Electricity-gas integrated energy system optimal operation in typical scenario of coal district considering hydrogen heavy trucks
GGraphical Abstract
Electricity-gas integrated energy system optimal operation in typical scenario of coal district con-sidering hydrogen heavy trucks
Junjie Yin,Jianhua Wang,Jun You
Power Grid
Coal
Natural Gas Network CH Coal d Hydrogen heavy trucksHydrogen heavy trucks
Hydrogenload
PEM Electrolysis
P2HElectricity
Power load Heat loadPower load Heat load
Methanation H ElectricityCO Hydrogen refueling station H Coal GasificationHeat
Hydrogen refueling station H Coal GasificationHeat H H P2M
Pipeline
Coal District
Transport coal
Energy Network
C2H a r X i v : . [ ee ss . S Y ] F e b ighlights Electricity-gas integrated energy system optimal operation in typical scenario of coal district con-sidering hydrogen heavy trucks
Junjie Yin,Jianhua Wang,Jun You• Advantages of hydrogen heavy trucks in typical scenario of coal industry district are discussed.• The efficient closed loop of hydrogen energy from generation to utilization is proposed.• P2G including power-to-hydrogen and power-to-methane is developed, combined with coal gasification technology.• The economy and low-carbon properties of the proposed IEGS mechanism are analyzed. lectricity-gas integrated energy system optimal operation in typicalscenario of coal district considering hydrogen heavy trucks
Junjie Yin a , Jianhua Wang a , ∗ and Jun You a a School of Electrical Engineering, Southeast University, Nanjing 210096, China
A R T I C L E I N F O
Keywords :Integrated energy systemPower-to-gasCoal-to-hydrogenHydrogen heavy trucksSecond-order cone programmingOptimized scheduling
A B S T R A C T
The coal industry contributes significantly to the social economy, but the emission of greenhousegases puts huge pressure on the environment in the process of mining, transportation, and powergeneration. In the integrated energy system (IES), the current research about the power-to-gas (P2G)technology mainly focuses on the injection of hydrogen generated from renewable energy electrolyzedwater into natural gas pipelines, which may cause hydrogen embrittlement of the pipeline and cannotbe repaired. In this paper, sufficient hydrogen energy can be produced through P2G technology andcoal-to-hydrogen (C2H) of coal gasification, considering the scenario of coal district is rich in coaland renewable energy. In order to transport the mined coal to the destination, hydrogen heavy truckshave a broad space for development, which can absorb hydrogen energy in time and avoid potentiallydangerous hydrogen injection into pipelines and relatively expensive hydrogen storage. An optimizedscheduling model of electric-gas IES is proposed based on second-order cone programming (SOCP).In the model proposed above, the closed industrial loop (including coal mining, hydrogen production,truck transportation of coal, and integrated energy systems) has been innovatively studied, to consumerenewable energy and coordinate multi-energy. Finally, an electric-gas IES study case constructed byIEEE 30-node power system and Belgium 24-node natural gas network was used to analyze and verifythe economy, low carbon, and effectiveness of the proposed mechanism.
1. Introduction
As we all know, the coal district is a typical large energyload of industry. In the production process of mining, prepa-ration, etc., coal mine machineries need to consume a lot ofelectricity and heat. In addition, heavy trucks transport coalto various destinations, which requires a large amount of en-ergy to drive the engine and is essential in the coal industrialproduction process. Moreover, the coal industry areas usu-ally suffer from serious environmental pollution problems,the main reasons include but not limited to coal dust, fac-tory emissions, vehicle exhaust, etc. Facing the tremendousenvironmental pressure and resource shortage, coal districtsthat rely on traditional energy supply methods are in urgentneed of transformation.Nowadays, the development of renewable energy, repre-sented by wind power (WP), solar photovoltaics (PV), etc.,has become an inevitable trend. Generally speaking, coalresources are distributed in inland mountainous areas, andthe local geographical features determine the abundant WPresources in these areas. However, the phenomenon of aban-doning WP and PV is still serious, mainly due to the insta-bility of renewable energy and the difficulty of being directlyintegrated into traditional energy networks.Based on the above analysis, an energy mechanism forthe typical coal districts has yet to be proposed. For coaldistricts, there are the following visions: giving full play tothe advantages of rich wind energy in coal districts, design- ∗ Corresponding author [email protected] (J. Wang)
ORCID (s): (J. Yin); (J.Wang) ing practical and effective energy supply structure systems,and realizing smooth, low-carbon and environment-friendlytransportation of coal resources. As an energy output ter-minal, it has important responsibilities for the entire energynetwork. Therefore, the following goals should be achieved:consuming renewable energy as much as possible, breakingthe status quo of the separate design and independent opera-tion of each existing energy supply system, and establishingthe integrated energy system (IES), in order to promote theoptimization of the energy structure and finally achieve thegrand goal of carbon neutrality.
Regarding IES, many studies mainly focuse on the cou-pling and interaction of power systems and natural gas sys-tems, i.e. , integrated electric-gas systems (IEGS) [1, 2]. Ac-cording to the type of conversion gas, Power-to-gas (P2G)technology can be divided into two types: power-to-hydrogen(P2H) conversion and power-to-methane (P2M) conversion.The hydrogen and methane produced in P2G plants can beused in following ways [3]:(1) Further synthesis to methane or other hydrocarbon fuelsthrough methanation equipment;(2) Injection the mixture of hydrogen and methane into nat-ural gas pipelines by hydrogen compressed natural gas(HCNG) technology [4];(3) Power generation with the help of internal combustionengine or combined heat and power (CHP) devices [5];(4) Hydrogen storage into tanks after pressurization [6];(5) Hydrogen refueling stations for vehicles or the use ofhydrogen in industry.
