Design and operation of a stochastic hydrogen supply chain network under demand uncertainty

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 9 6 5 e3 9 7 7

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journal homepage: www.elsevier.com/locate/he

Design and operation of a stochastic hydrogen supply chain network under demand uncertainty A. Almansoori a,*, N. Shah b a

Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK b

article info

abstract

Article history:

The design of a future hydrogen supply chain (HSC) network is challenging due to the: (1)

Received 27 September 2011

involvement of many echelons in the supply chain network, (2) high level of interactions

Received in revised form

between the supply chain components and sub-systems, and (3) uncertainty in hydrogen

13 November 2011

demand. Most of the early attempts to design the future HSC failed to incorporate all these

Accepted 15 November 2011

challenges in a single generic optimization framework using mathematical modeling

Available online 12 December 2011

approach. Building on our previous multiperiod MILP model, the model presented in this paper is expanded to take into account uncertainty arising from long-term variation in

Keywords:

hydrogen demand using a scenario-based approach. The model also adds another echelon:

Hydrogen supply chain

fueling stations and local distribution of hydrogen. Our results show that the future HSC

MILP stochastic model

network is somewhat similar to the existing petroleum infrastructure in terms of

Demand uncertainty

production, distribution, and storage. In both situations, the most feasible solution is

Risk analysis

centralized production plants with truck and rail delivery and small-to-large storage

Scenarios-based approach

facilities. The main difference is that the future hydrogen supply has the benefits of using

Great Britain

distributed forecourt production of hydrogen at local fueling stations via several production technologies. Finally, the performance of the studied models was evaluated using sensitivity and risk analyses. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Hydrogen fuel is envisioned to become a key element of the future energy mix, especially in the transportation sector [1e4]. Unlike gasoline, hydrogen can be harnessed from a wide range of energy sources including non-renewable sources such as hydrocarbons and renewable sources such as wind, biomass, or solar energy. Such advantage enables countries to diversify their energy portfolios and to secure fuel supplies. Moreover, since hydrogen is a good energy carrier, it can be stored in large amounts and converted readily to electricity when needed with almost zero emissions.

Even though hydrogen is a more diverse, sustainable, and environmentally friendly fuel, its widespread as a transport fuel necessitates the development of a sustainable supply chain network. As with the existing petroleum supply system, the future hydrogen supply chain (HSC) ought to include production sites, storage facilities, transportation options, dispensing stations and end-use applications. The HSC should be as ubiquitous as the one present now with refueling points supporting daily and seasonal demand fluctuations. The infrastructure should also be safe, cost-effective, and eco-friendly. In addition, the future supply chain network should exploit some components of the current petroleum

* Corresponding author. Tel.: þ971 2 607 5583; fax: þ971 2 607 5200. E-mail address: [email protected] (A. Almansoori). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.11.091

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infrastructure such as steam methane reforming plants and depleted gas fields or aquifers. Most of the literature reviews in the area of HSC design focus on evaluating the performance of a pre-determined hydrogen supply pathway using a steady-state simulation approach. The work of Simbeck and Chang [5], the US National Research Council [6], Thomas et al. [7], Ogden [8,9], Amos [10], and Guy [11] are extensively based on adopting the simulation approach. Others focus on studying individual components of the supply chain, such as production or storage technologies. Very little effort has been invested in realizing the capability of mathematical programming techniques to assist in identifying the optimum configuration of the future HSC. The aim of this work is to develop a comprehensive optimization framework that can support strategic decisions in HSC design and operation for vehicular use. The proposed optimization framework will make use of a scenario-based approach to capture uncertainty in demand through a mixed integer linear programming (MILP) model. The developed model is robust and capable of mapping out all possible configurations of the future HSC under demand uncertainty, and applicable to any geographical setting. The model is also capable of determining the number of fueling stations and the layout of the distribution network. The key factor in differentiating abovementioned studies is the performance criteria such as cost, environmental impact, energy efficiency or safety. Most of these studies analyze each component of the supply chain individually and then collectively form a specific hydrogen pathway. Each of these predefined pathways are then simulated and compared to select the “best” possible configuration based on a key performance indicator, where cost being the dominant measure. Also, most of these analyses are limited in their general applicability since they are based on a number of assumptions concerning the level of demand, distribution distances, and geographic location. In addition, the studies do not consider the local availability or logistics network of energy sources, demand uncertainty and different sizes of production plants and storage facilities. None of these studies look at integrating the components of the HSC within a single optimization framework to determine the optimal hydrogen supply configurations. To date, significant attention has been given to the role of optimization techniques in designing and operating a future HSC network. A number of mathematical models for planning and designing the future HSC have appeared in the literature. The work of Agnolucci [12], Karlsson and Meibom [13], Tzimas et al. [14], Ingason et al. [15], and Lin et al. [16] are some examples of these attempts. The main objective of these optimization frameworks is to compare and evaluate different alternatives of the hydrogen pathways and then integrate them within the existing energy supply chains. In an early attempt to design a hydrogen infrastructure, Hugo [17,18] developed an optimization-based formulation that investigates different hydrogen pathways in Germany. The model identifies the optimal infrastructure in terms of both investment and environmental criteria for many alternatives of hydrogen configurations. The model did not consider the issue of stationary storage of hydrogen to accommodate daily and seasonal variations of demand. The model also does not

