Design and Operational Planning of Energy Networks Based on

Article pubs.acs.org/IECR

Design and Operational Planning of Energy Networks Based on Combined Heat and Power Units Nikolaos E. Koltsaklis,† Georgios M. Kopanos,†,‡ and Michael C. Georgiadis*,† †

Aristotle University of Thessaloniki, Department of Chemical Engineering, 54124 Thessaloniki, Greece Imperial College London, Department of Chemical Engineering, Centre for Process Systems Engineering, SW7 2AZ London, U.K.

‡

S Supporting Information *

ABSTRACT: Energy planning aims at improving the overall efficiency, economic viability and reducing the environmental impact of energy management systems. Deregulation of electricity markets along with technology development have increased the level of competition allowing energy consumers to select among a variety of energy technologies, fuels and/or suppliers. This work presents a linear mixed integer programming model for the optimal design and operational planning of energy networks based on combined heat and power generators. The studied area is divided into a number of sections, each of which is characterized by a specific heat and electricity demand. Various energy generation technologies and heat storage tanks are modeled, while interchange of electricity can take place among the sections of the network, which is connected to the main power grid for potential power trade with it. There is also the option of an external heat source (i.e., a refinery) constituting an alternative supplier of heat to the sectors of the network. The objective function represents the minimization of total cost under full heat and electricity demand satisfaction. The applicability of the proposed model is illustrated using two illustrative examples, including a residential and an urban energy network. Finally, Monte Carlo simulations have been utilized to capture the effect of uncertainty characterizing some varying parameters, such as the heat demand (residential energy network) as well as the available heat from the refinery (urban energy network).

1. INTRODUCTION Nowadays, the development of high efficiency energy generation technologies is of top priority at an international level due to the volatility and the rising costs of energy resources, the depletion of fossil fuel resources, and severe environmental pollution. As a result, the energy supply chain and especially the power grids are currently undergoing a transformation process. Market deregulation and environmental regulations such as Kyoto Protocol and European Emission Trading Scheme have driven companies and investors to seek out new business areas. Because of the increasing concern regarding the environmental issues and the ratification of the Kyoto Protocol, cogeneration receives more attention as a way to contribute to more efficient energy use and carbon mitigation.1−3 Co-generation, also known as Combined Heat and Power (CHP), is an energy generation process that produces simultaneously power and heat from a single source. The main benefit of cogeneration is that its total efficiency is around the double of that of the single electricity production, which is due to the more efficient use of the thermal energy of the fuel resource used. This further implies lower fuel consumption and lower energy generation costs moderating the environmental footprint. Additionally, CHP plants can serve electricity markets with lower investments in the transmission and distribution infrastructure and with lower energy losses during transmission.4,5 One possible development path of the energy sector is the decentralization of the power system. Decentralized or distributed energy supply refers to the energy production close to the point of usage. It can denote a range of generator © 2014 American Chemical Society

sizesfrom individual households up to community or district level. In the 27 EU Member States, buildings currently make up almost 40% of total final energy consumption and the European Commission states that the greatest energy saving potential lies in buildings.6 Microgeneration is defined as “the small-scale production of heat and/or electricity from a low carbon source”. It has further been defined as anything below 50−100 kW, with the majority of household electricity-supply installations being below 3 kWe and slightly larger for heat supply.7 In this context, microgrid is defined as a low voltage distribution network with combination of distributed generators, energy storage devices, and controllable loads, which could operate islanded or connected to the central power grid.8 The concept of microgrid has recently gained significant interest from academia, equipment vendors, and energy vendors.9 Since the residential sector accounts for a high percentage of total primary energy consumption, it has recently attracted the interest of many investors for the application of micro-Combined Heat and Power (mCHP) systems. It is alleged that mCHPs offer significant benefits to energy suppliers (increased revenues, customer retention, etc.), to households (decreased energy bills) and to society as a whole (reduced CO2 emissions and primary energy consumption, avoidance of central plant and network construction etc.).10 Special Issue: Jaime Cerdá Festschrift Received: Revised: Accepted: Published: 16905

December 11, 2013 February 24, 2014 March 5, 2014 March 5, 2014 dx.doi.org/10.1021/ie404165c | Ind. Eng. Chem. Res. 2014, 53, 16905−16923

Industrial & Engineering Chemistry Research

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solar and wind farms, combustion of biomass and natural gas, fuel cells with syngas and hydrogen, as well as storage options for electricity and other energy resources. The objective to be optimized refers to the maximization of profits. A linear diversity constraint has been also introduced to facilitate the schedule implementation. Extending this work, Kwok et al.19 presented an MILP model for the scheduling of a microgrid at a daily level. Operational cost and/or environmental impact constitute the objective functions of the model. Scenario-based analysis was performed to investigate the influence of demand uncertainty and seasonal effect of weather in the operational flexibility of the system. Zhang et al.20 proposed an MILP model for the scheduling of smart homes’ energy consumption by minimizing the daily total cost. The microgrid studied involves a CHP generator, a boiler, a wind generator, and thermal and electrical storage. There is also interaction with the power grid. A peak demand charge scheme is also adopted in order to reduce the peak demand from grid. Ren et al.21 developed a MOLP model to determine the operational strategy of a distributed energy resources (DER) system based on economic and environmental criteria. A distributed energy system incorporating fuel cell and gas engine CHP plants, as well as PV cells has been installed. A compromise programming method has been also applied to select the final operating strategy from the set of possibly optimal solutions. Mitra et al.22 proposed a generalized formulation for the operational optimization of industrial CHP plants with given steam and electrical demand according to sensitive electricity prices. The objective function of the model concerns the maximization of CHP plant’s profits, while the constraints refer to the representation of the feasible operating region for each plant component, and their transitional behavior. In order to address issues related to the optimal design of distributed energy systems, several mathematical models have been developed in the literature. Shaneb et al.23 developed a LP model for the optimal design of a residential mCHP system taking only into account energy balance and capacity limits as representative constraints of the model. The objective function represents the minimization of the total annual cost. A sensitivity analysis was also performed in order to examine the influence of several parameters (e.g., capital cost, feed-in tariff, gas price, electricity price, electricity demand, electricity efficiency, demand representation) on the design decisions. Zhou et al.24 proposed an optimization approach for the design and operation of distributed energy systems based on the superstructure approach. Ren et al.10 proposed a MINLP model for the optimal design of a CHP-based energy system in a given residential building. The residential system consists of a CHP plant, a heat storage tank and a back-up boiler. The objective to be optimized is the minimization of the annual cost of the residential energy system including cost for buying electricity from the spot market, running cost of CHP plants and back-up boilers, annual investment costs for the CHP and the boiler as well as carbon emissions cost. Mavrotas et al.25 presented an MILP model for energy planning in units of tertiary sector with the aim of minimizing the annualized cost, including annualized investment cost and annual operational and maintenance cost. Monte Carlo simulation has been applied to evaluate the impact of uncertain parameters, such as natural gas and electricity price as well as discount rate. Zhou et al.26 presented a two-stage stochastic programming model for the optimal

