Authors : Joseph J. Akpan; Akhikpemelo Abraham; Ephraim R. Afia; Dan Eyo Dan-Abia

Volume/Issue : Volume 11 - 2026, Issue 9 - September

Google Scholar : https://tinyurl.com/2mafyr79

DOI : https://doi.org/10.38124/ijisrt/26sep1309

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : The introduction of multi-carrier microgrids (MCMGs) is a paradigm shift in the decentralised energy system, allowing for coordinated dispatch of coupled electrical, thermal, and natural gas subsystems. Despite this, the economic challenges of MCMGs are quite sensitive to multi-dimensional uncertainties such as the intermittent generation of renewable energy, the volatile market electricity prices, and the multi-energy load demands. Traditional deterministic or risk-neutral energy management systems optimise average performance, but are not designed to buffer microgrid operators from operational gaps and tail risks with high impact from low-probability events. In this paper, a new risk-constrained optimal energy management approach for multi-carrier microgrids is presented, which aims to minimise risk by employing a twostage stochastic mixed-integer linear programming (MILP) approach. The Conditional Value-at-Risk (CVaR) is incorporated as a primary operational objective function to capture and mitigate financial exposure during worst cases. Extensive uncertainty profiles are computed using Latin Hypercube Sampling (LHS), while being downscaled by a fast forward scenario-reduction technique. A modified IEEE 33-bus electrical network and a 6-node district heating system are used for the validation of the proposed model. It is shown that the proposed framework strategically sacrifices a marginal increase in the expected daily operating costs while offering a significant decrease in the tail-risk financial losses through tuning the risk-aversion parameter.

Keywords : Multi-Carrier Microgrids, Optimal Energy Management, Conditional Value-at-Risk, Two-Stage Stochastic Programming, Mixed-Integer Linear Programming, Uncertainty Modeling.

References :

1. S. Chu and A. Majumdar, “Opportunities and challenges for a sustainable energy future,” Nature, vol. 488, no. 7411, pp. 294–303, Aug. 2012, doi: 10.1038/nature11475.
2. J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicuña, and M. Castilla, “Hierarchical control of droop-controlled AC and DC microgrids, A general approach toward standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011, doi: 10.1109/TIE.2010.2066534.
3. F. Katiraei and M. R. Iravani, “Power management strategies for a microgrid with multiple distributed generation units,” IEEE Trans. Power Syst., vol. 21, no. 4, pp. 1821–1831, Nov. 2006, doi: 10.1109/TPWRS.2006.879260.
4. R. H. Lasseter, “Smart distribution: Coupled microgrids,” Proc. IEEE, vol. 99, no. 6, pp. 1074–1082, Jun. 2011, doi: 10.1109/JPROC.2011.2114630.
5. P. Siano, “Demand response and smart grids—A survey,” Renew. Sustain. Energy Rev., vol. 30, pp. 461–478, Feb. 2014, doi: 10.1016/j.rser.2013.10.022.
6. M. Geidl, G. Koeppel, P. Favre-Perrod, B. Klöckl, G. Andersson, and K. Fröhlich, “Energy hubs for the future,” IEEE Power Energy Mag., vol. 5, no. 1, pp. 24–30, Jan./Feb. 2007, doi: 10.1109/MPAE.2007.264850.
7. M. Mohammadi, Y. Noorollahi, B. Mohammadi-Ivatloo, and H. Yousefi, “Energy hub: From a model to a concept—A review,” Renew. Sustain. Energy Rev., vol. 80, pp. 1512–1527, Dec. 2017, doi: 10.1016/j.rser.2017.07.030.
8. S. Clegg and P. Mancarella, “Integrated modeling and assessment of the operational impact of power-to-gas (P2G) on electrical and gas transmission networks,” IEEE Trans. Sustain. Energy, vol. 6, no. 4, pp. 1234–1244, Oct. 2015, doi: 10.1109/TSTE.2015.2424885.
9. A. Sheikhi, M. Rayati, S. Bahrami, and A. M. Ranjbar, “Integrated demand side management game in smart energy hubs,” IEEE Trans. Smart Grid, vol. 6, no. 2, pp. 675–683, Mar. 2015, doi: 10.1109/TSG.2014.2377020.