include the logistics network of energy sources, the concept of importing these resources from abroad if there is a shortfall, and the effect of demand uncertainty on the hydrogen infrastructure. Li et al. [19] extended the work of Hugo [17,18] and included numerous combinations of potential technologies within the HSC, which are necessary in the strategic decision-making process for building up the future hydrogen infrastructure. Their work also takes into consideration all possible hydrogen alternatives and the interactions and trade-offs between the various supply chain components. Another noticeable study is the work of Kim et al. [20] who developed a steady-state, stochastic MILP model to take into account the effect of demand uncertainty in hydrogen activities. Their model examined the total cost of the hydrogen network for various configurations using a two-stage stochastic programming approach. Even though this work can be seen as the first stochastic approach to optimize an HSC, the work neglects the evolution of the hydrogen network over a long-term future planning horizon leading to phased infrastructure development. In addition, the multiple and diverse primary energy feedstocks as well as the determination of logistics of fueling stations were not incorporated. Shortly after their first work, Kim and Moon [21] extended their previous mathematical formulation and introduced a multi-objective optimization approach for the strategic design of a hydrogen infrastructure taking into consideration cost and safety. Guille´n-Gosa´lbez et al. [22] also presented a bi-criterion MILP optimization approach for planning and designing an HSC network considering both economics and environmental concerns. The work focuses on a detailed life-cycle environmental analysis and a novel algorithm to reduce the computational cost associated with solving the large-scale problem. More recently, Sabio et al. [23] have developed a decision-support tool to address the strategic planning of hydrogen networks with risk control under uncertainty in the operating costs. The main purpose of their work is to determine the optimal design of the HSC for a pre-defined hydrogen demand profile for vehicle use in Spain. Their optimization problem is formulated as a multiobjective, multi-scenario, stochastic MILP model accounting for the minimization of the expected total discounted cost and the worst case value. Thus, their model incorporates the trade-off between risk and cost at the decision-making level. Our work makes use of a scenario planning approach to capture uncertainty in hydrogen demand over a long-term planning horizon. The variation of demand will be represented by a moderate number of scenarios for which a probability of occurrence will be specified. A multi-stage stochastic MILP model is proposed to outline plausible configurations of the future HSC network. The goal of our formulation is to represent the possible future realization of unknown problem parameters through a set of scenarios, and to consider the range of scenarios in determining a robust solution. The decisions incorporated in the presence of the stochastic behavior are “here-and-now” decisions and “wait-and-see” decisions [24]. “Here-and-now” decisions have to be implemented prior to the realization of the uncertainty and they are used to describe the first-stage variables. These decisions are associated with predicting the structure of the network, for

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example the size, location, and capacity of production plants, before the actual demand to some future event is identified. On the other hand, “wait-and-see” decisions correspond to those decisions made after the uncertainty is unveiled and they relate to second-stage variables of the model. Examples of these decisions are production and transportation rates as well as network retrofits and capacity expansion, which can often be revised when most up-to-date information is revealed.

2.

Problem description

In our previous work [25,26] the aim was to plan and design an HSC network, consisting of hydrogen production plants, storage facilities and transportation modes. The earlier model was designed to satisfy the demand of hydrogen for a deterministic profile over a long-term planning horizon. The previous attempt also neglects to include hydrogen dispensing technologies (fueling stations) and the logistics associated with distributing hydrogen. Deterministic demand is seldom the case in real life applications. Demand usually undergoes numerous variations relative to manufacturers’ and customers’ needs. These variations, i.e. stochastic behavior, could largely affect the design and operation aspects of the future HSC. Therefore, this paper considers the case where demand is not known exactly but subject to some uncertainty. The paper also explores the concept of incorporating fueling stations into previous work, as well as the distribution of hydrogen from the production plants or storage facilities to these fueling stations. This work makes use of a scenario-based approach to capture uncertainly in the hydrogen demand. This uncertainty is characterized by a set of distinct realizations generating what is known as a scenario tree. A scenario tree comprises a number of nodes at which branching occurs. Each node determines the start and the end points of a particular time period. Paths from the root to the leave nodes (i.e. from first to last time period) represent a scenario. Each scenario encompasses a number of decisions that needs to be resolved. Using an S-shape demand trajectory [6,27e29], a scenario tree of the form shown in Fig. 1 was obtained. Within the figure, only three time periods (stages) and nine distinctive scenarios were considered. Each scenario has a definite demand value and probability of occurrence. Based on these two measures,

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the HSC network for each of these scenarios will be determined by the optimization procedure. Having multiple scenarios gives a better representation of what the future hydrogen network may look like, as each scenario contributes towards the final network cost. The stochastic behavior of the hydrogen demand is represented by a three-stage stochastic optimization problem. The first-stage assumes demand to be known (deterministic) while the second-stage takes into account demand variations (uncertainty) over the planning horizon. These two stages are formulated as an MILP model. The model of interest is constructed in a way that it can handle numerous scenarios. This formulation will allow the model to behave well under all demand fluctuations happening at some point during the life of the HSC network. In this paper, nine different demand scenarios are considered during the three time periods of interest. Each time period represents a 6-year interval starting from 2005 and ending in 2022. These demand scenarios were amalgamated to form one and three unique scenarios during the first and second time periods, respectively. The formulation of the tree structure was accomplished through using a condition known as non-anticipativity. This principle will be addressed later in the paper. The network design decisions concerning each scenario within the model framework include: (1) Allocation of primary energy sources, (2) Assignment of location, number, type, size of different production and storage facilities, (3) Establishment of different types of transportation links (modes), and (4) Determination of production rate, average stored inventory, and flow rate of hydrogen and primary energy sources. The design decisions associated with the first-stage is made prior to the realization of uncertainly and is usually referred to as “here-and-now” decisions. The future decisions correspond to those decisions made after the uncertainty is unveiled and are typically known as “wait-and-see” decisions. The model also explores the addition of a new echelon, i.e. fueling station, and reveals a number of new decisions. These decisions include the determination of the total number of fueling stations required to be installed into a particular grid, as well as the cost associated with operating these stations. Another decision is estimating the investment needed for the distribution of hydrogen within a grid. The objective of the multi-stage modeling under uncertainty is to choose the optimal decision variables that will minimize the cost of the first-stage and the expected cost of the subsequent stages.

10

3.

Hydrogen demand (million kg/d)

Low

8

Model structure

Medium

Stage 3

High

The superstructure of the proposed model consists of 7 main components: grid squares, production plants, storage facilities, transportation modes, product physical forms, primary energy sources, and fueling stations. A brief description of each of these components is summarized below.

6

4 Stage 2

2

3.1.

Stage 1

Grid squares

0 2005–2010

2011–2016

2017–2022

Time period (yr)

Fig. 1 e Demand scenario tree of interest.

The grid squares represent the geographical location required to map out all the possible configurations of the future HSC. Each grid square will cover an equal size of land area and may

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enclose different types and sizes of hydrogen production plants and/or storage facilities. Also, a grid square may contain several types of primary energy sources which can be utilized to produce different physical forms of hydrogen depending on consumers’ needs. The demand of hydrogen for each of these enclosed regions (i.e. grids) will vary depending on the grid’s population density and fuel consumption rate. Since the hydrogen demand of each grid is estimated based on a saturated hydrogen market, a penetration percentage of fuel cell vehicles is assumed for the different time periods of the planning horizons. This penetration percentage is assumed to follow an S-shape trajectory of the demand profile (see Fig. 1). In addition, it is unlikely that this demand profile will follow the same pathway. Instead, the demand profile will fluctuate deviating from the forecasted path. These fluctuations would obviously give rise to a large number of demand scenarios.

3.2.

