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Improving the performance of district heating systems by utilization of local heat boosters

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District Heating (DH) plays an important role into the Danish energy green transition towards the future sustainable energy systems. The new, 4 th generation district heating network, the so called Low Temperature District Heating (LTDH), tends to lower the supply temperature of the heat down to 40-50°C with return temperatures of 20-30 °C. This kind of heating system has many advantages and among all of them, it allows utilization of the heat coming from low exergy heat sources, as well as to decrease the grid heat losses. Electrical energy driven heat sources are also integrated into the future LTDH grid as they will have the strategical role of connecting the heating system with the electrical energy coming from the intermittent and fluctuating renewable energy sources such as wind and solar power. In this paper a case study of district heating system is presented and analysed. The goal was to evaluate the possibilities to lower the forward temperature of the heat supply in order to reduce the heat losses of the system. Booster heat pumps are introduced to increase the water temperature close to the final users. A Matlab model was developed to simulate the state of the case study DH network in terms of mass flow rates, temperatures and heat losses. After the model simulation, a new configuration of district heating with the introduction of three booster heat pumps was proposed. The new system's operation is determined based on a non-linear optimization problem in which the objective function was set to minimize the system heat losses. * Corresponding author 0303-1 1 This goal was achieved by lowering the forward temperature to 40°C and relying on the installed heat pumps to boost the water temperature to the admissible value needed for the domestic hot water preparation. Depending on the season, the optimized configuration allows decreasing the network heat losses in the range of 38-54%, higher reductions being achieved during colder seasons.
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IMPROVING THE PERFORMANCE OF DISTRICT HEATING SYSTEMS BY UTILIZATION OF LOCAL
HEAT BOOSTERS
A. Falcone
Department of Energy Engineering
Sapienza University of Rome, Rome, Italy
email: alessia.falcone23@gmail.com
D. F. Dominković*
Department of Energy Conversion and Storage
Technical University of Denmark (DTU), Frederiksborgvej 399, Roskilde, Denmark
e-mail: dodo@dtu.dk
A.S. Pedersen
Department of Energy Conversion and Storage
Technical University of Denmark (DTU), Frederiksborgvej 399, Roskilde, Denmark
e-mail: alpe@dtu.dk
ABSTRACT
District Heating (DH) plays an important role into the Danish energy green transition towards the
future sustainable energy systems. The new, 4th generation district heating network, the so called
Low Temperature District Heating (LTDH), tends to lower the supply temperature of the heat down
to 40-50°C with return temperatures of 20-30 °C. This kind of heating system has many advantages
and among all of them, it allows utilization of the heat coming from low exergy heat sources, as
well as to decrease the grid heat losses. Electrical energy driven heat sources are also integrated into
the future LTDH grid as they will have the strategical role of connecting the heating system with
the electrical energy coming from the intermittent and fluctuating renewable energy sources such as
wind and solar power. In this paper a case study of district heating system is presented and
analysed. The goal was to evaluate the possibilities to lower the forward temperature of the heat
supply in order to reduce the heat losses of the system. Booster heat pumps are introduced to
increase the water temperature close to the final users. A Matlab model was developed to simulate
the state of the case study DH network in terms of mass flow rates, temperatures and heat losses.
After the model simulation, a new configuration of district heating with the introduction of three
booster heat pumps was proposed. The new system’s operation is determined based on a non-linear
optimization problem in which the objective function was set to minimize the system heat losses.
* Corresponding author
0303-1
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This goal was achieved by lowering the forward temperature to 40°C and relying on the installed
heat pumps to boost the water temperature to the admissible value needed for the domestic hot
water preparation. Depending on the season, the optimized configuration allows decreasing the
network heat losses in the range of 38-54%, higher reductions being achieved during colder
seasons.
KEYWORDS
4th generation district heating, heat pump, sustainable energy systems, district heating, heat savings
1 INTRODUCTION
The worldwide problem of climate change and the increase of energy demand in the last decades
are moving societies toward more sustainable behaviours. Moreover, growing awareness about the
scarcity of natural non-renewable fossil fuel resources is leading to the use of new renewable
energy sources. Energy systems throughout the world are facing the challenge of supplying existing
and upcoming energy needs in a sustainable way that does not increase the carbon dioxide level in
the atmosphere. The climate change is real and it is evident from scientific observations such as the
increase of earth’s surface and ocean average temperatures, the increasing rate of the ice/snow
melted in the Polar regions and the consequential increase of the sea level [1]. The Danish
government wants Denmark to contribute actively to meet the calls from scientists that significant
