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Energy 261 (2022) 125219
Available online 24 August 2022
0360-5442/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
Modelling and analysis of offshore energy hubs
Hongyu Zhang a,∗, Asgeir Tomasgard a, Brage Rugstad Knudsen b, Harald G. Svendsenb,
Steffen J. Bakker a, Ignacio E. Grossmann c
aDepartment of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Høgskoleringen 1, 7491, Trondheim, Norway
bSINTEF Energy Research, Kolbjørn Hejes vei 1B, 7491, Trondheim, Norway
cDepartment of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA
ARTICLE INFO
Keywords:
Clean offshore energy hub
Sensitivity analysis
Deterministic mixed-integer linear
programming model
ABSTRACT
Clean offshore energy hubs may become pivotal for efficient offshore wind power generation and distribution.
In addition, offshore energy hubs may provide decarbonised energy supply for maritime transport, oil and gas
recovery, and offshore farming, while also enabling conversion and storage of liquefied decarbonised energy
carriers for export. In this paper, the role of offshore energy hubs is investigated in the transition of an offshore
energy system towards zero-emission energy supply. A mixed-integer linear programming model is developed
for investment planning and operational optimisation to achieve decarbonisation at minimum cost. We consider
offshore wind, solar, energy hubs and subsea cables. A sensitivity analysis is conducted on CO2tax, CO2budget
and the capacity of power from shore. The results show that: (a) a hard carbon cap is necessary for stimulating
a zero-emission offshore energy system, (b) offshore wind integration and power from shore can more than
halve current emissions, but offshore energy hubs with storage may be necessary for zero-emission production,
and (c) at certain CO2tax levels, the system with offshore energy hubs can potentially reduce CO2emissions
by 49% and energy losses by 10%, compared to a system with only offshore renewables, gas turbines and
power from shore.
1. Introduction
Offshore wind is an important pillar in the energy transition world-
wide [1] to meet global and regional climate targets [2]. Offshore
Energy Hubs (OEHs) and the hub-and-spoke concept, offer a transna-
tional and cross-sector solution for better harnessing offshore wind and
integration with the rest of the energy system [3]. An energy hub is a
physical energy connection point with energy storage where multiple
energy carriers can be converted and conditioned [4]. This paper
presents an optimisation model for the investment and operation of
OEHs. It includes analyses on the functioning of OEHs in the transition
of a large-scale energy system towards integrating more renewable
energy. A case study is demonstrated in the North Sea as this region
has huge potential for large-scale offshore wind [5] and hydrogen
production.
The energy transition is widely studied [6]. It includes research
on the usage of both renewable energy technologies [7] and energy-
efficient technologies [8]. Transitioning to renewable energy, such as,
wind, solar, and green hydrogen [9], is a necessity for the decarbon-
isation of energy systems [10]. Green hydrogen produced from wind
Abbreviations: NCS, Norwegian continental shelf; OEH, Offshore energy hub; PFS, Power from shore; Base, The case with only offshore renewables, gas
turbines and power from shore; S1, Scenario 1; S2, Scenario 2; MILP, Mixed-integer linear programming
∗Corresponding author.
E-mail address: hongyu.zhang@ntnu.no (H. Zhang).
and solar power may play an essential role in the transition. Offshore
regions with potentially abundant renewable energy sources are crucial
for the global energy transition [11]. Therefore, we analyse the poten-
tial value of offshore renewable technologies for the energy transition
of a regional offshore energy system and discuss how the study can be
applied globally to contribute to the global energy transition towards
zero emission.
Existing literature reviewed below shows that OEHs may be a
promising option for producing green hydrogen offshore. The efficiency
and cost analysis of OEHs has shown that an OEH is efficient and
cost worthy in electrofuel applications [12]. However, the energy loss
of a system with OEHs has not been considered. In this paper, we
aim to analyse the potential value of OEHs in terms of energy losses.
Producing green hydrogen offshore with OEHs and using the hub
generated electricity to firstly cover the nominal electrolyser capacity
may be cost competitive compared with current costs of grey and
blue hydrogen [13]. The energy storage function of OEHs has not
been considered, which makes their OEH essentially a conversion and
distribution hub. Offshore energy storage can be crucial because of the
https://doi.org/10.1016/j.energy.2022.125219
Received 12 October 2021; Received in revised form 24 June 2022; Accepted 18 August 2022
Energy 261 (2022) 125219
2
H. Zhang et al.
Fig. 1. Conceptual illustration of OEHs.
potential massive capacity [14]. Therefore, in this paper, we consider
OEHs with offshore hydrogen storage, see Fig. 1 for an illustration.
In addition to distributing offshore energy to onshore systems with
OEHs, existing literature also investigates using OEHs for decarbonised
energy supply for offshore industries [15], including offshore oil and
gas recovery [16], maritime cargo transport, and offshore farming [17].
The environmental value of OEHs has not been analysed in the lit-
erature. Cost estimation of electrifying offshore fields with OEHs is
presented in [18]. However, the costs data was not used for investment
planning to analyse the trade off of technologies. The value of OEHs for
offshore sectors on a large scale is not sufficiently studied. Although
green hydrogen is pointed out as promising storage that can provide
supply security for oil and gas operations, it was not analysed.
To bridge the gaps mentioned above, we develop a multi-carrier
Mixed-Integer Linear Programming (MILP) model for investment plan-
ning optimisation of an offshore energy system with a high degree of
operational details. We model a clean OEH with hydrogen storage. We
only consider producing green hydrogen from electrolysis. To analyse
the economic advantages of OEHs compared with other technologies,
we consider investments in offshore wind, offshore solar, OEHs and
Power From Shore (PFS). The investment planning model is applied to
an offshore energy system with the goal of decarbonising energy gener-
ation for offshore oil and gas installations in a given region. The oil and
gas industry involves multi-billion-dollar investments and profits [19]
whose decarbonisation needs may trigger large-scale investments in
OEHs. Offshore oil and gas is an important offshore sector in many
countries, and the North Sea region has the highest number of offshore
fields [20]. Therefore, studying the value of clean OEHs in the North
Sea energy system may provide global insights.
The contributions of the paper are: (1) an integrated investment and
operational model with the following features, (a) OEHs are modelled
for a large-scale offshore energy system, and (b) the hourly device-level
energy consumption of platforms is modelled; (2) the value of OEHs is
analysed in the North Sea offshore energy system transition towards
zero-emission energy supply.
The outline of the paper is as follows: Section 2presents a literature
review on energy system planning methods and OEHs and introduces
the background regarding the production and decarbonisation of off-
shore oil and gas. Section 3gives the problem description followed
by modelling strategies and assumptions. Section 4presents the MILP
model and the case study. Section 5describes the case study and input
data. Section 6presents the results and analysis of the case study.
Section 7discusses the implications of the results and summaries the
limitations of the research. Section 8concludes the paper and suggests
further research.
2. Literature review
In this section, we review the literature on energy system planning
methods and OEHs and give a background on the production process
of offshore fields and corresponding decarbonisation issues.
2.1. Energy system planning methods
From an energy system planning perspective, the model in this
paper is a bottom-up multi-carrier energy flow model. For an extensive
review on this topic, we refer to [21]. Bottom-up energy system models
represent the equilibrium of a part of the energy sector [22]. On the
other hand, top-down energy models try to depict the economy as a
whole on a national level to analyse the aggregated effects of energy
policies in monetary units. In this paper, we only use the bottom-up
approach without considering the effect from a higher level using a soft-
link or hard-link model because we are interested in the cost-optimal
system design under different policy and technical scenarios rather than
analysing its interaction with the macro economy.
For large-scale energy system planning problems, linear program-
ming (LP) is usually used because of its computational tractability and
sufficiency in modelling most investment and operational decisions
and constraints. For example, energy system planning models like
EMPIRE [23], and GENeSYS-MOD [24] are LP models. Even though
LP may be sufficient when dealing with very aggregated systems, for
problems with lumpy investments (e.g. OEHs or transmission lines),
LP cannot capture the economic scale of the investment decision,
and MILP models are preferred [25]. Mixed-integer nonlinear pro-
gramming is also used in a planning problem to capture the system
operations [26]. However, the computational difficulty may need to be
addressed first to make the problem solvable. Our model uses MILP
to provide more sensible investment decisions and avoid nonlinear
constraints by simplifying the problem to reduce computational costs.
2.2. OEHs
The potential value and functioning of OEHs have drawn increased
attention in several sectors. In the offshore oil and gas sector, it has
been found that creating small energy hubs to import energy from
various sources to offshore oil and gas platforms can achieve a massive
reduction of CO2emissions in the UK continental shelf [18]. They
mentioned that hydrogen-energy storage is green and provides supply
security for oil and gas operations. Energy-hub-based electricity system
design for an offshore platform considering CO2mitigation is presented
in [16]. By verifying the proposed approach on an existing platform, it
was found that CO2tax may play a decisive role in emission mitigation
of offshore platforms. In addition to clean OEHs that utilise offshore
wind, an OEH equipped with large gas turbines was proposed in [27].
Such an OEH serves as a centralised power generation system that offers
higher efficiencies than simpler in situ gas turbines [27].
OEHs may allow for better harnessing offshore wind to supply
more stable energy to offshore oil and gas platforms in the short
run and export clean energy to the continent in the long run. Con-
necting offshore wind in the North Sea, via an artificial island and
hub-and-spoke form, was shown in [28] to be more economical than
a traditional point-to-point connection if 10 GW offshore wind is built.
Hydrogen based OEHs also draw attention. An offshore artificial power-
to-gas island can produce and transport hydrogen through natural gas
pipelines [29]. Adding electrolysers to the offshore hub shows value
in mitigating active power variations and maintaining the voltage
of the hub [30]. Producing green hydrogen via OEHs to cover on-
shore energy demand and using hub generated electricity first to cover
nominal electrolyser capacity may have better economic performance
than producing hydrogen from natural gas [13]. In addition, techno-
economic analysis of offshore energy islands has shown that producing
hydrogen offshore may be more beneficial than onshore production
under some conditions. However, the development of offshore energy
islands for electrical transmission and hydrogen production is not
straightforward [31].