Productions plants

Like other fuels, hydrogen can be produced from various feedstocks utilizing different production technologies, which can be tailored to serve a wide range of production scales. The studied model incorporates both of these features as well as introduces a lower and upper bound on the production capacity. The model also accounts for the existing mercantile hydrogen production facilities such as any excess reforming capacity at refineries. The establishment of a production facility will be determined mainly by the demand of the grid, the failure of the grid to fulfill its hydrogen needs from neighboring grids, the trade-offs between establishing plants or transportation links, and whether to establish centralized or decentralized plants. The production decisions that would be determined by the model include: the number, location, and capacity of plant types, as well as the total production rates of hydrogen in each grid square.

3.3.

Storage facilities

Once hydrogen is produced, it must be stored in storage sites for a certain number of days in order to serve demand and supply fluctuations, and plant interruptions. The storage facilities should be designed to handle different physical forms of hydrogen (i.e. liquid or gas) and a wide range of storage capacity. The model is able to accommodate the state of the existing storage infrastructure especially the depleted oil or gas fields. The establishment of storage facility in each grid is essential to satisfy the grid’s local demand and may be independent of the production plant’s location, thus the storage facility serves as a distribution terminal. The storage decisions captured by the model include determining the number, location and capacity of storage types, and the total average amount of hydrogen stored in each grid.

3.4.

Transportation modes

A number of different transportation modes can be used to deliver hydrogen from production facilities to storage sites and finally to the fueling stations. The transportation means include a wide range of options such as pipeline, trucks, rail, etc. The model of interest takes into consideration the

capacity of each transportation option, the delivery distance, and the minimum and maximum flow rates of products between grids. The model also determines the establishment of transportation links between various grids which is justified based on the cost of the transportation mode versus the cost of establishing a new production facility. Moreover, the transportation decisions include whether to establish a link between grids and what the flow rate of hydrogen and primary energy sources should be.

3.5.

Product physical forms

The production plants can produce different physical forms of hydrogen depending on customers’ specifications. The two common and practical forms of hydrogen are compressed gas and cryogenic liquid. These different forms are a key factor in determining the transportation mode and the storage facility necessary, as well as the total cost of the future HSC network.

3.6.

Primary energy sources

Since hydrogen can be harnessed from a wide range of primary energy sources, including natural gas, oil, coal, biomass, and renewable electricity, it is essential to identify the type and location of these energy sources when designing a hydrogen infrastructure. Therefore, our model incorporates the geographical location, availability, quantity, and types of the primary energy sources. This consequently determines the type and size of production technologies that are selected. The main decision associated with the primary energy sources is whether to import resources from neighboring grids or from external sources, such as another country. Another decision determined by the model is how much of energy resources will be used to produce hydrogen and how much will remain unexploited for other purposes. Moreover, the model outlines the logistics associated with distributing energy feedstocks over a vast geographic region.

3.7.

Fueling stations

The key factors in the installation of fueling stations are characterizing the required demand and the form of product to dispense. These two factors will determine the size and type of fueling stations. Since we assume that all grids encounter a deterministic demand represented by a distinct scenario, the establishment of fueling stations is imperative to replenish consumers with their needs. Each type of fueling station will have a fixed capacity as well as capital and operating costs. The fueling decision includes the determination of the number of fueling stations required to be installed in each grid. Due to the introduction of fueling station, the establishment of transportation modes will take place between production plants or storage facilities and fueling stations. This establishment will happen in all grids due to the presence of production plants and/or storage facilities. The transportation modes will have a specific holding capacity, and maximum and minimum allowable flow rate.

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4.

Aegtk ¼Aegkðt1Þ þ Iegtk þ

Model formulation

A detailed description of the model notation is outlined in Table A.1 in Appendix A. The following section discusses the model constraints and objective function. The first part of the section summarizes the constraints that are used in the model, while the second part presents the objective function equations.

4.1.

DTigtk ¼ PFtk DTig

(1)

where PFtk is the penetration factor of hydrogen fuel cell vehicles during a particular time period t and demand scenario k. This factor is multiplied by the total equivalent demand in specific region in order to estimate the demand at the corresponding scenario and time period. Each grid within the supply chain network will fulfill its needs by local production facilities or by importing products from other neighboring grids. Therefore, the local demand, i.e. satisfied by local production, of product i in a grid g during time period t and scenario k is expressed by the following constraint: ci; g; t; k

(2)

The imported demand of product form i to a particular grid g during time period t and scenario k is equal to the sum of all flow rates imported to the grid of interest by all transportation modes l and from all neighboring grids g0 : ¼

XX

ci; g; t; k

Q

ilg0 gtk

(3)

g0

l

 (6)

gepj Ppjigtk ce;g;t;k : tst1

where Aegkðt1Þ is the average availability of primary energy sources at the end of the previous time period. A material balance on a grid g is written for each primary energy source e during time period t and scenario k: X

! QEeg0 gtk SSF ¼

X

g0

The total demand of hydrogen will start at a low level and then sharply increase until it reaches the saturation point. This pattern can be described by the following equation:

DIigtk

X

QEeg0 gtk  QEegg0 tk

g0

p;j;i

Iegtk þ

Demand constraints

DLigtk  PTigtk



X

QEegg0 tk þ

g0

X

gepj Ppjigtk ce; g;t;k

(7)

p;j;i

The first and second terms of the left-hand-side of Eq. (7) represent the import of primary energy sources from overseas and neighboring grids, respectively. These terms are multiplied by a safety stock factor (SSF) to store a small inventory of primary energy sources as a buffer against unpredicted contingencies in energy sources. The first term of the right-hand-side of the same equation indicates the export of primary energy sources to nearby grids, while the second term indicates the amount of primary energy sources consumed by a production plant. The factor gepj represents the utilization rate of energy resources by a production plant.

4.3.

