# Energy Hub Model for the Massive Adoption of Hydrogen in Power Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

_{2}emissions, and “green hydrogen” is produced from renewable sources through the water electrolysis [4]. This classification is referenced in the subsequent sections of the present study.

#### 1.2. Literature Review

#### 1.3. Contribution

- (1)
- A versatile framework based on multi-carrier energy hubs for simulation and optimization of design and operation. In detail, many components can be compared and assessed;
- (2)
- A detailed economic analysis for both design and operation;
- (3)
- A multi-objective approach aimed at balancing the minimization of costs, the grid interactions, primary energy use, and the impact on the greenhouse effect;
- (4)
- The consideration of the uncertainty on the most unpredictable input data (energy production from RES and final energy demands) is introduced in both case studies.

- Section 2. Materials and Methods, with the description of the energy hub model developed for this study and the main assumptions, showing the coordinated optimization of a multi-carrier energy system including hydrogen, power, and heating final demands. The data collection phase is also described;
- Section 3. Results, illustrating the results of the study for the reference case and for the stochastic scenarios;
- Section 4. Discussion and conclusions, recapping the main aspect of this paper and giving some insights for further deepen the topic.

## 2. Materials and Methods

#### 2.1. Energy Hub

- Increased efficiency through optimal interaction of various energy vectors and conversion units. For example, an electrical system with massive non-predictable renewable energy penetration might use the excess energy to charge electricity storage devices such as electric vehicles or to produce hydrogen;
- Increased security of supply through high availability of multiple power sources. MES are designed in such a way that each load does not depend on a single energy source or technology and can be met by the cheapest and most available energy carrier;
- Increased flexibility through greater degree of freedom in powering loads. An apparently polluting or expensive energy source might be substituted with a cleaner energy source.

- The hub operation is analyzed in several timesteps in steady-state conditions, when all transients or fluctuating conditions have damped out and all quantities remain essentially constant in each timestep;
- Within the EH, losses are considered only in converters and storages, although it is possible to include line gas/electricity lines losses;
- Unidirectional flows from the inputs to the outputs of the converters are usually assumed;
- Power flow through converter devices is univocally identified using the power and energy quantities, using constant efficiency terms to consider energy transformations and losses.

#### 2.2. Objective Functions

_{day}daily trends that are representative of the average annual trend, each day having K

_{hour}equivalent hours, the mathematical formulation for these objectives was structured as shown in Equations (1)–(4).

_{equip}is the total number of equipment assessed in the study, and the subscript O&M stands for operation and maintenance. The investment costs were assessed using a linear formulation rather than a unit cost formulation [45]. With Equation (1), the economic optimization was based on the purchase of the equipment to be installed inside the hub and their operating costs.

#### 2.3. Final Demands

#### 2.4. Constraints

#### 2.4.1. Constraints Describing Energy and Mass Balance Equations

_{grid,in}(t) − NG

_{GB}(t) = 0

_{2,grid,in}(t) − H

_{2,grid,out}(t) + H

_{2,EL}(t) − H

_{2,FC}(t) − H

_{2,TK,in}(t) + H

_{2,TK,out}(t) +

− H

_{2,dem,fl}(t) = H

_{2,dem,fix}(t)

_{grid,in}(t) − W

_{grid,out}(t) − E

_{EL}(t) · K

_{EL,eh}

_{2}· K

_{EL,h}

_{2w}+ E

_{FC}(t)/K

_{FC,h}

_{2e}· K

_{FC,h}

_{2w}+

− W

_{WSS,in}(t) + W

_{WSS,out}(t) − W

_{dem,fl}(t) = W

_{dem,fix}(t)

_{grid,in}(t) − E

_{grid,out}(t) + E

_{FC}(t) − E

_{ESS,in}(t) + E

_{ESS,out}(t) + E

_{RES}(t) − E

_{HP}(t) − E

_{EC}(t) +

− E

_{EL}(t) − E

_{dem,fl}(t) = E

_{dem,fix}(t)

_{grid,in}(t) − H

_{HT,grid,out}(t) + H

_{GB}(t) + H

_{FC}(t) + H

_{RES}(t) − H

_{TSS,in}(t) +

+ H

_{TSS,out}(t) + E

_{HP}(t) · K

_{HP,eh}− F

_{AC}(t)/K

_{AC,hf}− H

_{dem,fl}(t) = H

_{dem,fix}(t)

_{grid,in}(t) − F

_{grid,out}(t) + E

_{EC}(t) · K

_{EC,ef}+ F

_{AC}(t) − F

_{TSS,in}(t) + F

_{TSS,out}(t) − F

_{dem,fl}(t) =

= F

_{dem,fix}(t)

#### 2.4.2. Renewable Energy Sources

**ψ**and

**ω**parameters of the Beta distribution function according to the method illustrated in [27]. Available radiation data should be evaluated using the same tilt and azimuth angles of the PV system to be installed. Then, the Monte Carlo algorithm is run to generate the solar radiation scenarios and the air temperature scenarios according to their respective distribution functions.

- -
- Photovoltaic Systems (PV)

_{air}is the air temperature;

**G**is the global solar radiation, i.e., the sum of the three radiation components; NOCT is the normal operating cell temperature, i.e., the operating temperature to which the cell is brought in the case of G

_{sol}_{NOCT}irradiance of 800 W/m

^{2}and air temperature T

_{a,NOCT}of 20 °C. The cell temperature is then used to evaluate the PV efficiency according to the following equation [27]:

- -
- Solar Thermal Collector (STC)

**T**is the average temperature of the fluid in the collector, while η

_{m}_{0}, a

_{1}, and a

_{2}are the performance coefficients of the collector. The heat energy production is evaluated from the efficiency, the global solar radiation, the surface of each collector, and the number of collectors:

- -
- Concentrating Solar Power (CSP)

_{beam}. The direct radiation is then multiplied by the equivalent area, the conversion efficiency, the equivalent surface, and the number of units to obtain the electrical and thermal power:

#### 2.4.3. Energy Conversion Components

- -
- Gas-fired Boiler (GB)

_{GB}(t) = NG

_{GB}(t) · K

_{GB gh}· LHV

_{g}

_{GB}(t) ≤ S

_{GB}

_{GB}is the heating flow from the boiler, NG

_{GB}is the natural gas flowing into the boiler, K

_{GB gh}is the boiler efficiency, and S

_{GB}is the rated size of the boiler.

