on the Dutch North Sea
Niels A. Wouda
on the Dutch North Sea
Niels A. Wouda
17th February 2021
Abstract
This thesis optimises construction plans for the production side of a green hydrogen supply chain network with uncertain electricity supply. In such a supply chain hy-drogen is produced by means of electrolysis, using electricity intermittently produced at offshore wind parks constructed on the Dutch North Sea. We consider settings where the electrolysers are alternatively placed on- or offshore. We formulate determ-inistic and stochastic (two-stage recourse) mixed-integer linear programming models for these settings. Both modelling approaches result in similar costs and production shortfalls, suggesting there is little benefit to explicitly modelling wind uncertainty. Rather than solving difficult stochastic models, robust solutions can also be obtained from the deterministic model by constructing overcapacity in electricity generation. An overcapacity of just 10% sustains a service level of 80%, and an overcapacity of 25% a 98–99% service level. These overcapacities result in additional costs of less than 8% and 20%, respectively.
C O N T E N T S 1 Introduction 1 2 Literature review 3 3 Models 4 3.1 Offshore electrolysers . . . 7 3.2 Land-based electrolysers . . . 9 3.3 Integrated model . . . 10 4 Parameter justification 12 5 Results 17
5.1 Electrolyser placement and robust solutions . . . 18
5.2 Sensitivity analysis . . . 23
6 Conclusion 28
A Solution approach 36
1 I N T R O D U C T I O N
The Netherlands has committed itself to reduce carbon dioxide emissions by 55% in 2030, compared to 1990 levels. By 2050 these emissions need to be lowered further, by at least 95% (Rijksoverheid,2019). Significant investments in renewable electricity are needed to achieve this emissions reduction.
Direct use of renewable electricity is difficult to achieve at scale. First, most renewable electricity sources produce electricity intermittently. Since electricity is notoriously difficult to store, this intermittency makes it difficult to balance electricity production and demand. Second, and more importantly, electricity alone accounts for less than 20% of Dutch energy consumption: the rest is mostly consumed in the form of ‘molecules’, particularly natural gas and oil derivatives (Statistics Netherlands,2019,2020).
Such molecules can be created synthetically from renewable electricity, as a clean alternative to replace the roles of natural gas and oil as sources of energy. In addition, these molecules can be stored, thus mitigating the intermittent nature of renewable electricity generation. A promising synthetic molecule is green hydrogen, which is produced from renewable electricity by means of electrolysis. In the Dutch setting, due to the limited availability of land, offshore wind parks appear to be the most promising option to generate this renewable electricity.
In this thesis, we address the question where to build offshore wind parks to generate the renewable electricity, and where to build electrolysers to produce green hydrogen from this renewable electricity. There are two general options, each with their up- and downsides.
The first option is to build both wind parks and electrolysers offshore (van Stralen et al.,2020; Neptune Energy, 2019). Offshore wind parks are connected with offshore electrolysers via electrical cables. These offshore electrolysers are built on artificial islands, or on re-used gas platforms. The hydrogen produced there is brought to shore via gas pipelines. This setting is sketched in Figure1a. The advantage of this setting is that wind parks and electrolysers are built near each other, which reduces electrical cable lengths, and thus costs. Additionally, offshore electrolysers allow the exploitation of areas far offshore which cannot easily be reached with cables from land. Potential downsides of this setting are the cost of constructing artificial islands, and unclear cost and availability of re-using and converting offshore gas platforms for hydrogen production.
The second option is to build the electrolysers on land. Offshore wind parks are connected to land-based electrolysers, again via electrical cables. The hydrogen produced there is inserted directly into the onshore gas grid. This setting is sketched in Figure1b. An obvious benefit of this setting is that electrolysers can be constructed and operated on land more easily, and require no expensive land reclamation projects or existing offshore infrastructure to function. A downside is that longer, costlier electrical cables are required to connect offshore wind parks to the electrolyser plants.
(a) (b)
Figure 1: A schematic overview of the two settings. Electricity cables (orange) transport electricity generated at offshore wind parks to electrolysers in various locations, where the electricity is converted into hydrogen. Gas pipelines (blue) transport this hydrogen further inland to meet some demand. Figure1apresents the offshore setting, where electrolysers are built on artificial islands and re-used gas platforms. Figure1bpresents the land-based setting, where electrolysers are built on land. The integrated setting combines these into a single optimisation problem.
and helps investigate if and when the construction of artificial islands far offshore becomes viable.
Deterministic and stochastic mathematical programs are formulated for each setting. In particular, the deterministic models are mixed-integer linear programs combining integral investment decisions with a continuous flow problem. The stochastic models are formulated as two-stage programs with recourse, where the investment decisions and flow problems are split by stage. These models explicitly address the variability of wind electricity generation, which should result in more robust solutions.
Our main contributions are the following.
• We analyse the options introduced above, and conclude that land-based electrolysers should be preferred.
• We consider the effects of overcapacity on the expected number of years without production shortfalls (service level). We find that a 25% increase in overcapacity (at an additional cost of less than 20%) already results in a very robust green hydrogen supply chain that achieves a 98–99% service level.
• We present a large sensitivity analysis, investigating the effects of parameter changes on solution costs. Through this analysis we find that wind park and electrolyser con-struction costs, electrolyser efficiencies, and wind park capacity factors substantially influence solution costs.
choices. Section 5 discusses our findings. Here we also present a sensitivity analysis. Finally, Section6concludes the thesis.
2 L I T E R A T U R E R E V I E W
A substantial body of literature on hydrogen supply chain networks (HSCNs) exists. Rosen and Koohi-Fayegh(2016) present a general overview of the various components of a HSCN in practice, from production and transport to storage and utilisation. Li et al.(2019) offer a recent review of optimisation-oriented approaches to the HSCN design problem. Most of the papers they survey use some form of mixed-integer linear programming, sometimes including demand uncertainties (Nunes et al.,2015;Almansoori and Shah,2012). They, and others (Brandenburg et al.,2014;Banasik et al.,2018), identify a gap in the literature related to the modelling of operational uncertainties, for example those resulting from renewable energy sources in a green HSCN. In this thesis we take uncertainty in annual wind electricity generation into account.
Hydrogen is an energy carrier; not an energy source. As such, it needs to be produced from some feedstock. Many papers from before the Paris Agreement of 2015 assume fossil feedstocks would be used for this purpose. In particular natural gas—through steam methane reforming (SMR)—is often discussed as a cost-effective method of producing hydrogen (Almansoori and Shah,2009;Agnolucci et al.,2013). In the post-Paris Agreement era, more emphasis is placed on hydrogen production from renewable electricity, since that results in substantially reduced carbon emissions (Bhandari et al.,2014).
The use of renewable electricity presents new challenges: first, renewable electricity sources must be built from the ground up for hydrogen production at scale, whereas a natural gas infrastructure is often already in place for use in SMR; second, the intermittent availability of many renewable electricity sources complicates the design of robust and economical HSCNs (Caglayan et al., 2019). We next discuss several papers that use different sources of renewable electricity in green HSCNs to illustrate these difficulties.
Kim and Kim(2017) investigate a wind-powered HSCN for an island in South Korea. Their approach considers electricity production from onshore and offshore wind turbines. Hydrogen is produced at electrolyser plants, which are placed either on-site at large consumers, or in a central facility. A mixed integer linear program minimising total capital and operating costs is formulated. In a sensitivity analysis they find wind speeds and wind park construction costs are the most important cost factors. Additionally, their model decides to construct offshore wind turbines in only one of six scenarios, a result largely due to their increased cost relative to land-based wind turbines.
Jiang et al.(2019) andYang et al.(2020) consider a wind-powered HSCN, where the uncertainty of wind power is handled via a chance constraint. They observe significant economies of scale as hydrogen demand increases, and find that the overall costs depend largely on the unit cost of wind turbines and electrolysers. Finally, in their case study of a Chinese province, explicitly modelling wind availability via a chance constraint results in a small decrease in overall costs relative to the deterministic scenario.
