This is a self-archived – parallel published version of this article in the 

publication archive of the University of Vaasa. It might differ from the original. 

A Market-Based Mechanism for Local Energy 

Trading in Integrated Electricity-Heat Networks 

Author(s): Haghifam, Sara; Laaksonen, Hannu; Shafie-khah, Miadreza 

Title: A Market-Based Mechanism for Local Energy Trading in Integrated 

Electricity-Heat Networks 

Year: 2023 

Version: Accepted manuscript 

Copyright ©2023 Springer. This is a post-peer-review, pre-copyedit version of an 

article published in Trading in Local Energy Markets and Energy 

Communities: Concepts, Structures and Technologies. The final 

authenticated version is available online at: 

http://dx.doi.org/10.1007/978-3-031-21402-8_9 

Please cite the original version: 

 Haghifam, S., Laaksonen, H. & Shafie-khah, M. (2023). A Market-

Based Mechanism for Local Energy Trading in Integrated Electricity-

Heat Networks. In: Shafie-khah, M. & Gazafroudi, A. S. (eds.) Trading 

in Local Energy Markets and Energy Communities: Concepts, 

Structures and Technologies, 241–261. Lecturne Notes in Energy, vol. 

93. Cham: Springer. https://doi.org/10.1007/978-3-031-21402-8_9 

 



1 
 

A Market-based Mechanism for Local Energy Trading in Integrated 
Electricity-Heat Networks 

Sara Haghifam, Hannu Laaksonen, Miadreza Shafie-khah 
sara.haghifam@uwasa.fi , hannu.laaksonen@uwasa.fi , miadreza.shafiekhah@uwasa.fi 

School of Technology and Innovations, Flexible Energy Resources, University of Vaasa, Vaasa, Finland  
Abstract 
Due to the proliferation of power-to-X-to-power (P2X2P) conversion technologies across various 
energy systems, the sector-integration concept has gained considerable attention in recent years. In 
this context, to facilitate the integration of local energy systems at the distribution level and take 
advantage of their provided privileges, the development of an efficient and pragmatic market-based 
mechanism is required. Hence, the present chapter focuses on modeling a local energy market (LEM) 
framework that enables the integration of electrical distribution systems (EDSs) as well as district 
heating systems (DHSs) via power-to-heat (P2H) conversion technologies. The suggested LEM 
platform is based on a centralized one-sided auction-based energy trading process which is settled by 
the distribution system operator (DSO) with the objective of social welfare maximization. In the end, 
the raised LEM clearing model is applied on an integrated electricity-heat network (IEHN) in the 
presence of technical constraints of both EDS and DHS.   
Keywords: Local Energy Market; Integrated Electricity-Heat Network; Electrical Distribution 
System; District Heating System; Social Welfare. 
Nomenclature  

Acronyms   CHP Combined Heat and Power DG Dispatchable Generator DHS District Heating System DSO Distribution System Operator EB Electric Boiler ED Electric Demand EDS Electrical Distribution System HD Heat Demand HES Heat Exchanger Station HS Heat Station IEHN Integrated Electricity-Heat Network LEM Local Energy Market Power-to-Heat P2H Power-to-X-to-Power P2X2P PV Photovoltaic System WT Wind Turbine Sets and Indices  
𝑐ℎ CHP indices 
𝑑𝑔 DG indices 
𝑒𝑏 EB indices 
𝑒𝑑 ED indices 

mailto:sara.haghifam@uwasa.fi
mailto:hannu.laaksonen@uwasa.fi
mailto:miadreza.shafiekhah@uwasa.fi


2 
 

ℎ𝑑 HD indices 
𝑖, 𝑗 Set of nodes in EDS 
𝑖𝑗 Indices of lines in EDS 
𝑛 Set of nodes in DHS 
𝑛𝑚 Indices of pipelines in DHS 
𝑝𝑣 PV indices 
𝑡 Time indices 
𝑤𝑡 WT indices 
Ω𝐶𝐻𝑃 Set of CHPs connected to set of nodes 
Ω𝐷𝐺  Set of DGs connected to set of nodes 
Ω𝐸𝐵 Set of EBs connected to set of nodes 
Ω𝐸𝐷  Set of EDs connected to set of nodes 
Ω𝐻𝐷 Set of HDs connected to set of nodes 
Ω𝐻𝐸𝑆 Set of HESs connected to set of nodes 
Ω𝐻𝑆 Set of HSs connected to set of nodes 
Ω𝑃𝑉 Set of PVs connected to set of nodes 
Ωℎ𝑅 , Ωℎ𝑆  Set of return / supply pipelines in DHS 
Ωℎ𝑅−𝐵

