Example for modeling part load behavior¶

In this application of the ETHOS.FINE framework, a hydrogen system is modeled and optimized considering partload behavior of the electrolyzer.

All classes which are available to the user are utilized and examples of the selection of different parameters within these classes are given.

The workflow is structures as follows:

1. Required packages are imported and the input data path is set
2. An energy system model instance is created
3. Commodity sources are added to the energy system model
4. Commodity conversion components are added to the energy system model
5. Commodity storages are added to the energy system model
6. Commodity sinks are added to the energy system model
7. The energy system model is optimized
8. Selected optimization results are presented

1. Import required packages and set input data path¶

The ETHOS.FINE framework is imported which provides the required classes and functions for modeling the energy system.

In [33]:

import fine as fn
import pandas as pd
from getData import getData
from pathlib import Path

cwd = Path.cwd()
data = getData()

%matplotlib inline
%load_ext autoreload
%autoreload 2

import fine as fn import pandas as pd from getData import getData from pathlib import Path cwd = Path.cwd() data = getData() %matplotlib inline %load_ext autoreload %autoreload 2

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

2 Import efficiency curve data for partload operation¶

In [34]:

# Efficiency Curve for PEM Electrolyzer
# Data from EC Campus Mainz
Operation_level = [
    0.0208023774145616,
    0.0222882615156017,
    0.0222882615156017,
    0.0222882615156017,
    0.025260029717682,
    0.025260029717682,
    0.0267459138187221,
    0.0282317979197622,
    0.0297176820208024,
    0.0312035661218424,
    0.0326894502228826,
    0.0341753343239227,
    0.0356612184249628,
    0.0371471025260029,
    0.038632986627043,
    0.0416047548291233,
    0.0430906389301634,
    0.0445765230312035,
    0.0475482912332838,
    0.0430906389301634,
    0.0490341753343239,
    0.050520059435364,
    0.0520059435364041,
    0.0549777117384844,
    0.0579494799405646,
    0.0609212481426448,
    0.0638930163447251,
    0.0683506686478455,
    0.0713224368499256,
    0.075780089153046,
    0.0787518573551263,
    0.0832095096582466,
    0.087667161961367,
    0.0921248142644873,
    0.0980683506686478,
    0.104011887072808,
    0.108469539375928,
    0.114413075780089,
    0.120356612184249,
    0.12778603268945,
    0.13521545319465,
    0.142644873699851,
    0.151560178306092,
    0.157503714710252,
    0.166419019316493,
    0.173848439821693,
    0.181277860326894,
    0.190193164933135,
    0.196136701337295,
    0.202080237741456,
    0.209509658246656,
    0.216939078751857,
    0.224368499257057,
    0.233283803863298,
    0.240713224368499,
    0.246656760772659,
    0.25408618127786,
    0.26151560178306,
    0.270430906389301,
    0.276374442793462,
    0.283803863298662,
    0.292719167904903,
    0.298662704309063,
    0.306092124814264,
    0.313521545319465,
    0.319465081723625,
    0.328380386329866,
    0.335809806835066,
    0.343239227340267,
    0.349182763744427,
    0.356612184249628,
    0.364041604754829,
    0.371471025260029,
    0.38038632986627,
    0.389301634472511,
    0.398216939078751,
    0.407132243684992,
    0.416047548291233,
    0.423476968796433,
    0.430906389301634,
    0.439821693907875,
    0.448736998514115,
    0.457652303120356,
    0.465081723625557,
    0.472511144130757,
    0.481426448736998,
    0.490341753343239,
    0.497771173848439,
    0.50668647845468,
    0.514115898959881,
    0.523031203566121,
    0.531946508172362,
    0.540861812778603,
    0.551263001485884,
    0.560178306092124,
    0.567607726597325,
    0.576523031203566,
    0.585438335809806,
    0.595839524517087,
    0.604754829123328,
    0.613670133729569,
    0.619613670133729,
    0.62852897473997,
    0.638930163447251,
    0.646359583952451,
    0.656760772659732,
    0.664190193164933,
    0.673105497771173,
    0.684992570579494,
    0.692421991084695,
    0.699851411589896,
    0.710252600297176,
    0.717682020802377,
