A small hydrogen world: Dimensioning electrolyzer and fuel cell
capacity to realize self-sufficiency.
MSc Technology operations management
Emil Noordbruis University of Groningen Faculteit Economics and Business
2018 J.C. Kapteynlaan 7 9714CL Groningen 06 20781415 E.R.Noordbruis@student.rug.nl Student number: 2751038
Supervisor, University of Groningen: Dr. M.J. Land
Co-Assessor, University of Groningen: Prof. dr. ir. J.C. Wortmann
Abstract
3
TABLE OF CONTENT
1.INTRODUCTION ... 6
2. THEORETICAL BACKGROUND ... 8
2.1. Hydrogen storage systems ... 8
2.2. Electrolyzer ... 8
2.3. Fuel cells ... 9
2.4. Configurations of renewable hydrogen production ... 11
3. METHODOLOGY ... 13 3.1. Research design ... 13 3.2. Application at Holthausen ... 14 3.3. Model development ... 14 3.4. Measurement ... 18 3.4.1. Nomenclature ... 18 3.4.2. Component specifications ... 20 3.4.3. Energy prices ... 20 3.5. Scenarios ... 22 3.6. Model calculation ... 23 3.6.1. Objective function ... 23 3.6.2. Self-sufficiency ratio ... 25
3.6.3. Total renewable energy power output ... 26
3.6.4. Electrolyzer ... 28
3.6.5. Hydrogen storage ... 28
3.6.6. Fuel cell ... 29
3.6.7. DC/AC converter ... 29
3.6.8. Hydrogen load profile ... 29
3.6.9. Electrical load shape ... 31
4
3.7. Sensitivity analysis ... 35
3.8. Monte Carlo Simulation ... 36
3.9. Model validation ... 36
4. RESULTS ... 38
4.1. Results per scenario ... 38
4.2. Cost without hydrogen storage system ... 42
4.3. Electrolyzer and fuel cell capacity ... 43
4.4. Total cost ... 45
4.5. Result analysis ... 48
4.6. Sensitivity analysis: number of solar panels... 50
5. DISCUSSION ... 52
5.1. Limitations and future research ... 53
6. CONCLUSION ... 54
REFERENCES ... 56
APPENDIX ... 61
Microsoft Excel Code ... 61
Models for conceptual model validation ... 62
TABLE OF FIGURES AND TABLES
Table 1: Decision variables ... 18Table 2: Model variables ... 18
Table 3: Model parameters ... 19
Table 4: Components' specifications ... 20
Table 5: Electricity costs for different situations ... 21
Table 6: Scenarios ... 22
Table 7: Solar panel specifications ... 26
Table 8: Load shape parameters (Luo et al., 2017) ... 31
Table 9: Coefficient of variation ... 38
5
Table 11: Minimal cost per scenario ... 46
Table 12: Minimal cost per scenario 245 solar panels ... 49
Figure 1: Basic electrolysis by Smolinka et al., 2015 ... 9
Figure 2 Efficiency comparison betwen fuel cells and other conversion devices ... 10
Figure 3: Model steps ... 15
Figure 4: Simulation model steps ... 16
Figure 5: Hydrogen flow model ... 17
Figure 7: Solar power output 100 day ... 27
Figure 8: Solar power output 3 days ... 27
Figure 9: Mobility demand 50 random days ... 30
Figure 10: Representative load patterns (Luo et al., 2017) ... 32
Figure 11: Representative load pattern (Luo et al., 2017) ... 32
Figure 12: Representative load pattern: Mean ... 33
Figure 13: Representative load pattern: Standard deviation ... 34
Figure 14: Electricity demand 10 random days ... 34
Figure 15: Scenario 1 Salderingsregeling, current component prices ... 39
Figure 16: Scenario 2 Salderingsregeling, future component prices ... 39
Figure 17: Scenario 3 Terugleversubsidie (positive scenario), current component prices ... 40
Figure 18: Scenario 4 Terugleversubsidie (positive scenario), future component prices ... 40
Figure 19: Scenario 5 Terugleversubsidie (negative scenario), current component prices ... 41
Figure 20: Scenario 6 Terugleversubsidie (negative scenario), future component prices ... 41
Figure 21: Optimal electrolyzer capacity ... 43
Figure 22: Optimal fuel cell capacity ... 44
Figure 23: Total cost ... 45
Figure 24: Scenario 1 245 Solar panels ... 50
Figure 25: Scenario 2 245 Solar panels ... 50
Figure 26: Electrolyzer capacity 245 vs 490 solar panels ... 51
Figure 27: Model of Zhang et al. (2017) ... 62
Figure 28: Model of Avril et al. (2010) ... 62
6
1. INTRODUCTION
Currently the energy demand grows and, as a consequence, the search for new energy sources is evolving. However, the use of renewable energy sources and the sustainable energy techniques lead to problems concerning the power output. The problem with these energy sources, such as solar, wave and wind power, is the high intermittence of meteorological variables. The effect of meteorological variables leads to a fluctuating output of power (Sacramento et al., 2013; Jiaping et al., 2017), which is in many cases not synchronized with the demand. Furthermore, the duration of power is uncertain, unstable and uncontrollable (Ma and Zhao, 2015). To address the problem of intermittence, hydrogen storage systems provide a possible solution. Hydrogen production through electrolyzing water is widely agreed to be the most sustainable (Edwards et al., 2008; Ursua et al., 2012). Within these systems, the following components are needed; (i) a renewable energy source, (ii) an electrolyzer for production of hydrogen, (iii) a fuel cell and (iv) a hydrogen storage tank (Baghaee et al., 2017). This paper addresses critical questions related to the capacity of the electrolyzer and fuel cell.
Sustainable and renewable energy are well-developed and studied. However the concept of storing the produced renewable energy in hydrogen is relatively new and the use of hydrogen is also emerging. Hydrogen is classified as the fuel of the future (Sacramento et al., 2013). The transition from fossil fuel energy systems to a hydrogen-based economy involves overcoming significant barriers (Edwards et al., 2008). Earlier studies have aimed at solving the intermittence problem by battery storage systems, where fluctuations are balanced through battery systems (Hemmati and Saboori, 2017; Pamparana et al., 2017). However there are downsides to battery storage systems; battery storage is expensive, prone to safety risks and not lasting long enough (Ehteshami and Chan, 2014). Battery energy storage is not viable for large-scale energy storage (Zhang et al., 2017). Storing renewable energy in the form of hydrogen is the most promising option (Ehteshami and Chan, 2014).
7 of the existing studies focus on hydrogen storage systems where hydrogen is also used for other applications, such as heating and mobility (Amid et al., 2016).
In the Netherlands there are plans to change the current policy that compensates for injecting surplus energy into the electricity grid. This policy will be changed into a less financial attractive option (Regeerakkoord 2017 - 2021). Because this policy is changing, exporting the electricity to the main grid becomes less interesting, therefore alternatives need to be researched. Using more of the produced renewable energy by households, companies or farms themselves with the use of hydrogen storage systems might be the solution.
The components in a hydrogen storage system are relatively expensive, and determine a large share of the achievable self-sufficiency. It is thus important to investigate the trade-offs in a hydrogen storage system, in order to make progress towards self-sufficiency.
Given what is explained above, the following research question is formulated: ‘How are the trade-offs between (1) the capacity of the electrolyzer and fuel cell in a hydrogen storage system, (2) the costs and (3) self-sufficiency?’ The self-sufficiency ratio determines how much of the electricity and hydrogen demand of a household, company or farm is provided by the renewable energy source. To answer the main-question several aspects need to be considered, such as variability in supply and demand of energy and hydrogen demand for mobility and heating. This research will provide a simulation model in order to determine the optimal capacities for both the electrolyzer and fuel cell for a given set of self-sufficiency levels. Next to the optimal capacities, the model will determine the trade-offs between the total cost and self-sufficiency for different settings. By developing the model to specify the trade-offs this research will facilitate the development of the ‘hydrogen future’.
8
2. THEORETICAL BACKGROUND
This literature review aims to provide an overview of hydrogen storage systems, their components and possible configurations. The review will start with an elaboration on hydrogen storage systems and their importance. Then the electrolyzer and fuel cell will be discussed. Following this the different configurations for a hydrogen storage system will be mentioned.