10. P. Mancarella, “MES (multi-energy systems): An overview of concepts and evaluation models,” Energy, vol. 65, pp. 1–17, Feb. 2014, doi: 10.1016/j.energy.2013.10.041.
11. Y. Wang, J. Wang, C. Huang et al., “Optimal coordinated operation of a multi-energy microgrid considering multi-energy interaction,” Appl. Energy, vol. 267, Art. no. 114828, Jun. 2020, doi: 10.1016/j.apenergy.2020.114828.
12. Y. Liu et al., “Uncertainty modelling for multi-carrier energy systems,” IEEE Trans. Smart Grid, vol. 12, no. 5, pp. 4390–4400, Sep. 2021, doi: 10.1109/TSG.2021.3082531.
13. D. E. Olivares et al., “Trends in microgrid control,” IEEE Trans. Smart Grid, vol. 5, no. 4, pp. 1905–1919, Jul. 2014, doi: 10.1109/TSG.2013.2295514.
14. M. Di Somma et al., “Operation optimization of a distributed energy system considering energy costs and exergy efficiency,” Energy Convers. Manage., vol. 103, pp. 739–751, Oct. 2015, doi: 10.1016/j.enconman.2015.07.009.
15. A. S. Tam and W. W. Lee, “Multi-carrier demand characterisation under uncorrelated electrical and thermal peaks,” Energy, vol. 202, Art. no. 117700, Jul. 2020, doi: 10.1016/j.energy.2020.117700.
16. A. J. Conejo, M. Carrión, and J. M. Morales, Decision Making Under Uncertainty in Electricity Markets. New York, NY, USA: Springer, 2010, doi: 10.1007/978-1-4419-7421-1.
17. A. Parisio, E. Rikos, and L. Glielmo, “A model predictive control approach to microgrid operation optimization,” IEEE Trans. Control Syst. Technol., vol. 22, no. 5, pp. 1813–1827, Sep. 2014, doi: 10.1109/TCST.2013.2295737.
18. Y. Zhang, N. Gatsis, and G. B. Giannakis, “Robust energy management for microgrids with high-penetration renewables,” IEEE Trans. Sustain. Energy, vol. 4, no. 4, pp. 944–953, Oct. 2013, doi: 10.1109/TSTE.2013.2255135.
19. W. Su, J. Wang, and J. Roh, “Stochastic energy scheduling in microgrids with intermittent renewable energy resources,” IEEE Trans. Smart Grid, vol. 5, no. 4, pp. 1876–1883, Jul. 2014, doi: 10.1109/TSG.2013.2280604.
20. J. Wang, J. Wang, and Y. Xiao, “Risk-aware energy management of multi-energy microgrids,” Int. J. Electr. Power Energy Syst., vol. 125, Art. no. 106438, Feb. 2021, doi: 10.1016/j.ijepes.2020.106438.
21. S. Bahramirad, W. Reder, and A. Khodaei, “Reliability-constrained optimal sizing of energy storage system in a microgrid,” IEEE Trans. Smart Grid, vol. 3, no. 4, pp. 2056–2062, Dec. 2012, doi: 10.1109/TSG.2012.2217991.
22. Y. Wu et al., “Risk-constrained scheduling of islanded microgrids,” IEEE Trans. Power Syst., vol. 34, no. 4, pp. 2966–2976, Jul. 2019, doi: 10.1109/TPWRS.2019.2898711.
23. S. Ahmed et al., “A review of multi-carrier energy management and risk measures,” Renew. Sustain. Energy Rev., vol. 143, Art. no. 110880, Jun. 2021, doi: 10.1016/j.rser.2021.110880.
24. Y. Chen and F. Liu, “Stochastic and robust optimization of electrical microgrids with storage,” IEEE Trans. Smart Grid, vol. 10, no. 4, pp. 4230–4241, Jul. 2019, doi: 10.1109/TSG.2018.2853112.
