Available online at www.sciencedirect.com
ScienceDirect
Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy Procedia 142 Energy Procedia 00(2017) (2017)2072–2079 000–000 www.elsevier.com/locate/procedia
9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
Building an optimal hydrogen transportation system for mobility, International Symposium on District Heating and Cooling focusThe on15th minimizing the cost of transportation via truck Assessing feasibility of using heatDalmazzone demand-outdoor a, b Aminthe Lahnaoui *, Christina Wulf athe , Didier temperature function for a long-term district heat demand forecast Forschungszentrum Jülich, Institute of Energy and Climate Research - Systems Analysis and Technology Evaluation (IEK-STE), a
D-52425 Jülich, Germany
a a des Maréchaux, 91120 ParisTech, boulevard PALAISEAU, Francec, O. Le Correc I. Andrića,b,c*,ENSTA A. Pina , P.828, Ferrão , J. Fournierb., B. Lacarrière b
a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Abstract Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
The approach developed aims to identify the methodology that will be used to deliver the minimum cost for hydrogen infrastructure deployment using a mono-objective linear optimisation. It focuses on minimizing both capital and operation costs of the hydrogen Abstract transportation based on transportation via truck which represents the main focus of this paper and a cost-minimal pipeline system in the case of France and Germany. District networks are commonly addressed in the as onetheofhydrogen the most production effective solutions for decreasing the The paperheating explains the mathematical model describing theliterature link between via electrolysers and the greenhousefor gasmobility emissions from The the building sector. These require high investments are returned through the the heat distribution needs. main parameters and systems the assumed scenario frameworkwhich are explained. Subsequently, sales. Due toofthe changed conditions building renovation policies, as heat demand in the future could decrease, transportation hydrogen viaclimate truck using differentand states of aggregation is analysed, well as the transformation and storage of prolonging the is investment return period.a linear programming aiming to minimize the sum of costs of hydrogen transportation hydrogen. This used finally to build The main of this paper to assess the feasibilitywithin of using heat demand – outdoor temperature function for heat demand between thescope different nodes andistransformation/storage thethe nodes. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 vary in both construction ©buildings 2017 Thethat Authors. Published by Elsevierperiod Ltd. and typology. Three weather scenarios (low, medium, high) and three district renovation under scenarios were developed (shallow,committee intermediate, deep). To estimate Conference the error, obtained heatEnergy. demand values were Peer-review responsibility of the scientific of the 9th International on Applied compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showedinfrastructure, that when only weather change considered, the margin of optimisation error could be acceptable for some applications Keywords: Hydrogen, transportation, storage, is compression, liquefaction, cost (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.The Introduction decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On future the other function intercept 7.8-12.7% per decade (depending on the One of the big challenges of the of hand, our energy systems is increased to find a for balance between the increasing demand coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and on energy, the limited conventional resources and the necessity to lower the carbon emissions. This challenge is improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding author. Tel.: +49-2461-61-3275; fax: +49-2461-61-2540. Cooling. E-mail address:
[email protected].
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy. 10.1016/j.egypro.2017.12.579
2
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
2073
particularly apparent in the transportation sector. In the one hand, this sector shows a high energy demand, in the case of the European Union (EU), it needed 32% of the final energy demand in 2014 [1]. On the other hand, the expected further increase of transportation intensifies the dependency on conventional fuel accompanied by more carbon emissions as well. In fact, the transportation sector has been the only one with increasing emissions by 22% in the EU [1] during the last 25 years. To change these trends, the EU pushes towards decarbonising the transportation sector by fixing the threshold of oil dependency in transportation in 2050 to 70% less compared to 2008 [2]. The use of low carbon hydrogen in Fuel Cell Electric Vehicles (FCEV) is one of the promising alternatives to conventional fuels. Still, the main barrier restraining its deployment is the need to install and define an adequate infrastructure. Under this problematic, this study aims to provide an approach to identify the minimum cost for hydrogen infrastructure deployment using a mono-objective linear optimisation. The optimization of a possible future hydrogen infrastructure has been the subject of research in different studies. However, most of the existing analyses focuses on one way of hydrogen transportation, either via trucks or pipeline system [3],[4]. In cases, in which all transportation modes were taken into account, the geographical representation was omitted by restraining the study to a decomposition into grids [5] or the geographical visualization was limited to one region [6], [7] or one country [8], [9]. This paper presents the methodology allowing to build an optimum transportation network via trucks at different states of aggregation (pressure, aggregate condition etc.), including as well transformation (liquefaction, compression) and storage. This represents a primary study that will be completed by a second transport option via an endogenously optimized pipeline network. The approach will be applied for France and Germany to highlight the different European energy strategies, but also to investigate a potential collaboration in developing hydrogen infrastructure like the Scandinavian common strategy [10]. The overall methodology is presented in the first part introducing the different notations. Then the four model components are presented which includes demand estimation, hydrogen production, conversion of hydrogen for transportation and storage modes. The model calculation is then presented as a mixed-integer linear program by defining the objective function and the constrains associated with. Finally, a conclusion is conducted to show how this optimal road transportation will be associated to a pipeline network in order to present results for France and Germany.