2.1. Hydrogen storage systems
The electricity demand is variable in hourly, weekly and seasonal time lags (Zakari and Syri, 2015). It is now a tradition in power systems to maintain the capacity large enough to meet the peaks in demand, which occurs just a few times per year (Zakeri and Syri, 2015). Maintaining the capacity large enough to meet those peaks, may result in oversized, inefficient and uneconomical power systems (Zakari and Syri, 2015). Energy storage systems are a solution because they provide the ability to store the power during low demand, and this stored power can be used later in the peak hours (Blanco & Faaij, 2018). Not only the generation capacity, but also the transmission and distribution systems are constrained in peak hours (Sioshansi et al., 2009). An electrical energy storage system can reduce the risk of consequences of overloaded transmission and distribution systems (Zakari and Syri, 2015). The European Union (EU) has mentioned electricity storage as a strategic technology in order to achieve the EU’s energy targets by 2020 and 2050 (International Energy Agency, 2013). Storing energy is viewed as one of the solutions for stabilizing the electricity grid to prevent uneconomical power production and high prices in peak hours (Zakari and Syri, 2015).
According to Zakari and Syri (2015) hydrogen based storage has the lowest cost of storage in comparison to other storage systems (for example batteries, pumped hydro and flywheel). Ehteshami and Chan (2014) argue that storing renewable energy in the form of hydrogen is the most promising option. Besides a (renewable) electricity source there are three necessary elements in hydrogen storage system these are an electrolyzer, fuel cell and hydrogen storage tank (Baghaee et al., 2017). This research focusses on the electrolyzer and fuel cell which both will be further explained in the sections below.
2.2. Electrolyzer
9 hydrogen is produced by decomposing water into hydrogen and oxygen through electrolysis with water as the raw material. Water is widely agreed to be the most sustainable source for hydrogen production (Edwards et al., 2008; Ursua et al., 2012).
Electrolysis of water is a rather simple process. Two electrodes in a basic electrolyte are connected to a current. When there is sufficient voltage a redox reaction will take place. The process of producing hydrogen at the cathode and producing oxygen at the anode (Smolinka et al., 2015), is schematically shown in figure 1. The figure represents a basic electrolyzer; all electrolyzers share the basic design of two electrodes. The reaction of the water electrolysis is as follows: 2 𝐻2𝑂 → 𝑂2+ 2 𝐻2 .
Figure 1: Basic electrolysis by Smolinka et al. (2015)
The most common electrolysis systems are based on alkaline and PEM (proton-exchange membrane, or polymer-electrolyte membrane) electrolyzers (dos Santos et al., 2017). The alkaline electrolysis is the most developed technology, and is a simple method where the electrolytes have a basic character. Next to the alkaline system, the electrolysis can also be performed with a PEM electrolyzer, one of the most promising technologies for decomposing water. However it is little explored (Carmo et al., 2013). The efficiency of the alkaline system is between 62% and 82%, and for the PEM system between 67% and 82% (dos Santos et al., 2017).
2.3. Fuel cells
10 except for the storage of reactants. These are stored outside the fuel cells. Therefore the power of fuel cells is measured by the output (kW) rather than in capacity (kWh) (Dicks and Rand, 2018). Furthermore an important difference with battery stored energy is that fuel cells can produce electricity continuously as long as hydrogen and oxygen are supplied, while battery storage needs charging (Edwards et al., 2008).
The efficiency of the conversion process in a fuel cell is defined as the amount of useful energy that can be extracted from the process relative to the total energy consumed by that process (O'hayre et al., 2016). For a fuel cell, the maximum amount of energy available (ideal efficiency) to do the work is given by the Gibbs free energy, at room temperature and pressure, this results in a 83% reversible higher heating value efficiency (O'hayre et al., 2016). The real fuel cell efficiency is dependent on the reversible thermodynamic efficiency, the voltage efficiency and the fuel utilization efficiency (O'hayre et al., 2016). Since the efficiency of fuel cells is dependent on many factors, the efficiency of fuel cells is always within a certain range (Sharaf and Orhan, 2014). The real fuel cell efficiency is between 40% and 70% (dos Santos et al., 2017; Sharaf and Orhan, 2014). In figure 2, different conversion devices are shown, it can be concluded that fuel cells are quite efficient compared to others.
Figure 2: Efficiency comparison between fuel cells and other conversion devices (sharaf and Orhan, 2014)
11
2.4. Configurations of renewable hydrogen production
As mentioned earlier hydrogen production needs electricity. This energy can be generated by wind and photovoltaic systems in many different applications (Ursua et al., 2012). In the literature there is a clear division into two applications of hydrogen production and storage. This division is based on whether the application has a connection to the main-grid (Ursua et al., 2012; Hemmati and Saboori, 2017). Ursua et al. (2012) divide this into off-applications and on-applications. Off-applications are not connected to the energy grid and the hydrogen production is completely relying on the energy production of renewable sources.
For the off-applications there are two configurations possible. In the first configuration (i) the renewable energy source is connected to the electrolyzer to produce only hydrogen. This means that the output of the electrolyzer is highly dependent on the intermittence of renewable energy sources such as solar and wind power. (Ursua et al., 2012). The second configuration (ii) uses hydrogen storage tanks and fuel cells. With this configuration the surplus of renewable energy is used to produce hydrogen. This hydrogen is stored and will be used later when the demand is higher than the supply from renewable sources. In this configuration it is also possible to use the hydrogen for other applications (Ursua et al., 2012). For the on-applications, where the renewable energy source and the electrolyzer are both connected to the main-grid, there are three main configurations. With on-applications both the renewable energy source and the electrolyzer are connected to the main energy-grid. In the first configuration (iii) the output of the renewable sources is directly injected into the main grid and the electrolyzer is driven by power from the main grid. The capacity of the electrolyzer is based on the average output of the renewable energy sources. The benefit of this configuration is that the electrolyzer can operate in a steady state and is not affected by the intermittency of renewable energy sources. In this configuration the main-grid works as a virtual storage of renewable energy. A potential disadvantage is that the electrolyzer is not running completely on renewable energy, since the electrolyzer is working even when there is no output from the renewable energy sources (Ursua et al., 2012).
12 is subject to intermittence. The electrolyzer which is been sized to the output of the renewable sources will be underutilized much of the time (Ursua et al., 2012).
The third and last configuration (v) is related to the problems arising with the increasing penetration of renewable energy sources on the main-grid. In this configuration the electrolyzer helps to balance the system, by producing hydrogen when the electricity supply exceeds demand (Ursua et al., 2012). And with the use of fuel cells the energy can be injected back into the grid when the energy demand is high. This configuration is able to balance the energy grid, since it is able to respond to fluctuations by either taking electricity or providing electricity (Blanco & Faaij, 2018).
13
3. METHODOLOGY
3.1. Research design
The main purpose of this study is to identify the trade-offs between 1) the electrolyzer and the fuel cell capacity, 2) total cost and 3) self-sufficiency in an on-application, configuration
iv. This configuration best suits the normal setting of households, companies and farmers,
which all have a connection with the main-grid. This is important because with a connection to the main-grid it is still possible to function even when there is no power from either the renewable energy source or the fuel cell. Furthermore this configuration allows maximizing the use of the renewable energy by households, companies or farmers, because the renewable energy is first used to meet their electricity demand, and if there is a surplus the power is used for storing the renewable energy, therefore the losses of converting energy through different elements are minimized. By using optimization while simulating the demand functions, the optimal capacity for both the fuel cell and electrolyzer can be determined for a given set a self-sufficiency levels, while minimizing the total cost.
14
3.2. Application at Holthausen
The model will be applied at the new location of Holthausen New Energy Solutions. Their vision is reducing the global emissions, by applying hydrogen and other green technologies. They are showing the possibilities that hydrogen has at their own location which is currently under construction.
In the current situation Holthausen is planning to install solar panels and a hydrogen storage system in order to fulfill their hydrogen demand. In the model data and settings are used which are specific for their location. Such as; the type of solar panels, heating and mobility demand, and weather data from the nearest measuring station.