First Author et al.:
Preprint submitted to Elsevier
Page 1 of 10 omenclature
Abbreviations
C2H Coal-to-hydrogen of coal gasificationIEGS Integrated electric-gas systemIES Integrated energy systemP2G Power-to-gasP2H Power-to-hydrogenP2M Power-to-methanePV PhotovoltaicsSOCP Second-order cone programmingWP Wind power
Parameters and constants 𝛿 𝑊 𝑃
Abandoning WP punishment parameter 𝜌 Hot spare coefficient
LEL
Lower explosive limit of H /CH LFL
Lower flammability limit of H /CH UEL
Upper explosive limit of H /CH UFL
Upper flammability limit of H /CH 𝐶 𝑈 ∕ 𝐷𝑖,𝑡
Start/Stop cost of unit 𝑖 at time 𝑡𝐶 𝑚𝑛 Weymouth constant 𝐻 𝑖 , 𝐽 𝑖 Single start / stop cost of unit 𝑖𝑅 𝑑 , 𝑅 𝑢 Unit down / up ramping speedTS, TO Minimum stop / start time
Sets and indices ≥ Set of natural gas nodes , ≥ = {1 , , … , 𝑚, … , 𝑁 𝑔 } Set of load nodes , = {1 , , … , 𝑖, … , 𝑁 𝐿 } Set of thermal units , = {1 , , … , 𝑖, … , 𝑁 𝑈 } Variables 𝛼 𝑇𝑟𝑢𝑐𝑘𝑡
Transport consumption coefficient of hydrogen trucks 𝑓 𝐶𝑜𝑎𝑙 H ,𝑡 Flow rate produced by C2H at the time slot 𝑡𝑓 𝑇𝑟𝑢𝑐𝑘 H ,𝑡 Total hydrogen demand of heavy trucks at 𝑡𝛼 𝐶𝑜𝑎𝑙𝑡
Efficiency of coal gasification at the time slot 𝑡𝛼 CH elec ,𝑡 Power consumption parameter in process of electroly-sis corresponding to CH 𝛼 CH meth ,𝑡 Power consumption parameter in process of methana-tion corresponding to CH 𝛼 H ,𝑡 Power consumption parameter corresponding to H 𝛽 𝑡 Ratio of mined coal used as the raw material for coalgasification at the time slot 𝑡𝜂 𝑒𝑙𝑒𝑐,𝑡 Reaction efficiency of PEM electrolysis at 𝑡𝜂 𝑚𝑒𝑡ℎ,𝑡 Reaction efficiency of methanation at 𝑡𝑐 H ∕CH Concentration percentage of H /CH 𝜋 𝑚 The square of the pressure value at node 𝑚𝜋 𝑚 , 𝜋 𝑚 Threshold of the square of the pressure value of 𝑚𝑝 𝑚 , 𝑝 𝑚 Threshold of pipeline pressure 𝑠 𝑚 , 𝑠 𝑚 Threshold of natural gas source storage capacity 𝐶 CO Cost of CO emissions 𝐶 𝑓𝑖 Coal consumption cost of thermal power unit 𝑖𝐶 𝑔𝑚,𝑡 Cost of the natural gas network 𝐶 𝑊 𝑃,𝑡
Punishment cost of abandoning WP 𝐶 𝑇𝑟𝑢𝑐𝑘,𝑡
Cost of truck transportation
𝐶𝑜𝑛𝑠 H ,𝑡 Electricty consumption of producing H 𝐸 𝐶𝑜𝑎𝑙,𝑡
Profit from selling coal 𝑓 ′ H ,𝑡 H flow rate produced by P2G equipment for furthermethanation at 𝑡𝑓 H ,𝑡 H flow rate produced by P2G equipment for hydrogenrefueling station at 𝑡𝑓 𝑚𝑛 Natural gas flow from node 𝑚 to node 𝑛𝑀 𝑡 Weight of coal mined at the time slot 𝑡𝑝 𝑚 Pressure value of node 𝑚𝑃 𝑑,𝑖,𝑡 Load demand for electricity of node 𝑗 at time 𝑡𝑃 𝑖, max Maximum output value of unit 𝑖𝑃 𝑖, min Minimum output value of unit 𝑖𝑃 𝑖,𝑡 Output of thermal power unit 𝑖 at time 𝑡𝑃 𝑖𝑛𝑝𝑢𝑡 ∕ 𝑜𝑢𝑡𝑝𝑢𝑡,𝑖,𝑡 Power flow input/output of node 𝑖 at 𝑡𝑃 𝑙,𝑡 Power flow of line 𝑙 at time 𝑡𝑠 𝑚 Gas flow directly injected into the node 𝑚 from thesource 𝑢 𝑖,𝑡 Start and stop status of unit 𝑖 at time 𝑡 At present, some scholars are devoted to the research ofhydrogen compressed natural gas (HCNG) equipment, andhave achieved certain results in the study of the effect of hy-drogen content percentage on integrated systems [4]. How-ever, due to the characteristics of low density and high activ-ity, blending hydrogen reduces the amount of energy deliv-ered by the natural gas network under the same conditions.Hydrogen embrittlement may occur, which poses challengesto safety of the overall system. Due to the hazards of hydro-gen embrittlement caused by the activity of hydrogen molecules,some studies are devoted to solving the location of hydro-gen embrittlement cracks and performing subsequent repairwork of steel pipelines through precise positioning [7]. There- fore, countries have established strict limits on hydrogen blend-ing in natural gas networks (generally the volume of hydro-gen is up to 6%) [8]. Then, the direct use of hydrogen con-verted by P2G technology in the CHP system involves mul-tiple energy conversions, while each conversion is bound tobring about a large energy loss, so the gain is more than theloss. Also, High cost is the primary reason hindering large-scale storage of hydrogen energy, mainly due to pressurizedsystems and containers. Moreover, the current input cost ofhydrogen buses in some cities is too high to make profits.In a typical scenario of coal district, the conditions forthe development of the hydrogen heavy trucks are unique:not only are hydrogen sources abundant, but also the applica-
First Author et al.:
Preprint submitted to Elsevier
Page 2 of 10 ion space of hydrogen heavy truck is broad. Different fromthe high hydrogen price in resource-deficient areas, the coaldistrict has ample and cheap hydrogen, mainly from:(1) More than 90% hydrogen is produced from fossil energy( e.g. , coal, natural gas) or alcohols, which emits green-house gases[9];(2) Only 4% hydrogen is production obtained from renew-able energy electrolysis, has more room for development[10].(Relatively stable WP is more suitable than PV with greaterdaily volatility).Due to the huge demand for coal transportation in theseareas, the number of locally registered heavy trucks is alsovery large, usually reaching tens of thousands. The reasonsand significance of developing hydrogen heavy trucks are asfollows:(1) Hydrogen heavy trucks can be directly developed, whichare rigid demand, skipping low-profit fuel cell buses[11];(2) Fossil energy consumption and greenhouse gas emis-sions can be reduced by replacing diesel heavy trucks;(3) Compared with lithium power batteries, hydrogen heavytrucks are more suitable for heavy-duty and long-distancetransportation, and have the advantages of longer cruis-ing range, shorter charging time, and lighter weight;(4) Solar and wind energy can be effectively absorbed, andhydrogen can be used as a carrier of energy capture,avoiding the negative impact of electricity generated byrenewable energy directly connected to the grid [12];(5) Electrolysis using renewable energy is usually the clean-est way, which can be considered as negative greenhousegas production;(6) The current hydrogen produced by electrolysis in var-ious countries only accounts for 4-6% of the total hy-drogen production, which is still the main improvementdirection and policy preference area.
