Optimization of a Distributed Cogeneration System with solar district heating

Applied Energy 124 (2014) 298–308

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Optimization of a Distributed Cogeneration System with solar district heating Dario Buoro a, Piero Pinamonti a, Mauro Reini b,⇑ a b

Electrical, Management and Mechanical Engineering Dept., University of Udine, via delle Scienze 208, 33100 Udine, Italy Engineering and Architecture Dept., University of Trieste, via Valerio 10, 34127 Trieste, Italy

h i g h l i g h t s  Definition of a multi objective optimization model for a distributed renewable energy supply system.  Distributed Cogeneration System integrated with central solar field and long term heat storage.  Optimization of an industrial area energy system from environmental and economic points of view.  Investigation of the electricity carbon intensity variation on the optimal system configuration.

a r t i c l e

i n f o

Article history: Received 2 January 2013 Received in revised form 19 February 2014 Accepted 24 February 2014 Available online 3 April 2014 Keywords: Cogeneration Distributed renewable system Distributed energy system Seasonal thermal storage Solar field

a b s t r a c t The aim of the paper is to identify the optimal energy production system and its optimal operation strategy required to satisfy the energy demand of a set of users in an industrial area. A distributed energy supply system is made up of a district heating network, a solar thermal plant with long term heat storage, a set of Combined Heat and Power units and conventional components also, such as boilers and compression chillers. In this way the required heat can be produced by solar thermal modules, by natural gas cogenerators, or by conventional boilers. The decision variable set of the optimization procedure includes the sizes of various components, the solar field extension and the thermal energy recovered in the heat storage, while additional binary decision variables describe the existence/absence of each considered component and its on/off operation status. The optimization algorithm is based on a Mixed Integer Linear Programming (MILP) model that minimizes the total annual cost for owning, maintaining and operating the whole energy supply system. It allows to calculate both the economic and the environmental benefits of the solar thermal plant, cooperating with the cogeneration units, as well as the share of the thermal demand covered by renewable energy, in the optimal solutions. The results obtained analyzing different system configurations show that the minimum value of the average useful heat costs is achieved when cogenerators, district heating network, solar field and heat storage are all included in the energy supply system and optimized consistently. Thus, the integrated solution turns out to be the best from both the economic and environmental points of view. Ó 2014 Published by Elsevier Ltd.

1. Introduction Distributed cogeneration and trigeneration systems integrated with renewable energy systems allow achieving economic and energy savings, both in residential and industrial sectors [1]. Especially considering a set of industrial users, characterized by quite constant and high energy consumptions all year long, the ⇑ Corresponding author. Tel.: +39 3497974427. E-mail addresses: [email protected] (D. Buoro), [email protected] (P. Pinamonti), [email protected] (M. Reini). http://dx.doi.org/10.1016/j.apenergy.2014.02.062 0306-2619/Ó 2014 Published by Elsevier Ltd.

adoption of such smart a solution can lead to increase the whole energy efficiency of the system and thus to reduce costs, primary energy usage and polluting emissions. 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 [2–9]. The problem concerning with the optimization of complex distributed energy supply systems, including also Combined Heat and Power (CHP) and Combined Cooling Heat and Power (CCHP) systems was dealt with by Sakawa et al. [10] and by Weber et al. [11], while other references are available dealing with the optimal

D. Buoro et al. / Applied Energy 124 (2014) 298–308

299

Nomenclature

gboi ABS ATES BOI BTES CCHP C dem C el cep ces C fr cgas C heat CHP C inv C man COP C ope CS DCS DHN DRS Edem Ep Es

Boiler efficiency Absorption chiller Aquifer thermal energy storage Boiler Bore hole thermal energy storage Combined Cooling Heat and Power System Cooling demand Annual cost of electricity purchased in the conventional situation (€/y) Purchase price of electricity (€/kWhel) Sale price of electricity (€/kWhel) Annual cost of cooling energy produced in the conventional situation (€/y) Purchase price of natural gas (€/kWhth) Average heat cost (€/kWhth) Combined Heat and Power System Annual investment cost (€/y) Annual maintenance cost (€/y) Coefficient of performance Annual operating cost (€/y) Conventional system Distributed Cogeneration System District heating network Distributed renewable system Total electrical demand (kWhel/y) Purchased electricity (kWhel) Sold electricity (kWhel)