A hydrogen heating system will be used for heating the building. This system has an efficiency around 95%. Furthermore, as a company car they use their own made ‘Hesla’ an adapted Tesla which is able to generate electricity from a fuel cell.
3.3. Model development
A simulation model is built to find the optimal capacity for the electrolyzer and fuel cell for a given set of self-sufficiency levels. In figure 3 and 4 the simulation and optimization steps are shown. In figure 3 the steps are shown to collect the required input data which are needed to run the simulation, where figure 4 shows the steps which are taken in the simulation.
In block L, of figure 4, the usage of Excel Solver mentioned, the GRG nonlinear method is used since the cost function which is used to minimize while fulfilling different self-sufficiency levels as a constraint is nonlinear. This method is able to find the global optimum instead of local optima.
The model as presented in figure 5 is developed using earlier models of Hemmati and Saboori (2017), Baghaee et al. (2017), Avril et al. (2010) and Zhang et al. (2017). These models are based on storage of solar and wind power by using hydrogen and/or battery storage systems. The basic ideas from these models are used and adapted to the current situation.
15 electrical demand and the capacity of the electrolyzer, the energy is injected into the main grid. The hydrogen can be used for three different purposes, in order of priority: first for usage in the fuel cell, second for heating and thirdly for mobility. This priority rule is based on maximizing the fuel cells output, and therefore makes optimal use of the investment in the fuel cell capacity. If the hydrogen storage is lower than the hydrogen demand from heating or mobility the shortage is imported from an external source.
Collect weather data (From KNMI or other similar source)
Determine solar power output
Determine heating demand
1) Determine different scenarios for simulation
2) Determine different parameter settings for each scenario ; component prices and electricity policy
Determine self-sufficiency levels which will be used to calculate optimal capacities for the electrolyzer and fuel cell . n= each self-sufficiency level. For example n= 1 = self-sufficiency level of 100%, n =2 = self-sufficiency level of 99%
Determine number of runs (in the study 5 runs have been performed) Start A B C D E F Start simulation
16 Set self-sufficiency level n
1) Determine mobility demand 2) Determine electricity demand
Use Microsoft Excel Solver. Find optimal capacity for both the electrolyzer and fuel cell, which will minimize total cost and satisfy constraints
Next self-sufficiency level Next run
Next scenario
End Start
Set parameters based on scenario
Start run
1) Generate random numbers for mobility demand between 0 and 1 2) Generate random numbers for electricity demand between 0 and 1
H I J K L M N O
17
Electrical Load Electricity grid Total renewable
energy power output
Electrolyzer
Fuel cell Hydrogen storage
(tank)
Hydrogen load for mobility (P-mb) Hydrogen load for
heating (P-ht) DC/AC Inverter AC Bus DC Bus P-Gim (t) P-E-Load (t) P-ren (t) P-ren-el (t) P-FC-load (t) P-el-tank (t) P-tank-FC (t) P-tank-mb (t) P-tank-ht (t) Photovoltaic system P-pv (t) P-Gexp (t) P-inv (t) P-inv-load (t) P-Gexp (t) External hydrogen source
18
3.4. Measurement
3.4.1. Nomenclature
Table 1: Decision variables
Decision variables Description
𝑪𝑬𝑳 Capacity of electrolyzer
𝑪𝑭𝑪 Capacity of fuel cell
Table 2: Model variables
Variables Description
𝑷𝑬_𝒍𝒐𝒂𝒅 (𝒕) Distribution for electrical demand 𝑷𝑯𝟐_𝒍𝒐𝒂𝒅(𝒕) Hydrogen demand (heating + mobility)
𝑷𝑴𝑩 (𝒕) Hydrogen demand for mobility
𝑷𝒕𝒂𝒏𝒌_𝑴𝑩 (𝒕) Hydrogen demand for mobility self-fulfilled 𝑷𝒌𝒎′𝒔_𝒅𝒂𝒚 (𝒕) Distribution for number of kilometers/day
𝑷𝑯𝑻 (𝒕) Hydrogen demand for heating
𝑷𝒕𝒂𝒏𝒌_𝑯𝑻 (𝒕) Hydrogen load for heating self-fulfilled
𝑷𝑷𝑽 (𝒕) Power output of solar panel
𝑷𝒓𝒆𝒏 (𝒕) Power output of renewable energy sources
𝑷𝒓𝒆𝒏_𝒆𝒍 (𝒕) Power from the renewable energy source to the electrolyzer 𝑷𝒓𝒆𝒏_𝒊𝒏𝒗 (𝒕) Power from the renewable energy source to the electrical demand 𝑷𝑭𝑪_𝒍𝒐𝒂𝒅 (𝒕) Power from the electrolyzer to the electrical demand
𝑷𝒊𝒏𝒗_𝒍𝒐𝒂𝒅 (𝒕) Power from the renewable energy source and fuel cell inverted to the electrical demand
𝑷𝑮𝒊𝒎 (𝒕) Imported energy from the grid
𝑷𝑮𝒆𝒙𝒑𝒕 (𝒕) Exported energy to the grid
𝑬𝒕𝒂𝒏𝒌 (𝒕) Stored hydrogen [kWh]
19
Table 3: Model parameters
Parameters Description
𝑯𝑯𝑽𝑯𝟐 Higher heating value of hydrogen ŋ𝑯𝑻 Efficiency of heating system ŋ𝒊𝒏𝒗 Efficiency of inverter
ŋ𝑭𝑪 Efficiency of fuel cell ŋ𝒆𝒍 Efficiency of electrolyzer 𝑪𝒂𝒑𝑬𝑳 Capital cost of electrolyzer
𝑪𝒂𝒑𝑭𝑪 Capital cost of fuel cell 𝑪𝒂𝒑𝑺𝑻 Capital cost of storage tank
𝑪𝒂𝒑𝑺𝑷 Capital cost of solar panels
𝑶&𝑴𝑬𝑳 Operations and maintenance cost electrolyzer 𝑶&𝑴𝑭𝑪 Operations and maintenance cost fuel cell 𝑶&𝑴𝑺𝑻 Operations and maintenance cost storage tank 𝑶&𝑴𝑺𝑷 Operations and maintenance cost solar panel
𝑬𝒊𝒎𝒑 Price for importing 1 kWh 𝑬𝒆𝒙𝒑 Price for exporting 1 kWh
𝑷𝒓𝑯𝟐 Price for importing 1 kg H2
𝑵𝑺𝑷 Number of solar panels
t Time in hours t=1 first hour of simulation
T Total length of simulation in hours
i Length of warm-up
20
3.4.2. Component specifications
A literature review is performed in order to determine the hydrogen storage components’ costs. The research of Baghaee et al. (2017) and Zhang et al. (2017) are leading for cost indications for the components of the hydrogen storage system. In this study two different cost scenarios are used. The current scenario, where the costs are as presented in table 4, and a future optimistic scenario where the costs of the fuel cell and electrolyzer decrease with 75% and for the hydrogen storage tank with 50%. The optimistic scenario is likely achievable, since the U.S. Department of Energy (DOE) and the National Renewable Energy Laboratory (NREL) have estimated the production costs for the electrolyzer as 317€/kW and for the fuel cell at 178€/kW (Zhang et al., 2017). The calculation is based on the exchange rate EUR/USD 1.2108 applying on 30 April 2018.
Table 4: Components' specifications (Adapted from Baghaee et al., 2017 and Zhang et al., 2017)
Component Capital cost
(€/unit)
O&M1 (€/unit/year)
Life (years) Efficiency Unit
Electrolyzer 1652 21 20 0.75 1 kW Hydrogen storage tank 477 12 20 1 1 kg Fuel cell 2478 145 102 0.50 1 kW Solar power set (including inverter)2 290 2.9 20 n.a. 1 Panel 1
: Operations and maintenance cost. 2: Based on information from Holthausen
For the capital cost, the assumption is made that the costs are proportional to the capacity or number of units. For the electrolyzer, fuel cell and solar panels, multiple units are connected in order to meet a certain capacity. Thus if the capacity doubles the number of cells doubles as well.
3.4.3. Energy prices
21 together with an expert from Holthausen. The costs for exporting 1 kWh of electricity are estimated at €0.12 for the ‘terugleversubsidie’ in the positive case, the cost for the ‘terugleversubsidie’ in the negative case are set on €0.06. In the table 5 are for all different situations the import and export electricity prices given.