- -
- Reversible Heat Pump (HP)

_{HP}(t) = E

_{HP}(t) · K

_{HP eh}

_{HP}(t) = E

_{HP}(t) · K

_{HP ef}

_{HP}(t) ≤ S

_{HP}

_{HP}and F

_{HP}are the heating and cooling flows generated from the heat pump, respectively; E

_{HP}is the electricity input; K

_{HP eh}and K

_{HP ef}are the conversion factor from electricity to heating or cooling, respectively; and S

_{HP}is the rated size of the heat pump.

- -
- Absorption Chiller (AC)

_{AC}(t) = H

_{AC}(t) · K

_{AC hf}

_{AC}(t) ≤ S

_{AC}

_{AC}is the cooling flow from the chiller, H

_{AC}is the heating flow input, K

_{AC hf}is the conversion factor from heating to cooling, and S

_{AC}is the rated size of the absorption chiller.

- -
- Electrolyzer (EL)

_{2 EL}(t) = E

_{EL}(t) · K

_{EL eh}

_{2}

_{EL}(t) = H

_{2 EL}(t) · K

_{EL h}

_{2w}

_{EL}(t) ≤ S

_{EL}

_{EL eh}

_{2}is the electricity-to-hydrogen conversion efficiency and depends on the higher heating value of the hydrogen, on the compression efficiency, and on the efficiencies of the converters included to interface the RES plant with the electrolyzer; K

_{EL h}

_{2w}derives from the stoichiometric coefficients of the chemical reaction and represents the water required to produce one kilogram of hydrogen (water consumption of the electrolyzer cooling system is not taken into account); and S

_{EL}is the rated size of the electrolyzer.

- -
- Fuel Cell (FC)

_{FC}(t) = H

_{2 FC}(t) · K

_{FC h}

_{2e}

_{FC}(t) = H

_{2 FC}(t) · K

_{FC h}

_{2h}

_{FC}(t) = H

_{2 FC}(t) · K

_{FC h}

_{2w}

_{FC}(t) ≤ S

_{FC}

_{FC h}

_{2e}is the hydrogen-to-electricity conversion efficiency and depends on the hydrogen higher heating value, on the specific FC technology, and on the efficiencies of converters employed to interface the fuel cell with the power grid; K

_{FC h}

_{2h}is the hydrogen-to-heating conversion efficiency; K

_{FC h}

_{2w}derives from the stoichiometric coefficients of the chemical reaction; and S

_{FC}is the rated size of the fuel cell.

#### 2.4.4. Storage Systems

- -
- Electricity Storage System (ESS)

_{ESS}(t + 1) = SOC

_{ESS}(t) · (1 − E

_{ESS,loss}) + E

_{ESS,in}(t + 1) · K

_{ESS,in}+

− E

_{ESS,out}(t + 1)/K

_{ESS,out}

_{ESS}(0) = SOC

_{ESS}(T)

_{ESS,in}(t) ≤ δ

_{ESS,in}(t) · Q

_{ESS,in}

_{ESS,out}(t) ≤ δ

_{ESS,out}(t) · Q

_{ESS,out}

_{ESS,in}(t) + δ

_{ESS,out}(t) ≤ 1

_{ESS}≤ SOC

_{ESS}(t) ≤ S

_{ESS}

_{ESS,in}(t) ≤ S

_{ESS}· (1 − DoD

_{ESS})

_{ESS,out}(t) ≤ S

_{ESS}· (1 − DoD

_{ESS})

_{ESS}(t) stands for the electrical energy accumulated in the storage system, and K

_{ESS,in}and K

_{ESS,out}are the charging and discharging efficiencies of the electrical storage, respectively. E

_{ESS,in}(t) and E

_{ESS,out}(t) stand for the incoming and outgoing electricity flows of the storage, respectively. E

_{ESS,loss}is the self-discharge rate of the battery, modelled as a fraction of the electrical energy stored at each timestep; δ

_{ESS,in}(t) and δ

_{ESS,out}(t) are Boolean variables stating whether the ESS stands for in charging or discharging phase at time t, respectively; Q

_{ESS,in}and Q

_{ESS,out}are the upper limits to E

_{ESS,in}(t) and E

_{ESS,out}(t), respectively. DoD is the depth of discharge of the electrical storage system, and S

_{ESS}is the capacity of the ESS.

- -
- Thermal Energy Storage System (TSS)

_{TSS}(t + 1) = SOC

_{TSS}(t) · (1 − H

_{TSS,loss}) + H

_{TSS,in}(t + 1) · K

_{TSS,in}− H

_{TSS,out}(t + 1)/K

_{TSS,out}

_{TSS}(0) = SOC

_{TSS}(T)

_{TSS,in}(t) ≤ δ

_{TSS,in}(t) · Q

_{TSS,in}

_{TSS,out}(t) ≤ δ

_{TSS,out}(t) · Q

_{TSS,out}

_{TSS,in}(t) + δ

_{TSS,out}(t) ≤ 1

_{TSS}(t) ≤ S

_{TSS}

_{TSS,in}(t) ≤ S

_{TSS}

_{TSS,out}(t) ≤ S

_{TSS}

_{TSS}(t) is the thermal energy stored in the device, and K

_{TSS,in}and K

_{TSS,out}are the charge and discharge efficiencies of the thermal storage, respectively. H

_{TSS,in}(t) and H

_{TSS,out}(t) are the incoming and outgoing heating flows of the storage, respectively; H

_{TSS,loss}is the self-discharge rate of the storage, assumed as a fraction of the thermal energy stored at each timestep; δ

_{TSS,in}(t) and δ

_{TSS,out}(t) are Boolean variables stating whether the electrical storage is in charging or discharging phase at time t, respectively; Q

_{TSS,in}and Q

_{TSS,out}are the upper limits to H

_{TSS,in}(t) and H

_{TSS,out}(t), respectively; and S

_{TSS}is the capacity of the thermal storage.