𝑛 , Ωℎ𝑅−𝐸
𝑛  Set of return pipelines beginning / ending at node n 

Ωℎ𝑆−𝐵
𝑛 , Ωℎ𝑆−𝐸

𝑛  Set of supply pipelines beginning / ending at node n 
Ω𝑊𝑇 Set of WTs connected to set of nodes 
Ω𝑒 Set of lines in EDS Parameters  
𝑏𝑖𝑗 , 𝑔𝑖𝑗 Susceptance / conductance of line 𝑖𝑗 in EDS (ohm-1) 
𝐶𝑊 Specific heat capacity of water (J/g oC) 
𝐻𝐻𝐷 Heat demand of DHS (kW) 
𝐻𝑃𝑅 Heat-to-power ratio of CHPs 
𝐻𝑉𝑔𝑎𝑠 Heat value of natural gas (kWh/m3) 
𝐿𝑛𝑚 length of pipelines in DHS (km) 
𝑚 Mass flow rate of nodes in DHS (kg/s) 
𝑚𝑅, 𝑚𝑆 Mass flow rate of return / supply pipelines in DHS (kg/s) 
𝑃𝐶𝐻𝑃

𝑚𝑎𝑥 , 𝑃𝐶𝐻𝑃
𝑚𝑖𝑛 Maximum / minimum generated power of CHPs (kW) 

𝑃𝐸𝐵
𝑚𝑎𝑥 , 𝑃𝐸𝐵

𝑚𝑖𝑛 Maximum / minimum generated power of EBs (kW) 
𝑃𝐸𝐷  Electric demand of EDS (kW) 
𝑃𝑖𝑗

𝑚𝑎𝑥  Maximum capacity of line 𝑖𝑗 in EDS (kW) 
𝑄𝐷𝐺 , 𝑄𝑃𝑉 , 𝑄𝑊𝑇  Maximum quantity offers of DGs / PVs / WTs in LEM (kW) 
𝑇𝐴𝑚𝑏  Ambient temperature (oC) 
𝑇𝑅

𝑚𝑎𝑥 , 𝑇𝑅
𝑚𝑖𝑛 Maximum / minimum temperature of return pipelines in DHS (oC) 

𝑇𝑆
𝑚𝑎𝑥 , 𝑇𝑆

𝑚𝑖𝑛 Maximum / minimum temperature of supply pipelines in DHS (oC) 
𝑉𝑛𝑜𝑚 Nominal voltage (V) 
𝜆𝐷𝐺 , 𝜆𝑃𝑉 , 𝜆𝑊𝑇 Offer prices of DGs / PVs / WTs in LEM (€/kWh) 
𝜆𝑔𝑎𝑠   Natural gas price (€/m3) 
𝜆𝑔 Locational marginal price of PCC (€/kWh) 
𝜂𝐶𝐻𝑃−𝐸 , 𝜂𝐶𝐻𝑃−𝐻 Electricity / heat efficiency of CHPs (%) 
𝜂𝐸𝐵−𝐻 Heat efficiency of EBs (%) 
𝜗 Maximum voltage variation (%) 
𝜅 Heat transfer coefficient of pipelines in DHS (W/cm oC)  Variables  
𝐺𝐶𝐻𝑃 Gas flow to CHPs (m3) 
𝐻𝐶𝐻𝑃 Output heat of CHPs (kW) 
𝐻𝐸𝐵  Output heat of EBs (kW) 
𝑃𝐶𝐻𝑃  Output power of CHPs (kW) 
𝑃𝐷𝐺  Offer of DGs in LEM (kW) 
𝑃𝐸𝐵  Output power of EBs (kW) 
𝑃𝑔 Imported electricity from upstream grid (kW) 
𝑃𝑃𝑉  Offer of PVs in LEM (kW) 
𝑃𝑊𝑇  Offer of WTs in LEM (kW) 
𝑇𝑅 , 𝑇𝑆 Return / supply temperature of nodes in DHS (oC) 
𝑇𝑅,𝑖𝑛 , 𝑇𝑆,𝑖𝑛 Return / supply temperature at inlet of pipelines in DHS (oC) 



3 
 

𝑇𝑅,𝑜𝑢𝑡 , 𝑇𝑆,𝑜𝑢𝑡 Return / supply temperature at outlet of pipelines in DHS (oC) 
𝑉 Voltage magnitude (V) 
𝛥𝑉 Voltage deviation (V) 
𝛼, 𝛽 Dual Variables or shadow prices (€/kWh) 
𝜃  Voltage angle (rad) 

1. Introduction 
In recent years, a lack of fossil fuel sources and their irreversible environmental damages have 

led to a marked increase in the exploitation of renewable energy resources in power distribution 
systems [1]. Although the high penetration of renewable energies can overcome the above-mentioned 
challenges, the stochastic and intermittent nature of these units drives the need for flexibility in the 
electricity sector [2]. As one of the pragmatic and new solutions for flexibility provision at the 
distribution level, the coupling of different energy sectors, including the EDSs and DHSs, in the form 
of IEHNs has attracted more attention in the past few years [3]. To establish an IEHN via the sector-
coupling concept, the presence of P2X2P, more specifically P2H, conversion technologies in the 
energy systems is required [4], [5]. Combined heat and power (CHP) plants [6], electric boilers (EBs) 
[7], and electric heat pumps (EHPs) [8] are the most prevalent P2H elements in IEHNs.  

