074571e+09 6.16011452e+08 6.80e-11 4.69e-01 5.88e+04 0s
INFO:gurobipy: 4 9.00074571e+09 6.16011452e+08 6.80e-11 4.69e-01 5.88e+04 0s
5 7.35858685e+09 1.81084301e+09 4.59e-11 3.96e-01 3.86e+04 1s
INFO:gurobipy: 5 7.35858685e+09 1.81084301e+09 4.59e-11 3.96e-01 3.86e+04 1s
6 6.33968507e+09 2.73795791e+09 5.66e-11 2.52e-01 2.49e+04 1s
INFO:gurobipy: 6 6.33968507e+09 2.73795791e+09 5.66e-11 2.52e-01 2.49e+04 1s
7 6.26202300e+09 3.37798786e+09 6.73e-11 1.64e-01 1.98e+04 1s
INFO:gurobipy: 7 6.26202300e+09 3.37798786e+09 6.73e-11 1.64e-01 1.98e+04 1s
8 6.12060866e+09 3.55572950e+09 3.81e-09 1.65e-01 1.76e+04 1s
INFO:gurobipy: 8 6.12060866e+09 3.55572950e+09 3.81e-09 1.65e-01 1.76e+04 1s
9 5.89133720e+09 3.79679906e+09 8.50e-09 1.05e-01 1.44e+04 1s
INFO:gurobipy: 9 5.89133720e+09 3.79679906e+09 8.50e-09 1.05e-01 1.44e+04 1s
10 5.60340745e+09 4.29175282e+09 7.81e-09 4.50e-02 8.97e+03 1s
INFO:gurobipy: 10 5.60340745e+09 4.29175282e+09 7.81e-09 4.50e-02 8.97e+03 1s
11 5.35550281e+09 4.60362065e+09 1.47e-08 3.69e-02 5.13e+03 1s
INFO:gurobipy: 11 5.35550281e+09 4.60362065e+09 1.47e-08 3.69e-02 5.13e+03 1s
12 5.23979951e+09 4.77826178e+09 3.14e-08 2.19e-02 3.15e+03 1s
INFO:gurobipy: 12 5.23979951e+09 4.77826178e+09 3.14e-08 2.19e-02 3.15e+03 1s
13 5.17411808e+09 4.82657502e+09 4.62e-08 1.75e-02 2.37e+03 1s
INFO:gurobipy: 13 5.17411808e+09 4.82657502e+09 4.62e-08 1.75e-02 2.37e+03 1s
14 5.15205601e+09 4.86292976e+09 4.74e-08 1.39e-02 1.97e+03 1s
INFO:gurobipy: 14 5.15205601e+09 4.86292976e+09 4.74e-08 1.39e-02 1.97e+03 1s
15 5.09132844e+09 4.90014650e+09 4.61e-08 1.02e-02 1.30e+03 1s
INFO:gurobipy: 15 5.09132844e+09 4.90014650e+09 4.61e-08 1.02e-02 1.30e+03 1s
16 5.06117716e+09 4.94880536e+09 7.94e-08 5.16e-03 7.65e+02 1s
INFO:gurobipy: 16 5.06117716e+09 4.94880536e+09 7.94e-08 5.16e-03 7.65e+02 1s
17 5.04329009e+09 4.96517846e+09 7.92e-08 3.58e-03 5.32e+02 1s
INFO:gurobipy: 17 5.04329009e+09 4.96517846e+09 7.92e-08 3.58e-03 5.32e+02 1s
18 5.03113036e+09 4.97129205e+09 1.23e-07 3.00e-03 4.08e+02 1s
INFO:gurobipy: 18 5.03113036e+09 4.97129205e+09 1.23e-07 3.00e-03 4.08e+02 1s
19 5.02135327e+09 4.97741753e+09 1.56e-07 2.42e-03 3.00e+02 1s
INFO:gurobipy: 19 5.02135327e+09 4.97741753e+09 1.56e-07 2.42e-03 3.00e+02 1s
20 5.01660073e+09 4.98155209e+09 1.06e-07 2.04e-03 2.39e+02 1s
INFO:gurobipy: 20 5.01660073e+09 4.98155209e+09 1.06e-07 2.04e-03 2.39e+02 1s
21 5.01139899e+09 4.98435343e+09 2.15e-07 1.77e-03 1.85e+02 1s
INFO:gurobipy: 21 5.01139899e+09 4.98435343e+09 2.15e-07 1.77e-03 1.85e+02 1s
22 5.00931175e+09 4.99006277e+09 2.95e-07 1.24e-03 1.32e+02 1s
INFO:gurobipy: 22 5.00931175e+09 4.99006277e+09 2.95e-07 1.24e-03 1.32e+02 1s
23 5.00805337e+09 4.99128506e+09 2.78e-07 1.13e-03 1.15e+02 1s
INFO:gurobipy: 23 5.00805337e+09 4.99128506e+09 2.78e-07 1.13e-03 1.15e+02 1s
24 5.00706870e+09 4.99231207e+09 2.54e-07 1.03e-03 1.01e+02 1s
INFO:gurobipy: 24 5.00706870e+09 4.99231207e+09 2.54e-07 1.03e-03 1.01e+02 1s
25 5.00649779e+09 4.99317112e+09 2.48e-07 9.48e-04 9.14e+01 1s
INFO:gurobipy: 25 5.00649779e+09 4.99317112e+09 2.48e-07 9.48e-04 9.14e+01 1s
26 5.00573928e+09 4.99580951e+09 2.57e-07 6.94e-04 6.81e+01 1s
INFO:gurobipy: 26 5.00573928e+09 4.99580951e+09 2.57e-07 6.94e-04 6.81e+01 1s
27 5.00533128e+09 4.99638388e+09 4.54e-07 6.40e-04 6.14e+01 1s
INFO:gurobipy: 27 5.00533128e+09 4.99638388e+09 4.54e-07 6.40e-04 6.14e+01 1s
28 5.00510313e+09 4.99657375e+09 3.56e-07 6.22e-04 5.85e+01 1s
INFO:gurobipy: 28 5.00510313e+09 4.99657375e+09 3.56e-07 6.22e-04 5.85e+01 1s
29 5.00479799e+09 4.99696311e+09 3.38e-07 5.83e-04 5.38e+01 1s
INFO:gurobipy: 29 5.00479799e+09 4.99696311e+09 3.38e-07 5.83e-04 5.38e+01 1s
30 5.00462640e+09 4.99731721e+09 4.48e-07 5.49e-04 5.02e+01 1s
INFO:gurobipy: 30 5.00462640e+09 4.99731721e+09 4.48e-07 5.49e-04 5.02e+01 1s
31 5.00448569e+09 4.99751938e+09 3.79e-07 5.30e-04 4.79e+01 1s
INFO:gurobipy: 31 5.00448569e+09 4.99751938e+09 3.79e-07 5.30e-04 4.79e+01 1s
32 5.00426131e+09 4.99785436e+09 2.44e-07 4.97e-04 4.40e+01 2s
INFO:gurobipy: 32 5.00426131e+09 4.99785436e+09 2.44e-07 4.97e-04 4.40e+01 2s
33 5.00416903e+09 4.99820416e+09 2.28e-07 4.63e-04 4.10e+01 2s
INFO:gurobipy: 33 5.00416903e+09 4.99820416e+09 2.28e-07 4.63e-04 4.10e+01 2s
34 5.00389811e+09 4.99905986e+09 1.66e-07 3.80e-04 3.33e+01 2s
INFO:gurobipy: 34 5.00389811e+09 4.99905986e+09 1.66e-07 3.80e-04 3.33e+01 2s
35 5.00367542e+09 5.00009027e+09 2.97e-07 2.27e-04 2.46e+01 2s
INFO:gurobipy: 35 5.00367542e+09 5.00009027e+09 2.97e-07 2.27e-04 2.46e+01 2s
36 5.00349573e+09 5.00026542e+09 5.90e-05 2.13e-04 2.22e+01 2s
INFO:gurobipy: 36 5.00349573e+09 5.00026542e+09 5.90e-05 2.13e-04 2.22e+01 2s
