Capacity Planning For Electrolysis Plants
By W i l l i a m A . P r a a t
?, University of Groningen, Groningen, The Netherlands
Supervisors:
Dr. E. Ursavas Dr. X. Zhu
27 June 2020
A B S T R A C T
Electrolysis capacity is expected to grow exponentially in the coming years, developing efficient and ef- fective strategic capacity expansion and replacement plannings will be critical element of this growth.
This paper uses existing models of the strategic capacity expansion literature and developed a model specifically devoted to the green hydrogen production industry. Elements from existing models that were relevant have been combined into a mixed-integer model which has then been extended with extra ele- ments based on feedback from industrial experts. Using Python in combination with the Gurobi solver to find the optimal solutions of the experiments. Because of the introduction of performance degradation of systems this paper combines the functionality of a capacity expansion strategy and capacity replacement strategy into one model. The developed model is a decision support tool for managers to develop their strategic capacity plannings.
A practical case experiment of the HEAVENN project in the Northen Netherlands has been performed with input from industry experts. Three different demand growth scenarios have been developed which has then been optimized by the model. The differences in both capacity expansion and capacity replace- ment strategies of these scenarios provides great insights on how each situation is approached differently by the model to find the optimal solution. It provides insight on the degree of economies of scale that can be achieved, expected years of operations, and the build-up of the total project cost.
Keywords: Hydrogen, Electrolysis, Capacity, Strategic, Planning
? Corresponding author.
E-mail: w.a.praat@student.rug.nl Phone: +316 117 66 486
CONTENTS
1. Introduction 2. Literature review
2.1 Hydrogen production through electrolysis 2.2 Storage of hydrogen
2.3 Expected growth of demand for green hydrogen 2.4 Costs and efficiency
2.5 Hydrogen transportation
2.6 Models for strategic capacity planning 2.7 Contribution of study
3. Methodology
3.1 Problem description 3.2 Model introduction 3.3 Model validation 3.4 Sensitivity analysis 4. HEAVENN Business Case
4.1 Data collection 4.2 Experiment settings 4.3 Results
4.4 Discussion 5. Results
6. Discussion 6.1 Contributions 6.2 Limitations 6.3 Future research 7. Conclusions 8. Acknowledgments 9. Appendix
9.1 Interview transcripts
9.2 HEAVENN case experiment results
9.3 Code of optimization model
Fig. 1. Hydrogen production and distribution visualization (Turner et al., 2008)
1. Introduction
Due to the strong evidence that climate change is caused by human activities, the desire to produce energy and fuel in a sustainable manner has increased significantly in the past decades to eliminate our impact on the climate. Currently, the majority of the energy production is done though burning fossil fuels releasing polluting gasses which causes the so called greenhouse effect, warming the atmosphere of the earth (Schneider, 2016). Sustainable sources of energy which do not emit these gases are being used to replace the existing fossil fuel based energy market. However, most sustainable energy sources have various drawbacks that need to be addressed if humanity wants to become carbon neutral in the coming decades.
Sustainable energy sources, such as wind and solar, produce energy in an unpredictable manner. This results in a situation where supply does not always match demand, a classical exam- ple being the mismatch between the energy demand and supply of solar power during the day in California, causing a problem which often being referred to as the duck curve (Denholm et al., 2011). Naturally, overproduction of energy creates the desire of developing systems that can store this energy for later use in an environmental friendly and economical manner. The mismatch between the peak of energy demand and peak of sustainable energy production makes it almost impossible to embrace sustainable energy sources and getting rid of fossil fuels if this storage issue is not addressed. To resolve this issue, surplus energy during peak production hours should be stored so this can later be released when demand is higher than the production. Only when this is achieved our energy is can be produced by fully renewable energy sources, eliminating the need for burning fossil fuels.
One of the key promising technologies for achieving this is hydrogen, which can be produced by using electrical current to split water into its base components, a process which is named
electrolysis. Not only can hydrogen be used as temporarily energy grid storage, but also as fuel for vehicles. This system (Visualized in Figure 1), can be achieved by using electrolysis process and storing it in compressed gas form or by liquid form depending on the demands in that region. Although the production of hydrogen through electrolysis already exists for a considerable time, only recently large scale projects are being developed. However, how feasible is it to build high capacity hydrogen production plants? The feasibility of various types electrolysis methods (Turner et al., 2008) and the capacity of these plants is a topic that is becoming more relevant by the year.
Existing research on large capacity production of hydrogen though electrolysis has mostly focused on exploring the various feasible configurations of hydrogen production plants (Urs´ua et al., 2012). They highlight the importance of increasing the scale of operation of these projects to be able to handle the de- mand in the future. However, they neglect to to provide guid- ance to what degree or how fast the capacity should be in- creased. Agnolucci and Mcdowall (2013) provide a critical re- view on the existing hydrogen production infrastructure model studies. The majority of these models were developed for na- tional or regional scale levels, neglecting the smaller scale per- spective. This leaves a gap in the literature on capacity strategy in the hydrogen production industry. Capacity strategies in the field of operations strategy are often linked to the product pro- cess matrix, which determines the strategy based on the variety and scale of products to be produced (Olhager et al., 2001), this however falls short in the case of hydrogen production as this in- dustry is currently facing the classical chicken and egg problem, especially for vehicles. Meaning that demand will not increase because there is no supply, and supply will not increase when there is no demand (Ball and Weeda, 2015).
Although it is expected that the adoption of green hydrogen will follow a logarithmic ”S” curve (Agnolucci and Mcdowall, 2013), choosing the best capacity expansion plans for produc- tion locations will be challenging as when and how fast this adoption will take place is uncertain. The uncertainty of the growth of the green hydrogen industry is high as it is effected by many factors. Not only does the industry suffer from the chicken and egg problem, it also is going to depend highly on govern- mental regulations and support, hydrogen feedstock prices, and the availability and growth of green electricity (Ball and Weeda, 2015). Therefore, these factors must be considered that influ- ence the growth of the demand for green hydrogen production capacity.
As the strategic capacity planning will be a long-term plan- ning that considers a planning horizon that is longer than a decade, technological advancements must also be considered.
It is expected that electrolysis systems will become cheaper to
acquire and operate in the coming years (Buttler and Spliethoff,
2018). Including these expected advantages in technology and
cost will be a vital element a strategic capacity planning (Ra- jagopalan et al., 1998).
These elements combined result in a problem that the green hydrogen industry will face in the coming years. It is a problem of translating the projected long-term demand into a strategic capacity plan while considering technological advancements and the characteristics of electrolysis systems. This paper will develop a model to optimize the strategic capacity planning of an electrolysis plants with cost minimization as the goal.