In general, P2H solutions require techno-economic interactions with two local energy sectors, 
namely power and heat. Nevertheless, these kinds of interactions add new challenges to the optimal 
operation of IEHNs due to the lack of a suitable coordination platform [9]. To cope with this issue 
and implement sector-coupling at the distribution level, proposing an appropriate market-based 
framework is of great importance. Accordingly, local market-based solutions for sector-coupling 
have received widespread attention over the last few years. The following literature review highlights 
some important studies in this area: 

A decentralized optimization method has been raised in [10] to model a LEM for the 
coordinated operation of the EDS and DHS in the form of an IEHN. In the suggested framework, 
EDS and DHS are able to be operated independently by solving optimal power and thermal flows, 
respectively. A LEM has been designed in [11] to investigate the energy trading within an IEHN and 
in the presence of multiple strategic players. In the provided framework, locational marginal prices 
of electricity and heat achieved from optimal power and thermal flows have been exploited to settle 
the considered market. A bi-level optimization model has been presented in [12] for clearing a LEM 
and modeling its interaction with the wholesale electricity market. Accordingly, at the upper level, 
the DSO settles the LEM and determines locational marginal prices, while at the lower level, the 
wholesale market clearing, as well as the DSO’s interaction with this market, are specified. A linear 
optimization-based approach has been developed in [13] to model a LEM enabling the integration of 
the EDS and DHS at the distribution level. The market-clearing process has been conducted from a 



4 
 

central operator’s perspective to maximize consumers and producers’ surplus. A novel market-based 
platform has been introduced in [14] to couple the EDS and DHS and facilitate the utilization of P2H 
and storage technologies at the local level. The primary goal of this research work is to develop 
innovative market orders that respect energy system integration. A LEM mechanism has been 
suggested in [15] to provide the possibility of peer-to-peer power and heat energy trading and 
investigate the cooperative behaviors among peers. In this study, each peer is able to promote its own 
profit by determining the joined coalition and its role as a seller or buyer of heat and electricity within 
this coalition. In the end, a fully decentralized market-based framework has been employed in [16] 
that supports peer-to-peer energy trading among several price-maker agents at the distribution level. 
To determine the optimal strategy of participated agents in the designed LEM and improve their net 
profit, a linear optimization model has been utilized in this study.  

Due to the importance of establishing an efficient market-based environment for coupling of 
electricity and heat sectors at the local level, this chapter tends to model a LEM that enables the 
integration of EDSs and DHSs through CHPs and EBs, as fundamental P2H conversion technologies. 
The design of the considered LEM is based on a centralized one-sided auction-based energy trading 
process which is settled by the DSO with the objective of social welfare maximization. To this end, 
the schematic structure of the designed LEM, as well as the mathematical model for the market 
clearing process, are expressed in more detail in section 2. The implementation of a case study and 
its discussions are provided in section 3. Finally, the work is concluded in section 4. 
2. Methodology 

As briefly mentioned in the previous section, the main purpose of the current chapter is to 
design a LEM for facilitating energy trading within integrated energy networks. Before delving into 
the mathematical model of the proposed market-based framework, its overall structure and 
regulations are described.   

In this work, the considered LEM is designed based on a centralized one-sided auction format. 
In this case, it is assumed that a central operator is responsible for the operation of the IEHN at a 
specific time through the complete exchange of energy and information among two electricity and 
heat sectors. Hence, in order to identify the market settlement point, all participants are required to 
submit their bids/offers to the LEM operator. Furthermore, it is presumed that the clearing mechanism 
of the LEM is according to the one-sided auction method, in which only production offers are 
considered in the negotiation procedure [17]. As a result, since multiple energy carriers are traded 
simultaneously in the presented market-based platform, each offer contains specific information, 
including the type of energy, quantity as well as valuation of the offer, the delivery time, and location 



5 
 

of the injected energy to the network. On the other hand, the pricing system of the LEM is uniform, 
in which all players are paid at the same market clearing price regardless of their submitted offers. 
This clearing price is set at the offer price of the most expensive supplier chosen for providing the 
service [18].  