These papers all study HSCNs that (mostly) rely on land-based renewable energy sources. In the Dutch setting, however, offshore wind seems the most promising route to green hydrogen production, due to limited space on land for wind turbines and solar photovoltaics. In addition, the shallow Dutch North Sea makes constructing wind parks technologically feasible almost everywhere (for offshore settings where this is not possible, including those very far offshore,Babarit et al.(2018) consider fully floating wind turbines and electrolysers).
Connecting these wind parks constructed offshore to land-based electrolysers might be inferior to the construction of offshore electrolysers, nearer to these wind parks. This we argued already in Section1, but we now present several techno-economic studies exploring the feasibility of offshore electrolysers. The re-use of existing gas platforms off the Croatian coast is discussed bySedlar et al.(2019). Meier(2014) does the same for platforms off the Norwegian coast. Donkers(2020) considers plaform re-use in an abstract setting roughly reflecting Dutch conditions. DNV GL (2018) studies artificial islands and offshore gas platforms for electrolyser placement on the Dutch North Sea. However, each of these studies ignores the spatial context of where to build these electrolysers, assuming instead power is delivered in the abstract from some nearby wind park. In this thesis we do take that context into account.
3 M O D E L S
In this section we develop mathematical models for each setting. Section 3.1 develops models for the setting where electrolysers are placed offshore, on artificial islands or re-used gas platforms. Section3.2presents models for the setting where electrolysers are built on land instead. Section3.3synthesises both into an integrated model, covering each of the other two settings as an extreme case.
Each model constructs wind parks, electrolysers and electrical cables (‘assets’ in the HSCN) to meet some annual hydrogen demand target. Meeting demand is modeled as a flow problem on the HSCN. The flow through this network starts at the offshore wind parks, which are sources of electricity. This electricity flows over electrical cables to electrolyser nodes, where the electricity is converted into hydrogen. The aggregate amount of hydrogen produced there must be sufficient to meet annual demand. The goal is to minimise construction and maintenance costs of the assets that make-up the HSCN.
rate’). This number varies year-over-year, and is the source of uncertainty in annual electricity supply.
We want our construction decisions to be robust with respect to this uncertainty, that is, our solution should be able to meet demand sufficiently often. We next discuss two ways to model this requirement, corresponding to different interpretations of ‘robustness’.
L I M I T E D S H O R T F A L L A first measure of robustness requires that shortfalls between hydrogen demand and production are, on average, limited. We model this as a two-stage stochastic program with recourse. In the first stage assets are constructed here-and-now, subject to uncertain wind capacity factors. The first-stage objective is to minimise construction and maintenance costs and expected second-stage production shortfalls, scaled by a cost parameter. In the second stage a realisation of the wind capacity factors becomes known, and the flow problem is solved using the assets from the first stage. Any production shortfalls are met through imported hydrogen, which constitutes the recourse action. These shortfalls are minimised in the second-stage objective.
S E R V I C E L E V E L A stricter measure of robustness states that the solution should
satisfy a fixed service level: given uncertain wind capacity factors, the solution must satisfy demand in at least a fraction of 1 − α years, for some confidence level α ∈ [0,1]. A way to model this is via a chance constraint on the feasibility of the flow problem. Hand-waving some details, such a constraint has the form
Pr (flow problem is feasible) ≥ 1 − α.
Although this formulation is elegant, integer linear programs with chance constraints are notoriously difficult to solve (Luedtke et al.,2010). We attempted the sample average approximation solution method ofPagnoncelli et al.(2009) for a chance-constrained model formulation of the integrated model in Section3.3, but could not solve the resulting large mixed-integer program for more than about ten samples. As such, we do not pursue chance-constrained model formulations further.
An alternative method to achieve a particular service level is to construct overcapacity. The idea is that a HSCN built for a demand level is, in general, also sufficient for lower demand levels. We explore this further in Section5.
For each setting, we first develop a deterministic formulation where we fix the wind capacity factors. We then relax this restriction, and present a recourse formulation where wind capacity factors are randomly drawn from some distribution.
Table 1: Definitions of inputs and decision variables.
Notation Definition
Sets
Vw Potential offshore wind park locations.
Vp Offshore gas platforms.
Va Potential artificial island locations.
Vo Onshore gas grid connections (Callantsoog, Maasvlakte, and
Uithuizen).
Ee Edges (i, j) ∈ Ee represent potential electrical cables between
wind parks and electrolysers.
E Union of Eeand edges representing the gas and hydrogen grid
that connects electrolyser locations to grid connections in Vo. Parameters
ce
i j≥ 0 Cost of constructing a single electrical cable x
e
i j ∈ Z+ on edge
(i, j) ∈ Ee.
ch≥ 0 Cost of constructing and operating a one MW electrolyser.
cri≥ 0 Cost of re-using platform i ∈ Vp for hydrogen electrolysis. ca
i ≥ 0 Cost of constructing and operating an artificial island at location
i ∈ Va. Iw
i ≥ 0 Capacity of wind park i ∈ V
w.
Iei j≥ 0 Capacity of each electrical cable constructed along edge (i, j) ∈ Ee. Iai ≥ 0 Electrolyser capacity (in MW) of artificial island i ∈ Va.
Ir
i ≥ 0 Electrolyser capacity of re-used platform i ∈ V
p.
d ≥ 0 Hydrogen demand (in MWh-equivalent).
ki∈ [0, 1] Fixed capacity factor of wind park i ∈ Vw.
(κ1,. . . ,κ|Vw|) ∼ K Vector of wind capacity factors for wind parks i ∈ Vw, drawn from
joint distribution K .
η ∈ [0,1] Electrolyser efficiency.
Decisions
xi je ∈ Z+ Number of electrical cables built along edge (i, j) ∈ Ee.
xwi ∈ {0, 1} 1 if a wind park is built in location i ∈ Vw, 0 otherwise. xr
i ∈ {0, 1} 1 if platform i ∈ V
pis re-used, 0 if not.
xa
i ∈ {0, 1} 1 if an artificial island is constructed at location i ∈ V
a, 0 if not.
xaei ≥ 0 Electrolyser capacity built on island i ∈ Va.
3.1 Offshore electrolysers
In this setting we construct all assets offshore. Electrolysers are built on re-used platforms, or specially constructed artificial islands. The hydrogen produced there is brought to shore via the offshore gas grid, or dedicated new pipelines in case of artificial islands.
We introduce decisions xri ∈ {0, 1} for each platform i ∈ Vp, indicating whether the platform is re-used (1) or not (0). If platform i is re-used, a cost cri is paid, covering its lifetime expenses. A re-used platform has electrolyser capacity of Iri (in MW).
For the artificial islands, we introduce decisions xai ∈ {0, 1} for each island location i ∈ Va, indicating whether the island is constructed (1) or not (0). The islands are constructed at cost cai, which covers construction and lifetime operating expenses and also includes the cost of building and operating a gas pipeline to shore. If island i is constructed, electrolysers of capacity xaei ≥ 0 (in MW) can be constructed, at cost chper MW.
D E T E R M I N I S T I C In the objective function, we sum the costs of re-using platforms, constructing artificial islands and island-based electrolysers, wind parks, and electrical cables. It is given by:
O1(x) = ∑︂ i∈Vp critxri (re-using platforms) + ∑︂ i∈Va [︂ caixai + chxaei ]︂
(islands and island-based electrolysers) + ∑︂ i∈Vw cwi xwi (wind parks) + ∑︂ (i, j)∈Ee cei jxei j. (electrical cables)
We then propose the following model: min
x, f O1(x) (3.1)
such that the following constraints hold:
(island capacity) xaei ≤ Iaixai ∀i ∈ Va (3.2a)
xwi ∈ {0, 1} ∀i ∈ Vw (3.2b)
xri ∈ {0, 1} ∀i ∈ Vp (3.2c)
xai ∈ {0, 1}, xaei ≥ 0 i ∈ Va (3.2d)
xi je ∈ Z+ ∀(i, j) ∈ Ee. (3.2e)
Constraint (3.2a) states that up to Iai MW of electrolyser capacity can be constructed on island i ∈ Va, but only when that island has itself been constructed (xai = 1). The other constraints in this block are simple boxing constraints for the construction decisions.