    0.726597325408618,
    0.735512630014858,
    0.744427934621099,
    0.75334323922734,
    0.762258543833581,
    0.769687964338781,
    0.780089153046062,
    0.786032689450223,
    0.793462109955423,
    0.802377414561664,
    0.811292719167904,
    0.820208023774145,
    0.829123328380386,
    0.838038632986627,
    0.846953937592867,
    0.858841010401188,
    0.867756315007429,
    0.87667161961367,
    0.88707280832095,
    0.895988112927191,
    0.904903417533432,
    0.913818722139673,
    0.924219910846954,
    0.933135215453194,
    0.942050520059435,
    0.947994056463595,
    0.958395245170876,
    0.965824665676077,
    0.974739970282318,
    0.985141158989598,
    0.994056463595839,
]
Efficiency = [
    0.03449362655834178,
    0.05655553999159559,
    0.04920156884717763,
    0.07616612971004356,
    0.09332539571368476,
    0.115387309146939,
    0.13254657515058135,
    0.1497058411542229,
    0.1693164308726712,
    0.1864756968763127,
    0.2036349628799551,
    0.2256968763132085,
    0.2404048186020449,
    0.25511276089088053,
    0.27472335060932884,
    0.2918826166129703,
    0.30904188261661275,
    0.33110379604986695,
    0.34581173833870255,
    0.3212985011906424,
    0.3629710043423449,
    0.38013027034598645,
    0.3923868889200161,
    0.4095461549236585,
    0.42425409721249496,
    0.4365107157865246,
    0.44876733436055427,
    0.45857262921977887,
    0.4683779240790026,
    0.4830858663678382,
    0.4953424849418686,
    0.5075991035158983,
    0.517404398375122,
    0.5247583695195407,
    0.5321123406639585,
    0.5419176355231823,
    0.5517229303824059,
    0.5639795489564365,
    0.5713335201008543,
    0.5811388149600779,
    0.5884927861044958,
    0.5933954335341085,
    0.5982980809637204,
    0.6007494046785262,
    0.6007494046785262,
    0.6007494046785262,
    0.5982980809637204,
    0.5982980809637204,
    0.5958467572489144,
    0.5958467572489144,
    0.5958467572489144,
    0.5933954335341085,
    0.5933954335341085,
    0.5933954335341085,
    0.5909441098193018,
    0.5909441098193018,
    0.5909441098193018,
    0.5884927861044958,
    0.5884927861044958,
    0.5884927861044958,
    0.5884927861044958,
    0.5884927861044958,
    0.5884927861044958,
    0.5860414623896899,
    0.5860414623896899,
    0.5860414623896899,
    0.583590138674884,
    0.583590138674884,
    0.583590138674884,
    0.5811388149600779,
    0.5811388149600779,
    0.5786874912452721,
    0.5762361675304661,
    0.5762361675304661,
    0.5737848438156602,
    0.5737848438156602,
    0.5713335201008543,
    0.5713335201008543,
    0.5688821963860483,
    0.5688821963860483,
    0.5664308726712425,
    0.5664308726712425,
    0.5639795489564365,
    0.5639795489564365,
    0.5615282252416306,
    0.5590769015268245,
    0.5590769015268245,
    0.5590769015268245,
    0.5566255778120178,
    0.5566255778120178,
    0.5541742540972119,
    0.5541742540972119,
    0.5517229303824059,
    0.5517229303824059,
    0.5517229303824059,
    0.5492716066676,
    0.5492716066676,
    0.5492716066676,
    0.5492716066676,
    0.5468202829527942,
    0.5443689592379882,
    0.5443689592379882,
    0.5443689592379882,
    0.5443689592379882,
    0.5419176355231823,
    0.5394663118083762,
    0.5394663118083762,
    0.5370149880935703,
    0.5370149880935703,
    0.5345636643787645,
    0.5345636643787645,
    0.5321123406639585,
    0.5321123406639585,
    0.5296610169491526,
    0.5296610169491526,
    0.5272096932343466,
    0.5272096932343466,
    0.5272096932343466,
    0.5247583695195399,
    0.5247583695195399,
    0.522307045804734,
    0.522307045804734,
    0.522307045804734,
    0.522307045804734,
    0.519855722089928,
    0.519855722089928,
    0.519855722089928,
    0.517404398375122,
    0.5149530746603161,
    0.5125017509455102,
    0.5125017509455102,
    0.5100504272307043,
    0.5100504272307043,
    0.5075991035158983,
    0.5051477798010924,
    0.5051477798010924,
    0.5051477798010924,
    0.5026964560862865,
    0.5026964560862865,
    0.5026964560862865,
    0.5026964560862865,
    0.5002451323714806,
    0.5002451323714806,
    0.49779380865667455,
]