The schematic structure of the presented LEM platform for the integration of the EDS and DHS 
is illustrated in Figure 1. According to the figure, the DSO as a central operator is responsible for the 
LEM clearing and meeting the IEHN’s demands in the presence of both networks’ technical 
constraints. To this end, the DSO firstly collects offers from the existing market participants like 
dispatchable generators (DGs), wind turbines (WTs), and photovoltaic systems (PVs). Then, 
considering the locational marginal price of the PCC, as well as the operational condition of the 
available CHPs and EBs, this entity attempts to settle the market and determine accepted offers as 
well as distribution locational marginal prices for the optimal scheduling of the IEHN. The electric 
demand (ED) of the system is procured from DGs, WTs, PVs, CHPs, and the upstream grid, while 
the heat demand (HD) is procured from CHPs and EBs.        

 
Figure 1: Schematic structure of the proposed LEM framework. 

As stated above, the DSO as the market operator clears the suggested LEM platform with the 
objective of social welfare maximization [19], which is equal to the total energy cost minimization in 
this study. The mathematical formulation of the mentioned objective function is expressed by Eq (1). 
In this equation, the first term is related to the cost of imported electricity from the upstream grid. 
The second, third, and fourth terms are related to the marginal costs of the LEM participants. In the 
end, the fifth term is related to the operating cost of the CHP units. 

Electrical Distribution System
District Heating System

Local Energy Market
Power Flow Heat Flow Information Flow

DSO

DGs WTs PVs CHPs EBs



6 
 

𝑀𝑖𝑛 ∑ {𝑃𝑔(𝑡)𝜆𝑔(𝑡)

𝑡

+ ∑ 𝑃𝐷𝐺(𝑑𝑔, 𝑡)𝜆𝐷𝐺(𝑑𝑔, 𝑡)

𝑑𝑔

+ ∑ 𝑃𝑊𝑇(𝑤𝑡, 𝑡)𝜆𝑊𝑇(𝑤𝑡, 𝑡)

𝑤𝑡

+ ∑ 𝑃𝑃𝑉(𝑝𝑣, 𝑡)𝜆𝑃𝑉(𝑝𝑣, 𝑡) + ∑ 𝐺𝐶𝐻𝑃(𝑐ℎ, 𝑡)𝜆𝑔𝑎𝑠(𝑡)

𝑐ℎ𝑝𝑣

} 

(1) 

The considered objective function is subject to a set of linear technical as well as operational 
constraints, as follows: 

𝑃𝑔(𝑡) = ∑ {𝑉𝑛𝑜𝑚[𝛥𝑉(𝑖, 𝑡) − 𝛥𝑉(𝑗, 𝑡)]𝑔𝑖𝑗 − 𝑉𝑛𝑜𝑚
2 [𝜃 (𝑖, 𝑡) − 𝜃(𝑗, 𝑡)]𝑏𝑖𝑗}

𝑗:(𝑖,𝑗) ∈ Ω𝑒

, 𝛼(𝑖, 𝑡) 
∀𝑖 = 1, 𝑡 

(2) 
∑ 𝑃𝐷𝐺(𝑑𝑔, 𝑡) +

𝑑𝑔:(𝑑𝑔,𝑖) ∈ Ω𝐷𝐺

∑ 𝑃𝑊𝑇(𝑤𝑡, 𝑡)

𝑤𝑡:(𝑤𝑡,𝑖) ∈ Ω𝑊𝑇

+ ∑ 𝑃𝑃𝑉(𝑝𝑣, 𝑡) + ∑ 𝑃𝐶𝐻𝑃(𝑐ℎ, 𝑡)

𝑐ℎ:(𝑐ℎ,𝑖) ∈ Ω𝐶𝐻𝑃𝑝𝑣:(𝑝𝑣,𝑖) ∈ Ω𝑃𝑉

− ∑ 𝑃𝐸𝐵(𝑒𝑏, 𝑡) − ∑ 𝑃𝐸𝐷(𝑒𝑑, 𝑡)

𝑒𝑑:(𝑒𝑑,𝑖) ∈ Ω𝐸𝐷𝑒𝑏:(𝑒𝑏,𝑖) ∈ Ω𝐸𝐵

= ∑ {𝑉𝑛𝑜𝑚[𝛥𝑉(𝑖, 𝑡) − 𝛥𝑉(𝑗, 𝑡)]𝑔𝑖𝑗 − 𝑉𝑛𝑜𝑚
2 [𝜃(𝑖, 𝑡) − 𝜃(𝑗, 𝑡)]𝑏𝑖𝑗},

𝑗:(𝑖,𝑗) ∈ Ω𝑒

𝛼(𝑖, 𝑡) 

∀𝑖 ≠ 1, 𝑡 

(3) 