We also impose constraints for the flow problem:
(platform capacity) ∑︂
j∈Vw
fji≤ Irixri ∀i ∈ Vp (3.3b)
(island elec. capacity) ∑︂
j∈Vw
fji≤ xaei ∀i ∈ Va (3.3c)
(wind park capacity) ∑︂
j∈Vp∪Va
fi j≤ Iwi xwi ∀i ∈ Vw (3.3d)
(cable capacity) fi j≤ Iei jxei j ∀(i, j) ∈ Ee (3.3e)
fi j≥ 0 ∀(i, j) ∈ E. (3.3f)
Here, constraint (3.3a) states that demand must be met from hydrogen produced at offshore platforms (Vp) and artificial islands (Va). Constraints (3.3b) and (3.3c) state the electricity flow into platform and island-based electrolysers cannot exceed electrolyser capacities at these locations. Similarly, constraint (3.3d) states the electricity flow out of a wind park cannot exceed the nominal capacity Iwi of said wind park. Equation (3.3e) states that the flow fi j through an electrical cable cannot exceed the aggregate capacity Iei jxei j, that is, the
capacity of each cable multiplied by the number of cables constructed along edge (i, j) ∈ Ee. Finally, (3.3f) gives a boxing constraint for the flow variables f .
One additional flow constraint warrants special attention: (balance) η ∑︂ j∈Vw kjfji= ∑︂ j∈Vo fi j ∀i ∈ Vp∪ Va. (3.3g)
Flow balance constraint (3.3g) converts ‘electricity’ flows (originating at the wind parks) into ‘hydrogen’ flows (leaving electrolyser nodes). This conversion happens at each electrolyser node, through various conversion factors. First, wind capacity factors kj∈ [0, 1], for j ∈ Vw
are introduced, which convert nominal electricity output into averaged annual numbers. In essence, thus, the wind capacity factor regulates the fraction of the nominal capacity that is actually produced in a year. Then, the electrolyser efficiency factorη ∈ [0,1] is applied, which gives the fraction of input electricity that is converted into hydrogen. The remaining fraction 1 − η is generally lost as heat. Each of these conversion factors applies to the input electricity, so they are on the left-hand side of the balance constraint.
R E C O U R S E The model introduced just yet is fully deterministic, as we use some fixed
value kj for the wind capacity factors in constraint (3.3g). We now relax that restriction.
We formulate the decision problem as a two-stage stochastic program with recourse. In the first stage, construction decisions x are made here-and-now, subject to uncertain wind capacity factors. In the second stage a realisation of these wind capacity factors is observed, and the first stage decisions are used to solve the flow problem with these capacity factors. Assume the wind capacity factorsκj, j = 1,...,|Vw|, are drawn from some joint
distribu-tion K . We define the following first-stage (master) problem: M1 := min
x O1(x) + λEκ1,...,κ|V w|(︁S1(x,κ1,. . . ,κ|Vw|)
)︁
(3.4a)
Given a solution x to the first-stage problem, we define the following second-stage (sub) problem: S1(x,κ1,. . . ,κ|Vw|) := min f ,s s (3.5a) subject to (3.3b)–(3.3f) (3.5b) (demand) ∑︂ i∈Vo (︄ ∑︂ j∈Vp fji+ ∑︂ j∈Va fji )︄ + s = d (3.5c) (balance) η ∑︂ j∈Vw κjfji= ∑︂ j∈Vo fi j ∀i ∈ Vp∪ Va (3.5d) s ≥ 0. (3.5e)
In the two-stage model above, we took another step: we relaxed the hard constraint (3.3a) into a soft constraint in the sub problem via the introduction of a slack variable s ≥ 0, and added a multiplier λ ≥ 0 to the master problem’s objective. This ensures the technical condition of relatively complete recourse is satisfied (which states that for each vector x feasible for the first-stage problem, a feasible assignment ( f , s) can be found for the second-stage problem). In the first-stage master problem, the coefficient λ ≥ 0 has the interpretation of a price on the expected shortfall between demand and production. We consider this to be the (unit) cost of importing hydrogen from outside the model—either from abroad, or from some hydrogen storage facility. We explore the effect of different values ofλ further in Section5.
3.2 Land-based electrolysers
In this section we present a model that constructs wind parks offshore and electrolysers on land at the onshore gas grid connections in Vo. The wind parks and electrolysers are connected through electrical cables.
We introduce decisions xoi ≥ 0 for all i ∈ Vo, modelling the rated capacity (in MW) of the land-based electrolysers at location i ∈ Vo. These electrolysers are constructed at the usual cost chper MW.
D E T E R M I N I S T I C The objective sums the costs of costs of constructing and operating wind parks, onshore electrolysers, and electrical cable. It is given by:
O2(x) = ∑︂ i∈Vw cwi xwi (wind parks) + ∑︂ i∈Vo chxoi (land-based electrolysers) + ∑︂ (i, j)∈Ee cei jxi je. (electrical cables)
We propose the following model for this setting: min
such that the following boxing constraints on the construction decisions hold:
xwi ∈ {0, 1} ∀i ∈ Vw (3.7a)
xoi ≥ 0 ∀i ∈ Vo (3.7b)
xei j∈ Z+ ∀(i, j) ∈ Ee. (3.7c)
We also impose constraints for the flow problem:
(demand) ∑︂ i∈Vo (︄ η ∑︂ j∈Vw kjfji )︄ ≥ d (3.8a) (onshore capacity) ∑︂ j∈Vw fji≤ xoi ∀i ∈ Vo (3.8b)
(wind park capacity) ∑︂
j∈Vo
fi j≤ Iwi xwi ∀i ∈ Vw (3.8c)
(cable capacity) fi j≤ Ii je xei j ∀(i, j) ∈ Ee (3.8d)
fi j≥ 0 ∀(i, j) ∈ E. (3.8e)
Constraint (3.8a) states that demand must be met from hydrogen produced at onshore electrolysers (Vo). Conversion from electricity into hydrogen now happens directly at the onshore sinks rather than at offshore electrolyser nodes, as in the model of Section3.1. Constraint (3.8b) states electricity flows into the electrolysers cannot exceed electrolyser capacity. Similarly, equation (3.8c) states electricity generated at wind parks cannot exceed the nominal wind park capacity. Finally, equation (3.8d) states a capacity constraint on the electrical cables, and (3.8e) a boxing constraint.
R E C O U R S E For the recourse formulation, we define the following master problem: M2 := min
x O2(x) + λEκ1,...,κ|V w|(︁S2(x,κ1,. . . ,κ|Vw|)
)︁
(3.9a)
subject to (3.7a)–(3.7c). (3.9b)
Given a solution x to the first-stage problem, we define the following second-stage sub problem: S2(x,κ1,. . . ,κ|Vw|) := min f ,s s (3.10a) subject to (3.8b)–(3.8e) (3.10b) (balance) ∑︂ i∈Vo (︄ η ∑︂ j∈Vwκj fji )︄ + s = d (3.10c) s ≥ 0. (3.10d) 3.3 Integrated model
D E T E R M I N I S T I C The objective sums the construction and operating costs of the
de-cisions in Section3.1and Section3.2. It is given by: O3(x) = ∑︂ i∈Vp critxri (re-using platforms) + ∑︂ i∈Va [︂
caixai + chxaei ]︂ (islands and island-based electrolysers) + ∑︂ i∈Vw cwi xwi (wind parks) + ∑︂ i∈Vo chxoi (land-based electrolysers) + ∑︂ (i, j)∈Ee cei jxei j. (electrical cables)
We propose the following integrated model: min
x, f O3(x) (3.11)
such that the following constraints hold:
(island capacity) xaei ≤ Iaixai ∀i ∈ Va (3.12a)
xwi ∈ {0, 1} ∀i ∈ Vw (3.12b)
xri ∈ {0, 1} ∀i ∈ Vp (3.12c)
xio≥ 0 ∀i ∈ Vo (3.12d)
xei j∈ Z+ ∀(i, j) ∈ Ee. (3.12e)
Constraint (3.12a) states that up to Iai MW of electrolyser capacity can be built on island i ∈ Va, when that island has itself been constructed (xai = 1). Constraints (3.12b)–(3.12e) are simple boxing constraints for the construction decisions x.