design of district heating systems [12–15]. However, these optimization models generally consider residential users, rather than industrial ones as presented in this paper. In addition the solar thermal plant, possibly integrated with a long term storage, is generally taken into account as an alternative to CHP systems, so that the optimization deals only with one of the two solutions. An example of optimization models for industrial energy systems is proposed by Karlsson [16], a district heating networks is introduced by Chinese et al. [17], Lozano et al. [18] presents the thermoeconomic cost analysis of central solar heating plants, combined with a seasonal storage, while Barbieri et al. [19] analyze the incluence of the thermal energy storage size for micro-CHP systems. The current study presents the optimization of a distributed energy supply system, designed to satisfy the thermal, cooling and electrical demands of nine industrial facilities located in the northeast of Italy. The paper introduces the integration between conventional power sources and renewable energies in an industrial area, designing a solar district heating plant coupled with long term storage. This alternative is increasing in importance, as it is a valid solution to overcome the mismatch problem between the availability of the solar source and the energy user’s demand in the residential sector [20–22]. The aim of the paper is to understand if the integrated solution is still valid for industrial utilities characterized by the heat demand less affected by seasonal variations all year long, by means of the optimization of the synthesis, design and operation of the whole system. The results of the optimizations have been used to identify the heat average costs associated with different plant configurations. In the presented optimization the electrical energy, cold water and heat demands are known in advance and the layout and the size of the heating network is fixed. Notice that a model quite similar to the one presented in this paper can be used for optimizing DHN design too [23–27]. This paper differs from the previews ones as integrates renewable sources which was never considered in

ETC Fg FPC Hdem i ICE Inv IS j k MILP MTG n Obj PBP PES PTES Rdem REF rf R SDH STOR t TG TTES

Evacuated tubular collectors Natural gas consumption (kWh) Flat plate collectors Total thermal demand (kWhth/y) Interest rate Internal combustion engine Total investment cost (€) Isolated systems Technology User, coefficient Mixed Integer Linear Programming Microgas turbine Life span Objective function (€/y) Pay back period Primary energy saving Pit thermal energy storage Total cooling demand (kWhco/y) Mechanical chiller Capital recovery factor (y1 ) Thermal loss coefficient Solar District Heating Heat storage Time interval Gas turbine Tank thermal energy storage

previews studies. All users can be connected to each other through the DHN, therefore the related production units may send heat to other users through the DHN as well as to the storage. Moreover, only the production units related to users requiring cooling energy can be equipped with absorption chillers driven by cogenerated heat. The solar thermal plant is also part of the superstructure and it produces thermal energy that can be sent either to the users or to the long term storage. Heat and electric power can be provided either by a large centralized CHP plant (internal combustion engine ICE) or by small-scale CHP systems (ICE or micro gas turbines MTG), properly located close to, or inside, the factories. Conventional boilers and vapor compression chillers can also be installed inside the factories or in the centralized plant, and each unit is connected to the electricity network. The optimal solution is a compromise that depends on many variables; therefore it is very difficult to find the best solution without solving an optimization problem. In previous works of the authors, MILP models have been developed to optimize the design and operation of distributed CCHP systems in a tertiary sector scenario, considering different technologies and taking into account the effects of various economic support policies [23–26]. A similar model has been applied to an industrial area considering also the thermal inertia of the network in [28]. In this study, the integration between distributed energy supply system, solar thermal plant and heat storage is introduced, applying the model to an industrial scenario with the aim of determining which is the best configuration and operation in terms of both economic and environmental benefits, and how it is affected by the thermal storage heat losses. The model used to solve the optimization problem is based on a MILP algorithm. The objective function takes into account the total annual cost for purchasing, maintaining and operating the whole distributed energy system. The optimization is subject to the constraints that express components operation characteristics, energy

