Optimal design and operation of district heating and cooling networks with CCHP systems in a residential complex

Energy and Buildings 110 (2016) 135–148

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Optimal design and operation of district heating and cooling networks with CCHP systems in a residential complex Mohammad Ameri ∗ , Zahed Besharati Mechanical and Energy Eng. Department, Shahid Beheshti University, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 6 September 2015 Received in revised form 24 October 2015 Accepted 26 October 2015 Available online 2 November 2015 Keywords: Cogeneration CCHP District heating and cooling MILP

a b s t r a c t The aim of the paper is to describe a mixed integer linear programming (MILP) model for determining the optimal capacity and operation of seven combined cooling, heating and power (CCHP) systems in the heating and cooling network of a residential district (Shahid Beheshti Town) located in east of Tehran. In this model, by minimizing the initial and operating costs of energy supply system, capacity of various components, and optimal operation strategy are determined using continuous variables, and binary decision variables describe the existence/absence of each considered component and its on/off operation status. A distributed energy supply system is made up of district heating and cooling networks, gas turbines as the prime mover for CHP systems, photovoltaic systems (PV) and conventional equipments also, such as boilers and absorption and compression chillers. In this configuration, the required heat is obtained from natural gas consumption by cogeneration system and auxiliary boilers. Four different scenarios were defined to assess the impact of the use of photovoltaic and CCHP systems in the energy supply system in the residential complex. The economic and environmental results obtained from the scenarios revealed saving in costs and reduction in CO2 emissions in the optimal cogeneration system compared with using boilers to produce heat and of buying electricity from the grid. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The energy crisis and environmental impacts of fossil fuels are the main motivations for engineers to find more efficient energy conversion technologies [1]. Polygeneration, i.e. the combined generation of useful power, heat, cooling, possibly in combination with the production of other useful products, is attracting growing interest, due to its ability of maximizing overall energy efficiency [2]. In particular, in the emerging context of distributed generation, which is defined by Ackermann et al. [3], as the “installation and operation of electric power generation units connected directly to the distribution network or connected to the network on the customer side of the meter”, a further benefit is obtained in that energy services as the power generation occurs close to the point of use. While the definition by Ackermann et al. [3], is centred on power generation, in a polygeneration framework also heat and cooling are produced at customer sites, and can be either exploited locally or forwarded to other users by means of a suitable pipeline system. District heating (DH) pipes allow to distribute hot water or steam,

∗ Corresponding author. E-mail address: ameri [email protected] (M. Ameri). http://dx.doi.org/10.1016/j.enbuild.2015.10.050 0378-7788/© 2015 Elsevier B.V. All rights reserved.

while through district cooling (DC) systems, multiple facilities are chilled from remote cooling generation units [4,5]. In areas with warm climates such as central and southern part of Iran, where cogeneration viability is affected by the low thermal demand during summer, the employment of absorption chillers to produce cooling from the waste heat, can increase the feasibility of the combined heating and power (CHP) system [6]. Thus, if one can satisfy both heating and cooling demand by combining DH, DC and polygeneration systems in design, construction and operation levels, higher economic and energy efficiency can be achieved. However, the expected performances could not be obtained without adopting the configuration and the operation strategy resulting from an optimization procedure of the whole system [7–12]. Polygeneration system itself is a comprehensive design, especially equipment configuration [13,14], capacity optimization [15,16], operation strategy [17,18] and energy management [19]. Chicco et al. [20] have concluded that the optimization of multigeneration systems can be done by short-term or long-term models. In the first case, the analysis is centered on the operational planning of the given energy system in a certain period (e.g. one year), whereas the second model is focused on the plant design problem over its useful life. In this kind of optimization problems, the system operation is typically considered as a succession of

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steady state conditions, adopting a discrete time step not lower than 1 h, and a synthetic black-box approach is used to model the technologies by means of simplified plant performance maps. Many research papers are focused on the design and the optimal operation of distributed energy system networks, composed of CHP technologies, combined cooling, heating and power (CCHP) technologies, renewable power plants, thermal and electrical storage systems. Carvalho et al. [21] developed a mixed integer linear programming (MILP) model for the optimal synthesis of a combined cooling, heating and power system subject to environmental aspects. Lozano et al. [22] developed an optimization model to determine the preliminary design of CCHP systems with thermal storage, taking into account the legal constraints imposed on cogeneration systems in Spain. The majority of the literature on district heating and cooling (DHC) systems focus on the optimization of the energy conversion technologies, used in the district heating and cooling networks and their operational strategies [23–25]. However, there are a number of papers which deal with the design of the heating and cooling networks within the polygeneration systems by using different approaches. DHC was handled by Sakawa et al. [26], also by means of genetic algorithms to solve MILP models, as far as concerns the operational optimization of such systems. In fact, for Sakawa et al. [26], the shape and size of the network and of the heating and cooling production systems are pre-defined, while the goal of the optimization procedure is to decide which engines, heaters and chillers should be used, at which load and at which point in time. Weber et al. [27], addressed the issue of combining plant sizing and network configuration issues for DHSs by using a solution strategy founded on separate sub-models: in particular, a genetic algorithm have applied the list of available technologies and their efficiencies to choose size and energy conversion plants, while a separated MILP optimization model has used these data to configure a network of pre-defined diameter size and a single peak load boiler. Weber and Shah [8] proposed a single-level optimization approach for a UK district energy system allowing mixing of different energy services. A combined optimization of capacity, layout and operation has been presented by Soderman and Petterson [28]. Also, in this case only heating and electricity demand have been considered. An interesting work is reported by Mehleri et al. [29], where a MILP model of a distributed energy resource system is reported, taking into account site energy loads, local climate data, utility tariff structure, technical performance data of plants and geographical aspects, with the aim of minimizing the sum of annual capital, operational and maintenance costs. The proposed optimization algorithm permits to select the optimal capacity of plants, also determining their operating schedules, and to design the heating piping network. Bracco et al. [30] proposed a mixed-integer linear programming model to optimally design and operate a combined heat and power distributed generation system. In particular, the model is applied to an urban area with the aim of determining how many cogeneration gas internal combustion engines and gas turbines to be installed in the buildings and how the heat distribution network to be designed. The objective function of the optimization model is relative to capital and operational costs as well as carbon dioxide emissions. As a test case, the paper reports the results for an urban area located in the city of Arenzano in Italy. In particular, the environmental and economic benefits of a distributed generation system based on the use of cogeneration units are highlighted in the paper. In previous works, it is seen less frequently that the overall design and operation of CCHP systems within DHC networks and integration to be applied aiming at using renewable sources of energy. Since half of the electrical energy supply in Iran is done