We also impose constraints for the flow problem:
(demand) ∑︂ i∈Vo (︄ η ∑︂ j∈Vw kjfji+ ∑︂ j∈Vp∪Va fji )︄ ≥ d (3.13a) (balance) η ∑︂ j∈Vw kjfji= ∑︂ j∈Vo fi j ∀i ∈ Vp∪ Va (3.13b) (platform capacity) ∑︂ j∈Vw fji≤ Irixri ∀i ∈ Vp (3.13c)
(island elec. capacity) ∑︂
j∈Vw
fji≤ xai ∀i ∈ Va (3.13d)
(onshore capacity) ∑︂
j∈Vw
fji≤ xoi ∀i ∈ Vo (3.13e)
(wind park capacity) ∑︂
j∈Vp∪Va∪Vo
fi j≤ Iwi xwi ∀i ∈ Vw (3.13f)
(cable capacity) fi j≤ Iei jxei j ∀(i, j) ∈ Ee (3.13g)
Constraint (3.13a) states that demand must be met from hydrogen produced at onshore electrolysers (Vo) directly, or transported there from electrolysers on platforms (Vp) and islands (Va). Here two conversion factors are present for the electricity flowing into onshore electrolysers: kj, the wind capacity factor, and η, the electrolyser efficiency. Balance
constraint (3.13b) does the same for offshore electrolysers. Constraints (3.13c) to (3.13e) state the electricity flow into platform, island, and land-based electrolysers cannot exceed electrolyser capacity. Similarly, constraint (3.13f) states the electricity flow out of a wind park cannot exceed the nominal capacity of that wind park. Finally, equation (3.13g) is a capacity constraint on the electrical cables, and (3.13h) a boxing constraint.
Note that connecting an offshore wind park to a land-based electrolyser is never sub-optimal when the electrical cable needed to achieve this is shorter than a cable needed for an offshore connection. We use this observation to prune a substantial number of potential electrical cables from the model: all those that would be longer than connecting the wind park to the nearest onshore electrolyser.
R E C O U R S E For the recourse formulation, we define the following master problem:
M3 := min
x O3(x) + λEκ1,...,κ|V w|(︁S3(x,κ1,. . . ,κ|Vw|)
)︁
(3.14a)
subject to (3.12a)–(3.12e). (3.14b)
Given a solution x to the first-stage problem, we define the following second-stage sub problem: S3(x,κ1,. . . ,κ|Vw|) := min f ,s s (3.15a) subject to (3.13c)–(3.13h) (3.15b) (demand) ∑︂ i∈Vo (︄ η ∑︂ j∈Vw κjfji+ ∑︂ j∈Vp∪Va fji )︄ + s = d (3.15c) (balance) η ∑︂ j∈Vwκj fji= ∑︂ j∈Vo fi j ∀i ∈ Vp∪ Va (3.15d) s ≥ 0. (3.15e) 4 P A R A M E T E R J U S T I F I C A T I O N
E L E C T R O LY S I S We assume proton-exchange membrane (PEM) electrolysers will be
used, due to their compact size and overall promise (Schmidt et al.,2017). PEM electrolysers have an expected lifetime of forty to sixty thousand full load hours. When powered by wind energy, these load hours are commonly exhausted after 10 to 15 years. We assume an economic lifetime of 10 years, and scale our cost estimates to the 25 year economic lifetime of the HSCN as a whole.
Electrolyser construction costs have recently been estimated byProost(2019) at around
AC750 per kilowatt of installed (peak) capacity. As such, we assume a capital expenditure (CAPEX) of 750AC/kW. Annual operating and maintenance (O&M) costs are assumed to be 3% of CAPEX. This is in line with most literature, where O&M costs are typically estimated between 3–5% (Matute et al.,2019;Parra et al.,2019).
CAPEX costs have decreased rapidly in recent years, by as much as 40% in the last five years alone (BloombergNEF,2020). We estimated a simple log-linear model to the data presented inGlenk and Reichelstein(2019), where we fix the 2020 CAPEX estimate to 750
AC/kW. With this approach we find a 7.6% decrease in CAPEX per year. This suggests the point estimate for CAPEX (and, by extension, O&M) costs might be on the high side, and lower CAPEX costs should also be investigated.
Finally, we assume a conversion efficiency of 75%. This is again in line with most literature on PEM electrolysers, where efficiencies of 70% to 80% are commonly reported (Proost,2020;Van den Bos et al.,2020).
O F F S H O R E W I N D Wind turbines and wind parks have become larger in recent years, but power densities have not increased. This is likely due to larger turbines requiring more space to reduce interference (known as wake effects). A common rule of thumb scales the inter-turbine space by rotor diameters (Volker et al.,2017), which cancels increases in turbine size. We assume 5MW of installed capacity per km2, as found optimal inBulder et al.(2018). With modern wind turbines in the 10MW range, this works out to one turbine about every two km2.
Oh et al.(2018) present a CAPEX of aroundAC1.8 million per MW for wind parks in water depths up to twenty meters. In deeper waters up to 40–50m, costs increase by about 40% That depth is at the upper range of what is considered economical. Lensink and Pisca(2018) present similar CAPEXs for Dutch wind parks planned for construction in the coming ten years. In the period thereafter, CAPEX costs might decrease further: Ruijgrok et al.(2019) assume a CAPEX aroundAC0.9 million per MW for after 2030. Lensink and Pisca(2018) also present O&M costs of aroundAC50/kW per year. We use the numbers of
Lensink and Pisca(2018) to estimate wind park CAPEX and O&M costs, and compensate for water depths in the CAPEX estimate using the scaling factors ofOh et al.(2018). Finally, we discuss wind capacity factors. These capacity factors express the fraction of the year a wind turbine produces its rated capacity in electricity. For modern offshore turbines, annual capacity factors are commonly estimated between 40% to 50%.
0 5 10 15 20 Age (years) 0% 10% 20% 30% 40% 50% 60%
Annual capacity factor
Trend Cap. factor
0.00 0.02 0.04 0.06 0.08
Figure 2: Rolling twelve-month capacity factors against wind park age. The trend line is obtained from an estimated linear regression model of capacity factors (endogenous) against a constant and wind park age (exogenous). The histogram on the right gives the marginal distribution of wind capacity factors. Data fromSmith(2020) on Belgian, Danish, German and British offshore wind parks.
German and British wind parks in the North Sea instead. The fitted trend line suggests capacity factors have increased by about 0.8% annually over the past quarter century. Contemporary capacity factors are, on average, around 44%. Based on the trend line and the marginal distribution of wind capacity factors, we assume annual wind park capacity factors are identically distributed according to a triangular(30%, 40%, 55%) distribution. This distribution has a mean annual capacity factor of 41.7%.
Although we assume wind capacity factors are identically distributed for each wind park, we do not assume assume independence. That would be a far too strong assumption, because there must be strong spatial autocorrelations between annual wind capacity factors of neighbouring wind parks. Due to lack of data we cannot determine these dependencies based on historical offshore wind data, but the Royal Netherlands Meteorological Institute (KNMI) does publish wind speeds observed at 49 land-based weather stations (Royal Netherlands Meteorological Institute,2021). An analysis of twenty years of hourly wind speed data from these 49 stations suggests there is indeed a strong spatial autocorrelation. In particular, we find a correlation of almost 67% between observations at different weather stations. Further, this correlation appears robust to increasing distances between weather stations: even for those few stations that are 400 to 500km apart, the spatial correlation is still 54%. It is thus clear that wind speeds have strong spatial dependencies.