Production facilities constraints

Assuming a steady-state condition during each time period t and scenario k, the total production rate of product in a particular grid is equal to: PTigtk ¼

 X Qilgg0 tk  Qilg0 gtk þ DTigtk

ci; g; t; k

(8)

l;g0

The total production rate is also equal to the production rate of all types and scales of production plants established in a particular region: X

The sum of Eqs. (2) and (3) gives the total demand of hydrogen:

PTigtk ¼

DTigtk ¼ DLigtk þ DIigtk

The production rate of plant type p and size j producing product i established in grid g during time period t and scenario k is constrained by the number of production facilities and the minimum and maximum production limits:

4.2.

ci; g; t; k

(4)

Primary energy sources constraints

The average availability of primary energy sources e in a grid g and scenario k at the end of the first time period t1 is given as a sum of four terms. These are the initial average availability of primary energy sources, the import of primary energy sources from overseas, the transportation of primary energy sources between grids, and the rate of consumption of these sources. The terms are expressed respectively by the following constraint: Aegt1 k ¼

A0eg 

þ Iegt1 k þ

X

X

QEeg0 gt1 k  QEegg0 t1 k



ce; g; k

ci; g; t; k

(9)

max PCapmin pji NPpjigtk  Ppjigtk  PCappji NPpjigtk

cp; j; i; g; t; k

(10)

Distributed plants, i.e. small-scale plants, established in a region can only fulfill the demand of hydrogen in that particular grid. Therefore, products cannot be exported to neighboring grids but only satisfy local demand via the following constraint: X

Ppjigtk  DLigtk

ci; g; t; k : j ¼ small plants

(11)

p

g0

gepj Ppjigt1 k

Ppjigtk

p;j

(5)

p;j;i

The average availability of primary energy sources at the next time periods is equal to:

The following constraints make sure that plants with certain production technologies cannot be built in a particular size due to technical and economical limitations of the technology [6]. The following constraints demonstrate such restrictions:

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NPpjigtk ¼ 0 ci;g;t; k : p ¼ coal gasification & j ¼ small plants (12) NPpjigtk ¼ 0 ci; g; t; k : p ¼ biomass gasification & j ¼ small plants

where b represents the average number of days’ worth of storage in order to account for demand fluctuations. The average inventory of product form i kept in grid g by storage type s and size j during the time period t and scenario k cannot exceed certain limits:

(13) max SCapmin sji NSsjigtk  Ssjigtk  SCapsji NSsjigtk

NPpjigtk ¼ 0 ci; g; t; k : p ¼ electrolysis & j ¼ large plants

4.4.

(14)

Transportation constraints

Lave gtk ¼

X 2LLg m

m1

Umgtk

cg; t; k

(15)

The total number of plants established in each grid g during time period t and scenario k is given as follows: X

NPpjigtk ¼

X ðm  1ÞUmgtk

cg; t; k

(16)

m

p;j;i

To obtain a meaningful result, the binary variable Umgtk is enforced by: X

Umgtk ¼ 1 cg; t; k

(17)

m

The local demand satisfied by the total number of plants established for each scenario k and during time period t is expressed by the following constraints:   DMLmgtk  DLigtk  p 1  Umgtk ci; m; g; t; k

(18)

The above equation is written in this form to insure linearity. The subscript m is a counter that is equal to the number of plants established in a particular grid plus one (m ¼ 1, ., NPmax þ 1) and Umgtk is a binary variable that determines if m  1 plants are established in grid g. The term m  1 is introduced to allow some grids to have no production plants. The construction of a regional distribution network is stipulated by the following constraints: Qilmin Xilgg0 tk  Qilgg0 tk  Qilmax Xilgg0 tk

ci; l; g; g0 ; t; k : gsg0

(25)

In a similar manner to the above equation, the total average stored inventory of a product is: X

Local transportation of a product will only take place if the grid contains at least one production plant. The distribution of the product depends significantly on the average delivery distance within a grid and the local demand satisfied by the total number of plants established. Therefore, the average local delivery distance within a grid during time period t and scenario k is:

cs; j; i; g; t; k

T SCapmin sji NSsjigtk  Sigtk 

s;j

4.6.

X

SCapmax sji NSsjigtk

ci; g; t; k

(26)

s;j

Time evolution constraints

During the early stages of the transition to a hydrogen economy, hydrogen is expected to be supplied from existing petroleum refineries, chemical complexes or chlor-alkali plants. Hydrogen could also be obtained from an existing storage facility. Taking these options into account, the number of production plants and storage facilities in a particular grid and during the first time period are given by the following constraints, respectively. NPpjigt1 k ¼ NP0pjig þ IPpjigt1 k

cp; j; i; g; k

(27)

NSsjigt1 k ¼ NS0sjig þ ISsjigt1 k

cs; j; i; g; k

(28)

The parameters NP0pjig and NS0sjig are the number of existing production plants and storage facilities, respectively. The variables IPpjigt1 k and ISjigt1 k are the number of new production plants and storage facilities that need to be built early during the first time period at any given scenario. As the network evolves over time, new production plants and storage facilities will be invested in to meet the increased demand. Therefore, the number of production plants and storage facilities in each grid and during the subsequent time periods is equal to the number of the previously established facilities plus the number of new invested plants and storage facilities. This can be captured by the following constraints: NPpjigtk ¼ NPpjigkðt1Þ þ IPpjigtk

cp; j; i; g; t; k : tst1

(29)

NSsjigtk ¼ NSsjigkðt1Þ þ ISsjigtk

cs; j; i; g; t; k : tst1

(30)

(19)

4.7.

(20)

The total average inventory of product i in grid g at time period t and scenario k is:

The tree structure exhibited in Fig. 1 is represented in that form through a condition known as non-anticipativity. The non-anticipativity principle, which was introduced initially by Wets [30] states that if a set of scenarios have the same available information up to time period t then the values of the variables corresponding to these scenarios are identical up to time period t. Since the demand trajectory for the first time period is assumed to be deterministic, such non-anticipativity principle will lead to one discrete scenario. The decision variables associated with this discrete scenario will be similar up to the first time period. The following constraints guarantee this condition:

STigtk ¼ bDTigtk

Vot1 k ¼ Vot1 ðkþ1Þ

Xilgg0 tk þ Xilg0 gtk  1 ci; l; g; g0 ; t; k : gsg0 Yigtk  Xilgg0 tk

ci; l; g; g0 ; t; k : gsg0

(21)

Zigtk  Xilg0 gtk

ci; l; g; g0 ; t; k : gsg0

(22)

Yigtk þ Zigtk  1 ci; g; t; k

4.5.

(23)

Storage facilities constraints

ci; g; t; k

(24)

Non-anticipativity constraints

co; k : k < 9

(31)

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where V is any decision variable presented in the model. The index o denotes other indices incorporated in a particular variable such as e, g, g0 , i, p, j, s, and m. Obviously, only some of these indices will appear depending on the variable. The demand uncertainty encountered in the second time period is presented by nine scenarios which are ‘lumped’ together forming three different sets of scenarios. The decision variables involved in each of the three ‘lumped’ scenarios are identical up to that time period. Such similarity in these scenarios is ensured via the following non-anticipative constraints: Vot2 k ¼ Vot2 ðkþ1Þ

co; k : k < 3

(32)

Vot2 k ¼ Vot2 ðkþ1Þ

co; k : 3 < k < 6

(33)

Vot2 k ¼ Vot2 ðkþ1Þ

co; k : 6 < k < 9

(34)

In the last time period, there will be a unique set of variables for each of the nine scenarios. These sets of variables will yield into nine different hydrogen network configurations.