through gas turbines with low efficiency (total capacity: 10 GWe, average efficiency 29.4% [31]), a gas turbine was selected as the primary mover of CHP systems. Linearizing the performance curves of the cogenerators (the relationships between input and output streams), the MILP model is still a valid way to represent the system analysis. The authors describe a MILP model that has been developed in order to optimally design and operate an energy system in a residential town. With the support of the Ministry of Energy of Iran in installation of solar home systems with a subsidy of 50%, a photovoltaic (PV) system is included in the configuration of energy supply. Given the site’s energy loads, utility tariff structure, as well as the information (both technical and financial) for the PV, the gas turbine systems, the boilers, the chillers and the piping network, the model minimizes the overall cost of the energy system by selecting the sizes of the various components, the capacity of the PV systems, determining their operating schedules and designing the optimal route of the heating and cooling piping network. The paper is organized as follows. A problem description is given in Section 2. The mathematical model is described in detail in Section 3 whereas the results are reported in Section 4 where the specific case-study of the residential complex in eastern Tehran is analyzed. Finally, in Section 5 some conclusive remarks are reported.

2. Problem description As mentioned in the introduction, seven CCHP systems are composed of residential buildings connected with district heating and cooling networks and characterized by different electrical, heating and cooling demand profiles. In each CCHP site a certain number of gas turbines, traditional boilers and chillers can be installed in order to best satisfy its energy consumption. Furthermore, each CCHP site can exchange heating and cooling energy with the other sites connected by a pipeline. There is not the possibility of direct electricity exchange between sites; as a consequence, the surplus electricity produced by the gas turbines and/or the PV array located in each site is delivered to the distribution grid, and similarly it is possible to buy electricity from the grid when the buildings electrical demand exceeds the electricity produced by the CHP units. To consider local energy balances and overall network configuration at the same time, a model is proposed which combines an optimal network flow and capacity planning problem with an energy systems optimization problem. Fig. 1 shows the system superstructure described by the model. A typical site j can be equipped with a gas turbine and heat recovery steam generator (HRSG), a boiler, an absorption chiller, a compression chiller and a PV array that can be installed on the roofs of buildings. In Fig. 1 electricity, cooling energy and heat flows are represented in green, blue and red respectively. The model is completely general and it can be applied to different applications by changing the values that describe the components and the energy demands. In the optimization problem, the following data are given: • The hourly electrical, heating and cooling load profiles of buildings in the considered time horizon; • The technical performance data related to the gas turbines, boilers, chillers, PV unit and pipelines; • The geographical location of buildings; • The installation and maintenance costs of the gas turbines, boilers, chillers, PV unit and pipelines; • The fuel purchasing price; • The electricity selling and purchasing prices; • The hourly solar irradiance profile of the year;

M. Ameri, Z. Besharati / Energy and Buildings 110 (2016) 135–148

137

Fig. 1. Structure of the energy supply system described by the optimization model.

So as to minimize the total annualised cost, including capital and operational costs, a set of typical days that represent the building daily electrical, heating and cooling load profiles through the year was chosen. The optimization model is then applied to a time horizon constituted by the set of selected typical days. The main outputs of the optimization model are: • Existence and size of each component. • Operation status and load level of each component in each time interval. • Electricity to be exchanged with the electric network. • Thermal flow inside the district heating and cooling network. • Size of the pipelines. • Fuel primary energy consumed by each generation unit. • Electrical power generated by each gas turbine and PV system. Furthermore, the model gives as output the total cost, for installing and operating the whole system, and the CO2 emissions, both evaluated over the whole time horizon. Finally, the model quantifies the economic and environmental saving due to the operation of CCHP distributed systems in comparison with a separate production of heat and electricity.

3. Mathematical model The problem of determining the optimal design and operation of CCHP/DHC systems is stated in this section as a mixed-integer linear programming problem, in which both binary and continuous decision variables are considered and the relations among them are linear. Binary variables represent the existence and operation status of components, while all other variables are continuous. 3.1. The problem data The input data can be classified in three categories depending on their meaning. Let us first of all consider general data: • T set of time intervals in the considered horizon (t denotes the generic time interval and t is the length of each time interval [h]). • I set of CCHP sites (i denotes the generic site and the pair i, j indicates the connection between two sites). • GTi gas turbine in the site i (h denotes the generic gas turbine). • Bi boiler in the site i (q indicates the generic boiler). • ABSi absorption chiller in the site i. • ECi compression chiller in the site i. • PVi photovoltaic array in the site i.