Nomenclature ×𝑖𝑖 ,×𝑗𝑗 × 𝑆𝑆 ,× 𝑆𝑆′ ×𝑦𝑦 ×0 ,×𝑓𝑓
nodes location Hydrogen state of aggregation year initial and final condition
𝐿𝐿 driving distance 𝑇𝑇𝑙𝑙/𝑢𝑢 Loading and unloading time 𝑚𝑚𝐻𝐻2 truck capacity 𝑛𝑛𝑟𝑟𝑟𝑟 annual number of truck round trips 𝑛𝑛 𝑇𝑇 annual number of trucks 𝑆𝑆𝑎𝑎 average truck speed 𝑛𝑛𝑑𝑑 number of truck drivers 𝐹𝐹𝑝𝑝 fuel price 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐 truck cab cost 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 cab capital recovery factor 𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢𝑢𝑢 truck undercarriage cost 𝑇𝑇𝑇𝑇𝐻𝐻2 tube cost 𝐶𝐶𝐶𝐶𝐶𝐶𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇undercarriage and tube CRF 𝑇𝑇𝐶𝐶𝑑𝑑 driver wage 𝑇𝑇𝑇𝑇𝑇𝑇 truck capital cost
𝑆𝑆𝑆𝑆 𝑄𝑄 𝑃𝑃 𝑝𝑝 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 𝐶𝐶𝐶𝐶𝐶𝐶 CF 𝑐𝑐𝑇𝑇 𝐶𝐶𝐶𝐶𝑐𝑐 𝐶𝐶𝐶𝐶𝐿𝐿 𝐶𝐶𝐶𝐶𝑆𝑆 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇 𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝐹𝐹 𝑆𝑆𝑆𝑆𝑆𝑆 𝑂𝑂𝑂𝑂𝑡𝑡 𝑂𝑂𝑂𝑂𝑓𝑓 𝑂𝑂𝑂𝑂𝑠𝑠
Stored flow flow transported flow produced hydrogen installed capacity Maximum demand flow Minimum demand flow capital recovery factor capacity factor cost of liquefaction or compression work capital cost of compression capital cost of liquefaction capital cost of storage transportation capital cost transportation operation cost facility capital cost facility operation cost storage capital cost transportation operations and maintenance facility 𝑂𝑂&𝑀𝑀 operations and maintenance storage 𝑂𝑂&𝑀𝑀 operations and maintenance
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
2074
3
2. Methodology The problem focuses on the minimal cost of deploying hydrogen infrastructure under a given hydrogen production and consumption. For the demand estimation, it will be based on a European scenario giving the share of hydrogen in mobility. A fixed production will be derived from electrolysis mainly form the excess wind energy in Germany and France, and nuclear power plants in the case of France. The remaining hydrogen need will be imported. Once these input parameters are fixed, the minimal cost will be found by linking the different hydrogen production and distribution points taking into account the intermediate storage and transformation cost. As the hydrogen transportation via trucks fundamentally rely on the already existing road network. The network will be a part of a graph 𝐺𝐺(𝑁𝑁, 𝑽𝑽) of nodes 𝑁𝑁 and vectors 𝑽𝑽 that link this nodes [11]. The nodes include, production nodes 𝑃𝑃 ϲ 𝑁𝑁, with known location and production flow 𝑝𝑝𝑖𝑖 and with hydrogen at initial condition 𝑆𝑆0 (including initial state, and pressure in case of a gaseous state as well as temperature). By opposition, a set of distribution nodes 𝐷𝐷 ϲ 𝑁𝑁, with known location and the flow demand 𝑑𝑑𝑖𝑖 and with hydrogen at final condition 𝑆𝑆𝑓𝑓 . Storage nodes 𝑆𝑆𝑆𝑆 ϲ 𝑁𝑁 will be added if needed, where hydrogen will be stored at different conditions 𝑆𝑆. At a node 𝑖𝑖 ∈ 𝑁𝑁 the cost of changing a stored flow 𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆 of hydrogen from state S to another state S′ is given by (1): 𝐶𝐶𝑖𝑖𝑆𝑆𝑆𝑆′ ∗ 𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆
(1)
𝐶𝐶𝑖𝑖𝑖𝑖𝑆𝑆 ∗ 𝑄𝑄𝑖𝑖𝑖𝑖𝑆𝑆
(3)