37 5.00342027e+09 5.00083219e+09 1.26e-04 1.66e-04 1.78e+01 2s
INFO:gurobipy: 37 5.00342027e+09 5.00083219e+09 1.26e-04 1.66e-04 1.78e+01 2s
38 5.00339743e+09 5.00092004e+09 1.45e-04 1.59e-04 1.70e+01 2s
INFO:gurobipy: 38 5.00339743e+09 5.00092004e+09 1.45e-04 1.59e-04 1.70e+01 2s
39 5.00328416e+09 5.00130718e+09 2.49e-04 1.28e-04 1.36e+01 2s
INFO:gurobipy: 39 5.00328416e+09 5.00130718e+09 2.49e-04 1.28e-04 1.36e+01 2s
40 5.00325508e+09 5.00136165e+09 2.83e-04 1.23e-04 1.30e+01 2s
INFO:gurobipy: 40 5.00325508e+09 5.00136165e+09 2.83e-04 1.23e-04 1.30e+01 2s
41 5.00321153e+09 5.00174191e+09 3.24e-04 9.19e-05 1.01e+01 2s
INFO:gurobipy: 41 5.00321153e+09 5.00174191e+09 3.24e-04 9.19e-05 1.01e+01 2s
42 5.00319841e+09 5.00199854e+09 3.32e-04 6.37e-05 8.23e+00 2s
INFO:gurobipy: 42 5.00319841e+09 5.00199854e+09 3.32e-04 6.37e-05 8.23e+00 2s
43 5.00307541e+09 5.00215639e+09 3.64e-04 5.12e-05 6.31e+00 2s
INFO:gurobipy: 43 5.00307541e+09 5.00215639e+09 3.64e-04 5.12e-05 6.31e+00 2s
44 5.00303532e+09 5.00230958e+09 3.73e-04 3.51e-05 4.98e+00 2s
INFO:gurobipy: 44 5.00303532e+09 5.00230958e+09 3.73e-04 3.51e-05 4.98e+00 2s
45 5.00299294e+09 5.00233712e+09 3.64e-04 3.33e-05 4.50e+00 2s
INFO:gurobipy: 45 5.00299294e+09 5.00233712e+09 3.64e-04 3.33e-05 4.50e+00 2s
46 5.00292124e+09 5.00259355e+09 3.53e-04 1.01e-05 2.25e+00 2s
INFO:gurobipy: 46 5.00292124e+09 5.00259355e+09 3.53e-04 1.01e-05 2.25e+00 2s
47 5.00291871e+09 5.00260517e+09 3.47e-04 9.63e-06 2.15e+00 2s
INFO:gurobipy: 47 5.00291871e+09 5.00260517e+09 3.47e-04 9.63e-06 2.15e+00 2s
48 5.00291068e+09 5.00265136e+09 3.28e-04 6.13e-06 1.78e+00 2s
INFO:gurobipy: 48 5.00291068e+09 5.00265136e+09 3.28e-04 6.13e-06 1.78e+00 2s
49 5.00290506e+09 5.00266568e+09 3.11e-04 5.65e-06 1.64e+00 2s
INFO:gurobipy: 49 5.00290506e+09 5.00266568e+09 3.11e-04 5.65e-06 1.64e+00 2s
50 5.00289151e+09 5.00269598e+09 2.77e-04 4.64e-06 1.34e+00 2s
INFO:gurobipy: 50 5.00289151e+09 5.00269598e+09 2.77e-04 4.64e-06 1.34e+00 2s
51 5.00288417e+09 5.00273051e+09 2.55e-04 2.76e-06 1.05e+00 2s
INFO:gurobipy: 51 5.00288417e+09 5.00273051e+09 2.55e-04 2.76e-06 1.05e+00 2s
52 5.00287351e+09 5.00275671e+09 2.20e-04 2.03e-06 7.99e-01 2s
INFO:gurobipy: 52 5.00287351e+09 5.00275671e+09 2.20e-04 2.03e-06 7.99e-01 2s
53 5.00287154e+09 5.00276749e+09 2.12e-04 1.74e-06 7.11e-01 2s
INFO:gurobipy: 53 5.00287154e+09 5.00276749e+09 2.12e-04 1.74e-06 7.11e-01 2s
54 5.00285704e+09 5.00276913e+09 1.54e-04 1.68e-06 6.02e-01 2s
INFO:gurobipy: 54 5.00285704e+09 5.00276913e+09 1.54e-04 1.68e-06 6.02e-01 2s
55 5.00283098e+09 5.00282687e+09 4.58e-05 5.24e-10 2.80e-02 2s
INFO:gurobipy: 55 5.00283098e+09 5.00282687e+09 4.58e-05 5.24e-10 2.80e-02 2s
56 5.00283005e+09 5.00282983e+09 5.28e-06 1.02e-09 1.48e-03 2s
INFO:gurobipy: 56 5.00283005e+09 5.00282983e+09 5.28e-06 1.02e-09 1.48e-03 2s
57 5.00282996e+09 5.00282996e+09 1.39e-08 4.37e-10 1.91e-06 2s
INFO:gurobipy: 57 5.00282996e+09 5.00282996e+09 1.39e-08 4.37e-10 1.91e-06 2s
58 5.00282996e+09 5.00282996e+09 4.23e-09 5.24e-10 6.33e-12 2s
INFO:gurobipy: 58 5.00282996e+09 5.00282996e+09 4.23e-09 5.24e-10 6.33e-12 2s
INFO:gurobipy:
Barrier solved model in 58 iterations and 2.28 seconds (1.29 work units)
INFO:gurobipy:Barrier solved model in 58 iterations and 2.28 seconds (1.29 work units)
Optimal objective 5.00282996e+09
INFO:gurobipy:Optimal objective 5.00282996e+09
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
4407 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy: 4407 DPushes remaining with DInf 0.0000000e+00 2s
0 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy: 0 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy:
7139 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 7139 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 1.8538194e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.8538194e-09 2s
INFO:gurobipy:
Crossover time: 0.12 seconds (0.06 work units)
INFO:gurobipy:Crossover time: 0.12 seconds (0.06 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
11549 5.0028300e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy: 11549 5.0028300e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy:
Solved in 11549 iterations and 2.46 seconds (1.39 work units)
INFO:gurobipy:Solved in 11549 iterations and 2.46 seconds (1.39 work units)
Optimal objective 5.002829957e+09
INFO:gurobipy:Optimal objective 5.002829957e+09
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 61326 primals, 140166 duals
Objective: 5.00e+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-fix-s-lower, Line-fix-s-upper were not assigned to the network.