25. M. Mohammadi and W. B. Powell, “Uncertainty-aware control of battery-equipped power networks,” Energy Syst., vol. 11, no. 3, pp. 625–648, Aug. 2020, doi: 10.1007/s12667-019-00331-w.
26. Y. Zhou et al., “Thermodynamic and network constraints of coupled heat and gas systems,” Appl. Energy, vol. 306, Art. no. 117983, Jan. 2022, doi: 10.1016/j.apenergy.2021.117983.
27. J. Martínez-Crespo and J. Usaola, “MILP scheduling of integrated energy hubs with CHP and boilers,” Electr. Power Syst. Res., vol. 190, Art. no. 106730, Jan. 2021, doi: 10.1016/j.epsr.2020.106730.
28. J. Wang and N. Zhang, “Deterministic multi-carrier hub scheduling,” IEEE Trans. Sustain. Energy, vol. 11, no. 3, pp. 1650–1661, Jul. 2020, doi: 10.1109/TSTE.2019.2936780.
29. A. Kumar and S. N. Singh, “Sensitivity of deterministic multi-carrier models to real-time deviations,” IET Gener. Transm. Distrib., vol. 13, no. 18, pp. 4120–4128, Sep. 2019, doi: 10.1049/iet-gtd.2018.6830.
30. H. Farzin, M. Fotuhi-Firuzabad, and M. Moeini-Aghtaie, “A stochastic multi-objective framework for optimal scheduling of energy storage systems in microgrids,” IEEE Trans. Smart Grid, vol. 8, no. 1, pp. 117–127, Jan. 2017, doi: 10.1109/TSG.2016.2598678.
31. Z. Li et al., “Stochastic programming for multi-energy systems under uncertainty,” Energy, vol. 200, Art. no. 117523, Jun. 2020, doi: 10.1016/j.energy.2020.117523.
32. R. T. Rockafellar and S. Uryasev, “Conditional value-at-risk for general loss distributions,” J. Banking Finance, vol. 26, no. 7, pp. 1443–1471, Jul. 2002, doi: 10.1016/S0378-4266(02)00271-6.
33. P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, 3rd ed. New York, NY, USA: McGraw-Hill, 2007.
34. G. C. Pflug, “Some remarks on the value-at-risk and the conditional value-at-risk,” in Probabilistic Constrained Optimization, S. P. Uryasev, Ed. Boston, MA, USA: Springer, 2000, pp. 272–281, doi: 10.1007/978-1-4757-3150-7_15.
35. A. Alabdulwahab et al., “CVaR-based risk-constrained dispatch of multi-carrier systems,” IEEE Access, vol. 9, pp. 24110–24121, 2021, doi: 10.1109/ACCESS.2021.3056801.
36. N. Nikmehr and S. N. Ravadanegh, “Optimal power dispatch of multi-microgrids at future smart distribution grids,” IEEE Trans. Smart Grid, vol. 6, no. 4, pp. 1648–1657, Jul. 2015, doi: 10.1109/TSG.2015.2396992.
37. Y. Li et al., “Coupled electricity and district-heating test systems for multi-carrier studies,” Appl. Energy, vol. 355, Art. no. 122210, Feb. 2024, doi: 10.1016/j.apenergy.2023.122210.
38. X. Liu et al., “Hydrogen storage as a complement to batteries in multi-carrier hubs,” Int. J. Hydrogen Energy, vol. 48, no. 30, pp. 11210–11222, Apr. 2023, doi: 10.1016/j.ijhydene.2022.12.080.
39. J. Wang, N. Zhang, and D. S. Kirschen, “Operation of multi-carrier energy hubs with power-to-gas,” IEEE Trans. Power Syst., vol. 37, no. 3, pp. 2210–2222, May 2022, doi: 10.1109/TPWRS.2021.3119020.
40. A. Massaro et al., “Hydrogen-coupled multi-carrier microgrids,” Energy Convers. Manage., vol. 300, Art. no. 117910, Jan. 2024, doi: 10.1016/j.enconman.2023.117910.