reductions in greenhouse gas emissions are necessary, and this is why an historical new Energy
Agreement was signed in Denmark in 2012 which sets the framework for the national green
transition [2].
The Agreement involves a wide range of ambitious initiatives with the goal to bring Denmark
closer to the long term target of 100% renewable society in the energy and transport sectors by
2050. Moreover, the government has established as intermediate goal that the electricity and heating
supply must be fully independent of fossil fuels by 2035.
The transition from the current fossil fuel based energy systems into future sustainable energy
systems requires a large-scale integration of an increasing level of intermittent and low energy
density of renewable energy sources (RES) such as wind, geothermal and solar power. These
intermittent and/or low energy density sources have to be combined together with residual resources
such as waste and biomass. Many municipal and national studies have shown some possible
scenarios for the 100% renewable energy systems such as [3] [4] [5] [6] [7], and while they differ in
terms of how much individual technologies are introduced, the core elements of those scenarios
include: the expansion of renewable energy sources, large part of heating demand covered by
district heating systems including heat pumps, and transportation sector based on electricity.
In this context the district heating (DH) network will play an important role in the future sustainable
energy systems, as it allows implementing large scale renewable energy sources into the heating
system.
In a temperate climate such as the Danish one, heating plays an important role. Today 63% of
heating in private Danish houses for both space heating (SP) and domestic hot water (DHW) is
provided by district heating (DH) [8].
District heating makes use of heat produced in central locations and distributes it through pipelines
to a large number of end users that can be for example a neighbourhood, a town centre or a whole
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city. In that way, heat, that has no or very low value in one place, can be transformed to high value
energy source in places where there is a high demand for heat, such as small towns or large urban
communities. This approach allows any available source of heat to be used, making the system very
flexible and increasing both the security of supply and the production efficiency.
Establishing a district heating network also allows utilizing low-quality heat in the society. This
could be surplus heat from industry and waste incineration, and heat from combined heat and power
(CHP) production.
Combined heat and power production (CHP) is currently the main technology for producing heat in
the Danish DH systems [9], and this is one of the most important reason why it has been possible to
increase energy efficiency and to reduce the carbon emissions over several decades.
Nowadays, all centralised CHP plants and most decentralised CHP plants sell electricity at the
market price. Therefore, they must tend to optimise their production according to the market price
of electricity on the spot market, where prices are set for each hour one day in advance. This means
that the goal of CHP plant operators is to produce more electricity and heat in cogeneration when
electricity prices are high. Similarly, they try to minimise their production when electricity prices
are low [8]. The use of heat accumulators is then a viable option for better operation of the system.
Heat storage provides many advantages to the system as it improves the economy of a district
heating system, decouples consumption from production and allows implementation of sustainable
heat sources.
In Denmark, more than 42% of all electricity comes from the wind turbines. Due to the fluctuating
production from wind turbines, there is often surplus electricity at very low prices. In combination
with both short and long term storage, the surplus electricity can be used in the district heating
system to produce hot water, either directly by electric boilers or indirectly by heat pumps, in a
much cheaper way compared to the storing electrical energy in batteries.
The general trend in the development of the new generation of district heating systems is toward
lowering forward temperature [11].
Low temperature district heating (LTDH) system enables meeting of the two main requirements for
the future district heating and the whole energy sector: high energy efficiency and high share of
renewable energy. LTDH systems utilize supply and return temperatures of around 55/25°C which
are sensibly lower compared to the current standard medium temperature district heating system,
80/40°C.
A number of demonstration projects have proven that the district heating supply temperature at
slightly above 50°C can meet the end-user’s Space Heating (SH) and Domestic Hot Water (DHW)
demands in central-northern European climates, in properly designed and operated district heating
networks and in-house installations [13]. The major advantages due to the reduced network
temperature level are summarized in [14] and they include reduced network heat loss, increased
utilization of renewable energy, reduced pipeline thermal stress, reduced heat loss in thermal
storage units, improved power to heat ratio in CHP plants, increased heat pumps efficiency and
utilization of waste heat from industries.
As stated in [16], LTDH is one of the enablers of the transition to eco/low-carbon society. The
minimum supply temperature level into a DHN is determined by the space heating demand
requirements and by the hygienic and comfort standards of the domestic hot water.