In order to solve the above-mentioned challenges, mod-els of hydrogen heavy trucks and P2G equipment are estab-lished and second-order cone programming (SOCP) are ap-plied. The main contributions of this work are summarizedbelow.(1) The closed industrial loop between coal mining, hydro-gen production, truck transportation of coal, and inte-grated energy systems has been innovatively proposed.(2) P2G technology has been further expanded, by takinginto account the detailed chemical reaction process ofP2H and P2M. The proposed P2G technology adjustselectrolysis and methanation in real time to control thegeneration ratio of hydrogen and methane.(3) Reasonable use of hydrogen energy, as the fuel of hydro-gen heavy trucks, is proposed, which avoids hydrogenembrittlement and reduces the storage cost. (4) In the scenario of coal district, the models of hydrogenheavy truck, P2G equipment and IEGS are innovativelyproposed. Incorporating heavy trucks into the unifieddispatch of IEGS is conducive to making full use of hy-drogen energy, reducing carbon emissions, and achiev-ing clean and environmental protection.The remaining parts of this paper are organized as fol-lows. The scenario of coal district considering hydrogenheavy trucks and P2G equipment model are introduced inSection II. Section III describes the problem formulation andtransformation. Case study is provided to prove the validityof the proposed model in Section IV. Section V draws theconclusion on this paper.
2. Typical Scenario of Coal District
Power Grid
Coal
Natural Gas Network CH Coal d Hydrogen heavy trucksHydrogen heavy trucks
Hydrogenload
PEM Electrolysis
P2HElectricity
Power load Heat loadPower load Heat load
Methanation H ElectricityCO Hydrogen refueling station H Coal GasificationHeat
Hydrogen refueling station H Coal GasificationHeat H H P2M
Pipeline
Coal District
Transport coal
Energy Network
C2H
Figure 1:
Scenario of coal district considering hydrogen heavytrucks and P2G equipment model of WP to H and CH . As shown in Fig. 1, the closed industrial loop betweencoal mining, hydrogen production, truck transportation ofcoal, and integrated energy systems has been innovativelyproposed.
As summarized in section 1.2, more than 90% of hydro-gen is produced by fossil energy, and the chemical reactionequation is as follows:
C + H O △ ←←←←←←←←←←←←←←←←←→ CO + H Δ 𝐻 = +131 kJ∕mol (1) CO + H O ←←←←←←←←←←←←←←←←←→ CO + H Δ 𝐻 = −41 kJ∕mol (2)Due to the scenario of coal districts in this article, theprocess of producing hydrogen from fossil energy is onlycoal-to-hydrogen. Assuming that the weight of coal mined atthe time slot 𝑡 is 𝑀 𝑡 (ton), and 𝛽 𝑡 (%) is the ratio of mined coalused as the raw material for coal gasification, the amount ofhydrogen produced by coal in this time slot is 𝑓 𝐶𝑜𝑎𝑙 H ,𝑡 = 𝛼 𝐶𝑜𝑎𝑙𝑡 ( 𝛽 𝑡 𝑀 𝑡 ) (3) First Author et al.:
Preprint submitted to Elsevier
Page 3 of 10 able 1
Comparison of heavy trucks with different power types.Hydrogen truck Electric vehicle(EV) Diesel oil truckFilling time 10-15 min Several hours 10-15 minRecharge mileage 500-750 mile 100-300 mile 500-750 mile(Long-distance freight) (Short-distance freight)Impact on the grid Buffer Relatively large No impactEnergy sustainability Promising Depend on battery technology Large price fluctuations, limited reservesEmission Zero Zero High where 𝛼 𝐶𝑜𝑎𝑙𝑡 represents the efficiency of coal gasification atthe time slot 𝑡 . This process is abbreviated as coal-to-hydrogen(C2H). Since the chemical reaction in (1) requires heat ab-sorption, the reaction equipment involved in the process isalso one of the heat loads. Tab. 1 shows the comparison between hydrogen heavytrucks and electric vehicles and diesel trucks in many as-pects. It can be predicted that in the future when hydro-gen energy production technology continues to increase andcosts continue to fall, hydrogen heavy trucks will becomemore competitive.In the actual production process, the amount of coal minedis directly proportional to the required transport capacity ofheavy trucks. In this article, the load capacity and requiredquantity of each heavy truck are no longer considered sep-arately. But from a global perspective, the relationship be-tween the hydrogen consumption of hydrogen heavy trucksand the amount of coal mining is as follows: 𝑓 𝑇 𝑟𝑢𝑐𝑘 H ,𝑡 = 𝛼 𝑇 𝑟𝑢𝑐𝑘𝑡 (1 − 𝛽 𝑡 ) 𝑀 𝑡 (4)where 𝑓 𝑇 𝑟𝑢𝑐𝑘 H ,𝑡 is the total hydrogen demand of heavy trucksat 𝑡 and 𝛼 𝑇 𝑟𝑢𝑐𝑘𝑡 is the transport hydrogen consumption coef-ficient of trucks. (1 − 𝛽 𝑡 ) 𝑀 𝑡 represents the amount of coalthat needs to be transported except for C2H. In the current field of industrial production of hydrogen,the main technology is proton exchange membrane (PEM)electrolysers. Electric conversion to hydrogen is achieved byelectrolyzing water. The equation of the electrolyzed waterreaction is shown in Eq. (5). O electrify ←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←→ ↑ + O ↑ (5)Methanation is the conversion of COx to methane CH through hydrogenation. The reaction equations are shown inEqs. (6) & (7) . CO + 3 H ←←←←←←←←←←←←←←←←←→ CH + H O Δ 𝐻 = −206 kJ∕mol (6) CO + 4 H ←←←←←←←←←←←←←←←←←→ CH + 2 H O Δ 𝐻 = −164 kJ∕mol (7) P2H and P2M technology have their own characteristics:• P2H has higher reaction efficiency than P2M;• P2H technology conversion conditions is less difficultthan P2M , and the required cost is low;• Hydrogen cannot be injected into existing natural gaspipelines on a large scale, while methane can;• Methane is safer in view of the flammability limits[13]and explosion limits[14] ;• The production and combustion of hydrogen do not in-volve carbon emissions, and CO is consumed duringthe production of methane;• The calorific value of hydrogen is higher, which ofmethane is lower.a) Reaction efficiency constraints ⎧⎪⎨⎪⎩ 𝜂 𝑒𝑙𝑒𝑐,𝑡 > 𝜂 𝑚𝑒𝑡ℎ,𝑡 ≤ 𝜂 𝑒𝑙𝑒𝑐 ≤ ≤ 𝜂 𝑚𝑒𝑡ℎ ≤ (8)where 𝜂 𝑒𝑙𝑒𝑐,𝑡 and 𝜂 𝑚𝑒𝑡ℎ,𝑡 are used to represent the reactionefficiency of the above two processes in the time slot 𝑡 .Given two following assumptions:(1) In each time slot, the conversion efficiency of the elec-trolytic cell and methanation equipment 𝜂 𝑒𝑙𝑒𝑐,𝑡 , 𝜂 𝑚𝑒𝑡ℎ,𝑡 re-mains unchanged, i.e. , fixed value;(2) The chemical reaction process is a complete reactionand there is no reversible process.b) Conversion power consumption constraintIn the upper right corner of Fig. 1, the actual flow of theP2G equipment is drawn separately as Fig. 2, where eachvariable symbol ( e.g. , flow rate and energy consumptionparameters) is marked. 𝐶𝑜𝑛𝑠 H ,𝑡 = 𝛼 H ,𝑡 𝑓 H ,𝑡 (9) 𝐶𝑜𝑛𝑠 CH ,𝑡 = 𝛼 CH elec ,𝑡 𝑓 ′ H ,𝑡 + 𝛼 CH meth ,𝑡 𝑓 CH ,𝑡 = 4 𝛼 CH elec ,𝑡 𝑓 CH ,𝑡 + 𝛼 CH meth ,𝑡 𝑓 CH ,𝑡 (10) First Author et al.:
Preprint submitted to Elsevier
Page 4 of 10 ethanationCO Hydrogen refueling station H , t f ' , H t f 'H , H , t t f f + , CH t f ,eCH lec t a WP H , t a ,mCH eth t a PEM Electrolysis
Actual flowElec-to-H H -to-CH Actual flowElec-to-H H -to-CH Figure 2:
Schematic diagram of actual flow and variable sym-bols of P2G equipment. where
𝐶𝑜𝑛𝑠 H ,𝑡 represents the electric energy consump-tion used by the P2G equipment to produce H for hydro-gen refueling station; 𝑓 H ,𝑡 is the H flow rate for hydro-gen refueling station at the time slot 𝑡 ; 𝛼 H ,𝑡 is the powerconsumption parameter corresponding to H for hydro-gen refueling station. Similarly, 𝐶𝑜𝑛𝑠 CH ,𝑡 is the electricenergy consumed to produce CH ; 𝑓 ′ H ,𝑡 is H flow rateproduced for further methanation; 𝑓 CH ,𝑡 is the flow rateof CH ; 𝛼 CH elec ,𝑡 represents the power consumption pa-rameter in process of electrolysis corresponding to CH ,and 𝛼 CH meth ,𝑡 is that in process of methanation. In or-der to simplify the situation, only the chemical reactiondescribed in (7) is considered here, that is, carbon diox-ide and 4 times of the amount of the hydrogen producemethane under the action of high temperature and highpressure and a catalyst, i.e. , 𝑓 ′ H ,𝑡 = 4 𝑓 CH ,𝑡 . Thereforethe second equality is established in Eq. (10).c) Flammability& explosion limit constraint[13, 14]The minimum concentration (%) of gas in the air underflammable conditions is defined as the Lower flammabil-ity limit (LFL), and the highest is the Upper flammabilitylimit (UFL). Similarly, Explosion limits are expressed aslower explosive level (LEL) and Upper explosive limit(UEL), respectively. { LFL H ≤ 𝑐 H ,𝑡 ≤ UFL H LEL H ≤ 𝑐 H ,𝑡 ≤ UEL H (11) { LFL CH ≤ 𝑐 CH ,𝑡 ≤ UFL CH LEL CH ≤ 𝑐 CH ,𝑡 ≤ UEL CH (12)d) Calorific value constraintThe energy density of hydrogen is only about 25% ofmethane. When both release the same amount of energy,the volume of hydrogen is larger, and storage and trans-portation are more difficult. In this paper, 𝑞 H = 119 . MJ/kg, 𝑞 CH = 50 . MJ/kg.