Regarding the urban level, recent research has revealed that cities are responsible for around two-thirds of global energy consumption and 71% of energy-related direct greenhouse gas emissions. Due to that evolution, there is an increasing concern in improving the total energy efficiency of cities so that environmental impacts are reduced without negative influences on the economic activities and life quality. CHPs can achieve higher thermodynamic efficiencies and economies of scale in capital costs, comprising a challenging option for the total energy-efficiency improvement and carbon mitigation goals.6 Energy planning is a crucial and challenging task that should consider multiple aspects and decision criteria, and its goal is to secure the overall efficiency, the economic viability, and the environmental impact mitigation of the energy management systems. Planning and scheduling problems are commonly formulated as optimization models, which are solved by means of optimization algorithms.11 The development of optimization models for energy systems planning has attracted significant interest over past decades.12 Liu et al.13 presented a review and an energy systems engineering approach to the modeling and optimization of microgrids for residential applications, highlighting also the challenges and the prospects concerning the design and scheduling of such distributed energy systems. The microgrid planning and scheduling problem has been previously addressed in the literature employing different approaches. Most models use Linear Programming (LP), Mixed Integer Linear Programming (MILP), Mixed Integer Nonlinear Programming (MINLP), or even Multi-Objective Linear Programming (MOLP). Minimization of the total daily operational costs constitutes the typical objective function of these models, while minimization of the total daily primary energy consumption, maximization of profits at a daily level, and cost minimization along with environmental impact minimization are also considered. Shaneb et al.14 presented a LP model for the operational planning of a residential mCHP system, consisting of a mCHP, a back-up heater and a thermal storage device. A Proton Exchange Membrane Fuel Cell (PEMFC) unit was considered and tested in three different scenarios based on the Feed-InTariff (FIT) scheme, electricity trade potential, and introduction of carbon tax. Ren and Gao15 proposed an MILP model for the energy production planning of a mCHP installed in a residential building. Two technology types were considered (i.e., gas engine and fuel cell) and evaluated based on economic and environmental criteria. Kopanos et al.4 presented an MILP model for the operational planning of a mCHP-based network under the minimization of the total cost. Their model considered start-up and shutdown decisions, as well as minimum run and shutdown times. Wakui and Yokoyama16 presented an MILP model for the operational planning of a housing complex in Japan. The objective function is the minimization of the total daily primary energy consumption. Bosman et al.17 developed an MILP framework for the operational planning in a group of mCHP systems. Maximization of profits in the electricity market comprises the objective function of the model and the constraints take account of start-up and shutdown decisions, minimum run time and off-time as well as electricity and heat generation bounds. However, in this work, a back-up heater is not taken into consideration which could lead to the fact that heat demand is not to be satisfied. Naraharisetti et al.18 proposed an MILP model for the operations schedule of a microgrid at a daily level consisting of 16906

dx.doi.org/10.1021/ie404165c | Ind. Eng. Chem. Res. 2014, 53, 16905−16923


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Figure 1. Representative structure of the CHP-based system in each household/sector.

strategy of microgeneration systems in building applications. The model incorporates starting and shutdown decisions of the unit as well as partial load operation using a piecewise approximation. Finally, Zhang et al.31 developed an MINLP model for fair, optimized cost distribution among microgrid participants by utilizing Game Theory−Nash approach. The model determines the intra-microgrid electricity transfer price, flow of electricity transferred, unit capacity selection, and unit commitment by maximizing the benefits of all participants based on given upper bounds on the equivalent annualized cost. This work presents an MILP framework for the optimal design and operation of energy networks involving CHP units. The framework addresses systematically the following questions: • Which type of CHP unit or alternatively gas burner should be installed in each household of the microgrid? • When should the energy generation unit be activated or deactivated? • When should the heat storage tank be charged or discharged and at what rate? • When should electricity be imported or exported and how much? • How much will be the heat contribution from the external heat source? The main contributions and the salient features of the proposed approach include the integration of design and

design of distributed energy systems with a stage decomposition based solution strategy, taking into account both demand and supply uncertainty. Ren and Gao27 developed an MILP model for the integrated plan and evaluation of distributed energy systems by determining the optimal system configuration and operational strategies. Mehleri et al.28 introduced an MILP model for the optimal design and planning of a DER system along with the district heating pipeline network. The same authors3 presented an MILP model for the optimal design of distributed energy generation systems satisfying the heat and electricity demand at a neighborhood level. The system components include a variety of candidate technologies (mCHPs, back-up boilers, PV units), as well as a heating pipeline network allowing heat exchange among the different nodes. Bracco et al.29 proposed an MILP framework to optimally design and operate a CHP distributed generation system applied to an urban area. However, this work does not take into account important technical constraints such as minimum/maximum run time, heat losses in start-up periods, etc. Keirstead et al.6 presented an MILP model for the evaluation of urban energy system designs for a range of modeled city sizes and technology scenarios. The aim of this work is to assess how planning restrictions of the size of CHP systems might influence the total efficiency of an urban energy system. Collazos et al.30 presented an MILP model based on model predictive control to determine the optimal operational 16907



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Figure 2. Conceptual arrangement of both the residential and urban CHP-based energy network.

provided in section 6, along with the results of the Monte Carlo method performed for the heat demand in the residential microgrid and available external heat in the urban energy network. Finally, section 7 draws upon some concluding remarks.

operational planning decisions as well as the incorporation of a Monte Carlo-based method inside the optimization process. To the best of our knowledge, there are very few works in the literature that address simultaneously • the design and the operational planning problem, incorporating the whole range of the operational characteristics of the mCHPs (or generally CHPs), such as minimum run time, shutdown time, start-ups as well as partial and full load conditions and • uncertainty issues, since the combined utilization of the Monte Carlo method and the MILP model extends the applicability of the model being able to capture the volatility of some uncertain parameters. The remainder of the paper is organized as follows. The CHP-based energy network is introduced in section 2, followed by a description of the problem statement in section 3. Section 4 presents the mathematical formulation for the optimal design and operation of the CHP-based network. Section 5 includes the basic assumptions, data, and the description of the case studies considered. Discussion on the optimization results is

2. CHP-BASED ENERGY NETWORK Figure 1 depicts a representative structure of the mCHP system considered. Note that the external heat source is not included in the mCHP-based energy network to consider the cases where heating pipeline network is not available. Each household member of the residential microgrid is served exactly by one energy generation unit and a heat storage tank. The energy generation technology could be a mCHP unit or a heat generation process. The mCHP unit consumes typically natural gas and produces simultaneously power and heat with a given heat-to-electricity ratio. The electricity produced meets directly part or the whole of electrical demand (electricity and cooling load with the use of air-conditioning) while the generated heat is disposed to the heat storage tank, which 16908