- -
- Hydrogen storage tank (TK)

_{TK}(t + 1) = SOC

_{TK}(t) · (1 − H

_{2 TK,loss}) + H

_{2 EL}(t + 1) · K

_{TK,in}− H

_{2 TK,out}(t + 1)/K

_{TK,out}

_{TK}(0) = SOC

_{TK}(T)

_{2 EL}(t) ≤ δ

_{TK,in}(t) · Q

_{TK,in}

_{2 TK,out}(t) ≤ δ

_{TK,out}(t) · Q

_{TK,out}

_{TK,in}(t) + δ

_{TK,out}(t) ≤ 1

_{TK}(t) ≤ S

_{TK}

_{2 EL}(t) ≤ S

_{TK}

_{2 TK,out}(t) ≤ S

_{TK}

_{TK}is the hydrogen mass stored in the device, and K

_{TK,in}and K

_{TK,out}are the charge and discharge efficiencies of the hydrogen storage, respectively. T is the hour of the last timestep; H

_{2 EL}and H

_{2 TK,out}are the input and output hydrogen flows of the tank, respectively; H

_{2 TK,loss}is the leakage coefficient, assumed as a fraction of the stored hydrogen mass since the leakages are proportional to the pressure inside the tank. This aspect is unfortunately often neglected in the existing literature and is considered of paramount importance by the authors. δ

_{TK,in}and δ

_{TK,out}are Boolean variables that state whether the tank is charging or discharging at time t, respectively; Q

_{TK,in}and Q

_{TK,out}are the upper limits to H

_{2 EL}and H

_{2 TK,out}; and S

_{TK}is the capacity of the hydrogen tank.

#### 2.5. Case Study Description and Data Collection

_{2,grid,in}in the equations and figures).

**Figure 3.**Outdoor conditions in the city of Bolzano with the average values in colored line and uncertainty interval in grey. (