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The forward temperature can be reduced only to the level that guarantees the delivery of domestic
hot water with required temperature of 45°C for kitchen use and 40°C for other tapping use [DS
439,2009]. The design indoor comfort temperature in buildings is usually set to 20°C. In Denmark,
to prevent the growth of Legionella bacteria keeping the domestic hot water temperature no lower
than 50°C is recommended, if the system has water circulation. On the other hand, for systems with
storage tank, it is suggested to keep the temperature no lower than 55°C. However, there are no
regulations in Denmark dealing directly with Legionella prevention and control [17].
The required temperature for LTDH networks can be supplied with the most current heating supply
technologies such as CHP plants, boilers, waste incineration plants and renewable energy sources
such as solar heating and deep geothermal. However, in the urban area many other heat sources
exist, that have temperature below the minimum required by the DHN. These heat sources can be
for example sewage water, waste heat recovered from server centres or electric transformers,
shallow geothermal heat etc. Due to the temperature level below 50°C they belong to another
category of district heating named Ultra Low Temperature District Heating (ULTDH). This type of
district heating would have the great advantage of being able to exploit a wider range of available
waste heat, increasing the flexibility of the decentralized heat supply and achieving a more
sustainable development of the heating supply system. However, to satisfy the DHW requirements
the water temperature has to be increased utilising thermal boosters close to the end users such as
electrical heaters or small scale heat pumps. The feasibility of some ULTDH applications with
booster heat pumps installations for DHW preparation in single family houses has already been
studied in [18] , [19] and [20] where positive results are registered.
Compared to the other similar papers, idea of the research carried out in this paper was to assess the
potential heat savings on a real network case, as operating the network in reality can prove to be
different from the desired operation in the simulated environment.
The paper is organized in a way that the introduction section is followed by two models described
in methods section. Further on, in sections 3 and 4 case study on a real example is described and
obtained results are presented. Finally the last section deals with the concluding discussion.
2 METHODOLOGY
2.1 Problem Definition
In order to utilize all the benefits of low and ultra-low temperature district heating, local heat
boosters, located near the end customers are needed in order to boost the temperature of the heat
when there is an increased demand for it. Furthermore, in order to apply the concept of local heat
boosters to the real problem, one needs to simulate the behaviour of the real network in order to be
able to characterize changes of the network with local boosters included, compared to the original
network design. For this purpose, the initial iteration model has been developed in Matlab and it is
described in section 2.2. In order to detect the optimal position, as well as the capacity of the local
boosters, an optimization non-linear model has been developed in the section 2.3. By comparing the
results obtained from these two models, one can detect how useful is the low temperature district
heating grid compared to the classical operation of the district heating network.
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2.2 Model Description
To simulate the state of the network in terms of mass flow rates and temperatures, a sample model
has been developed in Matlab. The District Heating Network (DHN) can be topologically described
using the basic concepts of the graph theory. The standard network topology allows representing the
DHN in terms of nodes and branches in which every branch connects a pair of nodes and
corresponds to a supply and a return pipe.
The nodes can be divided into [21]: Plant nodes which represent the heat plant facilities or the
injection points of the heat in the network; Customer nodes which represent the end users to whom
the heat is delivered and they are typically a leaf node in the network; Intermediate nodes that are
neither plant nor customer nodes. They are junctions of two or more branches. Some of the
intermediate nodes may be branching nodes, i.e. nodes where three or more branches meet.
The model developed in this study is applied to a tree structure topology network without internal
loops. An example of a DHN representation is shown in Figure 1 below in which node 1 represents
the heating plant, nodes 2-4-5 can be customer nodes, or represent aggregated sub-networks/users,
and node 3 is a branching node. The same scheme is valid for both supply and return pipes. The
only difference between the two are the flows directions: for the supply pipes the water flows from
the node plant 1 till the leaf nodes, for the return ones it flows in the opposite direction from the leaf
nodes to the plant.
Figure 1 Example of DHN with tree topology scheme
To compute the mass flow rates in each branch and the temperature level at each node, the district
heating system model accepts as input parameters the heat demand of different customers and the
operational variables of the heat plant such as the supply and return temperature at the injection
point.
2.2.1 ESTIMATION OF MASS FLOW RATES
The estimation of the mass flow rates in the DH network is based on customer measurements or
forecasts for heat demand. The mass flow rates for DH water at customer nodes i are obtained as:
  