('ok', 'optimal')
# Total system costs
n.objective/1e9
5.0028299565370435
# Average electricity price
n.buses_t.marginal_price.mean()
name
PRT 61.053013
DNK 59.363296
dtype: float64
# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()
name
PRT 1254
DNK 1491
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 0.143151
DNK 0.170205
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(-100293619.69515777)
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK 0.889298
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 9.3
onwind 18.4
solar 0.0
PRT OCGT 29.4
onwind 11.1
solar 13.6
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(18675041.178988095)
c. Unlimited F.#
Assume F = 10 GW which is larger than maximal load in both countries.
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 = 10000,
x = 1,
r = 1,
)
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%|██████████| 6/6 [00:00<00:00, 36.04it/s]
Writing continuous variables.: 100%|██████████| 3/3 [00:00<00:00, 275.56it/s]
INFO:linopy.io: Writing time: 0.24s
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-u2601p7q.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-u2601p7q.lp
Reading time = 0.14 seconds
INFO:gurobipy:Reading time = 0.14 seconds
obj: 140166 rows, 61326 columns, 236551 nonzeros
INFO:gurobipy:obj: 140166 rows, 61326 columns, 236551 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 140166 rows, 61326 columns and 236551 nonzeros (Min)
INFO:gurobipy:Optimize a model with 140166 rows, 61326 columns and 236551 nonzeros (Min)
Model fingerprint: 0x09c93b86
INFO:gurobipy:Model fingerprint: 0x09c93b86
Model has 52566 linear objective coefficients
INFO:gurobipy:Model has 52566 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+04]
INFO:gurobipy: RHS range [2e+03, 1e+04]
Presolve removed 87581 rows and 17495 columns
INFO:gurobipy:Presolve removed 87581 rows and 17495 columns
Presolve time: 0.08s
INFO:gurobipy:Presolve time: 0.08s
Presolved: 52585 rows, 43831 columns, 131475 nonzeros
INFO:gurobipy:Presolved: 52585 rows, 43831 columns, 131475 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: 0.00s
INFO:gurobipy:Ordering time: 0.00s
INFO:gurobipy:
Barrier statistics:
INFO:gurobipy:Barrier statistics:
Dense cols : 5
INFO:gurobipy: Dense cols : 5
AA' NZ : 7.013e+04
INFO:gurobipy: AA' NZ : 7.013e+04
Factor NZ : 3.188e+05 (roughly 34 MB of memory)
INFO:gurobipy: Factor NZ : 3.188e+05 (roughly 34 MB of memory)
Factor Ops : 2.502e+06 (less than 1 second per iteration)
INFO:gurobipy: Factor Ops : 2.502e+06 (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 5.35677064e+10 0.00000000e+00 9.32e+04 0.00e+00 2.57e+07 0s
INFO:gurobipy: 0 5.35677064e+10 0.00000000e+00 9.32e+04 0.00e+00 2.57e+07 0s
1 7.18055530e+10 -6.14869369e+10 7.70e+03 3.49e+02 5.14e+06 0s
INFO:gurobipy: 1 7.18055530e+10 -6.14869369e+10 7.70e+03 3.49e+02 5.14e+06 0s
2 4.47082187e+10 -1.42932200e+10 1.68e-09 6.78e+00 6.20e+05 0s
INFO:gurobipy: 2 4.47082187e+10 -1.42932200e+10 1.68e-09 6.78e+00 6.20e+05 0s
3 1.69928130e+10 -1.02710038e+09 4.40e-10 9.39e-01 1.77e+05 0s
INFO:gurobipy: 3 1.69928130e+10 -1.02710038e+09 4.40e-10 9.39e-01 1.77e+05 0s
4 1.10869909e+10 9.56030563e+08 2.41e-10 5.56e-01 9.84e+04 0s
INFO:gurobipy: 4 1.10869909e+10 9.56030563e+08 2.41e-10 5.56e-01 9.84e+04 0s
5 8.78098305e+09 1.65413554e+09 1.60e-10 4.30e-01 6.90e+04 0s
INFO:gurobipy: 5 8.78098305e+09 1.65413554e+09 1.60e-10 4.30e-01 6.90e+04 0s
6 7.88868412e+09 2.29103602e+09 3.74e-10 3.03e-01 5.40e+04 0s
INFO:gurobipy: 6 7.88868412e+09 2.29103602e+09 3.74e-10 3.03e-01 5.40e+04 0s
7 7.64568598e+09 2.85509020e+09 6.17e-10 2.03e-01 4.61e+04 0s
INFO:gurobipy: 7 7.64568598e+09 2.85509020e+09 6.17e-10 2.03e-01 4.61e+04 0s
8 6.92697085e+09 3.21323807e+09 1.86e-08 1.56e-01 3.57e+04 0s
INFO:gurobipy: 8 6.92697085e+09 3.21323807e+09 1.86e-08 1.56e-01 3.57e+04 0s
9 6.74254729e+09 3.52248936e+09 1.87e-08 1.18e-01 3.09e+04 0s
INFO:gurobipy: 9 6.74254729e+09 3.52248936e+09 1.87e-08 1.18e-01 3.09e+04 0s
10 6.00484988e+09 3.87858916e+09 2.51e-08 6.75e-02 2.04e+04 0s
INFO:gurobipy: 10 6.00484988e+09 3.87858916e+09 2.51e-08 6.75e-02 2.04e+04 0s
11 5.66686952e+09 4.21140048e+09 2.87e-08 4.12e-02 1.39e+04 0s