Another set of inputs regards cost data: • C GT , CqB , C PV purchasing cost of gas turbine h, boiler q and photoh voltaic array [$/kW]. • C ABS , C EC size independent cost of absorption and compression f f chillers [$]. • CvABS , CvEC size dependent cost of absorption and compression chillers [$/kW]. • C DHC DHC network variable cost of based on the length of pipes l [$/m]. DHC DHC network variable cost based on the flow through the • Cw pipes [$/m kW]. • C GT , C B , C PV gas turbine, boiler and PV maintenance costs M M M [$/kWh]. • C ABS , C EC absorption and compression chillers maintenance costs M M [$/kWh]. • cf fuel purchasing cost for the boilers and the gas turbines [$/kWh]. • c s , c b electricity selling price, electricity purchasing price el el [$/kWh]. Finally, a set of technical data is considered: • Del , Dth , Dc electrical, heating and cooling demand of the site i i,t i,t i,t at time t [kWth , kWe , kWc ]. • Itt hourly solar irradiance [W/m2 ]. • Aup The upper bound on the surface of PV arrays in site i [m2 ]. i • Li,j distance between site i and site j [m]. • max W GT , min W GT maximum, minimum electrical power genh,t h,t erated by gas turbine h at time t [kWe ]. • CapGT rated power gas turbine h [kWe ]. h • max QqB , min QqB maximum, minimum thermal power generated by boiler q [kWth ]. • CapBq rated power boiler q [kWth ]. • Bq boilers efficiency. • max RABS , min RABS maximum, minimum cooling power generi i ated by absorption chiller in site i [kWc ]. • max REC , min REC maximum, minimum cooling power generated i i by compression chiller in site i [kWc ]. • COPE , COPA coefficient of performance of absorption and compression chillers. • maxFHi,j , minFHi,j maximum, minimum thermal flow that can be exchanged between site i and site j [kWth ]. • maxFCi,j , minFCi,j maximum, minimum cooling flow that can be exchanged between site i and site j [kWc ]. • ıc , ıh percentage losses along the district heating and cooling pipelines per length unit [km−1 ]. • max W b , max W s maximum electrical power withdrawable from i i the grid, injectable into the grid by site i [kWe ]. PV • e electrical efficiency of the PV panel. • Cprat rated capacity of the PV panel [kW/m2 ].

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3.2. The decision variables

fixed and variable costs. The capital cost CC is related to buying boilers, gas turbines and chillers and is defined as:

The decision variables can be classified in some sets, depending on their meaning. First of all, let us consider the design binary variables:

 i∈I



• • • •

yiABS equal to 1 if the absorption chiller is installed in site i. yiEC equal to 1 if the compression chiller is installed in site i. yiPV equal to 1 if the PV panel is installed in site i. yhi,j equal to 1 if a thermal pipeline is installed between site i and site j. • yci,j equal to 1 if a cooling pipeline is installed between site i and site j. In the previous definitions, it is assumed that if GTi = 0 for some i ∈ I (which means that in site i it is not possible to install gas turbine GT are not defined for for technical reasons), the relative variables yi,h

B and yPV are not that i. Similarly, if Bi = 0 or PVi = 0, variables yi,q i defined for that i. Other binary decision variables are:

• xGT equal to 1 if the gas turbine h in site i works at time t. i,h,t • xB equal to 1 if the boiler q in site i works at time t. i,q,t • xhi,j,t equal to 1 if the thermal flow transferred from i to j at time t. ABS , xEC , xc The same variables (xi,t i,j,t ) defined for the absorption i,t chillers, the electrical chillers and the cooling flow. Finally, the operative decision variables are:

• W GT , F GT , Q GT electrical power generated [kWe ], fuel primary i,h,t i,h,t i,h,t energy per time unit [kWPE ], thermal power generated [kWth ], by the gas turbine h in site i at time t. • F B , Q B fuel primary energy per time unit [kWPE ], thermal i,q,t i,q,t power generated [kWth ], by the boiler q in site i at time t. • RABS , Q ABS cooling power generated by the absorption chiller i,t i,t [kWc ], thermal power input from the gas turbine to the absorption chiller [kWth ], in site i at time t. • CapABS capacity of the absorption chiller installed in site i [kW]. i • REC , W EC cooling power generated by the electrical chiller [kWc ], i,t i,t electrical power input to the electrical chiller [kWe ], in site i at time t. • CapEC capacity of electrical chiller installed in site i [kW]. i • W b , W s electrical power withdrawn from the grid, injected into i,t

the grid by site i at time t [kWe ]. • CapDH , CapDC capacity of district heating and cooling pipeline i,j i,j installed between site i and site j [kW]. • FHi,j,t , FCi,j,t thermal and cooling flow transferred from site i to site j at time t [kW]. • APV surface of the PV panels in every site i [m2 ]. i PV • W PV , Wi,t,SAL electricity generated for self-use [kWe ], electrici.t,SELF ity sold [kWe ], from PV for every site i at time t.

CABS,EC = CRF2



GT ChGT · CapGT · yi,h + h



 B CqB · CapBq · yi,q

q∈B

h ∈ GT

CvABS · CapABS + CfABS · yiABS + CvEC · CapEC + CfEC · yiEC i i



(2) (3)

(4)

i∈I

To get the annualised capital cost, the capital recovery factor (CRF) of each equipment is used, where j is the interest rate and n is the lifetime of each component in years. CRF =

j · (1 + j)

n

(5)

n

(1 + j) − 1

The cost term CP related to the installation of district heating and cooling pipelines is defined as: CP = CRF3





DHC DHC Li,j Cw · CapDH + ClDHC · yhi,j + Cw · CapDC + ClDHC · yci,j i,j i,j



(6)

i,j ∈ I:i
In this case, the pipeline capital cost per length unit is obtained as a linear function of the capacity of pipeline installed (by using DHC and C DHC ); the total cost is then computed by coefficients Cw l multiplying the unitary cost for the length of the pipelines for all the couples of sites. The total investment cost of the PV units is given by:



CPV = CRF1

Cprat · C PV · APV i



(7)

i∈I

The total fuel cost CF can be calculated taking into account of the fuel consumed by the boilers and the gas turbines as follows: CF = t





i∈I t ∈T



GT cf · Fi,h,t

+





Q cf · Fi,q,t

(8)

q∈Q

h ∈ GT

The plant total maintenance cost CM is defined as: CM = t

   i∈I t ∈T

GT GT CM · Wi,h,t +

 q∈Q

h ∈ GT

B B PV PV CM · Qi,q,t + CM · (Wi.t,SELF



PV ABS ABS EC EC + Wi,t,SAL ) + CM · Ri,t + CM · Ri,t

(9)

where it is important to point out that the gas turbine and PV GT , C PV ) are expressed per unit of produced maintenance costs (CM M ABS and C EC are costs per unit of consumed B electricity, whereas CM , CM M primary energy and produced cooling power. The term CG indicates the costs related to withdrawing the electrical power from the grid and the revenues related to injecting the electrical power into the grid, as follows: CG = t