Table 5: Electricity costs for different situations
Situation Import electricity price
(𝑬𝒊𝒎𝒑)
Export electricity price (𝑬𝒆𝒙𝒑) Salderingsregeling 0.2193 €/kWh 0.2193 €/kWh** 0.05 €/kWh Terugleversubsidie (Positive scenario) 0.2193 €/kWh 0.12 €/kWh Terugleversubsidie (Negative scenario) 0.2193 €/kWh 0.06 €/kWh
22
3.5. Scenarios
In this simulation study different scenarios are introduced. These scenarios are related to energy prices and policies, component costs and different capacities for both the electrolyzer and fuel cell. Table 6 presents different scenarios.
Table 6: Scenarios
Scenario Electricity costs Components’ specifications
1 Salderingsregeling Current component prices
2 Salderingsregeling Future component prices
3 Terugleversubsidie (Positive scenario) Current component prices
4 Terugleversubsidie (Positive scenario) Future component prices
5 Terugleversubsidie (Negative scenario) Current component prices
23
3.6. Model calculation
Within this section the different functions and calculations are given for the model presented in figure 5. All abbreviations which are mentioned can be found in table 1, 2, or 3.
3.6.1. Objective function
The total costs function consists of the following sub functions. First of all the total investment costs, these costs represent the total investment that is needed in order to buy the components. Secondly the operations and maintenance (O&M) costs of these components. Thirdly the costs for importing and exporting electricity, and finally the import costs of hydrogen. 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝑠 = 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝐶𝑜𝑠𝑡 + 𝑂&𝑀 𝐶𝑜𝑠𝑡 + 𝐼𝑚𝑝𝑜𝑟𝑡 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑐𝑜𝑠𝑡 − 𝐸𝑥𝑝𝑜𝑟𝑡 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + 𝐻𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑖𝑚𝑝𝑜𝑟𝑡 𝑐𝑜𝑠𝑡 (1) 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝐶𝑜𝑠𝑡𝑠 = 𝐶𝐸𝐿∗ 𝐶𝑎𝑝𝐸𝐿 + 𝐶𝐹𝐶∗ 2𝐶𝑎𝑝𝐹𝐶+ max (𝑚𝑡𝑎𝑛𝑘) ∗ 𝐶𝑎𝑝𝑆𝑇+ 𝑁𝑆𝑃∗ 𝐶𝑎𝑝𝑆𝑃 (2)
𝑂&𝑀 𝐶𝑜𝑠𝑡𝑠 = (𝐶𝐸𝐿∗ 𝑂&𝑀𝐸𝐿 + 𝐶𝐹𝐶∗ 𝑂&𝑀𝐹𝐶+ max ( 𝑚𝑡𝑎𝑛𝑘) ∗ 𝑂&𝑀𝑆𝑇+ 𝑁𝑆𝑃∗ 𝑂&𝑀𝑆𝑃) ∗ 𝐿
8760 (3)
For both the investment as O&M costs function, the different costs for each component can be found in section 3.4.2. For the investment costs the costs for the fuel cell needs to be multiplied by 2, since all components have a life time of 20 years, and the fuel cell 10. Hence, after 10 years, the fuel cell needs replacement.
For the following functions (eq. 4 to 15) a distinction can be made between the warm-up period and the steady state. The simulation length is 4 years and the costs are calculated for aperiod of 20 years, so the costs functions of the simulation are extended to meet 20 years. 𝑖 = 𝑤𝑎𝑟𝑚 𝑢𝑝 𝑡𝑖𝑚𝑒. 𝐼𝑛 𝑡ℎ𝑖𝑠 𝑠𝑡𝑢𝑑𝑦: 1 𝑦𝑒𝑎𝑟 = 8760 ℎ𝑜𝑢𝑟𝑠
𝑇 = 𝑡𝑜𝑡𝑎𝑙 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑙𝑒𝑛𝑔𝑡ℎ. 𝐼𝑛 𝑡ℎ𝑖𝑠 𝑠𝑡𝑢𝑑𝑦: 4 𝑦𝑒𝑎𝑟𝑠 = 35064 ℎ𝑜𝑢𝑟𝑠
25 𝐻𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑖𝑚𝑝𝑜𝑟𝑡 𝑐𝑜𝑠𝑡𝑠 = ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑖𝑚𝑝𝑜𝑟𝑡 𝑐𝑜𝑠𝑡_𝑤𝑎𝑟𝑚 𝑢𝑝 + ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑖𝑚𝑝𝑜𝑟𝑡 𝑐𝑜𝑠𝑡𝑠_𝑠𝑡𝑒𝑎𝑑𝑦 𝑠𝑡𝑎𝑡𝑒 (13) 𝐻2 𝑖𝑚𝑝𝑜𝑟𝑡 𝑐𝑜𝑠𝑡𝑠_𝑤𝑎𝑟𝑚 𝑢𝑝 = ∑𝑖𝑡=0𝑃𝐻2_𝑙𝑜𝑎𝑑(𝑡)−𝑃𝑡𝑎𝑛𝑘−𝐻𝑇 (𝑡)−𝑃𝑡𝑎𝑛𝑘_𝑀𝐵 (𝑡) 𝐻𝐻𝑉𝐻2 ∗ 𝑃𝑟𝐻2 (14) 𝐻2 𝑖𝑚𝑝𝑜𝑟𝑡 𝑐𝑜𝑠𝑡𝑠_𝑠𝑡𝑒𝑎𝑑𝑦 𝑠𝑡𝑎𝑡𝑒 =∑ 𝑃𝐻2_𝑙𝑜𝑎𝑑(𝑡) 𝑇 𝑡=𝑖+1 −𝑃𝑡𝑎𝑛𝑘_𝐻𝑇 (𝑡)−𝑃𝑡𝑎𝑛𝑘_𝑀𝐵 (𝑡) (𝑇−𝑖) ∗ 𝐻𝐻𝑉𝐻2 ∗ 𝑃𝑟𝐻2∗ (L − i) (15 )
3.6.2. Self-sufficiency level
In order to determine how much of the load is covered by the renewable energy source the self-sufficiency ratio is used. The self-sufficiency level (SSL) is defined with eq. (16). It represents the percentage of the demand (both the electrical (PE-load) and the hydrogen demand
(PH2-load)) that is met by the renewable energy source and the hydrogen storage system. Within
this calculation instrument hydrogen can be used in the fuel cell, for heating and for mobility. In this case the renewable energy source is a photovoltaic system. The self-sufficiency ratio indicates the renewable energy penetration level.
In this case the self-sufficiency is measured after the warm-up period of 1 year, where t = 8760. T is the ending point for measuring self-sufficiency. This implies that in this case the ending is after 4 years thus at t = 35064. If the sufficiency is measured from t=0 the self-sufficiency level will decrease, since the system has had no time to reach a steady state.
26
3.6.3. Total renewable energy power output
The local weather data, including the solar irradiance and the outside temperature data can be obtained from Royal Netherlands Meteorological Institute. Hourly measurements can be collected from ±300 different measuring stations. Within this study the data from the measuring station Eelde is used since this location is the nearest to the location of Holthausen (±15km). The photovoltaic system is dependent on both the solar irradiance and the ambient temperature (Avril et al., 2010).
The electrical production of a photovoltaic panel Ppv can be determined with the temperature
of the cell Tc, the temperature of the cell in standard conditions Tc ref, the solar irradiance ξ, the
solar irradiance in standard conditions ξref, the standard peak power of a module P0max, and the
temperature coefficient of P0max µPmax (Avril et al., 2010):
𝑃𝑃𝑉 (𝑡) = ξ(𝑡)
ξ𝑟𝑒𝑓∗ [ 𝑃𝑚𝑎𝑥
0 + µ
𝑃𝑚𝑎𝑥(𝑇𝑐 (𝑡) − 𝑇𝐶 𝑟𝑒𝑓 )] (17)
The temperature of the cell Tc can be calculated from the outside temperature Text, when
knowing the nominal operating cell temperature (NOCT) (Avril et al., 2010): 𝑇𝑐 (𝑡) = 𝑇𝑒𝑥𝑡 (𝑡)+ (𝑁𝑂𝐶𝑇 − 20) ∗ ξ(𝑡)
800 (18)
The total power output of solar panels is the Ppv multiplied by the number of solar
panels 𝑁𝑆𝑃:
𝑃𝑟𝑒𝑛 (𝑡) = 𝑃𝑃𝑉 (𝑡) ∗ 𝑁𝑆𝑃 (19)
Within this simulation the following solar panels are used: QCells 285 Wp poly module, the
specifications of this solar panel can be seen in the table 7.