S U B M A R I N E E L E C T R I C A L C A B L E S Flament et al.(2014) present a detailed overview
of various cabling solutions. Based on their results, we consider a fixed cost ofAC200 million for the substations and converters (AC100 million for each pair). This might be on the low end, as they also report costs up toAC400 million for different configurations. In addition, we consider a cable cost ofAC0.4 million per km (based on a 1GW capacity rating), and a one-time installation cost ofAC1 million per km. Again, the cable costs might be on the low side. These CAPEX costs are broadly in line withVan Eeckhout et al.(2010) andXiang et al.
(2016), who go into more technical detail for cable set-ups with power-ratings of 300MW, 600MW, and 1.4GW. We assume an annual O&M cost of 2% of CAPEX.
S P A C E Most of the Dutch exclusive economic zone (EEZ) is heavily used. Jongbloed et al.(2014) investigate the available space for wind energy on the North Sea, but curiously restrict themselves to only the 100km nearest to the Dutch shore. This excludes a large part of the Dutch EEZ from consideration. Recently, Gusatu et al. (2020) broaden the analysis to the full EEZ. They find that most of the Dutch EEZ suitable (and available) for offshore wind parks is located in the northern part, beyond 100km from shore.
We take the data outlined in Table 1 of Gusatu et al. (2020) on a large number of offshore activities.1 We refer the interested reader there for a complete description of the data and source references. An overview of the Dutch North Sea is given in Figure3. Here the patchwork of activities becomes clear.
To be on the safe side, we assume offshore wind cannot be placed anywhere there is already an established use. Using a GIS, the remaining area of about 22500km2is divided into smaller areas of around 200km2 each, using a Voronoi tessellation. An area of 200km2 allows a wind park size of about 1GW, which is a compromise that balances computational difficulty and realism. After some processing we obtain 91 polygons of sizes between 100 and 300km2. The centroids of each polygon serve as the locations of the potential wind parks for modelling decisions, distance computations, and water depth measurements. The polygon area is used to compute the installed wind power capacity.
E X I S T I N G G A S I N F R A S T R U C T U R E Based on 2016 data, there are 135 offshore gas platforms on the Dutch North Sea (European Marine Observation and Data Network,
2016). Only five platforms have been removed in 2018–2020 (Nexstep,2020), so of these 135 platforms a large number remain. Once these platforms reach cessation of production (COP), they must either be decommissioned or re-used.
Energie Beheer Nederland(2018) present an overview of various COP timelines. In the worst case presented there, with sustained low gas prices, over three-quarters of existing platforms reach COP before 2027, and many before 2023. At higher gas prices, the COP date is pushed further into the future, but rarely beyond 2040. We thus make the case that most platforms will reach COP in the next two decades and are available for re-use in the hydrogen supply chain.
1 These data are—in principle—publicly available, but it is laborious to compile a complete data repository. I
Offshore platforms Pipelines
Potential island locations EEZ
(a)
Submarine cables Wind farm areas Sand extraction Shipping lanes Anchorage areas
Valuable and vulnerable marine areas Natura 2000
Military areas EEZ
(b)
Figure 3: An overview of activities and potential hydrogen production locations on the Dutch North Sea. Figure3ashows the existing offshore gas network (European Marine Observation and Data Network(2016) andEuropean Marine Observation and Data Network(2019)) and potential locations for artificial islands. Figure3b presents an overview of activities, based on data from various sources summarised in Table 1 ofGusatu et al.(2020).
Re-use costs consist of platform O&M and electrolyser costs. Total O&M costs for all offshore platforms amounted to roughly AC900 million in 2015, but have dropped in recent years (Energie Beheer Nederland,2016). Most of these costs are made on manned platforms, but personnel is no longer required in case a platform is re-used. As such, we assume O&M costs about halve toAC3 million per platform annually.
The electrolyser capacity of a re-used platform is difficult to determine, as we do not precisely know electrolyser sizes, nor the dimensions of the platform topsides. Topside weights, however, are known and can be used as a proxy: heavier topsides are generally larger, and can house a bigger electrolyser. The Q13-A platform of theNeptune Energy
(2019) project weighs some 1000 tonnes, and currently hosts a 1MW electrolyser in a 40ft container. This arrangement can likely scale up ten- to hundredfold, but remains a pilot study: a commercial set-up is many times more compact, and many platforms are larger than the Q13-A. We consider a scenario where a 1000 tonne platform hosts a 50MW electrolyser, and scale that number by tonnage for the other platforms.
A R T I F I C I A L E N E R G Y I S L A N D S A recent report by North Sea Energy estimates the
cost of constructing a 100 hectare (1km2) island between one and two billion euros (North Sea Energy,2020). Such an island is large enough to host up to 20GW of PEM electrolyser capacity. These costs depend a lot on sea depth and wave climate at the chosen location: to avoid having to discuss these in detail, we will assume the upper range estimate of two billion euros. Finally, the report presents expected annual maintenance costs ofAC3 million, which we take to be our O&M estimate.
The electrolysers on these islands are connected to the mainland gas grid via a new gas pipeline. For a 20GW island, at least two pipelines with a diameter of 36 inch are needed (North Sea Energy, 2020). These pipelines each cost around AC2 million per kilometre, which works out to aroundAC4 million per kilometre for both pipelines. Since gas pipelines require little maintenance, we assume an annual O&M cost of only 1%.
Finally, we briefly discuss how the island locations in Figure3awere determined. Since these islands are only one square kilometre in size, we do not consider existing activities (Figure3b) in our analysis. Using a GIS, isodistance lines of 75, 150, and 225km from the Dutch coast are drawn. On these lines locations are sampled, each approximately 50km apart. These distances were chosen such that all wind park locations are within 75km of the nearest island location, limiting electrical cable costs. This procedure results in seven possible island locations at 75km offshore, six at 150km, and four at 225km, for 17 island locations in total.
5 R E S U LT S
In Section 5.1 we discuss results for the different electrolyser placement settings, and robust solutions. These results and their discussion aim to clarify what good hydrogen production supply chains are, and how those might be realised on and around the Dutch North Sea. Then, in Section5.2, we formulate an experimental design for a sensitivity analysis, solve the experiments, and discuss the solutions.
We are particularly interested in the cost price of hydrogen that results from the supply chain construction decisions of each solution. As such, we do not directly report the objective values of the models in Section3in this section, but rather present these as the so-called (expected) levelised cost of hydrogen, or LCoH2. This measure gives the expected cost of
a kilogram of hydrogen, and we define it as the objective value divided by demand for hydrogen over the optimisation period of twenty-five years. Observe that this measure is independent of the scale of demand, whereas the objective values themselves are not.
These levelised costs can also be compared to contemporary industrial hydrogen prices, so it is helpful to know some ballpark estimates. International Energy Agency (2019) estimates that hydrogen produced from natural gas costs around 2–2.5AC/kg. As emission costs increase due to carbon taxes and emission ceilings, these prices might increase to 3
0 50 100 150 200 250
Demand (TWh/y)
0 1 2 3 4 5 6LC
oH
2(
/kg
)
Worst case
0 50 100 150 200 250Demand (TWh/y)
Average case
Integrated Land-based Offshore
0 50 100 150 200 250
Demand (TWh/y)
Best case
Figure 4: Levelised costs of hydrogen for various electrolyser placement locations (land-based, offshore, integrated) and wind capacity factors (worst (30%), average (41.7%), and best (55%)), for various demand levels.
All algorithms were implemented in Python 3.8, and the models were solved using the Gurobi 9.0 solver. The results were obtained on a computer cluster equipped with Intel Xeon 2.5 GHz processors. Unless otherwise specified, each model run was given two processor cores, 8GB of memory, thirty minutes of compute time, and an optimality tolerance of 1%. We use a barrier method for solving the root node of all MIP models, since trial runs suggest these models are (highly) degenerate.