 



b b s s PV cel · Wi,t − cel · Wi,t + Wi,t,SAL



(10)

i∈I t ∈T

3.4. The problem constraints

3.3. The objective function The objective function Obj is the total annual cost for owning, maintaining and operating the plant. It has to be minimized in order to obtain the optimal solution. Obj = min(CC + CP + CPV + CF + CM + CG )



CGT,B = CRF1

• yGT equal to 1 if gas turbine h is installed in site i. i,h • yB equal to 1 if boiler q is installed in site i. i,q

i,t

CC = CGT,B + CABS,EC

(1)

The capital cost of boilers and gas turbines is a function of capacity (variable costs), while the capital cost of chillers is composed of

In the MILP optimization model, three main different types of constraints; energy balances, components constraints and network constraints can be identified. First of all, energy balance constraints are needed to impose the electrical, thermal and cooling power balance for each site in each time interval: el PV b s EC Di,t = Wi.t,SELF + Wi,t − Wi,t − Wi,t +



h ∈ GT

GT Wi,h,t

(11)

M. Ameri, Z. Besharati / Energy and Buildings 110 (2016) 135–148 th Di,t =



GT Qi,h,t +

+



B Qi,q,t −

q∈B

h ∈ GT





Maximum capacity corresponding to a certain pipe diameter is a parameter calculated as shown for district heating (or cooling) in Eq. (31).

FHi,j,t

j ∈ I:i = / j

ABS FHj,i,t (1 − ıh · Li,j ) − Qi,t

(12)

j ∈ I:i = / j

c Di,t

=

ABS Ri,t

EC + Ri,t

−



FCi,j,t +

j ∈ I:i = / j



FCj,i,t (1 − ıc · Li,j )

h ∈ GT,

B B xi,q,t ≤ yi,q

i ∈ I,

q ∈ B,

ABS xi,t ≤ yiABS

i ∈ I,

t ∈ T

EC xi,t ≤ yiEC

i ∈ I,

t ∈ T t ∈ T

t ∈ T

xhi,j,t + xhj,i,t ≤ 1 i, j ∈ I : i < j,

(16)

For CCHP/DHC system, the heating and cooling energy transfer between sites is done through separate pipelines. Thus, similar relations are considered for a district cooling network. The following constraints impose that the electrical power withdrawn from the grid or injected into the grid does not exceed the maximum value:

Other constraints must be introduced to assure that the electrical power generated by gas turbines and the thermal power of boilers is between a minimum and a maximum value:

GT Wi,h,t

≤

GT max Wh,t

GT · xi,h,t

i ∈ I,

i ∈ I,



h ∈ GT,

h ∈ GT,

t ∈ T

(18)

t ∈ T



GT GT GT Wi,h,t + max Wh,t · 1 − xi,h,t − ε ≥ 0 i ∈ I,

(19)

h ∈ GT,

t ∈ T (20)

B ≤ max QqB min QqB ≤ Qi,q,t B B Qi,q,t ≤ max QqB · xi,q,t

i ∈ I,

i ∈ I,



q ∈ B,

q ∈ B,

t ∈ T

(21)

t ∈ T



B B Qi,q,t + max QqB · 1 − xi,q,t − ε ≥ 0 i ∈ I,

(22)

q ∈ B,

t ∈ T

(23)

where ε is a small tolerance. To determine the optimal operation and capacity of absorption chiller in CCHP system, the following formula is used: min RiABS · yiABS ≤ CapABS ≤ max RiABS · yiABS i ABS Ri,t ≤ CapABS i

i ∈ I,

t ∈ T

ABS ABS Ri,t ≤ max RiABS · xi,t

i ∈ I,



 ABS

ABS Ri,t + max RiABS · 1 − xi,t

i ∈ I,

t ∈ T

(24) (25)

t ∈ T

− ε ≥ 0 i ∈ I,

(27)

For compression chiller, similar relations above can be defined. The following constraints regard the pipelines. First of all, it is necessary to impose that the thermal (or cooling) flow is between a minimum and a maximum value: min FHi,j · yhi,j ≤ CapDH ≤ max FHi,j · yhi,j i,j

i, j ∈ I : i < j,

t ∈ T (28)

CapDH i,j

i, j ∈ I : i < j,

t ∈ T

(29)

FHi,j,t ≤ CapDH j,i

i, j ∈ I : i > j,

t ∈ T

(30)

FHi,j,t ≤

t ∈ T

(32)

b Wi,t ≤ max Wib

i ∈ I,

t ∈ T

(33)

s Wi,t ≤ max Wis

i ∈ I,

t ∈ T

(34)

The model with the constant efficiency assumption is a mixed integer linear programming (MILP) problem, whilst the other is a mixed integer nonlinear programming (MINLP) problem, because the performance curves will introduce nonlinear terms into the optimization problem. In this paper, the constraint equations of the model are linear. The energy and cost balances are inherently linear while solar modules, boilers and chillers can be regarded as components with constant efficiency. For boilers, the relation between the fuel primary energy per time unit and the thermal power is defined as follows: B Fi,q,t =

B Qi,q,t

Bq

i ∈ I,

q ∈ B,

t ∈ T

(35)

In order to linearly model both the electric and absorption chiller, the relationship between the input power and output cooling power of chillers is based on a simplified hypothesis of COP. It is assumed to be constant for any value of cooling power produced by the chillers. Thus, the input power required to supply the chillers are expressed by the following ratio for the electric and absorption chiller, respectively:

(26) t ∈ T

(31)

(15)

(17)

GT GT GT min Wh,t ≤ Wi,h,t ≤ max Wh,t

(DDH )2 · c · vmax · TDH 4

(14)

(13)

Moreover, the operational constraints are needed to assure that a gas turbine, boiler, chillers can work only if they have been installed, as follows: i ∈ I,

