Electrical Engineering

, Volume 101, Issue 3, pp 1033–1051 | Cite as

Dynamic behavior of multi-carrier energy market in view of investment incentives

  • Jaber Valinejad
  • Mousa MarzbandEmail author
  • Yijun Xu
  • Hasan Uppal
  • Ameena Saad Al-Sumaiti
  • Taghi Barforoshi
Original Paper


In this study, a dynamic two-level framework is proposed to model investment incentives in a multi-carrier energy market from a strategic company’s point of view. Capacity payment and firm contract are assumed as investment incentives to encourage the strategic producer to invest in generation units. In addition, financial incentives to invest in combined heat and power (CHP) include tax rebate and loans. Strategic company’s behavior is considered as a two-level model so that, in the first level, the objective function is to maximize the profit of the strategic producer by participating in an energy hub market. The strategic producer can invest in transmission lines, generation units, CHP, and gas furnace. In the second level, the aim is to maximize a multi-carrier energy social welfare encompassing heat, gas, and electric energy. In this model, units invested by rival companies are modeled using possible scenarios. Electric energy loads in this energy hub system are envisaged to be elastic, while heat loads are assumed to be inelastic to the market price. On the other hand, gas loads are indirectly elastic to the price. Besides, in the proposed framework, DC power flow and an exact gas flow model with the linearized Weymouth equation are used. The proposed model is implemented on two case studies including 6-bus system, and an energy hub system encompassing 24-bus IEEE RTS power system and 10-node natural gas system.


Energy hubs CHP Expansion planning Investment incentive Market Multiple energy systems (electric energy, natural gas, heat) 

List of symbols


\({S/S}^{\prime }\)

Index for scenario

\({y/y}^{\prime }\)

Dynamic stage number (year)


Demand block number

i / q /  / n

Number of new/existing//generation units for strategic//rival company


Demand number


Number of candidate production units for investment

\({b/b}^{\prime }\)

Power grid bus

\({l/l}^{\prime }\)

Gas network bus


CHP number


\(\text {TS}_{{yt}}\)

Weighting coefficient of demand block t in year y

\(\text {SP}_{s}\)

Likelihood of scenario s occurring in year y


SG’s investment funds


The cost of annual investment of the generation new unit (€/MW)

\(\text {OC}_{i}^{\text {Si}}/\text {OC}_{q}^{\text {Sq}}\)

New/existing generation units’ operating costs i/q of strategic company i

\(\text {OC}_{n}^{\text {NS}}\)

Generation units’ operating costs of rival company


Maximum consumption for demand c in block t and year y (MW)


The proposed price for demand c in block t and year y in scenario S

\(\text {CU}_{{yim}}\)

Candidate capacity for investment m in the new unit i (MW)

\(\overline{P}_{q}^{\text {Sq}}/\overline{P}_{n}^{\text {NS}}\)

Existing/generation units’s capacity q/n of strategic/rival company (MW)

\(S_{{bb^{\prime }}}\)

Susceptance of transmission line \(b-{b}^{\prime }\) (PU)

\(\overline{\text {PF}}_{{bb'}}/\overline{\text {'PF}}_{{bb'}}\)

Capacity of existing/new transmission line \(b-b^{\prime }\) (MW)


Annual discount rate


Volume/price of FC


Capacity payment rate (€/MWh)

\(\text {F.O.R}^{\text {Si}}/\text {F.O.R}^{\text {Sq}}\)

Mandatory exit rate of new/available plants


Capacity of candidate CHP to be invested (MW)


Capacity of candidate transmission line to be invested (MW)


Capacity of candidate gas furnace to be invested (MMBtu)


The annual cost resulted from investment of the new CHP (€/MW)


The annual cost resulted from investment of the new transmission line (€/MW)

\( Y^{F}_{l}\)

The annual cost resulted from investment of the new gas furnace (€/MW)

\(\eta ^{C2E}\ \eta ^{C2H}\)

Electric energy and heat conversion efficiency produced by CHP

\(\underline{\pi }_{l} \ \overline{\pi }_{l}\)

Minimum and maximum natural gas pressure at each gas bus (PSIG)

\(\underline{P}^{G}_{l}\ \overline{P}^{G}_{l}\)