−𝑃𝑖𝑗
𝑚𝑎𝑥 ≤ {𝑉𝑛𝑜𝑚[𝛥𝑉(𝑖, 𝑡) − 𝛥𝑉(𝑗, 𝑡)]𝑔𝑖𝑗 − 𝑉𝑛𝑜𝑚

2 [𝜃(𝑖, 𝑡) − 𝜃(𝑗, 𝑡)]𝑏𝑖𝑗} ≤ 𝑃𝑖𝑗
𝑚𝑎𝑥, 

∀(𝑖𝑗) ∈ Ω𝑒 , 𝑡 (4) 
−𝜗𝑉𝑛𝑜𝑚 ≤ 𝛥𝑉(𝑖, 𝑡) ≤ 𝜗𝑉𝑛𝑜𝑚, ∀𝑖, 𝑡 (5) 
𝑉(𝑖, 𝑡) = 𝑉𝑛𝑜𝑚 + 𝛥𝑉(𝑖, 𝑡), ∀𝑖, 𝑡 (6) 
−𝜋 ≤ 𝜃(𝑖, 𝑡) ≤ 𝜋, ∀𝑖, 𝑡 (7) 

Eqs (2) to (7) demonstrate technical constraints of the EDS that model the linear AC power 
flow in this work [20]. Accordingly, the power balance of the electricity sector is expressed by Eqs 
(2) and (3), and their dual variables or shadow prices are specified after the colon. The LEM clearing 
price or distribution locational marginal price of electricity is achieved from the shadow prices of the 
power balance constraints [21]. Moreover, the power flow in distribution lines, as well as voltage 
deviation of nodes, are limited by Eqs (4) and (5), respectively. Also, Eq (6) represents the voltage 
magnitude of nodes. Finally, the voltage angle of each node is restricted by Eq (7).  



7 
 

0 ≤ 𝑃𝐷𝐺(𝑑𝑔, 𝑡) ≤ 𝑄𝐷𝐺(𝑑𝑔, 𝑡), ∀𝑑𝑔, 𝑡 (8) 
0 ≤ 𝑃𝑊𝑇(𝑤𝑡, 𝑡) ≤ 𝑄𝑊𝑇(𝑤𝑡, 𝑡), ∀𝑤𝑡, 𝑡 (9) 
0 ≤ 𝑃𝑃𝑉(𝑝𝑣, 𝑡) ≤ 𝑄𝑃𝑉(𝑝𝑣, 𝑡), ∀𝑝𝑣, 𝑡 (10) 
𝐺𝐶𝐻𝑃(𝑐ℎ, 𝑡) =

𝑃𝐶𝐻𝑃(𝑐ℎ, 𝑡)
𝐻𝑉𝑔𝑎𝑠𝜂𝐶𝐻𝑃−𝐸(𝑐ℎ)⁄ , ∀𝑐ℎ, 𝑡 (11) 

𝐻𝐶𝐻𝑃(𝑐ℎ, 𝑡) ≤ 𝑃𝐶𝐻𝑃(𝑐ℎ, 𝑡)𝐻𝑃𝑅(𝑐ℎ)𝜂𝐶𝐻𝑃−𝐻(𝑐ℎ), ∀𝑐ℎ, 𝑡 (12) 
𝑃𝐶𝐻𝑃

𝑚𝑖𝑛(𝑐ℎ) ≤ 𝑃𝐶𝐻𝑃(𝑐ℎ, 𝑡) ≤ 𝑃𝐶𝐻𝑃
𝑚𝑎𝑥(𝑐ℎ), ∀𝑐ℎ, 𝑡 (13) 

𝑃𝐸𝐵
𝑚𝑖𝑛(𝑒𝑏) ≤ 𝑃𝐸𝐵(𝑒𝑏, 𝑡) ≤ 𝑃𝐸𝐵

𝑚𝑎𝑥(𝑒𝑏), ∀𝑒𝑏, 𝑡 (14) 
𝐻𝐸𝐵(𝑒𝑏, 𝑡) = 𝑃𝐸𝐵(𝑒𝑏, 𝑡)𝜂𝐸𝐵−𝐻(𝑒𝑏), ∀𝑒𝑏, 𝑡 (15) 

On the other hand, Eqs (8) to (15) display operational constraints of the existing energy 
resources in the IEHN. In this regard, inequalities (8), (9), and (10) restrict DGs, WTs, and PVs’ 
offers in the LEM to their maximum quantity offers, respectively. The relation between the gas flows 
to the CHP units and their output powers is determined by Eq (11). Furthermore, the relation between 
the output heat and the output power of CHPs is defined by Eq (12). Ultimately, the CHPs’ output 

powers are confined to their minimum and maximum values by Eq (13) [22]. As stated, EBs are P2H 
elements that consume electricity to produce thermal energy. In this context, the power consumption 
of these units is limited by Eq (14), and their generated heat is displayed by Eq (15) [23]. 