**a**) Air temperature and (

**b**) global solar radiation (sum of beam, diffuse, and reflected components).

## 3. Results

#### 3.1. Results for the Reference Case

#### 3.2. Uncertainty Assessment

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- IEA. Global Hydrogen Review 2022; IEA: Paris, France, 2022. [Google Scholar]
- Thapa, B.S.; Neupane, B.; Yang, H.S.; Lee, Y.H. Green Hydrogen Potentials from Surplus Hydro Energy in Nepal. Int. J. Hydrogen Energy
**2021**, 46, 22256–22267. [Google Scholar] [CrossRef] - Holden, N.; Costa, D.; Guimarães Da Silva, M.; Maniscalco, M.P.; Longo, S.; Cellura, M.; Miccichè, G.; Ferraro, M. Critical Review of Life Cycle Assessment of Hydrogen Production Pathways. Environments
**2024**, 11, 108. [Google Scholar] [CrossRef] - Ajanovic, A.; Sayer, M.; Haas, R. The Economics and the Environmental Benignity of Different Colors of Hydrogen. Int. J. Hydrogen Energy
**2022**, 47, 24136–24154. [Google Scholar] [CrossRef] - Howarth, R.W.; Jacobson, M.Z. How Green Is Blue Hydrogen? Energy Sci. Eng.
**2021**, 9, 1676–1687. [Google Scholar] [CrossRef] - Palmer, G.; Roberts, A.; Hoadley, A.; Dargaville, R.; Honnery, D. Life-Cycle Greenhouse Gas Emissions and Net Energy Assessment of Large-Scale Hydrogen Production via Electrolysis and Solar PV. Energy Environ. Sci.
**2021**, 14, 5113–5131. [Google Scholar] [CrossRef] - Di Carlo, S.; Genna, A.; Massaro, F.; Montana, F.; Riva Sanseverino, E. Optimizing Renewable Power Management in Transmission Congestion. An Energy Hub Model Using Hydrogen Storage. In Proceedings of the 21st IEEE International Conference on Environment and Electrical Engineering and 2021 5th IEEE Industrial and Commercial Power System Europe, EEEIC/I and CPS Europe 2021—Proceedings, Bari, Italy, 7–10 September 2021. [Google Scholar] [CrossRef]
- Esquivel-Elizondo, S.; Hormaza Mejia, A.; Sun, T.; Shrestha, E.; Hamburg, S.P.; Ocko, I.B. Wide Range in Estimates of Hydrogen Emissions from Infrastructure. Front. Energy Res.
**2023**, 11, 1207208. [Google Scholar] [CrossRef] - 2050 Long-Term Strategy—European Commission. Available online: https://climate.ec.europa.eu/eu-action/climate-strategies-targets/2050-long-term-strategy_en (accessed on 14 March 2024).
- Snam. The Hydrogen Challenge. The Potential of Hydrogen in Italy; Snam: Milan, Italy, 2019; pp. 1–13. [Google Scholar]
- Massaro, F.; Ferraro, M.; Montana, F.; Riva Sanseverino, E.; Ruffino, S. Techno-Economic Analysis of Clean Hydrogen Production Plants in Sicily: Comparison of Distributed and Centralized Production. Energies
**2024**, 17, 3239. [Google Scholar] [CrossRef] - Terna; Snam. Documento Di Descrizione Degli Scenari 2022; Terna: Rome, Italy, 2022; pp. 1–87. [Google Scholar]
- European Commission. Commission Staff Working Document—Implementing The Repower EU Action Plan: Investment Needs, Hydrogen Accelerator And Achieving The Bio-Methane Targets; European Commission: Brussels, Belgium, 2022. [Google Scholar]
- Hydrogen City. Available online: https://www.ghi-corp.com/projects/hydrogen-city (accessed on 1 April 2024).
- Crainz, M.; Curto, D.; Franzitta, V.; Longo, S.; Montana, F.; Musca, R.; Sanseverino, E.R.; Telaretti, E. Flexibility Services to Minimize the Electricity Production from Fossil Fuels. A Case Study in a Mediterranean Small Island. Energies
**2019**, 12, 3492. [Google Scholar] [CrossRef] - He, C.; Liu, T.; Wu, L.; Shahidehpour, M. Robust Coordination of Interdependent Electricity and Natural Gas Systems in Day-Ahead Scheduling for Facilitating Volatile Renewable Generations via Power-to-Gas Technology. J. Mod. Power Syst. Clean Energy
**2017**, 5, 375–388. [Google Scholar] [CrossRef] - Zeng, Q.; Fang, J.; Li, J.; Chen, Z. Steady-State Analysis of the Integrated Natural Gas and Electric Power System with Bi-Directional Energy Conversion. Appl. Energy
**2016**, 184, 1483–1492. [Google Scholar] [CrossRef] - Bai, L.; Li, F.; Cui, H.; Jiang, T.; Sun, H.; Zhu, J. Interval Optimization Based Operating Strategy for Gas-Electricity Integrated Energy Systems Considering Demand Response and Wind Uncertainty. Appl. Energy
**2016**, 167, 270–279. [Google Scholar] [CrossRef] - Hang, L.; Yuqiang, W.; Yifan, Z.; Ming, Z.; Rulei, H.; Junfei, H. Using Hydrogen Energy Storage System to Improve Wind Power Consumption and Low Voltage Ride through Capability. In Proceedings of the 2021 IEEE Sustainable Power and Energy Conference: Energy Transition for Carbon Neutrality, iSPEC 2021, Nanjing, China, 23–25 December 2021; pp. 274–280. [Google Scholar] [CrossRef]
- Dadkhah, A.; Van Eetvelde, G.; Vandevelde, L. Optimal Investment and Flexible Operation of Power-to-Hydrogen Systems Increasing Wind Power Utilisation. In Proceedings of the 2022 IEEE International Conference on Environment and Electrical Engineering and 2022 IEEE Industrial and Commercial Power Systems Europe, EEEIC/I and CPS Europe 2022, Prague, Czech Republic, 28 June–1 July 2022. [Google Scholar] [CrossRef]
- Sun, W.; Harrison, G.P. Active Load Management of Hydrogen Refuelling Stations for Increasing the Grid Integration of Renewable Generation. IEEE Access
**2021**, 9, 101681–101694. [Google Scholar] [CrossRef] - Ahmed, N.; Weber, H. Frequency Regulation by the Distributed Hydrogen Storage Power Plant (HSPP); IET: London, UK, 2022; pp. 497–502. [Google Scholar] [CrossRef]
- Wang, F.; Yang, H.; Yu, H.; Li, C.; Ren, W. Coordinated Optimization Model of the Wind Power Plant with Hydrogen Storage System and Demand Response. In Proceedings of the 5th IEEE Conference on Energy Internet and Energy System Integration: Energy Internet for Carbon Neutrality, EI2 2021, Taiyuan, China, 22–24 October 2021; pp. 1948–1954. [Google Scholar] [CrossRef]
- Liu, Z.; Liu, H.; Wang, S.; Ge, B.; Li, J.; Liu, S.; Gao, R.; Su, X. Fast Power Flow Calculation Method for Electricity Hydrogen Storage Integrated Energy Network. In Proceedings of the 5th IEEE Conference on Energy Internet and Energy System Integration: Energy Internet for Carbon Neutrality, EI2 2021, Taiyuan, China, 22–24 October 2021; pp. 1783–1788. [Google Scholar] [CrossRef]
- Sun, H.; He, C.; Yu, X.; Wu, M.; Ling, Y. Optimal Siting and Sizing of Hydrogen Refueling Stations Considering Distributed Hydrogen Production and Cost Reduction for Regional Consumers. Int. J. Energy Res.
**2019**, 43, 4184–4200. [Google Scholar] [CrossRef] - Coveri, M.; Di Silvestre, M.L.; Ferraro, M.; Massaro, F.; Montana, F.; Sanseverino, E.R.; Ruffino, S. Economic Optimization of the Hydrogen Demand in a Hard-to-Abate Industrial Sector. In Proceedings of the 2023 Asia Meeting on Environment and Electrical Engineering (EEE-AM), Hanoi, Vietnam, 13 November 2023; pp. 1–6. [Google Scholar]
- Mokaramian, E.; Shayeghi, H.; Sedaghati, F.; Safari, A.; Alhelou, H.H. A CVaR-Robust-Based Multi-Objective Optimization Model for Energy Hub Considering Uncertainty and E-Fuel Energy Storage in Energy and Reserve Markets. IEEE Access
**2021**, 9, 109447–109464. [Google Scholar] [CrossRef] - Heris, M.N.; Mirzaei, M.A.; Asadi, S.; Mohammadi-Ivatloo, B.; Zare, K.; Jebelli, H.; Marzband, M. Evaluation of Hydrogen Storage Technology in Risk-Constrained Stochastic Scheduling of Multi-Carrier Energy Systems Considering Power, Gas and Heating Network Constraints. Int. J. Hydrogen Energy
**2020**, 45, 30129–30141. [Google Scholar] [CrossRef] - Kholardi, F.; Assili, M.; Lasemi, M.A.; Hajizadeh, A. Optimal Management of Energy Hub with Considering Hydrogen Network. In Proceedings of the 2018 International Conference on Smart Energy Systems and Technologies, SEST 2018—Proceedings, Seville, Spain, 10–12 September 2018; pp. 5–10. [Google Scholar] [CrossRef]
- Zhang, W.; Han, D.; Sun, W.; Li, H.; Tan, Y.; Yan, Z.; Dong, X. Optimal Operation of Wind-Solar-Hydrogen Storage System Based on Energy Hub. In Proceedings of the 2017 IEEE Conference on Energy Internet and Energy System Integration (EI2), Beijing, China, 26–28 November 2017. [Google Scholar]
