Multicarrier Energy System Management as Mixed Integer Linear Programming


This paper presents the problem model of multicarrier energy system management. The proposed problem includes three types of energy that is as electrical, natural and heating. Electrical and gas energies are as hub input, and hub output is as electrical and heating. The electricity energy provides using (1) renewable energy sources (RESs), electrical energy storage system, combined heat and power (CHP) system that are managed by hub operator and are not to play at market and (2) electricity market with PoolCo and bilateral contracts models. Therefore, the proposed problem is as optimization problem that its objective function is minimizing energy cost of hub. The constraints are electrical, natural and district heating networks power flow, RES, storage system, CHP and market constraints, and limitation of all networks indexes. This problem is modeled as mixed integer nonlinear programming. But, this paper uses the equivalent mixed integer linear programming model for accessing to optimal solution with low calculation time and error. Finally, this problem applied to standard test network with GAMS software, and thus, the capability of proposed problem investigates.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


e, g, h, t, l, k :

Indices of electrical, gas, heating bus, time, linearization segments of piecewise method and circular constraint, respectively


Reference bus

φe, φg, φh, φt, φl, φk :

Sets of electrical, gas, heating bus, time, linearization segments of piecewise method and circular constraint, respectively


Objective function value ($)

Cele, Cgas, Ctem :

Energy cost of electrical, natural gas and district heating networks ($)

Cpoolco, Ctb :

Energy cost in PoolCo and bilateral contracts models ($)

E ST :

Stored energy in the storage system (pu)

PGCHP,ele, PGCHP,gas, PGCHP,tem :

Electrical, gas and heating power of CHP (pu)

PGgas, PGtem, PGele :

Generation power in electrical, natural gas and district heating networks (pu)

PGpoolco, PGtb :

Purchase power of PoolCo and bilateral contracts models (pu)


Generation power of RES (pu)

PLgas, PLtem, PLele :

Power flow of gas, heating and electrical network lines (pu)

PST,ch, PST,dch :

Charging and discharging power of storage system (pu)

QGele, QLele :

Generation reactive power, reactive flow from transmission lines (pu)

T :

Temperature (pu)

V, θ, ΔV :

Voltage magnitude (pu), voltage angle (rad) and voltage deviation (pu)

π, Δπ :

Gas pressure and pressure deviation (pu)

ALele, ALgas, ALtem :

Bus and line incidence matrix for electrical, natural gas and district heating networks without unit

\(c,\dot{m}\) :

Specific heat capacity of water, mass flow rate of water through pipeline (pu)

Emax, Emin :

Maximum and minimum stored energy in the storage system (pu)

g, b :

Conductance and susceptance of a line (pu)

PDele, PDgas, PDtem :

Consumption power in the electrical, natural gas and district heating networks (pu)

PGCHP,emax, PGCHP,gmax, PGCHP,hmax :

Maximum capacity of CHP in electrical, gas and heating parts (pu)

PGgas,max, PLgas,max :

Maximum capacity of gas line and generation (pu)


Generation active power of photovoltaic and wind systems (pu)

PGtem,max, PLtem,max :

Maximum capacity of heating line and generation (pu)

Pmax, Pmin :

Maximum and minimum purchase power of bilateral contracts models (pu)

P ST,max :

Maximum charge/discharge rate of storage system (pu)

QDele :

Reactive load (pu)

SLmax, SGmax :

Maximum capacity of electrical line and generation (pu)

Tmax, Tmin :

Maximum and minimum value of temperature (pu)

Vmax, Vmin :

Maximum and minimum value of voltage (pu)

λtb, λpoolco, λgas, λtem :

Energy price of bilateral contracts and PoolCo models, gas and heating network ($/MWh)

κ :

Pipeline constant (pu)

ηch, ηdch :

Charging and discharging efficiency of storage system

η CHP :

Efficiency of CHP

πmax, πmin :

Maximum and minimum value of pressure (pu)