An objective model will be formulated taking into account the demand for green produced hydrogen, costs, electrolyser performances, future technological advancements, and capacity limiting constraints. The developed model will be a decision support tool for managers in the green hydrogen industry that need to make strategic decisions on capacity. As a practical ex- ample the optimal capacity expansion for a selected electrolysis plant will be determined for a case of the HEAVENN project with three different demand growth scenarios.
HEAVENN is a large-scale project in The Netherlands that is developing the infrastructure to produce, store, and distribute hydrogen in the north of The Netherlands. One key element of this project is the placement of large scale (>50 Mega Watt) electrolysis production plants. In the case of the HEAVENN project however, the goal is to kick-start the hydrogen adoption by building an infrastructure that can facilitate the growth of this industry. Initially, a capacity leading strategy is used, meaning that there will always be overcapacity to ensure a steady supply that is capable of handing a growth in demand and achieving a high degree of flexibility (Olhager et al. (2001).
This project will be used to develop a practical case experiment.
In this experiment the model that is developed in this paper will be used in a practical setting so realistic results can be analysed. To develop this practical case experiment interviews with partners of the HEAVENN project will be interviewed, information and expertise will be gathered to develop a case experiment that is as realistic as possible.
This paper is structured as follows. The first section will fea- ture a literature study which discusses existing literature which are relevant to develop the model. This is then followed by the methodology section where the problem background is de- scribed, the model is introduced and validated, and a parameter sensitivity analysis is performed. The fourth section will con- tain the HEAVENN business case experiment which also in- cludes a section that discusses the results from the interviews.
Based on the findings of this discussion the model is improved and changed. The HEAVENN case section also contains prelim- inary results and a discussion of the resultsfrom the experiment.
This is then followed by the fifth and sixth sections, the gen- eral results and discussion. Finally, this paper concludes with a conclusion section for the final remarks.
2. Literature review
This literature study introduces and discusses existing relevant literature on the subjects that are key to the defined problem and that are relevant to the developed solution. Firstly, literature on the production and storage of hydrogen through electroly- sis is discussed. Required theoretical and practical background information and the existing constraints are introduced and will function as a foundation for the remaining of the literature study.
In section 2.3 the expected growth of demand for electrolysis systems is discussed. The hydrogen market, expected develop- ments, and demand growth projections are discussed and com- pared. Section 2.4 deals with the costs and efficiencies of the electrolysis systems, and how this is likely to develop in the coming decades. Section 2.5 discusses existing mathematical models and their elements. Finally, in section 2.6 the relevant models and literature will be compared and the gap in the litera- ture will be explained. With this identified gap the position and contribution of this study will be discussed.
2.1 Hydrogen production through electrolysis
There are two main commercially available water electrol- ysis technologies, Alkaline electrolysis and Polymer Elec- trolyte Membrane Electrolysis (Buttler and Spliethoff, 2018).
Although the characteristics of these technologies will not be discussed in detail in this paper, table 1 provides an overview of the key characteristics of both technologies. Although more technologies such as solid oxide electrolysis, core-shell cata- lysts, bulk metallic glasses, and nano structured thin films show promising improvements to the current technologies (Buttler and Spliethoff, 2018; Carmo et al., 2013), these will not be con- sidered in this paper as these are not yet commercially available.
However, this does imply that future technologies are likely to be superior which will have a major impact on the adaption of electrolysis. Buttler and Spliethoff (2018) highlight that the required capital to acquire electrolysis technologies is still de- creasing and is expected to continue to decrease in the coming decades, which is also confirmed by the study of Saba et al.
(2018). This further shows the future potential of electrolysis and its ambition to grow to industrial scale capacity. Although electrolysis is a relatively simple process to produce hydrogen, the electricity prices and the high acquesition cost of electroly- sis systems play a major role why this technology is not com- petitive yet (Turner et al., 2008). furthermore, when hydrogen is only produced when electricity prices are low the required stor- age capacity increases as there can be long periods of no pro- duction which increases the storage costs (Naterer et al., 2008).
2.2 Storage of hydrogen
Another key technological issue with the adaption of hydro-
gen as an energy storage solution is the required storage capac-
ity, efficient and safe storage of the hydrogen is therefore key
for the adaption of this technology (Barthelemy et al., 2017).
Table 1. Key performance characteristics of electrolysis technologies (Buttler and Spliethoff, 2018).
Technology System efficiency Degradation
(% per year)
Lifetime (hours)
Capital cost (Euro/kW)
Alkaline electrolysis 51-60% 0.25-1.5% 55.000-120.000 800-1.500
Polymer Electrolyte Membrane Electrolysis 46-60% 0.5-2.5% 60.000-100.000 1.400-2.100
Barthelemy et al. (2017) state that there are four forms of hy- drogen storage; compressed as a gas, liquefied by cooling it to cryogenic temperatures, Cryo-compressed form, and finally as a solid form. Of these technologies cryogenic and compressed storage are by far the most mature storage forms (Barthelemy et al., 2017). However, due to the lack of large-capacity hy- drogen storage infrastructure other solutions are being explored (Lord et al., 2014). Caglayan et al. (2020) and Lord et al. (2014) discuss the potential solutions currently being researched such as depleted oil and gas reservoirs, aquifers, and salt mines.
These solutions could potentially offer huge storage capacity, allowing electrolysis plants to temporarily convert vast amounts of energy as hydrogen gas for long-term storage. Using these large scale storage locations will require an infrastructure that is able to transport hydrogen between production, storage, can usage locations. when a pipeline infrastructure is used compres- sors at production sites might not be needed as there are elec- trolysis systems that produce hydrogen at a pressure similar to gas pipe networks, which is expected to be between 40-80 bar (Buttler and Spliethoff, 2018). This means that the electroly- sis plants themselves can operate without compressors to store their hydrogen when they are connected to a hydrogen pipeline network. When hydrogen is stored locally at the plant in cryo- genic or high-pressure compressed form then compressors need to be considered.
2.3 Expected growth of demand for green hydrogen Hydrogen has more markets than just temporarily energy stor- age, it is used by various sectors such as the petrochemical, agricultural, aerospace, and food processing industries (Naterer et al., 2008). They further expect that because of the increased demand in these, and other industries such as transportation, the market will grow significantly. However, Agnolucci and Mcdowall (2013) observed that most academic articles that try to optimize production and delivery infrastructures, at a scale smaller than a nation, do not include demand growth in their mathematical model. Agnolucci and Mcdowall (2013) further state that the demand growth of hydrogen will likely follow a logistic ”s” curve, similar to the adaption curve that have been observed with the adaption of other technologies. Because this paper is considering strategic timelines, which can consist of one ore multiple decades, it will be vital to take the growth of the hydrogen market into account. Mart´ınez-Costa et al. (2014) show that the growth of demand has been included in many other strategic capacity planning models in both deterministic
an stochastic manner. It can be concluded that in order to de- velop a strategic capacity plan the growth of demand is a key factor for this study.