5.1 Electrolyser placement and robust solutions
E L E C T R O LY S E R P L A C E M E N T C O S T S Since we consider three models and three realisations for the wind capacity factors, we have nine different combinations. We solve each combination over thirty different hydrogen demands, ranging from 8.7TWh to 261TWh annually (1 to 30GW, converted to annual numbers). This results in 270 distinct model runs. 198 out of these 270 (73%) runs completed on time and within the memory limits imposed. Twelve runs were infeasible, all for the largest demands and the worst case wind capacities.
Figure4gives the levelised cost of hydrogen for these electrolyser placement locations, wind capacity factors, and demands. It is immediately clear that wind capacity factors significantly influence the cost of hydrogen production: in the best case of 55% wind capacity, this is some 3.2AC/kg, which rises to over 6 AC/kg for the worst case of 30% annual wind utilisation.
are needed to provide electricity for increased hydrogen production, these wind parks must generally be placed in deeper waters where they are more expensive to construct. It seems likely that economies of scale will, in fact, occur as hydrogen production scales up over time (see alsoBerenschot and Kalavasta(2020)), which would enable key technologies to mature (electrolysers in particular), and costs to decrease.
The differences between electrolyser placement locations are small. For smaller de-mands land-based electrolysers are slightly cheaper than constructing electrolysers offshore. This reverses for demands larger than about 100TWh annually, but the differences are very small. The surprising conclusion thus appears to be that electrolyser placement does not have much impact on the resulting hydrogen cost price.
In the introduction we proposed re-using the offshore gas infrastructure for hydrogen production as a potentially cost-efficient way to produce hydrogen offshore. This does not appear effective in practice: none of the model instances re-uses more than five platforms (out of 135), and on average less than one platform is re-used in instances where re-use is an option. Re-use mostly happens at lower demand levels, where it is not yet optimal to construct one or more artificial islands. Once artificial islands become cost effective, platforms are rarely re-used. This suggests re-used platforms are almost never part of a (near-)optimal solution.
Figure9in AppendixBpresents a breakdown of costs into a number of categories, for each model setting and wind capacity factor. The cost composition is mostly similar across model settings: roughly 65% is attributable to wind parks, some 10–15% to the transport of electricity, and about 20–25% to electrolysers. Some costs are made constructing artificial islands and re-using platforms, but those are marginal compared to the other three categor-ies. Since wind parks and electrolysers are needed no matter where they are placed, it is now not hard to understand why each model setting results in similar hydrogen costs: the shared components make-up almost 90% of the objective values.
It is tempting to now consider only the differences between these model settings, and focus on components that make-up the remaining 10%-or-so of the hydrogen costs. We should resist this temptation, however, since it takes us far beyond the limits of the certainty we have in our parameter estimates, and thus the conclusions our results can reasonably support.
Based on our modelling results there does not appear to be an overriding economic reason to pursue offshore electrolyser construction. Our models are of course limited, and for example do not quantify ease of maintenance, ease of access, or even different electrolyser types that require more space. Qualitatively, however, it seems reasonable to conclude that land-based electrolysers score more favourably on these points than electrolyser placed offshore. A natural conclusion is thus that we should prefer land-based electrolysers, since we have found no evidence of any economic reasons not to do so.
costs are made constructing wind parks (about two thirds of total cost), electrolysers (one quarter), and electrical cables (roughly ten percent). Fourth, offshore electrolyser placement does not result in substantial savings: re-using platforms is rarely cost-effective, and, although artificial islands are used to place electrolysers offshore, this is only marginally cheaper than based electrolysers. There are many arguments in favour of land-based electrolysers that we could not capture in our models. As such, constructing most electrolysers on land is likely a very good—or at least not terribly sub-optimal—decision.
The discussion so far is based solely on deterministic modelling results. Since wind capacity factors have a large impact on hydrogen costs, we should also investigate results where their variability has been taken into account explicitly. We do so in the next section, where we present results on the recourse formulations.
L I M I T E D S H O R T F A L L Motivated by the similarity in costs across model settings as
presented in Figure 4, we consider only the integrated model in this section. Figure 4
also suggests hydrogen costs are not particularly sensitive to demand sizes, so we restrict ourselves to a single demand level of 10GW (88TWh annually).
The recourse models allow production shortfalls, which are assumed to be met from storage, or through imported hydrogen (we consider both options ‘imports’ with respect to our model). These shortfalls are priced at unit costλ, for which we need to determine a range of suitable values. Observe that if the recourse solution constructs any assets rather than importing all hydrogen, it never attains better costs than those of the best case of Figure4 where hydrogen costs of about 3AC/kg are achieved. Trial runs of the recourse model confirm that this is correct: for λ below 3.5 AC/kg, no assets are constructed and hydrogen is instead imported. For a reasonable upper bound on λ, we tested different values ofλ ∈ [5,8.5]. At λ = 6AC/kg, on average around 7% of demand is met from imports;
forλ = 7, this is 5%; for λ = 8.5, 3%. It thus appears that values of λ in the interval [3.5,8.5]
result in the most interesting conclusions. As such, in this section we solve the recourse model of Section3.3for twenty different values ofλ, evenly spaced in [3.5,8.5].
The recourse formulation of the integrated model is solved using the L-shaped algorithm ofVan Slyke and Wets(1969), which is explained briefly in AppendixA. This algorithm requires a finite number of scenarios for the second-stage, but the wind capacity factor distributions we estimated in Section4 are continuous. We discretise the distribution of Section4via sampling. In particular, we sample fifty different scenarios from the copula specified there. Each scenario consists of a vector of wind capacity factor realisations, one for each wind park.
4 5 6 7 8 ( /kg) 0 1 2 3 4 5 6 LC oH2 ( /kg ) Recourse Deterministic (a) 4 5 6 7 8 ( /kg) 0% 20% 40% 60% 80% 100% Expected shortfall Recourse Deterministic (b)
Figure 5: Figure5agives hydrogen costs as a function of the import priceλ. Each blue line presents one replication of the recourse model. Figure5bdoes the same for expected shortfalls. Shaded areas give the standard deviations as a measure of (annual) variability.
run is solved with three hours of clock time, which proved sufficient for 318 out of 400 (79.5%) to converge.
We also provide the expected value solution for each valueλ (‘deterministic’). This is essentially the recourse solution for the single scenario where all wind parks attain their expected annual wind capacity factor. This model is easy to solve and provides us with a benchmark to compare the recourse solutions with.
For each of the deterministic and recourse first-stage solutions, we solve the second-stage subproblem S3 10,000 times. These second-stage solutions provide a sense of the
variability in annual production shortfalls and average production costs associated with the construction plans of each first-stage solution.
Figure5 presents the cost of hydrogen and expected size of shortfalls, relative to the import priceλ. For values of λ below roughly 4AC/kg, imports are always used to supply demand. Then, for prices between 4 and 4.5 AC/kg, the situation rapidly reverses, and imports make up only a small percentage of total hydrogen supply for prices much above 4.6AC/kg. This range of prices corresponds exactly with the LCoH2 observed in the average
case of Figure4. At these prices, the model can, on average, achieve good results either by constructing its own HSCN, or importing hydrogen. The range of 4–4.5AC/kg thus marks the boundary between these two regimes.
Observe that the recourse and deterministic formulation achieve very similar costs, in particular forλ greater than 5AC/kg. For values of lambda between 4 and 5AC/kg, sampling fifty scenarios appears insufficient: the variability between replications is still significant. Normally, then, we would increase the number of samples and re-solve the recourse models. In our case, however, the expected LCoH2of the recourse models is, in general, not
formulation tends to the same level of limited shortfalls the deterministic formulations— optimistically—achieve early on. Clearly, then, the benefit of complex recourse models that explicitly take into account variability in wind capacity factors is only limited.
The small production shortfalls of Figure 5bat high values forλ suggest it might be possible to achieve good service levels even when imports are not available, if we construct additional production capacity. If so, we can find robust solutions already from simple deterministic models. We explore this further in the next section.