The total cost is presented as a product of a cost function 𝐶𝐶𝑖𝑖𝑆𝑆𝑆𝑆′ independent from the flow 𝑆𝑆𝑆𝑆𝑖𝑖𝑇𝑇 to keep the problem linear. As the cost is considered always positive, having a conversion that releases energy means that the cost ′ ′ associated to it is null (i.e ∀𝑖𝑖 ∈ 𝑁𝑁 𝑖𝑖𝑖𝑖 𝐶𝐶𝑖𝑖𝑆𝑆𝑆𝑆 = 0 𝑡𝑡ℎ𝑒𝑒𝑒𝑒 𝐶𝐶𝑖𝑖S S > 0). The cost of transported hydrogen 𝑄𝑄𝑖𝑖𝑖𝑖𝑆𝑆 from a Node i to a node j via road transportation as a physical state S can be defined as well as a product of a cost function per quantity of hydrogen transported 𝐶𝐶𝑖𝑖𝑖𝑖𝑆𝑆 and the hydrogen flow:
Fig. 2. Example of transportation network with the cost associated to the links and the nodes 3. Input parameters The hydrogen demand and production estimations are mandatory to determine the framework of the hydrogen penetration scenarios. The first one is based on the FCEV car park projection while the second one is based on the excess of electricity calculated from the projected installed nuclear power plant and wind installed capacity. Subsequently, the cost components of trucks and the underlying methodology are explained to help define the cost
4
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
2075
function of transportation 𝐶𝐶𝑖𝑖𝑖𝑖𝑆𝑆 . In the same way, compression and liquefaction of hydrogen define the cost function of transformation 𝐶𝐶𝑖𝑖𝑆𝑆𝑆𝑆′ . 3.1. Demand and production estimation
The share of new FCEV is considered equal for both France and Germany to 2.4 % by 2030 and 28.5 % by 2050 in case of high penetration of hydrogen [12] and linear between the two years. FCEV were considered to have a driving range 𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 of 4-6 kg hydrogen per 500 km [13]. This range will define the annual hydrogen demand 𝑑𝑑𝑦𝑦 limited between a maximum and minimum value and defined by equation (4): (4)
𝑑𝑑𝑦𝑦 (𝑖𝑖) = 𝑃𝑃𝑃𝑃𝑃𝑃𝑦𝑦 (𝑖𝑖) ∗ 𝐷𝐷𝑡𝑡𝑟𝑟𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 (𝑦𝑦) ∗ 𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ∗ 𝑝𝑝𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 (𝑦𝑦)
𝐷𝐷𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 is the yearly average distance in km travelled by a person deduced from the number of population Popy(i) and the total travelled distance Dtravel(y). The EUROPOP, the main scenario of European population growth projection, was used to project the need of transportation in the coming ten to 35 years.
250
2500
200
2000
150
1500
100
1000
50
500
0
2030
2035
2040
2045
2050
0
in thousand tonnes per year
Total wind installed capacity in GW
The production of hydrogen, reflects how different the strategies to implement hydrogen infrastructure can be depending on the potential resources and long term energy strategies. Production of hydrogen is based on the use of excess electricity from wind energy as a first choice, nuclear for France as a second choice and import finally. For that the location and technical data of the different wind farms and nuclear plants [14] were gathered and compared to the total installed capacity per technology and per country [14]. To determine the annual electricity generation, the same ratio of electricity generation in 2016 [15] to the installed capacity [14] is taken. In case of Germany that corresponds to 17.75 % and in France, it corresponds to 18.51 % for wind and 69.1 % for nuclear.