Studies have also been conducted on the impact of markets and
the design of markets in a system with OEHs. The impact of the
North Sea energy islands on national markets and grids is analysed
Energy 261 (2022) 125219
3
H. Zhang et al.
Fig. 2. Schematic of a topside structure of a typical North Sea oil and gas platform.
Source: Adapted from [46].
in [32] using a European electricity market model and a European
electricity network model, where the authors found that social welfare
increases but not for all the countries when the North Sea energy hub
is included in the system. Moreover, a separate offshore bidding zone
may lead to a more efficient offshore energy system with OEHs [33].
We consider a smaller system and focus on the optimal capacities
of new devices instead of analysing an extensive grid based on the
assumption that a certain amount of capacity of an OEH will be added.
The deployment plan for future European offshore grid development
with an energy hub is analysed in [34]. Unlike the study in this paper,
they assume some scenarios of future deployment of wind turbines and
transmission lines and analyse the system operation under different
operational scenarios, including line fault, breaker failure, and bus bar
fault. Compared with our study, they focus more on system operation
under a predefined system configuration. We notice that in the study
mentioned above, where the focus is on national markets, grid, and
system failure, the investment planning and operations of OEHs are
simplified. Therefore, we aim to contribute to more detailed modelling
of optimising investment planning and operation of OEHs.
In addition to OEHs, more research has been conducted on the
onshore energy system. The energy hub concept has been also used
to increase the energy flexibility in buildings [35] and electricity mar-
kets [36]. Energy hub is a promising option for exploiting the benefits
of multi-energy systems, such as coupled electricity and heating net-
works [37], integrated natural gas and electricity [38] and electricity–
thermal–natural gas coupling system [39]. In addition, the design [40]
and management [41] of energy hubs with penetration of intermittent
wind power has been studied using stochastic programming. Using
energy hubs for coping with wind power volatility shows value in re-
ducing operating cost, wind power curtailment and CO2emissions [42].
Energy hubs with power-to-gas and hydrogen storage can reduce emis-
sions, and produce hydrogen for end-use applications [43]. Onshore
energy hubs have much more versatile configurations and functioning
compared to OEHs. We refer the readers to [44,45] for comprehensive
reviews on the research works on energy hubs.
2.3. Offshore oil and gas fields
From the studies on offshore field production optimisation [47] and
offshore field infrastructure planning [48], we can see that platforms
and fields vary a lot due to, amongst others, geological characteristics,
reserves, and remaining lifetimes. In the following, we present a typical
composition and production process of NCS platforms.
A North Sea field normally consists of topside structures and subsea
production systems. A topside structure typically consists of a process-
ing plant, a utility plant, drilling facilities, and a living quarter [46],
see Fig. 2. The production plant receives and processes well streams.
A visualisation of the production process is presented in Fig. 3. Major
energy consumption takes place in the production plants. The energy
demand of production plants is conventionally fulfilled by gas turbines
located in the utility plant. In 2014, gas turbines with waste heat
recovery units covered approximately 90% of all heat demand for
operations on the NCS [49].
2.4. Decarbonisation of offshore fields
Norway was the world’s third-largest exporter of natural gas in
2019 [50]. Offshore oil and gas extraction was responsible for 26.6%
(13.3 Mt CO2equivalent) of the total Norwegian greenhouse gases
in 2020 [51]. Norway steps up its climate goal to reduce emissions
by 50%–55% by 2030 compared to 1990 levels [52]. Using OEHs to
effectively exploit offshore wind power to decarbonise the NCS en-
ergy system may contribute to meeting Norway’s and Europe’s climate
targets.
CO2tax is an important instrument for stimulating offshore en-
ergy system decarbonisation. In 2022, the tax is about 79 e/tonne
in Norway [53] with an ambition to increase it to 200 e/tonne by
2030 [54]. In addition, the EU Emissions Trading System is a ‘‘cap and
trade’’ system that also includes the emissions on the NCS [54]. Carbon
tax and the emissions trading system make a total carbon price of
approximately 160 e/tonne. In this context, oil and gas companies are
undertaking considerable investments in decarbonisation solutions to
address climate goals, such as PFS and offshore wind. Oil and gas com-
panies on the NCS have set climate targets. For example, Equinor [55]
and Vår Energy [56] aim to reduce greenhouse gas emissions by 40%
by 2030, and near zero emission by 2050.
Technologies for decarbonisation exist, and the question is to find
the best mixture of such technologies at acceptable costs. There are four
general approaches to reduce offshore CO2emissions, when maintain-
ing a certain activity level:
(a) Reducing CO2emissions by improving reservoir drainage and
processing energy efficiency [57]. Water injection and gas injection
are common reservoir drainage strategies used on the NCS. Pumping,
compression and separation are major processes for handling produced
fluids and gas in a processing system. Injection and processing account
for more than half of the power consumption at the fields on the NCS.
(b) Increasing the energy efficiency of gas turbines. Due to security
of supply requirements, gas turbines usually operate with a margin,
which leads to a low efficiency of around 33% [58]. Adding bottoming
cycles to the existing gas turbines can improve their energy efficiency.
However, unlike an onshore energy system, weight and space limitation
of an offshore installation restrict extra devices like a bottoming cycle.
(c) Supplying zero emission or low emission energy to offshore oil
and gas platforms. This includes PFS [59], switching fuel from natural
gas to ammonia or hydrogen, and connecting offshore wind farms
to platforms. In the past years, several offshore fields have received
PFS via HVDC/HVAC cables [60]. In Norway, the cost of abating CO2
emissions by taking PFS can vary from less than 100 to almost 800
e/tonne [61]. Many abatement projects bringing PFS, are in their
planning phase highly unprofitable even considering Norway’s plan to
increase CO2tax to 200 e/tonne in 2030. Besides, due to the capacity
limits of the onshore system, the available power is limited in some
cases.
Offshore wind is another technology to supply clean power to
platforms. Equinor’s Hywind Tampen project aims to be operational by
2022 [62]. The combination of an offshore platform with a wind farm
represents a potentially good match for the offshore petroleum sector’s
Energy 261 (2022) 125219
4
H. Zhang et al.
Fig. 3. Schematic of a potential decarbonised offshore field production process. A three-stage separator train separates well streams into produced water, oil, condensate and
gas. Typically the first stage separator takes out most of the water and gas at arrival conditions. Fuel gas is taken from the first stage separator. The residual mix of oil, gas
and water is heated before entering the second stage separator. Produced water is purified and discharged, and in some cases, reinjected into water injection wells to maintain
reservoir pressure. Water lift pumps will lift seawater for reinjection if needed. Produced oil is pressurised by pumps and exported. Produced gas is used as fuel gas, compressed
and exported, reinjected via dedicated wells for enhanced oil recovery or injected into the same wells for gas lift.
The grey dotted box includes the potential processes for decarbonisation. See Fig. 1 for a visualisation of the processes in an OEH.
desire for renewable energy with the offshore wind power industry’s
desire for an early market [63]. The stability and control issues for
an isolated offshore energy system consisting of a wind farm and
five platforms were addressed in [63]. Integrating large wind turbines
into a stand-alone platform is theoretically possible, but requires more
operational and economic work to prove its feasibility [64]. In [65],
authors found that local wind power production for matching the
offshore power demand improves both voltage- and frequency-stability
in an offshore system. An MILP model for determining optimal offshore
grid structures for wind power integration and power exchange named
Net-Op was presented in [66]. An extension of Net-Op that takes into
account investment cost, variability of wind/demand/power prices, and
the benefit of power trade between countries/price areas is presented
in [67].
(d) Deploying carbon capture and storage. Storing CO2in stable un-
derground formations, e.g., old and stable oil reservoirs, has a relatively
Energy 261 (2022) 125219
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H. Zhang et al.
long history. Since 1996, nearly one million tonnes of CO2per year have
been separated during the natural gas process from the Sleipner Vest
field and stored in the Utsira formation [59].
The first two approaches have a limited impact on emission reduc-
tion, whereas the third and fourth approaches can give up to 100%
reduction. We focus on supplying clean energy to offshore fields.
3. Problem description
First, this section introduces the proposed offshore energy system
planning problem with OEHs. Then, we present the time and geo-
graphical structures with the aim of reducing computational time of a
potentially large problem. Finally, we state the modelling assumptions.
The problem under consideration aims to make optimal investment
and operational decisions for the NCS energy system with OEHs, based
on the energy demand captured by the operational model. By solving
such a problem, we aim to find out under what conditions OEHs may
benefit the system and how OEHs operate with the rest of the system.
To model hourly energy demand, the following devices are con-
sidered: (a) separators; (b) pumps: water injection pumps, water lift
pumps, oil export pumps; (c) compressors: gas injection compressors
and gas export compressors. These devices have existing capacities,
and no investment is made in them. Moreover, we assume that device
efficiency, flow inlet/outlet pressures and hourly mass flow are given.
For the investments in decarbonisation solutions, we consider: (a)
offshore renewable energies (offshore wind and offshore solar); (b)
OEHs (electrolysers, hydrogen storage facilities and fuel cells); (c)
subsea cables (HVAC, HVDC and offshore and onshore converter sta-
tions); (d) electric boilers; (e) platform located batteries. The capital
expenditures, fixed operational costs are assumed to be known.
The problem is to determine: (a) capacities of decarbonisation tech-
nologies, and (b) operational strategies that include scheduling of
generators, storage and approximate power flow among regions to meet
the energy demand with minimum overall investment, operational and
environmental costs.
3.1. Modelling strategies and assumptions
A multilevel control hierarchy was defined in [68], arguing that
the repetitive use of static models can solve many important petroleum
production optimisation problems. A multi-period MILP model is devel-
oped for an integrated investment planning and operational problem
that combines short-term and long-term control hierarchies. Aggre-
gation, clustering and time sampling [69] are used to address the
multi-time-scale aspects [70] and solve a large-scale instance.
