Energy & Environmental Science
`
`Mining Bitcoins with Carbon Capture and Renewable Energy
`for Carbon Neutrality Across States in the USA
`
`Journal: Energy & Environmental Science
`
`Manuscript ID EE-ANA-12-2021-003804.R2
`
`Article Type: Analysis
`
`Date Submitted by the
`Author: 07-Jun-2022
`Complete List of Authors: Niaz, Haider; Cornell University
`Shams, Mohammad; Pukyong National University
`Liu, Jay; Pukyong National University, Chemical Engineering
`You, Fengqi; Cornell University,
`
`1
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`Exhibit 1031
`Crusoe v. Upstream
`PGR2023-00039
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`Page 1 of 22
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`Energy & Environmental Science
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`Title: Mining Bitcoins with Carbon Capture and Renewable Energy for Carbon Neutrality Across States in
`
`the USA
`
`Manuscript ID: EE-ANA-12-2021-003804.R2
`
`Broader context:
`
`Bitcoin mining's thirst for energy consumption and associated carbon emissions have raised concerns
`
`across the globe. The recent bitcoin boom led to a significant increase in electricity demand and carbon
`
`emissions. A few countries, such as China, Russia, and Iran, banned bitcoin mining to prevent grid
`
`imbalances and environmental damages. As a result, miners are moving to the U.S. for cheaper electricity
`
`and more mining freedom. However, concerns remain regarding economic and environmental integrity.
`
`This study, therefore, examines bitcoin's economic and environmental standing across the U.S. states for
`
`potential mining sites. Sustainable mining is achievable via initiatives, such as carbon capture and
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`renewable-powered mining farms. States with a large share of renewable energy in the electrical grid and
`
`lower electricity prices can potentially mitigate environmental damages. This study also compares the
`
`break-even selling prices of bitcoin to determine potential profit margins for mining sites in different
`
`states. The study's findings provide a deep understanding of the policy implications of balancing economic
`
`development and environmental protection. Incentives for carbon capture and eco-friendly mining will
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`benefit relevant stakeholders if policymakers and bitcoin investors take appropriate action.
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`Received 00th January 20xx,
`Accepted 00th January 20xx
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`DOI: 10.1039/x0xx00000x
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`Mining Bitcoins with Carbon Capture and Renewable Energy
`for Carbon Neutrality Across States in the USA
`Haider Niaz,a,b Mohammad H. Shams,c Jay. J Liu,*a,c and Fengqi You*b
`
`Bitcoin mining requires a significant amount of electricity to validate blocks, increasing greenhouse gas emissions.
`Therefore, major countries such as China, Iran, Russia, Turkey, and Vietnam are banning bitcoin mining to avoid
`grid imbalances, power failures, and environmental issues. To alleviate these concerns, we conducted a techno-
`economic analysis of 50 states and a federal district (Washington D.C.) in the US in terms of the feasibility of bitcoin
`mining using carbon capture and renewable energy. We analyzed the profitability of bitcoin mining in the US states
`using grid and renewable power resources along with high-temperature and low temperature direct air capture
`technologies for CO2 capture and storage and methanol as a product. From both economic and environmental
`perspectives, we evaluated the net CO2 emission for each state to determine its competitive advantages. Overall,
`this work offers a holistic overview of where bitcoin mining can be economically viable across US states.
`Additionally, it provides insights into achieving environmentally friendly cryptocurrency mining regulations based
`on carbon capture and renewable energy and gauging the costs of bitcoin mining powered by the grid and high
`renewable penetration across the US states while pursuing carbon neutrality.
`
`Introduction
`Currently, the use of fossil fuels is inevitable due to the lack of
`sustainable resources to meet the energy demand, leading to
`substantial carbon emissions. Although renewables also
`participate in electricity generation, their fluctuating nature and
`high capital expenses make them uncompetitive to provide
`affordable electricity. Among grid electricity consumers,
`besides industrial, commercial, and residential users, new
`consumers have recently emerged, i.e., crypto miners, raising
`concerns over both the adequacy of power grids and
`environmental aspects. Among various cryptocurrencies,
`bitcoin has caused the highest energy consumption and often
`resulted in grid failures due to electricity shortages 1. According
`to the Cambridge bitcoin electricity consumption index, bitcoin
`mining consumes an estimated 111.63 TWh of electricity yearly
`with estimated theoretical lower and upper bounds of 40.54
`and 418.46 TWh, respectively2. This estimated power
`consumption accounts for 2.91% of the annual electricity
`consumption of the US and corresponds to the electricity
`demands of some countries, such as Poland, Sweden, Finland,
`and Norway 3. In addition, bitcoin mining generates additional
`
`a. Department of Chemical Engineering, Pukyong National University, Busan 48513,
`Republic of Korea.