Fig. 2. Total wind installed capacity and hydrogen demand in France and Germany between 2030 and 2050
3.2. Transportation via trucks The cost of transportation depends on the distance driven 𝐿𝐿𝑖𝑖𝑖𝑖 and the amount transported 𝑄𝑄𝑖𝑖𝑖𝑖𝑆𝑆 of a hydrogen flow at state 𝑆𝑆 between two nodes (𝑖𝑖, 𝑗𝑗) ∈ 𝑁𝑁 2 When transporting hydrogen via trucks to the site, the driver will wait till the truck is unloaded. In this case there is an additional total load and unload time 𝑇𝑇𝑙𝑙/𝑢𝑢 𝑆𝑆 that depends on the hydrogen state 𝑆𝑆. It is considered that a truck of capacity 𝑚𝑚𝐻𝐻2 𝑆𝑆 transporting hydrogen at state 𝑆𝑆 is used to its maximum annual capacity. This allows using only one number of round trips 𝑛𝑛𝑟𝑟𝑟𝑟 defined using its annual availability, average speed 𝑆𝑆𝑎𝑎 and an annual number of trucks 𝑛𝑛 𝑇𝑇 :
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
2076
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
𝑛𝑛𝑟𝑟𝑟𝑟 𝑖𝑖𝑖𝑖 = ⌊ 2∗𝐿𝐿𝑖𝑖𝑖𝑖 𝑆𝑆𝑎𝑎
+𝑇𝑇𝑙𝑙/𝑢𝑢𝑆𝑆
⌋+1;
𝑆𝑆 𝑄𝑄𝑖𝑖𝑖𝑖
𝑛𝑛 𝑇𝑇 𝑖𝑖𝑖𝑖 = ⌊
𝑚𝑚𝐻𝐻2 𝑆𝑆 ∗ 𝑛𝑛𝑟𝑟𝑟𝑟 𝑖𝑖𝑖𝑖
5
(5)
⌋+1
The different parameters of the truck including the different capital costs of a truck ( 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢𝑢𝑢 and 𝑇𝑇𝑇𝑇𝐻𝐻2 𝑆𝑆 ) and the capital recovery factors [16] (𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 and 𝐶𝐶𝐶𝐶𝐶𝐶𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 ) were those of compressed truck at 165.5 bar, 250 bar, 350 bar, 500 bar and 540 bar, plus a liquid and liquid organic hydrogen carrier truck at atmospheric pressure. 3.3. Conversion and storage mode The annual cost work of transformation from state S to S’ 𝑐𝑐𝑇𝑇 (𝑆𝑆, 𝑆𝑆 ′ ) is the product of the capacity factor CF [16], the unit electrical energy cost and the work performed 𝑊𝑊̇𝑚𝑚 . In case of compression, the work is considered 70 % of the adiabatic work of a compressor of 5 stages delivering hydrogen up to 720 bar [17]. It is considered constant and equal to 12.5 kWh/kg in case of liquefaction. The capital cost of compression is determined using a sizing factor to adjust from the baseline size 𝑆𝑆𝑏𝑏,1 and the baseline pressure 𝑃𝑃𝑏𝑏 at a cost 𝐶𝐶𝑏𝑏,1 [18]: 𝑊𝑊̇𝑚𝑚∗𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆
𝐶𝐶𝐶𝐶𝑐𝑐 = 𝐶𝐶𝑏𝑏,1 ∗ 𝑆𝑆𝑏𝑏,1 ∗ (
𝐶𝐶𝐶𝐶∗8760∗𝑆𝑆𝑏𝑏
0.8
)
𝑃𝑃
∗( ) 𝑃𝑃𝑏𝑏
0.18
(6)
The same method was used to determine the capital cost for liquefaction 𝐶𝐶𝐶𝐶𝐿𝐿 and storage 𝐶𝐶𝐶𝐶𝑆𝑆 : 𝐶𝐶𝐶𝐶𝐿𝐿 = 𝐶𝐶𝑏𝑏,𝐿𝐿 ∗ 𝑆𝑆𝑏𝑏,𝐿𝐿 ∗ (