41. Y. Noorollahi, M. Mohammadi, and H. Yousefi, “Energy hub components and modelling practice,” Renew. Sustain. Energy Rev., vol. 78, pp. 1200–1215, Oct. 2017, doi: 10.1016/j.rser.2017.05.011.
42. A. Kumar et al., “Comparative assessment of hydrogen and battery storage,” Int. J. Hydrogen Energy, vol. 48, no. 15, pp. 5810–5825, Feb. 2023, doi: 10.1016/j.ijhydene.2022.11.045.
43. A. Akbari-Dibavar, K. Zare, and S. Nojavan, “Optimal scheduling of a multi-carrier energy hub with P2G,” J. Energy Storage, vol. 35, Art. no. 102269, Mar. 2021, doi: 10.1016/j.est.2021.102269.
44. J. Milewski et al., “Electrolyser modelling for power-to-hydrogen systems,” Int. J. Hydrogen Energy, vol. 50, pp. 105–118, Jan. 2025, doi: 10.1016/j.ijhydene.2024.10.120.
45. I. Eryazici, “Higher-heating-value conversion in P2G plants,” Energy, vol. 263, Art. no. 125800, Jan. 2023, doi: 10.1016/j.energy.2022.125800.
46. Y. S. Sanusi et al., “Volumetric hydrogen flow from electrolysers,” Int. J. Hydrogen Energy, vol. 44, no. 48, pp. 26110–26122, Oct. 2019, doi: 10.1016/j.ijhydene.2019.08.090.
47. S. Ahmad et al., “Dynamic modelling of hydrogen storage tanks,” J. Energy Storage, vol. 78, Art. no. 110050, Feb. 2024, doi: 10.1016/j.est.2023.110050.
48. W. Lok et al., “Hydrogen tank buffering of P2G–fuel-cell mismatch,” Appl. Energy, vol. 285, Art. no. 116410, Mar. 2021, doi: 10.1016/j.apenergy.2020.116410.
49. Y. Li et al., “A dynamic volume model of hydrogen storage,” Int. J. Hydrogen Energy, vol. 48, no. 12, pp. 4500–4512, Feb. 2023, doi: 10.1016/j.ijhydene.2022.10.150.
50. Y. Li, W. Wei, and S. Mei, “Energy management of multi-energy systems with CHP and storage,” IEEE Trans. Sustain. Energy, vol. 12, no. 1, pp. 120–132, Jan. 2021, doi: 10.1109/TSTE.2020.2985010.
51. P. Marocco et al., “Charge and discharge efficiencies of hydrogen tanks,” J. Energy Storage, vol. 60, Art. no. 106620, Apr. 2023, doi: 10.1016/j.est.2023.106620.
52. O. Abedinia et al., “Hydrogen fuel-cell cogeneration in multi-carrier hubs,” Energy, vol. 288, Art. no. 129800, Feb. 2024, doi: 10.1016/j.energy.2023.129800.
53. K. Almutairi et al., “Electrical and thermal output models of HFCs,” Int. J. Hydrogen Energy, vol. 52, pp. 310–322, Jan. 2025, doi: 10.1016/j.ijhydene.2024.11.080.
54. A. Hasan et al., “Fuel-cell cogeneration models for community energy systems,” Energy Convers. Manage., vol. 277, Art. no. 116640, Feb. 2023, doi: 10.1016/j.enconman.2022.116640.
55. A. G. Olabi et al., “Fuel cell application in the transport and energy sectors,” Energy, vol. 214, Art. no. 118965, Jan. 2021, doi: 10.1016/j.energy.2020.118965.
56. Y. Wang et al., “Dispatch of hydrogen fuel-cell cogeneration,” Appl. Energy, vol. 378, Art. no. 124500, Jan. 2025, doi: 10.1016/j.apenergy.2024.124500.
57. A. G. Anastasiadis et al., “CHP flexibility in multi-energy microgrids,” Energy, vol. 290, Art. no. 130120, Mar. 2024, doi: 10.1016/j.energy.2023.130120.
58. H. R. Massrur, T. Niknam, and M. Fotuhi-Firuzabad, “Investigation of carrier-energy interactions in multi-carrier microgrids,” IEEE Trans. Smart Grid, vol. 11, no. 2, pp. 1120–1132, Mar. 2020, doi: 10.1109/TSG.2019.2934500.