3. Problem Formulation min 𝐏 , 𝐅 , 𝚷 𝐶 𝑡𝑜𝑡𝑎𝑙 = 𝑁 ∑ 𝑖 =1 ( 𝑇 ∑ 𝑖 =1 𝐶 𝑓𝑖 ( 𝑃 𝑖,𝑡 ) + 𝐶 𝑈𝑖 + 𝐶 𝐷𝑖 ) (13) + 𝑁 𝑔 ∑ 𝑚 =1 𝑇 ∑ 𝑡 =1 𝐶 𝑔𝑚,𝑡 + 𝑇 ∑ 𝑖 =1 𝐶 𝑊 𝑃 ,𝑡 + 𝑇 ∑ 𝑖 =1 𝐶 𝑇 𝑟𝑢𝑐𝑘,𝑡 − 𝑇 ∑ 𝑖 =1 𝐸 𝐶𝑜𝑎𝑙,𝑡 𝑠.𝑡. (3) , (4) , (8) − (12) 𝑁 𝑈 ∑ 𝑖 =1 𝑃 𝑖,𝑡 = 𝑁 𝐿 ∑ 𝑖 =1 𝑃 𝑑,𝑖,𝑡 (14) ∑ 𝑃 𝑖𝑛𝑝𝑢𝑡,𝑖,𝑡 = ∑ 𝑃 𝑜𝑢𝑡𝑝𝑢𝑡,𝑖,𝑡 ∀ power nodes (15) 𝑁 𝑈 ∑ 𝑖 =1 ( 𝑢 𝑖,𝑡 𝑃 𝑖, max − 𝑃 𝑖,𝑡 ) ≥ 𝜌 𝑁 𝐿 ∑ 𝑖 =1 𝑃 𝑑,𝑖,𝑡 (16) 𝑢 𝑖,𝑡 = { , stop , start (17) 𝑢 𝑖,𝑡 𝑃 𝑖, min ≤ 𝑃 𝑖 ≤ 𝑢 𝑖,𝑡 𝑃 𝑖, max (18) − 𝑅 𝑑 ≤ 𝑃 𝑖,𝑡 − 𝑃 𝑖,𝑡 −1 ≤ 𝑅 𝑢 (19) 𝑡 +TS−1 ∑ 𝑘 = 𝑡 (1 − 𝑢 𝑖,𝑡 ) ≥ TS( 𝑢 𝑖,𝑡 −1 − 𝑢 𝑖,𝑡 ) (20) 𝑡 +TO−1 ∑ 𝑘 = 𝑡 𝑢 𝑖,𝑘 ≥ TO ( 𝑢 𝑖,𝑡 − 𝑢 𝑖,𝑡 −1 ) (21) 𝐶 𝑈𝑖,𝑡 ≥ max{ 𝐻 𝑖 ( 𝑢 𝑖,𝑡 − 𝑢 𝑖,𝑡 −1 ) , (22) 𝐶 𝐷𝑖,𝑡 ≥ max{ 𝐽 𝑖 ( 𝑢 𝑖,𝑡 −1 − 𝑢 𝑖,𝑡 ) , (23) 𝑃 𝑙, min ≤ 𝑃 𝑙,𝑡 ≤ 𝑃 𝑙, max (24) ∑ 𝑛 | ( 𝑚,𝑛 )∈ 𝐴 𝑓 𝑚𝑛 = ∑ 𝑛 | ( 𝑛,𝑚 )∈ 𝐴 𝑓 𝑛𝑚 + 𝑠 𝑚 ∀ 𝑚 ∈ 𝑔 (25) sign ( 𝑓 𝑚𝑛 ) 𝑓 𝑚𝑛 ≤ 𝐶 𝑚𝑛 ( 𝑝 𝑚 − 𝑝 𝑛 ) ∀ 𝑚, 𝑛 ∈ 𝑔 (26) sign ( 𝑓 𝑚𝑛 ) = { , flow direction is positive −1 , otherwise (27) 𝑠 𝑚 ≤ 𝑠 𝑚 ≤ 𝑠 𝑚 ∀ 𝑚 ∈ 𝑔 (28) 𝑝 𝑚 ≤ 𝑝 𝑚 ≤ 𝑝 𝑚 ∀ 𝑚 ∈ 𝑔 (29)where the coal consumption cost function 𝐶 𝑓𝑖 of ther-mal power unit 𝑖 can be expressed by the following quadraticequation: 𝐶 𝑓𝑖 ( 𝑃 𝑖,𝑡 ) = 𝑎 𝑖 𝑃 𝑖,𝑡 + 𝑏 𝑖 𝑃 𝑖,𝑡 + 𝑐 𝑖 (30)where 𝐶 𝑈𝑖 represents the start-up cost of unit 𝑖 , 𝐶 𝐷𝑖 rep-resents the shutdown cost of unit 𝑖 , 𝐶 𝑔𝑚,𝑡 represents the cost ofthe natural gas network. For simplification, it is assumed thatthe punishment cost of abandoning WP ( 𝐶 𝑊 𝑃 ,𝑡 ) is linearlypositively related to the amount of electricity abandoning. 𝐶 𝑇 𝑟𝑢𝑐𝑘,𝑡 indicates the cost of truck transportation, which is
First Author et al.:
Preprint submitted to Elsevier
Page 5 of 10 ositively related to the load capacity of the truck, when theload does not exceed the load capacity of the truck. 𝐸 𝐶𝑜𝑎𝑙,𝑡 indicates the profit from selling coal, which is proportionalto the weight of coal transportation. Constraints Eqs. (14)-(24) are related to the power system, including power bal-ance constraint, hot spare constraint, unit output constraint,unit ramp constraint, unit start and stop time constraint, start& stop cost constraint and line power flow safety constraint.And Eqs. (25)-(29) are related to the Natural gas system sys-tem, including flow balance constraint, Weymouth equationsconstraint[15], source quantity constraint and pressure rangeconstraint.