 
Where is the mass flow rate at customer nodes expressed in kg/s;  is the heat demand rate
of the customer expressed in W; c is the specific heat capacity of the water expressed in J/(Kg °C);
Tsi and Tri are the supply and return temperatures at the customer substation expressed in °C. At
each node the mass balance equation has to be satisfied. The incoming water subtracted by the
outgoing water equals the water consumption or supply at that node (zero at the intermediate
nodes):
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
 
 
Where: 
and 
are the mass flow rates inside the network branches;
is the water
consumption or supply at the specific node i.
For a complex system it is easier to write the mass balance equations for all the nodes in a matrix
form using the incidence matrix [22]. This matrix will have dimension NXB where N is the number
of nodes of the system and B is the number of branches. To describe the topology of the network,
the elements of the matrix will be equal to +1 if the node is the origin of a branch, -1 if the node is
the destination of the branch and 0 elsewhere.
For example, the incidence matrix of the network shown in Figure 1 which has 5 nodes and 4
branches would have dimensions [5x4]:
 
 
  
 
 
 
 
  
Writing all the equations in a matrix form gives:

Where:
is the vector containing all the mass flow rates in the branches;
is the vector of
external mass flow rates towards the customers.
Since the DH network is tree-like, then the values of mass flow rate of the return pipes are equal to
the supply ones. Hence, it is sufficient to compute only the mass flow rates for the supply system
and use the same values for the return pipes.
The equation system will be fully determined if the water flow rate at all except one customer or
plant node is known.
2.2.2 ESTIMATION OF TEMPERATURES
To estimate the temperature at each node it has to be considered that both supply and return pipes
lose some heat in their respective directions of flow due to conduction to the surrounding ground
[23].
Figure 2 Control volume for the internal flow in a pipe
Considering a control volume of the internal flow inside a pipe, as the one showed in Figure 2, the
energy balance equation can be written as:

 
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Where: is the water temperature in °C;
is the heat loss per unit length; it can be expressed as:
 
; is the overall heat transfer coefficient of the pipe in W/(m °C); is the
surrounding temperature in °C.
The solution to the first order differential equation gives the formula of the temperature drop
equation. Considering a branch i-j the temperature of the water at the end of the branch, in node j,
will be equal to:


Thus, in pipes, the water temperature drops according to a decreasing exponential function. This
temperature drop formula ignores the small temperature increase due to viscous friction.
Figure 3 Flow chart of the iterative algorithm
To compute the supply and return temperatures at each node of the network, the equation is applied
sequentially along the branches of the network starting from the heat plants.
When node j is the destination of multiple flows from different branches, each branch brings water
of different temperature into the node. Therefore, the temperature of the mixed water is computed
as a weighted average of the water temperatures in the incoming pipes.
Mass flows and temperatures depend on each other; hence, it is necessary to solve the system
iteratively. The solving sequence of the model is schematically represented in Figure 3. The starting
point of the iterations has been assumed considering zero heat losses in the system, i.e. the supply
temperature at each node is set equal to the maximum supply temperature at the heat plant and the
return temperature for all the nodes is equal to the return temperature at the plant. Then the mass
flow rates at customer nodes are computed based on the heat load requests and the mass flow rates
in the branches of the network are evaluated using the incidence matrix I. After computing all the
mass flow rates, in each iteration the temperatures are re-calculated based on the temperature drop
equation and those new values are used to re-compute the mass flow rates in the system. The
iteration continues until the norm of the temperature difference between the last two iterated values
is greater than the chosen tolerance value, which was for the purpose of this paper set to 10-6.
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2.2.3 ESTIMATION OF HEAT LOSSES AND VALIDATION OF RESULTS
The heat losses in the system can be calculated as the sum of the heat losses in all the network
branches. Those are function of the water temperature inside the pipes and can be calculated with
the formula:
 
Where is the temperature of the water calculated as an average between the inlet and the outlet
temperature at a specific branch. The calculation is made for both supply and return pipes.
Once the mass flows at all pipes and temperatures at the nodes are computed, to validate the
computational results of the district heating state, the network should satisfy the energy balance
according to which the total heat production from the injection point minus the customers’ heat
demand should be equal to the total heat losses in the branches:
  
Where:
  
is the total heat production at the injection point and the mass flow rate, , is calculated by
summing all the mass flow rates at the customer nodes.
2.3 The optimization problem
The goal of the optimization problem is to minimize heat losses in the district heating grid by
inclusion of local heat booster. The boosters are modelled as heat pumps and they have the function
of increasing the water temperature if it does not satisfy the domestic hot water requirements or heat
demand of the customers.
The modelled heat pumps have a configuration as the one showed in Figure 4. The district heating
hot water system is divided into two flows: one goes into the evaporator of the heat pump and the
other into the condenser. The two streams are mixed in the return flow, combining the residue heat
from the evaporator and the cold water coming from the heat exchangers with the secondary
network. The DH flow which runs through the evaporator represents the heat source for the heat
pump and it heats up the temperature of the rest of the flow that passes in the condenser.
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Figure 4 Booster heat pump configuration [15]
The exact location of the booster heat pumps in a certain branch of the network is one of the outputs
of the problem, together with temperatures at each node, mass flow rates and electricity needed to
run the heat pumps.
2.3.1 OBJECTIVE FUNCTION
The objective function of the optimization problem is to minimize the total heat losses in the
system, . Those are calculated as:
 
The formula is applied to all the branches of the network considering separately supply and return
pipes. The water temperature, , is equal to the average between the water temperature at the
beginning and at the end of the considered branch.
2.3.2 CONSTRAINTS
LINEAR EQUALITY CONSTRAINTS
The mass balance equation has to be satisfied at each branching node and before the heat pumps:
the incoming flow must be equal to the outgoing flow.