𝐿𝐿
𝑆𝑆𝑏𝑏,𝐿𝐿
0.65
)
; 𝐶𝐶𝐶𝐶𝑆𝑆 = 𝐶𝐶𝑏𝑏 ∗ 𝑆𝑆𝑏𝑏 ∗ (
𝑃𝑃𝑏𝑏
𝑆𝑆𝑖𝑖𝑇𝑇 𝑃𝑃 𝑆𝑆𝑏𝑏
)
0.75
𝑃𝑃
∗( ) 𝑃𝑃𝑏𝑏
0.44
(7)
Where the base case size for storage is chosen corresponding to the one at high pressure of 540 bar. L is the net production accounting from the losses, defined using the boil-off rate 𝐵𝐵𝐵𝐵𝐵𝐵 and the storage time 𝑆𝑆𝑆𝑆 [18]. 4. Model calculation
The problem is formulated as a mixed-integer linear problem expressed by equation (8) 𝐴𝐴𝐴𝐴 ≥ 𝑏𝑏 (8) min 𝑐𝑐 𝑇𝑇 𝑥𝑥 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑡𝑡𝑡𝑡 { 𝑥𝑥 ≥ 0 𝑥𝑥 ∈ ℕ𝑛𝑛 Where the two variables 𝑐𝑐 𝑇𝑇 correspond to the transposition of the vector 𝑐𝑐 representing all the cost function (of transportation and conversion) and the vector 𝑥𝑥 corresponds to the flows transported and stored. 4.1. Objective function
The aim of the proposed model is to minimize both capital and operation costs of the hydrogen transportation. The former are costs associated with the establishment of storage and transformation facilities and transportation links, and do not take into account the establishment of production plants. To compare investments with different economical live times the net present value (NPV) method is used [9] allowing to write the annual capital cost as a sum of CRF [16] as different costs (𝐶𝐶𝐶𝐶, 𝑂𝑂&𝑀𝑀, 𝐹𝐹𝐹𝐹 and 𝐿𝐿𝐿𝐿): 𝐶𝐶𝑎𝑎𝑎𝑎 = 𝐶𝐶𝐶𝐶 ∗ 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝑂𝑂&𝑀𝑀 + 𝐹𝐹𝐹𝐹 + 𝐿𝐿𝐿𝐿
(9)
𝑇𝑇𝑇𝑇𝑇𝑇 𝑆𝑆 ∗ (𝐶𝐶𝐶𝐶𝐶𝐶 + 𝑂𝑂𝑂𝑂) = (𝐶𝐶𝐶𝐶𝐶𝐶𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 + 𝑂𝑂𝑂𝑂) ∗ (𝑇𝑇𝑇𝑇𝐻𝐻2 𝑆𝑆 + 𝑇𝑇𝑇𝑇𝑢𝑢𝑢𝑢𝑢𝑢 ) + (𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 + 𝑂𝑂𝑂𝑂) ∗ 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐
(10)
The different components of one truck annual capital cost are defined in equations (10):
𝐹𝐹𝐹𝐹 = 2 ∗ 𝐹𝐹𝑝𝑝 ∗ 𝐿𝐿𝑖𝑖𝑖𝑖 ;
𝐿𝐿𝐿𝐿 = 𝑛𝑛𝑑𝑑 ∗ 𝑇𝑇𝐶𝐶𝑑𝑑 ∗ (
2.𝐿𝐿𝑖𝑖𝑖𝑖 𝑆𝑆𝑎𝑎
+ 𝑇𝑇𝑙𝑙/𝑢𝑢 𝑆𝑆 )
(10)
6
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
2077
The 2 factor in 𝐹𝐹𝐹𝐹 and 𝐿𝐿𝐿𝐿 come from the roundtrip. For the average speed considered, only one driver is needed below 450 km that we refer to 𝐿𝐿𝑙𝑙𝑙𝑙𝑙𝑙 . The annual cost will be equal then to the number of trucks multiplied by the annual cost of one truck, and to keep the problem linear the floor function is defined via the in-equation, allowing writing the annual number of trucks at a state 𝑇𝑇 between two nodes 𝑖𝑖 and 𝑗𝑗 constrained.
