Optimising storage locations

Functions to optimise hydrogen storage locations.

References

[1] (1,2)

Musial, W. D., Beiter, P. C., Nunemaker, J., Heimiller, D. M., Ahmann, J., and Busch, J. (2019). Oregon Offshore Wind Site Feasibility and Cost Study. Technical Report NREL/TP-5000-74597. Golden, CO: National Renewable Energy Laboratory. https://doi.org/10.2172/1570430.

[2] (1,2,3,4)

Dinh, Q. V., Dinh, V. N., Mosadeghi, H., Todesco Pereira, P. H., and Leahy, P. G. (2023). ‘A geospatial method for estimating the levelised cost of hydrogen production from offshore wind’, International Journal of Hydrogen Energy, 48(40), pp. 15000–15013. https://doi.org/10.1016/j.ijhydene.2023.01.016.

[3]

Pryor, S. C., Shepherd, T. J., and Barthelmie, R. J. (2018). ‘Interannual variability of wind climates and wind turbine annual energy production’, Wind Energy Science, 3(2), pp. 651–665. https://doi.org/10.5194/wes-3-651-2018.

[4] (1,2)

Dinh, V. N., Leahy, P., McKeogh, E., Murphy, J., and Cummins, V. (2021). ‘Development of a viability assessment model for hydrogen production from dedicated offshore wind farms’, International Journal of Hydrogen Energy, 46(48), pp. 24620–24631. https://doi.org/10.1016/j.ijhydene.2020.04.232.

[5]

Hydrogen Tools (no date) Lower and Higher Heating Values of Fuels. Available at: https://h2tools.org/hyarc/calculator-tools/lower-and-higher-heating-values-fuels (Accessed: 25 April 2024).

[6] (1,2,3,4)

Dinh, Q. V., Dinh, V. N., and Leahy, P. G. (2024). ‘A differential evolution model for optimising the size and cost of electrolysers coupled with offshore wind farms’.

[7] (1,2)

Dinh, Q. V., Todesco Pereira, P. H., Dinh, V. N., Nagle, A. J., and Leahy, P. G. (2024). ‘Optimising the levelised cost of transmission for green hydrogen and ammonia in new-build offshore energy infrastructure: pipelines, tankers, and HVDC’.

[8] (1,2,3)

Baufumé, S., Grüger, F., Grube, T., Krieg, D., Linssen, J., Weber, M., Hake, J.-F., and Stolten, D. (2013). ‘GIS-based scenario calculations for a nationwide German hydrogen pipeline infrastructure’, International Journal of Hydrogen Energy, 38(10), pp. 3813–3829. https://doi.org/10.1016/j.ijhydene.2012.12.147.

[9]

International Renewable Energy Agency (2022). Global Hydrogen Trade to Meet the 1.5°C Climate Goal: Technology Review of Hydrogen Carriers. Abu Dhabi: International Renewable Energy Agency. ISBN 978-92-9260-431-8. Available at: https://www.irena.org/publications/2022/Apr/Global-hydrogen-trade-Part-II (Accessed: 31 December 2023).

[10]

Siemens Energy (n.d.). Silyzer 300. Datasheet. Erlangen. Available at: https://assets.siemens-energy.com/siemens/assets/api/uuid:a193b68f-7ab4-4536-abe2-c23e01d0b526/datasheet-silyzer300.pdf (Accessed: 31 December 2023).

[11]

International Energy Agency (2019). The Future of Hydrogen: Seizing today’s opportunities. Paris: International Energy Agency. Available at: https://www.iea.org/reports/the-future-of-hydrogen (Accessed: 14 August 2023).

h2ss.optimisation.ref_power_curve(v)

Power curve for the reference wind turbine.

Parameters

vfloat

Wind speed [m s⁻¹]

Returns

float

Wind turbine power output at a given wind speed from the power curve [MW]

Notes

The NREL 15 MW reference wind turbine is used; see [1], Appendix D, p. 84, for the data used to generate the power curve.

h2ss.optimisation.weibull_probability_distribution(v, k, c)

Weibull probability distribution function.

Parameters

vfloat

Wind speed [m s⁻¹]

kfloat

Shape (Weibull distribution parameter, k)

cfloat

Scale (Weibull distribution parameter, C) [m s⁻¹]

Returns

float

Weibull probability distribution function [s m⁻¹]

Notes

The Weibull probability distribution function, \(f(v)\) [s m⁻¹] is based on Eqn. (1) of [2], where \(k\) and \(C\) [m s⁻¹] are the shape and scale Weibull distribution parameters, respectively, and \(v\) is the wind speed.

\[f(v) = \frac{k}{C} \, \left( \frac{v}{C} \right)^{k - 1} \, \exp \left( -\left( \frac{v}{C} \right)^k \right)\]

See also [3], Eqn. (2).

h2ss.optimisation.weibull_distribution(weibull_wf_data)

Generate a power curve and Weibull distribution.