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iv. Every energy generator type i ∈ IGEN := (i ∈ ICHP ∪ IHG) is characterized by a minimum (maximum) heat max generation capacity θmin i (θi ), a known electricity to heat generation ratio ρi, a given start-up cost φsi, and a minimum run (γi) and shutdown time (δi) . For heat generation units i ∈ IHG, notice that (i) ρi = 0 and (ii) minimum run and shutdown times are often negligible. During a start-up period there is a heat generation loss λi− in the energy generator i ∈ IGEN of site s ∈ Si, while a heat generation excess λi+ is observed during a shutdown period. v. Heat storage tanks i ∈ IHBT have a known heat loss rate ηsi, and a maximum (minimum) heat storage capacity min βmax i (βi ). vi. Each sector s ∈ S is characterized by given aggregated heat ζsth and electricity demand ζste at each time period t. The heat demand basically includes heating load and hot water needs, while electricity mainly stands for electricity and cooling load requirements. vii. There is an external heat source (e.g., refinery) that has a certain heat capacity αt that could be supplied to the sectors of the energy network (only in the urban energy network). The refinery’s heat purchase cost may be given (σt). max viii. Minimum (εmin t ) and maximum (εt ) total electricity generation levels for the energy network during each time period t may be also given. ix. The variable operating cost includes the fuel cost ξsit for operating the generators i∈IGEN of each sector s ∈ Si at time period t. x. The sectors can interchange electricity among them. In addition, electricity could be acquired from external networks (e.g., main electrical grid) in a given purchase tariff ψst that may depend on the sector s and the time period t. Finally, a generation Feed-In Tariff (FIT) according to which the national energy supplier makes a fixed payment πt to the sites for every kWh of electricity they generate through cogeneration units i ∈ ICHP (only in residential energy network), and an export FIT according to which the national energy supplier makes a fixed payment νt to the sites for every kWh of electricity (generated by cogeneration units i ∈ ICHP) exported back to the main electrical grid (in both residential and urban energy networks) are also taken into consideration. It is also assumed that exactly one heat storage tank and exactly one energy generation technology must be installed in each sector s. The key decisions to be made by the administrator of the energy network include • the selection and the sizing of the technology unit types to be installed, by defining binary variables Ysi that denote if a unit type i ∈ I with predetermined capacity is installed in sector s ∈ Si (i.e., Ysi = 1), or not (i.e., Ysi = 0), • the operating status for every installed energy generator in each time period t, by defining binary variables Xsit that denote if the energy generator i ∈ IGEN that has been installed in sector s ∈ Si is operating at the beginning of time period t (i.e., Xsit = 1) or not (i.e., Xsit = 0), • the heat Qsit and electricity generation level ρiQsit for every installed energy generator i ∈ IGEN of sector s ∈ Si during time period t, and

accordingly accommodates the heat load (heating load and hot water). The heat storage tank plays a crucial role in the operational planning of each household and of the microgrid as a whole, since it facilitates the decoupling of heat production from demand, providing in this way better efficiency and flexibility in the production scheduling. It should be noted that with the presence of a heat storage tank, unreasonable run times and frequent switch on and switch off actions for the mCHP unit, which could affect negatively the mCHP’s overall performance, condition, and technical lifetime, can be avoided. In general, the role of storage tank is to store heat in terms of hot water during periods of low thermal energy demand and to supply thermal energy during high heat load. Finally, if a gas burner (also driven by natural gas) is selected instead of a mCHP unit, its role is to provide the necessary amount of heat energythrough the heat storage tankto satisfy the heat requirements of each household. A residential energy microgrid could be formed by connecting a number of domestic mCHP systems. Figure 2 depicts a conceptual arrangement of the residential mCHPbased energy supply chain network (without the heat external source). By integrating several households into a microgrid, there is also the option of electricity trade with the power grid. In this study, a microgrid administrator is assumed to centrally control the microgenerators. The microgrid administrator utilizes the energy generators so as to satisfy in the most efficient and economical way the electricity and heat demand of each household, and determine the electricity interchange among the microgrid members, as well as the electricity flows between the residential network and the main power grid. As a result, the design, operation, and the overall management of the mCHP−based residential networks requires the development of a systematic optimization-based framework. The same concept is applied to an urban energy network consisting of sectors with quite higher electricity and heat demand than those of the residential energy network. For these reasons, an external heat source is incorporated in the proposed approach which is able to supplement additional amounts of thermal energy, as illustrated in Figures 1 and 2. Thus, the heat storage tank is supplied by heat from the CHP generator or the gas burner, as well as from the external heat source (i.e., the refinery), in order to accommodate the heat requirements of each sector. As expected, the available candidate energy generation and storage technologies are of different (higher) size, in comparison with those of the residential energy network, on the grounds of the increased electrical and thermal requirements.

3. PROBLEM STATEMENT The problem under consideration is formally defined in terms of the following items: i. A given time horizon that is divided into a set of uniform time periods t ∈ T. ii. An urban area that is divided into a finite number of sectors and/or households s ∈ S. iii. A set of technology types i ∈ I that are available to be installed in the sectors s ∈ Si. The following types of technologies are considered: (i) CHP units i ∈ ICHP, (ii) heat generation units i ∈ IHG, and (iii) heat storage tanks i ∈ IHBT. Each technology type i ∈ I of sector s ∈ Si has a given capital cost (ωsi). 16909



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• the heat Rsit transferred from the external heat source (e.g., refinery) to the heat storage tank i ∈ IHBT of sector s ∈ Si during time period t. So, as to minimize total capital, variable operating, start-up, heat purchase, and electricity trade costs in order to fully meet the total electricity and heat demand of the energy network.

4.3. Operating Constraints. Constraints 6 and 7 model the start-up and shutdown of energy generation units i ∈ IGEN. Table 1 demonstrates how these constraints work.4,17 Table 1. Modelling of Start-up Lsit and Shutdown Fsit Variables through Xsit Processing Variables constraints 6

4. MATHEMATICAL FORMULATION In this section, an MILP framework is presented for the design and planning problem described above. This work is an extension of the energy planning model developed by Kopanos et al.4 so as to incorporate design decisions. This work is focused on the design and operational planning of mCHP generators. The concept of a single large-scale CHP plant (i.e., a centralized approach) is generally out of the scope of this work. To facilitate the presentation of the proposed model, we use uppercase Latin letters for optimization variables and sets, lowercase Latin letters for indices, and lowercase Greek letters for parameters. 4.1. Objective Function. The objective function to be optimized concerns the minimization of the annualized total system cost, including the annualized capital cost for the installed technologies, energy generations technologies’ start-up cost, cost for purchasing heat from the external heat sources (available only in urban energy networks), fuel costs, electricity trade cost regarding the expenses for purchasing electricity from the national grid and revenues from selling surplus electricity to the grid, as well as a generation tariff incentive in order to promote electricity production from the mCHP technologies (only in residential energy networks). The objective function is given by