59. M. F. Zia, E. Elbouchikhi, and M. Benbouzid, “Gas boilers as backup heat in multi-energy systems,” Appl. Energy, vol. 331, Art. no. 120410, Feb. 2023, doi: 10.1016/j.apenergy.2022.120410.
60. M. Khalid et al., “Hybrid BESS–TES buffers in energy hubs,” J. Energy Storage, vol. 105, Art. no. 114500, Jan. 2026, doi: 10.1016/j.est.2025.114500.
61. A. Anwar et al., “SOC dynamics of BESS with mutual exclusion of charge and discharge,” IEEE Trans. Smart Grid, vol. 15, no. 1, pp. 450–462, Jan. 2024, doi: 10.1109/TSG.2023.3298100.
62. L. R. Rodríguez et al., “Standing losses in sensible thermal energy storage,” Appl. Therm. Eng., vol. 135, pp. 310–321, May 2018, doi: 10.1016/j.applthermaleng.2018.02.050.
63. R. B. Nelsen, An Introduction to Copulas, 2nd ed. New York, NY, USA: Springer, 2006, doi: 10.1007/0-387-28678-0.
64. M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics, vol. 21, no. 2, pp. 239–245, May 1979, doi: 10.1080/00401706.1979.10489755.
65. J. Dupačová, N. Gröwe-Kuska, and W. Römisch, “Scenario reduction in stochastic programming: An approach using probability metrics,” Math. Program., vol. 95, no. 3, pp. 493–511, Mar. 2003, doi: 10.1007/s10107-002-0331-0.
66. H. Heitsch and W. Römisch, “Scenario reduction algorithms in stochastic programming,” Comput. Optim. Appl., vol. 24, nos. 2–3, pp. 187–206, Feb. 2003, doi: 10.1023/A:1021805924152.
67. K. Bruninx and E. Delarue, “Scenario generation for stochastic unit commitment,” IEEE Trans. Power Syst., vol. 31, no. 6, pp. 4300–4309, Nov. 2016, doi: 10.1109/TPWRS.2016.2518259.
68. A. Gonzalez-Castellanos and D. Pozo, “Computational issues in multi-period stochastic MIP energy models,” Electr. Power Syst. Res., vol. 196, Art. no. 107220, Jul. 2021, doi: 10.1016/j.epsr.2021.107220.
69. S. Sheikhahmadi, S. Bahramara, J. Moshtagh, and M. Yazdani Damavandi, “A risk-based two-stage stochastic model for energy management of microgrids,” Energy, vol. 145, pp. 204–216, Feb. 2018, doi: 10.1016/j.energy.2017.12.122.
70. M. Vahedipour-Dahraie, H. Rashidizadeh-Kermani, and A. Anvari-Moghaddam, “Risk-constrained two-stage stochastic energy management,” Int. J. Electr. Power Energy Syst., vol. 121, Art. no. 106080, Oct. 2020, doi: 10.1016/j.ijepes.2020.106080.
71. X. Dong et al., “Two-stage day-ahead and real-time scheduling of multi-carrier microgrids,” Appl. Energy, vol. 303, Art. no. 117620, Dec. 2021, doi: 10.1016/j.apenergy.2021.117620.
72. Ö. Akülker et al., “First-stage unit commitment under multi-carrier uncertainty,” Energy, vol. 312, Art. no. 133500, Jan. 2025, doi: 10.1016/j.energy.2024.133500.
73. Y. Wang et al., “CVaR-constrained operational dispatch of energy hubs,” IEEE Trans. Smart Grid, vol. 10, no. 5, pp. 5200–5210, Sep. 2019, doi: 10.1109/TSG.2018.2878200.
74. R. T. Rockafellar and S. Uryasev, “Optimization of conditional value-at-risk,” J. Risk, vol. 2, no. 3, pp. 21–41, 2000, doi: 10.21314/JOR.2000.038.