Parameters

weibull_wf_datapandas.DataFrame

Dataframe of the Weibull distribution parameters for the wind farms

Returns

pandas.DataFrame

Dataframe of the Weibull distribution for each wind farm for wind speeds of 0 to 30 m s⁻¹ at an interval of 0.01

h2ss.optimisation.weibull_power_curve(v, k, c)

Weibull probability distribution function multiplied by the power curve.

Parameters

vfloat

Wind speed between cut-in and cut-out [m s⁻¹]

kfloat

Shape (Weibull distribution parameter, k)

cfloat

Scale (Weibull distribution parameter, C) [m s⁻¹]

Returns

float

Weibull probability distribution multiplied by the power curve [MW s m⁻¹]

h2ss.optimisation.number_of_turbines(owf_cap, wt_power=15)

Number of reference wind turbines in the offshore wind farm.

Parameters

owf_capfloat

Maximum nameplate capacity of the proposed offshore wind farm [MW]

wt_powerfloat

Rated power of the reference wind turbine [MW]

Returns

int

Number of wind turbines in the offshore wind farm comprising of reference wind turbines

Notes

The number of turbines, \(n\) of an offshore wind farm was determined using the floor division of the wind farm’s maximum nameplate capacity, \(P_{owf}\) [MW] by the reference wind turbine’s rated power, \(P_{rated}\) [MW].

\[n = \left\lfloor \frac{P_{owf}}{P_{rated}} \right\rfloor\]

h2ss.optimisation.annual_energy_production_function(n_turbines, k, c, w_loss=0.1, acdc_loss=0.982)

Annual energy production of the wind farm.

Parameters

n_turbinesint

Number of wind turbines in wind farm

kfloat

Shape (Weibull distribution parameter)

cfloat

Scale (Weibull distribution parameter) [m s⁻¹]

w_lossfloat

Wake loss

acdc_lossfloat

AC-DC conversion losses

Returns

tuple[float, float, float]

Annual energy production of wind farm [MWh], integral [MW], and absolute error [MW]

Notes

The annual energy production, \(E_{annual}\) [MWh], is based on Eqn. (3) of [2], where \(n\) is the number of turbines in the wind farm, \(w\) is the wake loss, which is assumed to be a constant value of 0.1, \(v_i\) and \(v_o\) [m s⁻¹] are the cut-in and cut-out speeds of the wind turbine, respectively, \(P(v)\) [MW] is the wind turbine power output, \(f(v)\) [s m⁻¹] is the Weibull probability distribution function, and \(\varepsilon\) is the AC-DC conversion loss.

\[E_{annual} = 365 \times 24 \times n \, \left( 1 - w \right) \, \varepsilon \, \int\limits_{v_i}^{v_o} P(v) \, f(v) \,\mathrm{d}v\]

In the function’s implementation, both the limit and absolute error tolerance for the integration have been increased.

h2ss.optimisation.annual_energy_production(weibull_wf_data)

Annual energy production of the wind farms.

Parameters

weibull_wf_datapandas.DataFrame

Dataframe of the Weibull distribution parameters for the wind farms

Returns

pandas.DataFrame

Dataframe with the annual energy production for each wind farm

h2ss.optimisation.annual_hydrogen_production(aep, eta_conv=0.7, e_pcl=0.003053)

Annual hydrogen production from the wind farm’s energy generation.

Parameters

aepfloat

Annual energy production of wind farm [MWh]

eta_convfloat

Conversion efficiency of the electrolyser

e_pclfloat

Electricity consumed by other parts of the hydrogen plant [MWh kg⁻¹]

Returns

float

Annual hydrogen production [kg]

Notes

Eqn. (4) of [2], Eqn. (9) of [4], and [6]. The value for the electricity consumed by other parts of the hydrogen plant is from Table 3 of [4] for proton exchange membrane (PEM) electrolysers predicted for the year 2030. This includes energy for water purification, hydrogen compression, and losses. The electrolyser conversion efficiency is based on [6]. See [5] for the heating values.

\[m_{annual} = \dfrac{E_{annual}}{\dfrac{LHV}{3,600 \, \eta} + E_{plant}}\]

where \(m_{annual}\) is the annual hydrogen production [kg], \(E_{annual}\) is the annual energy production of the wind farm [MWh], \(LHV\) is the lower heating value of hydrogen [MJ kg⁻¹], \(\eta\) is the conversion efficiency of the electrolyser, and \(E_{plant}\) is the electricity consumed by other parts of the hydrogen plant [MWh kg⁻¹].

h2ss.optimisation.transmission_distance(cavern_df, wf_data, injection_point_coords=(-6, -12, 53, 21))

Calculate the transmission distance to the injection point.

