District Heating and Cooling Review of Technology and Potential Enhancements

Introduction

The global population volition exceed 9.7 billion past 2050 (United Nations, 2013), which volition atomic number 82 to approximately 70% increment in the number of households from 1.9 billion in 2010 to 3.2 billion in 2050 (I.E. Bureau, 2012). Residential and commercial buildings account for most forty% and 26%, respectively, of total energy consumption in U.S. and European households (Mertens, 2013; I.Due east. Agency, 2012). Virtually 38% and 36% of U.S. and Eu carbon dioxide (CO_ii) emissions are besides associated with these buildings. Moreover, several unwanted side furnishings, such as urban heat island, are associated with the drastic increase in urbanization (Mirzaei, 2015; Mirzaei et al., 2015). Thus, these statistics emphasize the necessity of a global objective to reduce the CO_two emission by one-half by 2050, which is described as the goal of the Energy Technology Perspectives 2012 roadmap (EIA, 2011). This calls for increased efforts and market uptake from the edifice sector to reach the ambitious goal of net-nix energy buildings (NZEB) by 2050 given the 50% rising in energy demand predicted by the current consumption trajectory. Another example is European union obligation in 9% reduction in energy use by 2016 based on 2006/32/EC directive (European Parliament, 2006). The European countries are besides committed to increase the share of renewable free energy sources to twenty% past 2020 (P.H.A.F.South. Committee on Environment, 2011).

Different strategies in energy production, conversion, and user-side demand accept been proposed to conserve energy in the edifice sector, i.e., increasing the energy efficiency of buildings with refurbishment technologies such as thermal insulation, double and triple glazing, solar shadings, cavity wall, reflective blanket windows, efficiency enhancement, the functionality operation of HVAC equipment, integrating renewable strategies such as BIPV and solar collectors, utilizing natural ventilation. In addition to these technologies, one of the viable solutions is to ameliorate the energy efficiency in buildings, which can be achieved by using commune heating system (DHS) (International District Free energy Association, 2014; http://www.districtenergy.org/what-is-district-energy).

Traditional DHSs are generally used for residential space heating and domestic hot water, which are accounting for the largest share of energy consumption in buildings (International District Energy Association, 2014; http://world wide web.districtenergy.org/what-is-district-energy). Other advantages of DH are known as the improvement of resource and energy management and also reduction in the user-side costs, including performance, maintenance, and prophylactic expenses (Rezaie and Rosen, 2012). Moreover, flexibility and safety in selection of the free energy source such as biomass and geothermal free energy instead of fossil fuels, which dominates the electric current oestrus market, is another attractive selection of the DHSs (Hepbasli, 2010; Akhtari et al., 2014).

Despite the well-known advantages of DHS, its market share around the world is notwithstanding very depression while just about 6000 DHSs exist in European Matrimony with the market share of about 13% (Figure ane). Likewise many social, economic, and technological bug revolving around worldwide implementation of DHSs, the predominant reason for neglecting such systems is the lack of suitable tools to pattern, clarify, and optimize them (Connolly et al., 2014).

Figure 1. (Left) CHP % generation of gross electricity generation (EUStat).

Apart from such bug, one of the major limitations of DHS is lower thermal comfort, specially in older DHSs where occupants have very little control over the water temperature (International Commune Energy Association, 2014; http://www.districtenergy.org/what-is-district-energy). In denser urban regions, which expanding the DHS distribution network should follow the rules of the municipality, existing infrastructure, such as roads, water/sewage distribution networks, and city layout in some cases, are the common barriers against the optimal expansion of DHSs.

The discussed advantages and limitation in DHSs has persuaded the communities to move toward the implementation of novel ideas and strategies in energy sharing and management of DHSs. The new strategies are mainly focused on combining renewable energy, use of storage technologies, and establishing a linkage between heating and electricity systems to significantly reduce the dependency on the fossil fuel resources (International Commune Energy Association, 2014; http://www.districtenergy.org/what-is-district-free energy). One of the major challenges toward the design of such systems is associated with lack of bachelor tools, which tin can effectively model and optimize DHSs.

To shed more low-cal on the contempo achievements in modeling and optimization of DHSs, this paper aims to summarize the current state of the fine art. Thus, various definitions of DHS are first provided followed past the molding approaches utilized to investigate the performance of these systems. Eventually, modeling and optimization of DHS studies based on unlike climates, scales, energy sources, and implemented tools are farther summarized in this newspaper.

Complication Level of Commune Heating Systems

In general, a DHS consists of a oestrus source, a network of users, and a distribution network. The complication of a DHS varies in accordance with diverse parameters as stated below (Sakawa et al., 2002; Weber et al., 2007):

(a) Number of utilized technologies: 1 of the complexities of blueprint and optimization of the DHSs is the number of technologies available to be utilized in addition to the type of the heat source system. For example, in DHSs with geothermal energy source, the system could operate with the organic fluid instead of water (Weber et al., 2007), while in instance of having heat sink close to the DHS, the heat pump is more favorable. Moreover, a combination of sources can be used in DHS, while other renewable source of energies tin exist integrated to the system (Sakawa et al., 2002; Weber et al., 2007).

(b) Number of end-users: one of the master concerns in designing a district heating is the number and diverseness of the users continued to the system. A DHS located in a municipal surface area serves a variety of residential, commercial, and industrial buildings with different need levels (Pirouti et al., 2013).

(c) Temporal profile: dissimilar types of users connected to a system demand their own operating temperature and profiles (Weber et al., 2007). For example, the estrus need contour for industrial users will be effected less by seasonal changes during a yr, meaning that their required stop-use temperature is higher compared with residential users (Buoro et al., 2014).

(d) Spatial concerns: in addition to the coordinate of all users, the layout of a metropolis, in which a DHS is planned, plays a central role in design of distribution network. For example, interception with municipal infrastructures should be avoided when a network is designed. Other factors such as soil quality, topology of the region, and blazon of the users could similarly affect the blueprint of a DHS (Weber et al., 2007; Ben Hassine and Eicker, 2013).

Classification of Commune Heating Systems

In general, a DHS can exist categorized based on five main parameters including geographical atmospheric condition, scale of the DHS, oestrus density of the DHS, the level of stop-user demands, and type of heat sources.

Geographical Atmospheric condition

Geographical considerations, namely climatic weather condition and free energy source accessibility, will impact the overall pattern of a DHS. In particular, a DHS close to Northern latitudes with a colder climate requires higher rate of heat transfer per unit expanse compared to the DHS closer to the equatorial line with a warmer climate for similar types of buildings (Dalla Rosa and Christensen, 2011). This higher amount of heat transfer in DHSs can exist reached either by increasing the mass menses charge per unit of the fluid or by increasing the operational temperature of the system, which consequently increases the distribution oestrus loss of the system due to the higher operational fluid temperature (Hassine and Eicker, 2011).

Energy sources accessibility is a function of geographical and geological variation and, therefore, impacts the design considerations of a DHS. Investigating the distribution of different energy resources for different geographical locations addresses the accessibility of at least one of the main sources of renewable energy at whatsoever region. For example, comparing of the solar (Huld and Pinedo-Pascua, 2012) and current of air map of Europe (come across text footnote 1) shows that region with lower solar intensity take college current of air speeds and vice versa (Figure 2). Specifically, Scandinavian region has one of the lowest solar intensities while it is exposed to the highest air current speed in Europe.

Figure two. (Left) solar map of Europe (correct) wind map of Europeⁱ (Huld and Pinedo-Pascua, 2012).

Scale

Scale of a DHS plays a significant part in performance of such systems as the influential parameter in design stage varies in accord with the scale. From the spatial point of view, DHS tin can be designed equally a minor, medium, or large system (Figure iii).

Effigy 3. Schematic programme of the DHS based on the altitude from heat source.

Pocket-size DHS is referred to a network of users in which the distance from the estrus source is in the order of magnitude of less than few hundreds of meter (Weber et al., 2007). In fact, the associated temperature and pressure level drops are relatively low due to the short length of the pipelines in the distribution system (Hurtig, 2010). DHSs in the level of multi-residential buildings are more probable known as small systems with a relatively depression temperature drib.

The altitude betwixt the heat source and the users is mainly assumed to be from 200 to 300 k in the medium-scale DHS (Weber et al., 2007; Dalla Rosa and Christensen, 2011; Ancona et al., 2014). In general, these systems are formed as a close-loop network of buildings linked together with a piping organization. Similar to the small-scale-scale DHSs, pressure drop is a significant element in design of such systems, whereas for older generation or college operating fluid temperature systems, the heat loss is substantial and should be considered at the blueprint stage (Hassine and Eicker, 2011; Nuytten et al., 2013).

Large-scale DHS, by and large known every bit community size DHSs, consists of many users and a longer pipeline network compared with the latter groups. Due to longer length of the pipes in distribution network, the estrus loss is considerably pregnant and accounts for up to 15% of the total energy delivered by the arrangement (Hassine and Eicker, 2011; Xing et al., 2012).

Heat Density

Linear heating density of a network (LHD) is defined based on the ratio of its total almanac heating demand over trench length (Reidhav and Werner, 2008):

where Q _total is the total annual heating demand of the DHS, and L is the total trench length of the distribution network.

Based on this definition, higher LHD means college oestrus density of the network or users with a higher almanac demand. In systems with higher heat density, the importance of the estrus loss is less pregnant (Nuytten et al., 2013), and thus the system is designed simply based on the hydraulic equilibrium. The economic and ecology threshold for the LHD of different networks are varied from i MWh/one thousand for DHSs with biomass estrus source to 0.ii MWh/m for combined rut and power (CHP)-based systems (Reidhav and Werner, 2008; Nuytten et al., 2013).

Terminate-User Demand

Residential buildings utilise lower finish-use temperatures for heating while industrial users crave higher fluid temperatures. This ways that the demand level of users in a network results in different organisation of the DHS (Buoro et al., 2014). I system is to design a network based on the maximum demanded temperature (Pirouti et al., 2013), while some other option is to utilise a multi-loop network with dissimilar operational temperatures associated with each of them. Multi-loop networks further interact with each other through sets of heat exchangers (Figure iv). This implies that the main loop operates with the maximum temperature while secondary loops operate at lower temperatures in order to satisfy the temperature requirements of all users (Hassine and Eicker, 2011; Ben Hassine and Eicker, 2013).

Figure iv. Schematic plan of the DHS with primary and secondary loops.

Heat Source Type

In full general, oestrus sources are categorized as permanent and not-permanent types. In the permanent oestrus sources, the heat generation continuously exceeds the heat demand of the network where in the not-permanent sources the generation contour fluctuates during the time. In the latter scenarios, the generation mainly does non match with the user need profile, and therefore another energy source is mostly integrated to meet the meridian demand of the organisation.

Combined heat and power, geothermal, and biomass sources are known as permanent source (Hlebnikov and Siirde, 2009; Noussan et al., 2014; Sartor et al., 2014). On the other manus, convertible renewable sources into thermal energy such as wind and solar energy with high charge per unit of fluctuations are categorized equally non-permanent sources. Moreover, heat storage systems can be integrated into DHSs to store the surplus of generated heat at their off-acme time to be later utilized at the pinnacle time of the DHS (Avila-Marin et al., 2013; Nuytten et al., 2013).

Component Modeling of District Heating System

Accurate modeling and design of each DHS's component plays an of import function in its efficacy and efficiency. This section investigates various techniques employed to model DHS's components.

Heat Source

In full general, heat sources in DHSs are modeled based on their efficiency and estrus generation output. A minimum efficiency index has been divers depending on the type of the estrus source. For instance, the primary energy saving index (PES) has been defined to evaluate the efficiency of a CHP heat source (Noussan et al., 2014):

$\text{PES}=\left(1-\frac{1}{\frac{\text{CHP}H\mathrm{\eta }}{\text{Ref}H\mathrm{\eta }}+\frac{\text{CHP}\mathrm{Due\; east}\mathrm{\eta }}{\text{Ref}H\mathrm{\eta }}}\right)\times 100\%$

(2)

where CHP Hη is the estrus efficiency in cogeneration production, Ref Hη is the efficiency in separated heat generation, CHP Eastη is the electricity efficiency in cogeneration production, and Ref Hη is the efficiency in separated electricity generation.

The minimum value of the PES for CHP heat sources with the nominal size of smaller than 1 MW should be a positive value while this value is more than 0.1 for sources above 1 MW (Noussan et al., 2014). Same types of indices take been defined for other type of rut sources (Hepbasli, 2005).

Stop-User Profile

Accurate prediction of the energy need profile of users in smaller time interval such as hourly basis can affect the efficiency of a network besides every bit its optimization process (Ortiga et al., 2007). The DHS modeling of the users' network consists of two levels: agreement of the heating need profiles of the users in order to define the total load required for the network and adding of a heat exchanger for each user.

Since building heterogeneity in each commune system is elevated, particularly in the urban setting, and each building has its own backdrop and corresponding demand contour, determining the model which could predict the demand profile of the unabridged commune with acceptable accurateness, is essential. In general, at that place are different methods suggested to model and predict this demand. Many of these methods predict the free energy demand of a building in terms of its maximum energy demand, while others predict the actual profile of the building in smaller intervals such as an hourly basis.

Regardless of the method used, the heating need profile of each user consists of 3 major parts, including concrete and ecology characteristics of a building (i.e., R-value, infiltration rate, ambient air temperature, solar radiation, and humidity), human-related factors or social behavior of the occupants, and random factors that account for uncertainties. Dissimilar techniques accept been suggested in the literature in gild to predict the demand profile of the users because one or all of the above factors including historical approaches (Dotzauer, 2002; Ortiga et al., 2007), deterministic, and times series predictive methods (Eriksson, 2012).

Historical Methods

These methods use historical data obtained from both demand and supply sides to model the demand profile of the system.

Heating Degree 24-hour interval

Estrus loss in buildings is proportional to the difference between indoor and outdoor ambient temperature. This concept is used in the development of the Heating Degree Day method (HDD) (Day, 2006):

$\text{Estrus Loss}\left(\text{kW}\right)=\text{Overal Heat Loss Coefficient}\left(\text{kW}.{\text{K}}^{-\mathrm{one}}\right)\times \text{HDD}\left(\text{K}\right)$

(3)

Hither, the overall heat loss coefficient is determined based on the infiltration charge per unit and the summation of the UA value for all different envelope assemblies of the building. The infiltration rate can be defined either as an average or hourly charge per unit (24-hour interval, 2006).

Online and gratis historical atmospheric condition data are mainly assumed every bit reliable sources to obtain the HDD method (Verda et al., 2012; Pirouti et al., 2013).^{ii, 3} This method is widely used for modeling of small buildings in which the chief source of rut loss is unclear in their envelope. Al-Homoud (2001) compares this method with some other historical method known every bit the Bin method. Unlike the degree day method, the bin method is mainly used for larger scale buildings in which the internal load generation has a higher outcome, rendering the degree day method unfeasible. In both cases, the master concern in modeling is the outdoor air status of the buildings and the boilerplate envelope thermal resistance. The fact that factors such equally the social behavior of occupants and the thermal mass of the buildings have not been taken into account result in predominantly poorly accurate findings (Dotzauer, 2002). Furthermore, the low frequency of bachelor data results in inaccurate outcomes.

Energy Utilize Intensity and Load Cistron

Energy employ intensity (EUI) and load factor (LF) is another technique to approximate the users demand contour, whereby the historical supply data are provided. EUI is the rate of energy use per unit area (Sharp, 1996), and LF is the ratio of free energy consumption over the maximum possible energy generation of the supply side (Dalla Rosa and Christensen, 2011; Dalla Rosa et al., 2012):

$\text{LF}=\text{Consumption}\left(\text{kWh}\right)/\text{Peak Demand}\left(\text{kW}\right)\times \text{Time}\left(\text{h}\right)$

(4)

Knowing the EUI and LF of unlike users^iv results in calculation of the total free energy and peak heating demand required for each consumer. The supply energy demand calculates the annual average LF per expanse of different users. Mainly, the values are attainable based on region or reference archetype (encounter text footnotes iii and 4). Barnaby and Spitler (2005) used this method for load prediction based on different users' sector of the DHS and added them together to predict the users' heating demand profile. One of the main problems with this method is associated with non-existence of separated factors for ambient conditions.

Measurements

Measurement campaigns can provide reliable inputs to be inserted as the end-user demand profile of DHS (Sanaei and Nakata, 2012; Nuytten et al., 2013; Wang et al., 2013; Noussan et al., 2014). Achieving a high frequency dataset, however, is not ever a feasible option due to the extensive toll of the equipment and fourth dimension-consuming procedure.

Archetype Building

Another blazon of the widely used historical methods is prototype or archetype buildings. In this method, buildings with a same occupancy type are divided into subcategories, while a reference building is defined for each building. The need profile of other buildings located in each category is after defined based on the reference building with some aligning. The number of building categories used in this method and the number of adjustments required for modeling the demand profiles are the key parameters of the paradigm method. The nearly commonly utilized technique is the regression method. Lara et al. (2015) used the linear regression method in order to ascertain the useful parameter that can be employed every bit an input data for modeling of school buildings, whereas Filippin et al. (2013) used a multivariate regression method in evaluating the heating demand profile of a residential sector.

Deterministic Methods

Deterministic methods, also referred as simulation-based models, use the mathematical representation of the physical behavior of the buildings. Based on the volume of the used data, deterministic methods tin can exist categorized into ii major subdivisions, such as circuitous or software-based simulation models, which use different simulation software that takes into account all the dissimilar parameters affecting the demand contour of a building and simplified models, which basically simplify the level of the calculations taken into the account.

Circuitous Models

Energy simulation software, such every bit Energy Plus (Crawley et al., 2001) and TRNSYS (University of Wisconsin—Madison, Solar Energy Laboratory and Klein, 1979), is broadly used for modeling various blazon of buildings. Although they yield highly accurate demand profiles, the main disadvantage of these models is their dependency on information quantity and high computational cost for modeling each building (Ortiga et al., 2007; de Guadalfajara et al., 2012; Guadalfajara et al., 2014). For small-scale systems consisting of a limited number of buildings, using the comprehensive method tin can increase the accurateness of the simulation. Notwithstanding, providing the data and time required for modeling of many buildings in a city-broad scale is very extensive. The example of circuitous modeling is a work by Zhang et al. (2015, 2014) where a comprehensive method was utilized to model the demand contour of 95,817 buildings in Westminster, Uk.

Simplified Models

Simplified methods are adapted when the adaption of the comprehensive method is relatively all-encompassing for a large-scale community. These methods simplify physical characteristics of the buildings in order to predict their need profile. For example, Kim et al. (2014) considered the parameters including shape, orientation, and occupancy type in the modeling of the end-users' contour. They used the boilerplate energy required per foursquare meter of a dwelling house area of a edifice based on its monthly/yearly outdoor pattern temperature. In gild to take into account the shape and orientation of the edifice, new sets of coefficients were introduced: (1) the ratio of the outdoor surface to volume of the building (the shape factor) and (two) the orientation relative to the south (orientation factor) (de Guadalfajara et al., 2012). Wang and Xu (2006) used a simplified physical method to predict the demand profile load within which they also included the effect of thermal mass on load prediction by means of a genetic algorithm. Results obtained from their simulations illustrate a good correlation with bodily data for a residential building, which has a lower internal heat proceeds density. Inversely, this method is unsuitable for larger buildings with higher internal rut gain density.

Predictive Time-Serial Methods

The predictive fourth dimension-series methods rely on the mathematical curve fitting relations in order to predict the demand contour of the users.

Predictive Models

Dissimilar predictive models have been suggested for modeling the demand profile, including classical approaches [i.e., fourth dimension-series ARMA models, regression (Lei and Hu, 2009; Yun and Steemers, 2011; Guadalfajara et al., 2014), Kalman filter] and artificial intelligence (AI) methods [i.east., bogus neural network algorithms (ANN) (Hippert et al., 2001) and fuzzy neural network (FNN)] (Gross and Galiana, 1987).

ARMA Type. ARMA time-serial predict the profile of the finish-user by implementation of a linear combination between the previous value of the demand along with previous and current values of the noise (Gross and Galiana, 1987):

where Y _p(t) represents the day and the normal weather status for the pattern day, and Y(t) indicates the effect of deviation from the normal conditions design.

With slight departure from the general form, dissimilar kinds of ARMA-type models tin exist developed, e.g., Box-Jenkins (Tang et al., 1991), fourth dimension serial (Amjady, 2001), and ARIMA (Lee and Ko, 2011).

Kalman Filter. Similar to other predictive methods, this technique estimates the value of the variables for future time steps (t + Δt) based on the values of the variables at its current time step (t). In order to brand the best estimation, Kalman filter determine the all-time variable set, which minimizes the source role using the residual sequence method. In each stride, the Kalman filter will bank check the divergence betwixt the measurements and the model output and chose the variable set to minimize the difference. Since the difference from the measurement can be positive or negative, two different sets of rest sequences could exist assumed for the organization, such as residual for the hot side and balance for the cold side of the profile (Palsson, 1993).

Artificial Intelligence

Using predictive methods, such as artificial intelligence, is some other arroyo to predict the demand profiles of the edifice. The near mutual artificial intelligence methods used in the field of load prediction are ANN, FNN, and Support Vector Machine (SVM). The ANN has been widely used in research for predicting the load especially in forecasting the electricity consumption of buildings (Zhang et al., 1998). In most of the cases, ANN shows higher prediction functioning compared with other simulation-based methods. This higher accuracy with the ANN method is normally due to its college adjustability, as it considers the social parameters in load prediction due to the integration of real case information into the system preparation (Zhang et al., 1998; Hippert et al., 2001). Despite the high accuracy of the predictive methods, their main drawbacks are the over-fitting problem as well as the data requirements for the training proposes. Providing authentic, comprehensive archives of data for ANN is one of the chief drawbacks of this method. In cases where the data archive used for training the system is pocket-size, using the SVM methods (Chen et al., 2004) shows a better functioning. However, only a scarce number of studies were conducted using SVM in the concluding few years; hence, the information regarding the utilization of this model is limited.

Limitations of the Current Models

The main limitations of the methods have been used in prediction of the demand profile of the DHS could exist addressed as below:

• Feasibility of expanding i model to the unabridged district level: the first limitation of the presented methods is related to the limitation of these models in prediction of the total energy consumption of the entire district. Specially, in example of a larger district system that the heterogeneity of the buildings is elevated, this problem becomes more amplified. For example, HDD should be only used for prediction of the small-scale residential buildings while the Bin method is more than suitable for larger buildings with much higher internal rut generation density. Every bit a result, an archetype method with a combination of these methods should exist used to predict the total free energy load of the entire network.

• Blazon of prediction: another limitation of the presented works is the type of prediction. Most of the presented methods have been adapted to predict the total energy consumption. Even though at the pattern stage, DHSs are designed based on the total free energy consumption and the maximum superlative demand of the system, detail profile of the network is further required in society to improve the efficiency of the system and enhancing the energy distribution management. Table 1 summarizes different prediction methods that take been used to predict the consumption load of DHSs.

Table one. Summary of the method has been used for load prediction in DHS and blazon of building stocks.

Every bit illustrated in Table 1 most of the works that have been washed only focused on the total energy consumption of the networks and not the detail contour.

• Accuracy: accuracy of the prediction is the side by side limitation of the previous models. In case of load prediction for district systems, two different types of errors could exist defined; the offset blazon is the error associated with the entire district model, while the 2d one is associated with the modeling at the edifice level. As illustrated in Table ii the simulation error is mainly much lower at the district level in comparison with the building level 1, which is mainly related to beliefs of the users.

• Computational time: the computational fourth dimension of the stock modeling is 1 of the major limitations of the current DHS models.

Table 2. Summary of the accuracy level of the previous works.

Energy Distribution Network

A distribution network of a DHS is mainly designed in accordance with the scale of the system, geographical considerations, blazon of the users, and utilized estrus generations sources. Also the part of the distribution network in linking the generation side with the demand side of the cycle and defining the inter communication betwixt different components of the organization, the distribution network has an effect on the energy consumption of the system as well. In full general, the total energy required to be fed to the system is equal to:

where Q is the full free energy consumption of the DHS, Q _i is the demand profile of each user, and Q _loss is the heat loss of the system. Since most distribution networks piece of work within a specific temperature range, the heat loss from the system could exist considered equally a role of the size of the network and not a office of fourth dimension. As a result, the full energy requirement of the arrangement is equal to the summation of the profiles of unlike users in addition to the oestrus loss per network length. Since the DHS is blazon of the hydronic system, the modeling technique to design the distribution system can be either based on hydraulic or thermal equilibrium.

Hydraulic Equilibrium

The distribution organisation in the DHS works based on the transferring of heat through a heated fluid, and therefore, it should be designed based on the requirements of the hydraulic arrangement regardless of the menses rate and energy level of the fluid.

Mass Catamenia Balance

The mass period balance could be written for each point of the system as follows (Ben Hassine and Eicker, 2013; Kuosa et al., 2014):

${\displaystyle \sum _{\text{in}}}{Q}_{\text{in}}-{\displaystyle \sum _{\text{out}}}{Q}_{\text{out}}-{\displaystyle \sum _{\text{user}}}{Q}_{\text{user}}=0$

(7)

where Q _in is the mass flow rate enter the bespeak, Q _out is the mass period rate get out the indicate, and Q _user is the mass flow rate required by the utility. Depending on the type of the system, such as an open or closed loop, Q _user could exist considered every bit 0. Information technology is important to annotation that the system and network are assumed to be leak free without whatever loss of the fluid mass.

Energy Remainder

In the mass flow balance techniques, the free energy residuum could be written between any two points in the organization as below (Ancona et al., 2014):

where ΔH _ij represents the free energy loss between points i and j; H _i and H _j are, respectively, the free energy content of the fluid at points i and j. Because the DHS as a airtight system and without whatsoever loss in the liquid mass, the energy loss in the organisation could be written as a correlation to the pressure loss in the system represented in two different ways:

$\mathit{\Delta H}=f.\frac{L}{D}.\mathrm{\rho }.\frac{{\mathrm{\nu }}^{\mathrm{two}}}{2}\text{Distribution Pressure Drop}$

(ix)

$\mathit{\Delta H}=\mathrm{\beta }.\mathrm{\rho }.\frac{{\mathrm{\nu }}^2}{\mathrm{ii}}\text{Concentrated Pressure level Drop}$

(10)

In the distribution pressure loss, the friction loss due to pasty effect, generated by the pipe surface, is the governing parameter. The hydraulic diameter of the pipe, mass flow rate of the system, and roughness of the pipage surface are the parameters affecting the distribution pressure loss of the organization (Kuosa et al., 2014). Additionally, in concentrated force per unit area loss, head loss due to fittings and changes in diameter of the pipe are taken into the account (Ancona et al., 2014).

Thermal Equilibrium

Thermal equilibrium can exist represented as either a steady-state or dynamic equation. DHS with operational temperature lower than seventy°C or with depression heat propagation (well insulated) can be represented equally a steady-land system. Inversely, DHS operating with higher temperatures than 110°C or with high heat propagation can exist considered as dynamic system (Madsen et al., 1994; Lund et al., 2014). The thermal model could exist written based on two major sources of the temperature drop in the system, including temperature drib across the users and due to the heat loss in the system. The temperature drib across the users can be modeled based on a elementary convection oestrus transfer equation (Dahm, 1999; Wang et al., 2013):

where Q is the corporeality of the energy required by the system, U is the heat transfer coefficient, and ΔT is the temperature drop across the users.

On the other side, the temperature driblet due to oestrus loss in the arrangement occurs in both longitudinal and radial directions. Longitudinal rut loss is along the organization between dissimilar locations, whereas radial oestrus loss occurs in the surrounding environment. Both types of the oestrus transfer in the system could simply be modeled by using the enthalpy balance between whatsoever ii points (Hassine and Eicker, 2011; Kuosa et al., 2013):

$\frac{\partial \left(\mathit{mh}\right)}{\mathit{\partial t}}={\displaystyle \sum _{\text{in}}}{h}_{\text{in}}-{\displaystyle \sum _{\text{out}}}{h}_{\text{out}}-{\displaystyle \sum _{\text{loss}}}{h}_{\text{loss}}$

(12)

$\frac{\partial \left(\mathit{mh}\right)}{\mathit{\partial t}}={\dot{Q}}_{\text{c}}\left(\mathrm{ten}\right)-{\dot{Q}}_{\text{c}}\left(x+\mathit{dx}\right)-d{\dot{Q}}_{\text{1}}$

(xiii)

where ${\dot{Q}}_{\text{c}}$ is the convective heat catamenia, $d{\dot{Q}}_1$ is the radial heat flow and could be expressed equally beneath:

$d{\dot{Q}}_{\text{l}}=k.\mathit{dx}.\left(T-T_{\text{globe}}\right)$

(14)

where k is the radial heat manual coefficient and q ₁₀₀₀ is the flow rate. By replacing the $d{\dot{Q}}_{\text{fifty}}$ and ${\dot{Q}}_{\text{c}}\left(x\right)$ in the Eq. 12, the temperature at any betoken can exist calculated every bit follows (Figure 5):

$T_{\text{i}}^{\text{north}+1}=T_{\text{i}}^{\text{north}}+\mathrm{\Delta }t/{\mathrm{chiliad}}_{\text{i}}.C_{\text{p}}\left(q_{{\text{m}}_{\text{i}-1}}.C_{\text{p}}.T_{\text{i}-1}^{\text{n}}-q_{{\text{m}}_{\text{i}}}.C_{\text{p}}.T_{\text{i}}^{\text{n}}-d{\dot{Q}}_{\text{l}}\right)$

(sixteen)

where C _p is rut capacity, T ^{due north} is the temperature, Δt is the time step, and m _i is the mass of the h2o.

Figure 5. Oestrus flow in the piping system.

Based on the definition of the $d{\dot{Q}}_{\text{l}}$, one of the main factors influencing the amount of heat loss is the globe's temperature. In systems with a higher operating temperature, higher differences in temperature could result in college amounts of the heat loss in the system. Similarly, increased heat losses in a system could upshot in increased surrounding temperatures over fourth dimension, and consequently decreasing the estrus loss over time.

Holistic Modeling of District Heating System

Concrete and black box models are the approaches conducted in holistic modeling of the DHS (Palsson, 2000). The network has been considered as a whole package in the black box models where individual pattern of the components is overlooked. The whole organization is and then modeled by techniques such as the transfer function or ANN (Yabanova and Keçebas, 2013). Ane the other manus, in concrete models, each component of the DHS has been designed separately and as a set of equations describing the flow and pressure losses of that chemical element. Arsene et al. (2004) categorized the physical modeling as the link menses (Q), the loop corrective flow (ΔQ), the nodal heads (H), and finally the mixed node-loop approaches.

Due to a high number of the elements that need to be taken into consideration, solving such a organisation can be computationally expensive. Therefore, numerical approaches have been widely adult for solving the arrangement of equations of the hydraulic distribution networks. Some of these approaches are categorized past Arsene as:

• Numerical minimization method, finding the minimum value of the non-linear part subjected to linear constrained;

• Hardy-Cantankerous method, solving the system of non-linear equations (Chenoweth and Crawford, 1974);

• Newton–Raphson method, solving the system of non-linear equations (Donachie, 1974);

• Linear theory method, solving the system of not-linear equations (Collins and Johnson, 1975).

Based on the simplicity of the input data, the number of equations and size of the matrix of the equations (Calí and Borchiellini, 2002; Hassine and Eicker, 2011) besides every bit the accurateness of the results, the near frequent used method is a combination of Newton–Raphson and nodal head methods (Arsene et al., 2004; Hassine and Eicker, 2011). Due to weak convergence of the nodal equation algorithm for networks with low flow rate, another approach has been suggested past Arsene et al. (2004) called the loop equation method, which is once again a combination of a loop corrective and Newton–Raphson methods.

Further to the to a higher place mentioned studies, several commercial software accept been developed based on the loop equation method using the graph theory, such as TERMIS⁵ or SpHeat (Eicker, 2004). Tabular array 3 summarizes some of the current DHS modeling studies.

Table 3. Summary of the contempo DHS modeling studies.

Optimization of District Heating System

Different optimization methods accept been developed in order to decrease the heat loss besides equally the cost associated with performance and construction of the DHSs. Amidst various used methods, mathematical methods based on continuous or discrete variables, generic algorithm, neural network, and fuzzy logic systems are widely implemented techniques. Based on the divers type of the objective function, the DHS optimization is mainly formed on the basis of a single objective part or multi-objective functions. While most single variable function will exist solved using the deterministic numerical methods, the multi-objective functions use either weighted factors or pareto-front approaches. In the weighted factor approach, importance gene is fitted to unlike objectives of the optimization problem, based on the trial-and-error approach, to convert the multi-objective office to single objective problem, which provides a numerical solution for the problem. The post-obit chart shows different deterministic methods for the numerical optimization approaches.

$\left\{\begin{array}{c}\text{Discrete Variable:}\left\{\begin{array}{c}\text{Mixed-Integer Linear Programing}\left(\text{MILP}\right)\hfill \\ \text{Mixed-Integer Non-Linear Programing}\left(\text{MINLP}\right)\hfill \end{array}\right.\hfill \\ \text{Continuouse Variable:}\left\{\begin{array}{c}\text{Linear Programing}(\text{LP}):\text{Linear complementarity problem}\left(\text{LCP}\right)\hfill \\ \text{Non-Linear Programing}\left(\text{NLP}\right)\text{:}\hfill \\ \left\{\begin{array}{c}\text{Quadratic Programing}\left(\text{QP}\right)\hfill \\ \text{Semi-Difinite Programing}\left(\text{SP}\right)\hfill \end{array}\right.\hfill \end{array}\right.\hfill \end{array}\right.$

(17)

where the optimization problem tin can exist defined equally (Caputo et al., 2013):

$\text{min}Z=f\left(x,y\right)s.t.\left\{\begin{array}{c}h\left(x,y\right)=0\hfill \\ g\left(x,y\right)\le 0\hfill \\ \mathrm{ten}\in \mathrm{10},y\in {\left\{0,1\right\}}^{\text{m}}\hfill \end{array}\right.$

(18)

where the objective function f (ten, y) is subjected to the prepare of constraints. h(x, y) = 0 defines operation of the system, and k(10, y) ≤ 0 stands for feasible plan of the system. Moreover, two unlike types of variables could be defined for MIP problems; the continuous variable (10), representing the land variable and the discrete variable (y) with the value of 0 and one, representing the assignment of the equipment of a sequential task to the organization.

Optimization algorithms consist of both continuous and discrete variables where they furthermore characterized as mixed-integer linear programing (MILP) if all the equations are linear or mixed-integer non-linear programing (MINLP) if ane of the equations is non-linear. In the cases of having no detached variable, the optimization algorithm can be addressed with linear programing and non-linear programing (Biegler and Grossmann, 2004).

The schematic of the optimization procedure, presented in Eq. 17, serves as a basis of several optimization tools, which have been developed for optimization of the DHSs, e.g., general optimization toolboxes such every bit MATLAB or GenOpt (Attia et al., 2013), customized DHS optimization tools such as FreeOpt (Akhtari et al., 2014), cost-associated optimization tools with the thermal electrical load of the organization such as STEFaN (Connolly et al., 2014), network pipage size and routing optimization tool such as Small(Model for Optimization of Dynamic Energy Organisation with Time-Dependent and Boundary Status), the organization investment, and operational toll optimization at both supply and demand level (Henning, 1999).

Regardless of the blazon of optimizing algorithm, the main objective of such models is to minimize the operational cost, investment cost, and oestrus demand of the arrangement in addition to minimizing the environmental impacts such as CO₂ emission (Lu et al., 2014). Table 4 summarizes some of the recent DHSs optimization studies.

Table 4. Summary of the recent DHS optimization studies.

Decision

In this newspaper, the state of the art of modeling and optimization of DHSs is reviewed and limitations of the previous works have been summarized. One of the major limitations of the existing works is addressed as the procedure that could exist used in predicting the demand load of the entire commune network. In general, there are different methods suggested to model and predict the demand profile in DHSs. Many of these methods predict the energy demand of a building in terms of its maximum value, while others predict the actual profile of the system in a smaller interval such as an hourly footing. This limitation becomes more important in case of larger DHSs in which building heterogeneity is elevated. Table i summarizes the unlike approaches that have been used in predicting the load of the DHSs. It was concluded that near of the utilized approaches are but applicable to one type of edifice.

Also, the accurateness of the predictions of previous works has been addressed in Table 2. Since most of the existing models practise not take into consideration the consequence of the occupants' behavior in their modeling, the accurateness of the prediction, especially at the building level, is much lower in the previous works. In contrast, the accuracy significantly increases when the entire DHS is considered. This phenomenon can exist observed in previous works focused on DHSs with similar edifice types. Since more than one edifice is involved in the profile prediction of an entire commune network, their demand profiles overlap and therefore compensate the accumulated error in the load prediction; this process significantly increases prediction accuracy.

In terms of the distribution network, the existing works has been categorized in three levels, small size, mid-size, and large systems. This categorization has been summarized in Table 3. Even though in the mid-size and large size networks, there is a college heat loss ratios, thermal insulation of the distribution network is suggested to be a major drawback; however, for the newer DHS generations, working with lower temperature, this loss tin can be embedded as an into the demand load. Regarding the state of the art of the optimization methods, Table four provides a summary on the basis of their objective functions.

Author Contributions

BT, first writer. PM, second supervisor. AB, collaborator. FH, first supervisor.

Conflict of Interest Argument

The authors declare that the research was conducted in the absence of any commercial or fiscal relationships that could be construed every bit a potential conflict of interest.

Acknowledgments

The authors would like to express their gratitude to Concordia University for supporting this research through the Concordia Inquiry Chair program.

Footnotes

1. ^European Current of air Atlas. Copyright © 1989 by Risø National Laboratory, Roskilde, Denmark. http://www.wasp.dk/dataandtools#wind-atlas__european-wind-atlas
2. ^ Degree Days Weather Data for Energy Professionals. Available at: http://www.degreedays.net/
3. ^ Energy utilisation Data Handbook. (2013). Available at: http://oee.nrcan.gc.ca/publications/statistics/handbook2010/handbook2013.pdf
4. ^ Commercial & institutional consumption of free energy survey summary. (2008). Bachelor from: http://oee.nrcan.gc.ca/publications/statistics/cices08/pdf/cices08.pdf
5. ^ Termis District Energy Optimization Software. Bachelor at: http://software.schneider-electric.com/products/termis/

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