3.1.1. Time structure of the problem
The investment problem is optimised over a long-term horizon,
e.g., a few decades. The operational problem is optimised on an hourly
basis based on investment decisions. To combine these two control
hierarchies without increasing much the computational time, 𝑁rep-
resentative slices are selected, each containing ℎhours, and they are
scaled up to represent a whole operational year. A visualisation of the
time structure is in Fig. 4.
We use a node formulation to link investment planning with the
system operation. An illustration of a planning problem is presented
in Fig. 5. We define a point in time where investments are made as
an investment node 𝑖0. We then define the entire operational problem
succeeding an investment node as an operational node 𝑖. Finally, the
investment decision made in an investment node is examined by the
operational node succeeding the investment node.
Fig. 4. Illustration of combined hierarchies.
Source: Adapted from [71].
Fig. 5. Illustration of the linkage between investment planning and operational time
horizon.
3.1.2. Geographical structure of the problem
The problem potentially consists of many regions, and we imple-
ment a k-means cluster method based on the locations of fields to
reduce the problem size. There are two considerations when deciding
the number of clusters. Firstly, we assume the OEH connects the
surrounding fields via HVAC cables; thus, only fields with a feasi-
ble transmission distance (up to 100 km) are considered. Secondly,
we assume that the cluster centres are the locations for OEHs. We
prevent clusters with too few fields. For each cluster, we aggregate
the individual fields into one larger field with a distance to the OEH
equal to the average distance of the individual fields, and connect
fields to OEH in hub-and-spoke form. Currently, we do not consider
the interconnection among fields and clusters, resulting in reasonably
simple network topology.
3.1.3. Assumptions
Each platform is assumed to be a typical North Sea platform with
production processes as shown in Fig. 3. The energy consumption of
pumps, compressors and separators can be formulated as a function of
flow rate, pressure and temperature. For simplicity, the pressure levels
and temperatures are assumed to take values that are typical on the
North Sea, leading to a linear formulation. Kirchhoff voltage law is
omitted, and replaced by an energy flow model. We assume no mass
loss during production.
4. Mathematical model
This section presents a deterministic MILP formulated for the multi-
carrier energy system investment planning problem with high degree
of operational details. The model includes a long-term investment
planning horizon and a short-term operational horizon. The integrated
investment planning and operational model is partially based upon the
linear programming model developed in [72]. Integer variables are
used to improve the representation of the fixed capacity independent
investment costs. The complete MILP problem consists of Eqs. (1)–(3).
The complete nomenclature of the model can be found in Ap-
pendix A. The supplementary definitions of some model parameters
are presented in Appendix C. We use the conventions that calligraphic
Energy 261 (2022) 125219
6
H. Zhang et al.
capitalised Roman letters denote sets, upper case Roman and lower
case Greek letters denote parameters, and lower case Roman letters
denote variables. The indices are subscripts and name extensions are
superscripts. The same lead symbol represent the same type of thing.
The names of variables, parameters, sets and indices are single symbols.
4.1. Objective function
min 𝑐𝐼𝑁𝑉 +𝜅
𝑖∈
𝑐𝑂𝑃 𝐸
𝑖(1)
The objective function, Eq. (1), is to minimise the total investment
(𝑐𝐼𝑁𝑉 ) and operational (𝜅𝑖∈𝑐𝑂𝑃 𝐸
𝑖)costs over the planning horizon.
4.2. Investment planning constraints
The investment planning constraints are given by:
𝑐𝐼𝑁𝑉 =
𝑖∈0
𝑝∈𝐶𝐼𝑛𝑣𝑉
𝑝𝑖 𝑥𝐼𝑛𝑠𝑡
𝑝𝑖 +𝐶𝐼𝑛𝑣𝐹
𝑝𝑖 𝑦𝑝𝑖+𝜅
𝑖∈
𝑝∈
𝐶𝐹 𝑖𝑥
𝑝𝑖 𝑥𝐴𝑐𝑐
𝑝𝑖 (2a)
𝑥𝐴𝑐𝑐
𝑝𝑖 =𝑋𝐻𝑖𝑠𝑡
𝑝+
𝑖∈𝑖
𝑥𝐼𝑛𝑠𝑡
𝑝𝑖 , 𝑝 ∈, 𝑖 ∈(2b)
0≤𝑥𝐼𝑛𝑠𝑡
𝑝𝑖 ≤𝑄𝑝𝑦𝑝𝑖, 𝑝 ∈, 𝑖 ∈0(2c)
0≤𝑥𝐴𝑐𝑐
𝑝𝑖 ≤𝑋𝑀𝑎𝑥
𝑝, 𝑝 ∈, 𝑖 ∈(2d)
𝑦𝑝𝑖 ∈ {0,1,2,…, 𝑌𝑝𝑖}, 𝑝 ∈, 𝑖 ∈0(2e)
𝑥𝐼𝑛𝑠𝑡
𝑝𝑖 , 𝑥𝐴𝑐𝑐
𝑝𝑖 ∈R+
0,(2f)
𝑦𝑝𝑖 ∈Z+
0.(2g)
The total cost for investment planning, Eq. (2a), consists of actual in-
vestment costs (comprising capacity-dependent and
capacity-independent costs), as well as fixed operating and mainte-
nance costs. Here, 𝜅is a scaling factor that depends on the time step
between two successive investment nodes. Constraint (2b) states that
the accumulated capacity of a technology 𝑥𝐴𝑐𝑐
𝑝𝑖 in an operational node
equals the sum of the historical capacity 𝑋𝐻𝑖𝑠𝑡
𝑝and newly invested
capacities 𝑥𝐼𝑛𝑠𝑡
𝑝𝑖 in its ancestor investment nodes 𝑖. The integer variable
𝑦𝑝𝑖 gives the number of units of technology 𝑝∈in investment node
𝑖∈0. Parameter 𝑄𝑝represents the maximum capacity of a technology
unit, and parameter 𝑋𝑀𝑎𝑥
𝑝denotes the maximum accumulated capacity
of a technology. Parameter 𝑌𝑝gives the maximum number of units that
can be installed for the different technologies.
4.3. Operational constraints
We now present the operational constraints in one operational node
𝑖. Note that we omit index 𝑖in the operational model for ease of