Table 7: Solar panel specifications
𝑷𝒎𝒂𝒙𝟎 285 W
µ𝑷𝒎𝒂𝒙 -0.40%/°C
NOCT 45°C
Investment per panel (including inverter) €290
Life time of cells 20 years
27
Figure 6: Solar power output 100 day
Figure 7: Solar power output 3 days
In both figures, 6 and 7, show the solar power for a random period, a small fraction of the whole simulation length can be seen and it illustrates the fluctuations in solar power output. In figure 6 the differences in solar power output between days can be seen, where figure 7 shows how the solar power output fluctuates between hours. Within these figures, the variability of solar power can be seen. The assumption is made that the solar panels efficiency remains 100% over the years. Since the simulation only takes 4 years, consequently it is not possible to determine the effects of reduced solar power efficiency over the years.
The total power generated by the renewable energy source (Pren), in this case only solar
panels, is distributed through two streams. One stream (Pren – inv) is for meeting the electrical
0 10 20 30 40 50 60 70 80 90 100 1/1 8/1 15/1 22/1 29/1 5/2 12/2 19/2 26/2 5/3 12/3 19/3 26/3 2/4 9/4 kW
Maximum solar power output per day
Solar Power output 100 days
0 20 40 60 80 100 120 140 1 6 12 18 24 6 12 18 24 6 12 18 24 kW Hours
Solar power output 30/05-01/06
01/06
28 demand (PE – load) and goes through the inverter and the other stream transfers the extra power
to the electrolyzer (Pren-el) for hydrogen production. If the power output by the renewable
energy source is higher than the capacity of the renewable energy and the demand, the electricity will be fed into the electricity grid (PGexpt). This should be in balance:
𝑃𝑟𝑒𝑛 (𝑡) = 𝑃𝑖𝑛𝑣 (𝑡)+ 𝑃𝑟𝑒𝑛_𝑒𝑙 (𝑡)+ 𝑃𝐺𝑒𝑥𝑝𝑡 (𝑡)
ŋ𝑖𝑛𝑣 (20)
3.6.4. Electrolyzer
In this model the electrolyzer is directly linked with the hydrogen storage. Because the electrolyzer works at certain efficiency (ŋ𝑒𝑙) the produced hydrogen can be calculated by (Baghaee et al., 2017):
𝑃𝑒𝑙_𝑡𝑎𝑛𝑘 (𝑡)= 𝑃𝑟𝑒𝑛_𝑒𝑙 (𝑡)∗ ŋ𝑒𝑙 (21)
Where 𝑃𝑟𝑒𝑛_𝑒𝑙 (𝑡) ≤ 𝐶𝐸𝐿 is constrained by the maximum capacity of the electrolyzer.
3.6.5. Hydrogen storage
The stored hydrogen at a certain time can be obtained by:
𝐸𝑡𝑎𝑛𝑘 (𝑡) = 𝐸𝑡𝑎𝑛𝑘 (𝑡−1)+ 𝑃𝑒𝑙_𝑡𝑎𝑛𝑘(𝑡)− 𝑃𝑡𝑎𝑛𝑘_𝐹𝐶 (𝑡)− 𝑃𝑡𝑎𝑛𝑘_𝑀𝐵 (𝑡)− 𝑃𝑡𝑎𝑛𝑘_𝐻𝑇 (𝑡) (22) Where 𝑃𝑒𝑙_𝑡𝑎𝑛𝑘(𝑡) is the energy from the renewable energy source to the electrolyzer, 𝑃𝑡𝑎𝑛𝑘_𝐹𝐶 (𝑡) is the energy from the hydrogen tank to the fuel cell, 𝑃𝑡𝑎𝑛𝑘_𝑀𝐵 (𝑡) is the energy from the hydrogen tank to hydrogen vehicles, and 𝑃𝑡𝑎𝑛𝑘_𝐻𝑇 (𝑡) is the energy from the hydrogen
tank to heating applications. For the hydrogen storage tank the assumption is made, that the storage efficiency is 100%, as is done by Yilanci et al. (2009) and Ozden and Tari (2016). This means that there are no storage losses.
In order to determine the mass of the stored hydrogen at a certain time equation (23) should be used (Baghaee et al, 2017). Where the higher heating value (HHV) of hydrogen is equal to 39.7 kWh/kg (Kaviani and Kouhasri, 2009).
𝑚𝑡𝑎𝑛𝑘 (𝑡) =
𝐸𝑡𝑎𝑛𝑘 (𝑡)
𝐻𝐻𝑉𝐻2 (23)
29 variable would have been too complex to solve using Microsoft Excel, and thus increasing the run time exponentially.
3.6.6. Fuel cell
The output power of the fuel cell (PFC-load (t)) can be determined by multiplying the input
power with the efficiency of fuel cells (ŋ𝐹𝐶):
𝑃𝐹𝐶_𝑙𝑜𝑎𝑑 (𝑡)= 𝑃𝑡𝑎𝑛𝑘_𝐹𝐶 (𝑡)∗ ŋ𝐹𝐶 (24)
Where 𝑃𝐹𝐶_𝑖𝑛𝑣 (𝑡)≤ 𝐶𝐹𝐶 is constrained by the maximum capacity of the fuel cell.
3.6.7. DC/AC converter
The inverter is needed in order to convert the DC (direct current) power generated by solar panels (Pren-inv), or the fuel cell (PFC-inv) to AC (Alternating current) power. The inverter has an
efficiency (ŋ𝑖𝑛𝑣) of around 90% and is roughly supposed to be constant (Baghaee et al., 2017). The inverted power can be calculated:
𝑃𝑖𝑛𝑣_𝑙𝑜𝑎𝑑 (𝑡)= (𝑃𝐹𝐶_𝑙𝑜𝑎𝑑 (𝑡)+ 𝑃𝑟𝑒𝑛_𝑖𝑛𝑣 (𝑡)) ∗ ŋ𝑖𝑛𝑣 (25)
𝑃𝑖𝑛𝑣 (𝑡)=𝑃𝑖𝑛𝑣_𝑙𝑜𝑎𝑑(𝑡)+ 𝑃𝐺𝑒𝑥𝑝𝑡 (𝑡)
ŋ𝑖𝑛𝑣 = 𝑃𝑟𝑒𝑛(𝑡)+ 𝑃𝐹𝐶_𝑙𝑜𝑎𝑑 (𝑡)− 𝑃𝑟𝑒𝑛_𝑒𝑙 (𝑡) (26)
3.6.8. Hydrogen load profile
30
Figure 8: Mobility demand 50 random days
There are different methods for calculating the energy demand for heating, ventilation and air condition (HVAC) systems (Büyükalaca, et al., 2001). In this simulation model there is chosen for the degree-hours method, for its simplicity, and in addition to this it is a well-established tool for energy analysis (Satman and Yalcinkaya, 1999). The degree-hours method is a measuring method to indicate the energy demand in order to heat or cool buildings (Satman and Yalcinkaya, 1999). In this case only heating is considered, in order to determine the energy demand if cooling systems are needed, this can be modelled as well by adding another formula for CDH (cooling degree-hours).
𝑃𝐻𝑇 (𝑡) =𝐾𝑡𝑜𝑡
ŋ𝐻𝑇 ∗ HDH(𝑡) (30)
Where 𝐾𝑡𝑜𝑡 is the total heat-transfer coefficient of the building in W/°C, ŋ𝐻𝑇 is the efficiency of the hydrogen heating system, and HDH is the value of degree-hours for heating (eq. 31). 𝐾𝑡𝑜𝑡 is in this simulation, 270 W/°C.