`b. Smith School of Chemical and Biomolecular Engineering, Cornell University,
`Ithaca, New York 14853, United States of America
`c. Institute of Cleaner Production Technology, Pukyong National University, Busan
`48547, Republic of Korea
`† Footnotes relating to the title and/or authors should appear here.
`Electronic Supplementary Information (ESI) available: [details of any supplementary
`information available should be included here]. See DOI: 10.1039/x0xx00000x
`
`CO2 emissions associated with the vast electricity consumption,
`accounting for 90.76 million tons of CO2 emission annually 4. As
`the world is already scrambling to meet the goals of the Paris
`agreement, with the emergence of new grid consumers, the
`devastating impacts of cryptocurrency use are yet to be seen on
`the progress in achieving these goals 5. On September 14, 2021,
`China started a crackdown on crypto miners and banned all
`cryptocurrency transactions and mining activities. As a result,
`miners started to move to other cryptocurrency-friendly
`countries, such as Serbia, and predominantly to New York and
`Texas in the US, accounting for 19.9% and 14% of bitcoin’s hash
`rate share within the US, respectively 6.
`Nevertheless, it is unclear whether mining in these states will be
`viable for the economy and the environment. Therefore, the
`main goal of this study was to determine the best US states for
`investment in bitcoin mining farms by considering technical,
`economic, and environmental aspects.
`Blockchain consists of chronologically and cryptographically
`connected blocks that are a set of transaction records validated
`and approved by participating miners on the blockchain
`network 7. The network security is ensured by connecting each
`block in the chain pattern with the digital signature of the
`previous block. Any change in the block requires validation,
`which follows a series of steps and a protocol called the
`consensus mechanism. The commonly known blockchain
`consensus mechanisms include Proof of Stake (PoS) and Proof
`of Work (PoW) 8. Bitcoin follows a PoW mechanism that
`validates transactions and maintains a highly secure blockchain.
`However, this mechanism has been criticized for not utilizing
`computer resources efficiently, which comes with additional
`power consumption 9. Compared to PoS, PoW has proven to be
`
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`more reliable so far in maintaining the security of a distributed
`public network 10. Moreover, PoW is the only consensus
`mechanism that has been proven at scale, making it better than
`PoS and thus more effective 11.
`
`In 2008, Satoshi founded bitcoin, a digital currency that relies
`on a decentralized system, where participants provide
`computing power to validate transactions and secure network
`integrity by solving mathematical problems. Each verified
`transaction is incentivized with a digital currency known as
`bitcoin 12. The power needed to mine a bitcoin was initially low.
`However, in 2018, the computational power required for
`bitcoin mining increased four-fold, correspondingly increasing
`power consumption. Besides, the profitability of bitcoin mining
`highly depends on mining equipment and electricity
`affordability in the region. So, the location and the miner must
`be chosen carefully. With the increase in the bitcoin price,
`investors started investing in their own mining farms, while
`individual miners
`joined mining pools and
`supplied
`computational power to solve blocks to be added to the
`blockchain to mine bitcoins 13. All these miners consumed
`excessive power for their mining equipment and needed
`auxiliaries to provide cooling and ensure mining efficiency.
`Higher power consumption from the grid raised concerns as
`associated carbon emissions also increased. In this context,
`renewable energy can be a sustainable option to power bitcoin
`farms. However, their fluctuating nature makes them a less
`reliable resource unless coupled with energy storage options
`such as battery energy storage systems (BESS) or energy in the
`form of hydrogen 14. It is largely unknown whether investing in
`renewable
`infrastructure would be a plausible solution,
`considering the fluctuating bitcoin price and the intermittent
`nature of renewable energy. Relevant literature on economic
`and environmental assessments of using grid and renewable
`electricity for bitcoin farming is relatively scarce, making it hard
`for investors and policymakers to develop relevant solutions 15.