Moreover, how an organization deals with growing demand is a vital element to any firm as it has a major influence on their operations. Olhager et al. (2001) explore the strategic level of capacity planning and how organizations can strategically in- crease and decrease capacity based on demand. Organizations can determine many factors such as service levels, flexibility, and costs by following a capacity leading (Capacity is always bigger than demand), lagging (Demand is always bigger than capacity), or tracking (Try to match capacity and demand as close as possible). This decision will also be relevant for deter- mining the capacity of electrolysis plants and the timing of the construction. In the case of the HEAVENN project there will be an overall capacity leading strategy as it is the goal to de- velop a hydrogen market and infrastructure that can kick-start the adoption and resolve the chicken-and-egg problem.
Hydrogen is and will be used by many different industries and end-users. Below there are three subsections introducing the main use case for hydrogen and their current status.
2.3.1. Grid energy storage
Most renewable energy sources are unpredictable by nature as
weather conditions often determine the productivity. Especially
when the renewable energy industry will increase its share in
the energy market the desire to store this energy temporarily
becomes bigger as abundant energy is created (Jørgensen and
Ropenus, 2008). Hydrogen can play a vital role in solving this
problem as it can be used for long-term energy storage and grid
stability, which is referred to as power-to-gas (Le Duigou et al.,
2017). Because of extreme fluctuations in electricity produc-
tion that are likely to occur in the future there is a chance for
power-to-gas operators to leverage these price fluctuations. Un-
til recently no significant price differences in electricity have
been found because of fluctuating energy production (Mulder
and Scholtens, 2013). However, Sorknæs et al. (2019) argue that
with more recent data from Denmark in 2015, which produces
more renewable energy, does result significant price changes of
electricity. They further argue that the more renewable energy
capacity is added the more extreme the price fluctuations will
be more become. The increasing differences allow operators to
create hydrogen when energy is cheap and deliver electricity
back to the grid with a fuel cell when prices are high. However,
this process is, with the current technology, relatively inefficient
as significant amounts of energy is lost during the processes.
As efficiencies improve in the coming decades and electricity prices become cheaper and less stable the demand for this mar- ket will increase. Marchenko and Solomin (2015) even argue that with the current efficiencies and energy prices that long- term energy storage through hydrogen can be economically ef- fective. The decreasing cost of electrolysis systems and their improving performance allow electrolysis to become more com- petitive (Schmidt et al., 2017), in combination with the reducing electricity prices from renewable sources this will become more accessible.
2.3.2. Transportation
Although the battery electric vehicle (BEVs) has been popular- ized by Tesla motors in the last decade, fuel cell electric vehicles (FCEVs) are also slowly gaining popularity. Car manufacturers like Toyota and Hyundai are developing and producing cars and trucks that run on hydrogen as they argue it has benefits com- pared to BEVs. Although it is hard to predict if this market will end up being a monopoly or duopoly situation, it is expected that hydrogen will play a role in the future of transportation.
Therefore, the demand for green and sustainable hydrogen pro- duction is expected to grow significantly in the coming decades (Le Duigou et al., 2017).
2.3.3. Industry feedstock
Finally, there are many industrial markets that have been con- suming hydrogen for a long time to produce their products. Ar- tificial fertilizers, food processing, chemistry and steel produc- ing industries have been using hydrogen for various applications (Le Duigou et al., 2011). However, the hydrogen that they use is often ”grey”, meaning that this is produced with a process that emits gasses that contribute to the greenhouse effect. Therefore, green hydrogen which is produced though electrolysis can allow these markets to reduce their carbon footprint. Especially when electricity prices become low enough it is possible for green hy- drogen to become competitive with grey hydrogen and thus the demand for green hydrogen will further increase.
It can be concluded that the demand for green hydrogen comes in two forms; it will be used for energy storage, and it will be sold to be used for transportation and other markets. All of these markets show growth and are expected to grow in the future as electrolysis technology matures and energy prices fall (Le Duigou et al., 2011).
2.4 Costs and efficiency
The key reason why electrolysis has not seen wide accep- tance yet is because of its high required capital expenditure (CAPEX), high utility rates are needed to make hydrogen pro- duction economically viable (Mansilla et al., 2013). Schmidt et al. (2017) state that according to industry experts reducing
the cost of these systems is the key priority of manufactur- ers. Lower CAPEX allow the systems to have lower utiliza- tion to be economical viable, which allows the systems to run more frequently on times when energy prices are low. New and promising electrolysis technologies such as solid oxide elec- trolysis cells (SOEC) or PEMEL (proton exchange membrane electrolysis) show great potential to improve the cost/capacity ratio (Buttler and Spliethoff, 2018). Schmidt et al. (2017) state that according to industry experts most capital expenditures and operational expenditures (OPEX) will be mostly reduced with economies of scale. When production volumes of electrolysis systems increase, large-scale manufacturing methods will allow the average cost per system to come down significantly. It can be concluded that the cost of acquiring and operating electrol- ysis systems is going to improve in the coming decades, and that this is going to be facilitated by both new technologies and economies of scale.
Moreover, electrolysis systems suffer, just like any other as- set, from performance degradation and a limited lifespan. Es- pecially the ”stacks”, which are the cells that actually perform the electrolysis process, have a limited lifespan and are by far the most expensive component (Carmo et al., 2013). Moreover, Carmo et al. (2013) also highlight the performance degradation of the systems as they age which is also often a characteristic considered in the life cycle of an asset. Currently this degrada- tion is estimated at 2-4% per year (at a 90% utilization), but this expected to drop below 1% annually (at 90% utilization) in the coming years according to industry experts (Buttler and Spli- ethoff, 2018). Schmidt et al. (2017) state that the lifetimes of newer technologies are expected to increase, resulting in lower OPEX.
Finally, the efficiency electrolysis of the systems currently available is relatively low. Current alkaline electrolysis based systems have a system efficiency of around 55% (Buttler and Spliethoff, 2018). Although improving the efficiency has a rel- atively low priority, experts do project that efficiencies will im- prove in the coming decades (Schmidt et al., 2017), especially for technologies that are still under development such as SOEC.
This will allow electrolysers to use less electricity per kilo of hydrogen which will reduce the average price.
It can be concluded that both academics and the industry are expecting that electrolysis systems will improve in many aspects in the coming years. Lower CAPEX will allow oper- ators to focus on hydrogen production during times when en- ergy prices are low. Improving lifetimes of the systems and im- proving system efficiencies will allow electrolysis to become economical competitive to other hydrogen production methods.
When planning long-term capacity it is vital to keep factors
like performance degradation, lifetime of the machine, and the
price/capacity into account, this is why these factors will be in-
cluded in the model of this paper.