S E R V I C E L E V E L In this section we investigate the effect of overcapacity on the expected
service level, which we define as the fraction of years in which no production shortfalls occur (recall the discussion at the start of Section3). We defineδ ≥ 0 as the percentage overcapacity for a given demand level d. For this we scale the right-hand side of (3.13a) in Section3.3with 1 + δ, such that the constraint now reads
∑︂ i∈Vo (︄ η ∑︂ j∈Vw kjfji+ ∑︂ j∈Vp∪Va fji )︄ ≥ (1 + δ)d. (5.1)
A judicious choice ofδ saves considerable computational expense. In particular, if we select
δ properly, we can re-use the solutions to the integrated model presented in Figure4for
thirty different values of d. This works as follows. Take two demand levels 0 < d2< d1.
Then, there exists a positiveδ such that d1= (1 + δ)d2, and we writeδ = d1/d2− 1. Using
one of the solutions of Figure4computed for, say, d1, we can simply solve the subproblem
S3for d2, d3,. . . < d1, and computeδ given d1and one of these smaller demand levels. Since
these subproblems are simple LPs, solving them for many different wind capacity factor scenarios is tractable. Of these many scenario solutions we then tally the number of times imports are needed (which is when s > 0) to determine an empirical service level.
We consider twenty different values of d between 88 and 263TWh and the solutions that correspond to them in the average case panel of Figure4. Pairing each solution with demands smaller than the demand they were computed for, we obtain a total of 190 unique combinations. For each combination we solve the subproblem 10,000 times, and plot the results in Figure6.
In Figure6we observe that the construction plans result in a service level of about 50% at the demand level for which they were built (δ = 0). This quickly improves to almost 80% for an overcapacity of just 10%. Similarly, for an overcapacity of about 25%, a service level of 98–99% is achieved. Observe that these results hold for all different demand levels.
Equation (5.1) forces the model to construct additional electrolysers for a target demand level d: it scales the whole supply chain. Additional electrolysers are not necessary to achieve a more robust supply chain, provided the electricity produced at additional offshore wind parks makes its way to the existing electrolysers. In short, then, all that is required for a robust supply chain is overcapacity in electricity generation.
0% 5% 10% 15% 20% 25% 30% 35% 0% 20% 40% 60% 80% 100%
Empirical service level
Figure 6: Service level as a function ofδ, for twenty demand levels between 88 and 263TWh.
service level may be attained at additional costs around 20%. Second, this overcapacity in electricity generation needs to be connected to centralised electrolysers, and here land-based electrolysers appear most suitable. In addition, if wind parks are connected to land-based electrolysers, any electricity the wind parks produce could alternatively be used to power the onshore electrical grid. This is particularly relevant when constructing overcapacity in electricity generation, since that would by definition otherwise result in some unused (peak) electricity production.
We close this section with a note on the quality of our simple heuristic. Overcapacity in electricity generation is not necessarily a bad method to obtain a better service level. In the context of the models of Section 3, the only way to reliably decrease shortfalls is by increasing production capacity, which is precisely what we pursue here. Outside the context of our models, of course, storage might also allow balancing shortfalls between years. As such the trade-off between the optimal size of hydrogen storage facilities and potential excess production capacity could be an interesting direction for future research. 5.2 Sensitivity analysis
This section develops an experimental design and presents the experimental results.
Sec-tion5.2.1develops the experimental design, summarised in Table2. These experiments
are then solved, and Section5.2.2presents an analysis of the results. 5.2.1 Experimental design
Table 2: Experimental design. Parameter levels in bold are baseline values.
Parameter Levels
Electrolyser CAPEX (AC/kW) 375, 700
Electrolyser efficiency (%) 75%, 80%
Fixed cable cost (MAC) 200, 400
Variable cable cost (MAC/km) 0.4, 1
Demand (TWh/y) 44, 88, 131
Wind park CAPEX (MAC/MW) 0.9, 1.8, 3.6
Wind capacity factor (%/y) 41.7%, 45%, 50%
Wind park power density (MW/km2) 2.5, 5, 7.5, 10
combination of parameter levels. Since this quickly results in many experiments, we must be somewhat conservative in the number of parameters and levels to investigate.
Some experimental designs and sensitivity analyses for general HSCNs exist. However, most of these approaches are not directly applicable to green HSCNs like we consider here. An example is given by the experimental designs and sensitivity analyses ofOchoa Robles et al. (2018). They consider a general HSCN that is connected to gas and electrical grids such that the hydrogen feedstock is almost always available, which sidesteps the intermittent availability of electricity in case of a green HSCN. Intermittency strongly impacts the solution of a green HSCN. Thus, the setting ofOchoa Robles et al.(2018) is very different and the application of their experimental design to our problem suspect. Instead we develop our own experimental design.
Figure9 provides a good starting point for our experimental design. Since wind and electrolyser costs together account for almost 90% of the overall objective value, we should particularly investigate the parameters that influence these decisions in further detail.
modern, larger turbines capture more wind to turn into electricity than earlier models, and thus do well even in low wind conditions.
It might seem obvious that lower specific powers should be preferred, but it is often not that simple: a lower specific power implies a large turbine that produces relatively little electricity per km2, but does so fairly reliably. A high specific power results in much less reliable production, but at higher peak rates, and such turbines might fit better into the available sea area. This results in a difficult trade-off to make when deciding on the number of wind turbines to place in a given wind park.
The main point here is that wind capacity factors can be increased, at the expense of lower peak production per km2. We investigate this by considering different mean wind capacity factors. In particular, we consider mean capacity factors of 45% and 50% in addition to the initial wind capacity factor distribution (with mean 41.7%). These capacity factors are each considered for installed capacities of 2.5MW, 5MW, 7.5MW, and 10MW/km2.
We also investigate different construction costs for wind parks. We consider parameter levels where the CAPEX costs double fromAC1.8 million toAC3.6 million per MW of installed capacity, and those where CAPEX costs halve toAC0.9 million per MW.
For electrolysers a similar approach is taken. We consider an efficiency of 80% in addition to the 75% argued previously. We also halve the CAPEX costs, from 750AC/kW to 375AC/kW. This helps investigate the effects of learning and additional improvements that will likely bring down electrolyser costs further in the near future.
Since cable costs might be on the lower end of the scale, we consider a parameter level where the fixed costs increase fromAC200 million toAC400 million per cable. Additionally, we also consider a variable cable cost increase fromAC0.4 million toAC1 million per kilometre. We test each of these settings for demands of 5GW (≈ 44TWh annually), 10GW (88TWh), and 15GW (131TWh).
5.2.2 Analysis
The experimental design of Section 5.2.1results in 1728 unique experiments. To limit the computational burden, we only compute results for the integrated, deterministic model. Since the decisions in terms of wind parks and electrolysers quantities are similar for each model (including the recourse formulations), the conclusions drawn here should be broadly applicable to each of these models. We increase the time limit to one hour for the experiment instances. 1721 of the 1728 experiments (99.6%) solve within this time limit.
Recall that we have so far obtained solutions with hydrogen costs around 4–4.5AC/kg, and green hydrogen becomes cost-competitive for production prices below 3 AC/kg. This requires a total cost decrease of about 40%, which may be achieved from improvements to one or many parameters.
30% 20% 10% 0% 10% 20% 30% Change in LCoH2
Wind power dens. (MW/km2)
Wind cap. factor (%/y) Wind CAPEX (M /MW) Demand (TWh/y) Var. cable cost (M /km) Fixed cable cost (M ) Elec. efficiency (%) Elec. CAPEX ( /kW) 375 750 80% 75% 400 200 1 0.4 131 88 44 3.6 1.8 0.9 50% 45% 41.7% 10 7.5 5.0 2.5
Figure 7: One-way parameter interactions. Effect sizes are relative to the baseline level at 0%.
Notice that larger (smaller, respectively) demands result in higher (lower) hydrogen costs. This corroborates the results presented in Figure4.
The first set of parameters concerns electrolyser costs and efficiencies. If electrolyser CAPEX costs halve, the expected hydrogen costs drop by some 22%. The effect of efficiency increases is equally pronounced: a five percent increase from 75% to 80% results in a cost reduction of more than 6%. These effects are robust across almost all other parameter level changes. As electrolyser technology matures, both improvements could materialise already in the next decade.