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balances of nodes, and economic boundary conditions (e.g. incomes from the sale of electricity, prices of fuel and electricity, etc.). The optimization specifies the size, the kind and the location of cogeneration equipment, absorption machines, integration boilers and compression chillers present in the system superstructure, the size of the solar thermal power plant and of the heat storage as well as the optimal operation of each component inside the optimal solution. The conventional solution (CS) is also a possible option of the optimization: all the electricity would be bought from the grid, the thermal energy would be produced by boilers and the cooling energy by compression chillers, which are driven by electricity bought from the grid. The model has been used to obtain the optimal solution in different configurations of the energy system, comparing the CS with other interesting cases that comprehend isolated sites (IS), with CHP and CCHP systems in the units, distributed CHP systems (DCS) connected with a DHN and finally a distributed renewable system (DRS), with solar thermal field and heat storage. The DRS optimization model has been optimized for different sizes of the solar field and for different value of the storage thermal loss coefficient, in order to identify the size plant range that allows the heat cost to be reduce compared with the other situations. 2. Optimization model The model intends to provide a support for the identification of the optimal system configuration from the economic point of view. Recently a lot of research has been carried out to optimize the design and operation of distributed energy supply systems [29–31] integrated also with the district heating network [3,2,32–34]. The mathematical problem of optimizing the operation of an energy system composed of CHP/CCHP systems, solar thermal modules and DHN has to be generally regarded as a variational calculus problem because the optimization variables expressing partial load operation of each CHP engine are time dependent. However, a realistic description of the system may be represented by a MILP formulation by properly discretizing the load curves (in each time interval the thermal and the electrical demands are assumed to be constant) and approximating performance maps with a set of linear functions [35–37]. Even if this kind of linear, quasi-stationary model necessarily introduces some approximations, it generally implies a very small variation in the optimal annual cost, compared with more refined models, which take into account the non-linear behavior of components during transient [38]. In the present model the thermal losses along pipelines have been approximated as a fixed fraction of the thermal energy transferred in each time interval [9]. All other relations that describe the system (energy balances, load limits, cost of energy carriers) are intrinsically linear and they do not need to be approximated [39]. A detailed description of the model and the approximation introduced with the linearization of the performance curves can be seen in [27]. As mentioned in the introduction, the nine facilities involved in the study together with the central production unit can be connected to one another through a DHN of a predefined layout and size. The user energy demands are known in advance, as well. All users can transfer heat to and from the network, exchange heat with the long term storage as well as exchange electricity with the electric grid. Fig. 1 shows the system superstructure described by the model. A typical user k can be equipped with a cogenerator, a boiler, an absorption chiller and a compression chiller. The central unit includes a cogenerator, a boiler and a solar field. The district heating network connects all users to each other and to the heat storage. 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,

changing the values that describe the components and the energy demands. In a distributed generation context, the optimal solution depends on the trade-off between economies of scale, which play in favor of the centralization option, and the thermal dissipation, which play in favor of decentralized solutions. In this second case the adoption of absorption chillers integration in various units may be considered. A MILP model has been used for properly describing by means of binary variables the choice of centralized/decentralized components inside the system superstructure, as well as the on/off operation of chosen components, in the optimal operation strategy. 2.1. Decision variables The degrees of freedom that characterize the model are the decision variables, either binary or continuous. The optimization procedure finds the set of decision variables that allows the minimization of the objective function. The identified decision variables 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 flows inside the district heating network. – Size of the thermal energy storage. – Level of the thermal energy stored in the storage. Binary variables represent existence and operation status of components, while all other variables are continuous. The decision variables can be set by the designer to describe cases when only a subset of the components included in the superstructure is used. For example in the CS the district heating network has to be excluded by setting to zero the decision variable related to its existence. 2.2. 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. The objective function is linear with respect to all decision variables and is a linear combination of: – Annual investment cost of all components C inv . – Operating and maintaining cost C ope .

Obj ¼ C inv þ C ope

ð1Þ

The sum of the investment costs of all components (Inv) multiplied by the related capital recovery factor rf gives the annual investment cost C inv . Capital recovery factor takes into account the interest rate i and the life span n of each components j contained in the superstructure.

C inv ¼

X rf ðjÞ  Inv ðjÞ

ð2Þ

j nðjÞ

rf ðjÞ ¼

i  ð1 þ iÞ ð1 þ iÞ

nðjÞ

ð3Þ

1

The whole year has been subdivided in a set of discrete time intervals t. The annual operating and maintaining cost C ope associated to the energy supply system is expressed by:

C ope ¼

X  X cgas  F g ðtÞ þ cep  Ep ðtÞ  ces  Es ðtÞ þ C man ðj; tÞ t

j;t

ð4Þ

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

The maintenance cost C man ðj; tÞ of the jth component in the tth time interval is proportional to the energy produced [17,40]. 2.3. Model constraints In the MILP optimization model, three main different types of constraints can be identified: – Components constraints: relating output and input energy of each component. – Energy balances: ensuring that the amount of input energy is equal to the output, for each time interval and for each node. - Network constraints: describing thermal losses and the maximum thermal energy transfer from units to users. 2.3.1. Component constraints This kind of constraints have been introduced for each component. Equality constraints represent the relation between fuels, products and sub-products, while inequality constraints describe the load and size ranges. The thermal production of the solar thermal plant is related to the size of the plant. The energy production per surface unit has been supposed to be known in advance, for each time interval. This means that position and tilt angle are fixed. A long term thermal storage is considered a component too, and the equality constraints relate the thermal level of the storage to the input/output flow, taking into account the thermal losses. The stored energy depends on the temperature of the medium multiplied by the volume contained in the storage, so that volume and temperature cannot be both decision variables because each relation inside the model has to be linear. The volume has been chosen as a decision variable, while the temperature is considered constant. This choice corresponds to the hypothesis of a perfect stratification of the fluid inside the heat storage, so that if the storage is not completely empty the residual energy is stored at the same temperature required by the DHN. 2.3.2. Energy balances These constraints are equality constraints and represent the thermal, cooling and electric energy balances in each time interval. Taking the thermal balance as an example, for each production unit the heat produced by the cogenerator and by the boiler has to be equal to the heat used by the absorption chiller, consumed by the local user and sent to other users through the DHN. 2.3.3. Network constraints These constraints describe the DHN and limit the thermal flows in each pipeline based on its size. Moreover they represent the thermal energy balance of the network taking into account the thermal losses along each pipeline.

2.4. Average heat cost evaluation In the considered integrated system, conventional boilers, CHP systems and the solar system may cooperate together for the satisfaction of the required thermal demand. From this point of view, the effect of the solar system on the global performance can be highlighted by evaluating the average heat cost. The actual cost of the heat required by the users can be evaluated for each optimal solution by subtracting the electricity and cooling energy cost of the conventional situation from the objective function. Therefore the average heat cost C heat is:

Obj  C el  C fr C heat ¼ P k;t Hdem ðk; tÞ

ð5Þ

The cost of electricity and cooling energy of the conventional solution has been evaluated as:

C el ¼ cep 

X

Edem ðk; tÞ

ð6Þ

k;t

C fr ¼ C inv ;REF þ C man;REF þ cep 

X C dem ðk; tÞ k;t

COPðkÞ

ð7Þ

Notice that the minimization of the objective function correspond to the minimization of the average heat cost C heat because C el ; C fr ; Hdem are constant for the specific set of users. Eq. (5) holds for all different considered configurations. In the particular conventional situation the following Eq. (8) can be obtained, as it was expected.

C inv ;BOI þ C man;BOI cgas C heat ¼ P þ gboi k;t Hdem ðk; tÞ

ð8Þ

3. The case study The nine users considered in the study belong to different industrial sectors, such as plastic, food, furniture, engineering and tertiary. Despite the heterogeneity of the goods produced, the energy consumption shows quite regular trends throughout the year. The electrical, heating and cooling demands have been evaluated by means of energy audits. Fig. 2 represents a map of the whole industrial area. The blue line represents the layout of the main DHN that is 5 km long and provides the heat at 70 °C. This temperature seems to be quite low for conventional DHN, but for solar application, also lower temperatures are often considered [21,41]. The locations of the nine users are marked with red spots, while the yellow spot indicates the space available for positioning the central unit and the solar thermal storage. Fig. 3 shows the annual electric, heating and cooling load duration curves of the nine users. Electric load is higher than zero all

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Fig. 2. Map of the industrial area.

Fig. 3. Total users energy duration curves.

year long. This is because a certain amount of electricity is always required, even when factories are closed. Heating load is higher than zero for about 7000 h, higher than 2 MW for almost 6000 h and higher than 4 MW for almost 3000 h. Cooling load is also higher than zero all year round because of the presence of two food companies that must always keep the food refrigerated. Fig. 4 shows the aggregated electric demand of the nine users during 2 weeks, one in the winter and the other in the summer. These weeks are considered as typical weeks in the following, as they are representative of the different winter and summer energy demand. Figure shows the aggregated electric demand of the nine users in a typical winter and summer week. The profile is quite

Fig. 4. Total electric demand profiles in a typical winter and summer week.

predictable, with peaks during intensive working hours, low consumption during nights and a very low demand in the weekend, when the most of the factories are closed. The two trends are very similar; the difference is a higher consumption in summer because of the electricity required to power the air conditioning systems of the factories. Fig. 5 shows the aggregated heating demand of the nine users in a typical winter and summer week. It can be noted that heating load is slightly higher during winter week, when space heating is operating. The Saturday heat consumption is very small, while in Sunday neither process heat nor space heating is required. Fig. 6 shows the aggregated cooling demand of the two food factories in a typical winter and summer week. The two trends are

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Fig. 5. Total heating demand profiles in a typical winter and summer week.