- Geng, S.; Vrakopoulou, M.; Hiskens, I.A. Optimal Capacity Design and Operation of Energy Hub Systems. Proc. IEEE
**2020**, 108, 1475–1495. [Google Scholar] [CrossRef] - Nasir, M.; Rezaee Jordehi, A.; Tostado-Véliz, M.; Mansouri, S.A.; Sanseverino, E.R.; Marzband, M. Two-Stage Stochastic-Based Scheduling of Multi-Energy Microgrids with Electric and Hydrogen Vehicles Charging Stations, Considering Transactions through Pool Market and Bilateral Contracts. Int. J. Hydrogen Energy
**2023**, 48, 23459–23497. [Google Scholar] [CrossRef] - Mansour-Saatloo, A.; Agabalaye-Rahvar, M.; Mirzaei, M.A.; Mohammadi-Ivatloo, B.; Abapour, M.; Zare, K. Robust Scheduling of Hydrogen Based Smart Micro Energy Hub with Integrated Demand Response. J. Clean. Prod.
**2020**, 267, 122041. [Google Scholar] [CrossRef] - Daneshvar, M.; Mohammadi-Ivatloo, B.; Zare, K. An Innovative Transactive Energy Architecture for Community Microgrids in Modern Multi-Carrier Energy Networks: A Chicago Case Study. Sci. Rep.
**2023**, 13, 1529. [Google Scholar] [CrossRef] [PubMed] - Zhang, R.; Chen, Y.; Li, Z.; Jiang, T.; Li, X. Two-Stage Robust Operation of Electricity-Gas-Heat Integrated Multi-Energy Microgrids Considering Heterogeneous Uncertainties. Appl. Energy
**2024**, 371, 123690. [Google Scholar] [CrossRef] - Jiang, Y.; Ren, Z.; Li, W. Committed Carbon Emission Operation Region for Integrated Energy Systems: Concepts and Analyses. IEEE Trans. Sustain. Energy
**2024**, 15, 1194–1209. [Google Scholar] [CrossRef] - Geidl, M.; Andersson, G. Optimal Power Flow of Multiple Energy Carriers. IEEE Trans. Power Syst.
**2007**, 22, 145–155. [Google Scholar] [CrossRef] - Genna, A.; Di Carlo, S.; Massaro, F.; Montana, F.; Riva Sanseverino, E. Optimizing the Generation System in a Microgrid with Power, Thermal Energy and Mobility Demands. In Proceedings of the 21st IEEE International Conference on Environment and Electrical Engineering and 2021 5th IEEE Industrial and Commercial Power System Europe, EEEIC/I and CPS Europe 2021—Proceedings, Bari, Italy, 7–10 September 2021. [Google Scholar] [CrossRef]
- Tebibel, H. Methodology for Multi-Objective Optimization of Wind Turbine/Battery/Electrolyzer System for Decentralized Clean Hydrogen Production Using an Adapted Power Management Strategy for Low Wind Speed Conditions. Energy Convers. Manag.
**2021**, 238, 114125. [Google Scholar] [CrossRef] - Huo, D.; Gu, C.; Yang, G.; Blond, S. Le Combined Domestic Demand Response and Energy Hub Optimisation with Renewable Generation Uncertainty. Energy Procedia
**2017**, 142, 1985–1990. [Google Scholar] [CrossRef] - Favre-Perrod, P.; Geidl, M.; Koeppel, G.; Klöckl, B.; Andersson, G.; Fröhlich, K. The energy hub—A powerful concept for future energy systems. In Proceedings of the Third Annual Carnegie Mellon Conference on the Electricity Industry, Pittsburgh, PA, USA, 13–14 March 2007. [Google Scholar]
- Geidl, M. Integrated Modeling and Optimization of Multi-Carrier Energy Systems; ETH Library: Zurich, Switzerland, 2007. [Google Scholar] [CrossRef]
- MATLAB Webpage—Intlinprog Algoritm. Available online: https://www.mathworks.com/help/optim/ug/intlinprog.html (accessed on 9 August 2024).
- Short, W.; Packey, D.J.; Holt, T. A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies; NREL: Golden, Colorado, 1995.
- Cannata, N.; Cellura, M.; Longo, S.; Montana, F.; Riva Sanseverino, E.; Luu, Q.L.L.; Nguyen, N.Q. Multi-Objective Optimization of Urban Microgrid Energy Supply According to Economic and Environmental Criteria. In Proceedings of the 2019 IEEE Milan PowerTech, PowerTech 2019, Milan, Italy, 23–27 June 2019; pp. 1–6. [Google Scholar]
- Burachik, R.S.; Kaya, C.Y.; Rizvi, M.M. A New Scalarization Technique and New Algorithms to Generate Pareto Fronts. SIAM J. Optim.
**2017**, 27, 1010–1034. [Google Scholar] [CrossRef] - Zubo, R.H.A.; Mokryani, G.; Abd-Alhameed, R. Optimal Operation of Distribution Networks with High Penetration of Wind and Solar Power within a Joint Active and Reactive Distribution Market Environment. Appl. Energy
**2018**, 220, 713–722. [Google Scholar] [CrossRef] - Faraji, J.; Hashemi-Dezaki, H.; Ketabi, A. Optimal Probabilistic Scenario-Based Operation and Scheduling of Prosumer Microgrids Considering Uncertainties of Renewable Energy Sources. Energy Sci. Eng.
**2020**, 8, 3942–3960. [Google Scholar] [CrossRef] - Di Somma, M.; Buonanno, A.; Caliano, M.; Jin, L.; Rossi, M.; Graditi, G.; Comodi, G. Stochastic Energy Management for the Italian UNIVPM Campus as a Multi-Carrier Energy Hub Participating in the Day-Ahead Market. In Proceedings of the IEEE EUROCON 2023—20th International Conference on Smart Technologies, Torino, Italy, 6 July 2023; pp. 251–256. [Google Scholar]
- Ju, L.; Tan, Z.; Yuan, J.; Tan, Q.; Li, H.; Dong, F. A Bi-Level Stochastic Scheduling Optimization Model for a Virtual Power Plant Connected to a Wind–Photovoltaic–Energy Storage System Considering the Uncertainty and Demand Response. Appl. Energy
**2016**, 171, 184–199. [Google Scholar] [CrossRef] - EN 15316-4-3:2017; Energy performance of buildings—Method for calculation of system energy requirements and system efficiencies—Part 4-3: Heat generation systems, thermal solar and photovoltaic systems, Module M3-8-3, M8-8-3, M11-8-3. European Committee for Standardization: Brussels, Belgium, 2017.
- Masterplan Idrogeno. Euregio Tirolo-Alto Adige-Trentino Corridoio Dell’idrogeno Lungo l’asse Del Brennero; Tyrol–South Tyrol–Trentino Euroregion: Bolzano, Italy, 2021. [Google Scholar]
- Terna. Annuario Statistico CONSUMI; Terna: Rome, Italy, 2020. [Google Scholar]
- GSE (Gestore dei Servizi Energetici). Nota Teleriscaldamento e Teleraffrescamento 2020; GSE: Rome, Italy, 2022. [Google Scholar]
- UNI 10349-3:2016; Riscaldamento e Raffrescamento Degli Edifici—Dati Climatici—Parte 3: Differenze Di Temperatura Cumulate (Gradi Giorno) Ed Altri Indici. UNI: Milan, Italy, 2016.
- European Union Joint Research Centre (JRC) European Reference Life Cycle Database (ELCD). Available online: https://nexus.openlca.org/database/ELCD (accessed on 28 April 2020).
- ARERA Prezzi Dell’energia Elettrica per Usi Industriali Nel 2021 (al Netto e al Lordo Delle Imposte)—Da 2.000 a 20.000 MWh Annui. Available online: https://www.arera.it/fileadmin/allegati/dati/ra21/eepcfr2.xlsx (accessed on 7 April 2024).
- ARERA Prezzi Finali Del Gas Naturale per i Consumatori Industriali Nel 2021—Utenti Con Consumi Da 260-2.600 Migliaia Di Metri Cubi Annui. Available online: https://www.arera.it/fileadmin/allegati/dati/gas/gpcfr2.xlsx (accessed on 7 April 2024).
- Enel X Web Page. Available online: https://www.enelxstore.com/it/it/prodotti/ (accessed on 7 April 2024).
- Biancardi, A. The Cost of Capital in the Energy and Water Sectors in Italy; ARERA: Milan, Italy, 2016. [Google Scholar]
- Beccali, M.; Cellura, M.; Longo, S.; Nocke, B.; Finocchiaro, P. LCA of a Solar Heating and Cooling System Equipped with a Small Water—Ammonia Absorption Chiller. Solar Energy
**2012**, 86, 1491–1503. [Google Scholar] [CrossRef] - Mcmanus, M.C. Environmental Consequences of the Use of Batteries in Low Carbon Systems: The Impact of Battery Production. Appl. Energy
**2012**, 93, 288–295. [Google Scholar] [CrossRef] - Mavromatidis, G.; Orehounig, K.; Carmeliet, J. Design of Distributed Energy Systems under Uncertainty: A Two-Stage Stochastic Programming Approach. Appl. Energy
**2018**, 222, 932–950. [Google Scholar] [CrossRef]