`Little work has been conducted on bitcoin investments, making
`it difficult to analyze its potential in the long term. Orcutt
`discussed the bitcoin mining rush in Texas, US using wind farms
`and suggested installing 100 MW of electricity specifically for
`bitcoin mining 16. Chinese mining chip maker Bitman migrated
`to start a 50 MW facility in Rockdale, Texas, with an investment
`of around USD 500 million17. A German firm, Northern data, also
`plans to invest in Rockdale, Texas to build the world’s largest
`bitcoin mining facility16. Recently, Northern Data acquired the
`bitcoin mining company Bitfield N.V., becoming a global player
`with around 33,000 latest generations of application-specific
`integrated circuits (ASICs) 18. However, a considerable gap lies
`in the assessment of other states as potential bitcoin mining
`sites. Huge investments will likely follow, including that of the
`financial firm Square Inc. 19. From the operational and economic
`perspectives, Bastian-Pinto et al. discussed balancing
`renewable investments in wind farms and bitcoin mining by
`optimally selecting outputs (electricity and bitcoin mining) that
`can maximize return and reduce economic risks 20. Andoni et al.
`reviewed blockchains in the energy sector and emphasized the
`benefits of blockchain for energy system operation, market, and
`
`consumers 21. They further discussed how bitcoin mining could
`create balance in the energy market and act as shock absorbers
`in the volatile energy price market. Bitcoin mining can also serve
`as a balancing element when the renewable supply surges to
`accommodate any surplus generation from renewable power,
`hence
`reducing
`yearly
`curtailments22. However,
`the
`environmental
`impacts of grid-powered bitcoin mining
`outweigh its economic advantages.
`its
`Regardless of the benefits of the bitcoin economy,
`environmental impacts will be seen in the long term 23. Stoll et
`al. examined the carbon footprint of bitcoin 13. They reported
`an estimated 45.8 TWh with annual carbon emissions in the
`range of 22–22.9 Mt CO2 originating from bitcoin mining for the
`year 2018 alone, equivalent to emissions produced by countries
`such as Jordan and Sri Lanka. Although the fate of bitcoin is hard
`to predict, Mora et al. suggested that bitcoin will increase the
`electricity demand, which can cause a global temperature
`increase of above 2°C in just a few decades 24. Lars et al. also
`supported this prediction 25. In addition, non-functional and
`scrapped mining equipment added an annual 30.7 metric
`kilotons of e-waste as of May 2021 26. Renewable-powered
`bitcoin mining farms can be interesting to investigate as they
`can provide tangible support to balance energy supply and
`demand and reduce carbon emissions to a great extent.
`However, due to the massive
`investments needed for
`renewable infrastructure, comprehensive analysis in terms of
`cost benefits and environmental sustainability is required 19.
`A rigorous study is needed to explore the hidden economic and
`environmental impacts of bitcoin mining by the grid and
`renewable resources. Even though miners are rushing to Texas
`for cheaper electricity costs, the resulting environmental
`damages are still unknown. Besides, other US states may also
`provide competitive advantages over Texas. Therefore, we
`analyzed eight different scenarios with grid-only-powered
`(GOP) and high renewable penetration-powered (HRPP) bitcoin
`mining farms considering multiple factors that define each
`scenario’s actual economic and environmental standings for the
`US states. The tackled research gaps have been highlighted in
`the following study contributions:
`I.
`This study evaluated US states as potential candidates
`for GOP and HRPP bitcoin mining via carbon capture
`and utilization initiatives.
`The carbon footprint was estimated for each state.
`Furthermore, carbon emissions were calculated using
`the grid electricity consumption based on the non-
`renewable share for respective states.
`The electricity price, wind speed, solar irradiation, and
`state-wise solar capacity factor were collected for one
`year to determine the optimal grid and renewable
`share for a bitcoin mining farm.
`The direct air capture (DAC) and methanol production
`plants were then sized to capture the emissions. Based
`on their respective power consumption, the optimal
`numbers of electrolyzers (ELE), fuel cells (FCs), heat
`pumps (HP), BESS, hydrogen tanks (HTANKs), and
`green hydrogen needed were evaluated.
`
`II.
`
`III.
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`IV.