  1. Ayele GT, Haurant P, Laumert B, Lacarrière B (2018) An extended energy hub approach for load flow analysis of highly coupled district energy networks: illustration with electricity and heating. Appl Energy 212:850–867

    Article  Google Scholar 

  2. Chen Y, Wei W, Liu F, Wu Q, Mei S (2018) Analyzing and validating the economic efficiency of managing a cluster of energy hubs in multi-carrier energy systems. Appl Energy 230:403–416

    Article  Google Scholar 

  3. Derafshi Beigvanda S, Abdia H, La Scalab M (2017a) Economic dispatch of multiple energy carriers. Energy 138:861–872

    Article  Google Scholar 

  4. Derafshi Beigvanda S, Abdia H, La Scalab M (2017b) A general model for energy hub economic dispatch. Applied Energy 190:1090–1111

    Article  Google Scholar 

  5. Fortenbacher P, Ulbig A, Andersson G (2017) Optimal placement and sizing of distributed battery storage in low voltage grids using receding horizon control strategies. IEEE Trans Smart Grid 4(2):2383–2394

    Google Scholar 

  6. Generalized Algebraic Modeling Systems (GAMS).

  7. Giaouris D, Papadopoulos AI, Patsios C, Walker S, Ziogou C, Taylor P, Voutetakis S, Papadopoulou S, Seferlis P (2018) A systems approach for management of microgrids considering multiple energy carriers, stochastic loads, forecasting and demand side response. Appl Energy 226:546–559

    Article  Google Scholar 

  8. Hamidpour H, Aghaei J, Dehghan S, Pirouzi S, Niknam T (2018) Integrated resource expansion planning of wind integrated power systems considering demand response programmes. IET Renew Power Gener 13(4):519–529

    Article  Google Scholar 

  9. Hamidpour H, Aghaei J, Pirouzi S, Dehghan S, Niknam T (2019) Flexible, reliable and renewable power system resource expansion planning considering energy storage systems and demand response programs. IET Renew Power Gener 13(11):1862–1872

    Article  Google Scholar 

  10. La Scala M, Vaccaro A, Zobaa AF (2014) A goal programming methodology for multi-objective optimization of distributed energy hubs operation. Appl Therm Eng 71:658–666

    Article  Google Scholar 

  11. Lin H, Liu Y, Sun Q, Xiong R, Li H, Wennersten R (2018) The impact of electric vehicle penetration and charging patterns on the management of energy hub—a multi-agent system simulation. Appl Energy 230:189–206

    Article  Google Scholar 

  12. Moeini-Aghtaie M, Abbaspour A, Fotuhi-Firuzabad M, Hajipour E (2014a) A decomposed solution to multiple-energy carriers optimal power flow. IEEE Trans Power Syst 29:707–716

    Article  Google Scholar 

  13. Moeini-Aghtaie M, Dehghanian P, Fotuhi-Firuzabad M, Abbaspour A (2014b) Multiagent genetic algorithm: an online probabilistic view on economic dispatch of energy hubs constrained by wind availability. IEEE Trans Power Syst 5:699–708

    Google Scholar 

  14. Najafi A, Falaghi H, Contreras J, Ramezani M (2016a) Medium-term energy hub management subject to electricity price and wind uncertainty. Appl Energy 168:418–433

    Article  Google Scholar 

  15. Najafi A, Contreras FHJ, Ramezani M (2016b) A stochastic bi-level model for the energy hub manager problem. IEEE Trans Smart Grid 26(3):1–11

    Google Scholar 

  16. Pan Z, Guo Q, Sun H (2016) Interactions of district electricity and heating systems considering time-scale characteristics based on quasi-steady multi-energy flow. Appl Energy 167:230–243

    Article  Google Scholar 

  17. Pirouzi S, Aghaei J (2018) Mathematical modeling of electric vehicles contributions in voltage security of smart distribution networks. Simul-T Soc Mod Sim 95(5):429–439