Xsit

Xsi,t−1

0 0 1 1

0 1 0 1

constraints 7 Lsit − Fsit = = = =

0 −1 1 0

Lsit + Fsit

Lsit

Fsit

≤1 ≤1 ≤1 ≤1

0 0 1 0

0 1 0 0

Minimum run time and minimum shutdown times for each generation unit i ∈ IGEN are modeled by constraints 8 and 9, respectively. Lsit − Fsit = Xsit − Xsi , t − 1

i ∈ (I GEN ∩ Is),

∀ s ∈ S,

(6)

t∈T Lsit + Fsit ≤ 1


∀ s ∈ S,

t∈T (7)

t ′= max{1, t − γi + 1}

∑

Xsit ≥

Lsit ′

∀ s ∈ S,


t

t ∈ T : γi > 1

(8)

t ′= max{1, t − δi + 1}

∑

1 − Xsit ≥

Fsit ′

∀ s ∈ S,

t


t ∈ T : δi > 1

(9)

4.4. Correlation between Design and Operating Decisions. Constraints 10 further tighten the mathematical model by correlating design and operating decisions. Xsit ≤ Ysi

Next, the constraints involved in the proposed mathematical model are described. 4.2. Design Constraints. The design of the energy network is described by constraints 2−5. According to constraints 2, exactly one heat storage tank must be installed in each sector s ∈ Si. Constraints 3 ensure that exactly one energy generation technology will be installed at each sector s ∈ Si. Tightening constraints 4 and 5 ensure that at most one CHP and one heat generation technology can be installed in each sector, respectively.

∑

Ysi = 1

∑

Ysi = 1

∑

∑

Ysi ≤ 1

(10)


∀ s ∈ S,

(11)

Q sit = Q̃ sit − λi−Lsit + λi+Fsit

(3)

Ysi ≤ 1

t∈T

t∈T

∀s∈S


∀s∈S

i ∈ (I CHP ∩ Is)

i ∈ (I HG ∩ Is)

θiminXsit ≤ Q̃ sit ≤ θimaxXsit

(2)

i ∈ (I GEN ∩ Is)


4.5. Energy Generation Technologies Constraints. Upper and lower bounds for the heat generation for each energy generator i ∈ IGEN are imposed by constraints 11. Moreover, constraints 12 define the actual heat generated by the energy generation technologies i ∈ IGEN considering heat losses during the start-up period. For each time period and sector, big-M constraints 13 model the heat (generated by the energy generator installed in the sector) transferred to the heat storage tank of the sector (Q̅ sit). Note that M is an appropriate big number.

∀s∈S

i ∈ (I HBT ∩ Is)

∀ s ∈ S,

(4)

Q̅ sit ≥

∀s∈S

∑ i ′∈ (I GEN ∩ Is)

16910

t∈T

Q si ′ t − M(1 − Yis)

i ∈ (I HBT ∩ Is),

(5)

∀ s ∈ S, (12)

∀ s ∈ S,

t∈T



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Figure 3. Representative daily electricity demand per season and day type in the residential reference case.

Figure 4. Representative daily heat demand per season and day type in the residential reference case.

∑

Q̅ sit ≤

i ′∈ (I

i ∈ (I

GEN

HBT

Q si ′ t + M(1 − Yis)

Bsit = (1 − ηsi)Bsi , t − 1 + Hsitin − Hsitout

∀ s ∈ S,

∩ Is)

∩ Is),


t∈T

∀ s ∈ S,

i ∈ (I

t∈T

(14)

(13)

Hsitout = ζsthYsi Q̅ sit ≤ MYis

∀ s ∈ S,

HBT

∩ Is),


∀ s ∈ S,

t∈T (15)

t∈T

Hsitin = Q̅ sit + (1 − μst )R sit

4.6. Heat Storage Tank. Constraints 14 specify the energy balance in the heat storage tank for each sector s at each time period t. Heat is extracted from the heat storage tank (Hout sit ) to accommodate the heat demand, according to constraints 15. As constraints 16 state, heat is supplied to the heat storage tank (Hinsit) by the installed energy generation technology (Q̅ sit) and/ or the heat received (Rsit) from external sources (e.g., from the refinery). Parameter μst represents the heat losses percentage for providing heat from the external source to sector s. Heat storage capacity limits for each heat storage tank are given by constraints 17.

∀ s ∈ S,

i ∈ (I HBT ∩ Is), (16)

t∈T βi minYsi ≤ Bsit ≤ βi max Ysi

∀ s ∈ S,

i ∈ (I HBT ∩ Is), (17)

t∈T

4.7. External Heat Source Availability. The available heat from the refinery in each time period t is given by

∑ ∑

R sit ≤ at

s ∈ S i ∈ (I HBT ∩ Is)

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∀t∈T (18)



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4.8. Electrical Energy Balance and Production Limits. Constraints 19 describe the electricity balance for the overall energy network at each time period t, while constraints 20 correspond to minimum and maximum limitation of total energy generation from the urban energy network. Pt +

∑ ∑ s ∈ S i ∈ (I

εtmin ≤

CHP

ρi Q sit = Wt +

∩ Is)

∑ ζste

s ∈ S i ∈ (I CHP ∩ Is)

ρi Q sit ≤ εtmax

type of gas boiler and heat buffer tank gas burner 1 (GB1) gas burner 2 (GB2) heat buffer tank 1 (HBUF1) heat buffer tank 2 (HBUF2)

∀t∈T (19)

s∈S

∑ ∑

Table 3. Residential Case: Technical Characteristics of the Candidate Gas Burners and Heat Buffer Tanks