4.8.

Fueling constraints

The number of fueling stations within a grid g dispensing a product form i during time period t and scenario k depends on the total equivalent demand and the installed capacity of the fueling stations, as follows: NFSigtk ¼

DTigtk FCap



X

NPpjigtk

ci; g; t; k : j ¼ small plants

(36)

Facility capital cost

The facility capital cost over the entire planning horizon is related to the establishment of new production plants and storage facilities at each time period t and scenario k. It was assumed that no capital cost is associated with the establishment of fueling stations as the current gasoline stations will be converted to hydrogen stations. The conversion cost of these stations is assumed to be negligible. Nevertheless, the capital cost of the production plants is obtained by multiplying the plant capital costs by the total number of new plants. Likewise, the capital cost of storage facilities is

PCCpji IPpjig þ

p

X

!! (37)

SCCsji ISsjig

s

LR ¼ 1 þ ½kðt  1Þ

(38)

where the term t  1 represents the cost reduction with time and k is the percentage of the corresponding reduction per year. PRk is the probability of occurrence of the demand scenarios in reality.

4.10.

Transportation capital cost

The total transportation capital cost for all scenarios and time periods is equal to: P

TCC ¼

PRk

i;l;m;g;t;k

X

PRk

i;l;g;g0 ;t;k

p

PRk ¼ 1

X

where the first part of the right-hand-side of Eq. (37) denotes the capital cost of production plants while the second part denotes the capital cost of storage facilities. The learning rate (LR) is introduced to take into account the reduction in the cost of production and storage exogenous technologies as experience accumulates with time. This coefficient is defined as follows:

(35)

k¼1

PRk LR

j;i;g;t;k

þ

X

PRk

i;l;n;g;t;k

DMLmgt TMCil

2LLg

ðm  1ÞTMALl TCapil Qilgg0 t TMARl TCapil

2LRgg0 SPRl

DTigtk Wngtk ðn  1ÞTMALl TCapil

!!

þ LUTl SPLl !! þ LUTl 2LLg

þ LUTl SPLl

!! (39)

The first and second terms in Eq. (39) represent the capital transportation cost associated with the distribution of hydrogen within a grid (local distribution) and between grids (regional distribution), respectively. For more detail on the derivation of these two cost terms, refer to our previous work [25,26]. The last term in Eq. (39) represents the transportation capital cost associated with the secondary distribution of hydrogen within a grid. The term (n e 1) is introduced to determine the average delivery distance within a grid and is expressed as follows: X

NPpjigk þ

p;j;i

4.9.

X

FCC ¼

þ

The second term of the right-hand-side of Eq. (35) is brought in to account for the establishment of distributed plants with on-site production and dispensing facility; otherwise the term will be taken as zero. The second part of the Section 4 discusses the cost components of the objective function. As mentioned earlier, the objective of our optimization problem is to minimize the expected value of the network cost (both capital and operating) taken over all the scenarios. This minimization is achieved by assuming that each scenario k has a known probability of occurrence in practice denoted by PRk. The probabilities of the different demand scenarios are expressed as follows: NK X

obtained by multiplying the storage capital costs by the total number of new storage facilities. These costs are represented by the following objective function terms.

X

NSsjigk ¼

s;j;i

X ðn  1ÞWngtk

cg; t; k

(40)

n

where the first and second term of the left-hand-side of Eq. (40) denote the total number of production and storage facilities, respectively. Wngtk is a binary variable to determine if there are n  1 plants and storage facilities established and to exclude all other combinations (n ¼ 1, ., NPmax þ NSmax þ 1). To assure that only one combination of Wngtk is active, the following constraint should be written: X

Wngtk ¼ 1 cg; t; k

(41)

n

4.11.

Facility operating cost

The facility operating cost for all scenarios during the entire planning horizon is given as follows:

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X

FOC ¼

PRk

X

UPCpji Ppjigt þ

X

p

j;i;g;t;k

! USCsji Ssjigt þUFCi NFSigtk FCapi

s

(42) It must be noted that the last cost term of the above equation denotes the operating cost of the fueling stations.

4.12.

4.14.

Expected total network cost

The expected total daily cost of hydrogen network is minimized as follows:    1 FCC þ TCC minTDCexp ¼ min þ FOC þ TOC þ ESC NTP aCCF

(48)

Transportation operating cost

The transportation operating cost is categorized into: fuel, labor maintenance, and general costs. The daily fuel cost for all scenarios and time periods is equal to: P

FC ¼

PRk FPl

ðm  1ÞFELl TCapil ! 2LRgg0 Qilgg0 t

i;l;m;g;t;k

P

þ

PRk FPl

i;l;g;g0 ;t;k

X

þ

!

2LLg DMLmgt

PRk FPl

i;l;n;g;t;k

LC ¼

PRk DWl

i;l;m;g;t;k

þ

P

PRk DWl

i;l;g;g0 ;t;k

P

þ

PRk DWl

i;l;n;g;t;k

!

2LLg DTigtk Wngtk

(43)

ðn  1ÞFELl TCapil

DMLmgt

2LLg

ðm  1ÞTCapil

SPLl

2LRgg0

Qilgg0 t TCapil

!! þ LUTl !!

þ LUTl

SPRl

DTigtk Wngtk

2LLg

ðn  1ÞTCapil

SPLl

(44) !!

þ LUTl

The maintenance cost for all scenarios and time periods is equal to: P

MC ¼

PRk MEl

i;l;m;g;t;k

þ

P i;l;g;g0 ;t;k

P

þ

PRk MEl PRk MEl

i;l;n;g;t;k

!

2LLg DMLmgt ðm  1ÞTCapil !

2LRgg0 Qilgg0 t

(45)

TCapil 2LLg DTigtk Wngtk

!

ðn  1ÞTCapil

The general cost for all scenarios and time periods is equal to: P

GC ¼

PRk GEl

i;l;m;g;t;k

þ

P i;l;g;g0 ;t;k

P

þ

PRk GEl PRk GEl

i;l;n;g;t;k

DMLmgt

2LLg

ðm  1ÞTMALl TCapil Qilgg0 t TMARl TCapil ðn

2LRgg0 SPRl

DTigtk Wngtk  1ÞTMALl TCapil

SPLl

!! þ LUTl !!

þ LUTl 2LLg SPLl

(46) !!

þ LUTl

Finally, the total transportation operating cost is equal to the sum of all cost functions in Eqs. (43e46).

4.13.