In the unified power flow modeling and solving, the SOCP-based power flow model has been used in network planning[1] with binary decision variables, and the problems gener-ated are all modeled as mixed integer SOCP (MISOCP) [16].In order to eliminate the non-linearity caused by pressurevariables, make the following variable substitutions 𝜋 𝑚 = 𝑝 𝑚 . Thus, the constraint (29) can be rewritten as the follow-ing formula 𝜋 𝑚 ≤ 𝜋 𝑚 ≤ 𝜋 𝑚 ∀ 𝑚 ∈ 𝑔 (31)The non-convexity of the steady-state flow model is de-rived from Eq. (26), where the absolute value sign ( 𝑓 𝑚𝑛 ) is non-smooth and non-differentiable. To solvethis problem, a pair of binary variables 𝑓 + 𝑚𝑛 and 𝑓 − 𝑚𝑛 are in-troduced to represent the forward and backward flow direc-tions of the pipe 𝑚 − 𝑛 , respectively. Therefore, Eq.26 isequivalently replaced with ( 𝐹 𝑚𝑛 𝐶 𝑚𝑛 ) = ( 𝑓 + 𝑚𝑛 − 𝑓 − 𝑚𝑛 ) ( 𝜋 𝑚 − 𝜋 𝑛 ) ∀ 𝑚, 𝑛 ∈ 𝑔 (32)By using bilinear relaxation, the bilinear term on the rightside of (32) can be replaced by (33)-(37) (Note that since 𝑓 + 𝑚𝑛 and 𝑓 − 𝑚𝑛 are binary variables, this relaxation is strict): ( 𝐹 𝑚𝑛 𝐶 𝑚𝑛 ) = 𝜆 𝑚𝑛 ∀ 𝑚, 𝑛 ∈ 𝑔 (33) 𝜆 𝑚𝑛 ≥ 𝜋 𝑛 − 𝜋 𝑚 + ( 𝑓 + 𝑚𝑛 − 𝑓 − 𝑚𝑛 + 1 ) ( 𝜋 𝑙𝑚 − 𝜋 𝑢𝑛 ) (34) 𝜆 𝑚𝑛 ≥ 𝜋 𝑛 − 𝜋 𝑚 + ( 𝑓 + 𝑚𝑛 − 𝑓 − 𝑚𝑛 − 1 ) ( 𝜋 𝑢𝑚 − 𝜋 𝑙𝑛 ) (35) 𝜆 𝑚𝑛 ≥ 𝜋 𝑛 − 𝜋 𝑚 + ( 𝑓 + 𝑚𝑛 − 𝑓 − 𝑚𝑛 + 1 ) ( 𝜋 𝑢𝑚 − 𝜋 𝑙𝑛 ) (36) 𝜆 𝑚𝑛 ≥ 𝜋 𝑚 − 𝜋 𝑛 + ( 𝑓 + 𝑚𝑛 − 𝑓 − 𝑚𝑛 − 1 ) ( 𝜋 𝑙𝑚 − 𝜋 𝑢𝑛 ) (37)Eq. (33) can be relaxed according to the cone formatshown in (38), where the standard SOC formula of (38) isexpressed as ( 𝐹 𝑚𝑛 ∕ 𝐶 𝑚𝑛 ) ≤ 𝜆 𝑚𝑛 ∀ 𝑚, 𝑛 ∈ 𝑔 (38) ‖‖‖‖ 𝐹 𝑚𝑛 ∕ 𝐶 𝑚𝑛 𝜆 𝑚𝑛 − 1 ‖‖‖‖ ≤ 𝜆 𝑚𝑛 + 1 (39)
4. Case study
In order to verify the effectiveness of the method in thispaper, the above optimization program was developed usingMATLAB-YALMIP platform, and the CPLEX algorithm pack-age was used to solve the nonlinear mixed integer program-ming problem. The hardware environment of the test systemis Intel (R) Core (TM) i7-6500M CPU @ 2.50 GHz, 8 GBRAM, Win10 64 bit (operating system), Matlab R2019b (de-velopment environment), and the YALMIP version is R2020.IBM CPLEX ILOG is a high-performance mathematicalprogramming solver for linear programming, mixed integerprogramming.The unit commitment problem is essentially amixed integer programming (MIP) problem, which can besolved by MATLAB/CPLEX.
As shown in Fig. 3, the data of IEEE 30-node power sys-tem is utilized, and the rest of the data is shown in Tab. 2.The IEEE 30-node test case represents a part of the Amer-ican power system (located in the Midwest of the UnitedStates). The original IEEE 30-node scenario considers theprocessing conditions of 6 thermal power units. Here, Unit6 connected to node 8 is changed to WP equipment.The natural gas network data adopts Belgium 24-nodenetwork data [15]. According to the internationally acceptednatural gas sales rules, natural gas is priced according to itscalorific value. The commonly used unit is Million BritainThermal Unit (MBTU), while China’s natural gas transac-tion is based on volume as a reference and the unit is cubicmeter (m ). It is known that 1 MBTU ≈ , and theunit conversion can be obtained: 1 $/MBTU ≈ .The maximum value of daily output power of the WPunit is set as 15,000 kW. The fluctuation data of WP outputin each period is based on the project data of the Universityof Queensland in Australia. Now the unit output is increasedby 30 times. Set the abandoning WP punishment parameter 𝛿 𝑊 𝑃 = 0.08 $/kWh.
The WP output data from February 27, 2019 to Febru-ary 27, 2020 are selected, and the operation results in theproposed IEGS are shown in Fig. 4. The WP output at thesame time basically conforms to winter>annual>summer,in which winter is selected from December to February ofthe following year, and summer is selected from June to Au-gust. Combined with the weather data measured by the windproject, WP output is influenced by natural factors such astemperature , wind speed and so on.On the basis of ensuring the stable operation of WP out-put, in order to show the characteristics of energy-saving,clean, and fast absorption of P2G equipment, the compari-son results obtained are shown in Tab. 3. Due to the inde-pendent operation of the power system and the natural gassystem, and the direct connection of WP units to the grid,the electricity-gas system lacking a coupling and mutual aid
First Author et al.:
Preprint submitted to Elsevier
Page 6 of 10 ow gas
High gas
Norvegian gas
GravenvoerenLiège
BerneauWarnand-DreyeAnderlues
ZeebruggeDudzele
Brugge Zomergem
Gent
Antwerpen
Loenhout
PoppelHasselt
PéronnesMons Blaregnies
Namur WanseSinsin
Dutch gasAlgerian gas To France
To Luxemburg
Arlon
From storage
BrusselBrussel
14 15
24 25 26 From storage CH Coal District
Coal
P2M
P2H H C2H
Figure 3:
IEGS case study diagram.