DHSs contain supply pipelines that transfer hot water from heat sources to HDs, and return 
pipelines that return back cold water from HDs to heat sources [24]. Normally, these networks are 
controlled in four different modes, including constant-flow-constant-temperature, constant-flow-
variable-temperature, variable-flow-constant-temperature, and variable-flow-variable-temperature. 
Eqs (16) to (25) depict technical constraints of the DHS that model the constant-flow-variable-
temperature strategy in this work [25]. Notably, as non-linear hydraulic terms are eliminated in the 
considered model, the ultimate thermal model is linear.    

∑ 𝐻𝐶𝐻𝑃(𝑐ℎ, 𝑡) + ∑ 𝐻𝐸𝐵(𝑒𝑏, 𝑡)

𝑒𝑏:(𝑒𝑏,𝑛) ∈ Ω𝐸𝐵𝑐ℎ:(𝑐ℎ,𝑛) ∈ Ω𝐶𝐻𝑃

= 𝐶𝑊𝑚(𝑛, 𝑡){𝑇𝑆(𝑛, 𝑡) − 𝑇𝑅(𝑛, 𝑡)},  

∀𝑛 ∈ Ω𝐻𝑆, 𝑡 

(16) 
∑ 𝐻𝐻𝐷(ℎ𝑑, 𝑡)

ℎ𝑑:(ℎ𝑑,𝑛) ∈ Ω𝐻𝐷

= 𝐶𝑊𝑚(𝑛, 𝑡){𝑇𝑆(𝑛, 𝑡) − 𝑇𝑅(𝑛, 𝑡)}, 𝛽(𝑛, 𝑡)  

∀𝑛 ∈ Ω𝐻𝐸𝑆, 𝑡 

(17) 

𝑇𝑆,𝑜𝑢𝑡(𝑛𝑚, 𝑡) − 𝑇𝐴𝑚𝑏(𝑡) = {𝑇𝑆,𝑖𝑛(𝑛𝑚, 𝑡) − 𝑇𝐴𝑚𝑏(𝑡)}𝑒
−𝜅𝐿𝑛𝑚

𝐶𝑤𝑚𝑆(𝑛𝑚,𝑡), ∀𝑛𝑚 ∈ Ωℎ𝑆, 𝑡 (18) 



8 
 

𝑇𝑅,𝑜𝑢𝑡(𝑛𝑚, 𝑡) − 𝑇𝐴𝑚𝑏(𝑡) = {𝑇𝑅,𝑖𝑛(𝑛𝑚, 𝑡) − 𝑇𝐴𝑚𝑏(𝑡)}𝑒
−𝜅𝐿𝑛𝑚

𝐶𝑤𝑚𝑅(𝑛𝑚,𝑡), ∀𝑛𝑚 ∈ Ωℎ𝑅 , 𝑡 (19) 
𝑇𝑆

𝑚𝑖𝑛 ≤ 𝑇𝑆(𝑛, 𝑡) ≤ 𝑇𝑆
𝑚𝑎𝑥, ∀𝑛, 𝑡 (20) 

𝑇𝑅
𝑚𝑖𝑛 ≤ 𝑇𝑅(𝑛, 𝑡) ≤ 𝑇𝑅

𝑚𝑎𝑥, ∀𝑛, 𝑡 (21) 
𝑇𝑆,𝑖𝑛(𝑛𝑚, 𝑡) = 𝑇𝑆(𝑛, 𝑡), ∀𝑛𝑚 ∈  Ωℎ𝑆−𝐵

𝑛 , 𝑛, 𝑡 (22) 
𝑇𝑅,𝑖𝑛(𝑛𝑚, 𝑡) = 𝑇𝑅(𝑛, 𝑡), ∀𝑛𝑚 ∈  Ωℎ𝑅−𝐵

𝑛 , 𝑛, 𝑡 (23) 
∑ {𝑚𝑆(𝑛𝑚, 𝑡)𝑇𝑆,𝑜𝑢𝑡(𝑛𝑚, 𝑡)} = 𝑇𝑆(𝑛, 𝑡) ∑ 𝑚𝑆(𝑛𝑚, 𝑡)

𝑛𝑚 ∈ Ωℎ𝑆−𝐵
𝑛𝑛𝑚 ∈ Ωℎ𝑆−𝐸

𝑛

, ∀𝑛, 𝑡 (24) 
∑ {𝑚𝑅(𝑛𝑚, 𝑡)𝑇𝑅,𝑜𝑢𝑡(𝑛𝑚, 𝑡)} = 𝑇𝑅(𝑛, 𝑡) ∑ 𝑚𝑅(𝑛𝑚, 𝑡)