Fig. 6. Total cooling demand profiles in a typical winter and summer week.

very similar but the summer peaks are double if compared to the winter ones, because of the ambient temperature difference between the two seasons. Table 1 reports the peak power and the annual energy demand data of each user. Total peak power is the maximum hourly energy demand of the all users and it is lower than the sum of the single user peak. The whole year has been represented by 8064 time intervals, considering as an approximation 12 months composed by 28 days per month and 24 hours per day. This approximation is required to reduce significantly the decision variable numbers, by making months with the same number of days. The problem is considered quasi stationary and in each time interval all values and decision variables are constant. Fig. 1 shows the structure of a general user, connected to the DHN, to the electric grid and equipped with all the necessary machinery considered in the optimization. Considering the specific user energy demands the following equipment has been chosen for each unit. In the centralized unit a cogenerator and a boiler can be adopted. Unit 1 can incorporate a CHP system directly connected

with an absorption chiller (which cannot be driven by heat from the network due to the different temperature levels), a boiler and a compression chiller. User 2 does not require heating energy, so a boiler has not been included in the model. In this unit a compression chiller and an absorption chiller, which can be only powered by cogenerated heat, are included. The remaining production units have the same structure and include only a CHP system and a boiler (of variable sizes) because they do not require cooling energy. A preliminary analysis of the user energy requirements, shown in Table 1, has led to Table 2 that shows the minimum and maximum sizes and costs of the components considered in the optimization procedure, their life span and where the machines can be installed. MTG of fixed size have been considered for unit 1, 3–6, while the size of ICE in unit 2, 7–9 and of all boilers are decision variables of the optimization. The component prices have been considered linear with the size. For simplicity in the MILP model formulation, the maintenance costs for all cogenerators have been considered equal to 0.022 (€/kWhel), even if in this way the maintenance costs for MTG are slightly overestimated. This is not expected to strongly affect the optimal configuration, because the choice concerning CHP technologies has been made in advance for each production unit. Maintenance cost of 0.001 (€/kWhth) has been assumed for boilers, absorption machines and chillers. The evaluation of the system operative cost generally needs the hourly costs of the energy vectors to be defined as both input and output. The price of bought and sold electric energy has been assumed constant (in previous works [23–26,28] the hourly variation of prices did not affect the optimal solution). This choice is consistent with the real situation where the energy market determines the energy prices, without being affected by individual market operators. Table 3 shows the energy prices and the solar plant costs used in the application, with reference to a current Italian market scenario. A life span of 20 years is considered for the solar thermal panel and 40 years for both the DHN and the seasonal storage. The unitary heat storage cost generally depends on its kind, size and insulation, and can vary between 120 €/m3 and 180 €/m3 [42]. For the study 150 €/m3 has been assumed for a thermal loss coefficient k = 2 kJ/h m2 K, and 170 €/m3 for a thermal loss coeffiecient k = 0.45 kJ/h m2 K. Intermediate costs have been obtained by data linear interpolation. The interest rate assumed for the calculation of all capital recovery factors has been assumed equal to 6%.

4. The solar district heating system A DHN is an efficient way of providing heat to residential and industrial buildings, especially in countries where the heating season lasts longer. Most commonly, the prime engine of the thermal plant consists of a cogenerator. Recently some ‘‘smart’’ alternatives utilizing renewable energies are getting consensus as integration

Table 1 User’s energy demand data. Users

1 2 3 4 5 6 7 8 9 Total

Electric

Heating

Cooling

Peak power (kWel)

Year dem. (MWh)

Peak power (kWth)

Year dem. (MWh)

Peak power (kWhco)

Year dem. (MWh)

945 1181 801 652 742 652 2298 4774 1283 9636

4358 5152 1607 3147 3039 1713 8915 138,718 4819 45,021

518 – 686 996 516 136 2976 3720 387 6618

393 – 1008 1700 790 115 4453 14,956 119 23,537

836 1697 – – – – – – – 2391

3122 7753 – – – – – – – 10,875

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Table 2 Component costs and sizes. Component

Size (kW)

Cost (k€)

Units

Life span

Efficiency

ICE TG MTG Boiler ABS chiller Compr. chiller

300–4000 500 30–300 100–2500 900–1700 900–1700

350–3000 500 70–160 8–50 260–400 125–240

2, 1 3, 1, 1, 1,

15 15 15 15 20 10

gel ¼ 35  43% gel ¼ 38% gel ¼ 27  32% gth ¼ 95%

Table 3 Eenergy and solar thermal plant prices. Price Electricity purchased Electricity sold Natural gas DHN Heat storage Solar thermal panel

