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Doctoral Thesis

Hybrid energy transmission for multi-energy networks

Author(s): Favre-Perrod, Patrick

Publication Date: 2008

Permanent Link: https://doi.org/10.3929/ethz-a-005698158

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Diss. ETH No. 17905

Hybrid Energy Transmission forMulti-Energy Networks

A dissertation submitted toETH ZURICH

for the degree ofDoctor of Sciences

presented byPatrick Favre-Perrod

Dipl. El.-Ing. ETHborn January 12, 1979

citizen of Chateau-d’Oex (VD), Switzerland

accepted on the recommendation ofProf. Dr. Klaus Frohlich, examiner

Prof. Dr. Goran Strbac, co-examiner

2008

i

Acknowledgements

I express my gratitude to Prof. Dr. Klaus Frohlich for his supervisionof my thesis work, as well as to his team at the High Voltage Labora-tory of ETH Zurich for their support. The Vision of Future EnergyNetworks project involved many collaborations with colleagues atETH Zurich, RWTH Aachen, TU Delft and others as well as sup-port from our project sponsors (ABB, AREVA T&D, Siemens andthe Swiss federal office of energy). I sincerely thank all of them; thelist of the individuals is too long to fit on this page.

I am especially grateful to those who have reviewed my work:Dr. Timm H. Teich who helped translating my English into readableEnglish and Prof. Dr. Goran Strbac who kindly accepted to be the co-examiner of my work. Our discussions permitted to greatly improvethis thesis.

The main subject of this thesis, the combined transmission ofelectricity and chemical power with waste heat reuse, has emergedduring a diploma thesis by Ronny Frik and myself under the super-vision of Bernd Klockl. Many thanks to Ronny and Bernd for thisvery creative collaboration!

This thesis is the result of an effort to present my work in astreamlined way. During the preparation phase of its contents, somemore random discussions (not restricted to scientific matters) andcollegial support have been necessary. Thank you Andreas, Bernd,Chrisitan, Dominique and Peter (in alphabetic order): you have beengreat office mates!

Zurich, 4th October 2008, Patrick Favre-Perrod

ii

Summary

The extensive development of renewable, stochastic and distributedenergy sources will lead to major changes in the electricity grid. Pos-sible long term trends include a higher level of interaction betweendifferent energy carrier systems (electrical, chemical and thermal).This would facilitate storage solutions as well as the inclusion ofnew participants into public energy networks, e.g. new transporta-tion technologies like hybrid or plug-in cars.

A framework for the description of these upcoming multi-energynetworks has been developed in the “Vision of Future Energy Net-works” project. It consists of Energy Hubs, interfaces for networkparticipants and Energy Interconnectors, which transmit severalforms of energy. Combined infrastructures for multiple energycarriers are an innovative response to future challenges including theintegration of renewable sources and novel storage principles. Thiswork aims at proposing a principle scheme for multi-energy trans-mission, establishing a set of models for this scheme, assessing theachievable performance of such systems under realistic assumptionsand determining a suitable application range.

The interconnector principle described in this work is a novel ap-proach to energy transmission, thus it was necessary to determine apromising variant (variant selection), the relevant physical phenom-ena (model), their implication on the design and operation of an in-terconnector and the possible application range. The spectrum of thepossible energy carriers includes electricity, natural gas, hydrogen,liquid hydrocarbons, compressed air, district heating, district cool-ing, etc.. A promising solution with respect to the integration intofuture network concepts is the combination of electric and gaseouschemical energy transmission.

A set of models has been developed for this preferred variant. Thespecific formulation of the compressible, non-adiabatic gas flow withfriction has required an adaptation of existing formulations, whichyielded a numerical model. In a second step, analytical approxima-tions have been developed, in order to derive scaling laws for the

iii

interconnector layout.Based on these models, the relevant operational characteristics

of the interconnector system have been identified. The resultingdescription of the transmissible electric, chemical and thermal powerhas been used to derive a layout methodology for the interconnectorwith a given transmission capacity and transmission length.

In a final step, the layout strategy developed has been appliedto different scenarios describing various transmission distances andtransmissible powers. The comparison of the resulting interconnec-tor dimensioning shows that the most promising application areafor further study of the interconnector corresponds to the currentmedium voltage network level, i.e. the transmission of some tens ofMW of electric and chemical power over a distance of some tens ofkm.

The layout method can now be used in infrastructure scenariosto be developed in the future within the “Vision of Future EnergyNetworks” project, where interconnectors will form an importantpart of network development strategies.

iv

Zusammenfassung

Die Anbindung erneuerbarer, stochastischer und dezentraler Energie-quellen an das elektrische Netz wird dessen Betrieb und Gestaltungstark verandern. Die Nutzung zusatzlicher Interaktionsmoglichkeitenzwischen verschiedenen Energietragern (etwa durch dezentrale Kon-version) gehort zu den moglichen langfristigen Entwicklungstenden-zen. Dadurch wurden die Realisierung verschiedener Speichersystemeund die Anbindung neuer Teilnehmer (u.a. Hybridfahrzeuge) an dasoffentliche Energienetz erleichtert.

Das Projekt “Vision of Future Energy Networks” diente der Ent-wicklung eines Bezugsrahmens fur die Beschreibung so-genannterMulti-Energiesysteme. Die allgemeine Beschreibung erfolgt mit-tels Energie Hubs (als Schnittstelle zu den Netzteilnehmern) undInterconnectors (fur die Energieubertragung). Die kombinierteUbertragungs- und Verteilungsinfrastruktur fur verschiedene Ener-gietrager stellt einen innovativen Losungsansatz fur aufkommen-de Fragestellungen dar, z.B. die Anbindung neuer erneuerbarerQuellen an das Energienetz. Zielsetzungen dieser Arbeit sinddemnach die Formulierung eines Konzepts fur die kombinierteEnergieubertragung, die Erarbeitung eines Modellierungsrahmens,die Abschatzung der erreichbaren Leistungsmerkmale sowie dieIdentifikation einer moglichen Applikation dieses Konzepts.

Fur das in dieser Arbeit beschriebene Prinzip des Interconnec-tors mussten zunachst eine Vorzugsvariante definiert werden, diephysikalischen Prinzipien und deren Einfluss auf Systemauslegungund -betrieb ermittelt werden sowie der machbare Leistungsbereichidentifiziert werden. Die in Frage kommenden Energietrager sindelektrische Energie, Erdgas, Wasserstoff, flussige Kohlenwasserstof-fe, Druckluft, Fernwarme, Fernkuhlung, usw.. Eine vielversprechendeKombination im Hinblick auf deren Einbindung in kunftige Netze istdie Kombination der Ubertragung von elektrischer und chemischerEnergie.

Fur diese Vorzugsvariante wurden Modelle entwickelt, welchedie Beschreibung des kompressiblen, nicht-adiabatischen und rei-

v

bungsbehafteten Gasflusses umfassen. In einem weiteren Schrittwurden analytische Naherungen entwickelt, welche die Ableitungeiner Layout-Prozedur ermoglichten.

Schliesslich konnte diese Layout-Prozedur auf verschiedeneSzenarien angewandt werden, welche einen breiten Bereich anUbertragungslangen und -leistungen abdecken. Der Vergleich derresultierenden Interconnector-Auslegungen ergab, dass der meist-versprechende Anwendungsbereich des Interconnector-Prinzips imBereich einiger zehn MW elektrischer und chemischer Leistung ubereine Lange von einigen zehn Kilometern liegt.

Die hier entwickelte Layout-Prozedur kann im Rahmen der innachfolgenden Projektphasen zu entwickelnden Infrastrukturszena-rien angewandt werden.

Contents

Acknowledgements i

Summary ii

Zusammenfassung iv

1 Problem statement 11.1 Challenges in the present grid . . . . . . . . . . . . . . 11.2 Need for a revolution in energy T&D . . . . . . . . . . 21.3 Consequences for energy transmission . . . . . . . . . 3

2 Current approaches 52.1 Future electricity networks . . . . . . . . . . . . . . . . 52.2 Multi-Energy networks . . . . . . . . . . . . . . . . . . 6

3 Description of the work scope 93.1 Applicability study . . . . . . . . . . . . . . . . . . . . 103.2 Relation to other research activities . . . . . . . . . . 12

4 Interconnector principle 134.1 The framework . . . . . . . . . . . . . . . . . . . . . . 14

4.1.1 General concept . . . . . . . . . . . . . . . . . 144.1.2 The Energy Hub . . . . . . . . . . . . . . . . . 164.1.3 The Energy Interconnector . . . . . . . . . . . 17

vii

viii CONTENTS

4.2 Variants and parameters . . . . . . . . . . . . . . . . . 184.2.1 Preliminary selection of variants . . . . . . . . 184.2.2 Parameters . . . . . . . . . . . . . . . . . . . . 19

5 Interconnector modelling 235.1 Modelling approach . . . . . . . . . . . . . . . . . . . . 235.2 Model with a liquid medium . . . . . . . . . . . . . . . 25

5.2.1 General overview of the model . . . . . . . . . 255.2.2 Chemical model . . . . . . . . . . . . . . . . . 275.2.3 Electrical model . . . . . . . . . . . . . . . . . 305.2.4 Thermal model . . . . . . . . . . . . . . . . . . 335.2.5 Pump model . . . . . . . . . . . . . . . . . . . 35

5.3 Model with a gaseous medium . . . . . . . . . . . . . . 365.3.1 General overview of the model . . . . . . . . . 365.3.2 Gas flow . . . . . . . . . . . . . . . . . . . . . . 465.3.3 A model for numerical solutions . . . . . . . . 535.3.4 Analytical modelling . . . . . . . . . . . . . . . 545.3.5 Discussion of the simplified model . . . . . . . 59

5.4 Low temperature energy transmission . . . . . . . . . 62

6 Interconnector operation 656.1 Power limitations and dependences . . . . . . . . . . . 66

6.1.1 Description of the limitations . . . . . . . . . . 666.1.2 Permissible electrical losses . . . . . . . . . . . 736.1.3 Justification . . . . . . . . . . . . . . . . . . . . 766.1.4 Variable temperatures and voltages . . . . . . . 77

6.2 Impact of the auxiliary equipment . . . . . . . . . . . 786.3 Scaling laws . . . . . . . . . . . . . . . . . . . . . . . . 806.4 Derivation of the scaling laws . . . . . . . . . . . . . . 82

7 Dimensioning and application 857.1 Dimensioning and layout . . . . . . . . . . . . . . . . . 86

7.1.1 Parameters in the layout process . . . . . . . . 867.1.2 Layout based on scaling laws . . . . . . . . . . 867.1.3 Constrained and materials parameters . . . . . 91

CONTENTS ix

7.2 Possible applications . . . . . . . . . . . . . . . . . . . 1027.2.1 Applications investigated . . . . . . . . . . . . 1027.2.2 Resulting layout for the selected applications . 1037.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . 113

8 Conclusions 1158.1 Implications for the “Vision of Future Energy Net-

works project” . . . . . . . . . . . . . . . . . . . . . . 1158.2 Application of the interconnector . . . . . . . . . . . . 116

A Auxiliary equipment model 119A.1 Compressors . . . . . . . . . . . . . . . . . . . . . . . . 119A.2 Heat exchangers and recovery . . . . . . . . . . . . . . 121

A.2.1 Use of compression waste heat . . . . . . . . . 121A.2.2 Use of warm gas at the bus outlet . . . . . . . 125

A.3 Overall efficiency . . . . . . . . . . . . . . . . . . . . . 130

B Example 133

C Illustration examples 137C.1 Example 1: Distribution . . . . . . . . . . . . . . . . . 137C.2 Example 2: Regional distribution . . . . . . . . . . . . 139C.3 Example 3: Bulk transmission . . . . . . . . . . . . . . 140

D Heat exchangers layout 143

Bibliography 147

List of symbols 151

List of figures 161

List of tables 166

Curriculum vitae 169

x CONTENTS

Chapter 1

Problem statement

Energy networks of the future with a rising share of dis-tributed and stochastic energy resources are the generalcontext for this work. This chapter reviews relevant trends,action needed and the potential consequences for energytransmission. Multi-Energy networks, i.e. networks with astrong integration level between different energy carriers rep-resent a particular challenge for energy transmission.

1.1 Challenges in the present grid

After a long period of centralisation of energy generation, the shareof installed small scale generators has increased in recent years. Thedrivers for this evolution include [1, 2]:

• the use of renewable and environmentally friendly energysources,

• the opportunity to postpone transmission investments,

• the lower risks induced by a smaller generator size,

1

2 CHAPTER 1. PROBLEM STATEMENT

• as well as competition and energy efficiency policies.

Ensuring supply security and grid stability, understanding andpreventing negative effects on power quality, protection and voltagelevels as well as adapting the regulatory framework to the chang-ing conditions are some of the challenges resulting therefrom [3, 2].Considering all these factors, a major research effort is needed todetermine which network developments will lead to an improved sit-uation overall (in technical, environmental, economical or societalterms).

Besides their contribution to energy generation, distributed gen-erators have the technical potential to provide reactive power, fre-quency reserve and more. In general it is firmly understood that afurther increase in the share of distributed generation should be ac-companied by the establishment of an active network [3] (i.e. activelyusing the services provided by the distributed generators).

1.2 Need for a revolution in energy T&D

Several organisations and governmental bodies have acknowledgedthe necessity of a radical evolution in the structure and operation ofnetworks. At the European level, the SmartGrids technology plat-form has identified the main differences between the present andthe future grid. New features will include more flexibility in opera-tion (customised power quality, security and maintenance), demandside participation, full integration of distributed resources with cen-tralised ones, more distributed generators close to consumers and aharmonised legal framework.

A similar direction can be found in other strategy plans, e.g. thoseoriginating from the U.S. department of energy [4]. The generalconclusion is that radically new network schemes are not unlikely tobe worked out in the future. Among the discussed solutions, a trendtowards integrated systems englobing several energy carriers exists.The drivers for this evolution englobe the rising number of small-

1.3. CONSEQUENCES FOR ENERGY TRANSMISSION 3

scale co- and trigeneration plants, the inclusion of transportationapplications into energy networks as well as energy storage schemes.

1.3 Consequences for energy transmis-sion

Electricity transmission is also widely affected by these presently im-plemented or expected changes. The SmartGrids platform identifieda research task devoted to new architectures and tools for the trans-mission networks of the future, which includes the development ofintelligent (i.e. controllable) transmission devices as well as new mod-els and methods. The strategic research agenda [5] also acknowledgesthe potential of multi-energy systems, i.e. the optimisation of severalinfrastructures for simultaneously utilised different energy carriers.

Enabling technologies or concepts for the evolution of electric en-ergy transmission include composite core conductors, gas insulatedlines, evaporative cooling of power cables, conducting polymers andhigh temperature insulation materials [6]. Despite the trend to moredistributed generation, an increase in the installed transmission ca-pacities is expected, especially as a supporting measure for competi-tion [4, 7]. Finally underground transmission is of increasing interestsince it lowers the risk of blackouts in extreme weather conditionsand the acceptance of new cable lines might be higher than that ofnew overhead lines and its acceptance in urban areas is anyway likelyto be better than for overhead lines. The EU has launched an effortinto this direction in a background paper on underground energytransmission [8].

In the context of multi-energy networks, new approaches to en-ergy transmission will be needed as well. In such networks, com-bined transmission systems may offer benefits in terms of synergies,but they may as well introduce additional constraints into the net-work layout process. Despite some early approaches to this topic, itremains unclear which combination of carriers, principles and phys-ical dimensions are feasible. All aspects related to the operation

4 CHAPTER 1. PROBLEM STATEMENT

and scalability (feasible power levels, distances, interdependenciesbetween different energy carriers) of a combined transmission willtherefore need further clarification.