    Google Scholar 

  18. Pirouzi S, Latify MA, Yousefi GR (2015) Investigation on reactive power support capability of PEVs in distribution network operation. In: 23rd Iranian conference on electrical engineering (ICEE)

  19. Pirouzi S, Aghaei J, Shafie-khah M, Osório GJ, Catalão JPS (2017a) Evaluating the security of electrical energy distribution networks in the presence of electric vehicles. In: Proceedings of PowerTech conference, IEEE Manchester, pp 1–6

  20. Pirouzi S, Aghaei J, Latify MA, Yousefi GR, Mokryani G (2017b) A robust optimization approach for active and reactive power management in smart distribution networks using electric vehicles. IEEE Syst J 99:1–11

    Google Scholar 

  21. Pirouzi S, Aghaei J, Niknam T, Shafie-khah M, Vahidinasab V, Catalão JPS (2017c) Two alternative robust optimization models for flexible power management of electric vehicles in distribution networks. Energy 141:635–652

    Article  Google Scholar 

  22. Pirouzi S, Aghaei J, Niknam T, Farahmand H, Korpås M (2018a) Exploring prospective benefits of electric vehicles for optimal energy conditioning in distribution networks. Energy 157:679–689

    Article  Google Scholar 

  23. Pirouzi S, Aghaei J, Vahidinasab V, Niknam T, Khodaei A (2018b) Robust linear architecture for active/reactive power scheduling of EV integrated smart distribution networks. Electr Power Syst Res 155:8–20

    Article  Google Scholar 

  24. Pirouzi S, Aghaei J, Niknam T, Farahmand H, Korpås M (2018c) Proactive operation of electric vehicles in harmonic polluted smart distribution networks. IET Gener Transm Distrib 12:967–975

    Article  Google Scholar 

  25. Rezvani A, Gandomkar M, Izadbakhsh M, Ahmadi A (2014) Environmental/economic scheduling of a micro-grid with renewable energy resources. J Clean Prod 12:1–11

    Google Scholar 

  26. Shabanpour-Haghighi A, Seifi AR (2015a) Multi-objective operation management of a multi-carrier energy system. Energy 88:430–442

    Article  Google Scholar 

  27. Shabanpour-Haghighi A, Seifi AR (2015b) Energy flow optimization in multicarrier systems. IEEE Trans Ind Inform 11:1067–1077

    Article  Google Scholar 

  28. Shabanpour-Haghighi A, Seifi AR (2015c) Simultaneous integrated optimal energy flow of electricity, gas, and heat. Energy Convers Manag 101:579–591

    Article  Google Scholar 

  29. Shabanpour-Haghighi A, Seifi AR, Niknam T (2014) A modified teaching–learning based optimization for multi-objective optimal power flow problem. Energy Convers Manag 77:597–607

    Article  Google Scholar 

  30. Shahidehpour M, Yamin H, Li Z (2002) Market operations in electric power systems. The Institute of Electrical and Electronics Engineers Inc., New York

    Google Scholar 

  31. Skarvelis-Kazakos S, Papadopoulos P, Unda IG, Gorman T, Belaidi A, Zigan S (2016) Multiple energy carrier optimisation with intelligent agents. Appl Energy 167:323–335

    Article  Google Scholar 

  32. Wang Y, Cheng J, Zhang N, Kang C (2018a) Automatic and linearized modeling of energy hub and its flexibility analysis. Appl Energy 211:705–714

    Article  Google Scholar 

  33. Wang J, Zhong H, Ma Z, Xia Q, Kang C (2018b) Review and prospect of integrated demand response in the multi-energy system. Appl Energy 202:772–782

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to B. Bahmani-Firouzi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Afrashi, K., Bahmani-Firouzi, B. & Nafar, M. Multicarrier Energy System Management as Mixed Integer Linear Programming. Iran J Sci Technol Trans Electr Eng (2020).

Download citation


  • Multicarrier energy system
  • Electrical network
  • Natural gas network
  • District heating network