INFO:gurobipy: 11 5.66686952e+09 4.21140048e+09 2.87e-08 4.12e-02 1.39e+04 0s
12 5.43415306e+09 4.40991679e+09 1.68e-08 2.71e-02 9.80e+03 0s
INFO:gurobipy: 12 5.43415306e+09 4.40991679e+09 1.68e-08 2.71e-02 9.80e+03 0s
13 5.29268716e+09 4.54480730e+09 2.97e-08 1.85e-02 7.15e+03 0s
INFO:gurobipy: 13 5.29268716e+09 4.54480730e+09 2.97e-08 1.85e-02 7.15e+03 0s
14 5.16915079e+09 4.58304361e+09 2.62e-08 1.64e-02 5.61e+03 0s
INFO:gurobipy: 14 5.16915079e+09 4.58304361e+09 2.62e-08 1.64e-02 5.61e+03 0s
15 5.10495113e+09 4.61557701e+09 3.12e-08 1.45e-02 4.68e+03 0s
INFO:gurobipy: 15 5.10495113e+09 4.61557701e+09 3.12e-08 1.45e-02 4.68e+03 0s
16 5.03917152e+09 4.69566207e+09 6.24e-08 9.24e-03 3.29e+03 0s
INFO:gurobipy: 16 5.03917152e+09 4.69566207e+09 6.24e-08 9.24e-03 3.29e+03 0s
17 4.99248942e+09 4.71960198e+09 8.06e-08 7.74e-03 2.61e+03 0s
INFO:gurobipy: 17 4.99248942e+09 4.71960198e+09 8.06e-08 7.74e-03 2.61e+03 0s
18 4.97636788e+09 4.73119768e+09 1.07e-07 7.06e-03 2.35e+03 0s
INFO:gurobipy: 18 4.97636788e+09 4.73119768e+09 1.07e-07 7.06e-03 2.35e+03 0s
19 4.95054656e+09 4.75813197e+09 4.00e-07 5.25e-03 1.84e+03 0s
INFO:gurobipy: 19 4.95054656e+09 4.75813197e+09 4.00e-07 5.25e-03 1.84e+03 0s
20 4.94691945e+09 4.77293076e+09 3.74e-07 3.82e-03 1.66e+03 0s
INFO:gurobipy: 20 4.94691945e+09 4.77293076e+09 3.74e-07 3.82e-03 1.66e+03 0s
21 4.89311899e+09 4.78779104e+09 7.95e-07 2.78e-03 1.01e+03 1s
INFO:gurobipy: 21 4.89311899e+09 4.78779104e+09 7.95e-07 2.78e-03 1.01e+03 1s
22 4.87793614e+09 4.80072941e+09 1.73e-06 2.21e-03 7.41e+02 1s
INFO:gurobipy: 22 4.87793614e+09 4.80072941e+09 1.73e-06 2.21e-03 7.41e+02 1s
23 4.86974987e+09 4.81030428e+09 1.03e-06 1.79e-03 5.70e+02 1s
INFO:gurobipy: 23 4.86974987e+09 4.81030428e+09 1.03e-06 1.79e-03 5.70e+02 1s
24 4.86458528e+09 4.81834149e+09 1.47e-06 1.45e-03 4.44e+02 1s
INFO:gurobipy: 24 4.86458528e+09 4.81834149e+09 1.47e-06 1.45e-03 4.44e+02 1s
25 4.86076096e+09 4.82977770e+09 1.54e-06 9.55e-04 2.97e+02 1s
INFO:gurobipy: 25 4.86076096e+09 4.82977770e+09 1.54e-06 9.55e-04 2.97e+02 1s
26 4.85837538e+09 4.83492677e+09 8.72e-07 7.43e-04 2.25e+02 1s
INFO:gurobipy: 26 4.85837538e+09 4.83492677e+09 8.72e-07 7.43e-04 2.25e+02 1s
27 4.85655938e+09 4.83741371e+09 4.96e-07 6.38e-04 1.84e+02 1s
INFO:gurobipy: 27 4.85655938e+09 4.83741371e+09 4.96e-07 6.38e-04 1.84e+02 1s
28 4.85514803e+09 4.84020588e+09 8.43e-07 5.21e-04 1.44e+02 1s
INFO:gurobipy: 28 4.85514803e+09 4.84020588e+09 8.43e-07 5.21e-04 1.44e+02 1s
29 4.85400102e+09 4.84484221e+09 5.26e-07 3.25e-04 8.81e+01 1s
INFO:gurobipy: 29 4.85400102e+09 4.84484221e+09 5.26e-07 3.25e-04 8.81e+01 1s
30 4.85360032e+09 4.84617755e+09 4.44e-07 2.69e-04 7.14e+01 1s
INFO:gurobipy: 30 4.85360032e+09 4.84617755e+09 4.44e-07 2.69e-04 7.14e+01 1s
31 4.85329453e+09 4.84673889e+09 4.67e-07 2.36e-04 6.31e+01 1s
INFO:gurobipy: 31 4.85329453e+09 4.84673889e+09 4.67e-07 2.36e-04 6.31e+01 1s
32 4.85315955e+09 4.84785404e+09 6.06e-07 1.82e-04 5.11e+01 1s
INFO:gurobipy: 32 4.85315955e+09 4.84785404e+09 6.06e-07 1.82e-04 5.11e+01 1s
33 4.85307304e+09 4.84851021e+09 6.27e-07 1.58e-04 4.39e+01 1s
INFO:gurobipy: 33 4.85307304e+09 4.84851021e+09 6.27e-07 1.58e-04 4.39e+01 1s
34 4.85297888e+09 4.84910240e+09 1.11e-06 1.26e-04 3.73e+01 1s
INFO:gurobipy: 34 4.85297888e+09 4.84910240e+09 1.11e-06 1.26e-04 3.73e+01 1s
35 4.85291819e+09 4.84944621e+09 8.63e-07 1.11e-04 3.34e+01 1s
INFO:gurobipy: 35 4.85291819e+09 4.84944621e+09 8.63e-07 1.11e-04 3.34e+01 1s
36 4.85287948e+09 4.85041434e+09 1.06e-06 7.20e-05 2.37e+01 1s
INFO:gurobipy: 36 4.85287948e+09 4.85041434e+09 1.06e-06 7.20e-05 2.37e+01 1s
37 4.85280425e+09 4.85067294e+09 2.63e-06 6.26e-05 2.05e+01 1s
INFO:gurobipy: 37 4.85280425e+09 4.85067294e+09 2.63e-06 6.26e-05 2.05e+01 1s
38 4.85278953e+09 4.85124415e+09 1.53e-04 4.59e-05 1.49e+01 1s
INFO:gurobipy: 38 4.85278953e+09 4.85124415e+09 1.53e-04 4.59e-05 1.49e+01 1s
39 4.85278097e+09 4.85133561e+09 1.99e-04 4.23e-05 1.39e+01 1s
INFO:gurobipy: 39 4.85278097e+09 4.85133561e+09 1.99e-04 4.23e-05 1.39e+01 1s
40 4.85277868e+09 4.85154559e+09 2.11e-04 3.43e-05 1.19e+01 1s
INFO:gurobipy: 40 4.85277868e+09 4.85154559e+09 2.11e-04 3.43e-05 1.19e+01 1s
41 4.85277888e+09 4.85165548e+09 2.24e-04 3.14e-05 1.08e+01 1s