notation. Oil and gas recovery are modelled as this is the most likely
use in the short to medium term. The operational constraints can be
modified for other use, e.g., offshore fish farming, maritime, transport,
and others.
𝑐𝑂𝑃 𝐸 =
𝑡∈𝑛
𝑊𝑡
𝑔∈
𝐶𝐺
𝑔𝑝𝐺
𝑔𝑡 +
𝑧∈
𝑙∈{𝐻,𝑃 }
𝐶𝑆ℎ𝑒𝑑 ,𝑙𝑝𝑆ℎ𝑒𝑑 ,𝑙
𝑧𝑡 +
𝑧∈𝑂
𝜏𝐸𝑃
𝑧𝑡 𝑝𝑃 𝐹 𝑆
𝑧𝑡 (3a)
0≤𝑝𝑝𝑡 ≤𝑝𝐴𝑐𝑐
𝑝, 𝑝 ∈∗, 𝑡 ∈(3b)
0≤𝑝𝐺
𝑔𝑡 +𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 ≤𝑝𝐴𝑐𝑐 𝐺
𝑔, 𝑔 ∈, 𝑡 ∈(3c)
0≤𝑣𝑆𝐻 𝑦
𝑠𝑡 ≤𝑣𝐴𝑐𝑐𝑆 𝐻𝑦
𝑠, 𝑠 ∈𝐻𝑦 , 𝑡 ∈(3d)
0≤𝑝𝑆𝐸 +
𝑠𝑡 ≤𝛾𝑆𝐸
𝑠𝑞𝐴𝑐𝑐𝑆 𝐸
𝑠, 𝑠 ∈𝐸, 𝑡 ∈(3e)
0≤𝑝𝑆𝐸 −
𝑠𝑡 +𝑝𝑅𝑒𝑠𝑆𝐸
𝑠𝑡 ≤𝛾𝑆𝐸
𝑠𝑞𝐴𝑐𝑐𝑆 𝐸
𝑠, 𝑠 ∈𝐸, 𝑡 ∈(3f)
0≤𝑞𝑆𝐸
𝑠𝑡 ≤𝑞𝐴𝑐𝑐𝑆 𝐸
𝑠, 𝑠 ∈𝐸, 𝑡 ∈(3g)
−𝑝𝐴𝑐𝑐𝐿
𝑙≤𝑝𝐿
𝑙𝑡 ≤𝑝𝐴𝑐𝑐𝐿
𝑙, 𝑙 ∈, 𝑡 ∈(3h)
−𝛼𝐺
𝑔𝑝𝐴𝑐𝑐𝐺
𝑔≤𝑝𝐺
𝑔𝑡 +𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 −
𝑝𝐺
𝑔(𝑡−1) −𝑝𝑅𝑒𝑠𝐺
𝑔(𝑡−1) ≤𝛼𝐺
𝑔𝑝𝐴𝑐𝑐𝐺
𝑔, 𝑔 ∈, 𝑛 ∈, 𝑡 ∈𝑛(3i)
−𝛼𝐹
𝑓𝑝𝐴𝑐𝑐𝐹
𝑓≤𝑝𝐹
𝑓𝑡 −𝑝𝐹
𝑓(𝑡−1) ≤𝛼𝐹
𝑓𝑝𝐴𝑐𝑐𝐹
𝑓, 𝑓 ∈, 𝑛 ∈, 𝑡 ∈𝑛(3j)
𝑔∈𝑧
𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 +
𝑠∈𝐸
𝑧
𝑝𝑅𝑒𝑠𝑆𝐸
𝑠𝑡 ≥𝜎𝑅𝑒𝑠
𝑧𝑃𝐷𝑃
𝑧𝑡 , 𝑧 ∈𝑃, 𝑡 ∈(3k)
𝑔∈𝑧
𝑝𝐺
𝑔𝑡 +
𝑙∈𝐼𝑛
𝑧
𝜂𝐿
𝑙𝑝𝐿
𝑙𝑡 +
𝑠∈𝐸
𝑧
𝑝𝑆𝐸 −
𝑠𝑡 +
𝑟∈𝑧
𝑅𝑅
𝑧𝑡𝑝𝐴𝑐 𝑐𝑅
𝑟+
𝑓∈𝑧
𝑝𝐹
𝑓𝑡 +𝑝𝑍𝑂
𝑧𝑡 +𝑝𝑆ℎ𝑒𝑑 𝑃
𝑧𝑡 =𝑃𝐷𝑃
𝑧𝑡 +
𝑏∈𝐸
𝑧
𝑝𝐵𝐸
𝑏𝑡 +
𝑒∈𝑧
𝑝𝐸
𝑒𝑡+
𝑙∈𝑂𝑢𝑡
𝑧
𝜂𝐿
𝑙𝑝𝐿
𝑙𝑡 +
𝑠∈𝐸
𝑧
𝑝𝑆𝐸 +
𝑠𝑡 +𝑝𝐺𝑆ℎ𝑒𝑑 𝑃
𝑧𝑡 , 𝑧 ∈, 𝑡 ∈(3l)
𝑔∈𝑧
𝜂𝐻𝑟𝐺
𝑔𝑝𝐺
𝑔𝑡 +
𝑏∈𝐸
𝑧
𝜂𝐵𝐸
𝑏𝑝𝐵𝐸
𝑏𝑡 +𝑝𝑆ℎ𝑒𝑑 𝐻
𝑧𝑡 =
𝑃𝐷𝐻
𝑧𝑡 +𝑝𝐺𝑆ℎ𝑒𝑑 𝐻
𝑧𝑡 , 𝑧 ∈𝑃, 𝑡 ∈(3m)
𝜂𝐸𝐹 (
𝑓∈𝑧
𝐻𝑡𝜌𝐹𝑝𝐹
𝑓𝑡 −
𝑠∈𝐻𝑦
𝑧
𝑣𝑆𝐻 𝑦−
𝑠𝑡 ) =
𝑒∈𝑧
𝐻𝑡𝑝𝐸
𝑒𝑡 −𝜂𝐸𝑆
𝑠∈𝐻𝑦
𝑧
𝑣𝑆𝐻 𝑦+
𝑠𝑡 , 𝑧 ∈𝐻, 𝑡 ∈(3n)
𝐻𝑡(𝑝𝑅𝑒𝑠𝑆𝐸
𝑠𝑡 +𝑝𝑆𝐸 −
𝑠𝑡 )≤𝑞𝑆𝐸
𝑠𝑡 , 𝑠 ∈𝐸, 𝑡 ∈(3o)
𝑞𝑆𝐸
𝑠(𝑡+1) =𝑞𝑆𝐸
𝑠𝑡 +𝐻𝑡(𝜂𝑆𝐸
𝑠𝑝𝑆𝐸 +
𝑠𝑡 −𝑝𝑆𝐸 −
𝑠𝑡 ), 𝑠 ∈𝐸, 𝑛 ∈, 𝑡 ∈𝑛(3p)
𝑣𝑆𝐻 𝑦
𝑠(𝑡+1) =𝑣𝑆𝐻 𝑦
𝑠𝑡 +𝑣𝑆𝐻 𝑦+
𝑠𝑡 −𝑣𝑆𝐻 𝑦−
𝑠𝑡 , 𝑠 ∈𝐻𝑦 , 𝑛 ∈,𝑡 ∈𝑛(3q)
𝑡∈𝑛
𝑔∈
𝑊𝑡𝐸𝐺
𝑔𝑝𝐺
𝑔𝑡 ≤𝜇𝐸,(3r)
𝑝𝐿
𝑙𝑡 ∈R, 𝑝𝐺
𝑔𝑡, 𝑝𝑆 ℎ𝑒𝑑𝑃 , 𝑝𝑆ℎ𝑒𝑑 𝐻 , 𝑝𝑃𝐹 𝑆
𝑧𝑡 , 𝑝𝑝𝑡, 𝑝𝐴𝑐 𝑐
𝑝, 𝑝𝐺
𝑔𝑡, 𝑝𝐵 𝐸
𝑏𝑡 ∈R+
0,(3s)
𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 , 𝑝𝐴𝑐𝑐 𝐺
𝑔, 𝑝𝐺𝑆ℎ𝑒𝑑 𝑃
𝑧𝑡 , 𝑝𝐺𝑆ℎ𝑒𝑑 𝐻
𝑧𝑡 , 𝑣𝑆𝐻 𝑦+
𝑠𝑡 , 𝑣𝑆𝐻 𝑦−
𝑠𝑡 , 𝑣𝑆𝐻 𝑦
𝑠𝑡 , 𝑝𝐸
𝑒𝑡 ∈R+
0,(3t)
𝑣𝐴𝑐𝑐𝑆 𝐻𝑦 , 𝑝𝑆𝐸+
𝑠𝑡 , 𝑝𝑆𝐸 −
𝑠𝑡 , 𝑝𝑅𝑒𝑠𝑆𝐸
𝑠𝑡 , 𝑞𝐴𝑐𝑐 𝑆𝐸
𝑠, 𝑞𝑆𝐸
𝑠𝑡 , 𝑝𝐴𝑐𝑐𝐿
𝑙, 𝑝𝐴𝑐𝑐𝑅
𝑟, 𝑝𝐹
𝑓𝑡 ∈R+
0.(3u)
The operational cost 𝑐𝑂𝑃 𝐸 , which is included in the objective func-
tion, Eq. (1), for each operational node 𝑖, is described by Eq. (3a)
that includes total operating costs of generators 𝐶𝐺
𝑔𝑝𝐺
𝑔𝑡, energy load
shedding costs for heat 𝐶𝑆ℎ𝑒𝑑 𝐻 𝑝𝑆ℎ𝑒𝑑𝐻 and power 𝐶𝑆 ℎ𝑒𝑑𝑃 𝑝𝑆ℎ𝑒𝑑𝑃 and
electricity costs of onshore power 𝜏𝐸𝑃
𝑧𝑡 𝑝𝑃 𝐹 𝑆
𝑧𝑡 .𝐶𝐺
𝑔includes the variable
operational cost, fuel cost and the CO2tax charged on the emissions of
generator 𝑔. Constraint (3b) ensures that the devices including electric
boilers 𝑏∈𝐸, electrolysers 𝑒∈, and fuel cells 𝑓∈are within
their capacity limits. Constraint (3c) dictates that the power generation
of a gas turbine 𝑝𝐺
𝑔𝑡 plus the spinning reserve 𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 must not exceed
its capacity 𝑝𝐴𝑐𝑐𝐺
𝑔. Constraint (3d) states that the hydrogen storage
level 𝑣𝑆𝐻 𝑦
𝑠𝑡 should be less than the capacity 𝑣𝐴𝑐𝑐𝑆 𝐻𝑦
𝑠. Constraint (3e)
dictates that the power charged 𝑝𝑆𝐸 +
𝑠𝑡 should be within the charging
capacity. Constraint (3f) specifies that the discharging power 𝑝𝑆𝐸 −
𝑠𝑡
plus the power for reserve requirement 𝑝𝑅𝑒𝑠𝑆𝐸
𝑠𝑡 must not exceed the
discharging capacity. Constraint (3g) limits the energy storage level
𝑞𝑆𝐸
𝑠𝑡 to be within the capacity 𝑞𝐴𝑐𝑐𝑆 𝐸
𝑠. Constraint (3h) shows that the
power flow 𝑝𝐿
𝑡is within the transmission capacity 𝑝𝐴𝑐𝑐𝐿
𝑙. Constraints
(3i) and (3j) capture how fast gas turbines and fuel cells can ramp
up or ramp down their power output, respectively. The parameters
𝛼𝐺
𝑔and 𝛼𝐹
𝑓are the maximum ramp rate of gas turbines and fuel
cells, respectively. The operating reserve requirement, Constraint (3k),
dictates that the spinning reserve of gas turbines 𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 , plus the reserve
of the electricity storage 𝑝𝑅𝑒𝑠𝐸𝑆
𝑠𝑡 must exceed the minimum reserve
requirement, where 𝜎𝑅𝑒𝑠 is a percentage of the power load. The power
nodal balance, Constraint (3l), ensures that, in one operational period
𝑡, the sum of total power generation of turbines 𝑝𝐺
𝑔𝑡, power discharged
from all the electricity storage 𝑝𝑆𝐸 −
𝑠𝑡 , renewable generation 𝑅𝑅
𝑧𝑡𝑝𝐴𝑐 𝑐𝑅
𝑟𝑡 ,
fuel cell generation 𝑝𝐹
𝑓𝑡 , power transmitted to this region, and load shed
Energy 261 (2022) 125219
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Fig. 6. Illustration of the NCS energy system with energy hubs. L1 – L5 (dotted lines) are representative HVAC cables, while L6 – L10 (solid lines) are HVDC cables. Black dots
represent energy hubs and the red dots represent the onshore buses they connect to. Points with different shapes and colours represent NCS oil and gas fields.
𝑝𝑆ℎ𝑒𝑑 𝑃
𝑧𝑡 equals the sum of power demand 𝑃𝐷𝑃
𝑧𝑡 , power consumption of
electric boilers 𝑝𝐵𝐸
𝑏𝑡 , power consumption of all electrolysers 𝑝𝐸
𝑒𝑡, power
transmitted to other regions, and power generation shed 𝑝𝐺𝑆ℎ𝑒𝑑 𝑃
𝑧𝑡 . The
parameter 𝑅𝑅
𝑧𝑡 is the capacity factor of renewable unit that is a fraction
of the nameplate capacity 𝑝𝐴𝑐𝑐𝑅 . The subset of a technology in region
𝑧is represented by 𝑅𝑧∶= {𝑟∈∶𝑟is available in region 𝑧}, where
can be replaced by other sets of technologies. The heat energy balance,
Constraint (3m), states that the heat recovery of gas turbines 𝜂𝐻𝑟𝐺
𝑔𝑝𝐺
𝑔𝑡,
plus electric boiler heat generation 𝜂𝐵𝐸
𝑏𝑝𝐵𝐸
𝑏𝑡 , plus heat load shed 𝑝𝑆ℎ𝑒𝑑 𝐻
𝑧𝑡
equals the heat demand 𝑃𝐷𝐻
𝑧𝑡 plus the heat generation shed 𝑝𝐺𝑆ℎ𝑒𝑑 𝐻
𝑧𝑡 .