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`2 | Energy Environ. Sci. 2021, 00, 1-3
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`Data Gathering From Sources
`
`CO2 & MeOH Energy Demand
`
`Pt
`PPPePP PtPP
`PeP
`
`p
`Heat Pum p
`
`H2
`
`H2
`
`GrGrGreen H2reenn H
`
`
`
`
`
`n HHH2
`
`HTANK
`
`HTANKH K
`
`
`BESS
`BESSBES
`
`FC
`-
`
`+
`
`O2
`
`H2
`
`ELE
`
`MeOH
`
`CO2 & MeOH Optimization Model
`
`(cid:131) Power Purchase from Grid
`(cid:131) Annualized Cost of Equipment
`(cid:131) O&M cost of Equipment's
`(cid:131) Fixed Cost of Equipment’s
`(cid:131) Green Hydrogen Supply
`
`Heat Pum p
`
`H2
`
`H2
`
`Green H2
`
`FC
`
`HH
`HTANK
`
`+
`
`-
`
`O2
`
`H2
`
`BESS
`BESSBES
`
`ELE
`
`MeOH
`
`Grid Mix (%)
`50 %
`Calculate Grid Emissions From
`Fossil Fuels Based On Resource
`Mix (%)
`
`Fossil Share
`50 %
`X amount of
`CO2 Emissions
`
`Wind Speed
`
`Capacity Factor
`
`Elec. Prices
`
`Bitcoin Mining Farm Energy Demand
`Pe Pt
`
`
`PPPePPPP tPPePPPP PtPe t
`
`
`Heat Pum p
`
`CP
`
`
`
`LT DACLT
`
`Bitcoin
`Bit
`i
`Mining Farm
`
`HT DAC
`
`Bitcoin Mining Farm Optimization Model
`
`(cid:131) Power Purchase from Grid
`(cid:131) Annualized Cost of Equipment
`(cid:131) O&M cost of Equipment's
`(cid:131) Fixed Cost of Equipment’s
`(cid:131) CO2 Emission Penalty
`Equipment
`
`Solar Panels Wind Turbine
`
`BESS
`
`Grid Power
`G
`
`Techno-Economic
`Analysis & Break-
`Even Selling
`Price of Bitcoin
`(BESPBit)
`
`CAPEX & OPEX
`
`CO2
`MeOH
`Products
`
`Expenses
`
`Profit
`
`BESPBit
`
`
`
`Figure 1. Proposed framework for evaluating the BESPBit for various US states.
`
`V.
`
`These results were then used in the comprehensive
`economic analysis to evaluate the break-even selling
`price of bitcoin (BESPBit).
`Overall, this study will help investors and policymakers make
`informed decisions about cryptocurrency mining, paving the
`way for its sustainable implementation in the future.
`The rest of the paper is organized as follows. In Section 2,
`preliminaries are described. Section 3 describes the framework
`of the study. The case study and system description are
`
`elaborated in Section 4. Section 5 presents the results and
`discussion. Finally, the paper is concluded in Section 6.
`
`Preliminaries
`Bitcoin mining farms and miners
`Crypto mining farms are technically data centers equipped with
`devices with high computational power designed to solve
`complex mathematical problems to mine a cryptocurrency as
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`an incentive. Bitcoins can be mined in diverse ways: individually
`with small computational power, at a large scale with thousands
`of mining equipment and hash power, or by joining a mining
`pool where individuals sign up and supply their mining power
`and, as a result, earn their relative share. The devices that mine
`cryptocurrencies are called miners.
`DAC model
`DAC systems are the most developed and commercially
`available technology to capture CO2 in the air 27. Besides their
`commercial advancement, negative emissions can be achieved
`by CO2 storage and mineralization. Furthermore, captured CO2
`can be used as a feedstock for carbon-based fuels, other value-
`added chemicals, and building materials 28. Thus, the DAC
`approach was adopted for CO2 capture. It can either be a high-
`temperature aqueous solution (HT-DAC) or a low-temperature
`solid sorbent (LT-DAC) system. As the name suggests, HT-DAC is
`an energy-intensive process that captures CO2 in the air when
`the air meets a solvent in the absorption column under ambient
`conditions. The solution with captured CO2 goes through a
`regeneration cycle in which depleted CO2 air leaves the column,
`and the solvent then undergoes HT processing to recover the
`solvent and extract CO229. Similarly, LT-DAC uses
`low
`temperature and a solid sorbent to absorb CO2, which releases
`the captured CO2 from the air upon mild heating. Both
`technologies have their advantages and shortcomings: HT-DAC
`can handle larger quantities, whereas LT-DAC can handle one-
`third of the capacity of HT-DAC 29.