Chapter 2

Current approaches tofuture energy networks

Numerous research projects have been or are being devotedto future energy networks. This chapter is a descriptionof the most relevant related research activities which eitherrepresent the background or alternative research directionsfor the topic of this work. Active or smart networks, es-pecially at the distribution level, constitute the mainstreamof current research programmes. The modelling and de-velopment of integrated networks delivering several energycarriers is addressed in a few of these programmes. In thiscontext, some solutions involving multi-energy transmission(or heat recovery) have been proposed.

2.1 Future electricity networks

The majority of current research activities in the area of futureenergy networks is related to wider national or international pro-

5

6 CHAPTER 2. CURRENT APPROACHES

grammes. The U.S. department of energy has developed the “Grid2030” vision [4]. Its major elements are a national backbone (pos-sibly relying on superconductive cables), regional interconnectionsas well as local active grids. Based on this the visionary idea ofa SuperCity, where hydrogen could play a double role as a coolantfor superconductive apparatus and energy carrier (e.g. for electricitystorage), has emerged [9].

The concept of MicroGrids (small distribution networks with loadand sources of comparable size [10] are mainly promoted in Europe,e.g. in the (More-)MicroGrids projects. These projects aim at de-veloping controllers and control strategies as well as alternative net-work designs in order to increase the connected distributed genera-tion share. A variety of further projects at the national and Europeanlevels are thematically related to distributed generation, storage andenergy management.

Programmes promoting new functions in distribution networks(demand management, power quality selection, more use of IT, etc.)can be found world-wide, e.g. [11].

2.2 Multi-Energy networks

Some research activities extend their scope into other energy carriersystems. The NEMESS (Network Model of Energy-services SupplySystem) and DEECO (Dynamic Energy Emission and Cost Optimi-sation) frameworks e.g. are aimed at supporting the development of“regional energy concepts” [12]. Integrated planning has also beenapplied by SINTEF (Foundation for Scientific and Industrial Re-search, Norway) for the evaluation of upstream infrastructure neededby decentralised generators (e.g. road transport of biomass) [13]. Themethodology was developed from a model dedicated to the optimi-sation of mixed hydro-thermal systems and was extended to naturalgas systems including storage and combined heat and power [14].

New concepts for energy transmission in the context of severalsimultaneously utilised energy carriers have been proposed in the

2.2. MULTI-ENERGY NETWORKS 7

following projects:

• The SuperCable [15]: A conceptual study suggesting the useof superconductive (liquid) hydrogen-cooled cables for “bulk”energy transmission. A share of the hydrogen might be usedfor energetic purposes (i.e as an energy carrier). The context ofthis idea is large-scale generation using nuclear or fossil fuelledplants, thus the resulting transmitted electric power is of theorder of one to several GW.

• The ICEFUEL project [16]: The aim of this project is the de-velopment of a system for the hybrid transmission of cryogenicfuels (methane or hydrogen), electricity and data.

• Recovering heat from forced-cooled power cables has also beendiscussed. A study carried out in the Swiss network has shownthat the use of this heat is only energetically attractive in alimited number of circumstances [17].

A very specific approach has been chosen in each of these projects:the SuperCable and ICEFUEL projects are defined in order to pro-mote particular technologies (superconductivity and liquid hydrogentransmission), while the study on waste heat recovery was limited tothe analysis of existing assets. These studies are not accompanied bya vision for the integration of the new transmission system into a newor improved energy network. This study will be based on a generalnetwork development scheme, i.e. multi-energy networks and avoidthe consideration of controversial technologies like superconductivity.

8 CHAPTER 2. CURRENT APPROACHES

Chapter 3

Description of the workscope

This chapter describes the questions to be addressed withinthis work. As exposed in the previous chapters, multi-energytransmission has not yet been applied in practice. The fo-cus of this work will be on the choice of a suited principleand the investigation of its expected applicability range interms of transmitted power and transmission distance. Thisinvestigation will be based on physical properties and limi-tations imposed by material properties. As a consequence,studies on detailed designs for transmission devices will notbe useful in a first step and shall not be developed.

9

10 CHAPTER 3. DESCRIPTION OF THE WORK SCOPE

3.1 Applicability study on the principleof multi-energy transmission

Considering the potential benefits of multi-energy transmission, thenecessary tools for the evaluation of infrastructure scenarios involvingmulti-energy transmission shall be prepared. Within the wide rangeof available or upcoming energy carriers (e.g. electricity, heat, hydro-gen, methane, liquid hydrocarbons, carbon monoxide, compressedair, etc.) a meaningful combination is to be selected for furtherstudy. Firstly the selected carriers must cover the requirements aris-ing from future sources and sinks within the network, e.g. biomassgasification or solar hydrogen generation and hybrid vehicles. Sec-ondly, the selection of the carriers will be based on its implication onthe design of the transmission system: the use of gaseous or liquidchemical energy carriers may e.g. impact on the achievable perfor-mance (transmissible power, efficiency) of a combined transmissionsystem.

The next step is the determination of possible concepts and vari-ants for the selected combination of carriers. Possible overall trans-mission concepts including the auxiliary equipment shall be com-pared. Among the questions to be addressed are the placement ofcompressors, pumps and waste heat recovery equipment (if appli-cable). The parameters will be identified and their physical andtechnical limitations will help to determine the applicability of themost promising variant (the “favourite solution”).

Next the specific aspects of combined transmission have to beidentified: since auxiliary equipment is shared and several energycarriers are to be transmitted in the same system, a coupling amongthe permissible transmitted powers is likely. Limits to the scalabilityof the concept are also to be investigated: the dimensioning of sucha system will largely differ for uses ranging from distribution to bulktransmission and for varying ratios among the transmitted powersfor each energy carrier.

For the preferred variant, a suitable model must be found, which

3.1. APPLICABILITY STUDY 11

permits to describe the “external performance” of a largely unknownsystem, thus deferring the consideration of physical details wheneverpossible. The goal of this step is to obtain a model permitting theevaluation of the preferred concept and its description. Thus theresulting model will be abstract and does not address the detaileddesign, manufacturing, laying, etc. of the system. The determinationof the necessary depth of the description is part of this activity. Apotentially more complex part of the modelling process is the flowof a gaseous energy carrier with heat absorption. In this context,numerical simulations are likely to be the only precise approach. Forthe consideration of a large number of different configurations withininfrastructure scenarios (in the “Vision of Future Energy Networks”project, see also chapter 4) this is not satisfactory. Where needed,simplified models will thus be developed.

Using the developed model, the operation of a combined trans-mission system can be described. The prerequisite to that is theidentification of the relevant “questions”, i.e. identify the specificfeatures of the hybrid transmission approach as compared to thoseof decoupled systems. The first goal is to derive a description for thetransmission capability of a given system (maximum powers and pos-sibly other limitations). The second goal is to indicate how the trans-mitted powers can be varied, i.e. which voltages, currents, pressures,etc. must be variable for the operation of a combined transmissionsystem.

The identified constraints on certain parameters (e.g. materialparameters) will limit the achievable power level and transmissionlength. Thus, the concept of the interconnector is to be applied tosome general application scenarios in order to determine the roughdimensions, voltage level, etc. required for some relevant potentialapplications of the interconnector. This will help to determine wherethe priority efforts for further refinement studies should be applied.

The auxiliary equipment power requirement as well as the poten-tial for waste heat recovery will be discussed with respect to theircontribution to the total transmission efficiency.

12 CHAPTER 3. DESCRIPTION OF THE WORK SCOPE

3.2 Relation to other research activities

The context for this work is the “Vision of Future Energy Networks”project (described in chapter 4). This project will develop scenariosfor future energy network infrastructures where multi-energy trans-mission will be one of the investigated options for interlinking the“Energy Hubs”, which are the interface between the network andthe energy producers or consumers.

For the use in these scenarios, a layout procedure for the intercon-nector system is necessary. This procedure shall help to determinethe interconnector dimensions subsequently needed for its simulation(in the scenarios). As a consequence a particular objective of thisstudy is the provision of a suited layout procedure.

Chapter 4

Multi-energy networksand the EnergyInterconnector principle

In the first part of this chapter the “Vision of Future EnergyNetworks” framework is presented: a flexible description formulti-energy networks. Its building blocks are the EnergyHub (interface among the network participants) and the En-ergy Interconnector (a transmission link for several energycarriers). A wide spectrum of variants for the implemen-tation of the interconnector exists. In order to achieve thegoals of this investigation, a primary selection of a preferredvariant is done based on a discussion of the relevant designparameters, which could be identified at this early stage.

13

14 CHAPTER 4. INTERCONNECTOR PRINCIPLE

4.1 The “Vision of Future Energy Net-works” framework

4.1.1 General concept

In the “Vision of Future Energy Networks” project a generic schemefor the energy network of the future has been worked out [18, 19, 20].Figure 4.1 illustrates the basic structure of this modelling framework:

• “Energy” is not restricted to electricity. Each form of en-ergy produced or consumed by the network participants ispotentially considered in this multi-energy network approach(e.g. electric, chemical and thermal energy).

• The network participants are connected to customisable inter-faces, so-called Energy Hubs.

• Energy Hubs exchange different forms of energy. The interlinkbetween these hubs is called an Energy Interconnector.

• The proposed structure can be seen as a fractal structure: hubssupplying smaller areas can be gathered to larger hubs (sup-plying e.g. a small city), etc.1

The background for these ideas is many-sided. A first motivationfor the customised interface is the need to integrate an increasinglydiversified population of participants (consumers and producers likedistributed generators) having specific requirements (in terms of volt-age, frequency, power quality, ...). The hubs have also the potentialto make network power flows controllable. Some applications willbe more efficient if fuelled by chemical energy (e.g. possibly trans-portation) and the possibility to flexibly convert energy opens newopportunities for energy management (e.g. energy storage). Finallythe multi-energy approach serves to investigate multi-energy trans-mission, which will be the focus of this work.

1No decision on the adequate scale of a hub can be made now and the frame-work was expressly defined in order to address this problem.

4.1. THE FRAMEWORK 15

Hub

Hub

Hub

Interconnector

Hub

HubHub

Electric energy Thermal energyChemical energy

Figure 4.1: Illustration of the “Vision of Future EnergyNetworks” multi-energy network framework.


The definition of the “Vision of Future Energy Networks” frame-work is motivated by its potential advantages as compared to presentsolutions. These advantages include:

• New functionalities: e.g. energy storage (including sharing stor-age across different networks), the potential to include newparticipants (e.g. transportation), customised power (reliabil-ity, voltage, frequency).

• Taking into account any kind of energy production and con-sumption into the same model allows for a wider optimisation.

• Synergies, i.e. the deployment of technologies involving sev-eral carriers (like CHP2) or the sharing of auxiliary equipment(control, metering, cooling, etc.) are facilitated in this context.

The use of the “Vision of Future Energy Networks” framework isat least twofold: it permits the development of new network schemesand it provides a context for the evaluation of new ideas and trends,e.g. the Energy Interconnector. The distinctive elements of this ap-proach are: the multi-carrier paradigm, the inclusion of transporta-tion applications and the so-called greenfield approach (i.e. the ab-straction of pre-existing infrastructures in a first stage - This is con-sistent with the long-term view of the project).

4.1.2 The Energy Hub

The Energy Hub will act as the interface between any kind of pro-ducer and consumer of energy and as the connection point for energytransmission equipment. Its tasks will consist of converting, storing,conditioning and possibly managing energy. It therefore consists ofconversion and storage devices with the ability to match the con-sumer needs in a flexible manner like it is suggested in figure 4.2.Within the “Vision of Future Energy Networks” project, the follow-ing aspects of the energy hub have been covered to date: modelling

2Combined heat and power

4.1. THE FRAMEWORK 17

Interconnector

Heatstorage

Heat producer

Gas consumer

Heat consumer

Power plant

Electrical consumer

Gas producer

Electricalstorage

Chemicalstorage

Kineticenergystorage

Ele

ctr

oly

ser

Fuel cell

Th

erm

. to

el.

co

nve

rte

r

Mixed consumers

Interconnector

Electricity Hydrogen Heat

Figure 4.2: Illustration of the Energy Hub concept.

of mixed energy carrier flows, reliability aspects of such systems andstorage modelling and integration.

4.1.3 The Energy Interconnector

The basic idea of the Energy Interconnector is to combine the trans-mission of several energy carriers in the described multi-energy con-text. The expected advantages are a simplification of the layingprocess (as compared with the individual laying of several separateparallel systems), a possible simplification of the terminal equipment(since it may be shared) as well as the possibility to improve in linestorage capacity or efficiency.

Unresolved questions include the choice of the energy carriers,the geometry of the interconnector (and the layout procedure), theconcept for waste heat re-use, etc. Smaller possible variations in-clude the choice of materials and the dimensioning of the auxiliary


equipment.According to its defined scope (see chapter 3) this work will focus

on the development of a layout procedure. The questions will beaddressed in the following sequence:

• Figure out a “solution candidate” with some variants that canbe covered with a single model, i.e. select the combination ofenergy forms and carriers to be considered in the further work(section 4.2).

• Identify the missing “model parts” and work out a model. De-termine how general this model can be in order to answer rel-evant network layout questions (chapter 5).

• Characterise the operation of an interconnector system, includ-ing auxiliary equipment (chapter 6).

• Elaborate a layout strategy for the interconnector (section 7.1).

• Check the applicability of the concept to generic applicationscenarios (section 7.2).

It must be stressed that all these questions will only find a defini-tive answer in the context of the entire system, i.e. within the “Vi-sion of future energy network” framework. The question of the de-tailed design of the interconnector will only be of crucial interest oncean overall network layout has established its advantages over otherschemes.

4.2 Possible variants and parameters

4.2.1 Preliminary selection of variants

From a general perspective, the spectrum of the potential energycarrier combinations for the interconnector is wide. To develop amodel and a layout strategy, a choice has to be made regardingthe combination to be considered. Possible forms of energy include

4.2. VARIANTS AND PARAMETERS 19

electricity, chemical energy (gaseous or liquid, open or closed cycle),thermal energy (also open or closed cycles) and compressed media.Further possibilities may be water delivery or superconductive orcryogenic electricity transmission.

The choice of this “solution candidate” shall be based on thefollowing criteria:

• A direct use of the transmitted energy carriers is possible.

• There is flexibility in the conversion techniques from the trans-mitted energy carrier3.

• An acceptable conversion efficiency is feasible or can be ex-pected to be achieved.

• Open-cycle cooling of the electrical conductor is potentiallyfeasible.

As a consequence the variant studied in the rest of this work isthe combination of electric and (open cycle) gaseous chemical energytransmission. Electric energy transmission is modelled as d.c. Liquidchemical carriers will be considered in the basic model for comparisonpurposes. The modelled setup is coaxial (as shown in figure 5.1), witha solid insulation material.

4.2.2 Parameters

The “problem definition” will in general include the total length ofthe interconnector4 Ltot, and its capacity5 PchMax and PelMax.

The modelling was done in a way that allows an easy variationof three classes of “parameters” including6:

3i.e. no binding to a unique conversion technology.4i.e. the distance between two heat exchangers.5Since it does not radically change the discussion, the rated capacity is as-

sumed to be the potential maximum power transferred.6All variable names are explained in the list of symbols on page 151, at the

end of this thesis.


• Design parameters, which are those dimensions and propertiesthat can be widely varied to achieve the required transmissioncapacity:

– The inner radius of the interconnector Ri

– The electrical conductor total cross-sectional area7 AcTot

– The maximum d.c. voltage at the interconnector terminalsUinMax

• Design alternatives, which represent possible (discrete) choicesof materials or functionalities of parts or subsystems:

– The choice of the chemical medium: gaseous or liquid, aswell as its exact nature.