 
 
The heat loss equations for the branches without heat pump have a linear form since the length of
the pipes are fixed and the only unknown variable is :
 
The pipes which contain a HP are considered as divided in two branches: one before the heat pump
and one after it. For each of them the heat losses are calculated but the lengths are not decided a
priori (they are an output of the optimization). The sum of the branches’ lengths before and after the
HP has to be equal to the original pipe’s length without HP.

  
LINEAR INEQUALITY CONSTRAINTS
Many of the inequality constraints are represented by temperatures conditions such as:
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The temperatures at the beginning of a branch are always greater than the ones at the end of the
considered branch (with reference to the water flow direction) due to the heat transferred to the
surrounding ground;
Figure 5 Sample branch
The flow temperatures outside the evaporators are lower than the ones going inside;
 
The flow temperature outside the condensers is greater than the ones going inside;
 
The supply temperature at a customer node is always greater than the return temperature at the same
node;
 
NON-LINEAR EQUALITY CONSTRAINTS
These constraints include:
The heat loss equations for the branches with the heat pumps since, together with the temperature
variables, there are also the length variables;
 
The heat transfer equations for the HP condenser:
   
Where:  is the electric power input to at the compressor;
The temperature drop equations along the branches, referring to Figure 5:


The weighted average temperature in the nodes where there are mixing flows:
Figure 6 Mixing mass flow rates
  