𝐻𝐷𝐻(𝑡) = (𝑇𝑏− 𝑇𝑒𝑥𝑡 (𝑡))+ (31)
In which, 𝑇𝑒𝑥𝑡 (𝑡) is the outside temperature at a certain time and 𝑇𝑏 is the base temperature.
The base temperature is the temperature below when heating is needed.
𝑃𝑡𝑎𝑛𝑘_ 𝐻𝑇 (𝑡) = 𝑃𝐻𝑇 (𝑡)∗ ℎ𝑗 (𝑡) (32) ℎ𝑗(𝑡) = 1 𝑖𝑓 ℎ𝑒𝑎𝑡𝑖𝑛𝑔 𝑑𝑒𝑚𝑎𝑛𝑑 𝑐𝑎𝑛 𝑏𝑒 𝑠𝑒𝑙𝑓 𝑓𝑢𝑙𝑓𝑖𝑙𝑙𝑒𝑑 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡, 𝑒𝑙𝑠𝑒 ℎ𝑗(𝑡) = 0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 1/1 8/1 15/1 22/1 29/1 5/2 12/2 19/2 kg H2 Date
31 The total hydrogen demand can be calculated with:
𝑃𝐻2_𝑙𝑜𝑎𝑑(𝑡) = 𝑃𝑀𝐵 (𝑡)+ 𝑃𝐻𝑇 (𝑡) (33)
If the capacity of the hydrogen storage tank is not sufficient to meet the heating and mobility demand, hydrogen is imported from an external source. The hydrogen price is set at €10,- per kg. The price of hydrogen is based on information of Holthausen.
3.6.9. Electrical load shape
Within this simulation the electricity consumption must be estimated. The total yearly consumption of electricity is estimated to be 50.000 kWh, the quantification of the consumption is assessed and calculated by Holthausen.
A load shape is the curve that represents the electricity load as a function of time (Luo et al., 2017). Load shapes contain information how the electricity uses, changes during the day. Load shapes in commercial buildings are affected by factors such as the day of the week and the season (Luo et al., 2017; Jang et al., 2015). In this simulation model the general statistical method using 24-hour electric load from Luo et al. (2017) is used to estimate the electricity load pattern. The load shape parameters can be seen in table 8:
Table 8: Load shape parameters (Luo et al., 2017)
Load shape parameters Definition Value for Holthausen
Peak-base load ratio Ratio of peak load to base load on typical workdays
3.5
Workday/non-workday load ratio
Ratio of total daily load on typical workdays to non-workdays
1.8
On-hour duration Duration of a building’s operating
hours on typical workdays
32
Figure 9: Representative load patterns (Luo et al., 2017)
Figure 9 shows that there are three types of load patterns. The first load pattern has a normal curve corresponding to the normal operation schedule, rising at 8 am and falling around 6 pm. The building within this simulation model falls in this pattern, since they are only in operation during the day.
Figure 10: Representative load pattern (Luo et al., 2017)
In figure 10 the load pattern for all seasons is shown, the load pattern in the winter deviates from the other seasons. However, within this simulation study, the variation between seasons is not taken into account. This simplification has been made, first of all, since the variation between seasons is relatively low, thus not taking the seasons into account will lead only to small differences. Furthermore, by not taking into account the seasons the electricity demand function is simplified and as a result, the complexity of the model is reduced and the transparency will increase.
In figures 9 and 10 the mean electricity consumption per hour is given for working days. The hourly consumption of electricity is based on a normal distribution (Jardini et al., 2000). For both working-days and non-working-days the mean is presented in figure 11 and the standard deviation is presented in figure 12. For each hour t, the 𝑃𝐸−𝐿𝑜𝑎𝑑 (𝑡) can be determined by
33 probability is 0.4, so the electricity demand at this time period is Normal distributed (8.0, 1.1, 0.4) = 7.7 kWh (eq. 33).
𝑃𝐸_𝐿𝑜𝑎𝑑 (𝑡)= 𝑁𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 (𝑚𝑒𝑎𝑛; 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛; 𝑅𝑎𝑛𝑑𝑜𝑚 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦)
(34) Within eq. 34 autocorrelation is not fully taken into account. Autocorrelation is the similarity between observations as a function of time, when the time series data is influenced by its own history (Shiu and Lam, 2004). In other words, if the previous hour has a high consumption, it will be likely that the following hour will be relatively high as well, or vice versa. Many autocorrelation methods use a form of moving-average. The load pattern (figure 11) also has a moving average, thus partially is the autocorrelation already taken into account. The deviation between hours is large for the mean, and relatively small for the standard deviation. Thus the moving-average of the mean takes a large fraction of the autocorrelation into account.
Figure 11: Representative load pattern: Mean
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Working days 3.2 3.1 3.1 3.1 3.2 3.3 3.7 5.1 6.8 8.0 9.0 9.7 10.410.711.111.210.9 9.6 8.0 6.4 5.4 4.6 3.8 3.5 non-working days 3.1 3.1 3.1 3.1 3.1 3.1 3.2 3.4 3.7 3.9 4.0 4.1 4.2 4.3 4.4 4.4 4.3 4.1 3.9 3.6 3.5 3.3 3.2 3.1 0.0 2.0 4.0 6.0 8.0 10.0 12.0 kW h
34
Figure 12: Representative load pattern: Standard deviation
Based on the electricity demand distribution (eq. 34), the electricity demand can be randomly generated. In the figure below, the electricity demand for 10 random days can be seen.
Figure 13: Electricity demand 10 random days
3.3.7.1 Electrical balance
The system should always be in balance this can be seen in the following equation:
𝑃𝑖𝑛𝑣_𝑙𝑜𝑎𝑑 (𝑡)+ 𝑃𝐺𝑖𝑚 (𝑡)− 𝑃𝐺𝑒𝑥𝑝𝑡 (𝑡)− 𝑃𝐸−𝑙𝑜𝑎𝑑 (𝑡) = 0 (35) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Working days 0.5 0.4 0.4 0.4 0.5 0.5 0.4 0.6 0.9 1.1 1.3 1.4 1.5 1.5 1.5 1.6 1.6 1.4 1.1 0.9 0.7 0.6 0.5 0.5 Non-working days 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.4 0.4 0.4 0.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 kW h
Representative load pattern: Standard deviation
0.0 2000.0 4000.0 6000.0 8000.0 10000.0 12000.0 14000.0 16000.0 0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 kW Time (t) in hours
35
3.6.8. Operation strategy
If 𝑃𝑟𝑒𝑛 (𝑡) =
𝑃𝐸_𝑙𝑜𝑎𝑑 (𝑡)
ŋ𝑖𝑛𝑣 all renewable energy is used to meet the electricity demand.
If 𝑃𝑟𝑒𝑛 (𝑡) >
𝑃𝐸_𝑙𝑜𝑎𝑑 (𝑡)
ŋ𝑖𝑛𝑣 the surplus power is transferred to the electrolyzer. If the surplus power
exceeds the capacity of the electrolyzer, the power will be injected in to the main grid. If 𝑃𝑟𝑒𝑛 (𝑡) <
𝑃𝐸_𝑙𝑜𝑎𝑑 (𝑡)
ŋ𝑖𝑛𝑣 the shortage power will be supplied by the fuel cell. If the fuel cells
output (capacity) is lower than the shortage power or if the storage is empty, the remaining power shortage will be supplied from the main electricity grid.
If 𝐸𝑡𝑎𝑛𝑘 (𝑡) < 𝑃𝑀𝐵 (𝑡) 𝑜𝑟 𝑃𝐻𝑇 (𝑡) the full heating or mobility demand will be fulfilled by importing hydrogen from an external source. The cost for importing hydrogen are also taking into account.
For all components who uses hydrogen there is a priority rule, the hydrogen is used first for the fuel cell, second for heating and at last for mobility, see section 3.3.
3.7. Sensitivity analysis
To determine how different values of independent variables impact the dependent variables a sensitivity analysis is performed. The number of solar panels determines for a large part the self-sufficiency, both in meeting the electrical demand as in the share of renewable energy which is available for producing hydrogen. Hence it is important to determine the effects on the total costs and self-sufficiency if the number of solar panels decreases.