∀t∈T

ηth

5 10 10

0 0 0

0.80 0.80 0.99

20

0

0.99

electrical and Pth the thermal capacity of each technology, ηe denotes the electrical, and ηth the thermal efficiency of each technology (also in Table 3). Finally, factor HER represents the heat-to-power ratio of each technology. An interest rate of 7.5% is also assumed in the results reported in this work. Based on the technical lifetime of each technology and the interest rate considered, a capital recovery factor for each technology can be evaluated. Note that the proposed model gives the option to the user to use different interest rates and lifetime periods for different technologies. According to the main technical (electrical and thermal capacity, electrical and thermal efficiency, heat-to-power ratio) and economic (investment cost, start-up cost) parameters, these energy technologies will be assessed and the most suitable ones for the specific energy network will be selected. All the relevant operational and economic data of the residential energy system are summarized in Tables A1 and A2 of the Supporting Information. 5.2. Urban Energy Network. An urban energy network of four sectors is considered in this case study, including a city hall (CH), a school (SC), a public swimming pool (SP), and a residential complex (RC). Similar to the previous case study, four different seasons have been considered, autumn (Aut), summer (Smr), spring (Spr), and winter (Wtr), but one representative day type for each season. Figures 5 and 6 depict the typical electricity and heat demand profiles for a representative winter day. Note that it is assumed that there is no heat load during the summer season. The technical characteristics of all candidate technologies are presented in Tables 4 and 5.33−35 Five different technologies are considered including a gas engine (GE), three gas turbines (GT, MGT, GGT), two reciprocating engines (RE, GRE), a microturbine (MIT), and a phosphoric acid fuel cell (PAFC) with a wide range of electrical and thermal capacities. As abovementioned, Pe represents the electrical and Pth the thermal capacity of each technology, ηe denotes the electrical, and ηth the thermal efficiency of each technology, as well as the factor HER shows the heat-to-power ratio of each technology. As in the previous case study, an interest rate of 7.5% has been assumed for the results reported in this work. Depending on these technical (electrical and thermal capacity, electrical and thermal efficiency, heat-to-power ratio) and economic (investment cost, start-up cost, electricity and heat purchases cost) parameters, these energy technologies will be assessed and the most suitable ones for the specific energy network will be selected. All the relevant operational and economic data of the urban energy system are summarized in Tables A3 and A4 of the Supporting Information.

5. DESCRIPTION OF CASE STUDIES The proposed MILP model has been applied to two problem instances that concern a residential and an urban energy network, correspondingly. More specifically, the residential reference case refers to the climate type of a typical U.K. residential energy network, while the urban reference case represents the energy profile of a typical Mediterranean urban energy network. The main differences regarding the structure of the selected case studies concern the existence or not of the generation FIT scheme, providing the householders with a fixed payment for every generated kWh of electricity (involved only in the residential reference case), and the availability or not of an external heat source contributing to the heat demand satisfaction (involved only in the urban reference case). The main input data are presented in the following. 5.1. Residential Energy Network. A residential energy network that consists of three households is considered. Heat and electricity demand data for the reference case have been taken from the Milton Keynes Energy Park data set provided by the U.K. Energy Research Centre Energy Data Centre.32 Four different seasons are considered; autumn (Aut), summer (Smr), spring (Spr), and winter (Wtr). Also, two different day types are examined; weekdays (Wd) and weekends (We). Figures 3 and 4 illustrate the representative daily profile of the electricity and heat demand for the different seasons and representative day types considered in the residential reference case. The main technical characteristics of all candidate technologies (energy generation technologies and heat storage tanks) are presented in Tables 2 and 3.33−35 Four different mCHP technologies are considered, including an internal combustion engine (ICE), a Stirling engine (SE), a fuel cell (FC), and a gas turbine (GT) with the same electrical output capacity (1 kWe) and different heat capacities. Technical data include electrical and thermal efficiencies, total CHP efficiency and heat to electricity ratio. In Table 2, Pe represents the Table 2. Residential Case: Main Technical Characteristics of the Candidate mCHP Technologies

internal combustion engine (ICE) stirling engine (SE) proton exchange membrane fuel cell (PEMFC) gas turbine (GT)

min. operational capacity (kWth)

(20)

The overall design and production planning problem is formulated as an MILP problem, involving the cost minimization objective function 1 subject to constraints 2−20.

type of mCHP technology

rated capacity (kWth)

Pe Pth (kW) (kW)

ηe

ηth

ηCHP

HER

1

3.3

0.200

0.660

0.860

3.3

1 1

6.0 1.1

0.135 0.450

0.810 0.495

0.945 0.945

6.0 1.1

1

1.7

0.290

0.493

0.783

1.7

6. RESULTS AND DISCUSSION All case studies have been solved in an Intel Core i5 3350P 3.10 GHz with 4.0 GB RAM using GAMS 24.0.2/CPLEX 11 under 16912



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Figure 5. Representative daily electricity demand per sector during winter in the urban reference case.

Figure 6. Representative daily heat demand per sector during winter in the urban reference case.

default CPLEX settings.36 An optimality gap of 1% has been imposed and achieved in all case studies. 6.1. Residential Energy Network. 6.1.1. Cost Analysis. The total annualized cost of the design and operational planning of the residential energy network equals 1315.6 €. Considering only the cost components (i.e., the sum of capital, start-up, fuel and electricity purchases cost), total net cost equals 1981.6 € on an annual basis. Fuel cost constitutes the largest cost component accounting for 74.5% of the total net cost, followed by capital cost making up about 21% of the total. The percentage of electricity purchases cost is rather small, approaching 4% of the total and the remaining 0.5% corresponds to start-up cost, denoting the very small influence of this component on the total cost. The annual total net profit is equal to 691.9 €. The profit from electricity production subsidies possess the overwhelming part of the total (90.5%), being equal to 626.1 € and profits from electricity sales amount to 65.7 € (9.5%). The share of

total profit to the total net cost equals 34.9%. These are summarized in Table 6. 6.1.2. Technology Selection. As far as the installed technologies are concerned, these include a Stirling engine (SE) for the first household (s1) and two internal combustion engines (ICE) for the other two households (s2 and s3). Regarding heat buffer tanks, the smallest (in terms of capacityHBUF1) of the two available technologies is installed in all households, with a capacity of 10 kWth. Table 7 presents the technologies selected for installation in the residential case. 6.1.3. Electricity Balance. The general pattern of the electricity balance (except from summer) is that electricity generation is more than sufficient to meet the electricity demand of the residential network. As described above, three micro-CHP technologies have been selected in the households s1, s2, and s3, which not only contribute to the electricity demand satisfaction of their households but also supply with electricity the main power grid (electricity sales). Since heat 16913



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winter and spring, ranging from 26% to 53.5%, depending on each season day type, as reported in Table 8. The percentage of heat load satisfied by direct heat production and/or heat previously stored is determined, to a large extent, by electricity demand. If electricity demand satisfaction by local (within the network) production is more beneficial, heat demand is primarily satisfied by direct heat production and not by previously stored heat. This pattern is reversed when electricity purchases are more economical than local electricity production and thus, heat demand is chiefly or totally met by previously stored thermal energy and electrical demand by electricity purchases. 6.1.4. Heat Storage. Figure 8 depicts the heat storage level per season and day type. The main pattern regarding the heat storage strategy is the following: it occurs mainly in summer, peaking during the first half of the day, and it gradually decreases in order to meet the peak heat demand observed during the last hours of the day. Stored heat is also observed during winter in order to facilitate both electricity and heat demand satisfaction as described above. Noticeable amounts of stored heat are also reported during autumn weekend since again, heat demand peaks during the last hours of the day. In general, heat storage plays a balancing role to cover the heat demand fluctuations in the most efficient and economical way as well as to facilitate the electricity demand satisfaction through the control of heat generation. The stability and operational flexibility of the residential energy network is achieved through the heat storage process and the connectivity to the main electrical grid. At this point, note that the total heat stored at the beginning of each day is equal to the heat stored at the end of the day in order to reflect that the energy storage technologies can only deal with short-term, daily fluctuations. In our case, this initial level is set to 0 kWth. 6.2. Monte Carlo Simulation. The implementation of the Monte Carlo simulation is performed in GAMS. It simply requires an iterative algorithm, in each iteration of which the proposed model is solved. The MILP model has been solved for 1000 iterations (N = 1000) of the Monte Carlo method for each selected distribution type. The generated results comprise the optimal solution of each case (i.e., distribution type), and they are presented in the form of histograms and figures for the design variables of the technology selection and the annualized system cost. In the residential case, heat demand is considered as the only uncertain parameter, having a significant influence on the design decisions. Two probability distribution types have been used to capture the uncertainty of the heat demand: the uniform and the normal. The specific characteristics of each distribution for the heat demand are provided in Table 9. These include the minimum and the maximum value for the uniform distribution, as well as the mean and the standard deviation for the normal distribution. The uniform distribution expresses the highest uncertainty, because it has a constant probability distribution function between its two bounding parameters. The value of the selected uncertain parameter can vary within the interval of these bounds with equal probabilities. The normal distribution can be utilized when the value of the uncertain parameter tends to cluster around a single mean value. As previously described, the optimal technology selection of the residential reference case includes a Stirling engine (SE) for the first household (s1) and internal combustion engines (ICEs) for the other two households (s2 and s3). Not