– The material of the electrical conductor

– The presence or absence of waste heat reuse at the termi-nals

– The temperature range over which waste heat reuse willoperate

• Constrained parameters, which are parameters of the modelbut can not be freely changed in the design, because they arisefrom external influences or physical limitations:

– The specific thermal resistivity of the soil RthE

– The friction factor of the viscous fluid flow f

– Temperature limitations at the interconnector inlet andoutlet T1 resp. T2

– The maximum operating pressure pMax

– The maximum electric current density JMax

7including all phases

4.2. VARIANTS AND PARAMETERS 21

Restricting the parameters to this list allows one to develop aquite general model which ignores implementation details. On theother hand, simple adaptations allow one to approximate slightly dif-ferent arrangements like e.g. a.c. voltages or several parallel circuits.

This classification of the parameters will be used throughout thenext chapters devoted to the layout and application of the inter-connector. The design parameters are those parameters which canbe adjusted in order to achieve the desired maximum transmittablepowers, the design alternatives indicate how different “sub-variants”for the interconnector may be realised (e.g. using different chemicalenergy carriers) and the constrained parameters will play a role inthe determination of the physical limits to the applicability of theinterconnector principle.

Chapter 5

Interconnectormodelling

This chapter presents the various models of the intercon-nector which will be used in the upcoming discussion ofits operational characteristics and layout procedure. Twomain models describe the use of liquid or gaseous energycarriers. They describe the electrical, chemical and thermalparts of the interconnector. These parts are interdependent,which leads to a mathematical description which can onlybe solved numerically. A simplified set of models permittingthe development of analytical scaling laws has thus beendeveloped.

5.1 Modelling approach

The purpose of this study being the assessment of the general ideaof the interconnector, terminal powers are the most important infor-mation within the model to be developed. Therefore a generic model

23

24 CHAPTER 5. INTERCONNECTOR MODELLING

Pch

Pel1

PU

PCM

PQ

PR

Pel2

Figure 5.1: Illustration of the Energy Interconnector withelectric and chemical power transmission as well as wasteheat reuse.

according to figure 5.1 has been chosen. It consists of three elements:a hollow electrical conductor (through which a chemical medium canflow), a thermal insulation and the surrounding soil. The electricpower Pel1 and the chemical power Pch are transmitted. A part PUof the electrical losses PV is transmitted to the surrounding soil, therest is transmitted to the flowing medium PCM . The heat PQ ab-sorbed by the medium is the sum of PCM and the internal and wallfriction PR.

Several simplifications are made: temperatures in the electricalconductor and the chemical medium depend only on the axial coordi-nate x (i.e. considering a cross-section of the interconnector, the tem-perature of the conductor is the same for the whole cross-section).Some construction elements including the electrical insulation areomitted because their respective contributions to the relationshipsamong the terminal powers are not critical (or can be included byother means).

These simplifications obviously limit the achievable accuracy, butthey contribute to make the model usable in the context of this study,i.e. the model constitutes a general approach: it does not requireknowledge of the layout “details”, applies to several layout variants

5.2. MODEL WITH A LIQUID MEDIUM 25

and thus permits an insight into basic principles rather than intospecific details.

The model includes three parts:

• A model of the fluid flow: This part is specific for gaseousor liquid media. This flow is non-adiabatic, non-isothermal,compressible (except for liquid media) and with friction.

• An electrical model: Ohmic losses are modelled as d.c. losses(with according correction factors for skin and proximity ef-fects).

• A thermal model: Heat transfer between the conductor, the soiland the chemical media are modelled. Since the heat absorbedby the fluid is dependent on the electrical losses, electrical,chemical and thermal powers are coupled.

The models will be presented in the following sections. Sincethe resulting equations can only be solved numerically, a simplifiedmodel leading to partly analytical solutions will also be used, e.g. forthe derivation of scaling laws.

5.2 Model of the interconnector withtransport of a liquid medium

5.2.1 General overview of the model

The model of the interconnector with a liquid chemical medium isless complex because the only contribution to the pressure drop isfriction. The pressure drop per unit length is constant, which leadsto the simple expression for the mass flow rate:

m =

√4π2Ri

5 ρmMf Ltot

(p1 − p2) (5.1)


0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Pel/PelM ax

Pch/P

ch

Ma

x

T2 = 303 [K]

T2 = 305 [K]

T2 = 307 [K]

T2 = 308 [K]

T2 = 310 [K]

303 [K]

310 [K]

Figure 5.2: Transmittable chemical vs. electric power foran interconnector with a liquid chemical energy carrier fordifferent outlet temperatures T2 (example, Uin is kept con-stant).


The thermal power PU transmitted to the surrounding soil canbe determined with the thermal model presented in section 5.2.4.Since the temperature rise of the chemical medium depends on theelectrical losses, the transmitted electric and chemical powers arecoupled. In this simple case, the relationship is:

Pel =√AcTot Uin

2

4Ltot ρ

(cmM (T2 − T1) Pch

wm− f Ltot Pch

3

4π2Ri5 ρmM 2 wm3

+ PU

)(5.2)

Figure 5.2 illustrates this coupling between Pel and Pch: for in-creasing chemical power Pch, the increasing medium mass flow ratem can evacuate more heat, and thus the transmittable electric powerPel1 also increases. The same applies to increasing outlet tempera-ture T2. The main difference with gaseous chemical carriers is that forfixed inlet and outlet temperatures a biunique relation between thetwo kinds of power exists. Gaseous carriers provide more flexibilitysince the chemical and electric powers can be varied independently ofeach other within a certain range (the exact nature of this variationrange will be specified in chapter 6).

5.2.2 Chemical model

The models for liquid and gaseous carriers will be based on the samegeometry, shown in figure 5.3: a hollow electrical conductor is sepa-rated form the surrounding soil by a thermal insulation layer.

For liquids, the pressure difference between inlet and outlet is thefriction pressure drop1:

p1 = p2 + ∆pR (5.3)

1In the following description gravity will be ignored.


medium

conductor

soil

thermalinsulation

ground surface

wT

Ra

Ri

p(x)T (x)

p(x) + ∆pT (x) + ∆T

P′

Umg

P′

V

P′

R P′

CM

P′

Q

∆x

λI

λE

h

Figure 5.3: Cross-section and longitudinal view of the basicinterconnector model.


The pressure drop rate is constant over the line length since the flowvelocity remains constant:

∆pR = fLtot4Ri

ρmM v2 (5.4)

where the medium flow velocity v is:

v =m

ρmM π Ri2 (5.5)

The mass flow rate thus becomes:

m =

√4π2Ri

5 ρmMf Ltot

(p1 − p2) (5.6)

A pump is only required at the inlet and its compression power is:

PPump1 = m

(∆pRρmM

+v2

2

)(5.7)

Therefore the total electric power equivalent becomes:

PF1 =1η1PPump1 (5.8)

The Reynold’s number is:

Re =v d

ν=

2 mπ µM Ri

(5.9)

The viscosity µM is in the order of magnitude of 10−3 Nsm2 , the value

of Re will exceed 2000 in most cases. It is thus appropriate to use aconstant value for f in the subsequent steps.

The chemical power transmitted is proportional to the mass flowrate:

Pch = mwm (5.10)


The heat absorbed by the liquid is proportional to the temperaturedifference between inlet and outlet and the specific heat capacity ofthe medium cmM :

PQ = m cmM (T2 − T1) (5.11)

The thermal energy available at the line end is a function of theoutlet temperature T2 and the cold source temperature TK2, ideally:

Pth = m cmM (T2 − TK2) (5.12)

The heat transmitted to the environment is:

PU =T1+T2

2 + ∆TLK − TURthE

′ +RthI′ Ltot (5.13)

Where ∆TLK is the average temperature difference between the con-ductor and the medium. This has to be approximated based onexperimental data.

The friction losses can be computed based on the work of thefriction force per time unit:

PR =∆W∆t

(5.14)

=∆pR π Ri2 Ltot

∆t(5.15)

=f Ltot m

4π2Ri5 ρmM

(5.16)

5.2.3 Electrical model

It will be assumed that the electrical conductor in the energy in-terconnector occupies the geometrical area Ageom (for each phase ifapplicable). If kf is the fill factor of the conductor then the effectivecross-sectional area of each phase conductor is:

Ac = kf Ageom (5.17)


Thus the total conductor area is AcTot = nphAc, where nph is thenumber of the phases (or poles) and Ac is the conductor cross-sectionper phase. For d.c. transmission, the transmitted power is:

Pel =12AcTot Uin J (5.18)

If not stated otherwise, all examples and calculations in this workwill assume d.c. transmission.

The d.c. resistance of one phase is modelled to be linearly tem-perature dependent (with αc denoting the temperature coefficient ofthe conductor material):

R′

dc =ρcAc

=ρc20

kf Ageom(1 + αc (Tc − 273)) (5.19)

The a.c. resistance of the conductor additionally takes into accountlosses due to skin and proximity effects:

R′

ac = R′

dc (1 + ys + yp) (5.20)

ysR′

dc and ypR′

dc are the additional resistances due to skin andproximity effects respectively.

According to [21] the contribution of the skin effect can be ap-proximated using the auxiliary variable xs2:

xs2 = ks

2π µ0 µrc feR

′dc

(5.21)

where ks depends on the conductor geometry (see the example insubsection B) and

0 < xs ≤ 2.8 : ys = xs4

192+0.8 xs4

2.8 < xs ≤ 3.8 : ys = −0.136− 0.177xs + 0.0563xs2

3.8 < xs : ys = xs2√

2− 11

15

(5.22)

2The skin effect and proximity losses will be approximated by making theassumption that these are independent of each other [21].


The proximity effect losses are also geometry dependent. If theenergy interconnector is armoured or even shielded, losses in theseparts are also to be considered by adding a hypothetical armour andshield resistance (λ1R

′ac , resp. λ2R

′ac ) to the conductor resistance,

thus:R′I = R

′ac (1 + λ1 + λ2) (5.23)

Since the contribution of these losses is minor, d.c. transmission isenvisaged and design details are not available, these losses will beneglected in the following steps.

For d.c. transmission, the transmitted electric power Pel1 and thelosses PV are:

Pel1 =AcTot

2Uin J (5.24)

PV = RI′ Ltot Itot2 = AcTot Ltot ρ J

2 (5.25)

The specific electrical resistivity will be computed based on theaverage medium temperature to which a constant temperature ∆TLKis added (the precision is expected to remain acceptable).

ρ = ρc20

(1 + α

(T1 + T2

2+ ∆TLK − 293

))(5.26)

The following relationship between the losses and the transmittedpower comes out:

PV =4Ltot ρ

AcTot Uin2 Pel1

2 (5.27)

The energy balance also remains the same: the powers absorbedby the chemical medium PQ and the surrounding soil PU correspondto the sum of the electrical and friction losses PV and PR

PQ + PU = PV + PR (5.28)

Using the equations presented above, an analytical relationship


fric

tio

n

ab

so

rptio

n

el. lo

sse

s

transfer insulation soil

po

we

r flo

w t

o s

oil

T Tc TO

TU

PQ′

PR′ PCM

′PV

′ PU′

RthM′ RthI

′ RthE′

Figure 5.4: Thermal model for the energy interconnector.

between the chemical and electric transmitted powers can be derived:

Pel =√AcTot Uin

2

4Ltot ρ

(cmM (T2 − T1) Pch

wm− f Ltot Pch

3

4π2Ri5 ρmM 2 wm3

+ PU

)(5.29)

Figure 5.2 shows an example of this relationship for various outlettemperatures.

5.2.4 Thermal model

Since the temperature varies along the interconnector, the thermalmodel is based on the description of a length element dx of theinterconnector and the local specific thermal powers PR′, PQ′, PCM ′,PV′ and PU

′.The losses occurring in the electrical conductor and its shielding

are transmitted to the surrounding soil and the medium accordingto the thermal model depicted in figure 5.4: the ohmic and frictionlosses are heat sources, the soil and flowing medium are heat sinks.The thermal resistances represent: the interface between the mediumand the conductor (RthM ′), the insulation layer (RthI ′) and the soil(RthE ′). The losses due to friction PR directly occur in the flowing


medium. The electrical conductor is separated from the surroundingsoil by a thermal insulation layer with a specific thermal resistanceλI . All electrical conductors are modelled as a single heat sourcePV , which represents the total electrical losses across all phases. Thethermal resistivity of the electrical conductor is neglected (becausethe specific thermal conductivity of metals is several times higherthan for insulation materials).

R′

thI =1

2π λIln(Ra + wTRa

)(5.30)

The soil has the thermal resistance (according to [22] it will be as-sumed that the heat entirely flows towards the ground surface):

R′

thE =1

2π λEln(

2hRa + wT

)(5.31)

Since the actual thermal conductivity λE of the soil will highly de-pend on the considered soil, a constant value of the specific soilthermal resistance RthE ′ (independent of the outer radius) will beused throughout this work. This is further justified by the fact thatwithin the thermal model, the soil thermal resistance always appearstogether with the thermal resistance of the outer insulation.

The surface thermal resistance of the interface between the in-terconnector and the medium depends on the flow velocity and onlyempirical formulae are available. The approximation proposed in [23]was chosen:

R′

thM =1

2π Ri αLK(5.32)

where:αLK = α1 + α2

√v

1 m/s(5.33)

with α1 = 2, α2 = 12.The model of figure 5.4 yields an equation system describing the

thermal energy flow. Firstly, the power P′

U transmitted to the sur-rounding soil is proportional to the temperature difference between


conductor (Tc) and undisturbed soil (TU ). The remainder of the losspower is absorbed by the medium. The following equation systemcomes out:

P′

U =Tc − TU

R′

thI +R′

thE

(5.34a)

P′

CM = P′

V − P′

U (5.34b)

P′

V = R′

tot Itot2

=ρc20 J

2AcTot2

kf Ageom.tot(1 + ys + yp)︸︷︷︸

=:c4

(1 + αc (Tc − 293)) (5.34c)

Tc = T +R′

thM P′

CM (5.34d)

P′

Q = P′

R + P′

CM (5.34e)

Solving for PQ (the thermal power absorbed by the coolant):

P′

Q =c4 (1 + αc (T − 293))− T−TU

R′

thI +R′

thE

1− c4 αcR ′thM +

R′

thM

R′

thI +R′

thE︸︷︷︸:=c5

+ P′

R (5.35)

The friction losses PR are discussed in section 5.3.2.

5.2.5 Pump model

For liquid media, only one pump at the inlet of the interconnectoris necessary. A turbine at the outlet is feasible, but will not beconsidered here in order to obtain a worst case approximation of therequired auxiliary powers. The required pump power corresponds tothe work per time unit arising from the friction pressure drop plus akinetic component:

PPump1 = m

(∆pRρMm

+v2

1

2

)(5.36)


where:

v1 =m

ρmM π Ri2 (5.37)

The required auxiliary power is thus:

PF1 =PPump1η1Pos

(5.38)

Heat recovery only occurs at the outlet and is modelled identicallyto the situation with gaseous media, described in the appendix A.2.

5.3 Model of the interconnector withtransport of a gaseous medium

5.3.1 General overview of the model

Since the gas flow is compressible and the gas exchanges heat withthe surroundings, the temperature rise and pressure drop vary overthe interconnector length. Figure 5.5 shows the pressure and temper-ature profile for a typical situation3: the mass flow is directed fromx = 0 to x = Ltot, the pressure drops and the temperature increasesalong the interconnector. Since a rising temperature means moreheat transfer to the surroundings, the temperature profiles flattenstowards the line end. The electrical and thermal models are the sameas for liquid media.

The core of the model is the equation system describing the ther-mal power flows4:

PV′ = PU

′ + PCM′ (5.39)

PQ′ = PR

′ + PCM (5.40)

3in order to increase the “visibility” of the phenomena, “extreme” parameters(not necessarily realistic ones) have been chosen for the examples.

4the apostrophe in P ′ denotes specific power per unit length in W/m.