Minimum and maximum natural gas production (MMBtu)


Maximum natural gas flowed by pipelines (MMBtu)


Dispatch factor between gas furnace and CHP

\(\eta ^\mathrm{pip}\)

Pipeline constant (MMBtu/PSIG)


Head demand (MMBtu)


Tax rebate for investment in CHP


Loan factor for investment in CHP


The proposed price for buying heat/gas (€/MMBtu)

Decision variables

\(\overline{P}_{yi}^{\text {Si}}\)

Investment capacity of the new unit i of SG (MW)

\(P_{{ytis}}^{\text {Si}}/P_{{ytqs}}^{\text {Sq}}//P_{{ytns}}^{\text {NS}}\)

New/existing//generation unit’s i / q//n production capacity by strategic//rival GENCO in year y in demand block t and scenario s

\(\overline{P}_{{yy'i}}^{\text {Siq}}/P_{{yy'tis}}^{\text {Siq}}\)

Available capacity/produced power of the new unit i by the strategic company in year \(y^{\prime }\) in years after the construction year y (MW)

\(\text {OC}_{{yi}}^{\text {Siq}}/B_{{yy'tis}}^{\text {Siq}}\)

Operating cost/proposed price of the new unit i by the strategic company in year \(y^{\prime }\) in years after the construction year y (MW)

\(\text {CU}_{{ytim}}^{b}\)

For the candidate capacity h in investment year y, binary variable equals one, otherwise, it equals zero

\(B_{\text {ytis}}^{\text {Si}}/B_{\text {ytqs}}^{\text {Sq}}\)

New/existing generation unit’s proposed price i / q by strategic company in the block y, demand block t, and scenario s (€/MWh)

\(B_{{ytns}}^{\text {NS}}\)

Generation unit’s proposed price n by non-strategic company in the block y, demand block t, and scenario s (€/MWh)


Power consumption for demand c in year y, block demand t, and scenario s (MW)


The voltage angle of bus b in block demand t, and scenario s

\(U^{C}_{yk}/ U^{'C}_{yy'k}\)

Binary variable for CHP investment

\(U^{L}_{ybb'}/ U^{'L}_{yy'bb'}\)

Binary variable for transmission line investment

\(U^{F}_{yl}/ U'^{F}_{yy'l}\)

Binary variable for gas furnaces investment

\(\widetilde{P}^{C2E}_{ytk}\ \widetilde{P}^{'C2E}_{yy'tk}\)

Electricity produced by new CHP (MW)

\(\widetilde{P}^{C2H}_{ytk}\ \widetilde{P}^{'C2H}_{yy'tk}\)

Heat produced by new CHP (MMBtu)

\(\widetilde{P}^{G2C}_{ytl)}\ \widetilde{P}^{G2C}_{yy'tl)}\)

Gas required for supplying CHP (MMBtu)


Gas required for supplying thermal generation units (MMBtu)

\(\pi _{ytl}\)

Gas pressure at each gas bus (PSIG)


Gas produced by utility (MMBtu)


Natural gas flowed by pipelines (MMBtu)


Natural gas required for supplying existing gas furnace (MMBtu)

\(\widetilde{P}^{G2F}_{ytl}\ \widetilde{P}^{'G2F}_{yy'tl}\)

Gas required for supplying new gas furnace (MMBtu)


The proposed price by CHP for selling heat (€/MMBtu)


The proposed price by gas furnace for selling heat (€/MMBtu)


The proposed price by gas supplier for selling gas (€/MMBtu)



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Bradley Department of Electrical and Computer Engineering, Virginia TechNorthern Virginia CenterFalls ChurchUSA
  2. 2.Department of Physics and Electrical Engineering, Faculty of Engineering and EnvironmentNorthumbria University NewcastleNewcastle upon TyneUK
  3. 3.School of Electrical and Electronic EngineeringThe University of ManchesterManchesterUK
  4. 4.Advanced Power and Energy Center, Electrical Engineering and Computer ScienceKhalifa UniversityAbu DhabiUAE
  5. 5.Faculty of Electrical and Computer EngineeringBabol Noshirvani University of TechnologyBabolIran

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