2.5 Hydrogen transportation
The hydrogen produced at the production plant must, at some point, be transported to the points of use. This can be done by the use of a pipeline or vehicular transport, meaning by truck, ship, or train. vehicular transmission can be sufficient for ar- eas with low or medium demand (Baufum´e et al., 2013). How- ever, especially when volumes increase this type of transport becomes unfeasible due to its cost. In this case using a pipeline network will be more cost effective. Because The Netherlands already has a highly sophisticated natural gas pipeline network in place it is logical that using this existing infrastructure for hydrogen transportation should be considered. However, many practical questions regarding this potential solution still exist (Haeseldonckx and William, 2007). Haeseldonckx and William (2007) did find that existing infrastructure can be feasible for hydrogen or a natural gas-hydrogen mix transportation. In the HEAVENN project Gasunie is researching the option to use parts of the existing natural gas pipelines to develop a hydro- gen transportation network which is named the ”hydrogen back- bone”. This network will transport hydrogen throughout the Netherlands and is interconnected with surrounding countries.
Although the exact operational pressure is not known yet, it is expected that this will be between 4 en 8 MPa. However, Bau- fum´e et al. (2013) states that envisioned that the German en- visioned network will operate at pressures up to 10 MPa. This also means that electrolysis plants could operate without hav- ing to compress the hydrogen with a compressor, however this is going to depend on the selected electrolysis system as not all systems operate at gas pipeline pressures (Buttler and Spli- ethoff, 2018). Shiono et al. (2019) used Cox’s equation and the pressures at which the network will be operating at to deter- mine the maximum capacity of the pipeline. Using this equation in combination with the most common commercially available pipeline diameters it is clear that with current electrolysis sys- tems with a size of around 1MW it will be unlikely that the pipe network will become the bottleneck anytime soon. How- ever, the pipeline capacity limit should be considered when the production capacity of a plant grows to the hundreds of MW in scale.
2.6 Models for strategic capacity planning
Agnolucci and Mcdowall (2013) critically reviewed hydrogen infrastructure optimization literature and categorized them in the following categories; National scale, regional scale, and lo- cal scale studies. The local scale studies however are all focused on the optimization of placement for hydrogen fueling stations, and regional scale studies focus particularly on the optimiza- tion of the hydrogen supply chain as a whole. The literature of the hydrogen industry lacks to provide guidance from the per- spective of an organization when it comes to strategic capacity planning. However, the literature on strategic capacity planning in manufacturing industries has been extensively researched as
Mart´ınez-Costa et al. (2014) discuss. Their overview also dis- cusses papers with single product in combination with single, or multi-location optimization models such as the model from Chand et al. (2000). Their problem description comes close to the situation managers of electrolysis plants might face. How- ever, there are key aspects in the production of hydrogen that have specific constraints and factors that are missing in this model that have been identified in this literature study. The in- clusion of these factors aligns with the findings of Julka et al.
(2007), who found that not expanding the set of factors that are important for the capacity planning and expansion optimization study field.
Rajagopalan et al. (1998) developed a model that takes into account the technological improvements when making strate- gic capacity plannings, which is a step further than the model of Chand et al. (2000). However, the model from Chand et al.
(2000) includes a maximum asset lifetime and therefore also is including capacity replacement elements, which is not in- cluded in the model of Rajagopalan et al. (1998). Furthermore, the maximum lifespan of the purchased systems is not included in their model which is also key for the model that will be devel- oped. Rajagopalan (1992) developed a model that does take into account performance degradation. However, because this model does not allow older systems to be replaced with new systems it does not provide the insights on how this influences the capac- ity replacement strategy. de Matta and Hsu (2006) does include system deterioration in a capacity expansion and replacement setting. Their model is close to what this paper will develop as it has many features in common. However, their model does not take into account the technological advancements and the influences of that on the CAPEX and OPEX. Finally, both Ra- jagopalan et al. (1998) and Chand et al. (2000) assume that the demand always grows in each period. However, this is not real- istic for the hydrogen market as for example demand for energy storage can fluctuate depending on the seasons.
2.7 Contribution of study
This literature study introduced and discussed the relevant liter- ature to define the problem and understand its characteristics.
Existing models for strategic capacity planning that are dis-
cussed in section 2.6 do not offer the correct combination of
parameters and features that match the characteristics of hydro-
gen producing electrolysis plants and are therefore not suitable
for this problem. Important constraints and elements that needs
to be included in the model have been highlighted throughout
the literature study. The model that will be developed in the
next section will bridge the gap between the currently existing
models by using various elements from discussed models. Fur-
thermore, extra elements will be added to the model that are
relevant for this study. The main contribution to the literature
will be a model that matches the market characteristics of the
electrolysis market.
3. Methodology
3.1 Problem description
This paper considers the problem of strategic capacity planning for electrolysis plants with the goal to provide managers with a decision making support tool. Based on existing literature an objective model will be developed to minimize the total cost that are considered in the planning horizon. This model will provide managers guidance on developing a strategic capacity expan- sion and replacement plan for their production location. By us- ing this axiomatic and prescriptive approach, the key will be on achieving mathematical correctness Karlsson et al. (2016). The problem will be solved using a linear integer programming tech- nique which will be done by using Python as the programming language and Gurobi as the solver. Initially, the experiments and sensitivity analysis will be performed by using arbitrary data, the HEAVENN case experiment will use realistic data.
The problem is characterized by considering the acquisition, operating, and salvaging of electrolysis systems of a single pro- duction location within a finite planning horizon while expand- ing capacity to be able to satisfy demand. Because large-scale projects are often build in a modular manner (Buttler and Spli- ethoff, 2018; Urs´ua et al., 2012), this model assumes that capac- ity can be added in a relatively flexible manner. However, when capacity is being replaced or expanded, scale of economies should be considered as setup costs are often present in these situations (Rajagopalan et al., 1998; Ayers et al., 2010). There- fore, fixed setup costs are added when one or more electroly- sis systems are purchased at a given period. It is assumed that storage capacity for the hydrogen is infinite and that the energy grid connection does not have a capacity limit. Furthermore, the transportation of the hydrogen from the production location to the end-customers, through pipe or vehicular transport, has in- finite capacity.
In this strategic planning optimization model considers a pe- riod T with a finite horizon which is divided into periods t. It is assumed that one period t is a quarter of a year as it pro- vides a good level of detail in the planning while not being too detailed which can lead to long calculation times. In this time-frame, electrolysis systems with a specific capacity can be purchased and operated until its economical lifetime has been met. Electrolysis systems can be salvaged, resulting in salvage costs or profits depending on the value of the system. Systems in operation degrade over time lowering their performance over time, meaning that less hydrogen is produced for the amount of electricity used. Furthermore, OPEX are also considered for the systems that are in use in period t. OPEX accounts for the planned and unplanned maintenance that is performed on the system throughout their lifetime, and the electricity base-load that is often required to keep the systems on stand-by (Buttler and Spliethoff, 2018).