d = {"x": Operation_level, "y": Efficiency}
partLoadData = pd.DataFrame(d)

# Efficiency Curve for PEM Electrolyzer # Data from EC Campus Mainz Operation_level = [ 0.0208023774145616, 0.0222882615156017, 0.0222882615156017, 0.0222882615156017, 0.025260029717682, 0.025260029717682, 0.0267459138187221, 0.0282317979197622, 0.0297176820208024, 0.0312035661218424, 0.0326894502228826, 0.0341753343239227, 0.0356612184249628, 0.0371471025260029, 0.038632986627043, 0.0416047548291233, 0.0430906389301634, 0.0445765230312035, 0.0475482912332838, 0.0430906389301634, 0.0490341753343239, 0.050520059435364, 0.0520059435364041, 0.0549777117384844, 0.0579494799405646, 0.0609212481426448, 0.0638930163447251, 0.0683506686478455, 0.0713224368499256, 0.075780089153046, 0.0787518573551263, 0.0832095096582466, 0.087667161961367, 0.0921248142644873, 0.0980683506686478, 0.104011887072808, 0.108469539375928, 0.114413075780089, 0.120356612184249, 0.12778603268945, 0.13521545319465, 0.142644873699851, 0.151560178306092, 0.157503714710252, 0.166419019316493, 0.173848439821693, 0.181277860326894, 0.190193164933135, 0.196136701337295, 0.202080237741456, 0.209509658246656, 0.216939078751857, 0.224368499257057, 0.233283803863298, 0.240713224368499, 0.246656760772659, 0.25408618127786, 0.26151560178306, 0.270430906389301, 0.276374442793462, 0.283803863298662, 0.292719167904903, 0.298662704309063, 0.306092124814264, 0.313521545319465, 0.319465081723625, 0.328380386329866, 0.335809806835066, 0.343239227340267, 0.349182763744427, 0.356612184249628, 0.364041604754829, 0.371471025260029, 0.38038632986627, 0.389301634472511, 0.398216939078751, 0.407132243684992, 0.416047548291233, 0.423476968796433, 0.430906389301634, 0.439821693907875, 0.448736998514115, 0.457652303120356, 0.465081723625557, 0.472511144130757, 0.481426448736998, 0.490341753343239, 0.497771173848439, 0.50668647845468, 0.514115898959881, 0.523031203566121, 0.531946508172362, 0.540861812778603, 0.551263001485884, 0.560178306092124, 0.567607726597325, 0.576523031203566, 0.585438335809806, 0.595839524517087, 0.604754829123328, 0.613670133729569, 0.619613670133729, 0.62852897473997, 0.638930163447251, 0.646359583952451, 0.656760772659732, 0.664190193164933, 0.673105497771173, 0.684992570579494, 0.692421991084695, 0.699851411589896, 0.710252600297176, 0.717682020802377, 0.726597325408618, 0.735512630014858, 0.744427934621099, 0.75334323922734, 0.762258543833581, 0.769687964338781, 0.780089153046062, 0.786032689450223, 0.793462109955423, 0.802377414561664, 0.811292719167904, 0.820208023774145, 0.829123328380386, 0.838038632986627, 0.846953937592867, 0.858841010401188, 0.867756315007429, 0.87667161961367, 0.88707280832095, 0.895988112927191, 0.904903417533432, 0.913818722139673, 0.924219910846954, 0.933135215453194, 0.942050520059435, 0.947994056463595, 0.958395245170876, 0.965824665676077, 0.974739970282318, 0.985141158989598, 0.994056463595839, ] Efficiency = [ 0.03449362655834178, 0.05655553999159559, 0.04920156884717763, 0.07616612971004356, 0.09332539571368476, 0.115387309146939, 0.13254657515058135, 0.1497058411542229, 0.1693164308726712, 0.1864756968763127, 