Parameters

cavern_dfgeopandas.GeoDataFrame

Dataframe of potential caverns

wf_datageopandas.GeoDataFrame

Geodataframe of the offshore wind farm data

injection_point_coordstuple[float, float, float, float]

Injection point coordinates (lon-deg, lon-min, lat-deg, lat-min)

Returns

tuple[geopandas.GeoDataFrame, geopandas.GeoSeries]

The cavern dataframe and injection point

Notes

A hacky workaround was used to prevent “DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)” during the transformation of the injection point from a single-row series, i.e. assigning a duplicate row and dropping it after reprojecting.

h2ss.optimisation.electrolyser_capacity(n_turbines, wt_power=15, cap_ratio=0.83)

Calculate the electrolyser capacity for an offshore wind farm.

Parameters

n_turbinesint

Number of wind turbines in wind farm

wt_powerfloat

Rated power of the reference wind turbine [MW]

cap_ratiofloat

Ratio of electrolyser capacity to the wind farm capacity

Returns

int

Electrolyser capacity [MW]

Notes

In the offshore electrolyser concept of [6], the electricity from an offshore wind farm “is supplied to the electrolyser by medium voltage alternating current (AC) cable. The electrolyser requires direct current (DC) electricity input so this concept includes an AC-DC converter. The hydrogen obtained is compressed and delivered onshore by hydrogen pipelines”.

The “energy from the offshore wind farm is only subjected to wake losses and a small amount of electricity loss in the site network and the AC-DC converter before being supplied to the electrolyser. The hydrogen obtained will then be transported to onshore infrastructure by pipeline. The losses incurred by pipeline transmission are very low” [6].

The electrolyser capacity, \(P_{electrolyser}\) [MW] is rounded down to an integer and is the product of the number of reference wind turbines of the offshore wind farm, \(n\), the rated power of the reference wind turbine, \(P_{rated}\), and the ratio of the electrolyser capacity to the offshore wind farm capacity, \(F_{electrolyser}\).

\[P_{electrolyser} = \left\lfloor n \, P_{rated} \, F_{electrolyser} \right\rfloor\]

h2ss.optimisation.hydrogen_pipeline_density(pressure, temperature)

Calculate the density of hydrogen in the pipelines.

Parameters

pressurefloat

Pressure of hydrogen in the pipeline [Pa]

temperaturefloat

Temperature of hydrogen in the pipeline [°C]

Returns

float

Pipeline hydrogen density [kg m⁻³]

Notes

According to [8], the envisaged future hydrogen pipeline system is assumed to be operated at pressure levels up to 10 MPa. They used an average operating pressure of 6.5 MPa for transmission pipelines and calculated the density using the average soil temperature, which was assumed to be the operating temperature of the hydrogen [8].

h2ss.optimisation.capex_pipeline(e_cap, p_rate=0.0055, pressure=10000000.0, temperature=10, u=15)

Capital expenditure (CAPEX) for the pipeline.

Parameters

e_capfloat

Electrolyser capacity [MW]

p_ratefloat

Electrolyser production rate [kg s⁻¹ MW⁻¹]

pressurefloat

Pressure of hydrogen in the pipeline [Pa]

temperaturefloat

Temperature of hydrogen in the pipeline [°C]

ufloat

Average fluid velocity [m s⁻¹]

Returns

float

CAPEX of the pipeline per km of pipeline [€ km⁻¹]

Notes

See Eqn. (18) of [2] and Section 3.1 of [7], from which the following text has been taken.

The estimation of offshore pipeline costs is based on the onshore pipeline calculations of [8], multiplied by a factor of two to reflect the estimated cost scaling of onshore to expected offshore costs, as suggested by [9].

In the reference case, the resulting capital expenditure for transmission pipelines and associated recompression stations was represented by a second order polynomial function.

The electrolyser production rate was based on the Siemens - Silyzer 300 [10].