In the coming decades it is expected that the technology for electrolysis will continue to improve (Buttler and Spliethoff,
2018). Therefore, this model includes these technological im- provements in a similar manner as Rajagopalan et al. (1998) did. Each technological level m can have lower CAPEX, degra- dation performance, and OPEX. Technology levels are available from a specific t period and are known in advance.
The objective is to minimize the sum costs of all t periods in the planning horizon T, the defined problem can be resolved by finding this minimum. The problem is defined by making decision on when to acquire capacity and when to salvage it.
This results in a set of two decision variables for each period, annotations of these decision variables are listed below.
X
m(t) Number of electrolysis systems purchased of tech- nology level m in period t, assuming technology m is available in period t.
Y
m(t) Number of electrolysis systems of technology level m that are salvaged in period t.
The parameter annotations are presented below.
T Number of periods in the considered time-line.
M Number of technology levels for electrolysis systems in the considered time-line.
m
tThe period when technology level m has become available for purchasing.
S(t) Setup costs when one or more machines are pur- chased in period t.
A
m(t) CAPEX of an electrolysis system of technological level m in period t.
O
m(t) OPEX of a system of technological level m in period t. Including electricity costs.
L
m(t) Salvage profits or costs for salvaging a system of level m in period t.
K(t) Boolean operator that has a value of 1 when a sys- tem is purchased in period t and 0 when no system is purchased in period t.
D(t) Total demand in number of machines. For example, when D(t) = 3 there the demand equals to 3 systems.
U
m(t) The current capacity of a system based on the degra- dation of system of technology level m in period t.
3.1.1. Model novelty
The model that will be introduced in the next section based on the problem description that was discussed at the beginning of this section will be unique in multiple ways. First of all, this model is mostly based on a combination of the models of Ra- jagopalan et al. (1998), Rajagopalan (1992) and Chand et al.
(2000).
The model of Rajagopalan et al. (1998) features the element
of technological advancements, which is their main contribution
to the literature. Their total cost consists of the following ele-
ments: CAPEX, OPEX, Holding cost, and salvage profit. They
allow systems to be idle or active depending if they are needed
based on the demand. For idle systems only holding cost need
to be paid periodically, while active systems have both OPEX
and holding cost. The model of Chand et al. (2000) features aging of systems, systems need to be replaced after a specific amount of periods. Similar to Rajagopalan et al. (1998), they allow systems to be idle or active. Their total cost contains the following components: CAPEX, OPEX, storage cost, salvage profit, and setup cost. Note that because of the introduction of setup cost that there is an economies of scale element in this model. Finally, the system deterioration element from the model of Rajagopalan (1992) has included in the model as it is a vital element for the strategic capacity replacement planning element of this model.
Based on the problem description it can be concluded that the models discussed all contain elements that are relevant, but also elements that are not desired or unrealistic. The novelty of this system comes from the unique combination of elements of the model. The model will feature technological advancements, ag- ing of systems, and the total cost will consist of CAPEX, OPEX, salvage profits, and setup cost. Allowing systems to be idle will be removed as this is not realistic in the green hydrogen pro- duction industry as extremely high utilization rates are needed to reduce the average cost of the produced hydrogen. There- fore, the cost component of holding cost or storage cost will be removed as systems will not be able to be idle. The result is a model that features the key components from both models.
Although the elements of the model have been addressed in previous work before, the novelty comes from the unique combination of all elements that suit this specific problem de- scription. Because the green hydrogen production market has relatively unique characteristics no model exactly matches the problem description. The combined elements and assumptions in this model make it novel and an excellent fit with the green hydrogen market.Furthermore, as this model is being validated by industry experts later in this paper. Not only does this con- firm the value for the industry, it also allows the model to be potentially expanded even further.
3.2 Model introduction
Using the notations from section 3.1 the model will be devel- oped in this section. The total demand D(t) in for period t is assumed to be the aggregation of all the demand streams which are discussed in section 2.3. Due to energy price fluctuations, seasons, and weather conditions the demand is not strictly in- creasing. Setup costs occur when one ore more machines are purchased in a specific period. Equation 1 allows that these costs are only added when machines have been acquired in period t.
K(t) =
( 1 if X
m(t) > 1
0 if X
m(t) = 0 ∀ m, t (1) Let F
m(t) denote the number of systems of technology level m that are operational in period t, equation 2 defines this value.
The assumption is made that systems are acquired and salvaged at the beginning of the period.
F
m(t) =
t
X
i=1
(X
m(i) − Y
m(i)) ∀ m, t (2)
To prevent the objective function from salvaging more sys- tems than there are operational F
m(t) will have a non-negativity constraint.
F
m(t) > 0 ∀ m, t (3)
The total available capacity of the electrolysis systems in pe- riod t must be greater or equal than the demand in period t, this constraint is shown 4. Note that the first technology level m must be available at the first period t=0.
M
X
m=1
(U
m(t) · F
m(t)) > D(t) ∀ t (4)
From these notations the deterministic objective model to re- duce the total costs of the capacity expansion, plan given the constraints above, can be developed. This is presented in equa- tion 5. The objective function, which finds the optimal mini- mum costs, consists of four main components. The first compo- nent is the setup costs that occur when systems are purchased.
The next component are the CAPEX for the systems per sys- tems purchased. The third component are the OPEX of all the systems that are operational in a period. Finally, the last compo- nent is the salvage costs or profits when a system is being sal- vaged. Note that this last component is subtracted from the costs as salvaging a system can actually generate some profit. When salvaging a system costs money this value can become negative and thus can still increase the total costs. The total costs is the summation of these costs for each period t and technology level m.
min T C =
T
X
t=0
(S(t) · K(t) +
M
X
m=0
(A
m(t) · X
m(t) +
F
m(t) · O
m(t) − L
m(t) · Y
m(t)))
(5)
Finally, there are various parameters that have a non- negativity constraint, and the decision variables can only have positive integer values.
S(t), A
m(t), O
m(t), D(t),
U
m(t) > 0 ∀ m, t (6)
X
m(t), Y
m(t) ∈ N ∀ m, t (7)
Because all elements except the salvage values are non-
negative the total costs will always be positive. The potential
profits that can be made from salvaging a system cannot be higher than the CAPEX because assets lose value because of its age and deteriorating performance. Therefore, constraint 8 prevents that salvage profits can be higher than the acquisition costs and thus the objective function will always be greater than 0.
L
m(t) 6 A
m(t) ∀ m, t (8) This model is relatively simple as it simplifies some aspects that would be encountered in a real-world situation. The first key assumption is that the deterioration function in this model is based on the technological level of the system. This means that a system of technological level 2 purchased in period 5 has the same level of deterioration of a system with an equal tech- nology level that has been purchased in period 6. Furthermore, the OPEX has a similar simplification. The OPEX function is based on the technological level is also based on the technolog- ical level of the system.