Table 4. Urban Case: Technical Characteristics of the Candidate CHP Technologies Pe (kW)

type of CHP technology gas engine (GE) gas turbine 1 (GT) gas turbine 2 (MGT) gas turbine 3 (GGT) reciprocating engine 1 (RE) reciprocating engine 2 (GRE) micro-turbine (MIT) phosphoric acid fuel cell (PAFC)

Pth (kW)

ηe

ηth

ηCHP

HER

100 65

130 112

0.360 0.290

0.468 0.500

0.828 0.790

1.30 1.72

50

55

0.425

0.468

0.893

1.10

5000

5,701.3

0.405

0.462

0.867

1.14

1,000

1,145.5

0.418

0.479

0.897

1.15

1,000

1,148.1

0.375

0.431

0.806

1.15

200

218.1

0.320

0.349

0.669

1.09

400

230

0.350

0.201

0.551

0.58

Table 5. Urban Case: Technical Characteristics of the Candidate Gas Burners and Heat Buffer Tanks type of gas boiler and heat buffer tank gas burner 1 (GB1) gas burner 2 (GB2) heat buffer tank 1 (HBUF1) heat buffer tank 2 (HBUF2)

rated capacity (kWth)

min operational capacity (kWth)

ηth

200 400 150

0 0 0

0.80 0.80 0.99

300

0

0.99

Table 6. Residential Case: Cost and Revenues Components cost components

€

%

capital cost

414.7

21.0

start-up cost

10.0

fuel cost electricity purchases cost Total Net cost total cost

1476.7 80.1 1981.6 1315.6

0.51 74.5

revenues components electricity sales revenues electricity production FIT total net revenues

€

%

65.7

9.5

626.1

90.5

691.9

100.0

4.04 100.0 total net revenues/total net cost = 34.9%

Table 7. Installed Technologies in the Residential Case households

energy generation technology

heat storage tank

s1 s2 s3

SE ICE ICE

HBUF1 HBUF1 HBUF1

demand is low during summer, the optimal strategy features a significant share of electricity purchases from the central grid, especially on a weekday (64.7% of the total electricity demand), to meet the electricity demand. This can also be explained by the fact that the heat demand of household s2 is negligible in the summer and, thus, the largest part of electricity purchases is directed to its demand satisfaction (see Figure 7). Note that mCHP technologies are heat-driven and there is no need to produce excessive heat in the summer. Electricity sales comprise a noticeable part of electricity production during 16914



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Figure 7. Electricity balance during each season and day type in the residential case.

Table 8. Electricity Trade in the Residential Case

Table 9. Characteristics of the Applied Probability Distributions in Both the Residential and Urban Case

season

day type

electricity production to the electricity demand (%)

electricity purchases to the electricity demand (%)

electricity sales to the electricity production (%)

Aut Aut Wtr Wtr Smr Smr Spr Spr

Wd We Wd We Wd We Wd We

109.9 102.5 180.5 215.1 35.3 54.1 129.5 197.0

2.4 2.8 0.7 0.0 64.7 45.9 4.2 2.6

11.2 5.1 45.0 53.5 0.0 0.0 26.0 50.5

heat demand (residential case) reference case normal distribution case uniform distribution case

external heat availability (urban case)

HDR (HDR, 0.15*HDR)

500 kWth (500, 250) kWth

(0.5*HDR, 1.5*HDR)

(0, 3000) kWth

information to the decision makers about how the objective function and the key decision variables vary along the each selected value range. 6.2.1. Technology Selection. Figure 9 depicts the technology selection probability per household and probability distribution. The results of the normal distribution are more close to those of the residential reference case, since the

surprisingly, different types of probability distributions for the uncertain input parameters lead to different probabilities for the output variables. Therefore, these results can provide important

Figure 8. Heat storage level in each season and day type in the residential case. 16915



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Figure 9. Technology selection probability per household and probability distribution in the residential case.

Figure 10. Uniform probability distribution for the network technology selection in the residential case.

probability of selecting a SE for the first household is about 56%, and the corresponding probabilities of selecting ICEs in the other households are 76% and 96% for the second and the third household respectively. The results of the uniform probability distribution are quite similar to the reference case as the probability of selecting SE in s1 is about 53%, and the probabilities for selecting ICE in s2 and s3 are about 49% and 87%, correspondingly. Figure 9 shows that the installation of an ICE in s3 seems a robust decision in all examined probability distributions, while the highest uncertainty concerns the technology selection in s1 as ICE and SE constitute competitive technologies according to each applied probability distribution. High uncertainty is also reported in the decision for the technology installation in the household s2, on the grounds that SE and ICE have similar selection probabilities in the uniform distribution.

Small heat buffer tanks (HBUF1) comprise a robust selection in all cases, especially in the first two households (s1 and s2), since their selection probability is always 100%. The selection probability of the large heat buffer tank (HBUF2) in the third household (s3) is 8.5% and 3.3% for the uniform and the normal distribution correspondingly. Figures 10 and 11 show the total network technology selection for each implemented probability distribution. From Figure 10 (uniform distribution), it can be noticed that the selection of a SE in s1 and two ICEs in s2 and s3 (SE-ICE-ICE) bears a probability of about 22%, sharing the same probability with the network technology selection consisting of ICEs in all households. The most probable network technology selection includes SE-SE-ICE with a total probability of almost 24%, while the probability of ICE-SE-ICE amounts to almost 20%. The uniform distribution constitutes the most balanced case when considering the most probable optimal technology 16916



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Figure 11. Normal probability distribution for the network technology selection in the residential case.