The capital cost of compression and liquefaction and storage in the other hand are defined as a power function of the hydrogen flow. To write the transformation cost function 𝐶𝐶𝑖𝑖𝑆𝑆𝑆𝑆′ independent from the stored hydrogen the work [19] is used to demonstrate that the problem (11) is equivalent to (12) on a range [𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 ]: min 𝛽𝛽(𝑆𝑆) ∗ [𝑆𝑆𝑖𝑖𝑆𝑆 ]𝛼𝛼(𝑆𝑆)
(11)
min 𝛽𝛽(𝑆𝑆) ∑𝑛𝑛 1 [𝑓𝑓𝑖𝑖 (𝑥𝑥,𝛼𝛼(𝑆𝑆))∗𝜒𝜒[𝑥𝑥
𝑖𝑖−1 ,𝑥𝑥𝑖𝑖 ]
1 𝑥𝑥∈ [𝑥𝑥𝑖𝑖−1 ,𝑥𝑥𝑖𝑖 ] 𝜒𝜒[𝑥𝑥 ,𝑥𝑥 ] (𝑥𝑥)={ 0 𝑖𝑖𝑖𝑖 𝑛𝑛𝑛𝑛𝑛𝑛 𝑖𝑖−1 𝑖𝑖
(𝑥𝑥)]
(12)
With 𝛼𝛼(𝑆𝑆) and 𝛽𝛽(𝑆𝑆) depending on the type of transformation and storage and 𝑓𝑓𝑖𝑖 (𝑥𝑥) is the tangent line approximation on a segments [𝑥𝑥𝑖𝑖−1 , 𝑥𝑥𝑖𝑖 ] at the point ((𝑥𝑥𝑖𝑖−1 + 𝑥𝑥𝑖𝑖 )⁄2, 𝑓𝑓𝑖𝑖 ((𝑥𝑥𝑖𝑖−1 + 𝑥𝑥𝑖𝑖 )⁄2)).
4.2. Constrains
Assuming a hydrogen flow production 𝑃𝑃𝑖𝑖 at initial condition 𝑆𝑆0 from a total installed capacity 𝑝𝑝𝑖𝑖 and local consumption 𝑑𝑑𝑖𝑖 at final condition 𝑆𝑆𝑓𝑓 , the total production [consumption] should be equal to local consumption [production] and total flow leaving [entering] the node, allowing to write: 𝑃𝑃𝑖𝑖
𝑆𝑆0
𝑆𝑆
= 𝑑𝑑𝑖𝑖 𝑓𝑓 + ∑𝑗𝑗∈𝑁𝑁 ∑𝑆𝑆 𝑄𝑄𝑖𝑖𝑖𝑖𝑆𝑆
∀𝑖𝑖 ∈ 𝑃𝑃;
𝑆𝑆
𝑆𝑆0
𝑑𝑑𝑖𝑖 𝑓𝑓 = 𝑃𝑃𝑖𝑖
+ ∑𝑗𝑗∈𝑁𝑁 ∑𝑆𝑆 𝑄𝑄𝑗𝑗𝑗𝑗𝑆𝑆
∀𝑖𝑖 ∈ 𝐷𝐷
In a storage node all the flows entering the node at a condition 𝑆𝑆 are leaving it at condition 𝑆𝑆 ′ :
𝑆𝑆 ∑𝑗𝑗∈𝑁𝑁 ∑𝑇𝑇 𝑄𝑄𝑗𝑗𝑗𝑗𝑆𝑆 = ∑𝑘𝑘≠𝑗𝑗 ∑𝑇𝑇 𝑄𝑄𝑖𝑖𝑖𝑖 = ∑𝑇𝑇 𝑆𝑆𝑖𝑖𝑆𝑆
∀𝑖𝑖 ∈ 𝑆𝑆𝑆𝑆
(13)
(14)
From the definition (5) of truck numbers and the definition of the floor function ⌊𝑥𝑥⌋ ≤ 𝑥𝑥 < ⌊𝑥𝑥⌋ + 1, a constrain can be added. The limited number of drivers apply a condition on the distance that is shown in equation (15) 0 < 𝑛𝑛 𝑇𝑇 𝑆𝑆 𝑖𝑖𝑖𝑖 −
𝑚𝑚𝐻𝐻2
2∗𝐿𝐿𝑖𝑖𝑖𝑖 +𝑇𝑇 𝑙𝑙 𝑆𝑆 𝑆𝑆𝑎𝑎 𝑢𝑢 𝑆𝑆 ∗𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
𝑇𝑇 𝑄𝑄𝑖𝑖𝑖𝑖 ≤ 1;
𝐿𝐿𝑖𝑖𝑖𝑖 ≤ 𝐿𝐿𝑙𝑙𝑙𝑙𝑙𝑙
(15)
𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 (i) ≤ 𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆 ≤ 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 (𝑖𝑖)
(16)
Finally the production can be restrained by a lower limit and the stored capacity by the range demand: 𝑆𝑆
𝛼𝛼 ∗ 𝑝𝑝𝑖𝑖 0 ≤ 𝑃𝑃𝑖𝑖
5. Conclusion
𝑆𝑆0
𝑆𝑆
≤ 𝑝𝑝𝑖𝑖 0 ;
By combining the cost given in the objective function, the total annual cost to minimize is the sum of all costs including 𝑇𝑇𝑇𝑇𝑇𝑇, 𝑇𝑇𝑇𝑇𝑇𝑇, 𝐹𝐹𝐹𝐹𝐹𝐹, 𝐹𝐹𝑂𝑂𝐶𝐶, and 𝑆𝑆𝑆𝑆𝑆𝑆 defined in (17) and subject to all the constraints by (13), (14), (15) and (16).
𝑆𝑆 𝑆𝑆 ∗ 𝑇𝑇𝑇𝑇𝑇𝑇 𝑆𝑆 ∗ 𝐶𝐶𝐶𝐶𝐶𝐶; 𝑻𝑻𝑻𝑻𝑻𝑻 = ∑(𝑖𝑖,𝑗𝑗)∈𝑁𝑁2 ∑𝑆𝑆 𝑛𝑛 𝑇𝑇 𝑖𝑖𝑖𝑖 ∗ (𝐹𝐹𝐹𝐹 + 𝐿𝐿𝐿𝐿 + 𝑇𝑇𝑇𝑇𝑇𝑇 𝑆𝑆 ∗ 𝑂𝑂𝑂𝑂𝑡𝑡 ) 𝑻𝑻𝑻𝑻𝑻𝑻 = ∑(𝑖𝑖,𝑗𝑗)∈𝑁𝑁2 ∑𝑆𝑆 𝑛𝑛 𝑇𝑇 𝑖𝑖𝑖𝑖
(17)
𝑭𝑭𝑭𝑭𝑭𝑭 = ∑𝑖𝑖∈𝑁𝑁 ∑𝑆𝑆,𝑆𝑆′ 𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆 ∗ 𝐹𝐹𝐹𝐹𝐹𝐹𝑖𝑖𝑆𝑆𝑆𝑆′ ∗ 𝐶𝐶𝐶𝐶𝐶𝐶; 𝑭𝑭𝑭𝑭𝑭𝑭 = ∑𝑖𝑖∈𝑁𝑁 ∑𝑆𝑆,𝑆𝑆′ 𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆 ∗ [𝐹𝐹𝐹𝐹𝐹𝐹𝑖𝑖𝑆𝑆𝑆𝑆′ ∗ 𝑂𝑂𝑂𝑂𝑓𝑓 + 𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆′ ∗ 𝑂𝑂𝑂𝑂𝑠𝑠 ] + 𝑐𝑐𝑇𝑇 (𝑆𝑆, 𝑆𝑆 ′ ) (17) ′
𝑺𝑺𝑺𝑺𝑺𝑺 = ∑𝑖𝑖∈𝑁𝑁 ∑𝑆𝑆,𝑆𝑆′ 𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆 ∗ 𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑆𝑆 ∗ 𝐶𝐶𝐶𝐶𝐹𝐹
(17)
2078
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
7
The mixed-integer linear optimization allows building a network based on transportation of hydrogen via truck. The result will be shown to be a minimum spanning tree [20] of the graph 𝐺𝐺(𝑁𝑁, 𝑽𝑽) [21] where the nodes are the production, storage and distribution points and the edges corresponding to the linking roads. The leafs [22] are part of the production and distribution nodes. Then a minimum pipeline system corresponding to a spanning tree with the associated diameters minimizing the cost provided by [23] is built as well. Once these two spanning trees are built, different cut and paste algorithms [21] are implemented to build another spanning tree from the two existing one following the main algorithm; first, the minimum spanning tree corresponding to the pipeline system is considered as the initial minimum cost and all the tree leafs are numerated. For each set of leafs the cost by pipeline is compared to the cost by transportation via trucks from the other road tree. As soon as a link is not justified, it is replaced by the sub road tree linking the leafs and the pipeline flow is actualized as a certain flow is now transported via truck. This is repeated until all the leafs are covered and the final network is displayed showing the production and consumption nodes and the transportation link between them with the cost and the mode of transportation associated to it. Finally, the data of production and consumption are taken from France and Germany to display the transportation system. References [1] Commission E. EU transport in figures. 2015. [2] Union E. WHITE PAPER Roadmap to a Single European Transport Area. 2011. [3] Marcoulaki EC, Papazoglou IA, Pixopoulou N. Integrated framework for the design of pipeline systems using stochastic optimisation and GIS tools. Chemical Engineering Research and Design. 2012;90(12):2209-22. [4] Baufumé S, Grüger F, Grube T, Krieg D, Linssen J, Weber M, et al. GIS-based scenario calculations for a nationwide German hydrogen pipeline infrastructure. International Journal of Hydrogen Energy. 