INFO:gurobipy: 41 4.85277888e+09 4.85165548e+09 2.24e-04 3.14e-05 1.08e+01 1s
42 4.85277253e+09 4.85193506e+09 2.29e-04 2.13e-05 8.07e+00 1s
INFO:gurobipy: 42 4.85277253e+09 4.85193506e+09 2.29e-04 2.13e-05 8.07e+00 1s
43 4.85277283e+09 4.85246719e+09 1.94e-04 3.34e-06 2.94e+00 1s
INFO:gurobipy: 43 4.85277283e+09 4.85246719e+09 1.94e-04 3.34e-06 2.94e+00 1s
44 4.85276472e+09 4.85274768e+09 7.07e-05 2.80e-10 1.63e-01 1s
INFO:gurobipy: 44 4.85276472e+09 4.85274768e+09 7.07e-05 2.80e-10 1.63e-01 1s
45 4.85276349e+09 4.85276289e+09 5.66e-06 1.40e-09 5.77e-03 1s
INFO:gurobipy: 45 4.85276349e+09 4.85276289e+09 5.66e-06 1.40e-09 5.77e-03 1s
46 4.85276339e+09 4.85276339e+09 5.74e-07 2.33e-10 1.72e-06 1s
INFO:gurobipy: 46 4.85276339e+09 4.85276339e+09 5.74e-07 2.33e-10 1.72e-06 1s
47 4.85276339e+09 4.85276339e+09 2.84e-09 6.69e-10 1.81e-12 1s
INFO:gurobipy: 47 4.85276339e+09 4.85276339e+09 2.84e-09 6.69e-10 1.81e-12 1s
INFO:gurobipy:
Barrier solved model in 47 iterations and 1.11 seconds (0.84 work units)
INFO:gurobipy:Barrier solved model in 47 iterations and 1.11 seconds (0.84 work units)
Optimal objective 4.85276339e+09
INFO:gurobipy:Optimal objective 4.85276339e+09
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
4427 DPushes remaining with DInf 0.0000000e+00 1s
INFO:gurobipy: 4427 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:
1790 PPushes remaining with PInf 0.0000000e+00 1s
INFO:gurobipy: 1790 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 9.4184382e-10 1s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 9.4184382e-10 1s
INFO:gurobipy:
Crossover time: 0.09 seconds (0.05 work units)
INFO:gurobipy:Crossover time: 0.09 seconds (0.05 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
6219 4.8527634e+09 0.000000e+00 0.000000e+00 1s
INFO:gurobipy: 6219 4.8527634e+09 0.000000e+00 0.000000e+00 1s
INFO:gurobipy:
Use crossover to convert LP symmetric solution to basic solution...
INFO:gurobipy:Use crossover to convert LP symmetric solution to basic solution...
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
0 DPushes remaining with DInf 0.0000000e+00 1s
INFO:gurobipy: 0 DPushes remaining with DInf 0.0000000e+00 1s
INFO:gurobipy:
8012 PPushes remaining with PInf 0.0000000e+00 1s
INFO:gurobipy: 8012 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 1.5148721e-09 1s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.5148721e-09 1s
INFO:gurobipy:
Crossover time: 0.06 seconds (0.05 work units)
INFO:gurobipy:Crossover time: 0.06 seconds (0.05 work units)
Iteration Objective Primal Inf. Dual Inf. Time
INFO:gurobipy:Iteration Objective Primal Inf. Dual Inf. Time
14300 4.8527634e+09 0.000000e+00 0.000000e+00 1s
INFO:gurobipy: 14300 4.8527634e+09 0.000000e+00 0.000000e+00 1s
INFO:gurobipy:
Solved in 14300 iterations and 1.35 seconds (0.99 work units)
INFO:gurobipy:Solved in 14300 iterations and 1.35 seconds (0.99 work units)
Optimal objective 4.852763389e+09
INFO:gurobipy:Optimal objective 4.852763389e+09
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 61326 primals, 140166 duals
Objective: 4.85e+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-fix-s-lower, Line-fix-s-upper were not assigned to the network.
('ok', 'optimal')
# Total system costs
n.objective/1e9
4.852763388965552
# Average electricity price
n.buses_t.marginal_price.mean()
name
PRT 57.214036
DNK 57.214036
dtype: float64
# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()
name
PRT 1787
DNK 1787
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 0.203995
DNK 0.203995
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(0.0)
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK 0.191488
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 3.2
onwind 24.8
solar 0.0
PRT OCGT 27.5
onwind 11.9
solar 14.3
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(14834697.56278273)
d. Optimise F endogenously (assume it starts at 0 GW capacity).#
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,
)
costs.at["HVAC overhead", "capital_cost"]
np.float64(42.007473674372484)
costs.at["onwind", "capital_cost"]
np.float64(101644.12332388277)
Add captial costs and distance between the buses, and endogenise the capacity of the overhead AC line.