5.3. MODEL WITH A GASEOUS MEDIUM 37

0 0.2 0.4 0.6 0.8 10.92

0.94

0.96

0.98

1

x/Ltot

p(x

)/p

1

0 0.2 0.4 0.6 0.8 1290

300

310

320

330

x/Ltot

T(x

)[K

]

Figure 5.5: Example for a temperature T (x) and pressurep(x) profile of a gaseous medium along the interconnector.


The first equation describes the conductor, where the ohmic trans-mission losses PV ′ are partly transmitted to the surroundings (PU ′)and partly to the flowing chemical medium (PCM ′). The secondequation states that the power absorbed by the medium PQ

′ comesfrom the conductor (PCM ′) and from internal friction (PR′). Thesequantities are functions of the mass flow rate, the local temperatureand the local pressure. Together with the energy and momentumconservation laws a set of partial differential equations (PDEs) isobtained. The profiles in these examples were obtained with a nu-merical PDE solver, since no analytical solution exists.

Figure 5.6 shows the heat flows in the electrical conductor: theelectrical losses increase with temperature towards the line end.Where the conductor temperature is high, the share of the powertransmitted to the surroundings increases. Figure 5.7 shows theheat flows in the flowing medium: the heat PQ′ absorbed by themedium decreases along the interconnector (the heat transmittedfrom the conductor to the medium PCM

′ shows a similar behaviour)and internal friction PR

′ increases due to the pressure drop, whichleads to a higher flow velocity towards the outlet.

The computation of numerical solutions is time consuming andcan obviously only be done for fixed dimensions of the interconnectorand fixed material properties. In order to derive a layout procedure,a method to calculate the interconnector inlet and outlet power forthe entire operational area within reasonable time is needed. Fur-thermore, the identification of scaling laws is only possible on an an-alytical basis. An approximate analytical model has therefore beendeveloped and is presented in more details in section 5.3.4). Thismodel can be used for layout tasks, whereas the numerical modelmay be used in a second refinement step. The analytical model in-volves only the “overall” power flows, i.e. the integrals of the lossesand exchanged heat according to the following definition:

PV,Q,CM,R =∫ x=Ltot

x=0

PV,Q,CM,R′ dx (5.41)


0 0.2 0.4 0.6 0.8 1

2.5

2.6

2.7

2.8

x/Ltot

PV

′ (x)/

PQ

Lto

t

0 0.2 0.4 0.6 0.8 10

1

2

3

x/Ltot

PC

M′ (x)/

PQ

Lto

t

0 0.2 0.4 0.6 0.8 10

1

2

3

x/Ltot

PU

′ (x)/

PQ

Lto

t

Figure 5.6: Profiles of the electrical losses in the conductorPV′ and the heat flows at the interface with the soil PU

′ andthe medium PCM

′ (example).


0 0.2 0.4 0.6 0.8 10

1

2

3

x/Ltot

PQ

′ (x)/

PQ

Lto

t

0 0.2 0.4 0.6 0.8 1

0.2

0.25

0.3

0.35

x/Ltot

PR

′ (x)/

PQ

Lto

t

0 0.2 0.4 0.6 0.8 10

1

2

3

x/Ltot

PC

M′ (x)/

PQ

Lto

t

Figure 5.7: Profiles of the friction losses PR′, heat transfer

from the electrical conductor PCM′ and heat absorbed by a

gaseous medium (example).


0.8

50

.85

0.85

0.85

0.85

0.850

.90.9

0.9

0.9

0.9

0.9

50.9

5

0.95

0.95

11

1

1.0

5

1.05

m/mNom

p1/p

1M

ax

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Figure 5.8: Contour of the electric current density J in func-tion of the mass flow rate m and the inlet pressure p1 (ex-ample).


Interconnector

PPump1

PF1

Qw1

Pw1

PF1,tot

PF,totB

PQ

Qw2B

Pw2B

PPump2B

PF2B

PF2,totB

T0 T1h T1 T2 T3B T4

Figure 5.9: Interconnector system layout and power flowfor waste heat recovery variant B. The figure also illustratesthe naming convention used for temperatures and pressuresat the inlet and outlet of the interconnector.

The analytical model permits calculations of the interconnectorstate variables over a wide variation range, which will be useful inthe determination of its operation area. This can be illustrated bythe example shown in figure 5.8 which shows a contour plot of theelectric current density J in the conductor as a function of the inletpressure and the mass flow m (this is valid for constant inlet andoutlet temperatures T1 and T2, input voltage Uin and outlet pres-sure p2). This representation illustrates how the interconnector canaccommodate different combinations of J and m by varying the inletpressure.

Besides the interconnector itself, several other components willbe required to implement multi-energy transmission. The most im-portant ones are the compressors and heat exchangers needed toestablish the gas flow and to possibly cool it down at the inlet oroutlet of the interconnector. Several alternative configurations of


compressors and heat exchangers may be imagined. A model forthree variants is presented in the appendix A. The most relevantand general variant (variant B) is illustrated in figure 5.9: at the in-let and outlet a compressor develops the compression powers PPump1respectively PPump2. The thermal power Qw1,2 is extracted in theheat exchangers. Taking into account the respective compressionand conversion efficiencies the equivalent electric powers PF1,2 forthe compressors and Pw1,2 from the heat recovery process can becalculated. Put together, the net equivalent electric power require-ment of the auxiliary equipment at the inlet and outlet is denotedas PF1tot and PF2tot respectively. In general all these powers maybe positive or negative, provided that the equipment is designed forbidirectional energy flows.

Since the inlet and outlet pressures depend on m and J , a similarrelationship will also apply to the compressor powers. Figure 5.10shows this dependence for an example (for constant inlet and outlettemperatures T1 and T2, input voltage Uin and outlet pressure p2

as in figure 5.8). The contour lines of all the auxiliary powers havea sharp bend at their intersections with the horizontal axis becausethe conversion losses change their sign.

Once the power requirements of the auxiliary equipment areknown, transmission efficiencies may be calculated according tosection A.3; the following definition of the overall efficiency will beused:

ηtot =Pel1 − PV + Pch − PF2 + Pw2

Pel1 + Pch + PF1 − Pw1(5.42)

The power flows including the auxiliary power are shown in figure5.11(b): using the suggested definitions, all power flows at the inlet“enter” the interconnector and all power flows at the outlet “leave”the interconnector. As compared to the actual power flows shownin figure 5.11(a), the auxiliary power flows are summarised into apower flow at the inlet and at the outlet respectively. The power PUtransmitted to the surrounding soil is a loss power and therefore isnot part of the system output power.

The fact that the interconnector system is open implies that this


0 0.05 0.1 0.15−200

0

200

400

m [kg/s]

PF

1 [

kW

]

0 0.05 0.1 0.150

10

20

30

40

m [kg/s]P

w1 [

kW

]

0 0.05 0.1 0.15−400

−200

0

200

m [kg/s]

PF

2B [kW

]

0 0.05 0.1 0.150

20

40

60

m [kg/s]

Pw

2B [

kW

]

... @ J = 0.677 A/mm2

... @ J = 0.713 A/mm2

... @ J = 0.748 A/mm2

... @ J = 0.784 A/mm2

... @ J = 0.820 A/mm2

Figure 5.10: Auxiliary power requirements and possiblewaste heat recovery at the inlet and outlet of an intercon-nector in dependence upon gas mass flow (example).


Inte

rco

nn

ecto

r

Inle

t co

mp

resso

ra

nd

re

co

ve

ry

Ou

tle

t co

mp

resso

ra

nd

re

co

ve

ry

PF1

PQ

PF2

PchPchPchPch

Pel1Pel1 Pel1 − PVPel1 − PV

Pw1 Pw2PU = PV − PQ

(a) Power flows without combination of the auxiliarypowers

Inte

rco

nn

ecto

r

Inle

t co

mp

resso

ra

nd

re

co

ve

ry

Ou

tle

t co

mp

resso

ra

nd

re

co

ve

ry

PF1 − Pw1

PQ

Pw2 − PF2

PchPchPchPch

Pel1Pel1 Pel1 − PVPel1 − PV

(b) Power flows with combination of the auxiliary pow-ers

Figure 5.11: Power flows for the overall interconnector sys-tem including auxiliary power.


definition can lead to values greater than unity (e.g. if the gaseousmedium is available at a very high pressure p0). Nevertheless ηtotwill be used to analyse variations of the overall efficiency over theoperation area. For comparison purposes, electrical and chemicaltransmission efficiencies will be defined as follows:

ηel =Pel1 − PVPel1

(5.43)

ηch =Pch

Pch + PFTot(5.44)

A representative example of the efficiencies is given in figure 5.12.The different sharp bends of the contour lines arise from sign changesin the conversion losses of one of the auxiliary powers. The electricaltransmission efficiency decreases with Pel since the current densityincreases. The chemical efficiency increases with Pel since the fric-tion losses PR are lower for increasing Pel. As a result, the overalltransmission efficiency ηtot is maximal for “moderate” values of theelectric power.

5.3.2 Gas flow

The momentum and energy conservation

The flow of an ideal gas in a pipe with the cross-section Ai = π Ri2

is considered. In general, the gas will absorb heat form the pipe walland receive mechanical energy from the compressor end of the pipe,whereas it will increase its internal energy and give energy to theturbine end of the pipe (see figure 5.3). The analysis will be restrictedto steady state operation and interconnectors with a constant cross-sectional area (Ai = Ao). For a mass element ∆m = ρmM Ai ∆x the


974

974

979

979

981

981

981

982

982

982

983

983

983984

984

984

985

985 986

Pel/PelM ax

Pch/P

ch

Ma

x

Total transmission efficiency (‰)

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 10

0.2

0.4

0.6

0.8

1

970983

983

989

989

989

992

992

995

995

997

997

997

999

999

999

1000

1000

1000

Pel/PelM ax

Pch/P

ch

Ma

x

Chemical transmission efficiency (‰)

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 10

0.2

0.4

0.6

0.8

1

97

0

97

197

297

3

974

Pel/PelM ax

Pch/P

ch

Ma

x

Electrical transmission efficiency (‰)

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 10

0.2

0.4

0.6

0.8

1

Figure 5.12: Contour lines of the electrical, chemical andtotal transmission efficiency (example).


power balance5 equation is (see figure 5.13)6:

P′

Q ∆x+Ai pi vi−Ai po vo+m nF2

RgMm

(Ti − To)+m

2(vi

2 − vo2)

= 0

(5.45)where:

P′

Q ∆x heat absorbed by ∆m of a length ∆xAi pi vi work of the surrounding gas on ∆mAi po vo work of ∆m on the surrounding gas12 m nF

RgMm

(Ti − To) variation rate of the internal energy of ∆m12 m

(vi

2 − vo2)

variation rate of the kinetic energy of ∆m

Equation 5.45 can be transformed using:

ρmM =Mm p

Rg T(5.46)

v =m

π Ri2 ρmM

=mRg

Mm π Ri2

T

p(5.47)

and thus becomes

P′

Q ∆x− ∆ (Ai p v)︸︷︷︸Ai∆

“p mRg T

π Ri2 Mm p

”−mnF Rg2Mm

∆T − m

2∆(v2)

︸︷︷︸= m

2m2 Rg2

π2 Ri4 Mm

∆“T2

p2

”= 0

(5.48)The absorbed heat PQ originates from two mechanisms:

• conduction through the pipe wall (PCM )

• and friction in the medium itself (PR, see also section 5.3.2).

5or conservation of energy6m is positive for mass flow from x = 0 towards x = Ltot.


friction

inle

t fo

rce

ou

tle

t fo

rce

P′

Q ∆x

∆x

Api vi Apo vo

Figure 5.13: Mass element in the pipe.

For small ∆x the Taylor approximations ∆T = ∆x dTdx and

∆(T 2

p2

)= ∆x d

dx

(T 2

p2

)can be used. A first differential equa-

tion for non-isothermal gas flow is obtained:

P′

Q = mRgMm︸︷︷︸

=:c2

(nF2

+ 1) dT

dx− 1

2m3Rg

2

π2Ri4M2

m︸︷︷︸=:c2 c3

ddx

(T 2

p2

)(5.49)

An equivalent formulation of the differential equation 5.49 using onlyfirst derivatives of p and T is:

P′

Q − c2(nF

2+ 1) dT

dx− c2 c3 T

p2

dTdx

+ c2 c3T 2

p3

dpdx

= 0 (5.50)

Next the momentum conservation law is applied to a mass ele-ment ∆m in the pipeline (see figure 5.13). The forces applied on themass element are the hydrodynamic forces by the surrounding gasat both ends of the mass element as well as the friction losses at the


interface with the pipe walls and within the medium itself:∑F =

∆pKIN∆t

(5.51)

Ai (−∆p−∆pR) =∆(mv)

∆t(5.52)

Ai (−∆p−∆pR) = m∆v︸︷︷︸=:Ai∆pM

(5.53)

In short:∆p = −∆pR −∆pM (5.54)

Using 5.46 and 5.47:

∆pM =m2Rg

AiMm π Ri2︸︷︷︸

=:c3

∆(T

p

)(5.55)

The Taylor approximation of the last term is:

∆(T

p

)= ∆x

ddx

(T

p

)(5.56)

= −∆xp

(dTdx− T

p

dpdx

)(5.57)

This yields:

∆pM = c3∆xp

(dTdx− T

p

dpdx

)(5.58)

Using the Darcy-Weisbach approximation of the friction pressuredrop (see also section 5.3.2)7 yields:

∆pR = f∆x4Ri

ρmM v2

= fRg

4π2Ri5Mm

m2︸︷︷︸=:c1

∆xT

p(5.59)

7Assuming a positive mass flow m.


Substituting into 5.54 yields a second differential equation for thegas flow. The resulting equation system is:(

1− c3 Tp2

)dpdx

+c3p

dTdx

+ c1T

p= 0 (5.60a)

c2 c3T 2

p3

dpdx−(c2

(nF2

+ 1)

+ c2 c3T

p2

)dTdx

+ P′

Q = 0 (5.60b)

From equation 5.60b the heat absorbed by the gaseous mediumin a pipeline with length Ltot is:

PQ =∫ Ltot

0

c2

(nF2

+ 1) dT

dx+

12c2 c3

ddx

(T 2

p2

)dx

= c2

(nF2

+ 1)

(T2 − T1) +12c2 c3

(T2

2

p22− T1

2

p12

)(5.61)

In the literature similar equations are used for the simulation oftransient phenomena in gas pipelines and networks [24, 25].

Pipe friction

The flow equations 5.60a and 5.60b make use of the friction factorf carried over from equation 5.59. Its determination is based onempirical findings. According to [26] the friction pressure drop canbe approximated as:

∆pR = ρmM f∆x4Ri

v2 (5.62)

The Reynold’s number is defined by:

Re =2 ρmM v Ri

µM(5.63a)

=2 m

π Ri µM(5.63b)


Depending on the value of Re, a different calculation method for fhas to be used. For laminar flow (Re < 2000) f can be computedstraightforward:

Re < 2000 : f =64Re

(5.64)

For turbulent flow f is given in an implicit form:

Re > 2000 :−1√f

= −2 log10

(e/D

3.7+

2.51Re√f

)(5.65)

In the energy interconnector design strongly turbulent flow in moder-ately smooth pipes will be assumed, and therefore it will be adequateto assume a constant friction factor f along the entire pipe [27]. Thiscan be checked after the layout is completed.