CapDH = i,j

where  stands for water density (in kg/m3 ), DDH (in m) is the commercial diameter, c is the specific heat capacity of water, vmax is the maximum acceptable water velocity in pipes (m/s) and TDH is the temperature difference between water at the inlet and outlet of the pipe. A final constraint on the pipelines is necessary to impose. In each time interval, it is not possible that a positive heat (or cool) flow is transferred from site i to site j and, at the same time, from site j to site i:

j ∈ I:i = / j

GT GT xi,h,t ≤ yi,h

139

EC Wi,t =

ABS Qi,t =

EC Ri,t

COPE ABS Ri,t

COPA

i ∈ I,

t ∈ T

(36)

i ∈ I,

t ∈ T

(37)

A further technical constraint is imposed to ensure that the absorption chiller is only supplied by the gas turbine: ABS Ri,t

COPA

GT ≤ Qi,h,t

i ∈ I,

t ∈ T,

h ∈ GT

(38)

Fig. 2 shows a performance map of a market gas turbine [32]. Considering the fact that nonlinear relationships between the exhaust gas temperature and power output can be separated into sums and differences of nonlinear functions of single variables, the linearization techniques presented in Ref. [33] are employed, then

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Fig. 3. Map of the residential area.

Fig. 2. Available performance map of a market gas turbine [32].

the linearized performance maps gas turbines are imposed in the following constraints: GT GT GT Fi,h,t = ˛1,h · Wi,h,t + ˛2,h · xi,h,t

i ∈ I,

GT GT GT Qi,h,t = ˇ1,h,t · Wi,h,t + ˇ2,h,t · xi,h,t

h ∈ GT,

i ∈ I,

t ∈ T

h ∈ GT,

t ∈ T

(39) (40)

where ˛1,h , ˛2,h , ˇ1,h,t , ˇ2,h,t used to approximate the gas turbine performance maps with linear functions. PV is assumed to produce electricity in proportion to the capacity of the installed system and the amount of solar irradiation [29], as illustrated in Eqs. (41) and (42). PV PV PV Wi,t,SELF + Wi,t,SAL ≤ Itt · PV e · Ai PV PV Wi,t,SELF + Wi,t,SAL ≤ Cprat · APV i

i ∈ I,

i ∈ I,

t ∈ T

Fig. 4. Electrical, heating and cooling load requirements during the year.

connected with district heating and cooling networks and characterized by different electrical, heating and cooling demand profiles. Fig. 3 represents a map of the whole residential area. The area of the residential town is about 500,000 m2 , and 137 buildings are located in. To estimate the electrical, heating and cooling energy requirement, an energy simulation tool is used (EnergyPlus [34]) based on architectural drawings and raw data of the whole project. The annual variations of electricity, heating and cooling demands are shown in Fig. 4. Fig. 5 shows the consumption profiles for heating, cooling and electricity for the whole year for each of the seven sites used in our case studies. The site M4 is characterized by the highest electrical, cooling and thermal energy consumptions, whereas the M1, M2 and M5 have similar load profiles. The following main assumptions have been made in order to set the problem data:

(41)

t ∈ T

(42)

An additional constraint is needed to prevent the area of PV cells from exceeding the roof area of the each site which faces the sun, as described in Eq. (43). up

APV · cos  ≤ Ai · yiPV i

i ∈ I,

t ∈ T

(43)

where  is a tilt angle for the PV modules (e.g.

30◦ ).

4. Numerical study The optimization model, described in Section 3, has been applied to a residential complex located in the eastern Tehran, the capital of Iran. The seven CCHP systems are composed of some buildings 22000 20000

electricity heang cooling

Annual demand (MWh)

18000 16000 14000 12000 10000 8000 6000 4000 2000 0 M1

M2

M3

M4

M5

M6

Site Fig. 5. Annual electricity and heating requirements for each site.

M7

M. Ameri, Z. Besharati / Energy and Buildings 110 (2016) 135–148

Thermal demand for a typical winter day

Electrical demand for a typical winter day

8000 Thermal demand (kW)

7000 6000 5000 4000 3000 2000

3000 Electrical demand (kW)

M1,M2,M5 M3 M4 M6 M7

141

M1,M2,M5

2700

M3

2400

M4

2100

M6

1800

M7

1500 1200 900 600

1000

300 0

0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Hour Fig. 6. Electrical and thermal energy demand for a typical winter day.

Electrical demand for a typical summer day

Cooling demand for a typical summer day 4200 3900 3600 3300 3000 2700 2400 2100 1800 1500 1200 900 600 300 0

10000 8000 7000

Electrical demand (kW)

Cooling demand (kW)

9000

M1,M2,M5 M3 M4 M6 M7

6000 5000 4000 3000 2000 1000 0

M1,M2,M5 M3 M4 M6 M7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Hour

Fig. 7. Electrical and cooling energy demand for a typical summer day.

• The lifetime of gas turbines, boilers, PV panels and annual interest rate were considered 20 years and 12%, respectively. • The lifetime of chillers, DHC networks and annual interest rate were considered 25, 40 years and 12%, respectively. • Exhaust gas temperature is considered 150 ◦ C at the main chimney of HRSG. • A prudential value of ıh = 15% per km, and ıc = 5% per km has been introduced for the calculations of the heating and cooling networks, respectively. • Maintenance costs have been assumed to be equal to 0.02 and 0.015 $/kWh respectively, for gas turbines and PV systems and 0.013 and 0.001 $/kWh for boilers and chillers. • The exhaust gas mass flow rate from the gas turbine is equal to the HRSG inlet gas mass flow rate. There is not any leakage of the flue gas through the bypass stack. • Coefficients used to calculate the CO2 emissions have been assumed equal to 0.995 (natural gas oxidation factor), 0.2016 kgCO2 /kWhPE (natural gas emission factor) [30], 0.465 kgCO2 /kWhe (emission factor of the national electricity generation system) [37]. The optimization model has been run to determine the optimal configuration and operation of CCHP systems within DHC networks, considering a time horizon composed of typical days. The electrical, heating and cooling load profiles of the sites, for a typical winter day and a summer day, are reported in Figs. 6 and 7 respectively. In order to determine the best possible pipeline network, the distances between any pair of sites are given in Table 1. In Table 2, the nominal power, thermal efficiency and the investment cost of different types of boilers are listed [16]. Table 3 shows the candidate gas turbines assumed in this study and their characteristics [32]. The strength of solar radiation is very important in selecting a location for PV installation. The electricity output of a PV array

Table 1 Distances between sites (m).