0.2036349628799551, 0.2256968763132085, 0.2404048186020449, 0.25511276089088053, 0.27472335060932884, 0.2918826166129703, 0.30904188261661275, 0.33110379604986695, 0.34581173833870255, 0.3212985011906424, 0.3629710043423449, 0.38013027034598645, 0.3923868889200161, 0.4095461549236585, 0.42425409721249496, 0.4365107157865246, 0.44876733436055427, 0.45857262921977887, 0.4683779240790026, 0.4830858663678382, 0.4953424849418686, 0.5075991035158983, 0.517404398375122, 0.5247583695195407, 0.5321123406639585, 0.5419176355231823, 0.5517229303824059, 0.5639795489564365, 0.5713335201008543, 0.5811388149600779, 0.5884927861044958, 0.5933954335341085, 0.5982980809637204, 0.6007494046785262, 0.6007494046785262, 0.6007494046785262, 0.5982980809637204, 0.5982980809637204, 0.5958467572489144, 0.5958467572489144, 0.5958467572489144, 0.5933954335341085, 0.5933954335341085, 0.5933954335341085, 0.5909441098193018, 0.5909441098193018, 0.5909441098193018, 0.5884927861044958, 0.5884927861044958, 0.5884927861044958, 0.5884927861044958, 0.5884927861044958, 0.5884927861044958, 0.5860414623896899, 0.5860414623896899, 0.5860414623896899, 0.583590138674884, 0.583590138674884, 0.583590138674884, 0.5811388149600779, 0.5811388149600779, 0.5786874912452721, 0.5762361675304661, 0.5762361675304661, 0.5737848438156602, 0.5737848438156602, 0.5713335201008543, 0.5713335201008543, 0.5688821963860483, 0.5688821963860483, 0.5664308726712425, 0.5664308726712425, 0.5639795489564365, 0.5639795489564365, 0.5615282252416306, 0.5590769015268245, 0.5590769015268245, 0.5590769015268245, 0.5566255778120178, 0.5566255778120178, 0.5541742540972119, 0.5541742540972119, 0.5517229303824059, 0.5517229303824059, 0.5517229303824059, 0.5492716066676, 0.5492716066676, 0.5492716066676, 0.5492716066676, 0.5468202829527942, 0.5443689592379882, 0.5443689592379882, 0.5443689592379882, 0.5443689592379882, 0.5419176355231823, 0.5394663118083762, 0.5394663118083762, 0.5370149880935703, 0.5370149880935703, 0.5345636643787645, 0.5345636643787645, 0.5321123406639585, 0.5321123406639585, 0.5296610169491526, 0.5296610169491526, 0.5272096932343466, 0.5272096932343466, 0.5272096932343466, 0.5247583695195399, 0.5247583695195399, 0.522307045804734, 0.522307045804734, 0.522307045804734, 0.522307045804734, 0.519855722089928, 0.519855722089928, 0.519855722089928, 0.517404398375122, 0.5149530746603161, 0.5125017509455102, 0.5125017509455102, 0.5100504272307043, 0.5100504272307043, 0.5075991035158983, 0.5051477798010924, 0.5051477798010924, 0.5051477798010924, 0.5026964560862865, 0.5026964560862865, 0.5026964560862865, 0.5026964560862865, 0.5002451323714806, 0.5002451323714806, 0.49779380865667455, ] d = {"x": Operation_level, "y": Efficiency} partLoadData = pd.DataFrame(d)

3. Create an energy system model instance¶

The structure of the energy system model is given by the considered locations, commodities, the number of time steps as well as the hours per time step.

The commodities are specified by a unit (i.e. 'GW_electric', 'GW_H2lowerHeatingValue', 'Mio. t CO2/h') which can be given as an energy or mass unit per hour. Furthermore, the cost unit and length unit are specified.