Figure 12. Uniform probability distribution of the annualized cost in the residential case.

selection. As expected (due to the fact that normal distribution is more close to the reference case) and depicted in Figure 11, the optimal technology selection of the reference case (i.e., SEICE-ICE) shares a probability of 41% in the normal distribution case, while the second most probable network technology selection features ICE-ICE-ICE with a probability of almost 33%. In general, we can conclude that SE-ICE-ICE, ICE-ICEICE and SE-SE-ICE comprise the most competitive technology selections in the studied residential energy network, according to each probability distribution. 6.2.2. Annualized Cost. Figures 12 and 13 illustrate the histograms of the probability distribution of the annualized cost for the two applied types of distributions. Observe that the distribution of the annualized cost follows relative closely the distribution of the uncertain parameter, that is, heat demand. Not surprisingly, the results are more robust (higher frequencies) in the normal distribution. From these Figures,

we can also extract valuable information in the terms of probabilities. The green line in all histograms denotes the probability distribution of each value of the total cost. For instance, the probability that the annualized cost is below 1,400 € is almost 84% for the uniform distribution and around 92% for the normal distribution. Note that the optimal annualized cost of the Reference Case amounts to 1,315.6 €. The probability that the annualized cost is under 1315.6 € is around 55% for the uniform distribution and almost 70% for the normal distribution. This trend was expected since the application of the normal probability distribution is quite close to that of the reference case, because the normal distribution is applied when the value of the uncertain parameter can vary around a mean value, that is, the corresponding value of the reference case. 6.3. Urban Energy Network. 6.3.1. Cost Analysis. The total annualized cost of the design and operational planning of 16917



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Figure 13. Normal probability distribution of the annualized cost in the residential case.

Figure 14. Total net cost breakdown in the urban reference case.

the urban energy network amounts to 537 758 €. When considering only the net cost components (i.e., excluding revenues from electricity sales), the largest share of the total net cost is set to be taken by fuel cost, accounting for almost 64% of the total, followed by the capital cost (21%), electricity purchases cost (13%), heat purchases cost (2.5%), while the start-up cost (0.02%) is almost negligible, as depicted in Figure 14. 6.3.2. Technology Selection. As far as the installed technologies are concerned, the results indicate that the optimal solution includes three microgas turbines (MGT) CHP units of 50 kWe in the city hall (CH), in the school (SC), and in the swimming pool (SP), as well as a reciprocating engine (RE) CHP unit of 1 MWe in the residential complex (RC). Concerning heat buffer tanks, only large heat buffer

tanks (HBUF2) with a thermal capacity of 300 kWth are selected, as presented in Table 10, which summarizes the technology selection and and the total cost of the urban energy system reference case. 6.3.3. Electricity Balance. Table 11 presents the electricity trade during the representative day of each season in the urban reference case. The network’s electricity production is more than sufficient to meet the electricity demand during the winter, selling to the power grid a substantial amount of electricity produced. Since heat demand profile is assumed to be identical during autumn and spring, the results indicate that local electricity production meets almost the electricity demand during these seasons, while electricity purchases from the power grid make up a quite low share in the electricity demand satisfaction. However, this general pattern of significant onsite 16918



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optimal design and production planning of an urban energy system. The small differences between total heat demand and the sum of total real heat generation and net heat transfers from the refinery to the sectors are due to heat losses occurred during storage in the heat buffer tanks. Finally, Figure 15 depicts the structure of the total network and shows the net heat flows (including heat losses during their transfer) from the central refinery to each sector during all seasons and representative day types as a whole. 6.4. Monte Carlo Simulation. In this case, external heat source availability is assumed to be the uncertain parameter of our model and we examine its influence on the technology selection and the annualized urban energy network cost. Two main probability distributions have been applied so as to investigate the uncertainty of the external heat source availability: the uniform and the normal. The specific characteristics of each distribution for the refinery’s heat availability are provided in Table 9. These include the minimum and the maximum value for the uniform distribution, as well as the mean and the standard deviation for the normal distribution. 6.4.1. Technology Selection. Figure 16 depicts the technology selection probability per sector and probability distribution of the urban energy system. The results of the uniform distribution are close enough to those of the Reference urban energy system case, since the probability of selecting a MGT in the first three sectors (i.e., CH, SC, and SP) is about 88%, 92.5%, and 91%, correspondingly. Regarding the RC, the probability of selecting a RE is around 38%, while the one of selecting a MGT approaches 50%. When examining the energy network as a whole, the probability of selecting simultaneously the same technologies with those of the reference case in all sectors is around 26%. The probability of selecting a MGT in all sectors is almost 48%, highlighting that this technology composition constitutes the most appropriate decision when the amount of the available heat supply from an external source is characterized by high uncertainty and wide range of possible values. Analyzing further the results of the model, we can infer that the selection of a MGT in the school and swimming pool is very robust, as the accumulative probability equals 88%. Similar results are also reported in the normal distribution case, which are even closer to those of the reference urban energy system case, since the probabilities for selecting a MGT in the CH, SC, and SP, as well as a RE in the RC are 77.6%, 82.0%, 80.2%, and 88.8% respectively. When examining the urban network as a whole, the probability of selecting exactly the same technologies in all sectors with those of the reference case, is almost 61.0%. Note that while the installation of a MGT in all sectors is the most appropriate decision in the uniform distribution case, its probability is zero in the normal distribution case because a RE is installed in the residential complex with a probability of almost 89%. Additional information regarding the network technology selection in each selected probability distribution is provided as Supporting Information. When examining the installation of the heat buffer tanks, the large heat storage tanks (HBUF2) constitute the only choice in all cases, since they are characterized by a selection probability of 100% in both probability distributions. 6.4.2. Annualized Cost. As mentioned above, the total annualized cost of the design and operational planning of the network in the reference urban energy system case amounts to

Table 10. Total Cost and Technology Selection in the Urban Energy System Case urban energy system sectors

energy generation technology

city hall school swimming pool residential complex

MGT MGT MGT RE total cost: 537758.4 €

heat buffer tank HBUF2 HBUF2 HBUF2 HBUF2

Table 11. Electricity Trade in the Urban Energy System Case (kWhe) season

electricity demand

electricity production

electricity purchases

electricity sales

Aut Wtr Smr Spr

5101.6 5060.0 5221.3 5101.6

4996.7 8634.6 0.0 4996.7

104.9 108.0 5221.3 104.9

0 3682.6 0 0

electricity production is totally diversified in the summer, because there are no heat requirements and thus, the model determines that electricity purchases constitute the optimal solution for the electricity demand satisfaction. Not surprisingly, heat demand comprises the key element for the production scheduling of the urban energy system. Notice that the revenue from electricity sales to the power grid amounts to 54721 €, or 10.2% of the total annualized cost. 6.3.4. Heat Balance. As presented in Table 12, heat transfers from the refinery account for a significant share of the heat Table 12. Heat Balance in the Urban Reference Case (kWhth) reference case

net heat transfer from the refinery

real heat generation

heat demand

Aut-CH Wtr-CH Spr-CH Aut-SC Wtr-SC Spr-SC Aut-SP Wtr-SP Spr-SP Aut-RC Wtr-RC Spr-RC