**Figure 4.**Electric energy flows in the case of economic optimization (heat pump contribution is too low for the scale).

**Figure 5.**Heat energy flows in the case of economic optimization (heat pump contribution is too low for the scale).

**Figure 11.**Combined values of cost, primary energy consumption, and carbon emissions resulting from different scenarios.

Ref. | Optimization | Objective Function/Main Target | Hydrogen | Renewable Energies | Flexibility/Ancillary Services/Demand Response | Phases | Sensitivity or Uncertainty Assessment | Multi-Carrier (>2 Carriers) | Mathematical Model |
---|---|---|---|---|---|---|---|---|---|

[19] | No | Wind curtailment (costs) | Yes | Yes | No | Operation | No | No | Nonlinear |

[7] | Yes | Wind curtailment (costs) | Yes | Yes | No | Operation | No | No | Linear |

[20] | Yes | Costs | Yes | Yes | No | Design and operation | Yes (Sensitivity) | No | Linear |

[21] | No | Costs | Yes | Yes | Yes | Operation | No | No | Linear |

[22] | No | Grid interactions | Yes | Yes | Yes | Operation | No | No | Nonlinear |

[23] | Yes | Costs | Yes | Yes | Yes | Operation | No | No | MILP |

[24] | No | Power flow | Yes | Yes | No | Operation | No | No | Nonlinear |

[25] | Yes | Costs | Yes | No | No | Design | No | No | Nonlinear |

[26] | Yes | Costs | Yes | Yes | No | Design and operation | Yes (Sensitivity) | No | Linear |

[27] | Yes | Costs and emissions | Yes | Yes | Yes | Operation | Yes (Uncertainty) | Yes (4) | MINLP |

[28] | Yes | Costs | Yes | Yes | No | Operation | Yes (Uncertainty) | Yes (4) | Nonlinear |

[29] | Yes | Costs and emissions | Yes | Yes | No | Operation | No | Yes (4) | MILP |