The case study presented in our previous work [25,26] is revised here to capture uncertainty in hydrogen demand. The stochastic case study is also expanded to incorporate fueling stations. In this paper, three different hydrogen supply configurations are examined, which are summarized as follows:  Configuration 1: Production of liquid hydrogen in small, medium, and large plants via steam methane reforming, coal and biomass gasification, and water electrolysis technologies. Tanker trucks are used to deliver hydrogen to three different sizes of stationary storage facilities referred to as small, medium, and large liquid hydrogen tanks.  Configuration 2: Similar to the first scenario, however, both tanker trucks and railway tank cars will be used for delivery.  Configuration 3: Similar to the first scenario in terms of production, storage, and transportation technologies but fueling stations and secondary transportation are included. A key outcome of this exercise is the understanding of the data requirements for the application of hydrogen network design. In building the proposed model, a number of engineering-oriented methods were applied to validate the data as much as possible. These include comparison of similar data from alternative sources, comparison with petroleum supply chain data, first principles modeling, costing conversions and analysis, and thermodynamics and dimensional analysis. These attempts were helpful in generating a definitive data set that was used in our model. Due to the large amount of data, some of the input data required for the abovementioned configurations are described below. Additional cost data of the different hydrogen technologies can be found in the work of Almansoori and Shah [31]. It must be noted that some of the assumed data might be optimistic and does not seem closer to the evolution of the current hydrogen market. This is because the initial enthusiasm of introducing hydrogen vehicles has cooled down due to technical difficulties associated with the on-board hydrogen storage, the high cost of hydrogen delivery infrastructure, and the recent decline in the price of crude oil. Also the introduction of alternative fuels such as methanol, ethanol, and biodiesel has slowed down the progress of the hydrogen economy.

Primary energy sources cost

The cost of primary energy sources for all scenarios during the entire planning horizon is equal to: ESC ¼

Case study: Great Britain

FERl TCapil

The labor cost for all scenarios and time periods is equal to: P

5.

X k

PRk

X e;g;t

UICe Iegt þ

X e;g;g0 ;t

! UDCe LRgg0 QEeg0 gt

(47)

5.1.

Hydrogen demand

The penetration of hydrogen fuel cell vehicles for the three time periods was assumed to be 5%, 20%, and 50%, respectively. Due to the existence of uncertainty, the last two percentages were assumed possibly to fluctuate, deviating

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from the predicted path. This will result in nine scenarios each with different penetration percentages, as exhibited in Table 1. Since this study assumes deterministic behavior in the first time period, the penetration factor remains the same for all scenarios. The nine scenarios during the second time period were partitioned into a set of three distinct scenarios. Each of these clustered scenarios has the same penetration factor. For the third time period, each of the nine scenarios was given a different penetration factor (see Table 1). Based on these penetration percentages, the average daily demand of hydrogen during each scenario was estimated. This estimation was done by multiplying the corresponding percentages by the total equivalent demand, which was calculated at 100% market level. The values obtained in tonnes per day (t/d) are also listed in Table 1. The hydrogen demand of each grid for the nine scenarios over the first, second, and third time periods is tabulated in A.2 in Appendix A. It can be noted from Table A.2 that that the demand of hydrogen in each grid during the first time period is equal for all scenarios due to the deterministic assumption. However, for the second time period, only the same cluster of scenarios (k1ek3, k4ek6, and k7ek9) will have the same demand. On the other hand, the demand value of each grid and scenario during the third time period varies according to the penetration percentage assumed.

energy sources utilized by each type and size of the production technologies to generate a unit of hydrogen, i.e. rate of utilization (gepj). Moreover, the table lists the capital and the unit production costs (PCCpji & UPCpji) of the hydrogen production technologies mentioned earlier. During the early phase of the hydrogen economy, hydrogen will be supplied from existing sources such as petrochemical plants or petroleum refineries. In these refineries, hydrogen will be produced via steam methane reforming since it is currently the cheapest and most common method of production.

5.4.

The minimum and maximum storage capacities of liquid hydrogen storage facilities for three different sizes are shown in Table A.4. The table also shows the capital and unit storage costs for the different sizes of liquid hydrogen storage facilities. The storage facilities were designed to hold 10 days’ worth of stock of liquid hydrogen. As with the production plants, this study assumes a number of storage facilities to be available at the start of the planning horizon. These storage facilities will be located within the same grids as the production plants.

5.5. 5.2.

Primary energy sources

The initial average availability of primary energy sources in each grid was assumed based on the geographical location and proximity of feedstocks from the grid. The values are summarized in Table A.3. The cost values associated with distributing these energy sources throughout the hydrogen network are listed in Table A.4. These values are calculated by performing a detailed evaluation analysis on the availability of primary energy sources in Great Britain (see reference [31]). The evaluation analysis also includes an economic study to estimate the cost associated with handling and distributing the energy sources. Since this study allows for a small inventory of primary energy sources to be preserved, the safety stock factor was assumed to be 95%. This means that at least 5% of the feedstock must be kept in the respective grid for future utilization.

5.3.

Production plants

The minimum and maximum production capacities max ðPCapmin pji &PCappji Þ of each plant type with respect to size are given in Table A.4. Table also shows the amount of primary

Storage facilities

Transportation modes

The maximum allowable flow rate of liquid hydrogen by truck or rail is assumed to be equal to the maximum capacity of large plants (960 t/d). The minimum flow rate, however, is assumed to be equal to a fully-loaded transport unit. Additional parameters concerning the capital and operating costs estimation are listed in Table A.4. The table also shows that a few parameters depend mainly on whether hydrogen is distributed locally or regionally. These parameters include transport mode fuel economy, speed, and availability. The capital cost of truck transport consists of the tank unit cost, the truck cab cost and the undercarriage cost.

5.6.

Fueling stations

The hydrogen fueling station considered in this study is designed based on the average size of typical current petrol stations. The typical size of today’s petrol stations ranges from 100,000 to 250,000 gallons per month [6]. For the purpose of this analysis, liquid hydrogen based fueling stations will have a capacity of 5000 kg/d and a utilization rate of 90%. Since this study assumes the conversion of the current petrol fueling stations to hydrogen, no significant capital investment will be

Table 1 e Scenario penetration factor and average hydrogen demand for different time periods. Time period, t(yr)

t1 (2005e2010) t2 (2011e2016) t3 (2017e2022)

Scenario, k (%) & Demand, D (t/d) k1;D

k2;D

k3;D

k4;D

k5;D

k6;D

k7;D

k8;D

k9;D

05; 670 15; 2009 30; 4018

05; 670 15; 2009 40; 5358

05; 670 15; 2009 50; 6697

05; 670 20; 2679 40; 5358

05; 670 20; 2679 50; 6697

05; 670 20; 2679 60; 8037

05; 670 25; 3349 50; 6697

05; 670 25; 3349 60; 8037

05; 670 25; 3349 70; 9376

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required. However, there will be an operating cost which was estimated to be 0.39 $/kg [31].