 
The heat transfer equations at customer nodes to meet the heat load requirements:
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 
3 CASE DESCRIPTION AND INPUT PARAMETERS
The model described is applied to part of the DHN of the city of Roskilde. It is located in Denmark
30 km west of Copenhegen on the island of Zealand. It is the main city of Roskilde municipality
with a population of 50000 inhabitants. Roskilde network has five exchange stations where the heat
coming from a combined heat and power plant and a waste incinerator is delivered to the customers
throughout 286 km of district heating pipes [24]. The analised DHN is part of the newest DH zone,
in which there are dwellings built in the 1990s. This zone is called Marbjerg. The average heat load
consumption of a single family house has been calculated considering the consumptions of more
than 300 single family houses and results to be 12.5 MWh/year. The average hourly heat load
profile is shown in Figure 7.
Figure 7 Heat load profile of a single family house situated in Marbjerg with an average annual
consumption of 12.5 MWh
Marbjerg network has one injection point and it delivers heat throughout pre-insulated pipes. The
average yearly heat losses in the distribution system measured by the company are equal to 13%.
The network is shown in Figure 8.
Figure 8 Marbjerg newer DHN
0
0,5
1
1,5
2
2,5
3
3,5
1
352
703
1054
1405
1756
2107
2458
2809
3160
3511
3862
4213
4564
4915
5266
5617
5968
6319
6670
7021
7372
7723
8074
8425
kWh/h
hour
Heat Load Profile Marbjerg
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The distribution pipe system has a total length of 22 km divided in many types of tubes which differ
from each other for their geometry. They are all pre-insulated single pipes. To run the model
simulation, the operational variables at the injection node such as the supply and return
temperatures have to be known; these are shown in Figure 9.
Figure 9 Supply and return temperatures at the network injection point
The modelled branches of the network are showed in Figure 8. Those particular branches were
suitable as they supply water to single family house customers.
The investigated network is represented in Figure 10.
Figure 10 Scheme of the modelled part of Marbjerg network
It has one injection node, 1, two branching nodes, 2-4, and three customer nodes, 3-5-6, for a total
of five branches. The heat consumptions of the single family houses have been aggregated at the
leaf nodes to make an easier calculation of the district heating state. At node 3, there are 4 family
houses, whereas at node 5 and 6 there are 8 family houses. In reality those houses are disposed
along the branches, but to consider them in an aggregated way, the branches lengths have been
reduced in such a way to have the leaf node located just before the first houses of the branch. The
network scheme reported in Error! Reference source not found. is valid both for supply and
return pipelines. The geometry data and the overall heat transfer coefficient of the five branches are
reported in Table 1.
Table 1. Geometries and overall heat transfer coefficient of the analized network
A
B
C
D
E
DN
65
32
50
40
50
Length [m]
72
50
30
53
80
U [W/m K]
0.194
0.141
0.171
0.157
0.171
30
50
70
90
1
366
731
1096
1461
1826
2191
2556
2921
3286
3651
4016
4381
4746
5111
5476
5841
6206
6571
6936
7301
7666
8031
8396
⁰C
Hour
Temperatures T return T supply
0303-12
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The hourly supply temperature at node 1 is assumed to be equal to the supply temperature at
Marbjerg injection point minus 10 °C, so that it reflects the decreased water temperature in the
distance from Marbjerg injection point and the considered node 1. The ground temperature in
Denmark is assumed to be equal to 8°C [18]. The temperature at the aggregated customers’ supply
nodes must be at least 55°C so that considering a pinch temperature of 5°C in the heat exchanger
between primary and secondary network, the temperature requirements for the domestic hot water
preparation and to avoid legionella bacteria growth are satisfied. The return temperature at the
customer nodes, instead, has to be higher than 25°C to provide an indoor comfort temperature
between 18°C-20°C.
In the optimization problem the supply temperature at the injection point can vary in the range
between 40°C and 80°C. The lower bound of the return temperature at the injection point is set
equal to 20°C. The water temperature outside the heat pump evaporator has to be greater than 25°C
to simulate a reliable operation of the heat pump.
The mass flow rates are limited by the maximum velocity of the water in the pipes. The LOGSTOR
A/S Company recommends not exceeding the velocity of 1 m/s in smaller branches of distribution
pipes. Hence, the maximum volume flow [m3/s] has been calculated as the product between the
maximum velocity and the section area of the considered pipe; then the maximum mass flow rate
[kg/s] has been evaluated multiplying the volume flow rate with the water density. In the same way
a minimum water flow rate has been calculated considering a minimum water velocity of 0.1 m/s.
The mass flow rete bounds are shown in Table 2.
Table 2 Mass flow bounds
BRANCH
A
B
C
D
E
mass flow max
[kg/s]
4.5461
1.411242
2.854331
1.831319
2.854331
mass flow min [kg/s]
0.45461
0.141124
0.285433
0.183132
0.285433
Since the injection temperature can go below the required temperature limit at customer nodes,
additional energy has to be provided close to the end users. Hence, the electrical boosters
introduced in the new configuration are essential to guarantee a minimum water temperature in
order to satisfy the heat requirements and to prevent the proliferation of the Legionella bacteria. The
annual heat load request of the considered single family houses in Marbjerg is very low (12.5
MWh/year/house); hence, it is assumed that they are equipped with modern low energy heating
systems such as floor or wall heating. These systems can easily work with water temperatures
below 50°C (it is possible to lower the temperature even to around 30-40°C), while the older
radiator systems require temperatures of 50-70°C [25].
The new configuration has three electrical boosters located in the network branches B-D-E which
carry the water directly towards the single family houses, Figure 11 .
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Figure 11 Analysed DHN with booster heat pumps
This type of heat pump has a COP equal to approximately 5.5 [19], a value higher than the average
COPs because the temperature of the heat source is very high (at least equal to 40°C). The location
of the booster heat pumps in the branches B-D-E is not defined a priori in the new configuration,
instead, it is one of the outputs of the optimization problem.
4 RESULTS
4.1 State of the analysed network
Running the simulation for the 8760 hours, for the heat demand set for the year 2015, gives the
result shown in the following graphs. As it is possible to notice in Figure 12, the network heat