[30] | Yes | Costs | Yes | Yes | No | Operation | No | Yes (4) | Linear |

[31] | Yes | Costs | Yes | Yes | No | Design and operation | Yes (Uncertainty) | Yes (4) | MILP |

[32] | Yes | Costs | Yes | Yes | Yes | Operation | Yes (Uncertainty) | Yes (4) | MILP |

[33] | Yes | Costs | Yes | Yes | Yes | Operation | Yes (Uncertainty) | Yes (4) | MILP |

[34] | Yes | Costs | Yes | Yes | No | Operation | Yes (Uncertainty) | Yes (5) | MILP |

[35] | Yes | Costs | Yes | Yes | No | Operation | Yes (Uncertainty) | Yes (4) | MILP |

[36] | Yes | Emissions | Yes | Yes | Yes | Operation | Yes (Uncertainty) | Yes (5) | MILP |

This study | Yes | Costs, primary energy, emissions, grid interactions | Yes | Yes | Yes | Design and operation | Yes (Uncertainty) | Yes (7) | MILP |

Abbreviation | Meaning |
---|---|

AC | Absorption chiller |

BOP | Balance of plant |

C | Cost |

CED | Cumulative energy demand |

CVaR | Conditional value at risk |

DC | District cooling |

DH | District heating |

DHW | Domestic hot water |

E | Electricity |

EH | Energy hub |

EL | Electrolyzer |

ESS | Electrical energy storage |

F | Cooling |

FC | Fuel cell |

GB | Gas-fired boiler |

GWP | Global warming potential |

H | Heating |

H_{2} | Hydrogen |

HP | Heat pump |

K | Constant |

MES | Multi-carrier energy system |

NG | Natural gas |

PEMFC | Proton exchange membrane fuel cell |

RES | Renewable energy source |

TSS | Thermal energy storage |

TK | Tank |

TR | Transformer |

TSO | Transmission system operator |

W | Water |

Grid/Network | Costs | CED | GWP | Grid Interactions |
---|---|---|---|---|

E | C_{opex,E} = 0.30 EUR/kWh_{el} | CED_{E} = 11.8 MJ/kWh | GWP_{E} = 0.071 kgCO_{2eq}/kWh | 100,000 |

NG | C_{opex,NG} = 0.09 EUR/kWh_{th} | CED_{NG} = 4.12 MJ/kWh | GWP_{NG} = 0.037 kgCO_{2eq}/kWh | 100,000 |

H | - | - | - | 100,000 |

F | - | - | - | 100,000 |

H_{2} | C_{opex,H}_{2} = 20 EUR/kg | CED_{H}_{2} = 213.52 MJ/kg | GWP_{H}_{2} = 11.95 kgCO_{2eq}/kg | 100,000 |

W | C_{opex,W} = 2.19 EUR/kg | CED_{W} = 0 MJ/kg (negligible) | GWP_{W} = 0 kgCO_{2eq}/kg (negligible) | 100,000 |

Equipment | Conversion Factors | Costs | CED [MJ/kWh or MJ/kg] | GWP [kgCO_{2eq}/kWh or kgCO_{2eq}/kg] |
---|---|---|---|---|

GB | K_{GB gh} = 0.9 | C_{capex,GB} = 55.51 EUR/kWC _{capex,GB (}_{0)} = 118.8 EUR | 92.65 | 19.5 |

HP | K_{HP eh} = 5.7 | C_{capex,HP} = 111.93 EUR/kWC _{capex,HP (}_{0)} = 630.63 EUR | 1250.4 | 239.4 |

AC | K_{AChf} = 0.9 | C_{capex,AC} = 216.9 EUR/kW | 2338.42 | 147.5 |

EL | K_{EL eh}_{2} = 0.016 kg/kWh ^{1}K _{EL h}_{2w} = 8.55 kg/kg | C_{capex,EL} = 1274 EUR/kW | 168,635 | 28 |

FC | K_{FC h}_{2}_{e} = 12.23 kWh/kgK _{FC h}_{2h} = 20.11 kWh/kgK _{FC h}_{2w} = 9.47 kg/kg | C_{capex,FC} = 1532.44 EUR/kW | 71,466 | 11.87 |

PV | NOCT = 47 °C A _{PV} = 1.2 m^{2}η _{PV} = 0.21β _{PV} = −3.7 10^{−3} °C^{−1}η _{BOP} = 0.95P _{PV} = 0.25 kW/unit | C_{capex,PV} = 311.95 EUR/unit | 4582 | 358 |

CSP | K_{CSP,se} = 0.1394K _{CSP,sh} = 0.3964A _{CSP} = 400 m^{2}P _{CSP} = 1000 kW/unit | C_{capex,CSP} = 273,002.73 EUR/unit | 7210.6 | 3545.04 |

STC | A_{STC} = 1.867 m^{2}η _{0} = 0.734a _{1} = 1.529 W/m^{2} Ka _{2} = 0.0166 W/m^{2} K^{2}T _{m} = 40 °C | C_{capex,STC} = 500 EUR/unit | 3745.52 | 210.56 |

TK | K_{TK,in} = 1K _{TK,out} = 1H _{2} _{TK,loss} = 0.02 | C_{capex,TK} = 171.33 EUR/kgC _{capex,TK (}_{0)} = 716,859 EUR | 3222.2 | 0.048 |

ESS | K_{ESS,in} = 0.97K _{ESS,out} = 0.97ESS _{,loss} = 0.01DoD _{ESS} = 0.2 | C_{capex,ESS} = 419.37 EUR/kWhC _{capex,ESS(}_{0)} = 677,502.83 EUR | 540 | 76.28 |

TSS | K_{TSS,in} = 1K _{TSS,out} = 1TSS _{,loss} = 0.01 | C_{capex,TSS,H} = 26.18 EUR/kWhC _{capex,TSS,F} = 65.46 EUR/kWhC _{capex,TSS(}_{0)} = 266 | CED_{TSS,H} = 201CED _{TSS,F} = 504 | GWP_{TSS,H} = 11GWP _{TSS,F} = 27 |

^{1}including the power consumption to produce hydrogen (about 55 kWh/kg) and its compression to the tank pressure level of 500 bar (about 5 kWh/kg).