The main reason for this simplification is because F
m(t) does not know how old systems exactly are, it only is the sum of the number of systems in operation of a certain technological level. The model can be made more complex by also tracking the exact age of each system that is in operation. However, this will make the model more complex for the solver as more deci- sion variables will be introduced which will increase calculation times significantly.
Finally, In order to be able to use a solver the model needs to be translated into a MIP problem in python. To achieve this equation 1 needs to be changed to an activation constraint.
K(t) · BigInt >
M
X
m=1
(X
m(t)) ∀ t (9)
Using this constraint forces K(t) to be 1 when the model wants to purchase one or more systems from any technology level. The remaining constraints and the objective function are all linear and do not need to be changed.
3.3 Model validation
four different cases have been made. Each validation case will have a different set of parameter values which should re- sult in obvious expected outcomes. The cases are deliberately kept small in order to validate the output manually.
3.3.1. Validation case 1
This case consists of ten periods and three technology levels.
The first technology level will be available from the fist period, the second level is available from the 4th period, and the final level is available from the 7th period. The setup cost, CAPEX, and salvage profits are static and have the following values:
S(t) = 50, A
m(t) = 100, L
m(t) = 10. Systems deteriorate
with a relatively high 10% per period at technology level 0, while systems with tech level 1 deteriorate at 9% per period and systems of tech level 2 deteriorate with 8% per period. OPEX of a system starts with 10 and increases with 10% for every period after the technology level of the system has become available, for each technology level increment the operational cost are re- duced with 10%. The demand for each period can be observed in table 2.
Due to the significant setup cost there is a high incentive to cluster orders into low-frequency high-volume orders to achieve economies of scale. This will result in an overall overcapacity being available throughout the periods as capacity is acquired in bulk, and because of constraint 4 this capacity will be ac- quired in advance. Moreover, due to the increasing OPEX and decreasing performance of aging systems there is an incentive to salvage old systems. Although it is a relatively short simulation it is likely that systems of technology level 0 will be salvaged.
The results presented in table 2 show that systems have been acquired in four periods, at t = 1, 4, 6, 8. As one would expect at each purchase systems are acquired of the newest technological level available at that time as it offers the best performance for the cost. In period t=0 it can be observed that two systems are acquired, providing a capacity of 2, while the demand is only 0.5. This demonstrates that economies of scale is being applied to save cost as technically two machines are required from pe- riod t=2. Two systems are acquired in t=0 because it is cheaper to pay the setup costs only once and having it in operation for two extra months rather than paying setup costs twice. Further- more, when comparing the sum capacity with the demand for each period it can also be concluded that constraint 4 is working as intended. Finally, it can be observed that the number of op- erational machines F
m(t) is properly being calculated. F
m(t) increases when systems are being acquired and is reduced when systems are being salvaged.
3.3.2. Validation case 2
In the following case parameters will be used that is expected to result in a situation with no system salvages at all. Similar to the previous case there will be 10 periods and 3 technology levels.
These technology levels will be available in the same periods as the last case; 0, 4, and 7. The setup costs and salvage prof- its will remain the same, but this time the systems will have no performance degradation and the OPEX will not increase. The CAPEX will be 10 and will reduced by 10 for each technology level; so A
0(t) = 100, A
1(t) = 90, A
2(t) = 80 and the cost will remain the same throughout all periods. This should result in a situation where salvaging will be uneconomical, all ma- chines will stay in operation until the end once they have been acquired. Furthermore, it is expected that systems of the newest technology will be acquired because of the lower CAPEX.
Table 3 contains the results from the case and as expected, no
systems have been salvaged. Because no performance degrada-
tion is applied over time there is no need to renew systems. Fur-
Table 2. Model output case 1.
t 0 1 2 3 4 5 6 7 8 9 Cost
D(t) 0.5 0.8 1 0.8 2 2.5 2.2 3 5 8
K(t) 1 0 0 0 1 0 1 0 1 0 200.00
Sum Cap 2 1.8 1.62 1.46 3.13 2.84 3.51 3.21 8.87 8.14
X(0.t) 2 0 0 0 0 0 0 0 0 0 200.00
Y(0.t) 0 0 0 0 0 0 2 0 0 0 (20.00)
F(0.t) 2 2 2 2 2 2 0 0 0 0
Om(t) 10 11 12.1 13.3 14.6 16.1 17.7 19.5 21.4 23.6
O*F 20 22 24.2 26.6 29.3 32.2 0 0 0 0 154.31
Capacity 2 1.8 1.62 1.46 1.31 1.18 0 0 0 0
X(1.t) 0 2 0 0 0 0 0 200.00
Y(1.t) 0 0 0 0 0 0 0
F(1.t) 0 2 2 2 2 2 2
Om(t) 9 9.9 10.9 12 13.2 14.5 15.9
O*F 0 19.8 21.8 24 26.4 29 31.9 152.77
Capacity 1.82 1.66 1.51 1.37 1.25 1.14
X(2.t) 2 0 7 0 900.00
Y(2.t) 0 0 0 0
F(2.t) 2 2 9 9
Om(t) 8.1 8.91 9.8 10.8
O*F 16.2 17.8 88.2 97 219.26
Capacity 2 1.84 7.62 7.01
Total cost 2,006.34
Table 3. Model output case 2.
t 0 1 2 3 4 5 6 7 8 9
D(t) 0.5 0.8 1 0.8 2 2.5 2.2 3 5 8
K(t) 1 0 0 0 1 0 0 0 1 0 150.00
Sum Cap 1 1 1 1 3 3 3 3 8 8
X(0.t) 1 0 0 0 0 0 0 0 0 0 100.00
Y(0.t) 0 0 0 0 0 0 0 0 0 0
F(0.t) 1 1 1 1 1 1 1 1 1 1
Om(t) 10 11 12.1 13.3 14.6 16.1 17.7 19.5 21.4 23.6
O*F 10 11 12.1 13.3 14.6 16.1 17.7 19.5 21.4 23.6 159.37
Capacity 1 1 1 1 1 1 1 1 1 1
X(1.t) 0 2 0 0 0 0 0 200.00
Y(1.t) 0 0 0 0 0 0 0
F(1.t) 0 2 2 2 2 2 2
Om(t) 9 9.9 10.9 12 13.2 14.5 15.9
O*F 0 19.8 21.8 24 26.4 29 31.9 152.77
Capacity 2 2 2 2 2 2
X(2.t) 0 0 5 0 500.00
Y(2.t) 0 0 0 0
F(2.t) 0 0 5 5
Om(t) 8.1 8.91 9.8 10.8
O*F 0 0 49 53.9 102.91
Capacity 0 0 5 5
Total cost 1,365.05
thermore, because there is no performance degradation the sum of systems acquired is much lower compared to case 1. Even though the demand is exactly the same, less systems have to be in operation as the performance is always equal to the initial performance. As expected, now only one system is acquired in
period t=0 while in the previous case two systems were acquired
to be able to meet the demand in period t=2. Now that the sin-
gle system is just enough to deal with the demand in period t=2
no system is acquired and the acquisition of new systems is de-
layed to period t=4. Finally, the output shows that, as expected,
systems of the highest technology level available are acquired.