The hydrogen mass balance, Constraint (3n), states that hydrogen
produced by electrolyser equals the hydrogen injected into the storage
𝑣𝑆𝐻 𝑦+, plus the hydrogen directly supplied to fuel cells . Constraint (3o)
restricts the discharged energy and the energy for reserve purpose to
be less than the energy storage level 𝑞𝑆𝐸
𝑠𝑡 . Constraint (3p) states that
the state of charge 𝑞𝑆𝐸
𝑠𝑡 in period 𝑡+ 1 depends on the previous state of
charge 𝑞𝑆𝐸
𝑠𝑡 , the charged power 𝑝𝑆𝐸 +
𝑠𝑡 and discharged power 𝑝𝑆𝐸 −
𝑠𝑡 . The
parameter 𝜂𝑆𝐸
𝑠represent the charging efficiency. The parameter 𝐻𝑡is
the length of the period 𝑡. The hydrogen storage balance, Constraint
(3n), shows that the hydrogen storage level 𝑣𝑆𝐻 𝑦
𝑠𝑡 at period 𝑡+ 1 equals
to storage level at the previous period, plus the hydrogen injected
𝑣𝑆𝐻 𝑦+
𝑠𝑡 , minus the hydrogen withdrawn 𝑣𝑆𝐻 𝑦−
𝑠𝑡 . Constraint (3r) restricts
the total emission. The parameter 𝜇𝐸is the CO2budget. The symbol
𝐸𝐺
𝑔is the emission factor per unit of power generated. The parameter
𝑊𝑡is the length of a period after scaling. We only consider emissions
from the generators, but the model can easily be extended to include
other emissions. The complete MILP problem consists of Eqs. (1)–(3).
5. Case study
The case study is carried out on the North Sea part of the NCS,
considering 66 fields. The problem consists of 77 regions, divided into
66 fields, 5OHEs and 5onshore buses. By using the clustering approach
described in Section 3.1, the system can be represented using 5clusters
and henceforth go from 77 regions to 15 regions. The network topology
is exemplified in Fig. 6. The power demand of platforms is assumed to
be initially entirely supplied by gas turbines, as only a limited number
of platforms receives PFS. Four representative months with hourly
resolution are selected and scaled up to represent a whole year. In the
case study, parameter 𝑄𝑝is obtained from references. It is determined
based on the nameplate capacity of devices. The parameter 𝑋𝑀𝑎𝑥
𝑝is set
to a big number.
The field area geometry data is obtained from [73]. For each field,
one coordinate is picked from the multipolygon as its representative lo-
cation. The representative location, attributed cluster and the distance
to its cluster centre for each field are summarised in Table D.2.
One month from each season is selected. The production of fields
in each cluster is aggregated. A visualisation of the production data for
each field in the four representative months is presented in Fig. 7, the
data used for plotting is available at [74].
The operational data in the oil and gas industry is sensitive, and
usually not disclosed to the public. Aggregated data such as monthly or
yearly production of petroleum on the NCS can be obtained from [59].
One can also find monthly production and injection data for each
field from [75,76]. Neither of these can be directly used as inputs for
this study due to the time resolution difference. Therefore, reasonable
data generation is necessary. Raw data is collected from: (a) Norne
(1998–2006) and Volve (2008–2016) fields with hourly production and
injection data from [77], and (b) monthly production and injection data
of each field from [75]. We develop a data generation method that
considers the lifetimes of offshore fields [74].
We define a base case (Base) with offshore renewables, electric
boiler, battery and PFS as investment options. This case is then used
as a benchmark to check against the case with OEHs. The full model
given by Eqs. (1)–(3) takes approximately 2 hours to solve.
6. Results
We demonstrate the results of a static integrated investment plan-
ning and operational problem given by Eqs. (1)–(3), for a future point in
time. The problem consists of 461,208 continuous variables, 100 integer
variables and 980,013 constraints. The model was implemented in Julia
1.6.1 using JuMP [78] and solved with Gurobi 9.1.2 [79]. The code was
run on a MacBook Pro with 2.4 GHz 8-core Intel Core i9 processor, with
64 GB of RAM, running on macOS 11.6 Big Sur. The Julia code and
data for the case study have been made publicly available [74]. The
integrated investment and operational model given by Eqs. (1)–(3) is
solved to conduct sensitivity analysis on CO2tax, CO2budget and the
capacity of PFS. The results show that a system with OEHs can reduce
up to 49% CO2emissions and 10% energy loss compared with the one
with only offshore renewables, gas turbines and PFS.
6.1. Energy system analysis
In this section, we present results on energy consumption and
CO2emission of the initial system. By post-processing, we verify the
energy consumption of platforms is of the same order of magnitude
as the reported numbers. The resulted CO2emission is 5.54 Mt/yr.
In comparison, the reported total emission of the relevant fields was
6.89 Mt in 2019 [76]. The emissions from the model are expected to
be lower than 6.89 Mt since not all emission sources are considered.
Based on [80], one could assume that the major processes considered
Energy 261 (2022) 125219
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Fig. 7. Production profile in the representative months.
Fig. 8. Power consumption and supply (Only two lines are observable since power supply and demand match exactly. OCGT power equals power demand at all times).
Energy 261 (2022) 125219
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H. Zhang et al.
Fig. 9. Heat consumption and supply.
Fig. 10. Power demand in a year.
Table 1
Emission distribution by cluster.
cluster1 cluster2 cluster3 cluster4 cluster5
Emission distribution 6.8% 5.5% 44.8% 11.7% 31.2%
in this study make up about 80% of the total load. Therefore, 5.54 Mt
yearly emission is within the correct range, implying that the energy
load modelling is relatively accurate.
From Fig. 8, we can see that the power output of the Open Cycle
Gas Turbine (OCGT) matches the power demand at every operational
period. Heat recovery of OCGTs is assumed to be the only heat source.
Fig. 9 shows that heat recovery of OCGTs provides more than enough
heat due to high electricity generation. We can also see that energy
consumption can vary significantly. A breakdown of electricity load
is shown in Fig. 10, gas export compressors dominate the power con-
sumption in clusters 3–5. Water injection is the largest power consumer
in cluster 2since there are some mature fields (e.g., Ekofisk) whose
reservoir pressures are mainly maintained by water injection. OCGT
is the only energy and emission source in the initial setup. Therefore,
emission breakdown includes the emissions from the total energy con-
sumption of each region. Cluster 1has the second smallest share of
the total energy consumption, with a considerable amount of power
consumed by gas injection. The fields in cluster 1, such as Grane, have
the third-highest gas injection level among the 66 fields. From Table 1,
we find that emission mainly comes from the northern part of the North
Sea.
6.2. Sensitivity analysis of CO2tax
This section presents the results of sensitivity analysis of CO2tax.
We introduce CO2tax and still keep the carbon budget inactive. We
increase the carbon tax from 55 to 500 e/tonne with a step size of 5
e/tonne. PFS capacity limits are estimated from [61,81]. Note that the
cost of PFS may be underestimated since we only consider the costs of
subsea cables, onshore and offshore converter stations and electricity
bills. In reality, PFS projects may also involve investment in onshore
transmission lines or onshore power system capacity expansion. We
analyse the results from three metrics: cost, CO2emission and energy
Energy 261 (2022) 125219
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Fig. 11. Emission and cost comparison (CO2tax sensitivity analysis).
Fig. 12. Energy loss (CO2tax sensitivity analysis).
loss. Energy losses are from conversions, transmission, and generation
shed. The calculation is presented in Appendix B.
From Fig. 11, we can see that CO2tax as a single instrument may not
be enough to yield a zero emission system. We also find that near zero
emission can be achieved with a very high CO2tax. Therefore, a hard
carbon cap may be necessary for stimulating a zero emission system.
When CO2tax is 55 e/tonne, the system reduces about 65% of the
emissions compared to the initial 5.54 Mt/yr emission. Approximately
84% of the emissions can be cut if CO2tax is increased to 200 e/tonne
as planned. As OCGTs are replaced by renewable energy, energy loss
is reduced as well. OEHs can potentially reduce up to around 49%
more CO2emission, and 5% total cost than the case with only offshore
wind and PFS (Base) at certain CO2tax levels. From Fig. 12, we find
that energy loss during production accounts for 11% of the energy
loss. OCGTs lose 18 GWh of energy during an operational year. As
production from wind turbines replaces gas turbines, energy loss from
OCGT is reduced. However, due to the lack of energy storage, electricity
generation shedding increases because wind power is shed. We find that
OEHs can effectively reduce electricity generation shedding, although it
loses energy during conversion. Overall, energy loss is up to 10% lower
in the case of OEHs compared with Base at certain tax levels.
From Fig. 13, we find that different clusters show different levels
of sensitivity to CO2tax. Offshore wind is the first renewable energy
solution that is added to the system. Electric boilers are needed as
offshore wind replaces gas turbines partially. OEHs are installed when
CO2tax is above 290 e/tonne. Offshore solar is only added in cluster
5under very high CO2tax levels. OCGTs still operate even CO2tax
increases to 500 e/tonne. We can see that in a static planning problem,
if CO2tax is the only instrument and increases to 200 e/tonne as the
government’s plan in 2030, OEHs may not be necessary. However, CO2
tax combined with the EU emissions trading system may likely increase
the total CO2price to around 250 − 300 e/tonne, which is about the
breakeven price of OEHs. In addition, the potential benefits of the
OEHs may realise once they provide services to more sectors, such as
exporting hydrogen for industries or transportation.