𝑛𝑚 ∈ Ωℎ𝑅−𝐵
𝑛𝑛𝑚 ∈ Ωℎ𝑅−𝐸

𝑛

, ∀𝑛, 𝑡 (25) 
Accordingly, Eqs (16) and (17) show the heat balance of the system in heat stations (HSs) that 

are equipped with heat sources and heat exchanger stations (HESs) that are modeled as HDs, 
respectively [26]. The dual variable or shadow price of Eq (17) is presented after the colon that 
specifies the LEM clearing price or distribution locational marginal price of heat. The temperature 
drop caused by heat loss in supply and return pipelines is represented by Eqs (18) and (19), 
respectively. Inequalities (20) and (21) restrict the temperature of nodes in supply and return 
pipelines. Eqs (22) and (23) ensure that the inlet temperature of supply and return pipelines is equal 
to the nodes’ temperature. Finally, according to Eqs (24) and (25), the nodes’ temperature is computed 
as the mixture temperature of mass flows entering the nodes. 
3. Case Study 

In this section, the LEM clearing model is applied to an IEHN, including a 13-node EDS [27] 
and a 4-node DHS. The single-line diagram of this integrated system is depicted in Figure 2.  

 
Figure 2: Studied IEHN. 

i1

HS

PCC

i2 i3 i4 i5 i6

ED2 ED3 ED4 ED5 ED6

i13

ED13

DG2

i7

i11

ED11i12

ED12

WT

ED7
i8

i10

ED10

DG1

i9

ED9ED8
PV

CHP

EB

n1

HD1

n2

HD2
HD3

n3
n4



9 
 

Accordingly, the EDS contains two DGs, one WT, and one PV at nodes 10, 13, 12, and 9, 
respectively. The EDS nodes 6 and 8 are connected to the HS of the DHS, which is equipped with 
one CHP and one EB. The maximum quantity offers of the LEM participants as well as technical 
specifications of the existing P2H elements are provided in Tables 1 and 2, respectively.   

Table 1: Maximum offers of LEM participants. 
# Unit Maximum Quantity Offers (kW) 
DG 1 3000 DG 2 2000 WT 2000 PV 1500 

Table 2: Characteristics of P2H units. 
# Unit Minimum Power  (kW)  Maximum Power (kW)  Heat Efficiency (%) Electricity Efficiency (%) Heat-to-Power Ratio  

CHP 200 2000 55 45 1 EB 0 500 80  ̶ ̶  
Offer prices of the available market participants, as well as locational marginal prices of PCC, 

are illustrated in Figure 3. The electric and heat demand profiles of the studied IEHN are displayed 
in Figure 4. Furthermore, the peak demand of the system in each node is expressed in Table 3. 

On the other hand, it is assumed that the temperature of supply pipelines in the DHS varies 
between 60 oC and 100 oC, while the temperature of its return pipelines varies between 20 oC and 60 
oC. In addition, the ambient temperature is 10 oC, specific heat capacity of water is 4.182 J/g oC, and 
heat transfer coefficient of pipelines is 0.00455 W/cm oC [28].  

In the end, the natural gas price is considered a three-tariff price, and the heat value of natural 
gas is presumed to be 11.7 kWh/m3. 

 
Figure 3: Prices in the LEM clearing process. 

0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

P
ri

ce
 (

€
/k

W
h

)

Time (h)

Offer price of DG 1 Offer price of DG 2Offer price of WT Offer price of PVLocational marginal price of PCC



10 
 

 
Figure 4: Demand profiles of the IEHN. 

Table 3: Peak demand of the IEHN. 
# Node 1 2 3 4 5 6 7 8 9 10 11 12 13 

Electric Demand (kW) 0 890 628 1112 636 474 1342 920 766 662 690 1292 1124 Heat Demand (kW) 0 450 400 450  ̶ ̶  ̶   ̶ ̶  ̶  ̶   ̶   ̶
Accepted offers of the LEM participants, namely DGs, WT, and PV, as well as the output power 

of P2H elements, namely CHP and EB, are demonstrated in Figure 5. In this figure, the DSO’s 

imported electricity from the upstream grid is displayed as well. Notably, the line graph shows the 
system’s whole ED during the studied day.  

 
Figure 5: Optimal operating points of power resources in the LEM. 

As shown, the entire produced and imported powers have procured the required powers of the 
EB and ED. On the other hand, based on Figures 3 and 5, since the offer prices of WT and PV are 

0
0.2
0.4
0.6
0.8

1
1.2
1.4
1.6
1.8

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pro
file 

(PU
) 

Time (h)

Electric
Heat

-2000
0

2000
4000
6000
8000

10000
12000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pow
er (k

W)

Time (h)

PED PgPDG 1 PDG 2PWT PPVPCHP PEB



11 
 

lower than the offer prices of DGs and locational marginal prices of PCC in most hours of the day, 
their maximum quantity offers have been accepted in the LEM clearing process.  