Minimum Cost | Minimum Primary Energy Consumption | Minimal Carbon Emissions | Minimal Grid Interactions | 0.25 Weights Multi-Objective Optimization | |
---|---|---|---|---|---|

GB [kW_{th}] | 37,879 | 29,065 | 29,064 | 447,681 | 29,065 |

HP [kW_{fr}] | 5107 | 6390 | 6390 | 6390 | 6390 |

AC [kW_{fr}] | 6390 | 63 | 63 | 6390 | 6390 |

EL [kW_{el}] | 0 | 73 | 73 | 5,488,336 | 0 |

FC [kW_{el}] | 0 | 0 | 0 | 5,488,336 | 0 |

PV [n.] PV [kW] | 5,488,336 1,383,061 | 1,300,865 327,818 | 1,299,567 327,491 | 1,511,170 380,815 | 1,375,615 346,655 |

CSP [n.] CSP [kW] | 0 0 | 2 2000 | 2 2000 | 0 0 | 0 0 |

STC [n.] STC [m ^{2}] | 92 171.8 | 0 0 | 0 0 | 0 0 | 0 0 |

TK [kg] | 0 | 0 | 0 | 7,624 | 0 |

ESS [kWh_{el}] | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 |

TSS_{H} [kWh_{th}] | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 |

TSS_{F} [kWh_{fr}] | 0 | 2902 | 2944 | 6390 | 6390 |

**Table 6.**Objective functions in the reference case (values and percentage reduction with respect to the non-optimized scenario).

Non-Optimized Base Scenario | Minimum Cost | Minimum Primary Energy Consumption | Minimal Carbon Emissions | Minimal Grid Interactions | 0.25 Weights Multi-Objective Optimization | |
---|---|---|---|---|---|---|

Costs [million euros/year] | 1007 | −455.39 (−145%) | 0.83 (−100%) | 13.27 (−99%) | 1818 (+81%) | 190.6 (−81%) |

Primary energy consumption [TJ/year] | 37,252 | 4488 (−88%) | 3369 (−91%) | 3369 (−91%) | 98,138 (+163%) | 3965 (−89%) |

Carbon emissions [t CO _{2eq}/year] | 268,383 | 236,642 (−12%) | 173,588 (−35%) | 173,289 (−35%) | 194,924 (−27%) | 209,702 (−22%) |

Grid interaction penalty function [-] | - | 1.3 × 10^{13} | 2.2 × 10^{12} | 2.2 × 10^{12} | 6.0 × 10^{10} | 3.7 × 10^{11} |

**Table 7.**Comparison between the mode of the sizes of the energy hub equipment among 500 uncertain scenarios and the sizes obtained in the cases without uncertainty.

Minimum Cost | Minimum Primary Energy Consumption | Minimal Carbon Emissions | Minimal Grid Interactions | 0.25 Weights Multi-Objective Optimization | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Without Uncertainty | With Uncertainty | Without Uncertainty | With Uncertainty | Without Uncertainty | With Uncertainty | Without Uncertainty | With Uncertainty | Without Uncertainty | With Uncertainty | |

GB [kW_{th}] | 37,879 | 34,693 | 29,065 | 27,872 | 29,064 | 27,821 | 447,681 | 447,681 | 29,065 | 447,681 |

HP [kW_{fr}] | 5107 | 5108 | 6390 | 6390 | 6390 | 6390 | 6390 | 6390 | 6390 | 6390 |

AC [kW_{fr}] | 6390 | 6390 | 63 | 62 | 63 | 62 | 6390 | 6390 | 6390 | 6390 |

EL [kW_{el}] | 0 | 0 | 73 | 73 | 73 | 73 | 5,488,336 | 5,488,336 | 0 | 0 |

FC [kW_{el}] | 0 | 0 | 0 | 0 | 0 | 0 | 5,488,336 | 5,488,336 | 0 | 0 |

PV [n.] | 5,488,336 | 5,488,336 | 1,300,865 | 1,048,726 | 1,299,567 | 1,216,872 | 1,511,170 | 1,332,143 | 1,375,615 | 5,488,336 |

CSP [n.] | 0 | 0 | 2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 |

STC [n.] | 92 | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 54.64 |

TK [kg] | 0 | 0 | 0 | 0 | 0 | 0 | 7624 | 7624 | 0 | 0 |

ESS [kWh_{el}] | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 | 5,488,336 |

TSS_{H} [kWh_{th}] | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 | 447,681 |

TSS_{F} [kWh_{fr}] | 0 | 0 | 2902 | 0 | 2944 | 52.22 | 6390 | 6390 | 6390 | 0 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Massaro, F.; Di Silvestre, M.L.; Ferraro, M.; Montana, F.; Riva Sanseverino, E.; Ruffino, S.
Energy Hub Model for the Massive Adoption of Hydrogen in Power Systems. *Energies* **2024**, *17*, 4422.
https://doi.org/10.3390/en17174422

**AMA Style**

Massaro F, Di Silvestre ML, Ferraro M, Montana F, Riva Sanseverino E, Ruffino S.
Energy Hub Model for the Massive Adoption of Hydrogen in Power Systems. *Energies*. 2024; 17(17):4422.
https://doi.org/10.3390/en17174422

**Chicago/Turabian Style**

Massaro, Fabio, Maria Luisa Di Silvestre, Marco Ferraro, Francesco Montana, Eleonora Riva Sanseverino, and Salvatore Ruffino.
2024. "Energy Hub Model for the Massive Adoption of Hydrogen in Power Systems" *Energies* 17, no. 17: 4422.
https://doi.org/10.3390/en17174422