M1 M2 M3 M4 M5 M6

M1

M2

M3

M4

M5

0 240 180 350 380 700

240 0 380 380 510 800

180 380 0 300 240 540

350 380 300 0 220 420

380 510 240 220 0 310

M6 700 800 540 420 310 0

M7 670 700 570 340 360 250

Table 2 Characteristics of market available boilers [16]. Type

Investment cost ($/kW)

Thermal efficiency (%)

Nominal power (kW)

B1 B2 B3 B4 B5 B6 B7 B8 B9 B10

13.36 12.59 11.56 11.82 12.59 11.05 11.27 11.05 11.97 11.80

85 86 86 87 87 90 90 90 90 90

1300 1630 1950 2600 3250 3900 4560 5200 6500 7800

Table 3 Nominal performance (at ISOa conditions) and economic data of gas turbines [32].

Output power (kWe ) Electrical efficiency (%) Exhaust flow (kg/s) Exhaust temperature (◦ C) Investment cost ($/kW) a

Taurus60

Centaure50

Centaure40

Saturn20

5200 30.3 22 486 813.8

4600 29.3 19.1 509 835.3

3515 27.9 18.6 437 884.6

1210 24.4 6.45 516 1110.2

ISO: 15 ◦ C (59 ◦ F), sea level, no inlet or exhaust losses, relative humidity 60%.

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M. Ameri, Z. Besharati / Energy and Buildings 110 (2016) 135–148 Table 4 System characters for PV panels and chillers [5,29].

0.6

Irradiaon (kW/m2)

0.5 Winter Summer

0.4

Equipment

Characters

Values

PV unit

Efficiency (%) Rated capacity (kW/m2 ) Capital cost (×102 $/kW)

12 0.15 40

Electrical chiller

Size independent cost ($) Size dependent cost ($/kW) COP

11,357 127.5 4

Absorption chiller

Size independent cost ($) Size dependent cost ($/kW) COP

110,246 173.5 0.8

0.3 0.2 0.1 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour in a day

Fig. 8. Hourly irradiation for typical winter and summer days.

is directly proportional to the radiation input. Local climate and environment factors such as temperature extremes, humidity, precipitation, and wind will constrain the output of the PV array. Nevertheless, these are all secondly effects when compared with insolation intensity. The hourly irradiation for typical winter and summer days of Tehran are shown in Fig. 8. According to this profile, it can be seen that the maximum irradiation is at 11:00 in the late morning. Technical characteristics and costs of the PV system and chillers are given in Table 4 [5,29]. The PV arrays in each site will be installed according to the upper bound on the surface of buildings. The data related to the price of fuel, power sold and power bought from the national power grid and the cost of heating and cooling pipelines are shown in Table 5.

Table 5 Price list [16,35]. Items

Price

Natural gas fuel ($/kWh) Electricity purchased ($/kWh) Electricity sold ($/kWh) DHC network ($/m) DHC network ($/m kW)

0.044 0.2 0.13 328 0.068

Table 6 Optimization results. Scenario

1

2

3

4

Gas turbines (kW) Site M1 Site M2 Site M4 Site M5

0 0 0 0

Suturn20 (1210) Suturn20 (1210) Centaure50 (4600) Suturn20 (1210)

Suturn20 (1210) Suturn20 (1210) Taurus60 (5200) Suturn20 (1210)

Suturn20 (1210) Suturn20 (1210) Taurus60 (5200) Suturn20 (1210)

Boilers (kW) Site M1 Site M2 Site M3 Site M4 Site M5 Site M6 Site M7

B6 (3900) B6 (3900) B1 (1300) B10 (7800) B6 (3900) B3 (1950) B4 (2600)

B3 (1950) B3 (1950) B1 (1300) B1 (1300) B3 (1950) B3 (1950) B4 (2600)

B3 (1950) B3 (1950) B1 (1300) 0 0 B2 (1630) B5 (3250)

B3 (1950) B3 (1950) B1 (1300) 0 0 B2 (1630) B5 (3250)

Absorption chillers (kW) Site M1 Site M2 Site M4 Site M5

0 0 0 0

1725 1725 4742 1725

1725 1725 5332 1725

1725 1725 5332 1725

Electrical chillers (kW) Site M1 Site M2 Site M3 Site M4 Site M5 Site M6 Site M7 PV system (kW)

4853 4853 637 8920 4853 2426 3025 0

3159 3159 637 4246 3159 2426 3025 0

3159 3159 637 3635 3159 2426 3025 0

3159 3159 637 3635 3159 2426 3025 10365

Costs (×103 $) Total investment cost Annual inv. cost Cost of natural gas Maintenance cost Purchase electricity cost Objective function Objf reduction % wrt Scenario 1 PBP (years) CO2 emission (tons) Primary energy consumption (TOE)

5450.32 763.03 896.68 46.36 4709.52 5652.57 – – 30046 7799

13177.57 1844.86 2913.29 131.27 1123.09 4167.66 26.26 5.2 2022 6833

13700.25 1918.036 3108.05 145.27 734.63 3987.96 29.44 4.8 19283 6464

28507.47 3991.04 3108.05 207.38 31.27 3346.76 40.79 9.7 14262 4781

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In order to investigate various aspects that affect the optimal adoption of the CCHP system, as well as the design of the heating and cooling pipeline network, the following scenarios have been studied. • Scenario 1. Conventional system. It is the base scenario which indicates the conventional energy supply system. The electrical load is satisfied by utility grid and thermal load by the gas fired boilers. No CHP technology or heating and cooling piping network are considered. • Scenario 2. CCHP system. CCHP systems can be installed in each production unit, for partially replacing conventional boilers and compression chillers. • Scenario 3. CCHP/DHC system. All CCHP sites are connected with each other through a DHC network. • Scenario 4. CCHP/PV/DHC system. Besides the technologies assumed in Scenario 3, the PV units with a subsidy of 50%, are also considered. The model presented in the previous sections has been optimized for the four aforementioned scenarios by using CPLEX 12.6 solver in AIMMS 4.4 software [36]. Table 6 shows the optimal system configuration for those four scenarios. According to Table 6, no gas turbine is considered, for Scenario 1, and the electricity, heating and cooling demands are served through the grid, gas boilers and electrical chillers, respectively. For Scenario 2, the CCHP system is selected, one gas turbine

Generated thermal power (kWth)

Fig. 9. Optimal plan of CCHP system (Scenario 2).