In [35]:

locations = {"GermanyRegion"}
commodityUnitDict = {"electricity": r"GW$_{el}$", "hydrogen": r"GW$_{H_{2},LHV}$"}
commodities = {"electricity", "hydrogen"}
numberOfTimeSteps = 168
hoursPerTimeStep = 1

locations = {"GermanyRegion"} commodityUnitDict = {"electricity": r"GW$_{el}$", "hydrogen": r"GW$_{H_{2},LHV}$"} commodities = {"electricity", "hydrogen"} numberOfTimeSteps = 168 hoursPerTimeStep = 1

In [36]:

esM = fn.EnergySystemModel(
    locations=locations,
    commodities=commodities,
    numberOfTimeSteps=numberOfTimeSteps,
    commodityUnitsDict=commodityUnitDict,
    hoursPerTimeStep=1,
    costUnit="1e9 Euro",
    lengthUnit="km",
    verboseLogLevel=0,
)

esM = fn.EnergySystemModel( locations=locations, commodities=commodities, numberOfTimeSteps=numberOfTimeSteps, commodityUnitsDict=commodityUnitDict, hoursPerTimeStep=1, costUnit="1e9 Euro", lengthUnit="km", verboseLogLevel=0, )

4. Add commodity sources to the energy system model¶

4.1. Electricity sources¶

Wind onshore¶

In [37]:

esM.add(
    fn.Source(
        esM=esM,
        name="Wind (onshore)",
        commodity="electricity",
        hasCapacityVariable=True,
        operationRateMax=data["Wind (onshore), operationRateMax"][0:numberOfTimeSteps],
        capacityMax=data["Wind (onshore), capacityMax"],
        investPerCapacity=1.1,
        opexPerCapacity=1.1 * 0.02,
        interestRate=0.08,
        economicLifetime=20,
    )
)

esM.add( fn.Source( esM=esM, name="Wind (onshore)", commodity="electricity", hasCapacityVariable=True, operationRateMax=data["Wind (onshore), operationRateMax"][0:numberOfTimeSteps], capacityMax=data["Wind (onshore), capacityMax"], investPerCapacity=1.1, opexPerCapacity=1.1 * 0.02, interestRate=0.08, economicLifetime=20, ) )

Full load hours:

In [38]:

nbval-check-output

print(data["Wind (onshore), operationRateMax"].sum())

print(data["Wind (onshore), operationRateMax"].sum())

2300.4069071646272

5. Add conversion components to the energy system model¶

Electrolyzers¶

In [39]:

nSegments = 2  # Define number of segments for the piecewice linearization of the efficiency curve

esM.add(
    fn.ConversionPartLoad(
        esM=esM,
        name="Electroylzers",
        physicalUnit=r"GW$_{el}$",
        commodityConversionFactors={"electricity": -1, "hydrogen": 1},
        commodityConversionFactorsPartLoad={
            "electricity": -1,
            "hydrogen": partLoadData,
        },
        nSegments=nSegments,
        hasCapacityVariable=True,
        bigM=99999,
        investPerCapacity=900,
        opexPerCapacity=900 * 0.01,
        interestRate=0.08,
        economicLifetime=10,
        hasIsBuiltBinaryVariable=True,
    )
)

nSegments = 2 # Define number of segments for the piecewice linearization of the efficiency curve esM.add( fn.ConversionPartLoad( esM=esM, name="Electroylzers", physicalUnit=r"GW$_{el}$", commodityConversionFactors={"electricity": -1, "hydrogen": 1}, commodityConversionFactorsPartLoad={ "electricity": -1, "hydrogen": partLoadData, }, nSegments=nSegments, hasCapacityVariable=True, bigM=99999, investPerCapacity=900, opexPerCapacity=900 * 0.01, interestRate=0.08, economicLifetime=10, hasIsBuiltBinaryVariable=True, ) )

6. Add commodity storages to the energy system model¶

6.1. Electricity storage¶

Lithium ion batteries¶

The self discharge of a lithium ion battery is here described as 3% per month. The self discharge per hours is obtained using the equation (1-$\text{selfDischarge}_\text{hour})^{30*24\text{h}} = 1-\text{selfDischarge}_\text{month}$.