The work by the medium due to the friction pressure drop isconverted into heat either by friction on the pipe walls or by frictionin the medium itself according to (using equations 5.62, 5.46 and5.47):

∆QR = ∆WR (5.66)= ∆pRAi ∆x (5.67)

= fRg ∆x

4π2Ri5Mm

mT

pπ Ri

2 ∆x (5.68)

Thus, along a length ∆x of the pipe the following thermal power isdeveloped by friction:

∆PR =∆QR∆t

= fRg

4π Ri3Mm

m2 T

p

(∆x)2

∆t(5.69)

Equation 5.47 can again be used:∆x∆t

= v =mRg

Mm π Ri2

T

p(5.70)

The specific friction power per unit pipe length unit becomes:

P′

R =PR∆x

= fRg

2 m3

4π2Ri5Mm

2︸︷︷︸=c1 c2

T 2

p2(5.71)


5.3.3 A model for numerical solutions

The differential equations

Preparing the use of numerical solvers the per unit coordinate X isintroduced as follows8:

X =x

Ltot(5.72)

Thus:

dpdx

=1Ltot

dpdX

(5.73a)

dTdx

=1Ltot

dTdX

(5.73b)

Combining the equations from the electrical, thermal and chemi-cal models, yields the following equation system for the pressure andthe temperature profiles (see sections 5.3.2 and 5.2.4):(

1− c3Ltot

T

p2

)dpdX

+c3 Ltotp

dTdX

+ c1T

p= 0

(5.74a)

c2 c3Ltot

T 2

p3

dpdX−(c2Ltot

(nF2

+ 1)

+c2 c3Ltot

T

p2

)dTdX

+ P′

Q = 0

(5.74b)

where

c1 = fRg

4π2Ri5Mm

m2 (5.75a)

c2 = mRgMm

(5.75b)

c3 =m2Rg

AMm π Ri2 (5.75c)

8This is useful for numerical simulation since the one-dimensional discretisa-tion is independent of the geometry.


The specific heat absorption of the medium P′

Q is also temperatureand pressure dependent and has been treated in section 5.2.4.

A numerical model

These differential equations cannot be solved analytically, but usingnumerical partial differential equation solvers. The temperature andpressure along the interconnector can be evaluated for a specified ge-ometry (inner radius, length, etc.), material properties and operatingpoint (electrical losses, chemical throughput, inlet or outlet tempera-ture or pressure, etc.). Several software models have been developedfor different boundary conditions.

Using numerical PDE solutions to investigate several operatingpoints or geometries is inefficient since the determination of the out-let temperature and pressure requires the computation of the entiretemperature and pressure profiles. In addition, these PDEs cannotbe solved for the terminal powers. This means that an analyticalmodel would be useful, but that because of the nature of the prob-lem, this analytical model will have to be based on approximations.

5.3.4 Analytical modelling

Gas flow

Although the equation system 5.60b and 5.60a has no analytical so-lution, analytical expressions for p(x) and T (x) are the prerequisitesfor a model which can be solved analytically. Therefore the follow-ing approximation9 shall be used: a constant heat transfer P

′Q to

the flowing medium is assumed. A further assumption is that theheat absorption of the gaseous medium is similar to the one of non-compressible media. The temperature profile T (x) will therefore belinear:

9For all simplifications made in this section, it will be shown that this ap-proximation yields acceptable results in the most common cases.


T (x) = T1 +T2 − T1

Ltotx (5.76)

The pressure profile can be calculated using equation 5.49 andtaking into account that c2 c3 is so small that it can be neglected10:

p(x)2 − p12 = −

∫ x

0

2 c1 T (x)dx (5.77)

⇒ p(x) =

√√√√p21 − c1 Ltot

(2T1

x

Ltot+ (T1 + T2)

(x

Ltot

)2)

(5.78)

Substituting x = Ltot gives the outlet pressure of the pipeline:

p2 =√p1

2 − c1 Ltot (T1 + T2) (5.79a)

=

√p1

2 − f Rg

4π2Ri5Mm

Ltot (T1 + T2) m2 (5.79b)

Solving for the mass flow rate m yields11 (the chemical energy flowis assumed to be proportional to m according to Pch = wm m):

m = 2π

√Mm (p1

2 − p22)

f Rg Ltot (T1 + T2)Ri

5/2 (5.80)

10p(x) is a positive quantity.11m is still assumed to be positive.


The total stored mass of the gas in the interconnector is:

ms =∫ Ltot

0

Ai ρmM dx (5.81)

= π Ri2

∫ Ltot

0

Mm p (x)Rg T (x)

dx (5.82)

=π LtotMm p2R

2i

Rg T2

p1p2− 1

T1T2− 1

+ ln (Ξ)

√√√√√ T 21T 2

2− p2

1p2

2(T1T2− 1)3 (

1 + T1T2

)

(5.83)

where

Ξ =

(p1p2

+ T 21T 2

2+√(

T 21T 2

2− 1) (

T 21T 2

2− p2

1p2

2

))(

1 + p1p2

)T1T2

(5.84)

In the detailed calculations, the conditions for the validity of thissimplified approach should of course be verified. An example will bediscussed in section 5.3.5.

Approximated thermal model

As the precise temperature profile T (x) of the gaseous medium flow-ing through the energy interconnector is impossible to compute an-alytically, a simplified approximation of the thermal energy flow willbe used (based on the linear profile in equation 5.76). Thereforeequation 5.34a is integrated along the energy interconnector:

PQ = PV − TcAve − TUR

′thI +R

′thE

(5.85)

where TU is the soil temperature at infinite distance and TcAve is themean temperature of the gaseous medium in the energy interconnec-tor:

TcAve = ∆TLK +T2 + T1

2(5.86)


A constant temperature difference ∆TLK between the energy inter-connector and the gaseous medium is assumed. Thus the mean spe-cific power transmitted to the surrounding soil becomes:

PU′ =

TcAve − TURthI

′ +RthE′ (5.87)

And thus the thermal power transmitted to the soil over the entireinterconnector length is:

PU =∆TLK + 1

2 (T1 + T2)− TUR

′thI +R

′thE

Ltot (5.88)

The electrical losses in the conductor thus become:

PV = KV

(1 + αc

(∆TLK +

T1 + T2

2− 293

))J2 (5.89)

whereKV = Ltot kf AgeomTot ρc20 (1 + ys + yp) (5.90)

An analytical model based on simplified assumptions

Analytical expressions for each power flow can be derived using theapproximate pressure and temperature profiles (equations 5.78 and5.76) previously introduced. For these analytical profiles, it is possi-ble to calculate the chemical, thermal and electric power flows, theoverall electrical losses and the heat transmitted to the chemical car-rier as well as the surrounding soil. The local specific power is oflower importance in this analysis.

It is suitable (as will be shown later) to express each energy flowin terms of the input and output parameters for the chemical energycarrier p1, T1, p2 and T2.

The temperature profile from equation 5.76 and pressure profilefrom equation 5.78 apply. Solving for the mass flow and using the


definition of chemical power gives:

Pch = wm m

= 2π wm

√Mm (p1

2 − p22)


5/2 (5.91)

Combining this with previous results, the thermal power absorbedby the gaseous medium becomes:

PQ =π√Rg√p1

2 − p22Ri

52

f32 Ltot

32√Mm (T1 + T2)

32

(−f Ltot (2 + nF )

(T1

2 − T22)

+

4(p1

2 − p22)Ri(p1

2 T22 − p2

2 T12)

p12 p2

2

)(5.92)

The heat produced by friction losses becomes, if p22 T1

2 −p1

2 T22 < 0:

PR =π√Rg√p1

2 T 22 − p2

2 T 21 Ri

52√

f LtotMm (T1 + T2)(2√p1

2 − p22 (T1 − T2)√

p12 T2

2 − p22 T1

2+ ln(Υ)

)(5.93)

where

Υ =p2

2 T1 + p12 T2 +

√(p1

2 − p22)(p1

2 T22 − p2

2 T12)

p22 T1 + p1

2 T2 −√

(p12 − p2

2)(p1

2 T22 − p2

2 T12) (5.94)

For p22 T1

2 − p12 T2

2 > 0:

PR =2π√Rg√p2

2 T12 − p1

2 T22Ri

52√

f LtotMm (T1 + T2)(arctan(Γ2)− arctan(Γ1) +

√p1

2 − p22 (T1 − T2)√

p22 T1

2 − p12 T2

2

)(5.95)


where

Γ1 =

√p1

2 − p22 T1√

p22 T1

2 − p12 T2

2(5.96a)

Γ2 =

√p1

2 − p22 T2√

p22 T1

2 − p12 T2

2(5.96b)

The permissible electrical losses are (considering the thermal modelfrom figure 5.4):

PV = PCM + PU (5.97a)PCM = PQ − PR (5.97b)

The expressions 5.91, 5.92 and 5.97a give the chemical through-put, the absorbed heat and the permissible electrical losses for givenboundary conditions (p1, T1, p2 and T2). Considering equation 5.95,it is not possible to solve the flow equations for p1, T1, p2 and T2

analytically12. The determination of p1, T1, p2 and T2 for knownelectrical losses and chemical power thus involves an iterative nu-merical procedure but no numerical simulation.

The condition on p22 T1

2 − p12 T2

2 can be rewritten as follows(using equations 5.76 and 5.78):

p22 T1

2 − p12 T2

2 < 0 (5.98)

⇔ p22

(T1

2

T22 − 1

)4π2Ri

5Mm

f Rg Ltot (T1 + T2)< m2 (5.99)

This condition is fulfilled if T1 < T2, which is a design goal of theenergy interconnector.

5.3.5 Discussion of the simplified model

The figures 5.14 and 5.15 show comparisons between numerical (sim-ulated) and analytical (calculated) results. The most severe differ-ence shows with the outlet temperature T2 and with the thermal

12The solution involves transcendental functions.


0.75 0.8 0.85 0.9 0.95 1 1.05 1.10

1

2

3

4

J/JNom

p/p

No

m

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1250

300

350

400

J/JNom

T[K

]

0.75 0.8 0.85 0.9 0.95 1 1.05 1.10

1

2

3

4

J/JNom

ms/m

sN

om

p1 sim.

p1 calc.

p2

T1

T2 sim.

T2 calc.

sim.

calc.

Figure 5.14: Comparison between simulated (numerical)and calculated (analytical) temperature and pressure pro-files in dependance upon normalised current density (exam-ple).


0.75 0.8 0.85 0.9 0.95 1 1.05 1.10

1

2

3

4

J/JNom

p/p

No

m

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1250

300

350

400

J/JNom

T[K

]

0.75 0.8 0.85 0.9 0.95 1 1.05 1.10

1

2

3

4

J/JNom

ms/m

sN

om

p1 sim.

p1 calc.

p2

T1

T2 sim.

T2 calc.

sim.

calc.

Figure 5.15: Comparison between simulated (numerical)and calculated (analytical) specific power profiles in depen-dance upon normalised current density (example).


power absorbed by the gas PQ. Fortunately, the discrepancy of theauxiliary power requirement PF2 according to the two procedures isless severe. This could be confirmed in further examples.

Obviously these examples do not constitute a general proof ofthe adequacy of the simplified model. The purpose of the simplifiedmodel is to derive a rough layout rule. The results obtained shouldsubsequently be compared to numerical simulations once the resultof the layout procedure is known (an example will be provided inchapter 7).

5.4 Model of the interconnector withtransport of a gaseous medium andlow temperature energy transmission

The model developed in the previous section can be adapted in or-der to describe the situation of low temperature energy transmis-sion (variant C). In this case the soil temperature is higher than thetemperature of the chemical medium. The model of the auxiliaryequipment is discussed in section A.2, while the same interconnectormodel as for variants A and B can be used.

Figure 5.16 shows the dependence between the mass flow rateand the electric current density for a representative example. Thegeneral dependence is the same, with two main differences:

• There is no lower value for the electric current density J be-cause the thermal power flow between the surrounding soil andthe interconnector is reversed.

• A minimum value for the mass flow rate m exists. This corre-sponds to the situation where the gas flow is just sufficient tocool down the interconnector to the required temperature (andno additional electrical losses are permissible).

This solution will not be considered in more detail because it

5.4. LOW TEMPERATURE ENERGY TRANSMISSION 63

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

m/mnom

J/J

no

m

Jmax

J @ p1 = 36.5 bar

J @ p1 = 48.4 bar

J @ p1 = 60.0 bar

Figure 5.16: Permissible current density vs. mass flow ratefor an interconnector with low temperature energy trans-mission (example with T1 = 253 K and T2 = 293 K).


is not as advantageous from a system perspective as the preferredsolution selected in section 4.2.

Chapter 6

Operationalcharacteristics of theEnergy Interconnectorwith transmission of agaseous medium

This chapter describes the limitations which restrict the op-eration of an interconnector. A maximum for the transmit-table electric and chemical powers exists and the transmittedelectric and chemical powers are coupled, i.e. they cannot bevaried fully independently of each other. The dimensioningof the auxiliary equipment (compressors and heat exchang-ers) will also influence the operational area (combinationsof the transmitted electric and chemical power). The max-imum transmittable powers describe a particular design ofthe interconnector. In order to permit the determination of

65

66 CHAPTER 6. INTERCONNECTOR OPERATION

the necessary approximate dimensions of the interconnectorfor a given maximum power (electric and chemical), scalinglaws will be derived.

6.1 Power limitations and dependences

6.1.1 Description of the limitations

In order to develop a layout method for an interconnector system asdescribed above, a description of the maximum transmitted electricand chemical powers is needed. The coupling between the chemicaland electric powers (which arises from the fact that the flowing chem-ical medium removes some of heat form the conductor) has also to bedescribed. In summary, a description for the possible combinationsof the electric and chemical power, i.e. the permissible operationalarea is needed. This will be done using the simplified analyticalmodel presented in the previous sections.

Several classes of limitations can be distinguished:

• Design limitations: These include the maximum permissibleoperating voltage UinMax, the maximum pressure pMax andthe maximum outlet temperature T2Max.

• Physical limitations: E.g. some combinations of Pel and Pchare even not feasible for infinite pressure.

• Limitations given by the auxiliary equipment: Depending onthe ratings of the compressors, the operating range of the in-terconector may be further reduced. Finally the choice of therating of the waste heat recovery process may similarly restrictthe operational area.

Using the analytical model from section 5.3.4, the permissibleelectrical losses can be expressed as function of p2 (or p1), m, Uinand T2. The detailed equations are given in section 6.1.2 (equations

6.1. POWER LIMITATIONS AND DEPENDENCES 67

PchAMax

PchAPMax

PchAMin

PelchAMax

(PV chAMax)

PelchAMin

(PV chAMin)PelAMax

(PV AMax)

Pch

Pel

(PV )

Figure 6.1: Nomenclature for the maximum and minimumelectric and chemical powers.

6.2 and 6.3). As a result, it can be shown that at constant Uin andT2 (see section 6.1.2) two limits of the electric power exist for eachvalue of the chemical power (smaller than its maximum):

• A minimum value of the electrical losses PVMin. This limitcorresponds to the situation where the gas takes up no heatfrom the electrical conductor1 (thus PCM = 0).

• A maximum value of the electrical losses PelMax(m). This limitdepends on the maximum admissible pressure pMax. For infi-nite values of the pressure, the electric power remains limited.

For constant Uin and T2 the shape of the operational area is asshown in figure 6.1. The operational area is delimited by two curvesdescribing the minimum and maximum electric power as a function

1It is physically possible to establish a situation where the friction losses PRexceed the heat absorbed by the chemical medium PQ and thus contribute towarm up the surrounding soil. This situation is, however, unrealistic with respectto practical applications.


of the chemical power. The represented shape of these limitationcurves is characteristic for interconnectors with gaseous chemical me-dia. The figure also introduces a nomenclature for the minimum andmaximum transmissible powers. These values will be used to char-acterise an interconnector in the following sections. With the chosenmodel, the minimum electrical losses are independent of the massflow rate, and thus PelchAMin = PelchAMax.