5000 4000 3000 2000 1000 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Fig. 10. Thermal power generated in M4 for a typical winter day (Scenario 2).

1800 1500 1200 900 600 300 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Fig. 11. Thermal power generated in M1, M2, M5 for a typical winter day (Scenario 2).

of 4.6 MW is installed in site M4, gas turbines of 1.21 MW are installed in M1, M2 and M5 sites, while absorption chillers are selected in any of these sites (see Fig. 9). In the CCHP/DHC system (Scenario 3) the total power installed of gas turbines slightly increases, while the total power installed of the boilers decreases sensibly. In Scenario 4, PV units are allocated in all the sites, since the Iranian governmental policies concerning the electricity buyback price in the residential sector favour their implementation. Therefore, as expected, the result of the optimization algorithm was to invest the maximum possible capacity (about 10 MW) for PV units.

Generated cooling power (kW)

Generated thermal power (kWth)

6000

2100

0

7000 Boiler Gas turbine

Boiler Gas turbine

2400

6000 5500 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0

Electrical chiller

1

2

3

4

5

6

7

8

Absorpon Chiller

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Fig. 12. Cooling power generated in M4 for a typical summer day (Scenario 2).

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Electrical power (kW)

900

M1, M2, M5 M3 M6 M7

800 700 600 500 400 300 200 100 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Fig. 13. Electrical power purchased from the grid for typical winter day (Scenario 2).

Fig. 14. Optimal plan of CCHP/DHC system (Scenario 3).

Comparing the objective functions of the optimal solutions, it can be noted that the adoption of the CCHP/PV/DHC allows the lowest primary energy consumption and CO2 emissions. Nevertheless, the payback period of Scenario 3 is better. In the following, the analysis of the daily optimal operation of the CCHP system is reported taking into account the load profiles of a typical winter and summer day. First of all, referring to the site M4, the thermal power generation profiles are reported in Fig. 10. It is interesting to note that due to the high thermal energy demand

of the M4, the gas turbine is characterized by an elevated utilization factor and especially during the night. The only boiler installed in the M4, having a nominal thermal power of 1300 kWth , runs at hours four and five. The gas turbines of the M1, M2 and M5 are always in operation, but they supply the nominal electrical and thermal power when the thermal load of the buildings is higher (see Fig. 11). The boiler installed in these sites is always at partial load when it is on. The absorption chiller installed in the M4 operates at full load, in

Fig. 15. Thermal flows exchanged among sites.

Table 7 Optimization results of installed district heating pipeline (kW). Site

M5

M6

M7

M3 M4 M5

833 1987 0

0 0 1186

0 1411 0

Generated thermal power (kWth)

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145

1400 Boiler 1200 1000 800 600 400 200 0

Generated thermal power (kWth)

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Fig. 17. Thermal power generated in M3 (Scenario 3).

2400 Generated thermal power (kWth)

accordance with the M4 cooling load profile. Similarly to the boiler in the M1, the electrical chiller installed in M4 is always at partial load (see Fig. 12). It is also interesting to analyze the electricity exchange between each site and the distribution grid, remarking that in the site M4, the electrical energy from the grid is not withdrawn (see Fig. 13). Each site, that has an installed gas turbine, can be considered as an energy producer since a substantial amount of electricity is injected into the grid. This is mainly due to the fact that the cogeneration gas turbines produce a lot of thermal energy and, as a consequence, they generate a lot of electrical energy higher than the electrical load profiles. Hence, the surplus of produced electrical energy is injected into the grid. The main results of CCHP/DHC system (Scenario 3) are shown in Fig. 14, where the number of the gas turbines, boilers, absorption chillers and electrical chillers to be installed in each site is indicated. In particular, the optimization model suggests to install: Suturn20 gas turbine (1210 kWe ) in the M1, M2 and M5 and Taurus60 gas turbine (5200 kWe ) in the M4. About the heating and cooling distribution network, the optimal solution indicates that the installation of only four heating pipelines is profitable; in particular, as shown by the red lines in Fig. 14, the M4 is connected with both the M5 and M7, whereas M5 is also connected with the M6 and M3. Table 7 shows the capacity of installed heating pipeline in Scenario 3. The piping diameter corresponding to these capacities is a parameter calculated for heating pipeline in Eq. (31). In Fig. 15, it is possible to analyze the heat exchange between each couple of sites connected by a pipeline. The M1 and M2 are the sites which do not import heat from the other sites; on the other hand, the heat produced by the CHP unit (gas turbine and HRSG) satisfies all heat requirements of the site M4, since excess heat is transferred through the heating pipeline network from M4 to M7 and M5 to cover their heating loads. Site M5 serves as an intermediate node which transfers heat to site M3 and M6. The thermal power generation profiles of the CCHP/DHC system (Scenario 3) are reported in Figs. 16–18. Now, a CHP unit (gas turbine and HRSG) is allocated in site M5 (1210 kWe ). Since in site M3, no CHP unit is installed, the heating demands are satisfied from the heat transferred from M5 through the heating network (M5 is an intermediate node in the connection from M4 to M5). The gas turbines of the M1, M2 are always in operation. They supply the nominal thermal power when the thermal load of the buildings is higher (see Fig. 16). The boilers installed in these sites are always at partial load when they are on. Finally, the only gas

Gas turbine 2100 1800 1500 1200 900 600 300 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Fig. 18. Thermal power generated in M4 (Scenario 3).