563.1 548.8 502.3 518.5 978.1 586.3 2100.2 3345.8 2084.5 8550.1 7006.7 8558.8

751.3 1227.8 795.6 1049.5 1249.3 994.5 1097.5 1225.5 1108.2 6761.0 13 936.0 6761.0

1207.5 1690.0 1,207.5 1475.6 2,075.0 1475.6 2860.2 4060.0 2860.2 14 013.1 19 880.0 14 013.1

demand satisfaction in all sectors. This is expected due to the fact that the cost for purchasing heat from the refinery is quite lower when compared to that of onsite heat production from the installed CHPs. Also, notice that in the first two sectors (i.e., CH and SC) local heat generation exceeds the heat acquired from the refinery, while in the other two sectors, (i.e., SP and RC) that are characterized by higher heat energy requirements, external heat supply (from the refinery) is greater than their onsite generation. This trend can be explained by the fact that the first two sectors, CH and SC, operate their CHPs up to levels that are necessary in order to cover their electrical loads, and sell to the grid some additional amounts of electricity produced. Not surprisingly, the amount of available heat supply from an external source is of paramount importance for the 16919



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Figure 15. Total network configuration in the urban reference case (kWth).

Figure 16. Technology selection probability per sector and probability distribution in the urban energy system.

537 758 €. From Figure 17, we can derive the information that the probability that the annualized cost is below that optimal reference value is around 81% in the uniform distribution case, indicating the robustness of the optimal value of the reference case. Since the range of the uniform probability distribution is quite high (0−3000 kWth), the probability that the annualized cost exceeds 1 000 000 € is 1.5%, while being lower than 400 000 € corresponds to almost 55%.

For the normal distribution case, the probability that the annualized cost is below the optimal reference value is around 49%, indicating that the lower the range of the availability of the external heat source, the higher the total cost of the system. In this case, the probability that the cost is between 500 000 € and 600 000 € is 46.5%, while being higher than 1 000 000 € is almost 1% (see Figure 18). 16920



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Figure 17. Uniform probability distribution of the annualized cost of the urban energy system.

Figure 18. Normal probability distribution of the annualized cost of the urban energy system.

7. CONCLUDING REMARKS This work presents an optimization-based framework that addresses the design and operational planning of both residential and urban energy networks based on CHP generators. Two different case studies have been considered, and Monte Carlo analyses have been carried out to explore the influence of key varying parameters (i.e., heat demand for the residential case, and external heat source availability for the urban energy network). The results indicate that heat demand levels constitute the main driver of the technology selection and operational strategy of the energy network. Furthermore, the available heat supply from an external source comprises an equally crucial factor for this kind of decision making problems, on the grounds of offering more flexibility in satisfying the overall heat demand. Fuel cost comprises the most significant cost term in all cases, followed by capital cost and electricity

purchases cost. Current research focuses on incorporating renewable energy technologies into the proposed MILP model, in an attempt to integrate the design and operational planning of both the CHP generators and the intermittent renewable energy sources.

■

ASSOCIATED CONTENT

S Supporting Information *

Additional tables and figures as described in the text. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +30 2310 994184. Fax: +30 2310 996209. E-mail: [email protected]. 16921



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φsi = cost for starting-up the energy generation technology i ∈ IGEN of sector s ∈ Si ψst = purchase price of electricity from external networks of sector s ∈ Si at time period t ωsi = capital cost for technology unit type i ∈ I in sector s ∈ Si

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the European Commission’s FP7 EFENIS project (Contract No: ENER/FP7/296003) “Efficient Energy Integrated Solutions for Manufacturing Industries” is gratefully acknowledged.

■

Continuous Variables

Bsit = heat storage level in the heat storage tank i ∈ IHBT of sector s ∈ Si at the end of time period t Pt = electricity acquired from external networks in time period t Wt = electricity exported to external networks in time period t Q̅ sit = heat generation level for energy generation technology i ∈ IGEN of sector s ∈ Si in time period t Qsit = real heat generation (including heat losses in start-up periods) by the energy generation technology i ∈ IGEN of sector s ∈ Si in time period t Q̅ sit = heat generated by the energy generation technology i ∈ IGEN of sector s ∈ Si and delivered to its heat storage tank i ∈ IHBT in time period t Rsit = heat transferred from the external heat source to the heat storage tank i ∈ IHBT of sector s ∈ Si in time period t

NOMENCLATURE

Indices/Sets

i ∈ I = technology unit types (CHP, heat generators, heat storage tanks) s ∈ S = sectors/households t ∈ T = time periods

Subsets

ICHP = set of CHP units IGEN = set of all energy generation units IHBT = set of heat buffer tanks Is = set of available technologies types i ∈ I to be installed in sector s ∈ S Si = set of sectors s ∈ S wherein technology unit type i ∈ I could be installed

Binary Variables

Superscripts

e = electricity h = heat max = maximum min = minimum in = input out = output Parameters

at = available heat from the external heat source in time period t βi = storage capacity for heat storage tank i ∈ IHBT γi = minimum run time for energy generation technology i ∈ IGEN (in time periods) δi = minimum shutdown time for energy generation technology i ∈ IGEN (in time periods) εt = total electricity production for the energy network during time period t ζst = energy demand for sector s ∈ S at time period t ηsi = heat loss rate for the heat buffer tank i ∈ IHBT of sector s ∈ Si θi = heat generation capacity from energy generation technology i ∈ IGEN λi− = heat generation loss for the energy generation unit i ∈ IGEN during start-up λi+ = heat generation excess for the energy generation unit i ∈ IGEN during shutdown μst = heat losses percentage for providing heat from the external source to sector s at time period t M = big value parameter νt = selling tariff of electricity for the regional energy network to the main electrical grid at time period t ξsit = fuel cost for operating energy generation technology i ∈ IGEN of sector s ∈ Si in time period t πt = selling price of electricity produced by the cogenerators at time period t ρi = electricity to heat production ratio for CHP units i ∈ ICHP σt = purchase price of heat from external networks at time period t

■

Lsit = 1, if the energy generation technology i ∈ IGEN, installed in sector s ∈ Si, starts operating at time point t (i.e., Xsi,t−1 = 0 and Xsi,t = 1) Fsit = 1, if the energy generation technology i ∈ IGEN, installed in sector s ∈ Si, stops operating at time point t (i.e., Xsi,t−1 = 1 and Xsi,t = 0) Xsit = 1, if the energy generation technology i ∈ IGEN, installed in sector s ∈ Si, is operating at the beginning of time period t Ysi = 1, if the technology unit type i ∈ I is installed in sector s ∈ Si

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