Because the electrolyser plant is assumed to be operating at full capacity at all times, the CAPEX was calculated considering a 75% utilisation rate, i.e. the pipeline capacity is 33% oversized [11].

\[CAPEX = 2,000 \, \left( 16,000 \, \frac{P_{electrolyser} \times EPR}{\rho_{H_2} \, v_{H_2} \, \pi} + 1,197.2 \, \sqrt{\frac{P_{electrolyser} \times EPR}{\rho_{H_2} \, v_{H_2} \, \pi}} + 329 \right)\]

where \(CAPEX\) is the CAPEX of the pipeline per km of pipeline [€ km⁻¹], \(P_{electrolyser}\) is the electrolyser capacity [MW], \(EPR\) is the electrolyser production rate [kg s⁻¹ MW⁻¹], \(\rho_{H_2}\) is the density of hydrogen [kg m⁻³], and \(v_{H_2}\) is the average fluid velocity [m s⁻¹].

h2ss.optimisation.lcot_pipeline_function(capex, d_transmission, ahp, opex_ratio=0.02, discount_rate=0.08, lifetime=30)

Levelised cost of transmission (LCOT) of hydrogen in pipelines.

Parameters

capexfloat

Capital expenditure (CAPEX) of the pipeline [€ km⁻¹]

d_transmissionfloat

Pipeline transmission distance [km]

ahpfloat

Annual hydrogen production [kg]

opex_ratiofloat

Ratio of the operational expenditure (OPEX) to the CAPEX

discount_ratefloat

Discount rate

lifetimeint

Lifetime of the pipeline [year]

Returns

float

LCOT of hydrogen in the pipeline [€ kg⁻¹]

Notes

The OPEX is calculated as a percentage of the CAPEX. See the introduction of Section 3, Eqn. (1) and (2), and Section 3.5, Eqn. (22) of [7]; see Tables 2 and 3 for the assumptions and constants used.

\[LCOT = \frac{\mathrm{total\ lifecycle\ costs\ of\ all\ components}} {\mathrm{lifetime\ hydrogen\ transported}}\]

\[OPEX = CAPEX \times F_{OPEX}\]

\[LCOT = \frac{\left( CAPEX + \displaystyle\sum_{l=0}^{L} \frac{OPEX}{{(1 + DR)}^l} \right) \, d} {\displaystyle\sum_{l=0}^{L} \frac{AHP}{{(1 + DR)}^l}}\]

where \(LCOT\) is the LCOT of hydrogen in pipelines [€ kg⁻¹], \(CAPEX\) is the CAPEX of the pipeline per km of pipeline [€ km⁻¹], \(d\) is the pipeline transmission distance [km], \(OPEX\) is the OPEX of the pipeline [€ km⁻¹], \(DR\) is the discount rate, \(AHP\) is the annual hydrogen production [kg], \(L\) is the lifetime of the pipeline [year], and \(F_{OPEX}\) is the ratio of the OPEX to the CAPEX.

h2ss.optimisation.lcot_pipeline(weibull_wf_data, cavern_df)

Calculate the pipeline levelised cost of transmission.

Parameters

cavern_dfgeopandas.GeoDataFrame

Dataframe of potential caverns

weibull_wf_datapandas.DataFrame

Dataframe of the Weibull distribution parameters for the wind farms

Returns

pandas.DataFrame

Dataframe of potential caverns

h2ss.optimisation.rotor_area(diameter=248)

Wind turbine rotor swept area.

Parameters

diameterfloat

Wind turbine rotor diameter [m]

Returns

float

Wind turbine rotor swept area [m²]

Notes

\[A = \frac{\pi \, D^2}{4}\]

where \(A\) is the wind turbine rotor swept area [m²] and \(D\) is the rotor diameter [m].

h2ss.optimisation.power_wind_resource(v, rho=1.225, diameter=248)

Total wind resource power passing through a wind turbine’s rotor.

Parameters

vfloat

Wind speed [m s⁻¹]

rhofloat

Air density [kg m⁻³]

diameterfloat

Wind turbine rotor diameter [m]

Returns

float

Power contained in the wind resource [MW]

Notes

\[P_{wind} = \frac{\rho_{air} \, A \, v^3}{2 \times 10^6}\]

where \(P_{wind}\) is the power contained in the wind resource [MW], \(\rho_{air}\) is the air density [kg m⁻³], \(A\) is the rotor swept area [m²], and \(v\) is the wind speed [m s⁻¹].

h2ss.optimisation.power_coefficient(v)

Power coefficient of the reference wind turbine.

Parameters

vfloat

Wind speed [m s⁻¹]

Returns

float

Power coefficient

Notes

This is specific to the power curve of the NREL 15 MW reference wind turbine [1].

\[C_p = \frac{P}{P_{wind}} = \frac{P \times 2 \times 10^6} {\rho_{air} \, A \, v^3}\]

where \(P\) is the wind turbine power output [MW], \(P_{wind}\) is the power contained in the wind resource [MW], \(\rho_{air}\) is the air density [kg m⁻³], \(A\) is the rotor swept area [m²], \(v\) is the wind speed [m s⁻¹], and \(C_p\) is the power coefficient of the wind turbine.