turbine installed in the M4 operates at full load in accordance with the M4 thermal load profile. Table 8 shows installed capacity of photovoltaic system in each site for CCHP/PV/DHC system (Scenario 4). Fig. 19 shows the electricity balances for Scenario 4 considering a typical winter day in site M1. The gas turbines often supply the maximum electrical power (sum of generated for use and sold to the grid). For the PV units, most of electricity produced is sold to the grid, taking advantage of the high buy-back price, while the rest is used for self-satisfaction. In this site, buying electricity from the grid is only at 6 o’clock. In the site M4, the whole electricity produced by PV system, is sold to the grid (see Fig. 20). Fig. 21 summarizes the electricity balances for the Scenarios 2–4 considering typical winter and summer working days. In the 2nd scenario, the electricity loads of the seven sites are satisfied by electricity purchased from the grid and electricity generated by the CHP units, which are used not in sites M3, M6 and M7. In the 3rd scenario by using the district heating (DH) network between the sites, electricity purchased from the grid is reduced and electricity sales to the grid increases. In the 4th scenario, power demand is almost evenly covered by electricity produced by the CHP unit for self-use, electricity produced by PV arrays for self-use and power purchased from central grid. The implementation of the CCHP/PV technologies in the 4th scenario with the installation of the heating and cooling pipeline network leads to a 10% reduction of purchased electricity from the grid compared to the 3rd scenario.

Boiler Gas turbine

2400 2100

Table 8 Installed capacity of photovoltaic system for Scenario 4.

1800 1500 1200 900 600 300 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Fig. 16. Thermal power generated in M1 and M2 (Scenario 3).

Site

Surface of PV arrays (kW equivalent)

M1 M2 M3 M4 M5 M6 M7

16,000 (2400) 16,000 (2400) 1600 (240) 19,500 (5200) 16,000 (2400) 8000 (1200) 8000 (1200)

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M. Ameri, Z. Besharati / Energy and Buildings 110 (2016) 135–148 2200

Kw

2000 1800 1600 1400

Purchased electricity from the grid

1200

Electricity Sold to the grid from PV

1000 800

Electricity Generated for use from PV Electricity Sold to the grid from CHP

600 400

Electricity Generated for use from CHP

200 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour

Fig. 19. Electrical balance for site M1 for the 4th scenario in winter.

6400 5600 4800 Purchased electricity from the grid

Kw

4000

Electricity Sold to the grid from PV

3200

Electricity Generated for use from PV

2400

Electricity Sold to the grid from CHP

1600

Electricity Generated for use from CHP

800 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Fig. 20. Electrical balance for site M4 for the 4th scenario in summer.

Furthermore, a comparative study has been done in order to quantify the benefits, in terms of economic saving and CO2 emission reduction, of having a combined cooling, heating and power distributed generation system in buildings in spite of using boilers to produce heat and of buying electricity from the grid. Fig. 22 illustrates the economic results for the four scenarios. The left figure presents the annual investment cost for those scenarios. It is clear that the annual investment costs for Scenarios 2–4 are increased by the factor of 1.4, 1.5 and 4.2 with respect to the conventional one. The right figure shows the energy costs. The conventional system (Scenario 1), has an energy cost of 5652 k$. Compared with the conventional system, the annual energy costs of Scenarios 2 and 3 are reduced by 26.2% and 29.4%, respectively.

Scenario 2

The high reduction in 4th scenario (40.7%) is mainly due to the high electricity sales by the PV unit in a very profitable buy-back price, according to Iranian governmental policy. In order to correctly compare the four scenarios, the costs, CO2 emission and primary energy associated with the electricity injected into the grid in the optimized scenarios have not been considered. Fig. 23 illustrates the CO2 emissions and primary energy consumption for the four scenarios. The implementation of the CCHP technologies in the 2nd scenario as well as in the 3rd scenario with the installation of the DHC network, leads to a 32% and 35.8% reduction of emissions compared to the conventional scenario respectively. The additional consideration of the PV units in the 4th scenario reduces the CO2 emissions by 52.6% compared to the conventional scenario.

Scenario 3

Electricity Generated for use from CHP 34% 48% 18%

Electricity Sold to the grid from CHP

Electricity Generated for use from CHP 31% 43%

Purchased electricity from the grid

26%

Scenario 4

Electricity Generated for use from CHP Electricity Sold to the grid from CHP

21% 40%

6% 8% 25%

Electricity Generated for use from PV Electricity Sold to the grid from PV Purchased electricity from the grid

Fig. 21. Electricity balance for Scenarios 2–4.

Electricity Sold to the grid from CHP Purchased electricity from the grid

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Fig. 22. Investment and energy costs for the scenarios.

Fig. 23. CO2 emissions and primary energy consumption for the scenarios.

5. Conclusion The paper presents a MILP model for the optimization of complex distributed energy systems, based on the different types of production units that can be applied to residential users. The model can be used to identify the opportunities for the integration of photovoltaic and district heating and cooling systems. Moreover, it provides the optimal size and operation of each component, in particular of the gas turbines, boilers, chillers, PV units and of the DHC networks. In fact, all the potential benefits of complex cogeneration plants can be actually enjoyed only if the synthesis, design and operation of the whole integrated system are consistently optimized. The objective function of the optimization model is relative to capital and operational costs. As an illustrative example, the optimal CCHP/PV/DHC system of a residential complex of seven sites, in Tehran (Iran) is examined under different scenarios, thus demonstrating the applicability of the proposed optimization based approach. By applying the model to a real residential town situation, it shows that trigeneration system (CCHP) with district heating and cooling network is economically and environmentally profitable with respect to simple cogeneration system. The lowest energy cost is reached with the adoption of a solar PV and CCHP system, which includes the district heating and cooling network. This solution allows a 40.8% reduction of the energy cost with respect to the conventional solution and a 38.7% reduction of the primary energy consumption. Scenario 3 (CCHP/DHC) has the lowest payback period (57 months) and allows to save 35.8% of emissions compared to the conventional scenario. In conclusion, the adoption of the optimized cogeneration which includes PV and DHC system allows to reduce significantly both the energy supply cost and the primary energy consumption.

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