In section 6.1.2, the calculation of these maxima and minima isdescribed in more details. The minimum electrical losses can becalculated based on the simplified analytical model as well as thelosses at maximum pressure. It is, however, impossible to derivean analytical expression for PelAMax. This may represent a problemsince the aim of the layout strategy is to find out which dimensioningof the interconnector is necessary to achieve a given electric andchemical power transmission capability. In section 7.1.2 scaling lawsare presented which provide an alternative to repeated numericalsimulations of an interconnector with different geometries.

Obviously a variation of the outlet temperature T2 and the in-put voltage Uin below the maximum values is feasible. Lowering T2

means lowering the permissible electrical losses, thus the transmissi-ble electric power is reduced. Figure 6.2 illustrates the change of theoperational area for different values of T2. With increasing outlettemperature, the permissible electrical losses increase, which meansthat the transmittable electric power also increases. This means thatoperating areas for different values of T2 may overlap, which resultsin a further degree of freedom in the operation of an interconnectorsystem. Figure 6.3 illustrates this for a characteristic example: themaximum and permissible outlet temperature is plotted as a functionof the electric and chemical power. The volume contained within thetwo surfaces corresponding to the temperature limits corresponds tothe permissible range of the outlet temperature for each combinationof the chemical and electric powers.

The inlet temperature T1 may be varied as well. Figure 6.4 showsthe resulting change to the operational area: with increasing inlettemperature T1, the permissible losses increase and thus the trans-


0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

313

393

326

342

359376

Pel/PelM ax

Pch/P

ch

Ma

x

Figure 6.2: Operational area for an interconnector with agaseous chemical medium for different outlet temperaturesT2 (example). Parameter is the outlet temperature T2 [K].

0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1300

320

340

360

380

400

PelPch

T2[

K]

Figure 6.3: Maximum and minimum permissible outlet tem-perature in function of the operating point (example).


0.75 0.8 0.85 0.9 0.95 1 1.050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T1 = 293 [K]

T1 = 373 [K]

T1 = 307 [K]

T1 = 324 [K]

T1 = 340 [K]

T1 = 357 [K]

Pel/PelM ax

Pch/P

ch

Ma

x

Figure 6.4: Operational area for an interconnector with agaseous chemical medium for different inlet temperaturesT1 (example).

mittable electric power also increases. On the other hand, the shareof the ohmic losses which is evacuated by the medium is reduced,which implies a smaller difference between the maximum and mini-mum electric power.

The practical attractiveness of a variation in T1 and T2 duringoperation can be expected to be somewhat limited for the followingreasons:

• Allowing a higher inlet temperature T1 than the minimum pos-sible increases the electrical losses.

• Operating with a lower outlet temperature T2 will dramaticallydecrease the conversion efficiency (because of the decreasedcarnot efficiency) of the waste heat recovery process (if ap-plicable) and reduce the permissible losses and the availablethermal power.


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Pel1/PelM ax

Pch/P

ch

Ma

x

Uin

= 0.25 UinMax

Uin

= 0.50 UinMax

Uin

= 0.75 UinMax

Uin

= 1.00 UinMax

Figure 6.5: Operational area at different input voltages(example).

Thus from an operational perspective, T1 and T2 might only be ad-justed to allow for operating points which are not feasible for nominaltemperatures.

The transmission voltage may also be varied. This affects therelationship between the electric power Pel1 and the current densityJ . For d.c. transmission, this means:

Pel =AcTot

2Uin J (6.1)

The relation between m and J remains unchanged, which impliesthat for a lower transmission voltage, the operational area is shrunkalong the horizontal axis, as illustrated in figure 6.5. The possibilityto adapt the transmission voltage thus permits an increase of thetheoretical variation range for the electric power from close to zeroto its value at maximum voltage.


0.20.4

0.60.8

1

0

0.5

1

1.50.2

0.4

0.6

0.8

1

Pel1/PelM axPch/PchM ax

Uin

/U

inM

ax

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 6.6: Optimal transmission voltage (example).

0.20.4

0.60.8

1

0

0.5

1

1.50.88

0.9

0.92

0.94

0.96

0.98

1

Pel1/PelM axPch/PchM ax

η to

t

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

Figure 6.7: Total transmission efficiency with optimal trans-mission voltage (example).


The transmission voltage has a huge influence on the total trans-mission efficiency. As suggested in figure 5.12, ηtot depends on thetransmitted electric and chemical power. With variable Uin it isthus possible to select the value of the voltage yielding the highestefficiency. This voltage is in general smaller than the highest per-missible transmission voltage, as shown in figure 6.6. Even if it ispossible to select a transmission voltage with improved overall effi-ciency, the efficiency gets unacceptably low for small values of theelectric power. As shown in figure 6.7, this may set a practical lowerlimit to the transmissible electric power: the total transmission ef-ficiency has a reasonable value when one of the electric or chemicalpowers is at least 50% of its maximum. For low transmitted powers,the efficiency becomes unacceptably low.

6.1.2 Limits for the electrical losses at constanttemperatures and voltages

In a first step the coupling between the electric and chemical powerwill be discussed, assuming the temperatures T1 and T2 as well asthe voltage Uin are fixed. This means that the transmitted electricpower Pel is proportional to the electric current density J .

In similarity to the case of a liquid medium, the sum of the elec-trical and friction losses PV and PR corresponds to the power trans-mitted to the soil and the chemical medium PU and PQ.

PV + PR = PU + PQ (6.4)

Using equations 5.92, 5.88, 5.93 and 5.80, these losses can be ex-pressed as a function of the temperatures, mass flow rate and inletor outlet pressure (equations 6.2 and 6.3 respectively).

For each value of the chemical power, two limits for the permis-sible losses exist:

• A minimum current density JMin: this corresponds to the sit-uation PV = PU and PR = PQ, which means that the temper-ature rise of the gas is only due to friction. In theory, PR > PQ


PV

=−

m3R

2g T21

2π

2M2mp

21 R4i

+mRg

2Mm (

(nF

+4)(T

2 −T

1 )+

4m2R

g Ri T

22

4π

2Mmp

21 R5i −

fm

2Rg L

tot (T

1+T

2 ) )+

Ltot (

12(T

1+T

2 )−TU

+∆TLK )

R′

thE

+R

′thI

−

ln (4π

2Mmp

21 R5i −

fm

2Rg L

tot T

1+ √

fm

2Rg L

tot (4

π2M

mp

21(T

2 −T

1 )R

5i+fm

2Rg L

tot T

21 )4π

2Mmp

21 R5i −

fm

2Rg L

tot T

1 − √fm

2Rg L

tot (4

π2M

mp

21(T

2 −T

1 )R

5i+fm

2Rg L

tot T

21 ) )√Rg

(4π2M

mp

21(T

2 −T

1 )R

5i+fm

2Rg L

tot T

21 )4fLtot M

2m

(6.2)

PV

=m

3R2g T

22

2π

2M2mp

22 R4i

+mRg

2Mm (

(nF

+4)(T

2 −T

1 )−4m

2Rg R

i T21

4π2M

mp

22 R5i

+fm

2Rg L

tot (T

1+T

2 ) )+

Ltot (

12(T

1+T

2 )−TU

+∆TLK )

R′

thE

+R

′thI

−

ln (4π

2Mmp

22 R5i

+fm

2Rg L

tot T

2+ √

fm

2Rg L

tot (4

π2M

mp

22(T

2 −T

1 )R

5i+fm

2Rg L

tot T

22 )4π

2Mmp

22 R5i

+fm

2Rg L

tot T

2 − √fm

2Rg L

tot (4

π2M

mp

22(T

2 −T

1 )R

5i+fm

2Rg L

tot T

22 ) )√Rg

(4π2M

mp

22(T

2 −T

1 )R

5i+fm

2Rg L

tot T

22 )4fLtot M

2m

(6.3)


is also possible , but the considered operational area will berestricted to PR < PQ since this is sensible from the point ofview of the application (i.e. situations where the soil is heatedup by the friction losses in the gaseous medium will not beconsidered).

• A maximum current density JMax, due to the fact that thepressures are limited: p1 < p1Max and p2 < p2Max. In thefollowing it will be shown that the maximum current densitycorresponds to the highest values of p1 and p2.

The typical shape of the operational area delimited by the curvescorresponding to PVMin(m) and PVMax(m), is shown in figure 6.1.This figure also introduces the nomenclature for the maximum andminimum powers at the “edges” of the operational area. Conse-quently, the minimum electrical losses can be derived from equations5.88:

PVMin =Ltot

R′

thI +R′

thE

(∆TLK +

T1 + T2

2− TU

)(6.5)

From equation 5.80 it is clear that p2 = max ⇔ p1 = max (forconstant m). Thus it is equivalent to show that the electrical losseshave their maximum for p2 = max.

dPVdp2

∣∣∣∣J=min

> 0 (6.6)

anddPVdp2

> 0 for p2 > p2 |J=min (6.7)

As discussed in section 6.1.3, it can be shown that the conditionstated in equation 6.7 is fulfilled for:

f >6Ri

(5T2

2 − T12)

Ltot T2 (T1 + T2)(6.8)

A physical background for this condition can hardly be found.


Since it cannot be established that the conditions 6.6 and 6.8 areuniversally true, they must be checked each time a maximum electricpower is computed using the assumption that the electrical losses aremaximum at the highest permissible pressure2.

Independently of the permissible maximum operating pressurep1Max, a physical limit of the electrical losses PV can be defined asthe permissible losses at infinite inlet pressure:

PVMax = limp1,2→∞

PV = limp1,2→∞

PQ + limp1,2→∞

PU − limp1,2→∞

PR

(6.9)

PVMax =1

2Mm

(R

′thI +R

′thE

)(mRg (2 + nF )

(R

′thI +R

′thE

)(T1 + T2)

+ LtotMm (T1 + T2 − 2TU + 2∆TLK)) (6.10)

The upper and lower limits derived for the electrical losses (equa-tions 6.5 and 6.10) can be transposed into limits for the electriccurrent density.

JMax =

√PVMax

KV

(1 + αc

(T1+T2

2 + ∆TLK − 293)) (6.11)

JMin =

√PVMin

KV

(1 + αc

(T1+T2

2 + ∆TLK − 293)) (6.12)

6.1.3 Justification

As shown in the sign table 6.1, the strategy is to show that thederivative dPV

dp2is positive, which means that the maximum of PV is

reached when p2 is maxiumum3.2The implementation of this check is very simple.3As discussed earlier, this will also correspond to the maximum of p1 for fixed

m.


p2 = 0 p2 = pdz p2 = pfp p2 →∞dPVdp2

− − 0 + + + 0d2PVdp2

2f2w0 + + + 0 −

d3PVdp3

2f3w0 − − − − −

Table 6.1: Sign table for dPVdp2

. pdz and pfp are the zeros of

dPVdp2

and d2PVdp2

2respectively. They have no special meaning

in this context.

It can be shown that the sign of the derivative changes only oncefor positive values of the pressure according to table 6.1. The valueof pdz cannot be calculated analytically and thus for each calculationof the maximum losses, it must be checked if the derivative dPV

dp2is

positive for the minimum possible pressure (i.e. check if p2Min > pdz).A detailed calculation shows that the values of the derivatives atp = 0, i.e. f2w0 and f3w0 are negative if equation 6.8 is fulfilled.

In summary, the losses are maximum for p1 = p1Max if equation6.8 is fulfilled and dPV

dp2is positive for PV = PVMin.

6.1.4 Variable temperatures and voltages

If variable inlet and outlet temperatures or voltages are permissi-ble during operation, the operational area can be computed for eachvalue of these according to section 6.1.2. No general analytical de-scription of the operating area could be derived in either case, whichmeans that the determination of the operation area involves a re-peated calculation of the operational area for fixed temperatures andvoltages.

Regarding the maximum and minimum powers (as defined in fig-ure 6.1) the following general rules can be drawn with a physicalargumentation. The permissible electrical losses increase with the


average temperature of the medium in the interconnector, thus:

• The minimum transmissible electric power (for minimum chem-ical power) PelchAMin will always occur at the lowest permis-sible values of T1 and T2.

• The maximum transmissible electric power (for maximumchemical power) PelAMax will always occur at the highestpermissible values of T1 and T2.

For the operation with variable input voltage it is also true thatthe maximum electric power will be transmitted at the maximumvoltage.

6.2 Impact of the auxiliary equipment onsystem operation and layout

In addition to the transfer capacity limitations introduced in theprevious section, the influence of the auxiliary equipment must bediscussed. The required turbine power at the inlet e.g. depends onthe inlet pressure and the mass flow rate, which are dependent on theelectric and chemical power. A similar argumentation applies to theheat exchanger and the auxiliary equipment at the bus outlet. Themodels for the auxiliary equipment have been presented in section5.3 and appendix A. Since the power ratings of this equipment seta limit to their input and output mass flow rates, it is possible thatthe operational area becomes limited further by these ratings.

In general the ratings of the auxiliary equipment can be adaptedin order to fit the operational area. This is illustrated in figure 6.8:the limitations arising from the maximum and minimum turbine andheat exchanger powers are shown. The limitations are chosen in or-der to fit the operational area defined by the minimum and maxi-mum losses: the limitation curves for PF1,2Min,Max are tangentto the operational area defined by the minimum and maximum elec-tric power.

6.2. IMPACT OF THE AUXILIARY EQUIPMENT 79

0.8 0.85 0.9 0.95 1 1.05 1.1 1.150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pel/PelM ax

Pch/P

ch

AM

ax

lim. by PVMin

lim. by PVMax

lim. by pMax

lim. by PF1Max

lim. by PF1Min

lim. by PF2Max

lim. by PF2Min

Figure 6.8: Limitation of the operating area by the ratingsof the compressors (example). In this example, the ratingsare chosen in order not to limit the operation range.


6.3 Scaling laws

Based on the simplified analytical model introduced in section 5.3,some scaling laws can be derived. The scaling laws will be using thefollowing expressions (see also figure 6.1):

r1 =PelAMax

PelchAMin(6.13)

r2 =PchAMax

PelAMax(6.14)

More details on the calculations and the necessary simplificationsare given in section 6.3. It can be shown that for fixed r1,2, materialproperties, T1, T2 and Uin the following scaling laws apply (the ∼sign is used to indicate that two quantities are proportional to eachother):

PV AMax ∼ Ltot (6.15)PV chAMin ∼ Ltot (6.16)PelAMax ∼ Ltot (6.17)

PelchAMin ∼ Ltot (6.18)PchAMax ∼ Ltot (6.19)

Uin ∼ Ltot (6.20)

Ri ∼ Ltot3/5 (6.21)

The accuracy of the scaling laws can be assessed in the exampleshown in figures 6.9 and 6.10. Figure 6.9 shows the maxiumum andminimum transmittable powers in dependence of the transmissiondistance. Figure 6.10 shows the transmission voltage in dependanceof the transmission distance. As the figures show, these quantitiesare proportional to Ltot. Obviously this is not a formal proof forthe accuracy of the laws. Since the use of these laws will only be toobtain a set of initial values in the dimensioning process, this will beacceptable.

6.3. SCALING LAWS 81

0 50 100 150 200 2500

20

40

60

80

Ltot [km]

P[M

W]

PchAMax

PchAPMax

PelAMax

PelchAMin

Figure 6.9: Transmissible power for constant r1 and r2 (ex-ample).

0 50 100 150 200 2500

20

40

60

80

100

Ltot [km]

Uin

[kV

]

Figure 6.10: Maximum input voltage for constant r1 and r2

(example).


As discussed in section 6.1, operation with variable T2 and Uinis likely to be necessary. The use of the scaling laws can easily beadapted for variable inlet temperature and electric voltage:

• If T2 can be varied within [T2Min;T2Max], PelchAMin will corre-spond to T2Min and PelAMax to T2Max. PelchAMin and PelAMax

will be proportional to Ltot.

• If Uin is variable, the lower limit of the electric power maytheoretically reach zero independently of the line length.

In conclusion these scaling laws can be used to estimate theachievable maximum powers for any length based on the “one-time”calculation of these powers for a given length and a wide range of r1

and r2.

6.4 Derivation of the scaling laws

In order to derive a layout strategy and taking into account theimpossibility to solve the relevant equations analytically, a set ofscaling laws will be derived. T1, T2, pMax and JMax are set by designand materials limitations and are therefore independent of Ltot. Inthis section it will be shown that a scaling law for the interconnectordimensioning (with respect to its length) can be established if thefollowing quantities are kept constant:

r1 =PelAMax

PelchAMin(6.22)

r2 =PchAMax

PelAMax(6.23)

According to section 5.3 (and for d.c. transmission), the electricpower and the associated losses are:

Pel1 = Uin JAcTot

2(6.24)

PV = J2AcTot Ltot ρ (6.25)

6.4. DERIVATION OF THE SCALING LAWS 83

As a consequence:

AcTot =PV

JMax2 Ltot ρ

(6.26)

From 6.24 and 6.25:

Pel12

PV=

Uin2AcTot

2

4AcTot Ltot ρ(6.27)

⇒ PelAMax2

PelchAMin2︸︷︷︸

=r12

=PV AMax

PV chAMin(6.28)

⇒ PV AMax = r12 PV chAMin (6.29)

From sections 5.3 and 6.1.2:

PV chAMin = Ltot PU′ (6.30)

This means that the electrical losses at minimum transmitted elec-tric and chemical power are proportional to the total length of theinterconnector. Substituting in 6.26 yields the required conductorcross-section:

AcTot =r1

2 PU′

JMax2 ρ

(6.31)

Combining equations 6.29 and 6.30 shows that the losses at max-imum transmissible electric power are as well proportional to thetotal length.

PV AMax ∼ Ltot (6.32)

Using 6.24:PelAMax

Uin= const (6.33)

From equation 6.25 it appears that the losses are proportional to thetotal length for any operating point:

PV ∼ Ltot for each operation point (6.34)


Since PV − PU = PQ − PR and PV,U ∼ Ltot:

PQ − PR ∼ Ltot (6.35)

Using an appropriate approximation, it can be shown that:

PQ − PR =Ri

5/2

√Ltot

f (gas, T1, T2, p1, p2) (6.36)

Combining this result with equation 6.35 the scaling law for the innerradius can be calculated:

Ri ∼ Ltot3/5 (6.37)

Approximating the maximum chemical power by setting p2 = 04:

PchAMax = 2π

√Mm pMax

2


5/2 (6.38)

Combining with 6.37 shows that the maximum chemical power isalso proportional to Ltot.

PchAMax ∼ Ltot−1/2Ri5/2 (6.39)

⇒ PchAMax ∼ Ltot (6.40)

With r1,2 = const:

PelAMax ∼ Ltot (6.41)PelchAMin ∼ Ltot (6.42)

And using 6.33:Uin ∼ Ltot (6.43)

4This approximation leads to an overestimation of PchAMax. The validity ofthis approximation must be established by checking the result of a any layoutbased on the scaling laws with a numerical simulation.

Chapter 7

Dimensioning andapplication of theEnergy Interconnector

This chapter presents a layout procedure for an intercon-nector system. To circumvent a time consuming iterativeprocedure using numerical simulations, a procedure basedon the previously developed scaling laws is introduced. Thisprocedure is then applied to a set of generic applicationsand realistic values for all constrained design parameters(e.g. material properties) in order to determine in whichpower and distance range the interconnector could be usedprimarily.

85

86 CHAPTER 7. DIMENSIONING AND APPLICATION

7.1 Dimensioning and layout of an inter-connector system

7.1.1 Parameters in the layout process

In the model of the interconnector presented in chapter 5, three maintypes of parameters can be distinguished (as discussed in section4.2.2): design parameters, design alternatives and constrained pa-rameters.

The goal of the layout procedure will be to determine the combi-nation of the design parameters (Ri, AcTot and UinMax) yielding therequired maximum transmission powers over the given line length.This procedure will be presented in section 7.1.2. The effect of vari-ations in design alternatives and constrained parameters will also bebriefly discussed in section 7.1.3.

7.1.2 Layout based on scaling laws

The equations presented in the previous sections cannot be solvedanalytically for the terminal powers. The complexity of the under-lying differential equations also prevents a layout based on iterativenumerical simulations.

The following layout procedure based on the scaling laws previ-ously presented is thus suggested:

1. Store PelAMax/Ltot, AcTot, Uin/Ltot and Ri/Ltot3/5 as func-

tions of r1 and r2. This implies solving the simplified equations(section 5.3) iteratively for all combinations of r1 and r2 in agiven range. The results will be valid for a fixed selection ofthe constrained parameters.

Example: The procedure will be illustrated for an intercon-nector using hydrogen as the chemical energy carrier and the“standard” values for the constrained and material parametersdiscussed in sections 4.2.2 and 7.1.3. Figure 7.1 shows an ex-ample of data obtained from iterative solving of the analytical

7.1. DIMENSIONING AND LAYOUT 87

11.5

22.5

0

1

2

3

0

10

20

30

40

50

60

r1

r2

PelA

Ma

x/L

tot[M

W/km

]

Figure 7.1: Maximum permissible electric power per inter-connector length unit in dependence of r1 and r2 (usinghydrogen). This data is computed once for a given set ofmaterial and constrained parameters and provides the basisfor a layout based on scaling laws.


model: the permissible electric power per interconnector lengthunit in dependence of r1 and r2 (with hydrogen transmission).

2. The application is defined by Ltot, PchAMax and PelAMax.

Example: The example of a medium size city with PelAMax =250 MW, PchAMax = 210 MW and Ltot = 62 km will be dis-cussed in the following layout steps.

3. Determine r2 for the application:

r2 =PchAMax

PelAMax

Example: In the example:

r2 =210 MW250 MW

= 0.84

4. With the stored PelAMax(r1) curves, determine r1.

Example: In the example: PelAMax/Ltot = 4.032 MW/km.The corresponding value of r1 is computed as follows: Fig-ure 7.2 is obtained by interpolation of the data shown in figure7.1 for r2 = 0.84. From figure 7.2, the value of r1 correspond-ing to the investigated application can be determined. In thisexample r1 = 1.506.

5. Determine AcTot, Uin and Ri by interpolation and use of thescaling laws.

Example: Figure 7.3 shows the “stored” data for Ri/Ltot3/5.The value of Ri/Ltot3/5 corresponding to the investigation canbe interpolated for r1 = 1.506 and r2 = 0.84. The same can bedone for the transmission voltage Uin and the total conductorcross-sectional area AcTot. The results are:

RiLtot3/5 = 1.3007 cm

km3/5

AcTot = 2869 mm2

UinLtot

= 3.514 kVkm


1 1.5061 2 2.50

2

4.0323

6

8

10

12

14

16

18

r1

PelA

Ma

x/L

tot[M

W/km

]

Figure 7.2: Maximum permissible electric power per inter-connector length unit for r2 = 0.84.


11.5061

22.5

00.84

23

0

0.5

1

1.5

2

2.5

r1r2

Ri/

Lto

t[cm

/km

3/5 ]

Figure 7.3: Ri/Ltot3/5 in dependence of r1 and r2 (using

hydrogen).

For a line length of 64 km:

Ri = 15.47 cmAcTot = 2869 mm2

Uin = 217.8 kV

6. Check the layout against the analytical model and a numericalsimulation (since the scaling laws are approximations).

Example: The analytical model can be solved with the com-puted values for Ri, AcTot and Uin. The values of the transmis-sible power obtained in this way are close to the specificationof the application:

PelAMax = 249.89 MWPchAMax = 207.78 MW


This means that the scaling laws provide a good approximationof the analytical model. A numerical simulation of the inter-connector with Pel1 = PelAMax and Pch = PchAPMax yieldsthe following result:

p2

∣∣Pel=PelAMax

= 23.19 barT2

∣∣Pel=PelAMax

= 393.1 K

The corresponding values obtained with the analytical modelare: p2 = 23.27 bar and T2 = 393 K. The results of the ap-proximative layout procedure are confirmed by the simulationresults.

The essential features of this procedure are the possibility to au-tomate the layout and the relatively low computation time. Thisis needed in the topological investigations planned in the “Vision ofFuture Energy Networks” project.

7.1.3 Influence of constrained and materials pa-rameters

Maximum gas temperature

Two aspects will limit the permissible maximum gas temperature:

• The withstand capability of the materials (especially the elec-trical insulation). It is not in the scope of this work to discussnew insulation materials. Withstand temperatures can reach250 C for polytetrafluoroethylene (PTFE) or more commonly130 C for cross linked polyethylene (XLPE). The choice of theinsulation material thus sets a limit to the maximum gas tem-perature. As a conservative approach, it is assumed that thesevalues will apply for the design of the interconnector.

• The heat recovery process. Table 7.1 gives an overview of pos-sible recovery processes or heat consumers and their requiredtemperature levels.


Technology / User Temperature rangeORC Turbine 80 . . . 120 CThermoelectric converter 50 . . . 1000 CDistrict heating 70 . . . 120 CRoom heating (direct) 35 . . . 70 CHot water supply 65 . . . 70 C

Table 7.1: Temperature range for waste heat recoveryequipment or “direct” heat consumers.

The surface temperature at the interface with the soil is not consid-ered as a limit, since it may be (arbitrarily) reduced by additionalthermal insulation. The space requirements and cost may, however,become prohibitive.

The variation range for the outlet temperature may also be lim-ited by the technology used or the “direct” user of the recoveredheat. As a consequence it is reasonable to assume that temperaturesslightly above 100 C will be feasible. In most of the examples usedin this work, the maximum outlet temperature T2Max is 120 C.

Gas inlet temperature

The inlet temperature is in principle limited by the availability of acold source after the initial compression phase. An inlet temperatureexceeding the ambient temperature corresponds to the transmissionof thermal power. Figures 7.4 and 7.5 show the required inner radiusand transmission voltage for a prospective application of the inter-connector as a function of the inlet temperature. The permissibleelectrical losses decrease for higher inlet temperatures. In order toachieve the same transmitted power, the inner radius and the trans-mission voltage have to be increased. The error bars in figures 7.4and 7.5 show the effect of a 25% variation of the maximum powersand transmission length.

It can be anticipated that the value of thermal energy will de-


10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

T1 [C]

Ri[cm

]

Figure 7.4: Inner radius for an interconnector withPelAMax = 200 MW, PchAMax = 240 MW and Ltot = 50 kmfor various inlet temperatures (error bars: effect of a ±25%variation of PelAMax, PchAMax and Ltot).


10 20 30 40 50 60 700

50

100

150

200

250

300

T1 [C]

Uin

[kV

]

Figure 7.5: Inlet Voltage for an interconnector withPelAMax = 200 MW, PchAMax = 240 MW and Ltot = 50 kmfor various inlet temperatures (error bars: effect of a ±25%variation of PelAMax, PchAMax and Ltot).


crease in the future. For this reason it is unlikely that the inter-connector will be used for the transmission of thermal energy at theexpense of higher transmission voltages and increased radii. For allsubsequent calculations and examples, an inlet temperature of 20 Chas been chosen.

Electrical conductor

The material of the electrical conductor does not play a major rolein the layout procedure at this stage, since all aspects related tothe production and laying of the interconnector are excluded fromthe investigation. Materials with a higher conductivity will allowa higher current density, and thus the resulting specific losses areunlikely to differ significantly. As a consequence this is not discussedin this work. Copper will be used in all examples.

A better conductor material results in a (slightly) reduced outerdiameter of the interconnector. In the examples, copper will be used.The outer diameter does not appear directly in the calculation of thetransmissible electric and chemical powers.

Chemical medium

Several choices for the chemical energy carrier exist. Gaseous carri-ers like hydrogen, carbon monoxide, methane and ethane or liquidcarriers like methanol, ethanol and octane have been considered inthis work.

Within the two classes of liquid and gaseous carriers the maindifference among the different carriers is the ratio between the ab-sorbed thermal power and the chemical energy content. As pointedout in chapter 5 this relation is only dependent on the temperaturerise for liquid carriers, it is more complex for gaseous carriers (the re-lation is in fact variable and requires solving the equations presentedin section 5.3).

As discussed in section 7.1 devoted to the layout procedure, thecoupling between chemical and thermal power does not mean that a


0

1

2

3

4

5

6

7

8

9

P/L

tot[M

W/km

]

Hydrogen

Carbon monoxide

Methane

Ethane

PchAMax PchAPMax PelAMax PelchAMin

Figure 7.6: Minimum and maximum transmissible powersfor an interconnector with different gaseous chemical carriers(example).

particular application cannot be accommodated by the selection ofa suitable r1 factor. A different value of r1 will, however, impact onthe operational characteristics of the interconnector system, e.g. adifference arises in the compression and friction losses. These arehigher for gases with a smaller molar mass.

Figures 7.6 and 7.7 show the maximum transmittable electricand chemical powers for different gaseous respectively liquid energycarriers (for fixed r1 = 2.4 and r2 = 1.5). Since the permissibleelectrical losses are nearly independent of the energy carrier used,the transmissible powers vary approximately according to the ratiobetween the specific thermal capacity and the specific energy contentof the carriers.

In a preliminary survey of the possible energy carriers, hydrogenhas been identified as the most promising choice with respect to theoverall energy system.


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

P/L

tot[M

W/km

]

Methanol

Ethanol

Octane

PchLMax PelLMax

Figure 7.7: Minimum and maximum transmissible powersfor an interconnector with different liquid chemical carriers(example).

• Following the argumentation of section 4.2, gaseous carriers arepreferred.

• More conversion processes from or to hydrogen are known thanfor the other possible carriers.

• Several possibilities for direct use or delivery of hydrogen can beenvisaged in the near future (including transportation, biomassgasification and direct solar hydrogen generation).

• Hydrogen is part of numerous road maps developed within theresearch community and governmental bodies.

Gaseous carriers will thus be mainly considered in the discussion ofpotential applications for the interconnector principle.


0 0.02 0.04 0.06 0.08 0.10.8

1

1.2

1.4

1.6

f

Ri/

Lto

t3/5[cm

/km

3/5 ]

Figure 7.8: Inner radius of an interconnector in function ofthe friction factor for constant maximum chemical power(example).

Friction factor

The exact determination of the friction factor f is not possible atthis stage, since it is linked to presently unavailable design detailsand experimental data. However, in the chosen modelling framework,the friction factor is linked to the inner radius of the interconnector,which means that the uncertainty in f leads to an uncertainty inRi. Figure 7.8 shows the general dependence: a higher friction factorimplies a higher pressure drop and thus requires a larger inner radiusto transmit the same chemical power.

Maximum operating pressure

The maximum operating pressure is uncertain at this stage becauseno construction aspects have been considered at this stage. For thecalculations in this work, a maximum pressure of the order of sometens of bars has been assumed.


Cable Conductorcross-section

Maximumcurrent

mm2 A500/290 kV XLPE Cable 2500 1522 . . . 2670400/230 kV XLPE Cable 2500 1565 . . . 2739220/117 kV XLPE Cable 1600 1353 . . . 2195132/76 kV XLPE Cable 800 949 . . . 1467

Table 7.2: Examples of the ampacity of XLPE cables withcopper conductor [28]. The maximum current depends onthe type of burying.

Maximum electric current density

The current density in the electrical conductor influences the localconductor temperature. Because this is not modelled in detail, thelayout procedure used in this work is based on an arbitrary maximumcurrent density JMax.

Using a solid insulation material (as discussed in section 4.2)means that the achievable current densities will be within the samerange as for electrical cables. Examples of the ampacity and conduc-tor cross-section of power cables are given in table 7.2.