36
3.8. Monte Carlo Simulation
In this study the Monte Carlo simulation method is used. The Monte Carlo simulation method relies on repeated random sampling to model the probability of different parameters (Chin et al., 2003). This technique enables to determine the optimal capacity when variability of parameters is also taken into account by simulation. By performing the calculations multiple times, the optimal capacity for both the electrolyzer and fuel cell can be defined.
3.9. Model validation
In order to determine whether the model is accurate and credible validation is needed. Since the model is theoretical, the outcomes of the simulation cannot be compared to the real system measurements. Therefore the results are analyzed in order to verify that the model is a reasonable representation of the actual system.
The following methods will be used in order to determine the validity (Robinson, 1997): - Conceptual model validation: defining if the scope and level of detail of the model are
sufficient for its purpose.
The conceptual model is compared to other conceptual models from scientific papers. The conceptual model has many similarities, with the conceptual models from Baghaee et al. (2017), Avril et al. (2010) and Zhang et al. (2017). The only difference is the fact that the model presented in this study has the possibility to use the stored hydrogen in two different applications; heating and mobility. In order to verify if the modelling has been correct the model is discussed with an expert from Holthausen. The different conceptual models can be seen in the appendix.
- Data validation: Data which is been extracted from the real world for input in to the conceptual model and computer model, in order to perform simulation and experimentation. Inaccuracy in the input data will lead to inaccuracy of the simulation, therefore the data has to be controlled in order to make sure that the input data are as accurate as possible.
37 the daily mileage which has been based on 20.000 km/year. For both distributions multiple graphs have been made in order to determine if these figures seem accurate. A representation of these figures can be seen in figure 8 and 13.
- White-box validation: This validation ensures that the model is true to the real world. Various aspects of the model should be checked during the development of the model. Such as: weather data, distribution functions, control structure. This can be done by checking the code, visual checks and inspecting output reports.
Many visual checks have been performed by generating line graphs of each different variable. Looking at their minimum and maximum value and if these are in line with expectations. Furthermore, in order to determine if the GRG nonlinear method generates the global optimum, manually calculations have been performed and it can be concluded that in this situation the GRG nonlinear method is able to determine the global optimum.
38
4. RESULTS
In this section the results will be presented. In the first section all individual scenarios are presented. Secondly the analysis without any hydrogen storage systems is given. Thirdly the analysis for the fuel cell capacity, electrolyzer capacity and total cost are discussed. The results are finalized with a sensitivity analysis on the number of solar panels.
4.1. Results per scenario
In figures with multiple vertical-axis, it is important to read the total costs (blue line) on the left vertical-axis and the electrolyzer (red line) and fuel cell capacity (green line) on the right vertical-axis. The given capacities are the optimal capacity which minimizes the total cost. In all figures below the average is presented. The average is taken of 5 simulation runs. Since the coefficient of variation is low for the electrolyzer and fuel cell capacity, the average is taken. For some self-sufficiency levels of scenario 1 the coefficient of variation is given in table 9.
Table 9: Coefficient of variation
CV Scenario 1
Electrolyzer Fuel cell
100% 0,009 0,013 90% 0,006 0,025 80% 0,012 0,068 70% 0,004 0,029 60% 0,002 0,063 50% 0,005 0,125 40% 0,007 0,115
39
Figure 14: Scenario 1 Salderingsregeling, current component prices
Figure 15: Scenario 2 Salderingsregeling, future component prices
40
Figure 16: Scenario 3 Terugleversubsidie (positive scenario), current component prices
Figure 17: Scenario 4 Terugleversubsidie (positive scenario), future component prices
41
Figure 18: Scenario 5 Terugleversubsidie (negative scenario), current component prices
Figure 19: Scenario 6 Terugleversubsidie (negative scenario), future component prices
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 €- €100,000.00 €200,000.00 €300,000.00 €400,000.00 €500,000.00 €600,000.00 €700,000.00 €800,000.00 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00%100.00% Cap acity (k W) To ta l co st Self-sufficiency
Scenario 5 Terugleversubsidie (Negative cost scenario)
42
4.2. Cost without hydrogen storage system
Table 10 demonstrates that without any hydrogen storage system components the self-sufficiency levels are around 32%, for all scenarios. The total costs vary according to the electricity costs. For the ‘salderingsregeling’ and the ‘terugleversubsidie’ positive and negative scenario the cost are: around €274.000 (scenario 1 & 2), €211.000 (scenario 3 & 4) and €335.000 (scenario 5 & 6) respectively. Therefore, the differences in electricity policy have a large impact on the total costs when no hydrogen storage system components are used.
Table 10: Self-sufficiency and total cost without hydrogen storage system
Electrolyzer Fuel cell Number of
solar panels
Total cost
43
4.3. Electrolyzer and fuel cell capacity
Figure 20: Optimal electrolyzer capacity
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 30% 40% 50% 60% 70% 80% 90% 100% Cap acity k W Self-sufficiency (%)
Optimal electrolyzer capacity
44
Figure 21: Optimal fuel cell capacity
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 30% 40% 50% 60% 70% 80% 90% 100% Cap acity k W Self-sufficiency (%)
Optimal fuel cell capacity
45
4.4. Total cost
Figure 22: Total cost
46
Average of 5 runs Results 5 runs for minimal cost
Self-sufficiency Total cost Electrolyzer (kW)
Fuel cell
(kW) Self-sufficiency Total cost
Electrolyzer (kW) Fuel cell (kW) Scenario 1 42% € 264.476,62 3,68 0,04 43% € 262.111,22 4,08 0,04 45,00% € 257.509,25 4,87 0,06 44% € 259.564,20 4,46 0,05 45,00% € 257.650,46 4,91 0,06 45% € 257.315,68 4,87 0,05 45,00% € 257.139,90 4,85 0,05 46% € 261.094,49 5,29 0,07 45,00% € 257.277,29 4,88 0,05 47% € 260.394,56 5,71 0,08 45,00% € 257.001,50 4,85 0,05 48% € 262.512,84 6,14 0,09
Self-sufficiency Total cost Electrolyzer Fuel cell Self-sufficiency Total cost Electrolyzer Fuel cell
Scenario 2 45% € 246.496,66 4,88 0,05 46% € 247.769,84 5,29 0,07 50,00% € 248.897,69 7,13 0,21 47% € 245.933,26 5,72 0,09 50,00% € 248.395,26 7,08 0,20 48% € 246.266,42 6,15 0,11 50,00% € 243.594,92 7,10 0,19 49% € 245.971,54 6,62 0,15 50,00% € 243.574,57 7,07 0,17 50% € 245.583,36 7,09 0,19 50,00% € 243.454,36 7,09 0,17 52% € 248.728,78 8,02 0,25
Scenario 3 Self-sufficiency Total cost Electrolyzer Fuel cell Self-sufficiency Total cost Electrolyzer Fuel cell
38% € 210.795,31 2,15 0,02 40% € 209.654,79 2,91 0,02 40,00% € 208.899,74 2,94 0,02 41% € 209.929,56 3,29 0,03 40,00% € 209.579,76 2,93 0,02 42% € 214.923,92 3,68 0,03 40,00% € 210.506,39 2,90 0,02 43% € 214.400,77 4,05 0,04 40,00% € 209.116,61 2,91 0,02 44% € 212.731,50 4,48 0,05 40,00% € 210.171,45 2,88 0,02 45% € 212.461,11 4,86 0,05
47
Average of 5 runs Results 5 runs for minimal cost
Scenario 4
Self-sufficiency Total cost Electrolyzer (kW)
Fuel cell
(kW) Self-sufficiency Total cost
Electrolyzer (kW) Fuel cell (kW) 40% € 202.984,66 2,86 0,01 41% € 201.537,98 3,25 0,02 41,00% € 201.484,29 3,25 0,02 42% € 203.758,13 3,64 0,02 41,00% € 201.529,09 3,23 0,02 43% € 203.618,61 4,04 0,03 41,00% € 201.484,77 3,25 0,02 44% € 201.887,57 4,43 0,04 41,00% € 201.726,48 3,25 0,02 45% € 201.708,53 4,86 0,05 41,00% € 201.465,26 3,26 0,02 46% € 204.557,07 5,28 0,06
Scenario 5 Self-sufficiency Total cost Electrolyzer Fuel cell Self-sufficiency Total cost Electrolyzer Fuel cell
42% € 321.110,68 3,72 0,06 43% € 320.273,38 4,10 0,07 45.00% € 323.349,23 4,94 0,10 44% € 318.061,66 4,50 0,08 45,00% € 316.194,19 4,92 0,10 45% € 317.681,66 4,93 0,10 45,00% € 316.718,13 4,94 0,10 46% € 318.662,09 5,36 0,12 45,00% € 316.213,12 4,94 0,10 47% € 319.461,43 5,77 0,15 45,00% € 315.933,63 4,90 0,10 48% € 319.143,74 6,22 0,17
Scenario 6 Self-sufficiency Total cost Electrolyzer Fuel cell Self-sufficiency Total cost Electrolyzer Fuel cell
48
4.5. Result analysis
All scenarios do not have any effect on the optimal capacities, thus for all scenarios the optimal capacities are the same for a given self-sufficiency level. Since both the electrolyzer and fuel cell capacity follows the same shape and values for all scenarios. It can be seen that for the electrolyzer (figure 18) capacity all scenarios have roughly the same values and same shape. The same holds for the fuel cell (figure 19). The difference between the fuel cell and electrolyzer capacity is that the shape for fuel cell capacity is more concave. This is logical because the demand probability distributions remain the same, thus in order to meet a certain self-sufficiency level a specific capacity for both the fuel cell and electrolyzer is needed. The fuel cell capacity remains low. This can be explained due to conversion losses, which makes a fuel cell expensive compared to 1) importing electricity, 2) exporting electricity. Using the hydrogen in heating or mobility reduces the conversion losses and thus increases the self-sufficiency. For example; 100 kWh of renewable electricity is produced, through the electrolyzer (75% efficiency) 75 kWh is stored in hydrogen. This hydrogen can be used in heating (95% efficiency) or by the fuel cell (50% efficiency), the total conversion efficiency is thus for the fuel cell 37.5% and for heating 71.25%. Using it by the fuel cell results in 37.5 kWh of electricity while using it for heating results in 71.25 kWh of heat.