In [40]:

esM.add(
    fn.Storage(
        esM=esM,
        name="Li-ion batteries",
        commodity="electricity",
        hasCapacityVariable=True,
        chargeEfficiency=0.95,
        cyclicLifetime=10000,
        dischargeEfficiency=0.95,
        selfDischarge=1 - (1 - 0.03) ** (1 / (30 * 24)),
        chargeRate=1,
        dischargeRate=1,
        doPreciseTsaModeling=False,
        investPerCapacity=0.151,
        opexPerCapacity=0.002,
        interestRate=0.08,
        economicLifetime=22,
    )
)

esM.add( fn.Storage( esM=esM, name="Li-ion batteries", commodity="electricity", hasCapacityVariable=True, chargeEfficiency=0.95, cyclicLifetime=10000, dischargeEfficiency=0.95, selfDischarge=1 - (1 - 0.03) ** (1 / (30 * 24)), chargeRate=1, dischargeRate=1, doPreciseTsaModeling=False, investPerCapacity=0.151, opexPerCapacity=0.002, interestRate=0.08, economicLifetime=22, ) )

6.2. Hydrogen storage¶

Hydrogen filled salt caverns¶

The maximum capacity is here obtained by: dividing the given capacity (which is given for methane) by the lower heating value of methane and then multiplying it with the lower heating value of hydrogen.

In [41]:

esM.add(
    fn.Storage(
        esM=esM,
        name="Salt caverns (hydrogen)",
        commodity="hydrogen",
        hasCapacityVariable=True,
        capacityVariableDomain="continuous",
        capacityPerPlantUnit=133,
        chargeRate=1 / 470.37,
        dischargeRate=1 / 470.37,
        sharedPotentialID="Existing salt caverns",
        stateOfChargeMin=0.33,
        stateOfChargeMax=1,
        capacityMax=data["Salt caverns (hydrogen), capacityMax"],
        investPerCapacity=0.00011,
        opexPerCapacity=0.00057,
        interestRate=0.08,
        economicLifetime=30,
    )
)

esM.add( fn.Storage( esM=esM, name="Salt caverns (hydrogen)", commodity="hydrogen", hasCapacityVariable=True, capacityVariableDomain="continuous", capacityPerPlantUnit=133, chargeRate=1 / 470.37, dischargeRate=1 / 470.37, sharedPotentialID="Existing salt caverns", stateOfChargeMin=0.33, stateOfChargeMax=1, capacityMax=data["Salt caverns (hydrogen), capacityMax"], investPerCapacity=0.00011, opexPerCapacity=0.00057, interestRate=0.08, economicLifetime=30, ) )

7. Add commodity sinks to the energy system model¶

7.2. Hydrogen sinks¶

Fuel cell electric vehicle (FCEV) demand¶

In [42]:

FCEV_penetration = 3
esM.add(
    fn.Sink(
        esM=esM,
        name="Hydrogen demand",
        commodity="hydrogen",
        hasCapacityVariable=False,
        operationRateFix=data["Hydrogen demand, operationRateFix"][0:numberOfTimeSteps]
        * FCEV_penetration,
    )
)

FCEV_penetration = 3 esM.add( fn.Sink( esM=esM, name="Hydrogen demand", commodity="hydrogen", hasCapacityVariable=False, operationRateFix=data["Hydrogen demand, operationRateFix"][0:numberOfTimeSteps] * FCEV_penetration, ) )

8. Optimize energy system model¶

In [43]:

esM.optimize(
    timeSeriesAggregation=False,
    solver=fn.utils.ImplementedSolvers.STANDARD_SOLVER.value,
)

esM.optimize( timeSeriesAggregation=False, solver=fn.utils.ImplementedSolvers.STANDARD_SOLVER.value, )

Declaring sets, variables and constraints for SourceSinkModel
	declaring sets... 
	declaring variables... 
	declaring constraints... 
		(0.0164 sec)

Declaring sets, variables and constraints for ConversionPartLoadModel
	declaring sets... 
	declaring variables... 
	declaring constraints... 
		(0.0137 sec)

Declaring sets, variables and constraints for StorageModel
	declaring sets... 
	declaring variables... 
	declaring constraints... 
		(0.0239 sec)

Declaring shared potential constraint...
		(0.0002 sec)