`Methanol production facility
`The methanol facility utilizes CO2 and H2 as raw materials to
`produce MeOH. MeOH was chosen as a pathway due to
`multiple reasons, which can be listed as follows:
`I. MeOH is an attractive fuel in emerging economies as a
`liquid fuel to replace conventional carbon-intensive
`energy sources. 30,31
`Formaldehyde, the main derivative of MeOH, accounts
`for 31% of the world’s MeOH demand. Other uses
`include biodiesel, gasoline blending, and dimethyl
`ether. The high global MeOH demand drives its
`production growth, which is expected to increase at an
`average rate of 5% in the next five years and as a fuel
`at a rate of 6.5%30. Besides, MeOH is a versatile
`chemical compound that serves as a fuel and hydrogen
`energy carrier and is also a base chemical for the
`chemical and petrochemical industry 32. In addition,
`the global demand for MeOH is increasing due to its
`role in monomeric olefin production, such as ethylene
`and propylene, the bases of the plastic industry.
`Lastly, MeOH is the best option due to its technological
`maturity and compatibility with the current fuel
`infrastructure,
`production
`cost,
`and
`public
`acceptance32.
`Therefore, the MeOH pathway was explored for the GOP and
`HRPP scenarios owing to its rising global demand.
`
`III.
`
`II.
`
`Framework of the study
`
`Energy & Environmental Science
`
`The methodology adopted in this study to evaluate the BESPBit
`across various US states is described in the following steps.
`Step 1: As shown in Figure 1, the process starts with collecting
`the data for wind speed, solar irradiation, and average hourly
`monthly price for grid electricity. Furthermore, for the grid-
`based electricity, the percentage of resource mix (%), i.e., fossil
`or renewables was also collected for individual US states to find
`out the actual fossil-based contribution for mining bitcoins. By
`using the contribution fraction of the consumed respective
`fossil resource, i.e., coal, natural gas, oil, etc., the equivalent
`amount of CO2 emitted was calculated to size the system
`needed for the downstream process. The amount of CO2
`emissions from each of the respective fossil resources (per MW
`of produced power) was obtained from the US Energy
`Information Administration (EIA) and other sources31,33,34. The
`DAC and MeOH plants were introduced to make bitcoin mining
`environmentally sustainable despite
`their vast energy
`consumption.
`Step 2: Two scenarios were considered to power the bitcoin
`mining farm: GOP and HRPP scenarios. Only wind and solar
`resources were considered for renewable sources due to a lack
`of data resources for other renewable resources in other states.
`The time resolution for the data used was one hour for 1 year,
`i.e., 8760 points. An optimization model was run for the GOP
`scenario to evaluate the optimal number of solar panels, wind
`turbines, and grid power needed to run the mining farm and the
`cooling system. The objective function was set to minimize the
`annual cost while also considering the penalty of CO2 emissions
`when utilizing the grid-based power. By using the optimal grid
`share value, the equivalent amount of CO2 emissions was
`evaluated and used as a basis for the DAC plant.
`Step 3: Based on the amount of CO2 emissions calculated in Step
`2, the size of the DAC plant and its electrical and thermal
`requirements were evaluated. Two different DAC plants were
`considered: HT-DAC and LT-DAC plants. Both vary in cost,
`energy requirements, and their respective capturing capacities.
`Furthermore, two different routes were considered: CO2
`capture and storage and MeOH as a product. Later, the amount
`of grid power needed was evaluated for the GOP scenario to
`satisfy the electrical and thermal demand. In contrast, for the
`HRPP case scenario for CO2 capture and storage, and MeOH as
`a product, the optimal numbers of FCs, ELEs, HPs, BESS, and
`HTANKs, and green hydrogen supply needed to meet the energy
`demands were evaluated using an annual cost minimization
`objective function, similar to the one used for the mining farm
`but with additional equipment. Similarly,
`the optimal
`configuration was re-evaluated for MeOH as a product for all
`states.
`Step 4: Finally, using the optimal numbers evaluated from the
`optimization model for meeting mining farm energy demands
`and DAC and MeOH optimization models, the total number of
`equipment and their respective CAPEX and OPEX were
`recalculated. A comprehensive economic analysis was
`performed to determine the BESPBit for US states for each
`scenario.
`Step 5: The results were then compared for each scenario’s
`most and least favorable US states, respectively. Furthermore,
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`4 | Energy Environ. Sci. 2021, 00, 1-3
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`all cases were collectively compared, and recommendations
`and conclusions were drawn for each scenario’s best and worst
`states for bitcoin mining investments.
