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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

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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

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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

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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

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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.

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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

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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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