Declaring linked component quantity constraint...
		(0.0000 sec)

Declaring commodity balances...
		(0.2244 sec)

		(0.0000 sec)

Declaring objective function...
		(0.0556 sec)

GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --write C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmpnlz4bvqf.glpk.raw --wglp
 C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmp_asmbr5g.glpk.glp --cpxlp C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmpr71c0ir3.pyomo.lp
Reading problem data from 'C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmpr71c0ir3.pyomo.lp'...
C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmpr71c0ir3.pyomo.lp:24990: warning: lower bound of variable 'x352' redefined
C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmpr71c0ir3.pyomo.lp:24990: warning: upper bound of variable 'x352' redefined
3883 rows, 2707 columns, 10620 non-zeros
337 integer variables, all of which are binary
25327 lines were read
Writing problem data to 'C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmp_asmbr5g.glpk.glp'...
22278 lines were written
GLPK Integer Optimizer 5.0
3883 rows, 2707 columns, 10620 non-zeros
337 integer variables, all of which are binary
Preprocessing...
3703 rows, 2528 columns, 10261 non-zeros
337 integer variables, all of which are binary
Scaling...
 A: min|aij| =  2.126e-03  max|aij| =  1.000e+05  ratio =  4.704e+07
GM: min|aij| =  2.701e-01  max|aij| =  3.702e+00  ratio =  1.371e+01
EQ: min|aij| =  7.296e-02  max|aij| =  1.000e+00  ratio =  1.371e+01
2N: min|aij| =  4.233e-02  max|aij| =  1.560e+00  ratio =  3.684e+01
Constructing initial basis...
Size of triangular part is 3533
Solving LP relaxation...
GLPK Simplex Optimizer 5.0
3703 rows, 2528 columns, 10261 non-zeros
      0: obj =   0.000000000e+00 inf =   6.749e+03 (428)
Perturbing LP to avoid stalling [199]...
    720: obj =   2.007284998e+04 inf =   1.217e-08 (0) 5
Removing LP perturbation [2351]...
*  2351: obj =   1.444372714e+03 inf =   6.464e-12 (0) 13
OPTIMAL LP SOLUTION FOUND
Integer optimization begins...
Long-step dual simplex will be used
+  2351: mip =     not found yet >=              -inf        (1; 0)
+  2373: >>>>>   1.444372752e+03 >=   1.444372714e+03 < 0.1% (11; 0)
+  2373: mip =   1.444372752e+03 >=     tree is empty   0.0% (0; 21)
INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.3 secs
Memory used: 6.2 Mb (6512172 bytes)
Writing MIP solution to 'C:\Users\JA60A~1.BEL\AppData\Local\Temp\tmpnlz4bvqf.glpk.raw'...
6599 lines were written

Status: ok
Termination condition: optimal
Statistics: 
  Branch and bound: 
    Number of bounded subproblems: 21
    Number of created subproblems: 21
Error rc: 0
Time: 0.44152069091796875


Name: unknown
Lower bound: 1444.37275245145
Upper bound: 1444.37275245145
Number of objectives: 1
Number of constraints: 3883
Number of variables: 2707
Number of nonzeros: 10620
Sense: minimize

Solve time: 0.5904281139373779 sec.

Processing optimization output...
for SourceSinkModel ...(0.0779sec)
for ConversionPartLoadModel ...(0.0563sec)
for StorageModel ...  (0.0715sec)
		(0.2087 sec)

C:\Programming\FINE\fine\storage.py:2056: UserWarning: Charge and discharge at the same time for component Salt caverns (hydrogen)
  warnings.warn(

9. Selected results output¶

Sources and Sink¶

Show optimization summary

In [44]:

esM.getOptimizationSummary("SourceSinkModel", outputLevel=2)

esM.getOptimizationSummary("SourceSinkModel", outputLevel=2)

Out[44]:

			GermanyRegion
Component	Property	Unit
Hydrogen demand	operation	[GW$_{H_{2},LHV}$*h/a]	28588.126857
		[GW$_{H_{2},LHV}$*h]	548.265447
Wind (onshore)	NPVcontribution	[1e9 Euro]	2.210273
	TAC	[1e9 Euro/a]	2.210273
	capacity	[GW$_{el}$]	16.489969
	capexCap	[1e9 Euro/a]	1.847494
	commissioning	[GW$_{el}$]	16.489969
	invest	[1e9 Euro]	18.138966
	operation	[GW$_{el}$*h/a]	56346.216604
		[GW$_{el}$*h]	1080.612373
	opexCap	[1e9 Euro/a]	0.362779

Plot operation time series (either one or two dimensional)

ConversionPartLoad¶

Show optimization summary

In [45]:

esM.getOptimizationSummary("ConversionPartLoadModel", outputLevel=2)

esM.getOptimizationSummary("ConversionPartLoadModel", outputLevel=2)

Out[45]:

			GermanyRegion
Component	Property	Unit
Electroylzers	NPVcontribution	[1e9 Euro]	1441.053428
	TAC	[1e9 Euro/a]	1441.053428
	capacity	[GW$_{el}$]	10.068387
	capexCap	[1e9 Euro/a]	1350.437942
	commissioning	[GW$_{el}$]	10.068387
	invest	[1e9 Euro]	9061.548518
	isBuilt	[-]	1.0
	operation	[GW$_{el}$*h/a]	56031.729695
		[GW$_{el}$*h]	1074.581117
	opexCap	[1e9 Euro/a]	90.615485

Show operation time-series

Show operation color map

Storage¶

Show optimization summary

In [46]:

esM.getOptimizationSummary("StorageModel", outputLevel=2)

esM.getOptimizationSummary("StorageModel", outputLevel=2)

Out[46]:

			GermanyRegion
Component	Property	Unit
Li-ion batteries	NPVcontribution	[1e9 Euro]	0.392909
	TAC	[1e9 Euro/a]	0.392909
	capacity	[GW$_{el}$*h]	23.383499
	capexCap	[1e9 Euro/a]	0.346142
	commissioning	[GW$_{el}$*h]	23.383499
	invest	[1e9 Euro]	3.530908
	operationCharge	[GW$_{el}$*h/a]	3205.351317
		[GW$_{el}$*h]	61.472491
	operationDischarge	[GW$_{el}$*h/a]	2890.864408
		[GW$_{el}$*h]	55.441235
	opexCap	[1e9 Euro/a]	0.046767
Salt caverns (hydrogen)	NPVcontribution	[1e9 Euro]	0.716143
	TAC	[1e9 Euro/a]	0.716143
	capacity	[GW$_{H_{2},LHV}$*h]	1235.216115
	capexCap	[1e9 Euro/a]	0.012069
	commissioning	[GW$_{H_{2},LHV}$*h]	1235.216115
	invest	[1e9 Euro]	0.135874
	operationCharge	[GW$_{H_{2},LHV}$*h/a]	9593.994726
		[GW$_{H_{2},LHV}$*h]	183.994419
	operationDischarge	[GW$_{H_{2},LHV}$*h/a]	9593.994726
		[GW$_{H_{2},LHV}$*h]	183.994419
	opexCap	[1e9 Euro/a]	0.704073

Show battery storage color map

In [47]:

nbPeriods = int(numberOfTimeSteps / 24)

fig, ax = fn.plotOperationColorMap(
    esM,
    "Li-ion batteries",
    "GermanyRegion",
    variableName="stateOfChargeOperationVariablesOptimum",
    nbPeriods=nbPeriods,
)

nbPeriods = int(numberOfTimeSteps / 24) fig, ax = fn.plotOperationColorMap( esM, "Li-ion batteries", "GermanyRegion", variableName="stateOfChargeOperationVariablesOptimum", nbPeriods=nbPeriods, )

Show hydrogen storage color map

In [48]:

fig, ax = fn.plotOperationColorMap(
    esM,
    "Salt caverns (hydrogen)",
    "GermanyRegion",
    variableName="stateOfChargeOperationVariablesOptimum",
    nbPeriods=nbPeriods,
)

fig, ax = fn.plotOperationColorMap( esM, "Salt caverns (hydrogen)", "GermanyRegion", variableName="stateOfChargeOperationVariablesOptimum", nbPeriods=nbPeriods, )