losses are much higher when the supply temperature at the injection node increases.
Figure 12 Network heat losses and relative heat losses
The grid losses relative to the supplied power at the injection point are instead higher during the
summer. The supply temperature registered at each node decreases according to the temperature
drop equation, and the most critical nodes, with the greatest temperature decrease, are the furthest
from the injection node 1, as shown in Figure 13.
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Figure 13 Node supply temperatures
The total yearly heat losses calculated are equal to 13.8% of the injected power in the considered
network, while the real reported losses in this part of the network are equal to 13%. Hence, the
model reflects the real behavior of the grid and is considered to be validated.
4.2 Optimization Results
The optimization is performed for different days of the year. Due to computational time limits
specific weeks of the year have been chosen and analysed. The results have been taken then as
representatives for specific seasonal conditions. To minimize heat losses, the system locates the
heat pumps as close as possible to the end user consumers. The pipes B1, D1 and E1 have a length
almost equal to zero.
The optimal system configuration has always the forward temperature at the injection point equal to
its minimum possible value, i.e. 40°C. The water temperature is then boosted to 55°C by the heat
pump to satisfy the DHW temperature requirements and since the heat pump is situated at the end
of the branches, this water temperature is the same of the one entering the heat exchanger.
The system tends to have the mass flow rates always close to the lower bound, i.e. to 0.6 kg/s at the
injection point. This minimum value is enough to satisfy the heat load request for almost all the
hours of the year, except for the very cold days when the mass flow is slightly higher and reaches
values of 0.85 kg/s.
The optimized system configuration allows to considerably decrease the heat losses thanks to the
lower forward temperature. Some typical days, which reflect the seasonal operating conditions of
the network, are analysed.
During winter, the forward temperature has its highest values and referring to Figure 13, the first
2000 hours of the year have an average temperature of 68°C with peaks that can reach 75°C at the
injection node 1. Due to the high temperature values the heat losses in those hours are greater than
the average, and have peaks of 5.8 kWh. With the optimized system that considers the forward
temperature at the injection node always equal to 40°C, the heat losses are considerably lower.
Considering the coldest week of the year at the beginning of February (day of the year 34-35-36-37-
38-39-40), in which the average hourly heat loss with the old system configuration is 5.1 kWh, the
average hourly heat loss with new system configuration becomes equal to 2.3 kWh. Hence, a
reduction of 54% of the heat losses is achieved with this configuration. During summer, considering
the first week of July (Days 210-211-212-213-214-215-216), the average hourly heat loss is equal
0303-15
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to 4.7 kWh, instead the average heat loss calculated with the optimized system is equal to 2.9 kWh
that means a reduction of 38% of the heat losses.
Figure 14 Heat losses in Winter days
Figure 15 Heat loss in Summer days
It can be noticed that the heat losses are slightly higher during summer compared to the winter
values. This happens because the return temperature during the summer days, in which the heat load
request is very low, has a value of around 35°C at the injection node and it is higher compared to
the winter case where the return temperature at the same node is 25°C. The water is not able to
transfer all its heat content and consequently, it goes back to the injection point with a higher
temperature and loses more heat due to the higher temperature difference with the ground.
During mid-seasons, in spring and autumn, the behaviour of the optimized system is in between the
ones during summer and winter. Considering a week at the end of September, the hourly heat losses
with the new system configuration are equal to 2.5 kWh, corresponding to a decrease in heat loss of
43%. Almost the same result is found analysing the first week of April where a reduction of 44% in
heat loss is registered.
5 DISCUSSION AND CONCLUSION
In this paper the possibility of lowering the forward temperature of the district heating relying on
booster heat pumps has been analysed. From the obtained results some considerations can be made.
0
1
2
3
4
5
6
210 211 212 213 214 215 216
kWh
Day of the year
Summer week
New System Old System
0
1
2
3
4
5
6
34 35 36 37 38 39 40
kWh
Day of the year
Winter week
New System Old System
0303-16
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First of all, from the simulation of the considered part of Marbjerg network, the strategy by which
Roskilde Fors A/S operates the plant is clear: to follow the variation of the heat load request, the
forward temperature is kept as constant as possible and the mass flow rate varies according to the
heat load. During summer, when the heat load request is very low, according to this operational
mode, the mass flow rate at the injection point 1 is decreased and can reach values below 0.2 kg/s.
Figure 16 Mass flow rates at the external nodes of the system (left) and temperature gradient
between the first network node and the furthest one (right)
When the mass flow is so low, according to the temperature drop equation, the water temperature
will decrease much faster. In Figure 16, temperature difference between the first and the last node
of the analysed network is reported. Since the ground temperature is considered to be the same
throughout the year independently of the outside temperature and the specific heat of the water is
considered constant as well, the only variable parameter in the temperature drop equation remains
the mass flow rate. As it is possible to see on the right side of the Figure 16, during summer the
temperature difference between the first and last node can arrive at 4°C, which is a large
temperature drop compared to the appearance in winter time when the mass flow is higher. This
results in a high relative heat losses compared to those obtained operating the plant with a lower
forward temperature and a higher mass flow rate.
Although much time has been spent arguing the benefits of lowering the temperature of the district
heating networks, it is unpleasant fact that the real operation of the plant is not utilizing the
possibility of lowering the forward temperature of the DH system even in the periods of the year
when there is a clear possibility for such an operation. Thus, it will be as equally important to
address the possibilities for lowering the forward temperature in the DH system already today as to
focus on changing the paradigm of the temperature levels needed for the future low temperature DH