For the results of the total costs on the left three different starting points can be observed, these are the electricity costs and on the right two distinctions can be made, these are the component prices. As shown in figure 20 the minimum for each scenario lies around the same self-sufficiency level. In the table 11 the minimal costs for all six scenarios are between the self-sufficiency levels of 40-50%.
In the table 11 it can be seen that the self-sufficiency levels increase when the objective is to minimize costs, when the component prices decreases. This can be seen by comparing scenario 1, 3 and 5 with scenario 2, 4 and 6. Thus, decreasing component prices will lead to an increase in self-sufficiency levels in order to minimize costs.
49
Table 12: Minimal cost per scenario 245 solar panels
Average of 5 runs Results 5 runs for minimal cost
Self-sufficiency Total cost Electrolyzer (kW)
Fuel cell
(kW) Self-sufficiency Total cost
Electrolyzer (kW) Fuel cell (kW) Scenario 1 32,00% € 250.889,91 1,69 0,00 34,00% € 246.172,22 2,63 0,00 40,00% € 247.034,18 5,85146519 0,00 36,00% € 244.210,66 3,64 0,00 40,00% € 240.385,23 5,88133275 0,00 38,00% € 244.635,56 4,70 0,00 40,00% € 239.662,13 5,88066434 0,00 40,00% € 241.439,04 5,86 0,00 40,00% € 240.325,22 5,88067215 0,00 42,00% € 249.542,24 7,10 0,00 40,00% € 239.788,44 5,82759575 0,00
Self-sufficiency Total cost Electrolyzer (kW)
Fuel cell
(kW) Self-sufficiency Total cost
50
4.6. Sensitivity analysis: number of solar panels
For the number of solar panels the same analysis has been performed as in part 4.1. Scenario 1 and 2 are used in order to determine the effect of fewer solar panels on the self-sufficiency and total costs of the hydrogen storage system. In this case 245 solar panels are taken.
Figure 23: Scenario 1 245 Solar panels
Figure 24: Scenario 2 245 Solar panels
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 €0.00 €100,000.00 €200,000.00 €300,000.00 €400,000.00 €500,000.00 €600,000.00 30% 35% 40% 45% 50% 55% 60% 65% 70% Cap acity (k W) To ta l co st Self-sufficiency
Scenario 1; 245 solar panels
Total cost Electrolyzer Fuel Cell 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 €0.00 €50,000.00 €100,000.00 €150,000.00 €200,000.00 €250,000.00 €300,000.00 €350,000.00 €400,000.00 €450,000.00 €500,000.00 30% 35% 40% 45% 50% 55% 60% 65% 70% Cap acity (k W) To ta l co st Self-sufficiency
Scenario 2; 245 solar panels
51 Table 12 and figures 23 and 24 allow the following conclusions to be drwam. First, the fuel cell capacity is for all self-sufficiency levels zero. Secondly, with the use of a hydrogen storage system, the total cost can be decreased, thus even with fewer numbers of solar panels, it is still possible to reduce the total cost.
In figure 25 the electrolyzer capacity for scenario 1 and 2 are given. Where for each scenario the optimal electrolyzer capacity is given for 245 and 490 solar panels. With 245 solar panels the electrolyzer capacity increases harder since the total renewable energy is lower and in order to achieve a certain self-sufficiency more capacity is needed to reach the level of hydrogen production. Since the renewable energy is first used to meet the electricity demand. Therefore, a lower number of solar panels, results in a higher optimal capacity for the electrolyzer.
Figure 25: Electrolyzer capacity 245 vs 490 solar panels
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 20% 40% 60% 80% 100% Cao acity (k W) Self-sufficiency
Electrolyzer capacity 245 vs 490 solar panels
52
5. DISCUSSION
This research aimed to determine the trade-offs between 1) the capacity of the electrolyzer and fuel cell in a hydrogen storage system and 2) the total costs and 3) self-sufficiency. The developed model is able to give insights in the trade-off between the capacity of the electrolyzer and fuel cell. In this research multiple scenarios were analyzed in order to find the optimal configuration for component capacity within a hydrogen storage system for different scenarios.
The results show that for all scenarios a hydrogen storage system will reduce cost. When table 10 and 11 are compared, it can be seen that for all scenarios the total cost decrease with the use of a hydrogen storage system while also increasing the self-sufficiency from 32% to 40-50% depending on the scenario. For self-sufficiency levels of 60% or higher the cost increase exponentially (see figure 20) and are therefore not realistically achievable.
It is noteworthly that for all different scenarios the optimal capacities for the fuel cell and electrolyzer are the same. The fuel cell capacity is low, at 70% self-sufficiency the fuel cell capacity is still below 600W (see figure 19). Investing in the fuel cell is not attractive because it has multiple conversion losses. First in order to create hydrogen with the electrolyzer 25% is lost, and second after converting hydrogen back to electricity another 50% is lost. Thus, in this setting, and probably in more individual settings, such as households or farms, the fuel cell is too inefficient. Using the hydrogen in for example heating or mobility will result in higher self-sufficiency while the costs are lower. The conversion efficiency for the fuel cell is 37.5% and for heating 71.25%.
53
5.1. Limitations and future research
A clear limitation of this research is that a comparison with real world data was not possible. Therefore, it is appropriate to consider in a next study how the model behaves compared to an existing hydrogen storage system. A second limitation is that in this study input data of the electricity demand and mobility demand were not available. As a consequence probability functions were developed in order to simulate these demand functions. In future research it might be interesting to use real world data as input.
The model has the following assumptions that need to be further developed in order to approach real-world scenario’s even closer:
In this model the assumption has been made that the components are not affected by down-time in terms of failure and maintenance, as a consequence the system might have a better output than what would happen in real-world settings.
For the renewable energy output the simplification has been made that the solar panel output remains 100% over the years, while after 10 years the nominal power is reduced to 92% (Hanwha Q CELLS Corp., n.d.). This reduction in power might have a large impact on the achievable self-sufficiency.
The storage for hydrogen is in this study not taken into account in terms of storage size or as a decision variable. Within this study the storage costs are taken as a function of the maximum peak storage during the simulation run. In future research this might be interesting to take into account since hydrogen storage is relatively expensive (€477/kg).