6.

Results and discussion

For each of the examined hydrogen supply configurations, the network structure for only three demand scenarios over the three time periods of planning horizon will be presented. These demand scenarios are referred to as the “worst”, “middle”, and “best” paths. The corresponding paths are labeled as scenario number 1, 5, and 9, respectively. For each of the examined configuration, there will be 7 different hydrogen network structures over the first, second and third time periods. Despite the fact that the third time period consists of 9 different scenarios, only scenarios 1, 5, and 9 will be considered. Starting with the first hydrogen supply configuration, the network structures resulting from solving the stochastic MILP model are shown in Figs B.1eB.3 in Appendix B. As stated earlier, the demand of hydrogen was assumed to be deterministic during the first time period. This demand level is the consequence of 5% penetration of the transport market by hydrogen fuel cell vehicles. The network structure resulting from this penetration is shown in Fig. B.1. It is evident from the figure that the demand in most grids is met by medium-to-large steam methane reforming plants, which are assumed to exist prior to the hydrogen economy. Besides these large plants, grids with low demand, such as 2, 8, 12, 20, and 26, satisfy their needs by establishing small-scale steam reforming plants. The feedstock of these plants is obtained from the grid itself if this specific grid contains a natural gas terminal, or from nearby grids abundant with natural gas. The figure also shows that the over all demand of hydrogen is mainly fulfilled by three production sources located in grids 7, 17, and 29. This finding suggests that there is a high degree of centralization during the initial phase of the hydrogen market. During the second time period, the network structures for only three demand scenarios are examined. The first network structure, which is depicted in Fig. B.2 (a), assumes 15% penetration by hydrogen fuel cell vehicles. In this figure, the network structure remained similar to the one given in Fig. B.1 due to the minor increase in the demand level. To manage this increment, the production rate of the existing plants was raised slightly without installing new production facilities. However, when the demand reached 20%, only one small steam reforming plant was enough to cope with this demand addition (see Fig. B.2 (b)). The third network structure describes the demand at 25% of hydrogen fuel cell vehicles entering the current transport market. At this stage, more production plants were required to meet the corresponding demand. This can be demonstrated in Fig. B.2 (c) where five extra steam reforming plants were established. Of these plants, one small and one large plant were built in grid 14 to cover the demand of South Scotland and North England. Another large plant was built in grid 20 which satisfies the demand of neighbouring grids instead of importing hydrogen from grid 29. The last two small plants were built in grid 29 since this grid has the highest demand.

The network structures in Fig. B.3 demonstrate the demand level at 30, 50, and 70 percent, respectively. Out of the nine demand scenarios studied, these network structures were chosen because they represent the worst, middle and best paths during the third time period. When the demand grows to 30% (see Fig B.3 (a)), a new large steam methane reforming plant is installed in grid 16. This plant covers the demand of Wales and the South West of England instead of utilizing the plants in grid 17. Additionally, grid 14 has another large plant in order to meet the required demand. Moving to the middle network structure, it is interesting to note that the production sources were increased from five production nodes in Fig. B.3 (a) to eight in Fig B.3 (b). Hence, the hydrogen network started to become more decentralized as demand level increased. Also at this stage, building a coal gasification plant becomes attractive with respect to producing hydrogen via steam methane reforming due to the availability of large quantities of coal. This example is shown in grids 5 and 25 where each grid has a large-scale coal gasification plant. The feedstock of these plants was imported from nearby coal mines located at grids 7, 23 and 24. The last network structure describes the demand of hydrogen when it reaches 70%. As expected, satisfying this demand will lead to a solution with high a degree of decentralization (see Fig. B.3 (c)). The second hydrogen supply configuration studied in this study is related to transporting liquid hydrogen via tanker trucks and railway tank cars. As with the first supply chain configuration, only the network structures for demand scenarios 1, 5, and 9 over the three time periods will be outlined. These network structures are shown in Figs B.4eB.6, respectively. To avoid repetition, the network structures for the second configuration will not be analyzed in depth as was done with the first network configurations. However, the discussion will focus on the main factors that led to the differences between the single- and multimode network structures. The first factor behind this dissimilarity is the high storage capacity of railcars in comparison to tanker trucks. This implies that railcars would have fewer trips between the production sites and storage facilities. As a result, railcars could be dispatched to customers even at low-tomoderate utilization tank capacity, whereas trucks will be sent only at full tank capacity. The second factor is the low operating transportation cost of railcars. Thus, this would make long delivery distances more favored. In a multi-mode network, truck will be utilized only for short delivery distances. Examining the network structures of the single- and multimode cases shows that the type of transportation modes has a great affect on the arrangement of production plants. In the single-mode network, production plants were usually located in a way that minimized the delivery distance between production sources and customers. Also plant production will be increased until demand cannot be met by existing capacity. On the other hand, these two issues are more flexible in the multi-mode network since delivery distance is not a critical factor due to the cheap transport cost. The previous discussion can be illustrated by looking at Fig. B.2 and B.5 (c). Fig. B.2 (c) shows that there is no production plant in grid 5 because grid 7 together with grid 14 cover most parts of Scotland with the minimum possible delivery distances. However, in Fig. B.5 (c), grids 5 and 14 provide neighboring grids with hydrogen even though this results in longer delivery distances.