networks.
In the optimization carried out in this paper, the goal was to minimize the network heat losses and
therefore to find an optimal network configuration from a technical point of view.
The stated problem has many constraints that need to be satisfied and in particular lots of them are
non-linear. This circumstance makes the optimization problem computationally heavier.
Consequently, the choice to consider only specific seasonal representative days was made due to the
long computational time.
The computational time could be a limit for future computations of larger systems with a higher
number of non-linear constraints. A solution could be to simplify the problem formulation avoiding
inserting unnecessary non-linear constraints and tightening the range of variation of the different
variables involved in the problem.
0303-17
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The optimization goal stated in this project is achieved by lowering the temperature of supply and
return flow as much as possible. Since there were not any constraints regarding electricity or heat
prices, the optimized configuration always works with the minimum possible supply temperature,
equal to 40°C, and the minimum water flow rate needed to satisfy the required heat load at the
specific hour. In this way, the reduction of heat losses in the system is significant.
From the results it comes out that the heat losses during summer hours are slightly greater than
those ones in winter, with an average values of 2.9 kWh and 2.3 kWh, respectively. This happens as
the amount of heat transported by the minimum amount of mass flow rate admissible in the network
pipes is not totally transferred to the end users. The excess heat is carried by the return water that
has a higher temperature compared to the winter case (the average return temperature in summer is
35°C whereas in winter is 25°C) and this is translated in higher heat losses into the return pipes.
A solution to overcome this problem would be certainly represented by the installation of storage
tanks. The simulations do not take into account the storage; however, it would allow a better
performance of the network, minimizing heat losses further on. Heat storage would improve the
economy of the district heating system by decoupling the consumption request from the production,
and it would allow a more sustainable heat supply.
As stated before, the optimization does not take into account the costs of energy, therefore the
optimized solution tends to take to supply temperature at the lowest level possible and the rest of
heat needed to satisfy the heat load request is supplied by the heat pump. However, this technical
optimization could result unfeasible from an economical point of view. One potential future
development of this study could be taking into account also the heat production prices in a form of a
multi-objective optimization with both minimization of heat losses and minimization of costs set as
objective function.
In general, when the electricity prices are low, the CHP plants, which are the main heating source
for the Danish district heating networks, tend to minimize their production since lot of power if
forecasted from other sources. Therefore, they will consequentially reduce also their heating
production. This condition fits well with the heat pump operation schedule that will take advantage
of the low cost electricity to provide more heat to the district heating grid and to fill up the storages.
When the electricity prices are high, the CHP plants will increase their production. In this case if the
hot water storages are full, the heating could be provided firstly by those facilities in such a way to
maintain the district heating supply temperature at a low level. In this situation, the low supply
temperature of the DH allows to produce more electricity from the CHP power plants since the fluid
into the CHP turbines can be expanded till a lower temperature level. In this way a general
optimization of the energy supply systems can be achieved as well as a more sustainable operation
of heating and power plants.
Further studies on this project can be made also considering different network configurations. At
the moment the analysis has been carried out considering the installation of small scale heat pumps
very close to the end user customers. However, looking at the bigger network, one idea to reduce
the investment costs on multiple heat pumps could be to install less heat pumps with a higher heat
capacity at the beginning of the branches that supply heat to a high density populated area. The
bigger heat pumps could in this way have profit from the economy of scale.
Another implementation could be to divide the supply water flow into two different flows, one for
the DHW preparation and the other for the space heating system. In this way the electrical boosters
0303-18
18
can be used to increase only the water flow for DHW preparation since it needs to satisfy some
specific requirements and less electrical power would be utilized. In fact, considering new space
heating systems such as wall or floor heating, the supply temperature can be also around 30-40°C,
hence the boosting for that flow is not necessary needed except during specific climatic conditions.
Finally, further studies should address the thermal stress of the pipes. In fact, with the optimized
LTDH operation, the network will be subjected to very frequent variation of water temperature
inside the pipes. This dynamical load could lead to the damage of the network due to thermal stress
and hence this aspect has to be taken into account.
NOMENCLATURE
ABBREVIATIONS
CHP
Cogeneration of Heat and Power
GHG
Greenhouse Gases
COP
Coefficient of Performance
HEX
Heat Exchanger
DEA
Danish Energy Agency
HP
Heat Pump
DH
District Heating
LTDH
Low Temperature District Heating
DHN
District Heating Network
NPV
Net Present Value
DHW
Domestic Hot Water
MTDH
Medium Temperature District Heating
DKK
Danish Krone
RES
Renewable Energy Sources
DN
Nominal Diameter
SH
Space Heating
EU
European Union
ULTDH
Ultra-Low Temperature District Heating
ETS
Emission Trading System
VAT
Value Added Tax
SYMBOLS
Heat capacity of the water (J/(kg K))

Temperature difference in the heat exchanger (°C)
Mass flow rate (kg/s)
I
Incidence matrix
Heat demand at customers’ node (W)
Heat loss per unit length (W/m)
Supply temperature (°C)
U
Overall heat transfer coefficient (W/(m K))
Return temperature (°C)
L
Length of the pipe (m)
Ground Temperature (°C)

Heat losses (W)

Indoor house temperature (°C)

Heat production from the plant (W)
Average water temperature (°C)

Heat produced by the heat pumps (W)

Electric work (W)

Specific cost of heat (€/kWh)

Total cost for heat production (€)

Specific cost of electricity (€/kWh)
SUBSCRIPTS
i
Generic node i
b
branch
j
Generic node j
con
Condenser
k
Generic node k
ev
Evaporator
i-j
Constant quantity between nodes i and j
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0303-21
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