6.3. Sensitivity analysis of CO2budget
For the CO2budget, we use initial emissions as the starting point,
and reduce it by 5% until it hits 0. From Fig. 14, we find that the carbon
cap is binding most of the time, and we rarely see that emissions are
reduced more than the carbon cap. Thus, there is no difference in actual
emissions in Base and the system with OEHs. However, the cost is 25%
lower in a zero emission system with OEHs compared with Base.
We find that in a zero emission system without OEHs, energy loss
is around 530 TWh due to 90 GW of wind power capacity and 15
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Fig. 13. Capacities of technologies in each cluster (CO2tax sensitivity analysis), hydrogen storage is measured in tonne.
Fig. 14. Emission and cost comparison (CO2budget sensitivity analysis).
GW offshore solar capacity without storage. This may not be likely to
happen since some forms of storage would be added to compensate
for offshore wind in reality. From Fig. 15, we can see a large amount
of energy loss when reaching near zero emission system in Base. The
energy loss in Base is 10,749 GWh in a near zero emission system,
which is about twice as high as for the case with OEHs. A large
amount of wind power is installed to meet power demand at any
time. Therefore, the same capacity of wind that can cope with peak
demand hours, will also generate surplus power during normal hours.
This leads to increased energy losses as more wind replaces OCGT
without proper energy storage. In the case of OEHs, wind power can
be stored when excess power is generated. It is also worth noticing that
in the energy system without an OEH, energy storage is the battery
on the platforms, which can be infeasible due to space and weight
limitations. We observe that investments in batteries are only needed
when approaching zero emission in Base. No battery is needed in a
system with OEHs. In addition, the energy loss of OEHs is 28% of the
total loss, and the loss during production is about 50% of the total.
From Fig. 16, we find that cluster 3 receives PFS after a 5%
reduction of the carbon cap. Cluster 3 has the highest emission level but
the shortest distance from shore. Therefore, taking PFS and partially
electrifying the fields in cluster 3, can help the system reduce 5% of
the emissions in a cost efficient way. The system does not cut emissions
proportionally in each cluster, but cuts emissions from clusters with the
highest emission, such as cluster 3 and cluster 5. Therefore, it may be
necessary to consider the whole NCS when conducting system planning,
rather than consider each cluster separately and reach sub-optimality.
Cluster 2 is the most remote, more than 300 km from shore; PFS is
less economical than offshore wind. Therefore, offshore wind is added
to cluster 2 when the carbon cap drops to 2.77 Mt/yr. When the CO2
budget reduces to below 0.83 Mt/yr, CO2emissions are nearly zero
in clusters 1and 2. However, the carbon cap needs to reduce to zero
to shut down OCGTs completely in all clusters. Nearly 4,295 tonnes
of hydrogen storage capacity is needed in a zero emission NCS energy
system, and nearly half is installed in cluster 3.
6.4. Sensitivity analysis of the capacity of PFS
We now present the results of sensitivity analysis of the capacity
of PFS. The capacity of PFS affects the investments in offshore tech-
nologies. An onshore system has a limited capacity to transmit power
offshore. Although, onshore system expansion can affect this capacity
limit, it is not considered directly in this paper. Therefore, we conduct
sensitivity analysis to reveal the relationship between onshore power
system capacity and offshore decarbonisation technologies.
Energy 261 (2022) 125219
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Fig. 15. Energy loss.(CO2budget sensitivity analysis)
Fig. 16. Capacities of technologies in each cluster (CO2budget sensitivity analysis), hydrogen storage is measured in tonne.
6.4.1. Scenario 1 (S1)
The first scenario is to fix the CO2tax to 300 e/tonne, and increase
the PFS capacity of each onshore location from 0 MW to 1,000 MW
with a 10 MW step. The investment decisions remain the same when
the PFS capacity is higher than 710 MW. Therefore, we only present the
results from 0 MW to 710 MW. From Fig. 17, we can see that by having
710 MW capacity in each onshore location, the system can achieve
0.01 Mt/yr emission and reduce about 53% of the total cost. However,
increasing the capacity further does not cut emissions or costs further.
Fig. 19 shows that energy loss during transmission makes up 16% of
the total energy loss as we increase the onshore capacity. Electricity
generation shed decreases as onshore capacity increases because PFS
gradually replaces offshore wind, and less energy is lost from wind
turbines. From Fig. 18, we find that for onshore locations that connect
to cluster 1 and cluster 2, the needed onshore capacities are about
126 MW and 108 MW, respectively. There are also upper limits on the
installed capacity of PFS in the other clusters. We also notice that OEHs
are still needed in clusters 3 and 5 as we increase the onshore capacity.
However, eventually, OEHs are not needed since PFS can provide more
stable power and OEH with storage becomes less important.
6.4.2. Scenario 2 (S2)
In the second scenario, the CO2tax is fixed to 400 e/tonne. We
increase the onshore capacity from 0 MW to 1,000 MW, and present the
results until 770 MW. From 20, we can see that without PFS, the system
can achieve 0.63 Mt/yr emissions under S2 condition. Increasing the
Energy 261 (2022) 125219
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Fig. 17. Emission and cost (PFS capacity sensitivity analysis, S1).
Fig. 18. Capacities of technologies in each cluster (PFS capacity sensitivity analysis, S1), hydrogen storage is measured in tonne.
Fig. 19. Energy loss (PFS capacity sensitivity analysis, S1).
Energy 261 (2022) 125219
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H. Zhang et al.
Fig. 20. Emission and cost (PFS capacity sensitivity analysis, S2).
Fig. 21. Capacities of technologies in each cluster (PFS capacity sensitivity analysis, S2), hydrogen storage is measured in tonne.
Fig. 22. Energy loss (PFS capacity sensitivity analysis, S2).
Energy 261 (2022) 125219
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H. Zhang et al.
onshore capacity brings down 57% of the cost and also cut emission
further to near zero. Fig. 22 shows that about 22% of the energy
loss is from OEHs initially. OEHs are not needed when the onshore
capacity increases to around 390 MW for each location. By adding the
installed PFS capacity shown in Fig. 21, we find that a total onshore
capacity of 1.74 GW may help the offshore energy system achieve near
zero emission. We notice that the onshore system needs to provide an
averagely of 1.4 GW. By checking the average power transmission of
PFS, which might not be feasible without onshore system expansion.
7. Discussion
The analysis above shows that OEHs have potential value in emis-
sion reduction, energy losses and costs. The operational part of the
model provides energy consumption of fields that is consistent with
the analysis in [80], and aligned with officially reported numbers [59].
However, a similar investment planning problem is not found in the
literature. Therefore, the results from the paper may provide a possible
benchmark for future studies.
We demonstrate the case study on the NCS energy system. A unique
characteristic of the NCS is that PFS is nearly emission free because
nearly all Norwegian onshore power production is based on hydro
power. However, in many regions, there may be less intention to use
PFS because of the carbon intensity of the onshore power. In such a
case, using PFS to compensate for offshore wind volatility may be infea-
sible, and hydrogen production and storage may become more relevant.
This may affect the optimal investment planning of the system.
Based on the optimal solutions under different conditions showed
in Figs. 13,16,18 and 21, we notice that offshore wind is a relatively
cost efficient technology that can achieve moderate emission targets
of platforms. This may suggest that in countries where PFS is not an
option, offshore wind alone can still help emission reduction to a large
extent.
In addition, the results suggest that producing and storing hydrogen
offshore in OEHs proves to be economical under a strict carbon budget
and a high CO2tax. One reason is that PFS is considered as an option
for decarbonisation, and building cables is most likely cheaper than
building an OEH. However, taking PFS will increase the pressure on
the onshore system, and affect the security of supply of the onshore
system and the onshore electricity price. This may cause public oppo-
sition. The potential restriction and limitation of the onshore power
system may motivate offshore wind. Because OEHs can supply offshore
platforms, a major function may be to supply and benefit the onshore
system. Onshore wind power development is slow or even opposed in
some regions. OEHs may help the onshore system decarbonisation by
distributing offshore wind power to shore. Another insight is that a
future hydrogen market may be needed in such a model to analyse the
value of OEHs properly. Because the main function of OEHs is to supply
offshore fields in the short- to mid-term, and serve for clean energy
export in the long term. Including a hydrogen market can realise the
long-term value of OEHs. The model can then be used for the techno-
economical analysis of OEHs in onshore and offshore energy systems
for countries with different energy policies in terms of offshore wind,
onshore wind and green hydrogen.
Energy storage becomes very important in a system with higher
wind power penetration. Hydrogen can be a promising option for long-
term large-scale clean energy storage. Some offshore regions may have
massive underground storage capacity. In such a case, the model can
analyse whether OEHs with storage can be a cost-efficient solution for
large-scale storage to help introduce more wind power in the system,
and then help the energy transition towards zero emission.
Offshore energy system planning is of interest in many regions
around the world. Decarbonising platforms may be a target during the
planning in regions like the Gulf of Mexico and the Brazilian continental
shelf. The model can be applied for the analysis of such locations. The
model can also be used to analyse the interaction of an offshore energy
system and onshore energy system transition. Regardless of the case
study location, investment planning of an energy system typically aims
to find optimal investment decisions that can fulfil the required energy
load under some constraints. The model formulation is general, and
there are no case-specific constraints. All locations and transmission
lines are represented by nodes and arcs, respectively. A different con-
figuration for each location and a cost model for each branch can be
defined based on data. Model parameters, constraints, and variables can
be modified according to the specific problem of the study.
Although the paper gives several insights and implications, the case
study has some limitations: (a) we consider a simple network topology
without considering the interconnections between fields clusters, and
the interconnections may help OEHs distribute power; (b) we do not
consider the capacity expansion of the onshore power system; and (c)
we only consider using OEHs to decarbonise offshore fields, whereas,
in reality, such hubs can provide service to more onshore and offshore
industries, therefore, analysing OEHs also has relevance to onshore
systems.