Assuming that each successive technology level is an improve- ment in terms of acquisition cost, operational cost, and perfor- mance degradation, the optimal solution will always show that the highest technology level available is acquired at any given period. This also suggests that the same applies to salvaging systems, the systems of the lowest technological level currently in operation will be the ones being salvaged.
3.3.3. Validation case 3
This case has a different demand trend than the previous to cases. The demand will initially be high and will become lower for each successive period up until period t=5, then the de- mand will start growing again. This ”V” shaped demand will force many systems to be acquired initially and then to some degree systems will be salvaged as the demand is dropping.
When demand is increasing again new systems will need to be acquired. In this case only one technology level will be avail- able and systems will not suffer from performance degrada- tion or operational cost increase. The expected outcome is that some systems will be saved when demand is lower than the capacity. The amount of systems that will not be salvaged de- pends on a trade-off between paying the OPEX throughout the low-demand periods, or the CAPEX minus the salvage prof- its. When costs of keeping a system operational during low de- mand periods exceeds the cost of acquiring new system later it is expected to be salvaged. The following parameters have been used: A
0(t) = 100, L
0(t) = 10, O
0(t) = 20, and L
0(t) = 10.
Note that the operational cost has been increased, this is to force the salvaging of the systems when demand is decreasing.
The output of the model in table 4 clearly shows that the re- sults are as expected. Initially systems are acquired to be able to deal with the demand. Once demand starts to decrease systems are being salvaged as the benefits of salvaging and reacquiring systems outweigh the cost of keeping the systems in operation.
Only in periods t=3 and t=4 there is more capacity than there is demand. However, because the costs of keeping these systems in operation is lower than the acquisition costs and setup costs they are kept in operation.
3.3.4. Validation case 4
This fourth and final case should simulate a situation where no setup costs are applicable when acquiring new systems. Al- though this is not likely to be a realistic setting, the results of this test are rather predictable. When no setup costs are applied there will be no incentive to acquire systems in large quantities and low order frequency. Instead, it will be logical to acquire systems exactly when they are needed. Similar to the previous cases the simulation will be 10 periods long and three technol- ogy levels will be available at the first, fourth, and seventh pe- riods. In this case systems with higher technology levels will have lower acquisition costs similar to validation case 2. The
remaining parameter values are: L
0(t) = 10, O
0(t) = 20, L
0(t) = 10, and of course S(t) = 0. No deterioration is in- cluded in this case and the demand levels are equal to that of case 1.
The expectation for this case is that systems will be acquired exactly when they are needed when demand increases. Due to the lack of setup costs there is no economies of scale. Thus, sys- tems do not have to be acquired in batches. Instead, systems are acquired exactly when needed to save on operational cost. Fur- thermore, because systems do not deteriorate and do not have an increasing operational cost systems should not be salvaged as there is no benefit.
As table 5 shows, only when D(t) − D(t − 1) > 1 is true, more than one system is acquired such as in the case of periods 8 and 9. Compared to the previous cases it clearly shows that the acquiring of new systems is strictly following the demand.
Because there is no deterioration or an increase in operational cost due to the age of the systems no system is salvaged at any point.
3.4 Sensitivity analysis
In this section a specific set of parameters are being selected for sensitivity analysis. The parameters that are being considered is based on its properties and importance within the model. The selected parameters will be analysed on their influence on the total cost of the simulation. This is will be accompanied by a discussion and a breakdown of the observed results and practi- cal implications will also be addressed.
The first parameter that will be analysed on its sensitivity is the deterioration U
m(t). The foremost reason for this choice is because this is the main element that makes this model also a ca- pacity replacement planning tool. Both the model from (Chand et al., 2000) and (Rajagopalan et al., 1998), which the model of this paper is based upon, do not feature this element. Al- though the model from Rajagopalan (1992) does have this ele- ment, their model does not feature capacity replacement which is the case for this model. The deterioration of performance has been implemented in this model because deterioration is still an important characteristic of electrolysis. Setup costs will be the second parameter to be analysed on its sensitivity. As al- ready described in Case 4 of the model validation section, the setup cost will have a major impact on the way systems are be- ing acquired. When no setup cost would exist the moments of acquiring new systems would be rather obvious; when there is demand for it. However, literature has shown that setup costs basically always occur when purchasing a new product or as- set from direct or indirect cost. In the case of the HEAVENN project, determining the capacity of the systems is also going to depend heavily on the economies of scale that can be achieved.
They find that acquiring larger systems does bring significant
reductions to the CAPEX and thus the cost per produced unit
of hydrogen also goes down. By analyzing the sensitivity of the
Table 4. Model output case 3.
t 0 1 2 3 4 5 6 7 8 9
D(t) 5 4 3 2 1 3 5 7 10 12
K(t) 1 0 0 0 0 0 1 1 1 1 250.00
X(0.t) 5 0 0 0 0 0 2 2 3 2 1,400.00
Y(0.t) 0 1 1 0 0 0 0 0 0 0 (20.00)
F(0.t) 5 4 3 3 3 3 5 7 10 12
Om(t) 30 30 30 30 30 30 30 30 30 30
O*F 150 120 90 90 90 90 150 210 300 360 1,650.00
Capacity 5 4 3 3 3 3 5 7 10 12
Total cost 3,280.00
Table 5. Model output case 4.
t 0 1 2 3 4 5 6 7 8 9
D(t) 0.5 0.8 1 0.8 2 2.5 2.2 3 5 8
K(t) 1 1 1 1 1 1 1 1 1 1 0
Sum Cap 1 1 1 1 2 3 3 3 5 8
X(0.t) 1 0 0 0 0 0 0 0 0 0 100.00
Y(0.t) 0 0 0 0 0 0 0 0 0 0
F(0.t) 1 1 1 1 1 1 1 1 1 1
Om(t) 20 20 20 20 20 20 20 20 20 20
O*F 20 20 20 20 20 20 20 20 20 20 200.00
Capacity 1 1 1 1 1 1 1 1 1 1
X(1.t) 0 1 1 0 0 0 0 180.00
Y(1.t) 0 0 0 0 0 0 0
F(1.t) 0 1 2 2 2 2 2
Om(t) 20 20 20 20 20 20 20
O*F 0 20 40 40 40 40 40 220.00
Capacity 1 2 2 2 2 2
X(2.t) 0 0 2 3 400.00
Y(2.t) 0 0 0 0
F(2.t) 0 0 2 5
Om(t) 20 20 20 20
O*F 0 0 40 100 140.00
Capacity 0 0 2 5
Total cost 1,240.00
Table 6. Demand throughout periods of the experiments.
t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
D(t) 0.51 0.47 0.76 0.97 0.86 1.35 1.51 1.96 1.93 2.47 2.83 3.6 3.99 4.52 4.93
t 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
D(t) 7.59 6.3 8.89 11.41 11.65 12.65 18.81 18.7 29.73 29.86 39.3 49.49 44.76 54.26 61.88
setup cost some insight can be created on how this will the total cost.