The output heat of P2H elements, i.e., CHP and EB, are depicted in Figure 6. Similarly, the line 
graph shows the system’s whole HD during the studied day.  

 
Figure 6: Optimal operating points of heat resources in the LEM. 

Based on the DHS modeling in the previous section and Figure 6, it is observed that the 
generated heat at each hour has procured not only the HD but also heat loss in supply and return 
pipelines. Also, since the electricity price is low in the early hours of the day, the DSO has preferred 
to transform the power to heat by the available EB and satisfy the peak HD of the system. 

The amount of gas consumption by the available CHP unit in the IEHN, as well as the three-
tariff natural gas price, are depicted in Figure 7. Clearly, during the peak of electric and heat demands, 
the considered CHP has consumed the highest amount of gas. 

 
Figure 7: CHP’s gas consumption and natural gas price. 

0
200
400
600
800

1000
1200
1400
1600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hea
t (k

W)

Time (h)

HD
HCHP
HEB

0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5

200
220
240
260
280
300
320
340
360
380
400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

G
as

 P
ri

ce
 (

€
/m

3
)

Gas
 (m3

)

Time (h)

GCHP
Gas price



12 
 

Temporal and spatial variation of distribution locational marginal price of electricity in the 
LEM clearing procedure is presented in Figure 8.  

 
Figure 8: Variation of distribution locational marginal price of electricity.  

The generic temporal analysis shows that by increasing the ED, the distribution locational 
marginal price is increased as well. On the other hand, according to the spatial analysis, the increase 
in the ED during peak hours leads to congestion in the EDS, which changes the LEM clearing price 
at different nodes.  

To better investigate the spatial level, distribution locational marginal prices of the EDS nodes 
at hours 12 and 21 are represented in Figure 9.  

 
Figure 9: Distribution locational marginal prices at hours 12 and 21.  

Based on Figure 9, at hours 12, distribution locational marginal prices at nodes 1 to 4 are equal 
to locational marginal prices of PCC. Due to the congestion in line 4-5, the rest of the nodes’ marginal 

1
5

9
13

0
0.01
0.02
0.03
0.04
0.05
0.06
0.07

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Bus
 Nu

mbe
r

L
o

ca
ti

o
n

al
 M

ar
g
in

al
 P

ri
ce

 (
€

/k
W

h
)

Time (h)
0-0.01 0.01-0.020.02-0.03 0.03-0.040.04-0.05 0.05-0.060.06-0.07

0.03
0.035
0.04

0.045
0.05

0.055
0.06

0.065
0.07

1 2 3 4 5 6 7 8 9 10 11 12 13

L
o

ca
ti

o
n

al
 M

ar
g
in

al
 P

ri
ce

 (
€

/k
W

h
)

Bus Number

Hour 12
Hour 21



13 
 

prices have been affected by the offer prices of the LEM participants. In this context, PV as a marginal 
producer has determined distribution locational marginal prices at nodes 5 to 9 and 11 to 13. The 
marginal price of node 10 has resulted from offer price of DG 1, which is located at this node. The 
important point here is that while the offer price of DG 1 is lower than the offer price of PV, this unit 
has not been able to affect other nodes’ marginal prices due to the congestion in line 8-10. Similarly, 
at hour 21, distribution locational marginal prices at nodes 1 to 4 are equal to locational marginal 
prices of PCC. Because of the congestion in line 4-5, distribution locational marginal prices at nodes 
5 to 9 and 11 to 13 have been determined by DG 2 as a marginal producer. Also, because of congestion 
in line 8-10, DG 1 has only been able to impact the marginal price of node 10.  
4. Conclusion 

The high penetration of renewable energies has increased the need for flexibility in power 
distribution systems. Recently, the coupling of EDSs and DHSs in the form of IEHNs has been raised 
as one of the promising solutions for flexibility provision. Nonetheless, establishing IEHNs and 
optimally operating them requires the development of an appropriate and practical market-based 
mechanism. In this context, this chapter modeled a LEM for the integration of the EDS and DHS at 
the distribution level. The considered LEM was cleared by the DSO using a centralized one-sided 
auction to maximize social welfare. Then, the suggested LEM clearing model was applied to an IEHN 
under the technical constraints of both EDS and DHS. Output results specified that distribution 
locational marginal prices are affected by a set of factors, including the topology as well as demands 
of the network. 
Acknowledgment 
Sara Haghifam would like to acknowledge the Fortum and Neste Foundation that supports research, education, and 
development in natural, technical, and economical sciences within the energy industry. 
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