8. Conclusions and future work
This paper presents a multi-carrier offshore energy system invest-
ment planning optimisation model with a high degree of operational
detail to find cost-optimal solutions for decarbonising NCS energy sup-
ply. The major novelties and contributions are: (1) formulating OEHs
in an integrated MILP investment and operational model for large-scale
offshore energy system planning; (2) modelling the device-level energy
consumption of the offshore platforms with hourly time resolution on
a large scale; and (3) conducting a large-scale analysis of the value
of OEHs in the North Sea offshore energy system transition towards
decarbonised energy supply. Results from our case study indicate that:
(1) OEHs can reduce up to 10% of the energy loss and 49% of the
emissions with CO2tax above 290 e/tonne; (2) OEHs can reduce
energy loss by 53% in a near zero emission system; (3) a carbon
budget may be necessary to enable a zero emission energy system in
addition to CO2tax; and (4) the system cuts about 65% of the initial
emissions when CO2tax is 55 e/tonne, and approximately 84% of the
CO2emissions can be cut if CO2tax is increased to Norway’s target of
200 e/tonne.
Although the deterministic MILP model in this paper has led to
many insights, there are several possible extensions. A deterministic
optimisation model is not capable of representing load and supply
uncertainties. Therefore, we aim to develop a stochastic optimisation
model [82] and incorporate long-term and short-term uncertainties in
future work. In addition, multiple investment stages are needed to
represent the investment planning problem more realistically. Besides,
we only consider using OEHs for fields decarbonisation, which makes
OEHs seem less attractive than other technologies due to their high
costs. However, OEHs can have various advantages such as energy
provision to offshore fish farming, maritime transport, and using the in-
frastructure past the lifetime of the oil and gas fields for purposes such
as exporting hydrogen. These may motivate the investments in OEHs,
which we aim to include some of the aspects in future. Finally, more
work can be done on offshore network topology and the representation
of the onshore power system.
CRediT authorship contribution statement
Hongyu Zhang: Conceptualization, Methodology, Software, Valida-
tion, Formal analysis, Investigation, Visualisation, Data curation, Writ-
ing – original draft, Writing – review & editing. Asgeir Tomasgard:
Conceptualization, Supervision, Writing – review & editing, Funding
acquisition. Brage Rugstad Knudsen: Conceptualization, Supervision,
Writing – review & editing. Harald G. Svendsen: Conceptualization,
Writing – review & editing. Steffen J. Bakker: Conceptualization,
Writing – review & editing. Ignacio E. Grossmann: Conceptualization,
Supervision, Writing – review & editing.
Energy 261 (2022) 125219
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H. Zhang et al.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Data availability
We have shared the link to all the data and code.
Acknowledgements
This work was supported by the Research Council of Norway
through PETROSENTER LowEmission (project code 296207). We ap-
preciate the input from Per Eirik Bergmo, Heiner Schümann and Torleif
Holt, SINTEF Industry, Magnus Korpås, Department of Electric Power
Engineering, NTNU and Espen Flo Bødal, SINTEF Energy Research.
Appendix A. Nomenclature
Investment planning related sets
set of operational nodes
0set of investment nodes
𝑖set of investment nodes 𝑖(𝑖∈0)ancestor to operational
node 𝑖(𝑖∈)
set of technologies
Operation related sets
𝐸set of electric boilers
set of compressors
set of electrolysers
set of fuel cells
set of gas turbines
set of subsea cables
set of time slices
∗set of all electric boilers, electrolysers and fuel cells
(∗=𝐸∪∪)
𝑈set of pumps
set of renewable units (offshore wind and offshore solar)
𝐸set of electricity storage
𝐻𝑦 set of hydrogen storage facilities
set of hours in all time slices
𝑛set of hours in time slice 𝑛(𝑛∈)
set of all locations, including platforms 𝑃, OEHs 𝐻,
and onshore buses 𝑂(=𝑃∪𝐻∪𝑂)
Investment planning related parameters
𝜅scaling effect depending on time step between successive
investment nodes
𝐶𝐹 𝑖𝑥
𝑝𝑖 unitary fix operational and maintenance cost of tech-
nology 𝑝in operational node 𝑖(𝑝∈, 𝑖 ∈) [e/MW,
e/MWh, e/kg]
𝐶𝐼𝑛𝑣𝐹
𝑝𝑖 fixed capacity independent investment cost of technol-
ogy 𝑝in investment node 𝑖(𝑝∈, 𝑖 ∈0) [e]
𝐶𝐼𝑛𝑣𝑉
𝑝𝑖 unitary investment cost of technology 𝑝in investment
node 𝑖(𝑝∈, 𝑖 ∈0) [e/MW, e/MWh, e/kg]
𝑄𝑝capacity of a unit of technology 𝑝(𝑝∈) [MW, MWh,
kg]
𝑋𝑀𝑎𝑥
𝑝maximum accumulated capacity of technology 𝑝(𝑝∈)
[MW, MWh, kg]
𝑌𝑝𝑖 maximum number of newly invested units of technology
𝑝in investment node 𝑖(𝑝∈, 𝑖 ∈0)
Operation related parameters
𝛼𝐺
𝑔∕𝛼𝐹
𝑓maximum ramp rate of gas turbines /fuel cells (𝑔∈
, 𝑓 ∈) [MW/MW]
𝜂∗efficiency of compressors, electric boilers, fuel cells, gas
turbines, heat recovery of gas turbines electric stor-
age and transmission lines ∗= {C, BE, F, G, HrG, SE, L}
indexed by related sets
𝜂𝐸𝐹 conversion factor of electrolyser to inject hydrogen di-
rectly to fuel cell [MWh/kg]
𝜂𝐸𝑆 conversion factor of electrolyser to inject hydrogen to
the storage facility [MWh/kg]
𝛾𝑆𝐸
𝑠power ratio of electricity store 𝑠(𝑠∈𝐸) [MW/MWh]
𝜇𝐸yearly CO2emission limit (tonne)
𝜌𝐹
𝑓hydrogen consumption factor of fuel cell 𝑓(𝑓∈)
[kg/MW]
𝜎𝑅𝑒𝑠
𝑧spinning reserve factor on platform 𝑧(𝑧∈𝑃)
𝜏𝐸𝑃
𝑧𝑡 electricity price in onshore bus 𝑧in period 𝑡(𝑧∈𝑂, 𝑡 ∈
) [e/MW]
𝐶𝐺
𝑔total operational cost of gas turbine 𝑔(𝑔∈)[e/MW]
𝐶𝑆ℎ𝑒𝑑 ,𝑙 load shed penalty cost of power (𝑙=𝑃)and heat (𝑙=𝐻)
[e/MW]
𝐶𝐺
𝑔total operational cost of generating 1 MW power from
gas turbine 𝑔(𝑔∈) [e/MW]
𝐸𝐺
𝑔emission factor of gas turbine 𝑔(𝑔∈)[tonne/MWh]
𝐸𝐺
𝑔emission of CO2of gas turbine 𝑔burning fuel (𝑔∈)
[t/MWh]
𝐻𝑡number of hour(s) in one operational period 𝑡
𝑃𝐷𝑃
𝑧𝑡 power demand on platform 𝑧period 𝑡(𝑧∈, 𝑡 ∈)
[MW]
𝑅𝑅
𝑟𝑡 capacity factor of renewable unit 𝑟in period 𝑡(𝑟∈, 𝑡 ∈
)
𝑊𝑡weighted length of one operational period 𝑡
Investment planning related variables
𝑐𝐼𝑁𝑉 total investment and fixed operating and maintenance
costs [e]
𝑐𝑂𝑃 𝐸
𝑖total operational costs in operational node 𝑖(𝑖∈)[e]
𝑥𝐴𝑐𝑐
𝑝𝑖 accumulated capacity of device 𝑝in operational node 𝑖
(𝑝∈, 𝑖 ∈) [MW, MWh, kg]
𝑥𝐼𝑛𝑠𝑡
𝑝𝑖 newly invested capacity of device 𝑝in investment node
𝑖0(𝑝∈, 𝑖 ∈0) [MW, MWh, kg]
𝑦𝑝𝑖 number of units of newly invested technology 𝑝in in-
vestment node 𝑖0(𝑝∈, 𝑖 ∈0)
Operation related variables
𝑝𝐸
𝑒𝑡 power consumption of electrolyser 𝑒in period 𝑡(𝑒∈
, 𝑡 ∈) [MW]
𝑝𝐹
𝑓𝑡 power generation of fuel cell 𝑓in period 𝑡(𝑓∈, 𝑡 ∈)
[MW]
𝑝𝐵𝐸
𝑏𝑡 power consumption of electric boiler 𝑏in period 𝑡(𝑏∈
𝐸, 𝑡 ∈) [MW]
𝑝𝐴𝑐𝑐𝐹
𝑓accumulated capacity of fuel cell 𝑓(𝑓∈, 𝑡 ∈) [MW]
𝑝𝐺
𝑔𝑡 power generation of gas turbine 𝑔in period 𝑡(𝑔∈, 𝑡 ∈
) [MW]
𝑝𝑅𝑒𝑠𝐺
𝑔𝑡 power reserved of gas turbine 𝑔for spinning reserve
requirement in period 𝑡(𝑔∈, 𝑡 ∈) [MW]
𝑝𝐴𝑐𝑐𝐺
𝑔accumulated capacity of gas turbine 𝑔(𝑔∈)[MW]
𝑝𝐿
𝑙𝑡 power flow in line 𝑙in period 𝑡(𝑙∈, 𝑡 ∈) [MW]
𝑝𝐴𝑐𝑐𝐿
𝑙accumulated capacity of line 𝑙(𝑙∈) [MW]
𝑝𝑅𝑒𝑠𝑆𝐸
𝑠𝑡 power reserved in electricity store 𝑠for spinning reserve
requirement in period 𝑡(𝑠∈𝐸, 𝑡 ∈) [MW]
𝑝𝑆𝐸 +
𝑠𝑡 ∕𝑝𝑆𝐸 −
𝑠𝑡 charge/discharge power of electricity store 𝑠in period 𝑡
(𝑠∈𝐸, 𝑡 ∈) [MW]
𝑝𝐺𝑆ℎ𝑒𝑑 ,𝑙
𝑧𝑡 generation shed for power (𝑙=𝑃)and heat (𝑙=𝐻)at 𝑧
in period 𝑡(𝑧∈, 𝑡 ∈) [MW]
Energy 261 (2022) 125219
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H. Zhang et al.