`
`Mathematical Formulation
`Objective function
`In the proposed formulations, the total annual cost (TAC) of the
`system is minimized via the decision variables, including the
`
`number of units of each equipment type (i.e., (cid:1840)(cid:2900)(cid:2906), (cid:1840)(cid:2907)(cid:2904), (cid:1840)(cid:2889)(cid:2896)(cid:2889),
`(cid:1840)(cid:2890)(cid:2887), (cid:1840)(cid:2892)(cid:2900), (cid:1840)(cid:2886)(cid:2889)(cid:2903)(cid:2903), and (cid:1840)(cid:2892)(cid:2904)(cid:2885)(cid:2898)(cid:2895)), binary variables for on/off of
`the BESS, i.e., u(cid:3047)(cid:2869),u(cid:3047)(cid:2870)., electricity delivered to the equipment
`((cid:1842)(cid:1831)(cid:2889)(cid:2896)(cid:2889), (cid:1842)(cid:1831)(cid:2892)(cid:2900), and (cid:1842)(cid:1831)(cid:2886)(cid:2889)(cid:2903)(cid:2903)), electricity purchased from the grid
`((cid:1842)(cid:1831)(cid:2891)(cid:2902)(cid:2893)(cid:2888)), green hydrogen ((cid:1834)(cid:2902)(cid:2889)(cid:2898)), and hydrogen delivered to
`the FC and HTANK ((cid:1834)(cid:2890)(cid:2887) and (cid:1834)(cid:2892)(cid:2904)(cid:2885)(cid:2898)(cid:2895), respectively). The results
`
`from the optimization model will serve as a basis for the
`economic analysis.
`The formulated optimization problem used for calculating the
`optimal numbers of solar panels and wind turbines and grid
`electricity required for bitcoin mining for all scenarios is shown
`in Eqs. (1) and (2), which include annualized CAPEX, fixed and
`variable operations, and maintenance costs. It also considered
`the penalty for the use of grid electricity. The optimization
`problem for DAC and methanol plants can be seen in Eq. (1b).
`No grid electricity was considered for DAC and methanol plants;
`therefore, no CO2 emissions penalty costs were included in the
`objective function. The overall problem was formulated as a
`MILP problem and solved using the CPLEX solver in GAMS 35.
`
`(1)
`
`(2)
`
`(cid:963) {(cid:1842)(cid:1831)(cid:3047)(cid:3008)(cid:3019)(cid:3010)(cid:3005)(cid:942)(cid:1829)(cid:3047)(cid:3008)(cid:3019)(cid:3010)(cid:3005)+(cid:1827)(cid:1840)(cid:1829)(cid:3017)(cid:3023)+(cid:1827)(cid:1840)(cid:1829)(cid:3024)(cid:3021)+
`(cid:3021)(cid:3047)(cid:2880)(cid:2869)(cid:1827)(cid:1840)(cid:1829)(cid:3009)(cid:3017)+(cid:1827)(cid:1840)(cid:1829)(cid:3003)(cid:3006)(cid:3020)(cid:3020)+(cid:1841)&(cid:1839)(cid:3047)(cid:3017)(cid:3023)+(cid:1841)&(cid:1839)(cid:3047)(cid:3024)(cid:3021)+
`(cid:1841)&(cid:1839)(cid:3047)(cid:3009)(cid:3017)+(cid:1841)&(cid:1839)(cid:3047)(cid:3003)(cid:3006)(cid:3020)(cid:3020)+(cid:1832)(cid:1841)(cid:1829)(cid:3017)(cid:3023)+(cid:1832)(cid:1841)(cid:1829)(cid:3024)(cid:3021)+
`(cid:1832)(cid:1841)(cid:1829)(cid:3009)(cid:3017)+(cid:1832)(cid:1841)(cid:1829)(cid:3003)(cid:3006)(cid:3020)(cid:3020)+(cid:1842)(cid:1831)(cid:3047)(cid:3008)(cid:3019)(cid:3010)(cid:3005)(cid:942)(cid:1842)(cid:1829)(cid:3017)(cid:3006)(cid:3004)(cid:3016)(cid:2870)}
`(cid:963) {(cid:1834)(cid:3047)(cid:3019)(cid:3006)(cid:3015)(cid:942)(cid:1829)(cid:3009)(cid:3019)(cid:3006)(cid:3015)+(cid:1827)(cid:1840)(cid:1829)(cid:3017)(cid:3023)+(cid:1827)(cid:1840)(cid:1829)(cid:3024)(cid:3021)+(cid:1827)(cid:1840)(cid:1829)(cid:3006)(cid:3013)(cid:3006)+
`(cid:3021)(cid:3047)(cid:2880)(cid:2869)(cid:1827)(cid:1840)(cid:1829)(cid:3007)(cid:3004)+(cid:1827)(cid:1840)(cid:1829)(cid:3009)(cid:3017)+(cid:1827)(cid:1840)(cid:1829)(cid:3003)(cid:3006)(cid:3020)(cid:3020)+(cid:1827)(cid:1840)(cid:1829)(cid:3009)(cid:3021)+(cid:1841)&(cid:1839)(cid:3047)(cid:3017)(cid:3023)+
`(cid:1841)&(cid:1839)(cid:3047)(cid:3024)(cid:3021)+(cid:1841)&(cid:1839)(cid:3047)(cid:3006)(cid:3013)(cid:3006)+(cid:1841)&(cid:1839)(cid:3047)(cid:3007)(cid:3004)+(cid:1841)&(cid:1839)(cid:3047)(cid:3009)(cid:3017)+
`(cid:1841)&(cid:1839)(cid:3047)(cid:3003)(cid:3006)(cid:3020)(cid:3020)+(cid:1841)&(cid:1839)(cid:3047)(cid:3009)(cid:3021)+(cid:1832)(cid:1841)(cid:1829)(cid:3017)(cid:3023)+(cid:1832)(cid:1841)(cid:1829)(cid:3024)(cid:3021)+
`(cid:1832)(cid:1841)(cid:1829)(cid:3002)(cid:3024)(cid:3006)+(cid:1832)(cid:1841)(cid:1829)(cid:3007)(cid:3004)+(cid:1832)(cid:1841)(cid:1829)(cid:3009)(cid:3017)+(cid:1832)(cid:1841)(cid:1829)(cid:3003)(cid:3006)(cid:3020)(cid:3020)+(cid:1832)(cid:1841)(cid:1829)(cid:3009)(cid:3021)}
`represented as (cid:1842)(cid:1831)(cid:3047)(cid:3013)(cid:3016)(cid:3002)(cid:3005), (cid:1842)(cid:1829)(cid:3047)(cid:3013)(cid:3016)(cid:3002)(cid:3005), and (cid:1834)(cid:3047)(cid:3013)(cid:3016)(cid:3002)(cid:3005), respectively. For
`
`Constraints
`The overall electricity, cooling, and hydrogen balances can be
`
`the bitcoin scenario, only the grid, PV, WT, and BESS were
`considered, whereas, for the DAC and methanol plant, all
`equipment were considered with the addition of green
`hydrogen supply, except for the grid electricity. Therefore, the
`following constraints accounted for general scenarios. For
`respective case scenarios, equipment not considered was taken
`as zero.
`
`(cid:1842)(cid:1831)(cid:3047)(cid:3013)(cid:3016)(cid:3002)(cid:3005)(cid:3398)(cid:1842)(cid:1831)(cid:3047)(cid:3008)(cid:3019)(cid:3010)(cid:3005)+(cid:1842)(cid:1831)(cid:3047)(cid:3003)(cid:3006)(cid:3020)(cid:3020).(cid:3017)(cid:942)(cid:2015)(cid:3003)(cid:3006)(cid:3020)(cid:3020).(cid:3017)(cid:3398)(cid:1842)(cid:1831)(cid:3047)(cid:3003)(cid:3006)(cid:3020)(cid:3020).(cid:3014)(cid:942)
`(cid:2015)(cid:3003)(cid:3006)(cid:3020)(cid:3020).(cid:3014)+(cid:1842)(cid:1831)(cid:3047)(cid:3009)(cid:3017)+(cid:1842)(cid:1831)(cid:3047)(cid:3006)(cid:3013)(cid:3006)(cid:3398)(cid:1842)(cid:1831)(cid:3047)(cid:3007)(cid:3004)=(cid:1842)(cid:1831)(cid:3047)(cid:3024)(cid:3010)(cid:3015)(cid:3005)+
`(cid:1842)(cid:1831)(cid:3047)(cid:3020)(cid:3016)(cid:3013)(cid:3002)(cid:3019)
`(cid:1842)(cid:1829)(cid:3047)(cid:3013)(cid:3016)(cid:3002)(cid:3005)=(cid:1842)(cid:1831)(cid:3047)(cid:3009)(cid:3017)(cid:942)(cid:1829)(cid:1841)(cid:1842)(cid:3009)(cid:3017)
`
`(3)
`
`(4)
`
` PAPER
`
`(5)
`
`
`The upper (MAX) and lower (MIN) penetration limits of
`electricity (PE) from the electrical power grid were represented
`as, respectively,