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Table 2 e Summary of total cost and computational results for the studied network configurations. Scenario, k

k1 (6.25%) k2 (12.50%) k3 (6.25%) k4 (12.50%) k5 (25.00%) k6 (12.50%) k7 (6.25%) k8 (12.50%) k9 (6.25%) Total cost Number of constraints Number of continuous variables Number of integer variables Optimality gap (%) CPU time (d)

Configuration 1

2

3

0.39 0.99 0.59 1.09 2.73 1.46 0.72 1.54 0.87 10.39 379,820 200,980 77,724 6 3

0.39 0.99 0.60 1.03 2.47 1.44 0.66 1.55 0.88 10.02 563,658 231,886 108,630 3 3

1.29 2.19 1.88 2.25 4.05 3.03 2.17 3.20 2.68 12.21 430,336 202,060 168,606 9 3

30 25 Scenario probability (%)

The last network configuration addressed in this chapter is the extension of the first network configuration to account for fueling stations and secondary distribution of hydrogen. The network structures for this case study will not be shown since they resemble the ones given in Figs B.1eB.3. Only the number of fueling stations established in each grid is given here. Again, the obtained results are shown for scenarios 1, 5 and 9 over the examined three time periods (see Table A.5). The tabulated figures do not include the number of distributed plants. It can be seen from Table A.5 that grids with low demand, such as 8, 12, and 16, have no fueling stations due to the presence of distributed plants. These plants replace the need for installing fueling stations since they operate as fueling source. However, as the demand of these grids increased, new fueling stations were built due to the failure of existing plants to cope with the increased demand. In addition, the table shows that the number of fueling stations is dependent upon the demand of individual grids. Therefore, grids with a high demand level will have a large number of fueling stations. For the three examined HSC configurations, the average daily cost for the nine scenarios over the entire planning horizon is summarized in Table 2. The table also shows the expected total daily cost of the network under all demand scenarios. It can be seen from the table that the middle scenario (k5) has the highest cost. This is because the middle scenario was assumed to have the highest probability value, as indicated by the values within the pretenses in Table 2. This assumption was based on the fact that the demand trajectory is expected to follow this path during the dawn of the hydrogen economy. The studied models were formulated as MILP problems and solved using GAMS with CPLEX v9.0 code. A Pentium 4, 1.8 GHz Dell machine was used to execute the run. The computational results of these configurations are also summarized in Table 2. Although the model has a large dimension due to the introduction of demand uncertainty, the optimality gap and time required for solving these configurations are promising.

20 15 10 5 0

Total daily cost ($/d)

Fig. 2 e Cost of hydrogen network for the base case.

6.1.

Risk analysis

A risk analysis was conducted to study the effect of demand uncertainty in the outcomes of the total network cost. The analysis would also describe the distribution of the cost profile for all demand scenarios. The shape of this profile will determine the degree of risk since a wider distribution means a more risky solution. To perform the analysis, the first configuration was chosen as the base case for this study. Then, the probability of demand scenarios occurring during the network’s lifetime was plotted versus the average total daily cost at each scenario, as exhibited in Fig. 2. It can be noticed from Fig. 2 that the cost profile has a normal distribution. The middle histogram corresponds to scenario 5 which has the highest probability of occurrence, i.e. 25%. The average total daily cost of this scenario is about 11 million $/d. The worst-case scenario for this set of data has a cost of 6 million $/d with a probability of 6.25% while the best-case scenario has a cost of 14 million $/d with the same probability of occurrence. The last two cases represent scenarios 1 and 9, respectively. It can be inferred from Fig. 2 that the width of the cost profile is reasonable despite the wideness of the demand range. In order to arrive to a sensible meaning, the average total cost of the hydrogen network for each scenario was converted to $/t of hydrogen delivered. This conversion was carried out by calculating the average daily demand of hydrogen for each scenario over the planning horizon. Then, these values were

Table 3 e Average total cost of hydrogen network. Scenario, k k1 k2 k3 k4 k5 k6 k7 k8 k9

Network cost ($/t)

Network cost ($/km)

2824 2964 3002 3038 3072 3074 3114 3214 3262

0.180 0.189 0.191 0.193 0.195 0.196 0.198 0.204 0.208

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30

Scenario probability (%)

25 20 15 10 5 0

0.180

0.189

0.191

0.193

0.195

0.196

0.198

0.204

0.208

Unit cost ($/km)

Fig. 3 e Cost of hydrogen network per kilometer. divided by the daily cost to obtain the cost per tonne delivered for each scenario, as exhibited in Table 3. Finally, the average network cost was expressed in $/km to compare it to the cost of the current petrol supply network (see Table 3). It must be noted that the assumptions used to estimate the figures in Table 3 can be found in the work of Almansoori and Shah [31]. To visualize the shape of the cost histogram, the probability of each scenario was plotted versus the cost per kilometer, as shown in Fig. 3. From Fig. 3, the network cost for the middle-case scenario is 0.208 $/km. This value is compared to the cost of the existing petrol network. According to our calculation, the cost of a petrol network is 0.107 $/km [31]. Using the average annual distance travelled per vehicle, the cost of hydrogen and petrol infrastructures were estimated to be 3447 and 1780 $/yr/vehicle, respectively. It is evident from these values that the cost of a hydrogen infrastructure is roughly twice that for untaxed petrol. The main reasons behind this are the high costs of hydrogen production, storage, and distribution technologies. However, it is expected that in the near future the cost of hydrogen technologies will decrease enough to compete with its opponent. Despite the soaring cost of a hydrogen infrastructure, building such an infrastructure would improve the urban air quality, mitigate climate change, and reduce foreign oil imports.

7.

Conclusion

This paper addresses the effect of uncertainty on the design and operation of the future HSC network. A scenario-based approach is used to capture the uncertainty in demand over a long-term planning horizon. This uncertainty is represented by a multi-stage stochastic optimization problem formulated as an MILP model. The first-stage is assumed to have a deterministic behavior while the second and third stages are subject to demand variations. For each demand scenario, the network structure is revealed and its average total daily cost is determined. Also, the expected cost of the HSC network over all demand scenarios is resolved. In addition, the model accommodates fueling stations and hydrogen distribution logistics as well as a number of other strategic decisions. The feasibility of the derived models is tested by using Great Britain as the backdrop for our analysis. As a result, the

optimal network structures for three different HSC configurations are outlined. In all of these network configurations, steam methane reforming technology is mostly chosen as a means of producing hydrogen due to its economical benefits. In the case of natural gas shortages, other production technologies such as coal gasification and water electrolysis are utilized because of their local availability. These options are more profitable than importing natural gas from foreign countries. The size of these plants varied according to the local demand of each grid. For instance, during the early phase of hydrogen introduction distributed forecourt plants are established for the most part, however as demand reached its saturation point more centralized facilities emerged. The results obtained also show that the type of transportation mode has a great effect on the structure of HSC network. For example, the transport of hydrogen via trucks only resulted in short transportation links with high utilization capacities. On the other hand, allowing both rail and truck for hydrogen delivery resulted in longer transportation links with low-tohigh flow rates. It has been shown from the examined network configurations that the consideration of demand uncertainty may lead to significant changes in the structure and cost of the optimal supply chain network. Due to this a risk analysis is carried out to evaluate the degree of risk during the existence of uncertainty. The solution found suggests a reasonable cost distribution profile despite the wide range of demand.

Appendix. Supplementary data Supplementary data related to this article can be found online at doi:10.1016/j.ijhydene.2011.11.091.

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