Table 2
Initial data of thermal power units.Unit Node 𝑃 max 𝑃 min a b c 𝑅 𝑢 ∕ 𝑅 𝑑 TS/TD
𝐻 𝐽 (p.u.) (p.u.) (ton/(p.u.) ) (ton/(p.u.)) (ton) (p.u./h) (h) ($/time) ($/time)1 1 1.57 0.50 01524 38.5390 786.798 0.37 2 3937 196862 2 1.00 0.25 0.1058 46.1591 945.633 0.30 2 25000 125003 5 0.60 0.15 0.0280 40.3965 1049.998 0.15 2 15000 75004 8 0.80 0.20 0.0354 38.3055 1243.531 0.20 2 20000 100005 11 0.40 0.10 0.0211 36.327 1658.570 0.15 2 10000 5000 Time (h)
Dec-FebJun-AugAnnual
Figure 4:
Typical daily WP output line chart. relationship cannot absorb unstable and intermittent WP ina timely manner. In particular, the cost of abandoning WPis penalized, leading to higher operating costs for the IEGSwithout P2G equipment. If the ecological benefits broughtby the consumption of carbon dioxide gas by P2G equipment
Table 3
Comparison of total operating costs with or without P2G.Total operating costs with P2G without P2G($/day) . . are taken into consideration, the advantages of P2G equip-ment are more prominent. Select 14:00 data to draw Fig. 5, which is based onthe annual WP output. It can be seen that among the ini-tial energy sources, electricity and natural gas come fromthe power system and the natural gas system respectively,and renewable energy accounts for a considerable propor-tion. Through transitional energy conversion, the initial en-ergy can be transformed into hydrogen (supplied to hydrogen
First Author et al.:
Preprint submitted to Elsevier
Page 7 of 10 igure 5:
The energy conversion Sankey diagram of the proposedIEGS.
Table 4
Comparison of total operating costs considering carbon emissionstrading.Total operating costs China European Union($/day)Hydrogen truck . . Electric vehicle . . Diesel oil truck . . heavy trucks), methane (can be directly injected into natu-ral gas pipelines) and electricity (from power plants close toenergy-consuming terminals).In order to alleviate the greater environmental pressureand implement carbon neutral initiatives, carbon emissionstrading is considered in this section[17, 18]. According tothe Status Report 2019 of International Carbon Action Part-nership (ICAP), emissions trading systems of most countriesin the world currently are in force, scheduled or under con-sideration. This article uses the carbon emissions trading ofChina and the European Union as a measurement standard,and calculates the operating costs of the three heavy trucksmentioned in subsection 2.1.2.According to the results of carbon emissions trading in2020, prices in China are about 30-40 ¥/tCO , but that in theEU has exceeded 30 €/tCO . Taking into account carbonemissions trading, the revised total cost is ( 𝐶 𝑡𝑜𝑡𝑎𝑙 − 𝐶 CO ),where 𝐶 CO indicates the cost of CO emissions and propor-tional to the amount of CO emissions. Tab. 4 shows thatdiesel oil trucks or LNG trucks will be levied high carbonemission fees, which will continue to increase as carbon neu-trality advances. The current price of hydrogen heavy trucksis basically similar to that of electric vehicles, because inthe proposed scenario, the methanation process can absorba part of CO . Therefore, hydrogen heavy trucks can notonly achieve zero emissions on the basis of electric vehicles,but also absorb greenhouse gases, which are converted intoprofits here. With the continuous breakthrough of hydrogenenergy technology and the inclination of government poli-cies, the price of hydrogen energy will gradually drop andthe scale of production will gradually expand. Further, hy-drogen heavy trucks will have a broader prospect. Unit 1Unit 2Unit 3Unit 4Unit 5
Unit 1Unit 2Unit 3Unit 4Unit 5 U n it ou t pu t acc u m u l a ti on ( p . u . ) U n it ou t pu t ( p . u . ) Time (h) Time (h) (a) 𝜌 = 0 . U n it ou t pu t acc u m u l a ti on ( p . u . ) U n it ou t pu t ( p . u . ) Time (h) Time (h) (b) 𝜌 = 0 . Figure 6:
Unit output curves under different hot spare coefficient.
When the hot spare coefficient 𝜌 is 0.05, the cumulativeoutput ladder diagram of the unit is shown on the left sideof Fig. 6-(a), which is basically in line with the distributioncharacteristics of power consumption peaks and valleys inreality, that is, there is a peak power consumption aroundnoon during the day. In order to characterize the output sta-tus of each unit, draw the ladder diagram on the right sideof Fig.6-(a). Each curve is basically stable, and there areno several start and stop conditions within a short period oftime, which plays a good role in the overall stability of thesystem.Similarly, when the unit hot spare coefficient is 0.2, Fig.6-(b) are available. The cumulative output ladder diagram ofthe unit is shown on the left side of Fig. 6-(b). The ladder di-agram on the right side of Fig. 6-(b) shows the output statusof each unit and the curves are basically stable. However,some problems can be found in comparison with 𝜌 =0.05.The right side of Fig. 6-(b) shows that the output of one unithas a short start and stop near 19:00, which is caused by thehigher hot spare. Under the premise that a certain unit oper-ating life and system stability are lost, the system’s ability torespond to emergencies can be greatly improved. In this section, adjust the abandoning WP punishmentparameters appropriately, set to four values of 0.01, 0.05,0.08, and 0.12 respectively. The operation results of IEGSare shown in Tab. 3. When the abandonment punishmentparameter is too small, the operating cost is higher, secondonly to the operating cost under the condition of no P2G
First Author et al.:
Preprint submitted to Elsevier
Page 8 of 10 able 5
Comparison of total operating costs with different abandoning PVpunishment parameters.Abandoning PV punishment parameters Total operating costs($/kWh) ($/day )0.01 . . . . equipment, indicating that even if the punishment parame-ter is small, the amount of abandonment is large, which stillleads to the system. The overall operating cost is high. Withthe increase of the abandonment punishment parameters, theoperating cost of the system has been significantly reduced,which proves that considering the abandonment punishmentcost in the optimization objective can make the system fullyabsorb PV power. However, if the punishment parametersfor abandoning solar energy continue to increase, the operat-ing cost of the system will increase. This is because a smallamount of unconsumed PV will be multiplied by a largerpunishment coefficient, which will cause a certain punish-ment cost.Further, as shown in the dotted line in Fig. 7, it canbe estimated that although there is a nonlinear relationshipbetween the abandoning WP punishment parameter and theoperating cost, there should be a minimum value as shownin Fig. 7. When the abandonment punishment parametertakes this value, the total operating cost of the system is thesmallest, and the specific value needs to be further explored.Moreover, when the abandoning WP punishment parameteris less than the optimal value, the curve drops faster, and thedifference between the values of the abandoning WP punish-ment parameter is not very large, but a large amount of aban-donment energy multiplied by it will cause a larger punish-ment cost. Correspondingly, when the abandoning WP pun-ishment parameter is greater than the optimal value, even ifthe abandoning WP punishment parameter becomes signifi-cantly larger, the cost curve rises slowly because the amountof abandonment remains at a small amount. Figure 7:
Curve line chart of the influence of 𝛿 𝑊 𝑃 on 𝐶 𝑡𝑜𝑡𝑎𝑙
5. Conclusion
In view of the gradual transformation of the energy struc-ture and the continuous development of the Energy Internet,IESs are important research direction. This paper draws thefollowing conclusions:(1) Typical daily operating cost is significantly reduced by7.7%, by introducing the P2G model which converts sea-sonally volatile wind energy into hydrogen and methane.(2) Hydrogen heavy trucks have certain advantages in theproposed coal districts scenario, e.g. , zero emissionsand indirect consumption of renewable energy. Espe-cially after the introduction of carbon emissions trading,the cost advantage is more prominent, compared withelectric vehicles and diesel oil trucks.(3) The proposed P2G equipment and C2H technology im-prove the ability to absorb WP, enhance the reliabilityof the system, and solve the problem of volatility. Moreimportantly, the mechanism in the article circumventsthe potential risks caused by hydrogen mixing in naturalgas pipelines, the cost of which cannot be measured.(4) The abandoning WP punishment parameter is consid-ered in this article, and the optimal parameter is formu-lated according to the actual situation, which plays a cer-tain guiding role for the future energy market leverage.