2013;38(10):381329. [5] Almansoori A, Shah N. Design and operation of a future hydrogen supply chain: multi-period model. international journal of hydrogen energy. 2009;34(19):7883-97. [6] Yang C, Ogden JM. Renewable and low carbon hydrogen for California – Modeling the long term evolution of fuel infrastructure using a quasi-spatial TIMES model. International Journal of Hydrogen Energy. 2013;38(11):4250 [7] S. De-Léon Almaraz MB, C. Azzaro-Pantel, L. Montastruc, S. Domenech. Spatial-based approach of the hydrogen supply chain in the Midi-Pyrénées region, France. Proceedings 24th European Symposium on Computer Aided Process Engineering (2014). 2014. [8] Konda NM, Shah N, Brandon NP. Optimal transition towards a large-scale hydrogen infrastructure for the transport sector: the case for the Netherlands. International Journal of Hydrogen Energy. 2011;36(8):4619-35. [9] André J, Auray S, De Wolf D, Memmah M-M, Simonnet A. Time development of new hydrogen transmission pipeline networks for France. international journal of hydrogen energy. 2014;39(20):10323-37. [10] SHHP. Scandinavian hydrogen highway partnership. 2006. [11] Weisstein E. Graph. MathWorld2017. [12] IEA. Technology Roadmap, Hydrogen and Fuel Cells. 2015. [13] Stolten D. Hydrogen Science and Engineering: Materials, Processes, Systems and Technology, 2 Volume Set: John Wiley & Sons; 2016. [14] Thewindpower. Total installed capacity. In: Thewindpower, editor.2016. [15] Fraunhofer. Monthly electricity generation in Germany in 2016. 2017. [16] Short W, Packey DJ, Holt T. A manual for the economic evaluation of energy efficiency and renewable energy technologies: University Press of the Pacific; 2005. [17] Jensen JO, Li Q, Bjerrum N. The energy efficiency of onboard hydrogen storage: Sciyo; 2010. [18] Drennen TE, Rosthal JE. Pathways to a hydrogen future Thomas E. Drennen, Jennifer E. Rosthal [E-Book]. 1st [19] Vaziri AM, Kamyad AV, Jajarmi A, Effati S. A global linearization approach to solve nonlinear nonsmooth constrained programming problems. Computational & Applied Mathematics. 2011;30:427-43. [20] Weisstein E. Minimum Spanning Tree. MathWorld2017. [21] Bondy A, Murty USR. Graph Theory: Springer London; 2011. [22] Weisstein E. Tree Leaf. MathWorld2017. [23] André J, Auray S, Brac J, De Wolf D, Maisonnier G, Ould-Sidi M-M, et al. Design and dimensioning of hydrogen
8
Amin Lahnaoui et al. / Energy Procedia 142 (2017) 2072–2079 Author name / Energy Procedia 00 (2017) 000–000
transmission pipeline networks. European Journal of Operational Research. 2013;229(1):239-51.
2079