0.15 €/kWh 0.12 €/kWh 0.05 €/kWh 4500 k€ 150 €/m3 200 €/m2

to the CHP system. Considering the specific application presented in this paper, where users require low temperature heat (70 °C), the most interesting renewable source is solar energy. Among others, it also has the advantage of being a clean and safe source. Many large scale SDH systems have been built in central and northern Europe, mainly in Sweden, Denmark, Nederlands, Germany and Austria [43]. They consist of large collector fields integrated into a DHN for supplying heat to residential and industrial areas. The sizes of those plants allow lower specific investment costs compared to small applications. When the system is coupled with a seasonal heat storage it is possible to reach solar coverages of approximately 50% [44]. In a central solar district heating system the solar thermal field feeds in at the central node of the district heating network (see Fig. 1). The collector field is typically ground mounted close to the heating plant, as well as the large long term storage. Alternatively, in a distributed SDH system, the collectors are roof mounted on buildings at any place of the DHN and the heat is transferred to the heating plant via a collecting grid [45]. The most common collector types used in SDH applications, are evacuated tubular collectors (ETC) and flat plate collectors (FPC) without vacuum. Concentrating collectors (e.g. parabolic trough, Fresnel, etc.) may also be used, but they are not suitable for this application [46] because they cannot take advantage of the diffused irradiation, which is a large part of the total annual irradiation. Concerning the large scale heat energy storages, four main types are employed worldwide: – – – –

tank thermal energy storage (TTES); pit thermal energy storage (PTES); bore hole thermal energy storage (BTES); aquifer thermal energy storage (ATES).

The decision to use a certain type of storage depends mainly on its heat capacity and on the geological condition of the site. Exploiting the solar thermal energy is an effective opportunity for this specific application, considering that the location is characterized by a quite high solar irradiation and that the industrial users require low temperature heat. Furthermore, a SDH plant combined with the installation of a proper size storage is of great importance for effective use of the intermittent solar radiation [20]: the surplus of heat available during high irradiation periods can be stored for heat demand periods with low solar fraction (e.g. during night or in winter time). At the same time, the annual operating hours of the cogenerator increase: heat can be produced

7, 8, 9 Central 4, 5, 6 3, 4, 5, 6, 7, 8, 9, Central 2 2

COP = 0.7 COP ¼ 2:5  3:5

when heating demand is lower (e.g. during night or weekend), stored and then used when the request is higher [47]. This operation has significant energy and economic advantages, firstly thanks to the solar thermal system and secondly because the CHP guarantees a reduction in primary energy consumptions in comparison to the separate production of heat and power [48]. It is therefore necessary to perform a system optimization to identify the best configuration and the operation strategy that allow minimizing the objective function and the heat cost. 5. Results and discussions The model presented in previous paragraphs has been optiÒ mized by means of the commercial software X-press [49] in several cases: – Conventional solution (CS). – Isolated solution (IS): CHP and CCHP systems can be installed in each production unit, for partially replacing conventional boilers and compression chillers. – Distributed Cogeneration Solution (DCS): all users are connected each other through a DHN and CHP and CCHP systems can be adopted in each production unit. – Distributed renewable solution (DRS): as the former one, but with the addition of a centralized solar thermal plant and a thermal storage. The DRS has been optimized for different sizes of the solar field and for different values of the thermal loss coefficient related to the storage. The thermal loss coefficient R of the storage has been considered proportional to the energy contained in the storage in each time interval and it ranges between R ¼ 0:5% (value which approximate a real thermal loss K ¼ 2:00 kJ=h m2 K) and R ¼ 0:07% (value which approximate a real thermal loss K ¼ 0:45 kJ=h m2 K). The average heat annual cost computed for the conventional situation is equal to 5.47 c€/kWh. Fig. 7 shows the average heat cost obtained for the different cases analyzed varying the solar plant size and the storage thermal loss coefficient. The highlighted points A–D indicate the optimal solution for different values of the thermal loss coefficient. Fig. 7 shows that the isolated system is the best solution if solar plant cannot be adopted. Furthermore, the optimal solution with the DHN (DCS) is not economically convenient compared to the isolated solution. The integration of the DCS with the long term storage (DRS at 0%) allows a reduction in the average heat cost, but this optimal solution is still not convenient if compared to the IS. Only the integration of the solar thermal plant allows a reduction of the average heat cost with respect to the IS. In this case, a reduction of the thermal loss implies a reduction of the average heat cost. The optimal size of the solar plant depends on the thermal loss coefficient assumed, but generally the optimal solar plant produces between 55% and 60% of the annual thermal demand. Larger solar plants are not convenient because they require greater investment cost, which are not paid back by a real