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of Jiangsu Province (BK20181283).
CRediT authorship contribution statement
Junjie Yin:
Conceptualization of this study, Method-ology, Software, Formal analysis, Investigation, Data Cura-tion, Writing - Original Draft,Visualization.
Jianhua Wang:
Validation, Resources, Writing - Review & Editing, Super-vision, Project administration.
Jun You:
Writing - Review& Editing, Visualization, Supervision, Project administra-tion.
References [1] Y. Zhang, P. E. Campana, Y. Yang, B. Stridh, A. Lundblad, J. Yan,Energy flexibility from the consumer: Integrating local electricity andheat supplies in a building, Applied Energy 223 (2018) 430–442.[2] C. Sheng, Z. Wei, G. Sun, et al. , Steady state and transient simula-tion for electricity-gas integrated energy systems by using convex op-timisation, IET Generation, Transmission & Distribution 12 (2018)2199–2206.[3] G. Gahleitner, Hydrogen from renewable electricity: An internationalreview of power-to-gas pilot plants for stationary applications, Inter-national Journal of Hydrogen Energy 38 (2013) 2039–2061.[4] S. Zhou, K. Sun, Z. Wu, et al. , Optimized operation method of smalland medium-sized integrated energy system for P2G equipment understrong uncertainty, Energy 199 (2020) 117269.[5] L. Ni, W. Liu, F. Wen, Y. Xue, Z. Dong, Y. Zheng, R. Zhang, Opti-mal operation of electricity, natural gas and heat systems consideringintegrated demand responses and diversified storage devices, Journalof Modern Power Systems and Clean Energy 6 (2018) 423–437.
First Author et al.:
Preprint submitted to Elsevier
Page 9 of 10
6] Y. Qiu, S. Zhou, J. Wang, J. Chou, Y. Fang, G. Pan, W. Gu, Feasi-bility analysis of utilising underground hydrogen storage facilities inintegrated energy system: Case studies in china, Applied Energy 269(2020) 115140.[7] Y. Chen, H. Lu, J. Liang, A. Rosenthal, H. Liu, G. Sneddon, I. Mc-Carroll, Z. Zhao, W. Li, A. Guo, et al., Observation of hydrogentrapping at dislocations, grain boundaries, and precipitates, Science367 (2020) 171–175.[8] IEA, Limits on hydrogen blending in natural gas net-works, 2018, Technical Report, IEA, Paris, 2020. .[9] K. Kunstle, C. Koch, K. Reiter, Coal gasification apparatus, 1978.United States Patent No. 4095959, .[10] G. Pan, W. Gu, H. Qiu, Y. Lu, S. Zhou, Z. Wu, Bi-level mixed-integerplanning for electricity-hydrogen integrated energy system consider-ing levelized cost of hydrogen, Applied Energy 270 (2020) 115176.[11] J. Rolink, C. Rehtanz, Large-scale modeling of grid-connected elec-tric vehicles, IEEE Transactions on Power Delivery 28 (2013) 894–902.[12] X. Wu, H. Li, X. Wang, W. Zhao, Cooperative operation for wind tur-bines and hydrogen fueling stations with on-site hydrogen production,IEEE Transactions on Sustainable Energy 11 (2020) 2775–2789.[13] ISO 10156:2017(en), Gas cylinders-Gases and gas mixtures-Determination of fire potential and oxidizing ability for the selec-tion of cylinder valve outlets, Technical Report, ISO, 2017. .[14] ISO/IEC 80079-20-1:2017, Explosive atmospheres - Part 20-1: Ma-terial characteristics for gas and vapour classification - Test methodsand data, Technical Report, ISO/IEC, 2017. https://webstore.iec.ch/publication/26577 .[15] C. Borraz, R. Bent, S. Backhaus, H. Hijazi, P. V. Hentenryck, Con-vex relaxations for gas expansion planning, INFORMS Journal onComputing 28 (2016) 645–656.[16] L. Badesa, F. Teng, G. Strbac, Pricing inertia and frequency responsewith diverse dynamics in a mixed-integer second-order cone program-ming formulation, Applied Energy 260 (2020) 114334.[17] K. Ricke, L. Drouet, K. Caldeira, M. Tavoni, Country-level socialcost of carbon, Nature Climate Change 8 (2018) 895–900.[18] X. Zhang, A. Löschel, J. Lewis, D. Zhang, J. Yan, Emissions tradingsystems for global low carbon energy and economic transformation,Applied Energy 279 (2020) 115858.
First Author et al.: