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Edited by: Michel Feidt, UMR7563 Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée (LEMTA), France

Reviewed by: Subbu Kumarappan, The Ohio State University, United States; Samuele Lo Piano, Universitat Oberta de Catalunya, Spain

This article was submitted to Energy Systems and Policy, a section of the journal Frontiers in Energy Research

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

If the UK wishes to decarbonize its heat supply, increased implementation of district heating is needed. Currently, district heating implementation is low, accounting for only 2% of the total UK heat supply. Low district heating implementation is mainly due to the high network installation costs, particularly in rural areas with low heat demand density. Current academic models of district heating are complicated, time consuming and require validation with primary network data. This paper aims to report on the building of a simple model that can, quickly and easily, assess the economic and environmental feasibility of any new district heating network. A primary aim of the model is to be simple enough for non-technical individuals to use. The focus of the paper is on the modeling of the local heat demand, investigating the applicability of the same modeling technique to case studies with differing population densities. Results showed that case study areas with smaller population densities had higher proportion of domestic customers, therefore the modeling process will need to be modified to ensure that domestic customers are not included in future heat demand assessments. Case study areas with smaller population densities had significantly longer pipe networks, which will affect later techno-economic modeling. Monte Carlo simulations highlighted errors in the data collection process, which was changed to improve the accuracy of counting and measuring the building sizes.

An example of the node, subnode structure used in the model.

The EU aims to, by 2020, reduce CO_{2} emissions to 20% of the 1990 levels (European Parliament, _{2}e, current UK emissions have been decreasing, down to 467.9 MtCO_{2}e in 2016; however further work must be done to meet the EU targets (BEIS,

District heating is a method of providing thermal energy to a number of customers from a centralized heat source (or sources) through the pumping of a heat transfer fluid around a pipe network. District heating is based around a network comprised of: thermal energy generating unit(s), the pipe network, and customer substations (Frederiksen and Werner,

This paper explores the initial stages of such a model, focusing on modeling the hourly variation in the local area heat demand, using Darley Dale in Derbyshire, UK as a case study. Darley Dale has a population of 5,400 (ONS,

In the UK, a rural area is classified as an area with a population of fewer than 10,000 people (ONS, ^{2} [Department of Energy and Climate Change (DECC), ^{2} (BEIS,

The potential for new rural district heating networks should even be considered in countries, such as Sweden, where the urban heat market is almost saturated with district heating. Rural district heating has only been implemented to a large extent in Iceland and Denmark (Reidhav and Werner, ^{2} whereas rural areas tend to have heat loads < 10,000 MWh/km^{2} (BEIS,

Many types of district heating models exist, with a differing range of goals and uses. Selecting the model most suitable for use in a particular case and application requires a thorough understanding of the range of models that exist, along with each models' uses and limitations. District heating models can consider anything from the entire network structure to an individual customer. In this paper only models of entire district heating networks will be considered.

District heating models can be either statistical or physical. Statistical models are time series or neural network based, are easy to build and understand but require primary measurements for validation (Wojdyga,

Physical models consider the entire structure of a district heating network, which makes them easy to modify but complex and computationally intensive. Instead of primary measurement validation, physical models only require simple network data inputs such as the network topology, pipe and insulation specifications and the pump characteristics (Larsen et al.,

Physical models need to be simplified to reduce the computing power required, simplification is achieved through the node method, otherwise called the process of aggregation. The node method substitutes the existing loop and tree structure of a network with lines and short branches, reducing the network complexity and computational intensity. The simplified models are generated using steady state flow conditions. During aggregation, important physical properties such as water volumes, time delays and mass flows are preserved (Palsson et al.,

Another method that can be used to simplify district heating networks is studying the relevant influences that the differing factors have on the overall heat demand. Studying the factors identifies influential factors that must be conserved and insignificant factors that can be omitted. The most influential factors on the heat demand are the outdoor temperature and the customer behavior (Dotzauer,

Short term heat demand can be modeled deterministically or predictively using time series. Deterministic models use complex simulations to predict the physical behavior of the buildings in the study. The complex deterministic simulations require simulation software as shown in Table

Simulation software used in the modeling of district heating.

EnergyPlus | Talebi et al., |

TRNSYS | Heller, |

MODEST | Holmgren and Gebremedhin, |

TERMIS | Gabrielaitiene et al., |

DHEMOS | Johansson, |

Simulink | Lim et al., |

eQUEST | Talebi et al., |

Deterministic models generate accurate results but require extensive data inputs and have high computational costs. The non-technical staff member who this paper is aimed at is unlikely to have access or be able to operate engineering specific software, therefore deterministic modeling is unsuitable for use.

Predictive models use equations to fit curves to the demand profiles (Talebi et al.,

It is possible to model a district heating network using historical data, where the district heating model is validated using the historical operating records of an existing network (Noussan et al.,

Another historical modeling type uses customer meter readings to model a district heating network. Meter reading modeling types use the water temperature, flow rate or gas bills to model the overall network heat demand (Wang et al.,

To reduce the number of buildings being individually modeled in the work and consequently reduce the complexity of the model, a district heating network can be modeled using the archetype building method. The archetype method works by grouping all buildings into a series of categories and representing each category with an archetype building. The accuracy of archetype modeling is heavily dependent on the number of archetype categories used and the accuracy of each individual archetype model. Individual archetype models are regression based, finding a typical demand profile for that building category (Talebi et al.,

Current district heating models have limitations, which impact district heating implementation (Talebi et al.,

The overall aim of this paper was to produce a heat demand model that was simple enough for a non-technical individual to use. The model quantified the hourly variation in the local area heat demand using a node structure that was easy to modify. The model was built using the heating degree day and archetype building methods.

The initial stage of the modeling work was to follow a geographical information systems (GIS) technique to build an energy map of the area. The energy map looked at both commercial and domestic buildings and identified the areas of high heat demand density and customers with a large heat demand. The commercial energy mapping was based on a technique used by Parsons Brinckerhoff (Parsons Brinckerhoff, ^{2}. The EIA energy consumption study split the typical energy use of archetype buildings into individual uses. CIBSE and EIA studies combined were used to give the annual thermal energy use for heating in kWh/m^{2} of archetype building categories. Google Maps and Google Street View were used to identify every possible heat user in the local area alongside the location, use and total measured floor area. The use of Google Maps introduced error; the error was acceptable as the energy maps only estimated and did not quantify the energy demand. Domestic energy mapping was carried out though converting population density into energy density (Finney et al.,

The energy maps were used to give an estimation of the yearly heat demand in the local area but did not model the heat demand on an hourly basis and were not accurate. The hourly heat demand modeling was done based on an industrial, archetype building model, which was centered around heat demand curves generated Arup (Arup, ^{2}) changed over a day. For each building type twelve curves were generated, each one representing a typical day of heat demand variation for each of the 12 months. The industrial model grouped every building into one of the following categories: retail, commercial, food and drink, hotels, residential, non-residential institutions and assembly and leisure. The monthly degree day values were determined using daily temperature data from a local weather station throughout the course of each year, as shown in Equations (1, 2):

Where

The monthly degree day value (_{dd}) (°C/h) was based on the sum of the hourly differences between the reference temperature (_{ref, t}) (°C) and the external temperature (_{t}) (°C), provided the reference temperature was greater than the external temperature, divided by the number of hours in the month (_{max}) (hour). The monthly degree day values were used to make monthly temperature dependent factors (TDF), as shown in Equation (3).

The monthly TDF was the ratio between the monthly degree day value and the maximum monthly degree day value (_{dd} _{(max)}) (°C/h).

The industrial model gave curves of hourly heat demand per unit area of total floor space for each archetype building type for each of the 12 months. The aim of this paper was to generate curves of hourly thermal load, representing every building within a set area, for each of the four heating seasons. As a result, significant adaption had to be made to the industrial method. The 12 monthly curves were averaged into four heating season curves. The four seasons ran from 20th March to 20th June, 21st June to 21st September, 22nd September to 21st December and 22nd December to 19th March. The curves of hourly thermal load for each building type were calculated as shown in Equation (4).

The hourly heat demand (_{Area}) (MW/m^{2}) and the total building floor area (^{2}). The individual archetype building heat demands were compiled to make a total hourly building heat demand within a set area as shown in Equation (5).

The total hourly building heat demand within a square of 100 m^{2} (_{Square}) (MW) was a sum of all of the individual hourly building heat demands (_{i}) (MW) for the N buildings within that area.

The paper calculated the total hourly building heat demand within a modeled area. The modeled area was split into a node, subnode structure. The structure was based around a heat source, splitting the modeled area into nodes, then subnodes and finally squares of 100 m^{2} size, as shown in ^{2} via the center of the node and subnode. An assumption was made that no distance of pipe is needed to connect the buildings located inside the squares of 100 m^{2} to the pipe connection at the center of the square.

For each square, the total number of buildings in each archetype building category was counted and used to calculate the total floor area of that building category as shown in Equation (6). Equation (6) was based on an assumed area for each building type in the study.

The total area of building category _{A, Tot}) (m^{2}) was proportional to the assumed area of buildings of that category (_{A, Assumed}) (m^{2}) and the number of buildings of that category (_{A}).

In rural areas the distances between the heat source and customers could be over 1 km (Finney et al.,

The time taken for the water to travel down a pipe (

Heat losses were calculated per meter of pipe length, as shown in Equation (8).

The heat loss (_{L}) (MW) was proportional to the thermal conductivity (_{i} –_{o}) (°C). Heat loss was inversely proportional to the natural log of the outer pipe diameter (_{o}) (m) over the inner pipe diameter (_{i}) (m).

The heat demands experienced in the center of each subnode, node and at the heat source were calculated, as shown in Equations (9–11).

The heat demand experienced in the center of each subnode, node or the heat source (_{Subnode}_{Node}) (MW) was a sum of all the heat demands of the components (_{Square}, _{Subnode}, or _{Node}) (MW) and the heat losses experienced in the pipes (_{l}) (MW) for the N components within that area. Where n represents the possibly different “Subnodes” or “Nodes.”

The model generates hourly curves of the heat demand experienced by the heat source for each of the seasons. The model was simple to understand, did not require large amounts of computing power and was quick to run. The node, subnode structure enabled easy modification through the addition or removal of nodes, subnodes, or squares. An example of a modification of the model is through a maximum allowable heat loss in each pipe. A maximum allowable heat loss as a percentage of the total heat demand in each pipe could be set. Any pipe that exceeded the maximum allowable heat loss was deleted. Deleting pipes instantly removed any nodes, subnodes or squares with heat losses that exceeded the set value and were unsuitable for use in the district heating network.

A disadvantage of the model was the number of assumptions used, including: that each building in a category was of the same set size, each building in a category had a heat demand curve as described by the industrial model and each pipe length traveled in the straight line distance from the customer to the heat source via the center of the subnode and node. The effect of the inaccuracies on the results was assessed using Monte Carlo simulations in the Goldsim software package (Goldsim,

One of primary the goals of the paper was to investigate if the same generic modeling process could be used in areas of different population densities, such as rural and urban or towns and cities or if the model would need modification from population density to population density. To investigate the effects of the different population densities, three case studies were modeled: a rural location, a heavily populated urban location and a sparsely populated urban location. As the comparison was between areas of different population densities, not different areas in the world the same weather data was used for all three. The weather data came from a weather station in the Derbyshire Dales, located at 53°15′41.0″N 1°44′03.5″W (Met Office,

The first case study was based around HJ Enthoven, a lead-acid battery recycling plant located in Darley Dale, England. HJ Enthoven is the largest producer of recycled lead in Europe, producing 80,000 tons of lead and propylene annually from over 150,000 tons of lead-acid batteries (ECOBAT,

The second case study was based around Veolia Sheffield, a municipal solid waste incineration plant. The plant is capable of producing up to 19 MW of electricity and 60 MW of heat, combusting 225,000 tons of waste per annum (Veolia,

The third case study was based around a British Steel plant located in Hayange, France. The plant manufactures steel rail sections, special profiles, and wire rod, employing over 400 people (British Steel,

The model was run for the three case study areas, generating hourly curves of heat demand for each of the four heating seasons, as shown in Figure

Figure

Buildings used in each case study model.

House (detached) | 340 | 2 | 54 |

House (semi-detached) | 344 | – | 8 |

House (terraced) | 227 | 15 | 100 |

Block of flats | 4 | 1 | 2 |

Supermarket | 3 | – | 1 |

Shops (miscellaneous) | 69 | – | 24 |

Office | 5 | 4 | 7 |

Warehouse | 9 | 58 | 26 |

Shopping center | 1 | – | – |

Church | 3 | – | 1 |

Medical center | 1 | – | – |

Village hall | 1 | – | – |

Manor house | 1 | – | – |

School | 1 | – | – |

Library | 1 | – | – |

Pub | 1 | – | – |

Restaurant | – | – | 2 |

As the aim of paper was investigate if the same modeling technique could be used in different areas of population density, all buildings in the case study areas were included, even domestic buildings. Figures ^{2} were counted, will need to be modified to ensure that only larger domestic buildings, such as a block of flats, are included. Blocks of flats, as well as housing associations, are often regarded as anchor loads for a new district heating network (Hawkey,

Anchor loads are heat customers with large, stable and constant heat demands that are key to a network's success (Hawkey et al.,

Figure

Table

The size and locations of the heat source (in red) and customers (in black), showing the clusters of heat customers (in black rings) in each case study area.

Figure

The case studies with smaller population densities (case studies 1 and 3), have total pipe lengths of 22.0 and 32.8 km, respectively. The case study with the larger population density (case study 2), has a significantly smaller pipe length of 5.4 km. The rough differences in pipe length between more and less densely populated areas is by a factor of 4–6. As the capital costs of the pipe lengths and the heat losses are both proportional to pipe length (Raine,

The three case studies varied significantly in the number, and locations of the customers as well as heat losses in the pipes. The less densely populated case studies have hundreds of individual customers on the network, with at least 70% of the customers coming from domestic sources. The customers were shown to be clustered in the built up land surrounded by areas of green space. The heat losses in the less densely populated case studies were shown to be 40 and 45% of the overall heat demand. In comparison, the more densely populated case study was shown to have less than a hundred individual customers, with < 25% of the customers being from domestic sources. The customers were shown to have a greater dispersion around the heat source. The heat losses in the more densely populated case study were shown to be 7% of the overall heat demand. It was shown that the less densely populated case studies have pipe lengths 4–6 times longer than the more densely populated case studies. The overall heat demand of the network is dependent on the number, type and location of the customers and the heat losses in the pipe.

A primary goal of this paper was to keep the methodology simple enough to allow a non-technical individual to use, meaning several assumptions were made. The assumptions introduce the possibility of inaccuracy into the model, the extent of which was assessed both internally and externally. The internal assessment was completed using Monte Carlo simulations. Normally, the external assessment would be completed using primary district heating network data or a similar model. No existing district heating networks provided primary data for use in this study and due to novel nature of the work, external models that could be used as a comparison do not exist. Using an existing model would require more assumptions to be made than are already in the work, the accuracy of which would need assessing. Instead, the external validation comes from the industry confidence in the industrial model; the industrial model is generated based on industry experience (Arup,

Monte Carlo simulations were used to assess the accuracy of the key assumptions. Monte Carlo simulations re-ran the model thousands of times, varying the inputs, and measuring the variation in the model output. The assumptions that were assessed are: (1) the assumption that each building in the same archetype category is of a standard assumed size, (2) the assumption that each building in the same archetype category has the same hourly heat demand profile as described by industry and (3) the assumption that the pipe route runs in the shortest possible straight line distance from the heat source to the customer via the center of the nodes and the subnodes.

It is expected that on a network wide scale the inaccuracies from the assumptions will not be significant due to the large sample size, meaning that the average will not be significantly affected. In cases with large variance in the input data however, the average is likely to be significantly affected, meaning that the inaccuracies from the assumptions will be significant. The data used to validate the assumptions came from a series of studies into building size and heat demand variation [Burzynski et al.,

The probability distributions that were loaded into Goldsim are based off the distributions found studying the variation in building sizes, heat demands and networks lengths. The distributions were as follows. For the building size assumption (1): a normal distribution with a mean of 1 and a standard deviation of 1.96. For the building heat demand assumption (2): a normal distribution with a mean of 1 and a standard deviation of 0.212. For the network route variation assumption (3): a pareto distribution with a shape factor of 5 and a lower bound of 1. In the loaded distributions, a value of 1 means that the building size, heat demand or network route is unchanged. A value higher or lower than 1 changes the building size, heat demand or network route by a factor of that value. The Darley Dale case study was used to run the Monte Carlo simulations during the winter season. The probability distributions were run 1,000 times in the Goldsim software. One thousand simulations allowed the model output to reach convergence, which is achieved when less than a 1% change in standard deviation occurs; as shown in Figure

The results of the Monte Carlo simulations are show in Figure

Results of the Monte Carlo simulations for the assumptions in the model, after 1,000 simulations. The mean result, 50th percentile, is shown with a black line. The range of percentiles to the extremes of 5th and 95th are denoted by the color bands.

The input and output ranges for the Monte Carlo simulations, showing the assumption of standard building sizes, standard heat demand profiles and a straight line network route.

Input and output uncertainty for the different Monte Carlo studies.

Type of assumption | Building size (1) | 98 | 89 | 67 | 49 | 30 | 10 | 0 | 11 | 34 | 61 | 96 | 158 | 229 |

Heat profile (2) | 49 | 34 | 22 | 14 | 8 | 3 | 0 | 3 | 8 | 14 | 22 | 34 | 48 | |

Network route (3) | 5 | 5 | 4 | 3 | 2 | 1 | 0 | 1 | 3 | 6 | 12 | 24 | 48 |

Figure

It was not definitively determined if the assumption of standard heat demands (2) creates an acceptable spread of results. Figure

The distribution of the heat demands found by the Monte Carlo simulations of the assumption of an average heat demand profile (2) compared against the distribution of heat demand variations found in the literature, which were used as the inputs into the Monte Carlo simulations.

Figure

Thus far, the Monte Carlo analysis was performed investigating one variable at a time instead of globally, where all of the assumptions are varied simultaneously. Global assessment was vital to comprehensively assess the accuracy of the multiple assumptions. As stated, the assumption of standard building sizes was inaccurate, therefore will be omitted from future work. In future work the building sizes (1) will be measured manually, creating a more accurate model. The global assessment now requires the assumptions of standard heat demand profiles (2) and network route length (3) to be done simultaneously as shown in Figure

Figure

The modeling technique was altered to remove the assumption of standard building sizes (1), by measuring the buildings in the local area. It was useful to observe the extent that the change to the modeling technique would have had on the results. The modeling process used in Figure

Figure

A comparison of the original (assumed building sizes) and refined (measured building sizes) models for local area heat demand.

In the new methodology, there are two possible ways to measure the size of the buildings. The ideal measurement, which would be possible for the non-technical individual at a local authority is to access the building records available. The second technique is to use Google Maps to measure the floor area of a building and use Google Street View to count the number of floors in the building. Using building records should not introduce any error into the work, using Google Maps to measure area has been shown to have errors of 3.54% (Lopes and Nogueira,

The distribution of the heat demand from the global (including the error from the measurement process) and individual Monte Carlo simulations as well as the distributions of heat demand and network route length as found in the literature.

Figure

The hypothesis of this paper proposes a new model that could be used to estimate the hourly heat demand variation of any new district heating network whilst being simple enough that a non-technical staff member could use it. Case studies were investigated to see if the same modeling technique could be used for areas of different population densities. Monte Carlo simulations assessed the accuracy of the assumptions made in the modeling process.

Networks with large population densities were shown to have significantly shorter pipe lengths, resulting in reduced heat losses and installation costs. This may require networks with differing population densities to have differing business cases and incentives in later techno-economic work. Networks with small population densities were shown to be comprised of a large proportion of small domestic customers. In future work, the modeling process will need to be modified to ensure that domestic customers are omitted from the modeling process or, the business case of networks with small population densities may fail. The number, type and location of the customers included in the network, along with the overall pipe length and heat losses in the pipes affects the overall heat demand.

Individually, the assumption of the shortest possible network route (3) and standard building heat demand profiles (2) were found to be acceptable. The network route assumption (3) was shown to be acceptable as a 90% variation in the input uncertainty only causes 29% variation in the output uncertainty. The heat demand assumption (2) was shown to be acceptable as the probability distribution of the results were shown to be identical to the probability distribution in the heat demands of actual buildings. The simultaneous assumptions of a standard heat demand profile (2) and network route (3) were assessed using Monte Carlo simulations. The output distribution of the combined assumptions is similar to the input distribution of the results found in literature, therefore both assumptions can be kept simultaneously in future modeling work.

The assumption of standard building sizes (1) was

IB was the postgraduate research student who carried out the modeling. PS and SB were the Ph.D. supervisors who directed the research.

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

We gratefully acknowledge the Engineering and Physical Sciences Research Council (EPSRC) for funding a CDT Studentship to IB under the Centre for Doctoral Training in Energy Storage and its Applications (EP/L016818/1). PS is grateful for funding from the EPSRC Grand Challenge Network, CO2Chem Network: Establishing the UK as World Leaders in Carbon Dioxide Utilisation (EP/P026435/1). IB is grateful to Robin Idle, H. J. Enthoven and Sons for the provision of energy use data and their experience with the Lead-Acid battery process and to Arup for their help with the heat profile models.