System Simulation of Thermal Energy Storage involved ...

Master of Science Thesis

KTH School of Industrial Engineering and Management

Energy Technology EGI-2014-102MSC EKV1063

Division of Heat and Power Technology

SE-100 44 STOCKHOLM

System Simulation of Thermal

Energy Storage involved Energy

Transfer model in Utilizing Waste

heat in District Heating system

Application

Ludwin Garay Rosas

2040

6080

100

5

10

15

20

0

5

10

15

Transport distance [km]Annual heat demand [GWh]

Num

ber

of

trucks [

-]

2

4

6

8

10

12

14

16

18

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Master of Science Thesis EGI 2014: EGI-

2014-102MSC EKV1063

System simulation of Thermal Energy

Storage involved Energy Transfer model in

Utilizing Waste heat in District heating

system Application

Ludwin Garay Rosas

Approved

Examiner

Dr. Jeevan Jayasuriya

Supervisor

Dr. Jeevan Jayasuriya

Commissioner

Contact person

Abstract

Nowadays continuous increase of energy consumption increases the importance of replacing fossil fuels

with renewable energy sources so the CO2 emissions can be reduced. To use the energy in a more efficient

way is also favorable for this purpose. Thermal Energy Storage (TES) is a technology that can make use

of waste heat, which means that it can help energy systems to reduce the CO2 emissions and improve the

overall efficiency. In this technology an appropriate material is chosen to store the thermal energy so it can

be stored for later use. The energy can be stored as sensible heat and latent heat. To achieve a high energy

storage density it is convenient to use latent heat based TES. The materials used in this kind of storage

system are called Phase Change Materials (PCM) and it is its ability of absorbing and releasing thermal

energy during the phase change process that becomes very useful.

In this thesis a simulation model for a system of thermal energy transportation has been developed. The

background comes from district heating systems ability of using surplus heat from industrials and large

scale power plants. The idea is to implement transportation of heat by trucks closer to the demand instead

of distributing heat through very long pipes. The heat is then charged into containers that are integrated

with PCM and heat exchangers.

A mathematical model has been created in Matlab to simulate the system dynamics of the logistics of the

thermal energy transport system. The model considers three main parameters: percentage content of PCM

in the containers, annual heat demand and transport distance. How the system is affected when these

three parameters varies is important to visualize. The simulation model is very useful for investigation of

the economic and environmental capability of the proposed thermal energy transportation system.

Simulations for different scenarios show some expected results. But there are also some findings that are

more interesting, for instance how the variation of content of PCM gives irregular variation of how many

truck the system requires, and its impact on the economic aspect. Results also show that cost for

transporting the heat per unit of thermal energy can be much high for a small demands compared to larger

demands.

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Table of Contents

Abstract ........................................................................................................................................................................... 2

Abbreviations ................................................................................................................................................................. 4

Nomenclature................................................................................................................................................................. 5

Acknowledgements ....................................................................................................................................................... 7

1 Introduction .......................................................................................................................................................... 8

1.1 Background .................................................................................................................................................. 8

1.2 Objectives ..................................................................................................................................................... 8

1.3 Scope ............................................................................................................................................................. 9

1.4 Methodology ................................................................................................................................................ 9

1.5 Literature review ........................................................................................................................................10

1.5.1 Energy storage ..................................................................................................................................10

1.5.2 Phase Change Material ....................................................................................................................11

1.5.3 Energy System ..................................................................................................................................13

2 Model ...................................................................................................................................................................14

3 Results ..................................................................................................................................................................18

3.1 All main parameters as variables .............................................................................................................18

3.2 Constant percentage content of PCM ...................................................................................................25

3.3 Constant annual heat demand .................................................................................................................32

3.4 Constant transport distance .....................................................................................................................38

4 Discussion and conclusion ...............................................................................................................................43

5 Future work .........................................................................................................................................................50

Bibliography .................................................................................................................................................................51

Appendix-1: Matlab simulation code, all main parameters as variables .............................................................52

Appendix-2: Matlab simulation code, constant PCM% ........................................................................................57

Appendix-3: Matlab simulation code, constant demand .......................................................................................63

Appendix-4: Matlab simulation code, constant distance .......................................................................................67

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Abbreviations

PCM Phase Change Material

TES Thermal Energy Storage

HTF Heat transfer Fluid

TTB Track, Train or Boat

LHTES Latent Heat Thermal Energy Storage

SHTES Sensible Heat Thermal Energy Storage

O&M Operation and Maintenance

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Nomenclature

maxE Maximum storage capacity per container [MWh]

PCML Latent heat of fusion of the PCM [kJ/kg]

PCM Density of the PCM [kg/m3]

containerV Volume of the containers [m3]

PCMm Mass of PCM per container [kg]

SCE Actual storage capacity per container [MWh]

%PCMf Packing factor of PCM in the containers [%]

chargingt Time for charging a container [h]

dischargingt Time for discharging a container [h]

travelt Transport time [h]

d Transport distance [km]

v Mean velocity of the trucks [km/h]

totalt Total time for a transportation cycle of a truck [h]

loads,possibleN

Daily number of possible transportations of heat

loads per truck [-/day]

loads,requiredN Daily number of required heat loads [-/day]

demandE Annual heat demand [GWh/year]

trucksN Number of trucks needed [-]

consumptionf Fuel consumption factor [l/km]

emissionf Fuel emission factor [kg/l]

CO2,emissionm Annual CO2 emissions [kg/year]

PCMprice Price of PCM per kg [SEK/kg]

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PCMcost Annual cost for the PCM [MSEK/year]

PCMLC Life cycle of the PCM [years]

PCMn Number of times the PCM can be used [-]

truckprice Price of a truck [MSEK]

truckscost Annual cost for the trucks [MSEK/year]

truckLC Life cycle of the trucks [years]

fuelprice Price of fuel per liter [SEK/l]

fuelcost Annual fuel cost [MSEK/year]

salaryprice Daily salary for a truck driver [SEK/day]

salarycost Annual cost for the salaries [MSEK/year]

totalcost Total annual cost [MSEK/year]

1MWhcost Cost per unit of transported thermal energy [SEK/MWh]

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Acknowledgements

I would like to express my gratitude to my master thesis supervisor Dr. Jeevan Jayasuriya for his support

and guidance during this master thesis. Another person that I would like to thank is Dr. Justin Chiu, who

also has provided me with some advices and ideas. I really appreciate all the help I have received

throughout this work.

Finally I would also like to thank all the people that in some way have helped me to come to this final

stage of my studies, especially teacher and friends from KTH that have helped me to improve and enlarge

my technical knowledge.

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1 Introduction

1.1 Background

Sustainable energy utilization is very important today. Due to the threats of global warming, the world has

found a greater challenge to find ways to reduce the fossil fuel. New technologies are important in order

to make use of the energy in a more efficient way. Thermal Energy Storage (TES) is one of the potential

options in reducing thermal energy wastage and hence improve the energy efficiency in industrial

applications. Energy systems including TES are very likely to improve the overall efficiency of the system

since it can reduce the need for production of thermal energy.

In a cold country like Sweden the heating demand for space heating during the winter can reach extremely

high levels. District heating is then suitable for heating houses and buildings in communities that are well

populated. Waste heat can be used for district heating, which is also preferable from an environmental

perspective. In a district heating system, the heat is supplied in means of hot water, flowing in distributed

piping system. Piping system is appropriated when the demand is at a reasonable distance from the supply.

When a certain community (heat demand) is located somewhat far from the available district heating

networks, smaller-scale boiler or similar heat generation is normally used to supply heat to the community.

But further investigation within this area has been done to find more feasible solutions. One idea is that

available heat from larger waste heat sources or larger-scale CHP plants can be charged in phase change

material (PCM) and transported to the smaller communities which are located at a distance from available

district heating networks. For this concept it is also appropriate to include a container, which means that a

PCM filled container can be used for storing the heat and then transported closer to locations where the

heat demand is existent. This is particularly interesting for heat demands which are not significantly large

to justify the construction of pipelines. Industrial waste heat has good potential to be used as heat source

for this purpose. However, to obtain high storage capacity and good charging rate, the container has to

include an appropriate technology. Furthermore the heat can be transported by truck, train or boat,

depending on the distance, geographical location and circumstance. Once the small-scale utility has started

to receive external energy, the operational time for the boiler will be reduced, thus the operation and

maintenance cost for the utility will also be reduced. With help of a water accumulator included in the

small-scale utility the heat can be discharged regardless of the heat demand. This makes it possible to have

discharges more frequently, which means that more than one container can work in the process. (Hauer,

et al., 2010) (Cabeza, 2013)

1.2 Objectives

The main objective of this thesis is to investigate the economic and environmental capability of proposed TES based energy transportation system for delivering heat requirements of communities located at distance from district heating networks. Heat is collected from waste heat resources or from CHP plants and transported on road to demand locations.

A mathematical model is to be developed to simulate and analyze the dynamics of this energy transportation system. The model will take into account variables as annual heat demands, distances to transport, cost of infrastructure and performances of energy storage components to predict the economic value of energy delivered at the user end and environmental benefits of the operation.

The outcome of the analysis is expected to answers to the following:

Technical – the influence of storage capacity and the charging/discharging rate of the container on the overall operational performance of the system.

Economical – the influence of the capacity of the demand, distance between supply demand location and the technical performances of thermal energy storage and transport system for determining the unit cost of heat delivered.

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Environmental – to estimate the environmental benefits of the system operation in the means of avoided CO2 emissions from conventional heat generation systems for the existing heating demands.

1.3 Scope

There are certain parameters in the simulation model that are quite difficult to estimate or find

information about and some of them are also unknown. The rates for charging and discharging of the

thermal energy are some of them, but also some parameters related to different costs and life cycles are

not completely verified. This model will therefore consider and be built on certain assumptions, where

some of them probably will be very close to the real values, while some other might be bit more varying.

1.4 Methodology

The energy model in this work was created in MATLAB, due to its advantages when it comes to handle

more than one variable with quite wide ranges of study. It was created as a simulation model with input

parameters that execute calculations to eventually achieve the requested results as output parameters and

graphs.

Estimation of the number of trucks that the transport system requires is a central part, since this

parameter has huge impact on the output parameters. The first step is to decide the size of the container

and the PCM that will be used for storing heat. Thereafter the ratio between volume of PCM and heat

exchanger will be chosen in order to determine storage capacity and charging/discharging rates, these

parameters can then decide the charging and discharging time. The storage capacity is also used to

determine the number of heat loads that are needed in the transport system, but for this calculation the

size of heat demand is also needed. Travel time is another parameter and is simply based on travel

distance and mean velocity of the truck.

When all the time parameters and number of heat loads required for meeting the demand are determined,

the appropriate number of container used in the system can be found. Obviously the number of truck will

be the same, since every single truck is connected to only one container. These steps can be summarized

as follows:

PCM

Storage capacity

Charging time Size of container Charging rate

Ratio PCM/heat

exchanger Discharging rate Discharging time

Energy demand Number of heat loads

Storage capacity

Travel distance Travel time

Mean velocity

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Number of heat loads

Number of containers Travel time

Charging time

Discharging time

Once the number of trucks needed in the system is determined, calculations for emissions and costs can

be started. There will be no emission from the heat itself, since it is waste heat that is already generated

from larger CHP plants or surplus heat from industrials. The CO2 emissions will instead come from the

transportation and it should also be compared to emissions that come from a small scale CHP plant that is

not supported with transportation of waste heat by TES.

There are two different costs in this transportation system, one is the investment cost and the other is

operational and maintenance costs (O&M). Cost for trucks, containers, PCM and heat exchangers are

included in investment cost. O&M costs include continuous cost, which are fuel for the transport and

salaries to the truck drivers. Another analysis within the economic aspect that is of great importance is the

transport cost per unit of thermal energy. Transport cost per unit of thermal energy supplied at user end

gives the possibility to compare the overview of the economic performance of the transport system with

other means of heat generation and transportation systems that provides heat to district heating system.

In order to visualize the techno-economic performance of the energy system some parameters of the

system has been considered as variables. The most significant parameters influencing the system

performance are the percentage content of PCM in the containers, heat demands and travel distance.

These parameters will vary between certain ranges and provide values that make it possible to plot

illustrative graphs.

1.5 Literature review

Before developing the simulation model a literature review has to be done. This will make things more

clear, how the technologies works and how parameters are related to each other. The literature study is

mostly based on scientific articles about TES and PCM, but also reports from projects within the same

areas and course literature about energy systems are included in the review.

1.5.1 Energy storage

Energy storage is an excellent method for using energy in a more efficient way in systems where the

production exceeds the demand. It makes it possible to make use of excess energy that otherwise would

have been wasted, by storing it for later use. Obviously the gap between demand and supply then

decreases, which means that the performance of the energy system improves. Since the use of primary

energy source reduces, energy storage is favorable from both an environmental and economic perspective.

(Hauer, et al., 2010)

There are a couple of methods for storing energy, for instance: mechanical energy storage (for instance

pumped hydropower storage and flywheel energy storage), electrical storage (batteries), and TES. For

storing heat, TES is most suitable since the energy form heat can remain and due to the high flexibility of

adapting to the heat demand. Thermal energy can be stored at temperatures between -40˚C and 400 ˚C,

which means that also cooling can be stored. TES is normally divided into sensible heat thermal energy

storage (SHTES), latent heat thermal energy storage (LHTES) and thermo-chemical storage (TCS).

(Sharma, et al., 2007) (Hauer, et al., 2013)

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SHTES is based on the specific heat and temperature change of a storage liquid or solid, Water is the

most common to use as storage medium since it is inexpensive and has high specific heat capacity. By

ensuring a high thermal insulation of the storage tank this is a very effective way of storing thermal energy

in water. (Hauer, et al., 2013)

LHTES uses the phase change process in a material to store energy, where the most used phase changes

are melting and solidification. Phase changes including evaporation and condensation have higher latent

heat, but too large volume changes, which make them complex and impractical to implement in a TES

system. (Agyenim, et al., 2009)

TCS uses reversible chemical reactions to store and release thermal energy. It is the absorbed and released

energy in breaking and reforming molecular bonds that is used in this technology. (Sharma, et al., 2007)

SHTES systems are in general cheaper than LHTES and TCS, but on the other hand SHTES requires

larger volumes due to its low energy density. However, LHTES and TCS are economically feasible for

applications with high number of cycles. SHTES systems are today commercially available while systems

based on LHTES and TCS to a large extend are under development. (Hauer, et al., 2013)

1.5.2 Phase Change Material

Phase change materials (PCM) are materials that are used for LHTES. By using PCM, the storage density

increases, since a lot of heat can be absorbed in the material during the melting process. When the

material later starts to solidify heat will be released and it can then be used for heating purpose. During the

phase change process the PCM is also kept within a small temperature span, which is another advantage

of these kinds of materials. The PCM technology for TES can be applied in two different manner, one

with the heat transfer fluid (HTF) in direct contact with the PCM, and another with submerged heat

exchanger. The focus in this work will be on submerged heat exchangers. (Hauer, et al., 2010)

A drawback of PCM is that the conductivity in general is quite low, which leads to low charging and

discharging rate of heat to the PCM materials. One way to enhance the charging rate is to increase the

surface area of the heat exchanger. But by doing this the storage capacity will decrease, so apparently there

is a trade-off between storage capacity and charging power that has to be examined. Adding fins to the

heat exchanger is another way to increase the conductivity, but the result will be the same, a decrease of

storage capacity. (Cabeza, 2013)

LHTES has been developed a lot in recent years and seems to be an interesting technology for present

and future application. PCM materials can also be used in buildings, not precisely as insulation material,

instead more as a temperature regulator. (Cabeza, et al., 2009)

A lot of materials that have potential to be used as PCM have been studied, but only a few have been

commercialized. There are a couple of companies around the world that offer these materials. Over 50

different examples for PCMs can be found among companies located in Germany, Sweden, France,

Australia and Japan, with prices varying between 0.5-10 €/kg. (Mehling, et al., 2007)

When choosing an appropriate PCM there are a couple of properties to consider and they are usually

divided as follows:

Thermal – The phase change temperature has to be around the desired operating temperature

range. To achieve high storage density the latent heat of fusion and the volumetric mass density

have to be high. It is also favorable if the material has high specific heat capacity so high

additional sensible heat can be obtained. Furthermore the thermal conductivity of both solid and

liquid phases should be as high as possible so the charging and discharging can be performed

faster.

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Physical - The melting and solidification process should be congruent so the storage capacity can

be constant. Small volume change and small vapor pressure during phase change is preferable to

avoid containment problem.

Chemical – The material should have no corrosiveness and low or none subcooling. The cycling

stability should be high so the material can maintain its properties after a large numbers of

freeze/melt cycles. For environmental and safety reasons the material must be non-toxic, non-

flammable and non-explosive.

Economic – From an economical perspective the material should be abundant and of course it is

fine if the price is not too expensive. (Agyenim, et al., 2009)

PCM has to be encapsulated in most of the cases. The reason is simply to avoid the PCM from mixing

with the HTF or the environment. The two main principals of encapsulation are microencapsulation and

macro encapsulation. In micro encapsulation small spherical or rod-shaped particles are enclosed in a thin,

high molecular weight polymeric film, with a diameter smaller than 1mm. The PCM can then be

incorporated in any matrix that is compatible with the encapsulated film. Macro encapsulation uses larger

packages, usually a larger diameter than 1 cm. (Cabeza, et al., 2010)

PCM is normally divided into organic and inorganic materials. Examples of organic materials are paraffins,

fatty acids and sugar alcohols. They cover a small temperature range, from 0˚C to 150˚C, and have a

density that is smaller than 1 g/cm3. Inorganic materials cover a wide temperature interval. For example

water with melting point at 0˚C, and salts that can have melting points up to around 900˚C. Inorganic

materials usually have high densities, higher than 1g/cm3, as well as higher thermal conductivity. (Mehling,

et al., 2007)

In previous studies erythritol have been evaluated as possible PCM to be used for storing thermal energy.

This material has a suitable melting point of 120 ˚C as well as high latent heat of fusion, 340 kJ/kg. Other

candidates are presented in Table 1, where suitable melting point is assumed to be 90-120˚C. (Setterwall,

et al., 2011) (Cabeza, et al., 2010)

PCM Melting point (˚C) Heat of fusion (kJ/kg)

Xylitol 93-94,5 263

(NH4)Al(SO4)·6H2O 95 269

Methyl fumarate 102 242

RT110 112 213

Polyethylene 110-135 200

Acetanilide 118.9 222

Table 1. PCM that could be used in the transport system

The density and thermal conductivity is unknown for most of these materials, only Xylitol has a density

that is known, which is 6.7-8.3 kg/m3. This means that the choice of material can only be based on heat of

fusion, which can be unreliable. By comparing the materials with highest heat of fusion, xylitol and

(NH4)Al(SO4)·6H2O, it will be a choice between an organic and an inorganic material. Inorganic PCM

tends to have higher energy storage capacity and thermal conductivity, which means that

(NH4)Al(SO4)·6H2O should be the choice among these materials. But erythritol will remain as the best

choice to be used as PCM in a LHTES.

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1.5.3 Energy System

Energy systems can contain a wide variety of technologies, different energy sources and the most

fundamental of everything, the law of conservation of energy. The systems should also include

organizational structures and embedded aims. However a lot of systems are complex and contradictory,

which can make them hard to understand. Modeling is a very useful tool when studying energy systems

and has to take various aspects into account. A model is a formal description of a system that can be done

in different ways, depending on the perspective. (Lundqvist, 2010)

There are different definitions of systems. T. J. Kotas wrote a book about this topic and defined it in this

way: “A system is an identifiable collection of matter whose behavior is the subject of study”. It is always

surrounded by a system boundary that can coincide with real boundary or be purely imaginary. Once the

boundary is defined, it will be easier to explore what’s included, and then it will also be easier to study the

system. A system can either be opened or closed. In an opened system there is flow of matter across the

system boundary, while the flow stays inside the boundary in a closed system. (Kotas, 1995)

A system can also be described more briefly, according to the philosopher C. West Churchman:-”A

system is a set of parts coordinated to accomplish a set of goals”. This definition is very general and vague

and seems to only be useful for getting a brief overview of the system. (Churchman, 1968)

For the transportation system in this thesis the boundary will enclose supply, where the heat is charged

and the demand, not the whole way out the citizens in the community, only to the smaller scale CHP

utility. Of course the transportations will be included in the system since it is the link between supply and

demand. Since there will be flow across the boundary this system will be assumed as opened.

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2 Model

The relationship between storage capacity and charging times is very fundamental in this model, where the

percentage of PCM is the link between these parameters. The simulation model contains different parts,

but the structure and calculations are almost the same for all of them. The main parameters are percentage

content of PCM, transport distance and annual heat demand, these can be chosen as constants or

variables. However the simulation model will never include more than one of these parameters as

constant. The most important to find out with help of the simulation models are; how many trucks that

should be included in the system, level of CO2 emission, cost for keeping the system working and the

generation price for the heat in the unit SEK/MWh.

In the first part all the main parameters are chosen as variables. The model will then for every

combination of distance and demand do calculations for all the percentage of PCM that are included in

the chosen range. The purpose of varying the content of PCM is to find the best solution for each

combination of distance and demand. There can be a lot of different opinions about what “the best

solution” is, but at the end it all comes down to priority. In this thesis the first priority is to find the cost

per unit of thermal energy and secondary the CO2 emissions. The cost per unit of thermal energy is very

important since the whole system has to be feasible from an economical point of view, otherwise it can be

hard to find companies interested in this new technology. But of course the emissions cannot totally be

ignored for a low cost of thermal energy. With help of plots from the simulations, it will be possible to

identify these situations, where cost per unit of thermal energy is low but the emissions are very high.

In the other three parts of the simulation model, one of the main parameters is constant while the other

two are variables. The results will first be obtained as 3D-plots, but from these plots it is also possible to

generate more common xy-plots with two of the main parameters as constants and only one as variable.

The simulation model starts with calculating how much thermal energy that can be transported in each

container as maximum. The following calculation is then needed:

max PCM PCM containerE L V (1)

Where PCM

L and PCM

is the latent heat and the density of the PCM respectively, and container

V is the volume

of the container. With the choice of erythritol as PCM and a 20 foot container, the following values will

be used in the calculation:

PCM

3

PCM

3

container

336kJ/ kg

1400kg/ m

33.1m

L

V

(Cabeza, et al., 2010) & (Containerhandel AB)

The maximum load in a 20 foot container is 21.6 tonnes. (Containerhandel AB) This means that the

weight of a load of erythritol that completely fills the container has to be verified:

PCM 1400 33.1 46314kgm

The mass apparently exceeds the limitations, which means that the maximum load in each container will

be 21.6 tonnes in this model. It also has to be mentioned that the heat exchangers that will be made of

aluminum will not contribute to a higher weight even though its density is higher, since the tubes will be

very thin. With the maximum load of 21.6 tonnes, the maximum storage capacity becomes:

max

7258MJ0.336 21600 7258MJ 2.016MWh

3600s/ hE

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Thereafter the percentage content of PCM in the containers is chosen, and can be either a specific value

or a range. The storage capacity and charging rates can then be determined:

SC max %PCME E f (2)

The relationship between the charging rates and content of PCM is under development. There has been a

study within this area (Hassan, 2014), but still there is a need of more investigation to formulate

established equations. For the moment there will instead be a quite simple assumption of the relationship

between percentage of PCM and charging times, as follows:

charging

2

%PCM6t f (3)

discharging

2

%PCM4t f (4)

The next step is then to choose values for the mean velocity of the vehicle, transport distance and annual

heat demand, where distance and heat demand could be either fixed values or ranges. With the velocity

and distance, the travel time as well as how long time a cycle takes can be calculated. Cycle time is simply

how long time it takes from starting charging a container until it’s back at the charging station again, which

means that it includes charging, discharging and travel time twice between supply and demand:

travel

dt

v (5)

total charging discharging travel

2t t t t (6)

The cycle time is then used for calculating how many loads each truck is able to deliver per day:

loads,possible

cycle

h/ day24N

t (7)

This value has to be rounded downwards, because the trucks are supposed to start and end at the charging

station to make it easier for the truck drivers and other staff that work in the energy system to have the

same working hours every day. This means that if the cycle time is more than 24 hours, this value will be

rounded down to 0 and further calculations will not be possible to make for these kinds of situations. Of

course it is also obvious that a cycle time longer than 24 hours will not be possible to implement in the

system if the trucks are supposed to start and end at the charging station.

The demand is together with the storage capacity used for calculating how many loads that are required to

be transported per day:

demand

loads,required

SCdays/year365

EN

E

(8)

With these two numbers, the number of trucks needed for the system can finally be determined:

loads,required

trucks

loads,possible

NN

N (9)

The calculated number of trucks has to be rounded upwards in order to achieve a number that really will

contribute to meet the heat demand. If it’s rounded down it will not be enough heat loads transported.

Once the number of trucks is determined, calculations for costs and emissions can be performed. The

CO2-emissions comes from the fuel, which means that consumption and emissions factors are needed.

For transportation by truck the following values are used:

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consumption0.3l/ km

2.63kg/ lemission

f

f

(Andersson, 2005) & (Bourelius, 2011)

The distance and number of loads that are required in the system are at this stage known and the total

annual emissions of carbon dioxide can then be calculated:

CO2,emission loads,required consumption emission

days

year2 365m d N f f (10)

There are different costs for the transport system. One of them is the cost for PCM and is calculated

according to the following formula:

PCM PCM PCM

PCM trucks

PCM

pricecost

LC

f mN

(11)

Where the values for the price for PCM used in this model is:

PCMprice 25SEK / kg

The life cycle for the PCM is dependent on the number of cycles that the material resists and how many

cycles that are done annually, defined as follows:

PCM

PCM

loads,possibledays/year

LC365

n

N

How many times the PCM can be charged and discharged is assumed to be:

10000PCMn

The annual cost for trucks is the price for the trucks in the system divided by the life cycle.

truck trucks

trucks

truck

pricecost

LC

N (12)

The price and life cycle for a truck are assumed to be:

truck

truck

price 1MSEK

LC 20 years

In the price of truck, the price of container is also included. It is simpler to have them together as one

parameter, since they will work as one unit in the energy system.

The annual fuel cost has to consider transport distance, fuel consumption, fuel price and of course the

number of working days per year. The formula used for this calculation is then:

fuel loads,required consumption fuel

days

yearcost 2 price 365d N f (13)

The only new parameter in this formula is the price of fuel:

fuelprice 14.5SEK / l (Statoil Fuel and Retail Sverige AB, 2014)

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The annual cost for salary is the salary per day multiplied by the number of trucks and the number of

working days per year:

salary salary trucks

days

yearcost price 365N (14)

Where the salary is assumed to be:

salaryprice 1000SEK/ day

With all the cost determined, the total cost will of course be the sum of all the cost in the transport

system:

total PCM trucks fuel salary

cost cost cost cost cost (15)

The next step is then to decide how much the cost will be for generating 1MWh thermal energy to the

district heating system:

total

1MWh

demand

costcost

E (16)

The ranges that were chosen for the study of the simulation model, where trucks are assumed to be the

transport mode are shown in Table 2. The idea was to not start with too wide ranges, because it might be

easier to start with quite small ranges and then look for trends or pattern, and later expand the ranges if

it’s necessary.

PCM [%] Distance [km] Demand [GWh]

min 30 10 1

max 99 100 20

Table 2. Ranges of study for the simulation model

The range for PCM volume in the containers could have been chosen from 1-99%, but to low values can

make the scales of the graph too difficult to read at some parts. It’s is also more reasonable to fill the

containers closer to 99% than 1%, since the storage capacity cannot be too low. Energy systems with

distances shorter than 10 km or heat demands lower than 1GWh are not likely to implement this

technology. In order to not start with too wide ranges, 100km and 20 GWh were chosen as upper limits

for distance and demand.

-18-

3 Results

3.1 All main parameters as variables

Results for the simulation when the main parameters; percentage content of PCM in the containers,

annual heat demand and transport distance are all varied, are shown in Figure 1 to Figure 7. Ranges for

these parameters were for PCM 30-99%, transport distance 10-100 km and annual heat demand 1-20

GWh. The graphs show results from different perspectives, where every combination of distances and

demands is visualized and calculated with the percentage of PCM that gives the lowest cost per MWh.

Calculations where done for all the percentage of PCM, but only the one that gave the most feasible

solution for each combination of distance and demand are shown in the figures.

The first graph shows how many trucks that the transport system requires depending on the heat demand

and the distance. Thereafter graphs related to the environmental aspect are presented, showing the level of

emissions from the system and also the potential of reduction compared to heat generation by oil. Finally

costs are presented, both in total and per MWh of thermal energy.

Figure 1. The required number of trucks as function of transport distance and annual heat demand

Figure 1 shows that longer distances and higher heat demands requires more trucks, which is quite logical.

Higher demands will require more heat loads and therefore more trucks will also be needed. Longer

distances will require more trucks when the possibility to deliver a certain number of loads is no longer

possible.

2040

6080

100

5

10

15

20

0

5

10

15

Distance [km]Annual heat demand [GWh]

Num

ber

of

trucks [

-]

2

4

6

8

10

12

14

-19-

Figure 2. Annual CO2 emissions as function of annual heat demand and transport distance

The CO2 emissions that come from the fuel consumption during the transportations will obviously

increase when the distance is increases. Higher heat demands will also result in higher emissions since

higher demands require more loads to be transported. Due to the choice of different percentage contents

of PCM, some values between 20 and 60 km have extra high emissions (Figure 2). The chosen values for

percentage of PCM give the lowest cost per unit of thermal energy, but apparently some of them give

higher emissions.

2040

6080

100

5

10

15

20

0

500

1000

1500


CO

2 e

mis

sio

n [

tonnes]

200

400

600

800

1000

1200

1400

-20-

Figure 3. Annual CO2 reduction compare to a case where the heat is generated from oil.

Figure 3 shows how much CO2 emissions that can be avoided by implementing a transport system of

waste heat instead of generating heat from oil. The potential for reduction is higher for short distances

with high heat demand. But a change in heat demand will have more impact on the potential for

reduction, than a change in transport distance. The reason for this is that the emissions from oil, only

come from the combustion, no transportation is assumed for the heat generation from oil.

2040

6080

100

5

10

15

20

0

1000

2000

3000

4000


CO

2 e

mis

sio

n [

tonnes]

500

1000

1500

2000

2500

3000

3500

4000

4500

-21-

Figure 4. Annual total cost as function of annual heat demand and transport distance

The annual total cost for the thermal energy transport system (Figure 4) is higher for longer distances and

higher demands, which is reasonable since both investment cost and O&M cost will increase when one of

these variables increases. Longer distances require more fuel for transportation while higher demands

require more heats loads, which results in more fuel consumption and eventually more trucks and drivers

too.

2040

6080

100

5

10

15

20

0

5

10

15


Cost

[MS

EK

]

2

4

6

8

10

12

14

16

-22-

Figure 5. The thermal energy cost per MWh as function of annual heat demand and transport distance

If the cost instead is presented per unit of generated thermal energy (Figure 5) it will be different

compared to the total cost (Figure 4). The distance will have higher impact and a change in demand will

almost have no impact on this cost. Only increases and decreases for demands around the range of 1-

3GWh will show clear changes.

2040

6080

100

5

10

15

20

0

200

400

600

800

1000


heat

cost

[SE

K/M

Wh]

300

400

500

600

700

800

900

1000

-23-

Figure 6. The thermal energy cost per MWh as function of transport distance

The curves in Figure 6 come from Figure 5 and shows how the cost per unit of thermal energy changes

for some of the annual heat demands. Here it’s clearer that this cost is almost independent of the heat

demand, since all the curves except for the one for 1GWh, are more or less following the same curve.

The price for 1MWh of thermal energy in Sweden through district heating was in 2014 in average around

820kr for apartment and 880kr for villas. (Svensk Fjärrvärme, 2014) With these prices in account,

500SEK/MWh might be a maximum acceptable cost for heat generation by a transport system. This

means that transportation by truck can only be feasible for a maximum distance of 40km and the demand

shouldn’t be too low.

0 20 40 60 80 100200

300

400

500

600

700

800

900

1000

1100

Distance [km]

heat

cost

[SE

K/M

Wh]

1 GWh

6 GWh

11 GWh

16 GWh

20 GWh

-24-

Figure 7. The thermal energy cost per MWh as function of annual heat demand for different transport distances

The curves in Figure 7 also come from Figure 5 and shows how the cost per unit of thermal energy varies

for some of the transport distances. Except from what was said before regarding the impact from the heat

demand, it seems that for longer distances, the cost tends to fluctuate more when the demand varies. This

graph also shows that a heat demand of minimum 2GWh can be feasible, since curves for 10km and

31km show costs under 500SEK/MWh for these demands.

0 5 10 15 20200

300

400

500

600

700

800

900

1000

1100

Annual heat demand [GWh]

heat

cost

[SE

K/M

Wh]

10 km

31 km

52 km

73 km

100 km

-25-

3.2 Constant percentage content of PCM

Results for the case where the percentage of PCM is constant and the demand and distance are variables

are presented in Figure 8–Figure 16. In this simulation the percentage content of PCM is 70% and the

ranges of transport distance and annual heat demand are 10-100 km and 1-20 GWh respectively. The first

graph shows how many trucks that the transport system requires. Thereafter graphs related to the

environmental aspect are presented, showing the level of emissions from the system and also the potential

of reduction compared to heat generation by oil. Finally costs are presented, both in total and per MWh of

thermal energy. Results for how the cost per unit of thermal energy is varied are also presented for 80%

PCM.

Figure 8. The required number of trucks as function of transport distance and annual heat demand

Result for this part of the simulation shows that the number of trucks needed in the system is constant at

many parts for a certain demand (Figure 8). An increase in distance will only require more trucks when

the new distance doesn’t allow the truck to deliver the same amount of heat load as before. In this

simulation this happened at around 35km and 95km.

2040

6080

100

5

10

15

20

0

5

10

15

20

Distance [km]

Constant PCM,70%


Num

ber

of

trucks [

-]

2

4

6

8

10

12

14

16

18

20

-26-

Figure 9. Annual CO2 emissions as function of annual heat demand and transport distance


2040

6080

100

5

10

15

20

0

500

1000

1500


CO

2 e

mis

sio

n [

tonnes]

200

400

600

800

1000

1200

1400

1600

1800

2040

6080

100

5

10

15

20

0

1000

2000

3000

4000


CO

2 e

mis

sio

n [

tonnes]

500

1000

1500

2000

2500

3000

3500

4000

4500

-27-

Results from the emissions don’t show anything remarkable (Figure 9 and Figure 10). Higher demands

and distances will require more fuel and therefore the emissions will also increase. The potential to avoid

CO2 emissions will be higher for high heat demands since the heat generation from oil will only emit CO2

at the combustion process. Higher distances will for that reason have less impact in this aspect compared

to lower heat demands.

Figure 11. Annual total cost as function of annual heat demand and transport distance

The graph for the total cost shows some similarity from the graph of number of trucks (Figure 9). This is

reasonable since the number of trucks in the system will impact both investment cost and O&M cost. For

instance more trucks will require larger amount of PCM and more truck drivers. But this graph also has

similarities from the graph of CO2 emissions (Figure 9), which is related to the fuel cost.

2040

6080

100

5

10

15

20

0

5

10

15

20


Cost

[MS

EK

]

2

4

6

8

10

12

14

16

18

20

-28-

Figure 12. The thermal energy cost per MWh as function of annual heat demand and transport distance

Figure 12 shows that, apart from the lowest heat demands, the cost per unit of thermal energy is nearly constant for a constant transport distances. This means that total annual cost is almost proportional to the heat demands, which also can be seen in Figure 11.

2040

6080

100

5

10

15

20

0

200

400

600

800

1000


heat

cost

[SE

K/M

Wh]

300

400

500

600

700

800

900

1000

-29-

Figure 13. The thermal energy cost per MWh as function of distance for different heat demands, with constant percentage content of PCM of 70%

Figure 14. The thermal energy cost per MWh as function of demand for different transport distances with constant percentage content of PCM of 70%

0 20 40 60 80 100200

300

400

500

600

700

800

900

1000

1100

Distance [km]

heat

cost

[SE

K/M

Wh]

1 GWh

6 GWh

11 GWh

16 GWh

20 GWh

0 5 10 15 20200

300

400

500

600

700

800

900

1000

1100


heat

cost

[SE

K/M

Wh]

10 km

31 km

52 km

73 km

100 km

-30-

Figure 15. The thermal energy cost per MWh as function of distance for different heat demands, with constant percentage content of PCM of 80%

Figure 16. The thermal energy cost per MWh as function of demand for different transport distances with constant percentage content of PCM of 80%

0 20 40 60 80 100300

400

500

600

700

800

900

1000

1100

Distance [km]

heat

cost

[SE

K/M

Wh]

1 GWh

6 GWh

11 GWh

16 GWh

20 GWh

0 5 10 15 20300

400

500

600

700

800

900

1000

1100


heat

cost

[SE

K/M

Wh]

10 km

31 km

52 km

73 km

100 km

-31-

Comparison for the cost per unit of thermal energy between 70% (Figure 13 and Figure 14) and 80%

content of PCM (Figure 15 and Figure 16), shows that a raise from 70% to 80% PCM will result in lower

costs for longer distances while the costs for shorter distances will increase. Another difference between

these two cases is that there is only at one point where the cost will change drastically for 80% content of

PCM. This point can be found at around 45km. For 70% PCM there are two points and these are found

at around 35km and 95km. These points are related to the number of trucks that are needed in the system,

which change drastically at the same points. For 1GWh the change in price will not be as large as for the

other heat demands that are shown in these figures.

-32-

3.3 Constant annual heat demand

Results for the case where the demand is constant and the distance and percentage of PCM are variables

are presented in Figure 17Figure 23. In this simulation the annual heat demand is 10GWh while the ranges

for percentage of PCM and transport distance are 30-99% and 10-100km respectively. Also results for this

simulation are presented in the same order, starting with number of trucks required for the system.

Thereafter graphs related to the environmental aspect are shown and finally the economic aspect.

Figure 17. Required number of trucks as function of percentage of PCM and transport distance

Figure 17 shows that the PCM content in the containers can contribute to more trucks as well as fewer.

Normally a higher content of PCM will contribute to a larger storage capacity so fewer heats loads will be

required. But a higher content of PCM also increases the charging and discharging time and at some

points the trucks will not be able to deliver the same amount of heat loads, more trucks will then be

needed.

2040

6080

100

40

60

80

0

5

10

15

Distance [km]

Constant demand,10GWh

PCM content [%]

Num

ber

of

trucks [

-]

4

6

8

10

12

14

-33-

Figure 18. Annual CO2 emissions as function of percentage of PCM and transport distance

An increase in percentage of PCM will to a very large extend contribute to a lower CO2 emissions. Longer

distance will of course also result in more emissions. For a lower percentage content of PCM, the

emission level is more sensitive to a change in distance.

2040

6080

100

40

60

80

0

500

1000

1500

2000

Distance [km]PCM content [%]

CO

2 e

mis

sio

n [

tonnes]

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

-34-


Figure 20. Annual total cost as function of percentage of PCM and transport distance

2040

6080

100

40

60

80

0

500

1000

1500

2000


CO

2 e

mis

sio

n [

tonnes]

500

1000

1500

2000

2040

6080

100

40

60

80

0

5

10

15


Cost

[MS

EK

]

4

6

8

10

12

14

16

18

-35-

Figure 21. The thermal energy cost per MWh as function of percentage of PCM and transport distance

In this simulation, the graph for the total annual cost (Figure 20) has the same shape as the graph for the

cost per unit of thermal energy (Figure 21). The reason is simple, since the heat demand is constant the

total cost will be divided by the same value all over the graph.

2040

6080

100

40

60

80

0

500

1000

1500


heat

cost

[SE

K/M

Wh]

400

600

800

1000

1200

1400

1600

1800

-36-

Figure 22. The thermal energy cost per MWh as function of transport distance for different percentages of PCM

Figure 22 show that a low percentage content of PCM is not feasible from an economic perspective. This

is quite reasonable since this leads to low storage capacities and therefore more heat load will also be

required.

0 20 40 60 80 100200

400

600

800

1000

1200

1400

1600

1800

2000

Distance [km]

heat

cost

[SE

K/M

Wh]

30 %PCM

48 %PCM

66 %PCM

84 %PCM

99 %PCM

-37-

Figure 23. The thermal energy cost per MWh as function of percentage of PCM for different transport distances

Figure 23 shows that the negative effect from a low percentage content of PCM is more significant for

higher transport distances. But this graph also shows that too high percentage content of PCM will have a

negative impact for high distances.

30 40 50 60 70 80 90200

400

600

800

1000

1200

1400

1600

1800

2000

PCM content [%]

heat

cost

[SE

K/M

Wh]

10 km

31 km

52 km

73 km

100 km

-38-

3.4 Constant transport distance

Results for the case where the distance is constant and the demand and percentage of PCM are variables

are presented in Figure 24Figure 30. In this simulation the transport distance is 50km, while the ranges for

percentage of PCM and annual heat demand are 30-99% and 1-20GWh respectively. Also results for this

simulation are presented in the same order, starting with number of trucks required for the system.

Thereafter graphs related to the environmental aspect are shown and finally the economic aspect.

Compared to previous simulations with different variables, these graphs don’t show so much new

discoveries. The PCM content as variable shows the same impact on the results as before. An increase in

PCM content can both result in more trucks and higher total cost, as well as fewer trucks and lower total

annual cost. The impact from the percentage of PCM will be more consequent when it comes to the

emissions, where an increase will result in lower CO2 emissions.

Figure 24. Required number of trucks as function of percentage of PCM and annual heat demand

5

10

15

20

40

60

80

0

5

10

15


Constant distance, d=50km

PCM content [%]

Num

ber

of

trucks [

-]

2

4

6

8

10

12

14

16

-39-

Figure 25. Annual CO2 emissions as function of percentage of PCM and annual heat demand


5

10

15

20

40

60

80

0

500

1000

1500

2000

Annual heat demand [GWh]PCM content [%]

CO

2 e

mis

sio

n [

tonnes]

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

5

10

15

20

40

60

80

0

1000

2000

3000

4000


CO

2 e

mis

sio

n [

tonnes]

500

1000

1500

2000

2500

3000

3500

4000

-40-

Figure 27. Annual total cost as function of percentage of PCM and annual heat demand

Figure 28. The thermal energy cost per MWh as function of percentage of PCM and annual heat demand

5

10

15

20

40

60

80

0

5

10

15


Cost

[MS

EK

]

2

4

6

8

10

12

14

16

18

5

10

15

20

40

60

80

0

200

400

600

800

1000

1200


heat

cost

[SE

K/M

Wh]

600

700

800

900

1000

1100

1200

-41-

Figure 29. The thermal energy cost per MWh as function of demand for different percentages of PCM

Figure 30. The thermal energy cost per MWh as function of percentage of PCM for different heat demands

0 5 10 15 20500

600

700

800

900

1000

1100

1200

1300


heat

cost

[SE

K/M

Wh]

30 %PCM

48 %PCM

66 %PCM

84 %PCM

99 %PCM

30 40 50 60 70 80 90500

600

700

800

900

1000

1100

1200

1300

PCM content [%]

heat

cost

[SE

K/M

Wh]

1 GWh

6 GWh

11 GWh

16 GWh

20 GWh

-42-

The irregularity impact from the percentage of PCM can be seen in Figure 30, where most of the curves

fluctuate at certain critical points. One of these points can clearly be seen at around 80%. For four of the

curves in the graph the cost per unit of thermal energy have a large increase when the percentage content

of PCM exceeds 80%. This happens because the need for more trucks increases drastically at this point.

-43-

4 Discussion and conclusion

Before discussing the results, it is important to highlight that these results are simulated for a case where

the relationships between percentage of PCM and charging times are assumed to be quadratic with a

maximum charging time of 6 hours and a maximum discharging time of 4 hours. Some small changes in

this relationship can have great impact on the simulation, which means that these numerical results are

only valuable for this specific case. Furthermore some other parameters in the model might have to be

changed for a real situation. However it is still possible to find patterns that show how the system is

affected when some of the parameters are varied.

When one of the main parameters is constant, the obtained graphs are easier to understand and explain,

the main reason is that the content of PCM is either constant or varied regulated. A general result that is

shown in all the simulations is that higher demands and longer distances, in a wider perspective, require

more trucks for the system. This is quite reasonable since higher demand normally requires more heat

loads and longer distances requires more loads due to fewer possible transportations per truck. A change

in content of PCM can result in both more and fewer trucks, dependent on how large the change is and

the sizes of demands and distance.

How many heat loads that each truck can deliver per day is completely dependent on the times for

charging, discharging and transport. Shorter distances and lower contents of PCM contribute to lower

times and can in that way make it possible to deliver more heat loads per day. The number of heat loads

that is required to meet the demand is on the other hand independent of the distance and instead

dependent of the demand. The required heat loads per day will of course increase when the demand

increases. A decrease in percentage of PCM can make the system to require more heat loads and at the

same time help the system to transport more heat loads, which means that this parameter can affect the

number of trucks needed for the system to two different directions. This is also why the variation of PCM

content gives irregular variation of number of trucks needed for the system.

It is also important to mention that a certain number of trucks cover certain ranges of annual heat

demand, transport distance and percentage of PCM. This means for instance that an increase of annual

heat demand not always requires more trucks to the energy system. More loads will most likely be

required but not always more trucks. The required number of loads is more sensitive to a change in

demand, but this number can also remain unchanged if the change in demand is very small. In similar way

a longer transport distance will not always require more trucks, even though it results in fewer possible

heat loads to be transported.

Another general conclusion is that longer distances and higher demands will contribute to more emissions

of CO2, while higher content of PCM will contribute to lower emissions. The CO2-emissions is dependent

on the fuel consumption, which means that higher annual demands will contribute to higher emissions

since more loads will require more fuel for the transportation. Longer distances between supply and

demand will also lead to higher emissions due to the simple fact that longer distances require more fuel.

Lower percentage of PCM results in lower storage capacity that eventually can require more heats loads to

be transported, but at the same time it also makes it possible to transport more heat loads. However the

simulations show the total result for a change in PCM, which is that a lower content of PCM to a very

large extend results in higher emissions. In some cases a small change in percentage of PCM will not affect

the emissions, but a decrease in PCM will never reduce the emissions. The lower the percentage of PCM

is the more will a change in distance or demand affect the level of emission. Higher distance makes the

emissions more sensitive to changes in PCM content and demand, and in the same manner higher

demands makes the emissions more sensitive to changes in PCM content and distance. Compared to heat

generation from fossil fuel, the potential for CO2 reduction gets higher the shorter the distance is and the

higher the demand is. The reason is that in a system with fossil fuel, the CO2 emission is proportional to

-44-

10 20 30 40 50 60 70 80 90 100

2

4

6

8

10

12

14

16

18

20

Distance [km]

Annual heat

dem

and [

GW

h]

40

50

60

70

80

90

the demand and increases much faster than in a system where transportation of thermal energy is

implemented. In this system the CO2 emission is almost proportional to the distance. This simulation

model can therefore also be useful to find critical transport distances, which means distances that results

in higher emissions, thus unfeasible from an environmental perspective.

The costs for fuel and salary contribute much more the total cost than costs for trucks and PCM. The

reason for this is that trucks and PCM are assumed to be used over a quite long period, while large trucks

require a lot of fuel. The shapes of the graphs for total costs show influences from graphs for both

number of trucks and CO2 emissions. This is very reasonable since the number of trucks is direct

proportional to the costs for trucks and salaries while the emissions are proportional to the fuel cost.

In the first simulation where all the three main parameters are variables many conclusions from the other

simulations can be verified, but some new are also exposed. For instance this simulation shows that the

best choice of percentage of PCM varies a lot for different combinations of demands and distances, which

can be seen in Figure 31. It’s quite difficult to show clear relationships, but small patterns show that for

situations where the distance is longer than 60 km and the annual demand is greater than 6GWh, the

model chooses very high percentages of PCM. For distances shorter than 20 km, the model tends to

choose percentages of PCM lower than 50 %. A small conclusion from this simulation is that for longer

distances it tends to be more suitable to have a higher storage capacity. This can also be seen in

simulations for other cycle times but for small cycle times this is more unclear. For long distances in this

simulation it is probably more feasible to have larger storage capacities and thereby avoid too much

transportation and fuel consumption. In shorter distances the fuel cost is much smaller and that is

probably why smaller content of PCM can be chosen for shorter distances. By doing the simulation for

other charging times it is also discovered that when the charging times are varied but the summation of

the theses times are unchanged, there are no changes in choice of PCM. This is because the cycle time will

remain the same and therefore also the number of possible transportations will be unchanged.

Figure 31. Graph that show the best choice of percentage of PCM as function of demand and distance, from two different angles

By analyzing the cost per MWh, it is showed that the cost increases with the distance, which is normal

since the costs for fuel and salaries are what most affect the total cost. But by following constant demands

and studying how the heat cost per MWh varies with the distance, it appears that demands of 6GWh and

higher give almost the same curves. The difference between demands lower than 6GWh differs much

more. This comparison can be seen in Figure 32Figure 34

2040

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100

5

10

15

20

40

50

60

70

80

90


PC

M c

onte

nt

[%]

40

50

60

70

80

90

-45-

Figure 32. The thermal energy cost per MWh for different demands as function of distance


0 20 40 60 80 100200

300

400

500

600

700

800

900

1000

1100

Distance [km]

heat

cost

[SE

K/M

Wh]

1 GWh

2 GWh

3 GWh

4 GWh

5 GWh

0 20 40 60 80 100200

300

400

500

600

700

800

900

1000

Distance [km]

heat

cost

[SE

K/M

Wh]

6 GWh

7 GWh

8 GWh

9 GWh

10 GWh

-46-


The reason for this kind of variation of the thermal energy cost is related to how the different cost varies.

When the demand reaches a certain level, the total cost will become almost proportional to the demand.

The fuel consumption is almost completely proportional to the annual heat demand. In a range of small

demands the other cost varies quite much. But as the demand increases even more also these costs will

become proportional and it will then result in a total cost proportional to the demand. This can also be

seen when the contribution from the different costs to the total converges, which is the same as

proportional total cost since the fuel cost is practically proportional already from the beginning. How the

percentages of the different costs vary with the annual demand, for a transport distance of 50km and

percentage of PCM of 70%, are shown in Table 3. These variations can also be seen in graphs for

different transport distances in Figure 35.

Annual heat

demand [GWh]

costPCM

[%]

costfuel

[%]

costtrucks

[%]

costsalary

[%]

1 6,1 40,7 6.4 46.8

2 6,1 40,7 6.4 46.8

3 5.0 50.7 5.3 38.9

4 5.3 47.8 5.6 41.2

5 5.5 46.2 5.8 42.5

6 5.0 46.2 5.8 42.5

7 5.2 49.0 5.5 40.3

8 5.3 47.8 5.6 41.2

9 5.0 50.7 5.3 38.9

10 5.2 49.5 5.5 39.9

12 5.0 50.7 5.3 38.9

14 5.2 49.0 5.5 40.3

16 5.1 50.0 5.4 39.4

0 20 40 60 80 100200

300

400

500

600

700

800

900

Distance [km]

heat

cost

[SE

K/M

Wh]

11 GWh

12 GWh

13 GWh

14 GWh

15 GWh

0 20 40 60 80 100200

300

400

500

600

700

800

900

Distance [km]

heat

cost

[SE

K/M

Wh]

16 GWh

17 GWh

18 GWh

19 GWh

20 GWh

-47-

0 5 10 15 2010

20

30

40

50

60

70


Fuel cost

as p

erc

enta

ge o

f th

e t

ota

l cost

[%]

10 km

31 km

52 km

73 km

100 km

18 5.1 50.0 5.4 39.4

20 5.0 50.7 5.3 38.9

Table 3. The percentage cost for the different costs as function of the demand

Figure 35. Graphs that show contributions from the different cost to the total cost for different transport distances

The graphs in Figure 35 show that the investment cost is relatively low compared to the O&M cost. The

difference can be even clearer if these costs are separated from each, which can be seen in Figure 36Figure

37.

0 5 10 15 204

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9


PC

M c

ost

as p

erc

enta

ge o

f th

e t

ota

l cost

[%]

10 km

31 km

52 km

73 km

100 km

0 5 10 15 204

5

6

7

8

9

10


Tru

ck c

ost

as p

erc

enta

ge o

f th

e t

ota

l cost

[%]

10 km

31 km

52 km

73 km

100 km

0 5 10 15 2030

35

40

45

50

55

60

65

70


Sala

ry c

ost

as p

erc

enta

ge o

f th

e t

ota

l cost

[%]

10 km

31 km

52 km

73 km

100 km

-48-

Figure 36. O&M cost for per unit of delivered thermal energy as function of distance for different heat demands

Figure 37. Investment cost per unit of delivered thermal energy as function of distance for different heat demands

0 20 40 60 80 100200

300

400

500

600

700

800

900

1000

1100

Distance [km]

heat

cost

[SE

K/M

Wh]

1 GWh

6 GWh

11 GWh

16 GWh

20 GWh

0 20 40 60 80 10050

60

70

80

90

100

110

Distance [km]

heat

cost

[SE

K/M

Wh]

1 GWh

6 GWh

11 GWh

16 GWh

20 GWh

-49-

The conclusions from the simulation can be summarized as follows:

The distance only affects the possible number of loads that can be delivered, not the required.

The demand only affects the number of loads that is required, not the possible delivered.

The percentage of PCM affects both the number of loads that can be delivered and the required.

The number of trucks required is therefore dependent on the demand, distance and percentage of

PCM.

An increase in transport distance always increases the CO2 emission.

An increase in demand contributes to more CO2 emission.

A decrease of percentage of PCM contributes to more CO2 emission.

This transport system has higher potential to reduce CO2 emission for cases with high demand

and short distance.

For most of the cases the investment cost is much smaller than the O&M cost, especially for

cases with long distances.

Therefore the total cost is most dependent on O&M cost.

The cost per MWh of thermal energy is high for small annual heat demands.

The cost per MWh of thermal energy decrease to a certain level when the demand increases,

thereafter the cost per MWh is almost constant.

-50-

5 Future work

One weakness that the simulation model has is that the salary is based on the number of trucks. Since the

working hours will be different for different combinations of distance, demand and percentage of PCM

the salary should also vary according to the number of working hours. Some small modifications can be

done in the model, but still it can be difficult to find something that covers everything during a day of

work. For instance there can be scenarios where the charging times are very long, the truck driver will

then have long breaks and the questions will then be how much he should be paid for these hours.

The assumption that all the truck drivers have to start and end at the charging station every day, make it

necessary to have requirement for daily numbers of loads to be transported. But it is of course possible

and quite simple to modify the model so another time span can be used, for instance having weakly

required numbers of loads instead of daily. By doing this the transportation can be done more frequently

and reasonably fewer trucks will be needed in the system. But on the other hand it can be good to have

one or more extra trucks if one of them needs reparation or maintenance. The other trucks can then work

more frequently and hopefully deliver the required number of loads. It is also highly possible that some

extra thermal energy already is stored at the discharging station from previous discharges. The investment

cost for PCM, trucks and containers are also quite cheap compared to the O&M cost.

To obtain very accurate data with this simulation model, more research has to be done within the

relationship between storage capacity and charging/discharging rates. Finding how the percentage of PCM

really affects these parameters would make this simulation model more valuable since it is a very central

part in the model.

-51-

Bibliography

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formulation for latent heat thermal energy storage systems (LHTESS). Renewable and Sustainable Energy

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Andersson, Marie. 2005. Tunga lastbilars koldioxidutsläpp, en kartläggning av tillståndet i Sverige. 2005.

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drar-at-samma-hall/.

Cabeza, L.F., et al. 2009. Experimental study on the performance of insulation materials in

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1908341891.

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Mehling, Harald and Cabeza, Luisa F. 2007. Phase Change Material and Their Basic Properties.

Thermal Energy Storage for Sustainable Energy Consumption. s.l. : H. Ö. Paksoy, 2007.

Setterwall, Fredrik, et al. 2011. Värmetransport med fasomvandling. s.l. : Fjärrsyn, 2011.

Sharma, Atul, et al. 2007. Review on thermal energy storage with phase change materials and

applications. Renewable and Sustainable Energy Reviews. 2007.

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Svensk Fjärrvärme. 2014. Svensk Fjärrvärme. [Online] 2014. http://www.svenskfjarrvarme.se/statistik--

pris/fjarrvarmepriser/.

-52-

Appendix-1: Matlab simulation code, all main

parameters as variables

clear all close all clc

m=21600; %kg

%pcm L=0.336; %MJ/kg rho1=1400; %kg/m3 V=5.89*2.35*2.39; %m3 m1=V*rho1; %kg if m1>m m1=m; end E=L*m1; %MJ P=E/3600; %MWh

%*************** PCM=30:1:99; %%PCM Di=10:3:100; %km, transport distance De=1:1:20; %GWh, annual demand v=60; %m/s, mean velocity during the transportation %***************

SC=P*PCM/100; %MWh CR=6*(PCM/100).^2; %h DCR=4*(PCM/100).^2;%h

TN=[]; DD=[]; DI=[]; DE=[]; TTNN=[]; pcm=[]; LOADSp=[]; LOADSr=[]; TH=[]; COST=[]; CO2=[]; CO2r=[]; HeatC=[];

for di=Di %km for de=De %GWh tt=di/v*ones(1,size(CR,2))'; %h, transport time demand=de*1000; %MWh loads=demand./SC; %annual number of loads needed

dd=demand./365; %MWh daily demand CT=CR'+2*tt+DCR'; %h, cycle time

p9=floor(24./CT).*SC'; %MWh daily possible delivered energy per truck d=dd./p9; %number of cycles needed in order to meet the daily demand

p6=floor(24./CT); %number of loads that can be transported per day & truck

-53-

p7=ceil(loads'./365); %number of loads needed per day

p8=ceil(p7./p6); %number of trucks required

p10=ceil(p7./p6).*p9; %MWh, daily total possible energy discharing per day

%costs and emissions ppcm=25; %kr/kg cpcm=m1*PCM'./100*ppcm; %kr cy=10000; %no. of cycles that the pcm is assumed to resist lc_pcm=cy./(p6*365); %years

co2o=0.250; %g/kWh, emissions from oil co2c=0.370; %g/kWh, emissions from coal

lc_t=20; %lc_t=10^6./(2*di.*p6*365); % years, alternative lc_t based on driven km ctruck=10^6; %kr salary=1000; %kr/h

price=14.5; %kr/l cons=0.3; %l/km; emiss=2.63; %kg/l

co2=365*di.*p7*2*cons*emiss; %kg co2r=co2o*10^6*de-365*di.*p7*2*cons*emiss; %kg

costt=p8*ctruck./lc_t; %kr costp=cpcm.*p8./lc_pcm; %kr costf=365*di.*p7*2*price*cons; %kr costs=salary*365*p8; %kr cost=costt+costp+costf+costs; %kr, annual total cost

heatc=cost/(de*1000);

TT=[SC' CR' tt DCR' CT p6 p7 p8 p9 p10 ... PCM' cost co2 heatc co2r];

% disp('column 1: Storage capacity') % disp('column 2: Charging time') % disp('column 3: Transport time') % disp('column 4: Discharging time') % disp('column 5: Cycle time') % disp('column 6: Number of possible transported loads per day & truck') % disp('column 7: Number of loads required per day') % disp('column 8: Minimum number of trucks in order to meet the daily

demand') % disp('column 9: Amount heat that can be transported per truck and day') % disp('column 10: Amount of transported energy with the minimum number of

trucks that meet the demand') % disp('column 11: %PCM')

Tn=sortrows(TT,[14 13 8 -10]); TN=[TN;Tn(1,:)]; DD=[DD;dd];

DI=[DI;di]; DE=[DE;de];

-54-

end TTNN=[TTNN TN(end-(size(De,2)-1):end,8)]; pcm=[pcm TN(end-(size(De,2)-1):end,11)]; LOADSp=[LOADSp TN(end-(size(De,2)-1):end,6)]; LOADSr=[LOADSr TN(end-(size(De,2)-1):end,7)]; TH=[TH TN(end-(size(De,2)-1):end,3)*2]; COST=[COST TN(end-(size(De,2)-1):end,12)]; CO2=[CO2 TN(end-(size(De,2)-1):end,13)]; HeatC=[HeatC TN(end-(size(De,2)-1):end,14)]; CO2r=[CO2r TN(end-(size(De,2)-1):end,15)];

end

figure [X,Y]=meshgrid(Di,De); surf(X,Y,TTNN) xlabel('Transport distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Number of trucks [-]') axis tight % xlim([Di(1) Di(end)]) % ylim([De(1) De(end)]) zlim([0 max(max(TTNN))]) colorbar grid on

figure surf(X,Y,pcm) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('PCM content [%]') axis tight colorbar grid on %axis square

figure surf(X,Y,LOADSp) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Number of loads per truck (possible)[-]') axis tight zlim([0 max(max(LOADSp))]) colorbar grid on

figure surf(X,Y,LOADSr) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Number of loads (required)[-]') axis tight zlim([0 max(max(LOADSr))]) colorbar grid on

figure surf(X,Y,CO2/1000) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]')

-55-

zlabel('CO2 emission [tonnes]') axis tight zlim([0 max(max(CO2/1000))]) colorbar grid on

figure surf(X,Y,CO2./(Y*1000)) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('CO2 emission [g/kWh]') axis tight zlim([0 max(max(CO2./(Y*1000)))]) colorbar grid on

figure surf(X,Y,CO2r/1000) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('CO2 reduction [tonnes]') axis tight zlim([0 max(max(CO2r/1000))]) colorbar grid on

figure surf(X,Y,COST/10^6) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Cost [MSEK]') axis tight zlim([0 max(max(COST/10^6))]) colorbar grid on

figure surf(X,Y,HeatC) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('heat cost [SEK/MWh]') axis tight zlim([0 max(max(HeatC))]) colorbar grid on

a1=floor(size(HeatC,1)/4); figure plot(X(1,:),HeatC(1,:),'.-',X(1,:),HeatC(1+a1,:),'.-

',X(1,:),HeatC(1+a1*2,:),'.-',X(1,:),HeatC(1+a1*3,:),'.-

',X(1,:),HeatC(end,:),'.-') xlabel('Distance [km]') ylabel('heat cost [SEK/MWh]') legend([num2str(Y(1,1)) ' GWh'],[num2str(Y(1+a1,1)) '

GWh'],[num2str(Y(1+a1*2,1)) ' GWh'],... [num2str(Y(1+a1*3,1)) ' GWh'],[num2str(Y(end,1)) '

GWh'],'Location','NorthEastOutside') grid on

a2=floor(size(HeatC,2)/4);

-56-

figure plot(Y(:,1),HeatC(:,1),'.-',Y(:,1),HeatC(:,1+a2),'.-

',Y(:,1),HeatC(:,1+a2*2),'.-',Y(:,1),HeatC(:,1+a2*3),'.-

',Y(:,1),HeatC(:,end),'.-') xlabel('Annual heat demand [GWh]') ylabel('heat cost [SEK/MWh]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+a2)) '

km'],[num2str(X(1,1+a2*2)) ' km'],... [num2str(X(1,1+a2*3)) ' km'],[num2str(X(1,end)) '

km'],'Location','NorthEastOutside') grid on

-57-

Appendix-2: Matlab simulation code, constant PCM%


m=21600; %kg


%*************** PCM=70; %%PCM Di=10:3:100; %km, transport distance De=1:1:20; %GWh, annual demand v=60; %m/s, mean velocity during the transportation %***************

SC=P*PCM/100; %MWh, storage capacity per container CR=6*(PCM/100).^2; %h, charging timne DCR=4*(PCM/100).^2; %h, discharging time

TN=[]; TTNN=[]; pcm=[]; LOADSp=[]; LOADSr=[];

for di=Di %km for de=De %GWh tt=di/v*ones(1,size(CR,2))'; %h, transport time demand=de*1000; %MWh loads=demand./SC; %annual number of loads needed

dd=demand./365; %MWh, daily demand CT=CR'+2*tt+DCR'; %h, cycle time

p9=floor(24./CT).*SC'; %MWh, daily possible energy discharging per truck d=dd./p9; %number of cycles needed in order to meet the daily demand





TT=[SC' CR' tt DCR' CT p6 p7 p8... p9 p10 [PCM]'];

-58-

TN=[TN;TT];

end %The following four matrixes show no. of trucks, %pcm, no. of possible

loads that %can be transported per day and no. of required loads per day, for the %chosen distances and demand. TTNN=[TTNN TN(end-(size(De,2)-1):end,8)]; pcm=[pcm TN(end-(size(De,2)-1):end,11)]; LOADSp=[LOADSp TN(end-(size(De,2)-1):end,6)]; LOADSr=[LOADSr TN(end-(size(De,2)-1):end,7)]; end

figure [X,Y]=meshgrid(Di,De); surf(X,Y,TTNN) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Number of trucks [-]') title(['Constant PCM,' num2str(PCM) '%']) axis tight zlim([0 max(max(TTNN))]) colorbar grid on

% figure % surf(X,Y,pcm) % xlabel('Distance [km]') % ylabel('Annual heat demand [GWh]') % zlabel('PCM content [%]') % axis tight % colorbar % grid on

figure surf(X,Y,LOADSp) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Number of loads per truck (possible)[-]') axis tight zlim([0 max(max(LOADSp))]) colorbar grid on

figure surf(X,Y,LOADSr) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Number of loads (required)[-]') axis tight zlim([0 max(max(LOADSr))]) colorbar grid on

%costs and emissions ppcm=25; %kr/kg cpcm=m1*pcm./100*ppcm; %kr cy=10000; %no. of cycles that the pcm is assumed to resist lc_pcm=cy./(LOADSp*365); %years

-59-

co2o=0.250; %kg/kWh, emissions from oil co2c=0.370; %kg/kWh, emissions from coal

lc_t=20; %years %lc_t=10^6./(2*X.*LOADSp*365); % years, alternative lc_t based on driven km ctruck=10^6; %kr salary=1000; %kr/day


CO2=365*X.*LOADSr*2*cons*emiss; %kg CO2r=co2o*10^6*Y-365*X.*LOADSr*2*cons*emiss; %kg

costt=TTNN*ctruck./lc_t; %kr costp=cpcm.*TTNN./lc_pcm; %kr costf=365*X.*LOADSr*2*price*cons; %kr costs=salary*365*TTNN; %kr cost=costt+costp+costf+costs; %kr, annual total cost

figure surf(X,Y,CO2/1000) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('CO2 emission [tonnes]') axis tight zlim([0 max(max(CO2/1000))]) colorbar grid on

figure surf(X,Y,CO2./(Y*1000)) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('CO2 emission [g/kWh]') axis tight zlim([0 max(max(CO2./(Y*1000)))]) colorbar grid on

figure surf(X,Y,CO2r/1000) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('CO2 reduction [tonnes]') axis tight zlim([0 max(max(CO2r/1000))]) colorbar grid on

figure surf(X,Y,cost/1000000) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('Cost [MSEK]') axis tight zlim([0 max(max(cost/1000000))]) colorbar

-60-

grid on

figure heatc=(cost)./(Y*1000); surf(X,Y,heatc) xlabel('Distance [km]') ylabel('Annual heat demand [GWh]') zlabel('heat cost [SEK/MWh]') axis tight zlim([0 max(max(heatc))]) colorbar grid on

a1=floor(size(heatc,1)/4); figure plot(X(1,:),heatc(1,:),'.-',X(1,:),heatc(1+a1,:),'.-

',X(1,:),heatc(1+a1*2,:),'.-',X(1,:),heatc(1+a1*3,:),'.-

',X(1,:),heatc(end,:),'.-') xlabel('Distance [km]') ylabel('heat cost [SEK/MWh]') legend([num2str(Y(1,1)) ' GWh'],[num2str(Y(1+a1,1)) '

GWh'],[num2str(Y(1+a1*2,1)) ' GWh'],... [num2str(Y(1+a1*3,1)) ' GWh'],[num2str(Y(end,1)) '

GWh'],'Location','NorthEastOutside') grid on

a2=floor(size(heatc,2)/4); figure plot(Y(:,1),heatc(:,1),'.-',Y(:,1),heatc(:,1+a2),'.-

',Y(:,1),heatc(:,1+a2*2),'.-',Y(:,1),heatc(:,1+a2*3),'.-

',Y(:,1),heatc(:,end),'.-') xlabel('Annual heat demand [GWh]') ylabel('heat cost [SEK/MWh]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+a2)) '



%%%%%%% aa=floor(size(cost,1)/4); pcostt=costt./cost*100; pcostp=costp./cost*100; pcostf=costf./cost*100; pcosts=costs./cost*100;

% figure % plot(X(1,:),pcostt(1,:),'.-',X(1,:),pcostt(1+aa,:),'.-

',X(1,:),pcostt(1+aa*2,:),'.-',X(1,:),pcostt(1+aa*3,:),'.-

',X(1,:),pcostt(end,:),'.-') % xlabel('Distance [km]') % ylabel('Truck cost as percentage of the total cost [%]') % legend([num2str(Y(1,1)) ' GWh'],[num2str(Y(1+aa,1)) '

GWh'],[num2str(Y(1+aa*2,1)) ' GWh'],... % [num2str(Y(1+aa*3,1)) ' GWh'],[num2str(Y(end,1)) '

GWh'],'Location','NorthEastOutside') % grid on aa=floor(size(cost,2)/4); figure

-61-

plot(Y(:,1),pcostt(:,1),'.-',Y(:,1),pcostt(:,1+aa),'.-

',Y(:,1),pcostt(:,1+aa*2),'.-',Y(:,1),pcostt(:,1+aa*3),'.-

',Y(:,1),pcostt(:,end),'.-') xlabel('Annual heat demand [GWh]') ylabel('Truck cost as percentage of the total cost [%]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+aa)) '

km'],[num2str(X(1,1+aa*2)) ' km'],... [num2str(X(1,1+aa*3)) ' km'],[num2str(X(1,end)) '


% aa=floor(size(cost,1)/4); % figure % plot(X(1,:),pcostp(1,:),'.-',X(1,:),pcostp(1+aa,:),'.-

',X(1,:),pcostp(1+aa*2,:),'.-',X(1,:),pcostp(1+aa*3,:),'.-

',X(1,:),pcostp(end,:),'.-') % xlabel('Distance [km]') % ylabel('PCM cost as percentage of the total cost [%]') % legend([num2str(Y(1,1)) ' GWh'],[num2str(Y(1+aa,1)) '


GWh'],'Location','NorthEastOutside') % grid on aa=floor(size(cost,2)/4); figure plot(Y(:,1),pcostp(:,1),'.-',Y(:,1),pcostp(:,1+aa),'.-

',Y(:,1),pcostp(:,1+aa*2),'.-',Y(:,1),pcostp(:,1+aa*3),'.-

',Y(:,1),pcostp(:,end),'.-') xlabel('Annual heat demand [GWh]') ylabel('PCM cost as percentage of the total cost [%]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+aa)) '



% aa=floor(size(cost,1)/4); % figure % plot(X(1,:),pcostf(1,:),'.-',X(1,:),pcostf(1+aa,:),'.-

',X(1,:),pcostf(1+aa*2,:),'.-',X(1,:),pcostf(1+aa*3,:),'.-

',X(1,:),pcostf(end,:),'.-') % xlabel('Distance [km]') % ylabel('Fuel cost as percentage of the total cost [%]') % legend([num2str(Y(1,1)) ' GWh'],[num2str(Y(1+aa,1)) '


GWh'],'Location','NorthEastOutside') % grid on aa=floor(size(cost,2)/4); figure plot(Y(:,1),pcostf(:,1),'.-',Y(:,1),pcostf(:,1+aa),'.-

',Y(:,1),pcostf(:,1+aa*2),'.-',Y(:,1),pcostf(:,1+aa*3),'.-

',Y(:,1),pcostf(:,end),'.-') xlabel('Annual heat demand [GWh]') ylabel('Fuel cost as percentage of the total cost [%]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+aa)) '



-62-

% aa=floor(size(cost,1)/4); % figure % plot(X(1,:),pcosts(1,:),'.-',X(1,:),pcosts(1+aa,:),'.-

',X(1,:),pcosts(1+aa*2,:),'.-',X(1,:),pcosts(1+aa*3,:),'.-

',X(1,:),pcosts(end,:),'.-') % xlabel('Distance [km]') % ylabel('Salary cost as percentage of the total cost [%]') % legend([num2str(Y(1,1)) ' GWh'],[num2str(Y(1+aa,1)) '


GWh'],'Location','NorthEastOutside') % grid on aa=floor(size(cost,2)/4); figure plot(Y(:,1),pcosts(:,1),'.-',Y(:,1),pcosts(:,1+aa),'.-

',Y(:,1),pcosts(:,1+aa*2),'.-',Y(:,1),pcosts(:,1+aa*3),'.-

',Y(:,1),pcosts(:,end),'.-') xlabel('Annual heat demand [GWh]') ylabel('Salary cost as percentage of the total cost [%]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+aa)) '



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Appendix-3: Matlab simulation code, constant demand


m=21600; %kg


%*************** PCM=30:3:99; %%PCM Di=10:3:100; %km, transport distance De=10; %GWh, annual demand v=60; %m/s, mean velocity during the transportation %***************



for di=Di %km for ipcm=PCM %GWh tt=di/v*ones(1,size(CR,2))'; %h, transport time demand=De*1000; %MWh loads=demand./SC; %annual number of loads needed


p9=floor(24./CT).*SC'; %MWh daily possible energy discharging per truck d=dd./p9; %number of cycles needed in order to meet the daily demand






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TN=[TN;TT];

end %The following four matrixes show no. of trucks, %pcm, no. of possible

loads that %can be transported per day and no. of required loads per day, for the %chosen distances and demand. TTNN=[TTNN TN(end-(size(PCM,2)-1):end,8)]; pcm=[pcm TN(end-(size(PCM,2)-1):end,11)]; LOADSp=[LOADSp TN(end-(size(PCM,2)-1):end,6)]; LOADSr=[LOADSr TN(end-(size(PCM,2)-1):end,7)]; end

figure [X,Y]=meshgrid(Di,PCM); surf(X,Y,TTNN) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('Number of trucks [-]') title(['Constant demand,' num2str(De) 'GWh']) axis tight zlim([0 max(max(TTNN))]) colorbar grid on

% figure % surf(X,Y,pcm) % xlabel('Distance [km]') % ylabel('PCM content [%]') % zlabel('PCM content [%]') % axis tight % colorbar % grid on figure surf(X,Y,LOADSp) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('Number of loads per truck (possible) [-]') axis tight zlim([0 max(max(LOADSp))]) colorbar grid on

figure surf(X,Y,LOADSr) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('Number of loads (required) [-]') axis tight zlim([0 max(max(LOADSr))]) colorbar grid on


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co2o=0.250; %g/kWh co2c=0.370; %g/kWh

lc_t=20; %lc_t=10^6./(2*X.*LOADSp*365); % years, alternative lc_t based on driven km ctruck=10^6; %kr salary=1000; %kr/day


CO2=365*X.*LOADSr*2*cons*emiss; %kg CO2r=co2o*10^6*De-365*X.*LOADSr*2*cons*emiss; %kg

costt=TTNN*ctruck./lc_t; %kr costp=cpcm.*TTNN./lc_pcm; %kr costf=365*X.*LOADSr*2*price*cons; %kr costs=salary*365*TTNN; %kr cost=costt+costp+costf+costs; %kr, annual total cost

figure surf(X,Y,CO2/1000) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('CO2 emission [tonnes]') axis tight zlim([0 max(max(CO2/1000))]) colorbar grid on

figure surf(X,Y,CO2./(De*1000)) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('CO2 emission [g/kWh]') axis tight zlim([0 max(max(CO2./(De*1000)))]) colorbar grid on

figure surf(X,Y,CO2r/1000) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('CO2 reduction [tonnes]') axis tight zlim([0 max(max(CO2r/1000))]) colorbar grid on

figure surf(X,Y,cost/1000000) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('Cost [MSEK]') axis tight zlim([0 max(max(cost/1000000))]) colorbar grid on

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figure heatc=cost./(De*1000); surf(X,Y,heatc) xlabel('Distance [km]') ylabel('PCM content [%]') zlabel('heat cost [SEK/MWh]') axis tight zlim([0 max(max(heatc))]) colorbar grid on


',X(1,:),heatc(1+a1*2,:),'.-',X(1,:),heatc(1+a1*3,:),'.-

',X(1,:),heatc(end,:),'.-') xlabel('Distance [km]') ylabel('heat cost [SEK/MWh]') legend([num2str(Y(1,1)) ' %PCM'],[num2str(Y(1+a1,1)) '

%PCM'],[num2str(Y(1+a1*2,1)) ' %PCM'],... [num2str(Y(1+a1*3,1)) ' %PCM'],[num2str(Y(end,1)) '

%PCM'],'Location','NorthEastOutside') grid on


',Y(:,1),heatc(:,1+a2*2),'.-',Y(:,1),heatc(:,1+a2*3),'.-

',Y(:,1),heatc(:,end),'.-') xlabel('PCM content [%]') ylabel('heat cost [SEK/MWh]') legend([num2str(X(1,1)) ' km'],[num2str(X(1,1+a2)) '


km'],'Location','NorthEastOutside') xlim([min(min(Y)) max(max(Y))]) grid on

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Appendix-4: Matlab simulation code, constant distance


m=21600; %kg


%*************** PCM=30:3:99; %%PCM Di=50; %km, transport distance De=1:1:20; %GWh, annual demand v=60; %m/s, mean velocity during the transportation %***************



for de=De %km for ipcm=PCM %GWh tt=Di/v*ones(1,size(CR,2))'; %h, transport time demand=de*1000; %MWh loads=demand./SC; %annual number of loads needed


p9=floor(24./CT).*SC'; %MWh daily possible energy discharging per truck d=dd./p9; %number of cycles needed in order to meet the daily demand






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TN=[TN;TT];

end TTNN=[TTNN TN(end-(size(PCM,2)-1):end,8)]; pcm=[pcm TN(end-(size(PCM,2)-1):end,11)]; LOADSp=[LOADSp TN(end-(size(PCM,2)-1):end,6)]; LOADSr=[LOADSr TN(end-(size(PCM,2)-1):end,7)]; end

figure [X,Y]=meshgrid(De,PCM); surf(X,Y,TTNN) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('Number of trucks [-]') title(['Constant distance, d=' num2str(Di) 'km']) axis tight zlim([0 max(max(TTNN))]) colorbar grid on

% figure % surf(X,Y,pcm) % xlabel('Annual heat demand [GWh]') % ylabel('PCM content [%]') % zlabel('PCM content [%]') % axis tight % colorbar % grid on

figure surf(X,Y,LOADSp) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('Number of loads per truck (possible)[-]') axis tight zlim([0 max(max(LOADSp))]) colorbar grid on

figure surf(X,Y,LOADSr) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('Number of loads (required)[-]') axis tight zlim([0 max(max(LOADSr))]) colorbar grid on


co2o=0.250; %kg/kWh, emissions from oil co2c=0.370; %kg/kWh, emissions from coal

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lc_t=20; %years %lc_t=10^6./(2*Di.*LOADSp*365); % years, alternative lc_t based on driven

km ctruck=10^6; %kr salary=1000; %kr/day


CO2=365*Di.*LOADSr*2*cons*emiss; %kg CO2r=co2o*10^6*X-365*Di.*LOADSr*2*cons*emiss; %kg

costt=TTNN*ctruck./lc_t; %kr costp=cpcm.*TTNN./lc_pcm; %kr costf=365*Di.*LOADSr*2*price*cons; %kr costs=salary*365*TTNN; %kr cost=costt+costp+costf+costs; %kr, annual total cost

figure surf(X,Y,CO2/1000) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('CO2 emission [tonnes]') axis tight zlim([0 max(max(CO2/1000))]) colorbar grid on

figure surf(X,Y,CO2./(X*1000)) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('CO2 emission [g/kWh]') axis tight zlim([0 max(max(CO2./(X*1000)))]) colorbar grid on

figure surf(X,Y,CO2r/1000) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('CO2 reduction [tonnes]') axis tight zlim([0 max(max(CO2r/1000))]) colorbar grid on

figure surf(X,Y,cost/1000000) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('Cost [MSEK]') axis tight zlim([0 max(max(cost/1000000))]) colorbar grid on

figure

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heatc=cost./(X*1000); surf(X,Y,heatc) xlabel('Annual heat demand [GWh]') ylabel('PCM content [%]') zlabel('heat cost [SEK/MWh]') axis tight zlim([0 max(max(heatc))]) colorbar grid on


',X(1,:),heatc(1+a1*2,:),'.-',X(1,:),heatc(1+a1*3,:),'.-

',X(1,:),heatc(end,:),'.-') xlabel('Annual heat demand [GWh]') ylabel('heat cost [SEK/MWh]') legend([num2str(Y(1,1)) ' %PCM'],[num2str(Y(1+a1,1)) '

%PCM'],[num2str(Y(1+a1*2,1)) ' %PCM'],... [num2str(Y(1+a1*3,1)) ' %PCM'],[num2str(Y(end,1)) '

%PCM'],'Location','NorthEastOutside') grid on


',Y(:,1),heatc(:,1+a2*2),'.-',Y(:,1),heatc(:,1+a2*3),'.-

',Y(:,1),heatc(:,end),'.-') xlabel('PCM content [%]') ylabel('heat cost [SEK/MWh]') legend([num2str(X(1,1)) ' GWh'],[num2str(X(1,1+a2)) '

GWh'],[num2str(X(1,1+a2*2)) ' GWh'],... [num2str(X(1,1+a2*3)) ' GWh'],[num2str(X(1,end)) '

GWh'],'Location','NorthEastOutside') xlim([min(min(Y)) max(max(Y))]) grid on

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