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.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%|██████████| 7/7 [00:00<00:00, 61.25it/s]
Writing continuous variables.: 100%|██████████| 4/4 [00:00<00:00, 75.49it/s]
INFO:linopy.io: Writing time: 0.18s
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-mvni6q7s.lp
INFO:gurobipy:Read LP format model from file /private/var/folders/zg/by4_k0616s98pw41wld9475c0000gp/T/linopy-problem-mvni6q7s.lp
Reading time = 0.28 seconds
INFO:gurobipy:Reading time = 0.28 seconds
obj: 140167 rows, 61327 columns, 254072 nonzeros
INFO:gurobipy:obj: 140167 rows, 61327 columns, 254072 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 140167 rows, 61327 columns and 254072 nonzeros (Min)
INFO:gurobipy:Optimize a model with 140167 rows, 61327 columns and 254072 nonzeros (Min)
Model fingerprint: 0x8395d133
INFO:gurobipy:Model fingerprint: 0x8395d133
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, 9e+03]
INFO:gurobipy: RHS range [2e+03, 9e+03]
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: 70105 rows, 43832 columns, 191955 nonzeros
INFO:gurobipy:Presolved: 70105 rows, 43832 columns, 191955 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 : 1.744e+05
INFO:gurobipy: AA' NZ : 1.744e+05
Factor NZ : 7.483e+05 (roughly 50 MB of memory)
INFO:gurobipy: Factor NZ : 7.483e+05 (roughly 50 MB of memory)
Factor Ops : 8.510e+06 (less than 1 second per iteration)
INFO:gurobipy: Factor Ops : 8.510e+06 (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 4.74162353e+10 0.00000000e+00 9.69e+04 0.00e+00 2.08e+07 0s
INFO:gurobipy: 0 4.74162353e+10 0.00000000e+00 9.69e+04 0.00e+00 2.08e+07 0s
1 5.72962595e+10 -7.59755270e+10 1.63e+04 2.65e+02 5.21e+06 0s
INFO:gurobipy: 1 5.72962595e+10 -7.59755270e+10 1.63e+04 2.65e+02 5.21e+06 0s
2 4.07511813e+10 -3.44552017e+10 6.40e-10 4.83e+00 5.56e+05 0s
INFO:gurobipy: 2 4.07511813e+10 -3.44552017e+10 6.40e-10 4.83e+00 5.56e+05 0s
3 1.24969540e+10 -9.17636724e+08 1.66e-10 2.75e-01 9.23e+04 0s
INFO:gurobipy: 3 1.24969540e+10 -9.17636724e+08 1.66e-10 2.75e-01 9.23e+04 0s
4 7.97621588e+09 1.58008531e+09 7.28e-11 9.60e-02 4.35e+04 0s
INFO:gurobipy: 4 7.97621588e+09 1.58008531e+09 7.28e-11 9.60e-02 4.35e+04 0s
5 7.03236504e+09 2.30239305e+09 5.09e-11 7.70e-02 3.21e+04 0s
INFO:gurobipy: 5 7.03236504e+09 2.30239305e+09 5.09e-11 7.70e-02 3.21e+04 0s
6 6.98990268e+09 2.41435210e+09 5.09e-11 7.37e-02 3.10e+04 0s
INFO:gurobipy: 6 6.98990268e+09 2.41435210e+09 5.09e-11 7.37e-02 3.10e+04 0s
7 6.80231225e+09 2.83242181e+09 8.73e-11 6.02e-02 2.69e+04 0s
INFO:gurobipy: 7 6.80231225e+09 2.83242181e+09 8.73e-11 6.02e-02 2.69e+04 0s
8 6.15299644e+09 3.77387229e+09 6.99e-09 2.46e-02 1.61e+04 0s
INFO:gurobipy: 8 6.15299644e+09 3.77387229e+09 6.99e-09 2.46e-02 1.61e+04 0s
9 5.86067534e+09 4.11415608e+09 3.18e-09 1.62e-02 1.18e+04 0s
INFO:gurobipy: 9 5.86067534e+09 4.11415608e+09 3.18e-09 1.62e-02 1.18e+04 0s
10 5.55990825e+09 4.60073663e+09 5.09e-09 4.94e-03 6.47e+03 0s
INFO:gurobipy: 10 5.55990825e+09 4.60073663e+09 5.09e-09 4.94e-03 6.47e+03 0s
11 5.43305626e+09 4.71349625e+09 7.69e-09 3.39e-03 4.85e+03 0s
INFO:gurobipy: 11 5.43305626e+09 4.71349625e+09 7.69e-09 3.39e-03 4.85e+03 0s
12 5.36000388e+09 4.79794557e+09 7.12e-09 2.38e-03 3.79e+03 0s
INFO:gurobipy: 12 5.36000388e+09 4.79794557e+09 7.12e-09 2.38e-03 3.79e+03 0s
13 5.29217666e+09 4.87997649e+09 8.36e-09 1.39e-03 2.78e+03 0s
INFO:gurobipy: 13 5.29217666e+09 4.87997649e+09 8.36e-09 1.39e-03 2.78e+03 0s
14 5.23881707e+09 4.95639054e+09 1.37e-08 6.15e-04 1.90e+03 1s
INFO:gurobipy: 14 5.23881707e+09 4.95639054e+09 1.37e-08 6.15e-04 1.90e+03 1s
15 5.20965030e+09 4.98740701e+09 2.36e-08 4.81e-04 1.50e+03 1s
INFO:gurobipy: 15 5.20965030e+09 4.98740701e+09 2.36e-08 4.81e-04 1.50e+03 1s
16 5.18706084e+09 5.02447712e+09 1.70e-08 4.43e-04 1.10e+03 1s
INFO:gurobipy: 16 5.18706084e+09 5.02447712e+09 1.70e-08 4.43e-04 1.10e+03 1s
17 5.16895631e+09 5.04686160e+09 1.30e-08 3.71e-04 8.22e+02 1s
INFO:gurobipy: 17 5.16895631e+09 5.04686160e+09 1.30e-08 3.71e-04 8.22e+02 1s
18 5.15521217e+09 5.05217039e+09 9.27e-09 3.50e-04 6.94e+02 1s
INFO:gurobipy: 18 5.15521217e+09 5.05217039e+09 9.27e-09 3.50e-04 6.94e+02 1s
19 5.14465599e+09 5.06860837e+09 1.16e-08 2.45e-04 5.12e+02 1s
INFO:gurobipy: 19 5.14465599e+09 5.06860837e+09 1.16e-08 2.45e-04 5.12e+02 1s
20 5.13540944e+09 5.07253719e+09 3.37e-08 2.26e-04 4.24e+02 1s
INFO:gurobipy: 20 5.13540944e+09 5.07253719e+09 3.37e-08 2.26e-04 4.24e+02 1s
21 5.13017518e+09 5.07637124e+09 1.79e-08 2.04e-04 3.62e+02 1s
INFO:gurobipy: 21 5.13017518e+09 5.07637124e+09 1.79e-08 2.04e-04 3.62e+02 1s
22 5.12292050e+09 5.08065406e+09 6.92e-08 1.79e-04 2.85e+02 1s
INFO:gurobipy: 22 5.12292050e+09 5.08065406e+09 6.92e-08 1.79e-04 2.85e+02 1s
23 5.11795300e+09 5.08522557e+09 9.73e-08 1.50e-04 2.21e+02 1s