3.4.1. Experiment setting
Both experiments will use the parameter settings described in this section. Firstly, to ensure that the changes of the parameters in the experiments have a significant impact both the simulation duration and number of technology levels must be longer com- pared to the model validation cases. The used parameter values are listed below:
T = 29
M = 5 Technology levels which become available at periods t = 0, 5, 11, 17, 23
S(t) = 50 ∀ t
A
m(t) A
0(t) = 100, A
1(t) = 90, A
2(t) = 80, A
3(t) = 70, A
4(t) = 60 ∀ t
O
m(t) Base cost: O
0(t) = 20, O
1(t) = 17, O
2(t) = 14, O
3(t) = 11, O
4(t) = 8.
For each period after the period at which is has
become available the cost increase with 2%, thus:
Fig. 2. Demand growth throughout the periods of the experi- ment.
O
m(t) = b
m∗ 1.02
(t−mt)where b
mequals the base operational cost of technology level m.
L
m(t) L
0(t) = 10, L
1(t) = 12, L
2(t) = 14, L
3(t) = 16, L
4(t) = 18, ∀ t
U
m(t) Base deterioration rates: m = 0: 4%, m = 1: 3.75%, m = 2: 3.25%, m = 3: 2.75%, m = 4: 1.5%. Then U
m(t) = (1 − b
m)
(t−mt)where b
mequals the base deterioration.
Finally, the demand has the values of table 6, figure 2 vi- sualizes the demand of the experiment. The figure shows that demand growth is exponential and is not strictly increasing.
CAPEX, setup, and salvage cost parameters do not change over time with this experiment.
3.4.2. System deterioration
The degradation of a system U
m(t) depends on two fac- tors, the age of the system and its technological level. Chang- ing the rate of deterioration in this model has a direct influ- ence on constraint 4. U
m(t) can range between 0 and 1, ini- tially when the systems become available in a period they start with U
m(t) = 1. Then depending on the technology level this value gets lower each period. When the value of this parameter gets lower it results in a lower total capacity, constraint 4 forces that the loss of performance is compensated with the acquisition of extra systems if the total capacity in period t is lower than the demand in period t. One can therefore expect that a higher rate of deterioration will result in more systems to be acquired throughout the simulation. Moreover, higher deterioration rates will make these systems less favourable to operate as they rela- tively provide lower capacity for their OPEX compared to other systems that have lower deterioration rates. This will increase the likelihood to salvage these systems when systems deterio- rate faster.
In this experiment the deterioration rates presented in the ex-
[]Table 7. Deterioration experiments.
m
Exp. Change 0 1 2 3 4
1 -0.50% 3.50% 3.25% 2.75% 2.25% 1.00%
2 -0.40% 3.60% 3.35% 2.85% 2.35% 1.10%
3 -0.30% 3.70% 3.45% 2.95% 2.45% 1.20%
4 -0.20% 3.80% 3.55% 3.05% 2.55% 1.30%
5 -0.10% 3.90% 3.65% 3.15% 2.65% 1.40%
base – 4.00% 3.75% 3.25% 2.75% 1.50%
6 0.10% 4.10% 3.85% 3.35% 2.85% 1.60%
7 0.20% 4.20% 3.95% 3.45% 2.95% 1.70%
8 0.30% 4.30% 4.05% 3.55% 3.05% 1.80%
9 0.40% 4.40% 4.15% 3.65% 3.15% 1.90%
10 0.50% 4.50% 4.25% 3.75% 3.25% 2.00%
Fig. 3. Results of deterioration experiment.
periment setting section will be changed for each experiment.
U
m(t) decreases over the periods and the rate of this decrease in this experiment is determined by the base deterioration rate.
This base deterioration improves with each new technology level. In this experiment the base deterioration rates of all tech- nology levels will be changed equally with linear increments of 0.1%, the exact deterioration per technology level per experi- ment can be seen in table 7.
It is expected that the changes of the deterioration will have significant influences on the total cost of the experiments.
Higher deterioration rates will cause earlier replacement of the systems, resulting in higher CAPEX during the simulation.
Moreover, the increased deterioration will also overall require more systems to be in operation to compensate for the deterio- ration causing an increase of the OPEX as well. It is expected that the linear increase of deterioration rates will cause an expo- nential growth in total cost.
The results from this experiment that are presented in figure
3 show that the results are not aligned with the expectations de-
Fig. 4. Cost build-up of experiments.
scribed above. The change in total cost show about a four times bigger change compared to the deterioration changes. However, although the growth of total cost seems to be linear, the trend does seem to have slight deviations. This can be explained by the fact that the acquisition and salvaging of systems is binary and thus some experiments might have relatively more over ca- pacity and this costs than other simulations.
Figure 4 show that the total cost show a relatively stable in- crease when the deterioration levels are increased, however, the underlying cost elements show a less clear pattern. The figure shows the cost differences of the experiment compared to the base case. Because the salvage profits were quite stable through- out the experiments it has not been included in the graph. An interesting observation is that initially simulations follow the same sequences of acquisition and salvaging of systems and higher the period count gets the greater the differences. This can be explained by the curve and characteristics of the demand plays. Initially demand is low and the capacity requirement con- straint forces the model to follow an optimal sequence due to the setup cost. However, later in the simulation, when deterioration differences also start to occur, more variation is occurring. The varying deterioration levels in the experiments begin to create significant differences in the performance of the systems and thus force the model to keep systems in operation for longer or acquire more systems.
3.4.3. Setup cost
Setup cost S(t) are only paid in a period when systems are be- ing acquired in that period. In this experiment the setup cost does not change over time, the cost remain static over time dur- ing the simulation for simplicity. When systems are acquired in a period K(t) is forced to take the value of 1 because of constraint 1, in this case the setup costs are added to the total cost. In this experiment the setup cost will change to analyse
Table 8. setup cost used for experiments.
Exp. setup cost
1 0
2 10
3 20
4 30
5 40
Base 50
6 60
7 70
8 80
9 90
10 100
11 110
12 120