The second set of parameters concerns electrical cable costs. We noted in Section4that the values we selected there might be on the low side, so we (more than) doubled them for the experimental design. Notice that the cost per kilometre (‘variable’ cost) does not substantially impact hydrogen cost. The cost of substations and converters (‘fixed’ cost) has a greater impact: if these costs doubleAC400 million per cable, hydrogen costs increase by almost 6%. Parameter levels that lower base electricity requirements reduce this cost increase, but that interaction effect is very small and typically in the order of one percent or less. As such the solution appears robust to cost changes in electrical cables.
Third, we discuss parameters that relate to wind parks. Recall that costs related to wind parks comprise around 70% of the solution costs.
The solution is sensitive to changes in wind CAPEX costs. When they halve to AC0.9 million per MW hydrogen costs decrease by some 15%. If average wind capacities increase to 50%, their interaction results in cost decreases of almost 30%. On the other hand, doubled wind CAPEX costs result, on average, in increased costs of almost 30%. This increase cannot be compensated completely by any other change in parameter levels, although electrolyser CAPEX reductions and improvements in wind capacity factors come close.
2.5 5 7.5 10
41.7%
45%
50%
Wind cap. factor (%/y)
6.2% 0.0% -2.1% -3.3% -2.0% -7.7% -9.5% -10.6% -12.0% -17.2% -18.8% -19.2% 2.5 5 7.5 10 0.9 1.8 3.6 Wind CAPEX (M /MW) -10.6% -15.0% -16.7% -17.1% 6.2% 0.0% -1.9% -3.1% 38.9% 30.3% 27.5% 25.7% 41.7% 45% 50% 0.9 1.8 3.6 -15.2% -21.7% -29.5% 0.0% -7.7% -17.0% 30.2% 20.2% 7.9% 2.5 5 7.5 10 44 88 131 Demand (TWh/y) 4.1% -2.1% -3.2% -3.2% 6.4% 0.0% -2.2% -3.3% 7.7% 1.7% -0.9% -2.7% 41.7% 45% 50% 44 88 131 -1.6% -9.0% -18.0% 0.0% -7.6% -17.1% 1.3% -6.5% -16.1% 0.9 1.8 3.6 44 88 131 -15.8% -1.4% 27.8% -15.2% -0.0% 30.1% -14.5% 1.1% 32.5% 2.5 5 7.5 10 0.4 1
Var. cable cost (M
/km) 6.0% 0.0% -1.9% -2.9% 7.3% 0.8% -1.1% -2.1% 41.7% 45% 50% 0.4 1 0.0% -7.7% -17.0% 0.9% -6.8% -16.2% 0.9 1.8 3.6 0.4 1 -15.1% -0.0% 30.3% -14.2% 1.1% 31.4% 44 88 131 0.4 1 -1.4% -0.0% 1.3% -0.3% 0.9% 2.1% 2.5 5 7.5 10 200 400
Fixed cable cost (M
) 5.8% -0.0% -1.7% -2.6% 12.6% 5.6% 3.4% 2.3% 41.7% 45% 50% 200 400 0.0% -7.7% -17.0% 5.6% -2.5% -12.3% 0.9 1.8 3.6 200 400 -15.4% 0.0% 30.9% -9.7% 6.0% 37.3% 44 88 131 200 400 -1.3% 0.0% 1.3% 4.2% 5.6% 6.9% 0.4 1 200 400 0.0% 1.1% 5.8% 6.6% 2.5 5 7.5 10 75% 80% Elec. efficiency (%) 6.1% 0.0% -2.1% -3.2% -0.7% -6.7% -8.3% -9.0% 41.7% 45% 50% 75% 80% 0.0% -7.6% -17.1% -6.5% -13.6% -22.3% 0.9 1.8 3.6 75% 80% -15.2% 0.0% 30.1% -20.4% -6.4% 21.9% 44 88 131 75% 80% -1.5% 0.0% 1.3% -7.5% -6.4% -5.4% 0.4 1 75% 80% -0.0% 1.0% -6.3% -5.5% 200 400 75% 80% -0.0% 5.6% -6.3% -1.1% 2.5 5 7.5 10
Wind power dens. (MW/km2)
375 750 Elec. CAPEX ( /kW) -17.0%-22.7% -24.3% -25.0% 5.4% -0.0% -1.8% -2.8% 41.7% 45% 50%
Wind cap. factor (%/y)
375 750 -22.4% -28.4% -35.6% -0.0% -7.6% -17.0% 0.9 1.8 3.6 Wind CAPEX (M /MW) 375 750 -36.7% -23.4% 3.2% -13.4% 0.0% 26.6% 44 88 131 Demand (TWh/y) 375 750 -23.5% -22.4% -21.4% -1.3% -0.0% 1.2% 0.4 1
Var. cable cost (M /km)
375
750
-22.4% -21.7%
0.0% 0.8%
200 400
Fixed cable cost (M )
375 750 -22.9% -18.1% -0.0% 5.0% 75% 80% Elec. efficiency (%) 375 750 -22.4% -27.5% 0.0% -6.4%
Figure 8: Two-way parameter level interactions, as percentage changes in LCoH2. Effect sizes are relative to a baseline level (fixed to 0%).
50% decreases costs by 17%. Notice that an increased wind capacity factor of 50% results in greater cost decreases than halving wind CAPEX costs.
consider when developing wind parks, even when that results in less intensive use of space overall.
6 C O N C L U S I O N
This thesis considered the production side of a green hydrogen supply chain network. In our setting, offshore wind electricity is the feedstock for electrolysers, and we investigated various placement decisions for the wind parks and electrolysers. In Section3we formu-lated mathematical models for these settings. Using the parameter values of Section 4, we then presented our modelling results in Section 5. Section5.1 presented results on electrolyser placement decisions and various robust formulations, and in Section5.2we presented and discussed a large numerical sensitivity analysis.
C O N C L U S I O N We first address where to place electrolysers. The modelling results suggest this has negligible impact on costs, and any decision is acceptable. Placing electro-lysers on offshore gas platforms is almost never cost-effective, so the role of these platforms in the future energy system appears limited. The options thus reduce to electrolysers on land or on artificial islands. There are many qualitative arguments to prefer land-based electrolysers in this case. This argument is supported by our investigation into service levels and overcapacity in electricity generation.
Second, although green hydrogen can be produced today for 4–4.5AC/kg, these prices are not yet cost-competitive. A cost reduction of about 40% is needed for that to occur, to costs below 3AC/kg. Through a sensitivity analysis we showed this can be achieved in many ways. The most likely contributors to this goal are reductions in electrolyser and wind park construction costs, and improvements in electrolyser efficiencies and increased wind capacity factors. The solutions are very sensitive to these parameters, such that even modest improvements to each of these parameters could make green hydrogen cost-competitive.
Third, robust solutions are relatively inexpensive to obtain. When they occur, shortfalls between production and demand rarely exceed a few percent of demand. Overcapacity in electricity generation can prevent these shortfalls altogether: an overcapacity of just 10% sustains a service level of 80%, and an overcapacity of 25% a 98–99% service level. These overcapacities result in additional costs of less than 8% and 20%, respectively.
F U T U R E R E S E A R C H Several elements of this thesis warrant further study.
Another direction concerns the demand side of a hydrogen supply chain. We treated demand as an abstract, yearly quantity and showed robust solutions can be constructed at limited additional costs. The optimal size and location of hydrogen storage facilities in matching instantaneous demand and supply should also be investigated, as these will be critical in translating our model results into useful construction plans. Additionally, the effect of these storage facilities on service levels is worth exploring in the future.
A last research direction involves a change in perspective. In this work we concerned ourselves with space, answering the question where to place wind parks and electrolysers, and in what quantities. Another question relates to time, studying optimal or near-optimal deployment pathways for the transition to a hydrogen economy. Such a research topic requires detailed forecasts of future demands, and learning rates for electrolyser and wind park improvements.