INFO:gurobipy: 23 5.11795300e+09 5.08522557e+09 9.73e-08 1.50e-04 2.21e+02 1s
24 5.11663186e+09 5.08710414e+09 9.56e-08 1.38e-04 1.99e+02 1s
INFO:gurobipy: 24 5.11663186e+09 5.08710414e+09 9.56e-08 1.38e-04 1.99e+02 1s
25 5.11450133e+09 5.09207733e+09 1.64e-07 1.01e-04 1.51e+02 1s
INFO:gurobipy: 25 5.11450133e+09 5.09207733e+09 1.64e-07 1.01e-04 1.51e+02 1s
26 5.11302319e+09 5.09290376e+09 1.70e-07 9.53e-05 1.36e+02 1s
INFO:gurobipy: 26 5.11302319e+09 5.09290376e+09 1.70e-07 9.53e-05 1.36e+02 1s
27 5.11237519e+09 5.09371523e+09 2.20e-07 8.99e-05 1.26e+02 1s
INFO:gurobipy: 27 5.11237519e+09 5.09371523e+09 2.20e-07 8.99e-05 1.26e+02 1s
28 5.11125954e+09 5.09715142e+09 2.63e-07 6.45e-05 9.51e+01 1s
INFO:gurobipy: 28 5.11125954e+09 5.09715142e+09 2.63e-07 6.45e-05 9.51e+01 1s
29 5.11087291e+09 5.09757921e+09 2.02e-07 6.17e-05 8.96e+01 1s
INFO:gurobipy: 29 5.11087291e+09 5.09757921e+09 2.02e-07 6.17e-05 8.96e+01 1s
30 5.11010107e+09 5.09785118e+09 4.07e-07 5.99e-05 8.26e+01 1s
INFO:gurobipy: 30 5.11010107e+09 5.09785118e+09 4.07e-07 5.99e-05 8.26e+01 1s
31 5.10967198e+09 5.09849786e+09 4.32e-07 5.57e-05 7.54e+01 1s
INFO:gurobipy: 31 5.10967198e+09 5.09849786e+09 4.32e-07 5.57e-05 7.54e+01 1s
32 5.10939154e+09 5.09907026e+09 3.46e-07 5.20e-05 6.96e+01 1s
INFO:gurobipy: 32 5.10939154e+09 5.09907026e+09 3.46e-07 5.20e-05 6.96e+01 1s
33 5.10920716e+09 5.09934580e+09 3.69e-07 5.01e-05 6.65e+01 1s
INFO:gurobipy: 33 5.10920716e+09 5.09934580e+09 3.69e-07 5.01e-05 6.65e+01 1s
34 5.10910926e+09 5.09982117e+09 3.76e-07 4.71e-05 6.26e+01 1s
INFO:gurobipy: 34 5.10910926e+09 5.09982117e+09 3.76e-07 4.71e-05 6.26e+01 1s
35 5.10892493e+09 5.10037786e+09 2.84e-07 4.35e-05 5.76e+01 1s
INFO:gurobipy: 35 5.10892493e+09 5.10037786e+09 2.84e-07 4.35e-05 5.76e+01 1s
36 5.10871557e+09 5.10072502e+09 4.29e-07 4.13e-05 5.39e+01 1s
INFO:gurobipy: 36 5.10871557e+09 5.10072502e+09 4.29e-07 4.13e-05 5.39e+01 1s
37 5.10857307e+09 5.10122967e+09 5.00e-07 3.80e-05 4.95e+01 1s
INFO:gurobipy: 37 5.10857307e+09 5.10122967e+09 5.00e-07 3.80e-05 4.95e+01 1s
38 5.10846403e+09 5.10144430e+09 5.57e-07 3.65e-05 4.74e+01 1s
INFO:gurobipy: 38 5.10846403e+09 5.10144430e+09 5.57e-07 3.65e-05 4.74e+01 1s
39 5.10835048e+09 5.10189234e+09 4.51e-07 3.37e-05 4.36e+01 1s
INFO:gurobipy: 39 5.10835048e+09 5.10189234e+09 4.51e-07 3.37e-05 4.36e+01 1s
40 5.10809251e+09 5.10233344e+09 1.47e-07 3.07e-05 3.89e+01 1s
INFO:gurobipy: 40 5.10809251e+09 5.10233344e+09 1.47e-07 3.07e-05 3.89e+01 1s
41 5.10795016e+09 5.10266997e+09 2.34e-07 2.85e-05 3.56e+01 1s
INFO:gurobipy: 41 5.10795016e+09 5.10266997e+09 2.34e-07 2.85e-05 3.56e+01 1s
42 5.10780695e+09 5.10303660e+09 3.89e-07 1.57e-05 3.22e+01 1s
INFO:gurobipy: 42 5.10780695e+09 5.10303660e+09 3.89e-07 1.57e-05 3.22e+01 1s
43 5.10766504e+09 5.10331365e+09 5.20e-07 6.40e-06 2.94e+01 1s
INFO:gurobipy: 43 5.10766504e+09 5.10331365e+09 5.20e-07 6.40e-06 2.94e+01 1s
44 5.10762093e+09 5.10337912e+09 4.01e-07 6.26e-06 2.86e+01 1s
INFO:gurobipy: 44 5.10762093e+09 5.10337912e+09 4.01e-07 6.26e-06 2.86e+01 1s
45 5.10760972e+09 5.10355934e+09 3.96e-07 5.92e-06 2.73e+01 1s
INFO:gurobipy: 45 5.10760972e+09 5.10355934e+09 3.96e-07 5.92e-06 2.73e+01 1s
46 5.10752274e+09 5.10377613e+09 3.84e-07 5.53e-06 2.53e+01 1s
INFO:gurobipy: 46 5.10752274e+09 5.10377613e+09 3.84e-07 5.53e-06 2.53e+01 1s
47 5.10738408e+09 5.10420497e+09 6.30e-07 4.79e-06 2.15e+01 1s
INFO:gurobipy: 47 5.10738408e+09 5.10420497e+09 6.30e-07 4.79e-06 2.15e+01 1s
48 5.10726389e+09 5.10446737e+09 5.00e-07 4.32e-06 1.89e+01 1s
INFO:gurobipy: 48 5.10726389e+09 5.10446737e+09 5.00e-07 4.32e-06 1.89e+01 1s
49 5.10722448e+09 5.10492443e+09 5.64e-07 3.42e-06 1.55e+01 1s
INFO:gurobipy: 49 5.10722448e+09 5.10492443e+09 5.64e-07 3.42e-06 1.55e+01 1s
50 5.10721177e+09 5.10497675e+09 5.92e-07 3.31e-06 1.51e+01 1s
INFO:gurobipy: 50 5.10721177e+09 5.10497675e+09 5.92e-07 3.31e-06 1.51e+01 1s
51 5.10718342e+09 5.10503236e+09 6.12e-07 3.18e-06 1.45e+01 1s
INFO:gurobipy: 51 5.10718342e+09 5.10503236e+09 6.12e-07 3.18e-06 1.45e+01 1s
52 5.10714797e+09 5.10517063e+09 5.30e-07 2.89e-06 1.33e+01 1s
INFO:gurobipy: 52 5.10714797e+09 5.10517063e+09 5.30e-07 2.89e-06 1.33e+01 1s
53 5.10712232e+09 5.10530428e+09 5.46e-07 2.62e-06 1.23e+01 1s
INFO:gurobipy: 53 5.10712232e+09 5.10530428e+09 5.46e-07 2.62e-06 1.23e+01 1s
54 5.10707097e+09 5.10536288e+09 5.25e-07 2.48e-06 1.15e+01 1s
INFO:gurobipy: 54 5.10707097e+09 5.10536288e+09 5.25e-07 2.48e-06 1.15e+01 1s
55 5.10705132e+09 5.10556729e+09 3.65e-07 2.09e-06 1.00e+01 1s
INFO:gurobipy: 55 5.10705132e+09 5.10556729e+09 3.65e-07 2.09e-06 1.00e+01 1s
56 5.10691121e+09 5.10565063e+09 8.47e-07 6.98e-10 8.51e+00 1s
INFO:gurobipy: 56 5.10691121e+09 5.10565063e+09 8.47e-07 6.98e-10 8.51e+00 1s
57 5.10689214e+09 5.10598786e+09 6.62e-07 1.35e-09 6.10e+00 1s
INFO:gurobipy: 57 5.10689214e+09 5.10598786e+09 6.62e-07 1.35e-09 6.10e+00 1s