`
`(6)
`
`electrical grid constraints are defined later in the section. The
`
`respectively, were represented as
`
`(cid:1834)(cid:3047)(cid:3013)(cid:3016)(cid:3002)(cid:3005)=(cid:1834)(cid:3047)(cid:3006)(cid:3013)(cid:3006)+(cid:1834)(cid:3047)(cid:3019)(cid:3006)(cid:3015)(cid:3398)(cid:1834)(cid:3047)(cid:3009)(cid:3021).(cid:3017).(cid:2015)(cid:3009)(cid:3021).(cid:3017)+(cid:1834)(cid:3047)(cid:3009)(cid:3021).(cid:3014)(cid:942)
`(cid:2015)(cid:3009)(cid:3021).(cid:3014)(cid:3398)(cid:1834)(cid:3047)(cid:3007)(cid:3004)
`(cid:1842)(cid:1831)(cid:3014)(cid:3010)(cid:3015)(cid:3008)(cid:3019)(cid:3010)(cid:3005)(cid:3409)(cid:1842)(cid:1831)(cid:3047)(cid:3008)(cid:3019)(cid:3010)(cid:3005)(cid:3409)(cid:1842)(cid:1831)(cid:3014)(cid:3002)(cid:3025)(cid:3008)(cid:3019)(cid:3010)(cid:3005)
`These parameters ((cid:1842)(cid:1831)(cid:3014)(cid:3010)(cid:3015)(cid:3008)(cid:3019)(cid:3010)(cid:3005), and (cid:1842)(cid:1831)(cid:3014)(cid:3002)(cid:3025)(cid:3008)(cid:3019)(cid:3010)(cid:3005)) representing the
`upper and lower limits of green hydrogen, (cid:1834)(cid:3014)(cid:3010)(cid:3015)(cid:3019)(cid:3006)(cid:3015) and (cid:1834)(cid:3014)(cid:3002)(cid:3025)(cid:3019)(cid:3006)(cid:3015) ,
`(cid:1834)(cid:3014)(cid:3010)(cid:3015)(cid:3019)(cid:3006)(cid:3015)(cid:3409)(cid:1834)(cid:3047)(cid:3019)(cid:3006)(cid:3015)(cid:3409)(cid:1834)(cid:3014)(cid:3002)(cid:3025)(cid:3019)(cid:3006)(cid:3015)
`
`(7)
`The main units include the PVs, WTs, ELEs, FCs, HPs, HTANKs,
`and BESS. The governing operation equations and sizing
`constraints are discussed below 36.
`Power generated by wind turbines is dependent on the incident
`wind speed. Furthermore, the wind turbine characteristics are
`the key players in power generation including the cut-in speed
`and the cut-out speed (m/s). A piecewise linear equation was
`used to calculate the wind turbine output power as a function
`of incident wind speed, as shown in the equation below 37:
`
`(cid:1842)(cid:1831)(cid:3045)(cid:3024)(cid:3021),(cid:1874)(cid:3045)<(cid:1874)(cid:3047)(cid:3046)<(cid:1874)(cid:3030)(cid:3042)(cid:3048)(cid:3047)
`(cid:1842)(cid:1831)(cid:3047)(cid:3024)(cid:3021)=(cid:3422)
`
`(cid:1842)(cid:1831)(cid:3045)(cid:3024)(cid:3021)(cid:942)(cid:3049)(cid:3295)(cid:3294)(cid:2879)(cid:3049)(cid:3278)(cid:3284)(cid:3289)(cid:3049)(cid:3293)(cid:2879)(cid:3049)(cid:3278)(cid:3284)(cid:3289),(cid:1874)(cid:3030)(cid:3036)(cid:3041)<(cid:1874)(cid:3047)(cid:3046)<(cid:1874)(cid:3045)
`0,(cid:1867)(cid:1872)(cid:1860)(cid:1857)(cid:1870)(cid:1875)(cid:1861)(cid:1871)(cid:1857)
`(cid:1842)(cid:1831)(cid:3047)(cid:3024)(cid:3021) is the wind power output (in MW) at time t. (cid:1842)(cid:1831)(cid:3045)(cid:3024)(cid:3021) is the
`rated output of the wind turbine (in MW). (cid:1874)(cid:3045),(cid:1874)(cid:3030)(cid:3036)(cid:3041),(cid:1874)(cid:3030)(cid:3042)(cid:3048)(cid:3047) are the
`respectively (in m/s). (cid:1874)(cid:3047)(cid:3046) is the wind speed at any given location
`
`
`
`(8)
`
`rated wind speed and the cut-in and cut-o