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Fig. 7. Average heat cost for different cases, varying the solar plant size and storage thermal loss.

reduction of the thermal energy produced by fossil fuel equipment. Moreover, if longer thermal storage cycles were adopted, the thermal losses through the storage wall would be grater, so that

a greater amount of the thermal energy recovered by the solar plant would be lost. Table 4 shows the results of the optimization for cases IS, DCS and DRS varying the thermal loss coefficient R. In the IS at least a boiler or a cogenerator is installed in each production unit, to provide the thermal energy required. In the DCS the total power installed of cogenerators and boilers slightly decreases, while in the DRS, thus considering the solar plant, the total power installed decreases sensibly. Also the variation of the thermal loss coefficient R affects the total power installed, and for the case DRS D the boilers are not included in the optimal solution. The volume of the storage adopted in the DRS optimal solutions ranges between 3100 and 4000 m3. Storages of these dimensions are classified as tank thermal energy storage (TTES) and they result very small if compared to seasonal thermal storage of other solar district heating plants [50]. In this application case study, the optimal solar plant produces about 14,000 MWh/y which is about 55% of the total annual thermal demand. Comparing the objective functions of the optimal solutions it can be noted that the adoption the DRS allows the lowest total annual cost when the lowest thermal loss (DRS D) is assumed. The adoption of the optimal solutions allows a reduction of the total

Table 4 Optimization results. IS

DCS

DRS A

DRS B

DRS C

DRS D

Cogenerators (kW) Central unit Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

– – 826 – 300 – – 2140 1933 –

– – 909 – 300 – – 822 1600 376

– – 918 – – – – 413 874 229

– – 923 – – – – 408 848 211

– – 918 – – – – 396 635 168

– – 913 – – – – 398 657 172

Boilers (kW) Central unit Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

– 518 – 686 – 516 136 758 1588 387

– 360 – 280 346 529 241 398 – –

– – – – 511 – – – – –

– – – – 217 – – – – –

– – – – 51 – – – – –

– – – – – – – – – –

Absorption chillers (kW) Unit 1 Unit 2

900 1700

900 1700

900 1700

900 1700

900 1700

900 1700

Compression chillers (kW) Unit 1 Unit 2 Heat storage size (m3) Solar field (MWh/y)

– 1700 – –

– 1700 – –

– 1700 3150 13,130

– 1700 3289 14,110

– 1700 3883 14,310

– 1700 3922 14,820

Total investment cost (k€) Annual inv. cost (k€/y) Purchase electricity cost (k€/y) Sold electricity income (k€/y) Cost of natural gas (k€/y) Maintenance cost (k€/y) Operating cost (k€/y)

3699 529 4153 262 3333 525 7750

8259 876 3946 228 3319 558 7594

9896 972 4847 53 2090 368 7252

8865 967 4891 47 2041 360 7245

10,218 990 5189 30 1735 308 7203

10,230 992 5182 29 1736 308 7198

Objective function (k€/y) Objf reduction % wrt CS Average heat cost (c€/kWh) PBP (years) Primary energy cons. (TOE/y) CO2 emissions (ton/y) PES

8279 4.43% 3.84 4.6 11,280 31,697 4.92%

8470 2.23% 4.18 8.7 10,978 30,849 7.47%

8224 5.06% 3.75 7.9 10,069 28,294 15.1%

8212 5.20% 3.70 7.8 10,043 28,222 15.6%

8193 5.42% 3.63 7.8 9916 27,865 16.4%

8189 5.46% 3.61 7.8 9908 27,844 16.5%

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annual cost with respect to the conventional solution ranging between 2.2% and 5.4%, while the primary energy consumption can be reduced up to 16.5%. Fig. 8 reports some interesting results of the optimization obtained for different sizes of the solar plant, or, in other words, for different value of the annual solar thermal production. Fig. 8a shows the storage volume and it can be noted that increasing the solar plant size the optimal volume increases too, up to a limit of about 4000 m3 when the solar plant produces about 70% of the annual thermal demand. Further increasing of the solar plant size does not affect the optimal storage size. The thermal production of cogenerators is shown in Fig. 8b and it can be noted that it decreases while increasing the solar plant

size, because the thermal energy produced by cogenerators is replaced by the solar thermal energy. A different trend characterizes Fig. 8c, which reports the thermal energy produced by boilers. In this case, increasing the solar plant size the heat produced by boilers also increases, because they somehow replace cogenerators and they cover thermal peaks. In fact, it would be too much expensive and thus not convenient to adopt larger cogenerators to be used at full load only for few hours a year. Fig. 8d reports the thermal energy wasted trend (e.g. throughout cooling towers) and it can be noted that increasing the solar plant size the wasted energy increases as well. This happens because the storage has weekly charging/discharging cycles and not

Fig. 8. Results obtained varying the solar plant size and the storage thermal loss coefficient.