58 5.10685732e+09 5.10602341e+09 8.06e-07 1.28e-09 5.63e+00 1s
INFO:gurobipy: 58 5.10685732e+09 5.10602341e+09 8.06e-07 1.28e-09 5.63e+00 1s
59 5.10684874e+09 5.10610799e+09 1.01e-05 4.47e-10 5.00e+00 1s
INFO:gurobipy: 59 5.10684874e+09 5.10610799e+09 1.01e-05 4.47e-10 5.00e+00 1s
60 5.10683153e+09 5.10623271e+09 3.37e-05 1.08e-09 4.04e+00 1s
INFO:gurobipy: 60 5.10683153e+09 5.10623271e+09 3.37e-05 1.08e-09 4.04e+00 1s
61 5.10680622e+09 5.10632886e+09 7.38e-05 5.53e-10 3.22e+00 1s
INFO:gurobipy: 61 5.10680622e+09 5.10632886e+09 7.38e-05 5.53e-10 3.22e+00 1s
62 5.10679997e+09 5.10637876e+09 8.62e-05 2.62e-10 2.84e+00 1s
INFO:gurobipy: 62 5.10679997e+09 5.10637876e+09 8.62e-05 2.62e-10 2.84e+00 1s
63 5.10677936e+09 5.10652031e+09 1.20e-04 5.77e-09 1.75e+00 1s
INFO:gurobipy: 63 5.10677936e+09 5.10652031e+09 1.20e-04 5.77e-09 1.75e+00 1s
64 5.10675011e+09 5.10667756e+09 7.87e-05 3.93e-09 4.87e-01 1s
INFO:gurobipy: 64 5.10675011e+09 5.10667756e+09 7.87e-05 3.93e-09 4.87e-01 1s
65 5.10673448e+09 5.10668325e+09 5.92e-05 3.29e-09 3.44e-01 1s
INFO:gurobipy: 65 5.10673448e+09 5.10668325e+09 5.92e-05 3.29e-09 3.44e-01 1s
66 5.10672781e+09 5.10668423e+09 4.92e-05 2.99e-09 2.93e-01 2s
INFO:gurobipy: 66 5.10672781e+09 5.10668423e+09 4.92e-05 2.99e-09 2.93e-01 2s
67 5.10671374e+09 5.10668669e+09 3.09e-05 2.00e-09 1.82e-01 2s
INFO:gurobipy: 67 5.10671374e+09 5.10668669e+09 3.09e-05 2.00e-09 1.82e-01 2s
68 5.10671324e+09 5.10668783e+09 3.02e-05 1.72e-09 1.71e-01 2s
INFO:gurobipy: 68 5.10671324e+09 5.10668783e+09 3.02e-05 1.72e-09 1.71e-01 2s
69 5.10670762e+09 5.10668859e+09 2.24e-05 6.98e-10 1.28e-01 2s
INFO:gurobipy: 69 5.10670762e+09 5.10668859e+09 2.24e-05 6.98e-10 1.28e-01 2s
70 5.10669525e+09 5.10669341e+09 5.14e-06 1.99e-09 1.24e-02 2s
INFO:gurobipy: 70 5.10669525e+09 5.10669341e+09 5.14e-06 1.99e-09 1.24e-02 2s
71 5.10669373e+09 5.10669368e+09 3.51e-08 7.57e-10 3.03e-04 2s
INFO:gurobipy: 71 5.10669373e+09 5.10669368e+09 3.51e-08 7.57e-10 3.03e-04 2s
72 5.10669371e+09 5.10669371e+09 8.49e-10 3.75e-09 4.30e-09 2s
INFO:gurobipy: 72 5.10669371e+09 5.10669371e+09 8.49e-10 3.75e-09 4.30e-09 2s
INFO:gurobipy:
Barrier solved model in 72 iterations and 1.68 seconds (2.03 work units)
INFO:gurobipy:Barrier solved model in 72 iterations and 1.68 seconds (2.03 work units)
Optimal objective 5.10669371e+09
INFO:gurobipy:Optimal objective 5.10669371e+09
INFO:gurobipy:
Crossover log...
INFO:gurobipy:Crossover log...
INFO:gurobipy:
4432 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy: 4432 DPushes remaining with DInf 0.0000000e+00 2s
0 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy: 0 DPushes remaining with DInf 0.0000000e+00 2s
INFO:gurobipy:
7072 PPushes remaining with PInf 0.0000000e+00 2s
INFO:gurobipy: 7072 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 1.0000895e-09 2s
INFO:gurobipy: Push phase complete: Pinf 0.0000000e+00, Dinf 1.0000895e-09 2s
INFO:gurobipy:
Crossover time: 0.11 seconds (0.08 work units)
INFO:gurobipy:Crossover time: 0.11 seconds (0.08 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
11507 5.1066937e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy: 11507 5.1066937e+09 0.000000e+00 0.000000e+00 2s
INFO:gurobipy:
Solved in 11507 iterations and 1.84 seconds (2.15 work units)
INFO:gurobipy:Solved in 11507 iterations and 1.84 seconds (2.15 work units)
Optimal objective 5.106693708e+09
INFO:gurobipy:Optimal objective 5.106693708e+09
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 61327 primals, 140167 duals
Objective: 5.11e+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
5.106693707557571
# Average electricity price
n.buses_t.marginal_price.mean()
name
PRT 61.081714
DNK 59.417098
dtype: float64
# Hours with almost zero price
n.buses_t.marginal_price[n.buses_t.marginal_price < 2].count()
name
PRT 1250
DNK 1483
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 0.142694
DNK 0.169292
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(-93730605.83284725)
n.lines_t.p0["PRT-DNK"] * n.lines_t.p0["PRT-DNK"]
snapshot
2015-01-01 00:00:00 128100.934790
2015-01-01 01:00:00 257722.952776
2015-01-01 02:00:00 530208.540960
2015-01-01 03:00:00 811442.419235
2015-01-01 04:00:00 811442.419235
...
2015-12-31 19:00:00 811442.419235
2015-12-31 20:00:00 811442.419235
2015-12-31 21:00:00 811442.419235
2015-12-31 22:00:00 811442.419235
2015-12-31 23:00:00 811442.419235
Name: PRT-DNK, Length: 8760, dtype: float64
# Utilisation of transmission line
n.lines_t.p0.abs().mean() / n.lines.s_nom_opt
name
PRT-DNK 0.854408
dtype: float64
# Capacity of transmission line
n.lines.s_nom_opt["PRT-DNK"]
np.float64(900.8009875853653)
# 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 10.3
onwind 18.4
solar 0.0
PRT OCGT 28.8
onwind 10.7
solar 13.5
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(18886469.938808523)