75. J. Xiao et al., “Expected-cost versus tail-risk trade-offs in microgrid EMS,” Energy, vol. 210, Art. no. 118550, Nov. 2020, doi: 10.1016/j.energy.2020.118550.
76. M. Khasanov et al., “Degradation costs of storage in second-stage recourse models,” J. Energy Storage, vol. 106, Art. no. 114800, Feb. 2026, doi: 10.1016/j.est.2025.114800.
77. S. Ahmadi et al., “Multi-carrier nodal balance under uncertainty scenarios,” IEEE Trans. Sustain. Energy, vol. 13, no. 3, pp. 1500–1512, Jul. 2022, doi: 10.1109/TSTE.2022.3155000.
78. F. García-Muñoz et al., “Real-time ramping of multi-carrier assets,” Electr. Power Syst. Res., vol. 212, Art. no. 108400, Nov. 2022, doi: 10.1016/j.epsr.2022.108400.
79. A. Fusco et al., “Dimensionality of two-stage stochastic MILP energy models,” Comput. Chem. Eng., vol. 170, Art. no. 108100, Feb. 2023, doi: 10.1016/j.compchemeng.2022.108100.
80. A. Tabares and P. Cortés, “Complexity of multi-period multi-scenario energy MILPs,” Omega, vol. 122, Art. no. 102950, Jan. 2024, doi: 10.1016/j.omega.2023.102950.
81. Gurobi Optimization, LLC, Gurobi Optimizer Reference Manual, v11.0, 2025. [Online]. Available: https://www.gurobi.com.
82. L. A. Wolsey, Integer Programming, 2nd ed. Hoboken, NJ, USA: Wiley, 2020.
83. R. E. Bixby, “A brief history of linear and mixed-integer programming computation,” Documenta Math., Extra Vol. Optimization Stories, pp. 107–121, 2012, doi: 10.4171/dma/e-11.
84. Y. Mu et al., “A 24-hour multi-carrier microgrid case study,” Appl. Energy, vol. 292, Art. no. 116850, Jun. 2021, doi: 10.1016/j.apenergy.2021.116850.
85. C. Peng and J. Wang, “IEEE 33-bus and 6-node district-heating co-simulation,” Energy, vol. 291, Art. no. 130300, Mar. 2024, doi: 10.1016/j.energy.2024.130300.
86. R. Hemmati, H. Saboori, and M. A. Jirdehi, “Multicarrier conversion and storage buffers,” Energy, vol. 193, Art. no. 116750, Feb. 2020, doi: 10.1016/j.energy.2019.116750.
87. T. Almeida et al., “Expected cost versus CVaR Pareto fronts for energy hubs,” IEEE Trans. Power Syst., vol. 37, no. 4, pp. 3100–3110, Jul. 2022, doi: 10.1109/TPWRS.2021.3128000.
88. J. Hu et al., “Intraday hydrogen-subsystem dispatch under tail risk,” Int. J. Hydrogen Energy, vol. 47, no. 80, pp. 34000–34012, Oct. 2022, doi: 10.1016/j.ijhydene.2022.08.020.
89. J. Duan et al., “Intra-day P2G–HFC tracking in multi-carrier hubs,” Appl. Energy, vol. 358, Art. no. 122550, Mar. 2024, doi: 10.1016/j.apenergy.2023.122550.
90. Y. Zhang et al., “Hydrogen ecosystems under tail-risk electricity prices,” Energy, vol. 315, Art. no. 134000, Feb. 2025, doi: 10.1016/j.energy.2024.134000.
91. J. Horrillo et al., “Multi-energy storage as a tail-risk buffer,” J. Energy Storage, vol. 107, Art. no. 115000, Feb. 2025, doi: 10.1016/j.est.2024.115000.
92. X. Yang et al., “HFC cogeneration on electrical and thermal vectors,” Int. J. Hydrogen Energy, vol. 54, pp. 450–462, Feb. 2025, doi: 10.1016/j.ijhydene.2024.12.050.
93. X. Yang et al., “Cross-vector hydrogen synergies in community energy systems,” Appl. Energy, vol. 332, Art. no. 120500, Feb. 2023, doi: 10.1016/j.apenergy.2022.120500.