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seasonal. Hence, the thermal energy produced in surplus during summer which cannot be stored when the storage is already full, has to be wasted. The adoption of a larger thermal storage would involve to an investment cost sensibly greater which would not be paid back by the related savings, thus making the total annual cost increase. Therefore, exceeded a certain dimension of the thermal storage, the investment marginal cost related to a kWh results to be greater than the marginal cost of the heat produced by boiler and/or cogenerators. Hence, it is more convenient to waste the exceeding heat (instead of storing it) and produce it by boilers and/or cogenerators when necessary. In cases where the thermal demand is concentrated in winter, as it is typical of residential users, the marginal cost of heat would be greater because the usage coefficients of boilers and cogenerators would be lower. In this case, a seasonal thermal storage may be convenient, allowing a greater amount of the energy produced by the solar plant to be stored instead of wasted. Fig. 8e shows the thermal losses through the storage wall and it can be seen that, as expected, they depend on the loss coefficient and on the storage volume. Reached the 75% (17,000 MWh/y) of the thermal demand covered by solar thermal production, the thermal loss diminishes if the solar plant size increases. This is because increasing the solar plant size the optimal storage volume does not increase over a certain limit (Fig. 8a); in such a situation the heat produced by the solar plant is often used directly, without being stored, so that the thermal losses through the wall of the storage decrease.

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The heat required by absorption machine (Fig. 8f) is not affected by the solar plant size and it is about 5000 MWh/y 10% all year long. Fig. 9 reports the trends of the thermal energy demand, of the stored energy and of the in/out storage thermal flow in a typical summer week. In can be noted that during week-end the thermal demand is null, and consequently all heat produced by solar panels is stored in the thermal storage. This heat is then used in the following working days when the thermal demand is not null. This trend can be noted in each week of the year and thus it can be stated that, in this application case, the storage has weekly charging/ discharging cycle. A further optimization has been conducted forcing that the heat produced by the solar plant is equal to 14,820 MWh/y and that thermal energy cannot be wasted. In this case the thermal storage has seasonal charging/discharging cycle (see Fig. 10). The energy produced by solar field during the summer season is stored and it is used during the fall–winter season. The maximum energy stored is about 800 MWh, which is about eight times the maximum energy stored in the other optimal solutions (see Fig. 9, stored thermal energy). In this case, the total annual cost and the average heat cost are greater (8298 k€/y and 4.07 c€/kWh respectively) if compared to DRS D. As concerning the configuration, the size of the cogenerators installed in unit 7, 8 and 9 are reduced, while the size of the boiler installed in unit 4 is increased.

6. Conclusions

Fig. 9. Optimal operation of the storage in a typical summer week.

Fig. 10. Energy stored trend for DRS it R = 0.07% and 14,820 MWh/y produced by the solar plant, without wasting energy in a typical summer week.

The paper presents a MILP model for the optimization of complex distributed energy systems, based on different types of production units, that can be applied to various kind of users such as industrial and residential. The model can be used to identify the opportunities for the integration of solar district heating systems. Moreover it provides the optimal size and operation of each component, in particular of the thermal solar field and of the heat storage. 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 proposed model has been applied to a specific case study of a distributed energy supply system serving nine industrial facilities located in the North-east of Italy. If the solar field adoption is not allowed, the configuration which brings to the lowest annual cost is the isolated solution (i.e. without the district heating network) and it includes both boilers and cogenerators. This allows a 4.5% reduction of the total annual cost, with respect to the conventional solution, and a 5% reduction of the primary energy consumption. The lowest cost is reached with the adoption of a distributed solar system, which includes the district heating network, the thermal storage and the solar field. This solution allows a 5% reduction of the total annual cost with respect to the conventional solution and a 15% reduction of the primary energy consumption. The optimal sized solar field produces about 55–60% of the user annual thermal demand. A larger solar field makes the average heat cost increasing because involves higher investment costs which are not paid back by the savings allowed by the additional heat capacity. As concerning the optimal operation, it emerges that the heat storage has a weekly charging/discharging cycle, instead as a seasonal cycle, as it was expected. This happens because, when a certain dimension of the thermal storage is exceeded, the marginal cost of the exceeding capacity is greater than the marginal cost of the heat produced by boilers or cogenerators ‘just in time’. The

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