Table D.2
Field location data.
Field Longtitude Latitude Cluster Distance to centre (km) Field Longtitude Latitude Cluster Distance to centre (km)
ALVHEIM 1.94 59.54 4 21.28 OSEBERG SØR 2.94 60.31 4 56.09
ATLA 2.57 59.65 4 26.79 REV 1.92 58.02 4 55.10
BØYLA 1.89 59.29 4 28.83 RINGHORNE ØST 2.51 59.27 4 24.71
BALDER 2.41 59.27 4 22.46 SIGYN 2.02 58.28 4 27.28
BLANE 2.49 56.84 2 51.14 SINDRE 2.35 61.23 2 8.90
BRAGE 3.06 60.48 1 36.29 SKIRNE 2.47 59.60 1 18.79
BYRDING 3.53 61.13 1 41.11 SKOGUL 2.22 59.78 1 35.63
EDVARD GRIEG 2.33 58.85 3 43.47 SLEIPNER ØST 1.98 58.41 3 12.61
EKOFISK 3.23 56.49 2 10.82 SLEIPNER VEST 1.66 58.39 2 20.45
ELDFISK 3.32 56.38 2 24.70 SNORRE 2.06 61.40 2 17.81
EMBLA 3.27 56.29 2 33.02 STATFJORD 1.80 61.17 2 22.36
ENOCH 1.52 58.63 3 26.41 STATFJORD ØST 1.99 61.31 3 12.38
FLYNDRE 2.63 56.55 2 34.31 STATFJORD NORD 1.91 61.43 2 24.38
FRAM 3.48 61.05 1 31.54 SVALIN 2.40 59.14 1 36.57
FRAM H-NORD 3.50 61.10 1 37.58 SYGNA 2.00 61.46 1 25.91
GIMLE 2.35 61.25 5 8.59 TAMBAR 3.01 56.94 5 40.88
GINA KROG 1.70 58.54 3 12.92 TOR 3.30 56.63 3 8.07
GJØA 3.93 61.30 1 68.12 TORDIS 2.11 61.25 1 3.81
GRANE 2.44 59.11 4 39.71 TROLL 3.91 60.50 4 48.72
GUDRUN 1.72 58.81 3 34.85 TRYM 4.24 56.40 3 67.95
GULLFAKS 2.12 61.19 5 7.32 TUNE 2.61 60.41 5 54.21
GULLFAKS SØR 2.03 61.17 5 12.55 ULA 2.87 57.07 5 56.73
GUNGNE 1.89 58.35 3 18.34 UTGARD 1.54 58.34 3 29.08
HEIMDAL 2.22 59.55 4 10.21 VALE 2.29 59.68 4 24.91
HOD 3.43 56.18 2 48.13 VALEMON 2.25 60.99 2 28.90
ISLAY 1.93 60.54 5 79.72 VALHALL 3.43 56.23 5 42.42
IVAR AASEN 2.12 58.92 3 46.13 VEGA 3.36 61.34 3 61.26
JOHAN SVERDRUP 2.63 58.66 3 43.96 VESLEFRIKK 2.88 60.74 3 20.24
KNARR 2.71 61.78 5 65.69 VIGDIS 2.12 61.34 5 10.65
KVITEBJØRN 2.48 61.04 5 27.90 VILJE 2.28 59.64 5 20.43
ODA 3.04 57.06 2 53.15 VISUND 2.62 61.42 2 29.58
OSEBERG 2.69 60.54 1 40.92 VISUND SØR 2.34 61.27 1 8.44
OSEBERG ØST 2.96 60.58 1 27.71 VOLUND 2.00 59.45 1 15.66
𝑝𝑃 𝐹 𝑆
𝑧𝑡 power supply from onshore bus 𝑧in period 𝑡(𝑧∈𝑂, 𝑡 ∈
) [MW]
𝑝𝑆ℎ𝑒𝑑 ,𝑙
𝑧𝑡 load shed for power (𝑙=𝑃)and heat (𝑙=𝐻)at 𝑧in
period 𝑡(𝑧∈, 𝑡 ∈) [MW]
𝑞𝑆𝐸
𝑠𝑡 energy level of electricity store 𝑠at the start of period 𝑡
(𝑠∈𝐸, 𝑡 ∈) [MWh]
𝑞𝐴𝑐𝑐𝑆 𝐸
𝑠accumulated storage capacity of electricity store 𝑠(𝑠∈
𝐸) [MWh]
𝑣𝑆𝐻 𝑦+
𝑠𝑡 ∕𝑣𝑆𝐻 𝑦−
𝑠𝑡 injection/withdraw of hydrogen to (from) hydrogen stor-
age 𝑠in period 𝑡(𝑠∈𝐻𝑦 , 𝑡 ∈) [kg]
𝑣𝑆𝐻 𝑦
𝑠𝑡 storage level of hydrogen storage 𝑠in period 𝑡(𝑠∈
𝐻𝑦 , 𝑧 ∈𝐻,𝑡 ∈) [kg]
𝑣𝐴𝑐𝑐𝑆 𝐻𝑦
𝑠accumulated storage capacity of hydrogen store 𝑠(𝑠∈
𝐻𝑦 , 𝑡 ∈) [kg]
Appendix B. Calculation of energy loss
The indices, summation and multiplication of one hour are omitted.
𝑞𝐿𝑜𝑠𝑠 =𝑝𝐺𝑆ℎ𝑒𝑑 +𝑝𝐺𝑆 ℎ𝑒𝑑𝐻 + ( 1
𝜂𝐺−1−𝜂𝐻𝑟𝐺 )𝑝𝐺+ (1 − 𝜂𝑙)𝑝𝑙
+𝑝𝐸−𝜃𝐻𝑦 (𝑝𝐹
𝜂𝐹𝜃𝐻𝑦 −𝑣𝑆 𝐻𝑦−+𝑣𝑆 𝐻𝑦+)+( 1
𝜂𝐹− 1)𝑝𝐹,
where (1 − 𝜂𝑙)𝑝𝑙calculates the total energy losses of electricity storage,
separators, compressors, pumps, electric boilers and transmission lines.
The hydrogen energy content is denoted by 𝜃𝐻𝑦 .
Appendix C. Definitions of model parameters
The total operational cost of a gas turbine is defined by
𝐶𝐺
𝑔=𝐶𝑂𝑃 𝐸𝑋
𝑔+
𝐶𝐹 𝑢𝑒𝑙
𝑔+𝐶CO2𝐸𝐹 𝑢𝑒𝑙
𝑔
𝜂𝐺
𝑔
,(C.1)
and the emission factor of gas turbine is defined by
𝐸𝐺
𝑔=
𝐸𝐹 𝑢𝑒𝑙
𝑔
𝜂𝐺
𝑔
,(C.2)
where 𝐶𝑂𝑃 𝐸𝑋
𝑔is the variable operational cost of gas turbines. The 𝐸𝐹 𝑢𝑒𝑙
𝑔
is the fuel cost of gas turbines burning fuel with energy content 1 MWh.
The parameter 𝐸𝐹 𝑢𝑒𝑙
𝑔is the emission of CO2of gas turbines burning fuel
with energy content 1 MWh. The efficiency of gas turbines is denoted
by 𝜂𝐺
𝑔.
Power demand of a platform
𝑃𝐷𝑃
𝑧𝑡 =
𝑐∈𝑧
𝑉𝐶
𝑧𝑡 𝑍𝑅𝑇
𝜂𝐶(𝛼− 1) 𝛾
𝛼−1
𝛼
𝑐− 1+
𝑝∈𝑈
𝑧
𝜅𝑃 𝑢
𝑝𝑉𝑃 𝑢
𝑝𝑡 ,(C.3)
equals to the power consumption of all compressors and all pumps. The
power consumption of a compressor is given by 𝑉𝐶
𝑧𝑡 𝑍𝑅𝑇
𝜂𝐶(𝛼−1) 𝛾
𝛼−1
𝛼
𝑐− 1,
where 𝑉𝐶
𝑧𝑡 is the gas compressed by a compressor, 𝜂𝐶is the isentropic
efficiency of a compressor, 𝛼is the polytropic exponent of a compressor,
𝛾𝑐is the compression ratio of a compressor, 𝑍is compressibility factor,
𝑅is the characteristic gas constant and 𝑇is the temperature. The
power consumption of a pump is given by 𝜅𝑃 𝑢
𝑝𝑉𝑃 𝑢
𝑝𝑡 , where 𝑉𝑃 𝑢
𝑝𝑡 is the
fluid pumped by a pump, 𝜅𝑃 𝑢
𝑝is the electricity demand as fraction of
amount of fluid pumped. The detailed derivation of power consumption
of compressors and pumps is presented in [83].
Hydrogen consumption factor of fuel cell is given by
𝜌𝐹=1
𝜂𝐹
𝑓𝜃𝐻𝑦 ,(C.4)
where 𝜂𝐹
𝑓is the efficiency of fuel cells and 𝜃𝐻𝑦 is the energy content of
hydrogen.
Weighted length of a operational period is defined by
𝑊𝑡=𝑊𝑁
𝑛𝐻𝑡, 𝑛 ∈, 𝑡 ∈𝑁,(C.5)
where 𝑊𝑁
𝑛is the weight of each slice 𝑛and 𝐻𝑡is the length of
operational period 𝑡.
Energy 261 (2022) 125219
18
H. Zhang et al.
Appendix D. Input data
Table D.2 provides an overview over the locations of the different
fields.
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