Since the expected currents in the interconnector are high, thismaximum current density is likely to be below 1 A/mm2 (assumingcopper as the conductor material). Where nothing else is stated, aconservative value of 0.8 A/mm2 will be used.

The impact of a variation of the maximum current density fromJMax(1) to JMax(2) can easily be computed for constant transmittedpower and losses:

Pel1′ = const (7.1)

PV′ = const (7.2)


Using the model presented in section 5.3, AcTot and Uin become:

AcTot(2)

AcTot(1)=(JMax(1)

JMax(2)

)2

(7.3)

Uin(2)

Uin(1)=JMax(2)

JMax(1)(7.4)

This means that a variation of the maximum current density can becompensated by adapting the conductor cross sectional area AcTotand transmission voltage Uin.

Auxiliary equipment

From the rating of the auxiliary equipment it is possible to estimatethe size of the required heat exchanger. The procedure applied for theapproximation of the exchanger volume will be described in chapterD of the appendix.

A calculation of the heat exchanger volumes corresponding to a100 km interconnector according to the examples shown in figure 7.6shows that exchanger volumes some tens of m3 might be necessaryunder the assumption that the inlet pressure of the exchanger ismaintained above 5 bar1.

Because the space requirement of the heat exchanger may rep-resent a limitation for the applicability of the interconnector, therelated questions will need more attention when more detailed lay-outs are under discussion.

Soil properties and thermal insulation

A generic mean value for the soil thermal resistance has been usedthroughout the examples, since actual soil properties may vary basedon its exact nature.

1This is likely to be feasible if the interconnector voltage can be adapted.


1 1.5 2 2.5 3 3.5 40

1

2

3

4

5

6

RthI′ [Km/W]

P/L

tot[M

W/km

]

PchAMax

/ Ltot

[MW]

PchAPMax

/ Ltot

[MW]

PelAMax

/ Ltot

[MW]

PelchAMin

/ Ltot

[MW]

Figure 7.9: Maximum chemical and electric power at con-stant r1, r2 for various thermal resistances of the outer in-sulation (example).

The choice of the thermal resistance of the outer insulation maybe driven by security, performance and cost aspects. Since one mo-tivation for the interconnector is the potential reuse of ohmic losses,a high thermal resistance of the insulation layer was chosen in eachexample.

The figure 7.9 illustrates that for constant r1 and r2 the maxi-mum transmissible powers decrease with a better insulation, becauseelectrical losses are subject to a lower limit under such conditions. Inother terms, to achieve the same transmitted powers with a betterinsulation, a higher value of r1 must be selected (which impacts onthe transmission efficiency).


7.2 Possible applications of the intercon-nector principle

In this final section the layout procedure developed here is appliedto potential generic application scenarios for future energy trans-mission. This will illustrate which kind of application leads to areasonable interconnector size and voltage level.

7.2.1 Applications investigated

In order to get a first idea of the size of an interconnector for dif-ferent types of applications, a set of potential applications has beendefined. Two types of descriptions will be used: transmission linesand areas. For these potential applications, the transmitted electricpower is within the range of current values, while the chemical powerrequirement is subject to further discussion. The chosen values corre-spond to an intermediate scenario where at least part of the mobilitysector is supplied with hydrogen or another gaseous chemical energycarrier.

Table 7.3 shows the list of these applications2. The applica-tions are specified by the maximum transmitted powers and linelength. For areas, the underlying assumptions are also given: a self-sufficiency degree s (in terms of maximum power) as well as a numberof connections nc (it was assumed that these areas are supplied overseveral connections)3.

The layout procedure developed can be applied to these generalspecifications. This will allow for the determination of a range for thethree main “dimensions” of an interconnector: its inner radius Ri,its maximum transmission voltage Uin and the cross-sectional areaof the electrical conductor AcTot. Based on the resulting layouts

2The emphasis of this work is not on determining as realistic as possibleapplications, but to obtain an insight into the approximate interconnector layoutrequired for differing applications.

3It will be assumed that the maximum load is equally shared among them.

7.2. POSSIBLE APPLICATIONS 103

Application PelMax PchMax Ltot nc s[MW] [MW] [km]

MVDC 200 240 50 – –HVDC 2000 2400 600 – –LV 0.5 0.6 15 – –MV 250 300 50 – –HV 1000 1200 300 – –Switzerland 300 400 500 6 80%Baden 7 9 15 3 30%EPFL 10 12 15 1 0%50 households 0.06 0.07 2 1 0%

Table 7.3: List of the investigated “generic” applications(nc: number of connections for the consumer, s degree ofself-sufficiency).

the soundness and feasibility of the interconnector principle in theseapplications can be discussed.

7.2.2 Resulting layout for the selected applica-tions

The figures 7.10, 7.11(a) and 7.12 show the required Ri, Uin andAcTot for a hydrogen interconnector using the assumptions previ-ously discussed in section 7.1.3. The definition of the applications issubject to discussion: in order to indicate the variation of Ri, Uinand AcTot in function of the application specifications, the effect of avariation of 25 % of any combination of the application specificationsis represented as error bars in the figures 7.10, 7.11(a) and 7.12.

The required inner radius and transmission voltage rise with thetransmitted power and distance. The value of the transmission volt-ages (shown in figure 7.11(a)) seems to be in line with current prac-tice for the “medium voltage” applications while it reaches unrealis-


0

10

20

30

40

50

60

70

80

Ri[cm

]

MVDC

HVDC

MV

HV

Switzerland

Figure 7.10: Inner radius for a hydrogen interconnector forvarious applications and assumptions previously introducedfor the material and design parameters (error bars: result ofa 25% variation in the specifications of the application).


0

500

1000

1500

2000

2500

3000

Uin

[kV

]

MVDC

HVDC

MV

HV

Switzerland

(a) T2 = 120 C

0

500

1000

1500

2000

2500

3000

Uin

[kV

]

MVDC

HVDC

MV

HV

Switzerland

76.7 82.0

(b) T2 = 220 C

Figure 7.11: Transmission voltage (d.c.) for a hydrogen in-terconnector for various applications and assumptions pre-viously discussed for the material and design parameters.


0

1000

2000

3000

4000

5000

6000

7000

Acto

t[m

m2]

MVDC

HVDC

MV

HV

Switzerland

Figure 7.12: Conductor cross-sectional area for a hydrogeninterconnector for various applications and with the assump-tions introduced for the material and design parameters.


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Ri[cm

]

LV

Baden

EPFL

50 households

Figure 7.13: Inner radius for a hydrogen interconnector for“small scale” applications and with the assumptions intro-duced for the material and design parameters.

tic values for “high voltage” applications. As figure 7.11(b) shows,a higher outlet temperature of the gas would allow for lower trans-mission voltages (but decreased transmission efficiencies). The innerradius required for the transmission of high powers is also impressive(though this issue could possibly be solved by using parallel systems).

The variation of the cross-sectional area AcTot is less pronounced.The layout method implies that the same maximum current densityand temperatures were assumed for all cases. This explains the lowvariations in AcTot, since the “required” local thermal power willbe of the same order of magnitude for all cases (thus the resultingcomparable cross-sectional areas).

Figures 7.13, 7.14 and 7.15 show the interconnector dimensionsRi, Uin and AcTot for small scale applications. The resulting in-ner radius and transmission voltage appear to be reasonable. Thetotal cross-sectional area is, however, larger than the “traditional”


0

5

10

15

20

25

Uin

[kV

]

LV

Baden

EPFL

50 households

(0.103)

Figure 7.14: Transmission voltage for a hydrogen intercon-nector for “small scale” applications and with the assump-tions introduced for the material and design parameters.


0

500

1000

1500

2000

2500

Acto

t[m

m2]

LV

Baden

EPFL

50 households

Figure 7.15: Conductor cross-sectional area for a hydrogeninterconnector for “small scale” applications and with theassumptions introduced for the material and design param-eters.


0.5

0.6

0.7

0.8

0.9

1

1.1η T

otB

AM

ax

LV

Baden

EPFL

50 households

Figure 7.16: Efficiency ηTotBAMax for a hydrogen intercon-nector for “small scale” applications and with the assump-tions introduced for the material and design parameters.

solution. The assumption that the inlet and outlet temperaturesare similar for each application, which arises from the proposed in-terconnector concept, implies that the electrical losses need to becomparatively higher for those applications with lower losses. Thetotal efficiency ηtotBMax (see section A.3 in the appendix) for theapplications shown in figure 7.13 are 62.4 % (LV), 97.7 % (Baden),98.2 % (EPFL) and 54.3 % (50 households) respectively, as shown infigure 7.16. This is unacceptably low.

Since alternative chemical carriers have different properties, aninfluence of the carrier choice on the interconnector layout exists. Acomparison between different gaseous chemical carriers is shown infigures 7.17, 7.18 and 7.19 where Ri, Uin and AcTot are shown forthe MVDC application. Hydrogen, methane and ethane have simi-lar energy densities wm, while carbon monoxide is a comparativelyheavy molecule with a low energy density. This implies that an in-


0

5

10

15

20

25

30

Ri[cm

]

Hydrogen

Methane

Ethane

Carbon monoxide

Figure 7.17: Inner radius of an interconnector for variouschemical carriers (application: MVDC).

terconnector using carbon monoxide will have a comparatively largerradius, based on the assumption that construction aspect will limitthe maximum operation pressure (figure 7.17).

The ratio between the specific energy content and the thermalcapacity4 impacts on the transmission voltage: Methane and ethane“contain” more chemical energy for the same absorbed heat. There-fore lower ohmic losses are permissible, which means that the trans-mission voltage of an interconnector using methane and ethane ishigher for the same transmissible power and maximum current den-sity.

4In reality the relevant figure is not the thermal capacity but the polytropiccoefficient describing the gas flow.


0

50

100

150

200

250

300

350

400

450

500

Uin

[kV

]

Hydrogen

Methane

Ethane

Carbon monoxide

Figure 7.18: Transmission voltage of an interconnector forvarious chemical carriers (application: MVDC).

0

1000

2000

3000

4000

5000

6000

Acto

t[m

m2]

Hydrogen

Methane

Ethane

Carbon monoxide

Figure 7.19: Conductor cross-sectional area of an intercon-nector for various chemical carriers (application: MVDC).


7.2.3 Discussion

The result of the layout procedure applied to the generic applicationsshows the following:

• Inner radius: pipes corresponding to the calculated sizes arereadily available. For the small scale applications (LV, Baden,EPFL, 50 households), the pipe section appear to be rathersmall.

• Maximum transmission voltage: the layout procedure leads tohigher voltages for higher transmitted powers and longer dis-tances. This corresponds to the prevailing practice.

• Conductor cross-sectional area: the low variation in the re-quired cross-sectional area can be explained by the more orless invariant thermal power flow to the surrounding soil.

With respect to the feasibility of the interconnector in the var-ious contexts investigated, the following remarks apply, under theassumptions postulated for these examples:

• Inner radius: Production and laying of pipes with a diameterover 50 cm which incorporate an electrical conductor (and itsinsulation) is certainly problematic.

• Maximum transmission voltage: besides the high values re-quired for “high voltage” applications, the required transmis-sion voltages in the case of hydrogen are within the feasiblerange.

• Conductor cross-sectional area: AcTot represents the total re-quired cross section which is (at least) divided into two poles.The calculated cross-sections seem feasible, especially in thecontext of medium voltage applications.

• Total efficiency: the potential for acceptable values of the totalefficiency is restricted to the “large scale applications”.


In appendix C, examples corresponding to the three applicationranges “low”, “medium” and “high” voltage are presented in moredetail. They illustrate the general findings discussed above.

Based on these considerations, the most promising applicationrange for the interconnector concept as presented here appears to bein the power range of present “medium voltage” applications. Thechoice of hydrogen as a chemical carrier is supported by the results ofthe comparison, since hydrogen interconnectors require lower voltagelevels.

Chapter 8

Conclusions

8.1 Implications for the “Vision of Fu-ture Energy Networks project”

This work has clarified the potential role and implications of multi-energy transmission within the “Vision of Future Energy Networks”project. A favoured solution is proposed for inclusion in future in-frastructure scenarios.

The integration of different energy carriers into future networkswill permit improvements in the network performance as well as im-proved functionality (e.g. energy management). This trend opensthe way for hybrid energy transmission, where the combination ofelectricity and e.g. hydrogen will play a predominant role. From a“high level” perspective, i.e. without consideration of implementa-tion and design details, this work has provided the following results:a generic modelling framework is available, relevant parameters havebeen identified and the resulting limitations of the application of theinterconnector principle can be discussed on this basis.

The developed model is generic, which means that few indicationson the detailed layout of the interconnector are needed. This suits

115

116 CHAPTER 8. CONCLUSIONS

the “Vision of Future Energy Networks” project needs. Furthermorethe proposed layout procedure does not imply a high computationalcomplexity or “manual intervention”, which makes it useful for thetopological optimisation activities within the project.

In general, the layout methodology presented in this work showsthat increasing the transmissible power is feasible by increasing thetransmission voltage and the interconnector inner radius. Based onmaterial properties and physical limitations (like the coupling amongthe transmitted powers), a promising power range for an interconnec-tor system appears to be the “MVDC” application (Pel = 200 MW,Pch = 240 MW and Ltot = 50 km). For “smaller” applications(i.e. less power transmitted over shorter distances), the required con-ductor cross-section is rather high and the total transmission effi-ciency drops to unacceptably low values. Larger scale applicationswould require extreme voltages, which will be very difficult to imple-ment.

From the study of the generic applications, a preferred applica-tion (MVDC) has been defined. Longer distances may be achievedwith several interconnector sections (and intermediary compressorstations); higher transmitted electric and chemical powers can beachieved with several parallel interconnectors.

8.2 Application of the interconnectorprinciple: Future work

This work permitted to highlight a preferred application for the in-terconnector. The envisaged next steps will be focussing on thisapplication:

• By sharpening the specification of the application in order tobecome more precise with respect to the parameters specifiedin section 7.1.3.

• By investigating possible detailed designs, specifically for thisparticular application.

8.2. APPLICATION OF THE INTERCONNECTOR 117

Finally, the description of a multi-energy system and a combinedmulti-energy transmission concept can show up interesting develop-ment directions for the energy systems of the future even though itis clear that the implementation of the concept as a whole in the ex-act form as presented here is not likely: the multi-energy frameworkwill be used as a basis for infrastructure scenarios and case studiesin subsequent (sub-)projects and the developed tools will certainlyfind applications in the future optimisation and evolution of presentenergy networks.

118 CHAPTER 8. CONCLUSIONS

Appendix A

Model of the auxiliaryequipment for aninterconnector withtransport of a gaseousmedium

A.1 Compressors

At the inlet of the interconnector, a compressor is necessary to com-press the gaseous medium to its inlet pressure p1. During the com-pression, which is assumed to be adiabatic1, the gas temperaturerises to T1h.

T1h =(p0

p1

) 1−κκ

T0 (A.1)

1This assumption corresponds to a worst case analysis.

119

120 APPENDIX A. AUXILIARY EQUIPMENT MODEL

where κ is given by the nF degrees of freedom of the gas:

κ =nF2 + 1nF2

(A.2)

The compressor power needed can be subdivided into three terms:the hydrodynamic work (per time unit), the increase of the kineticenergy of the gaseous medium and the increase of the inner energyof the gaseous medium2.

PPump1 = p1A1 v1 − p0A0 v0 +m

2(v1

2 − v02)

+∆U∆t

(A.3)

Only ideal gases will be considered3, so the rate of change of its innerenergy is:

∆U∆t

=nF2

m

MmRg

((p0

p1

) 2nF+2

− 1

)T0 (A.4)

Using equation 5.47:

pAi v =m

MmRg T (A.5)

Substituting and assuming v02 is so small that it can be neglected4:

PPump1 =∆U∆t

+Ai(p1 v1h − p0 v0) +m

2v1h

2 (A.6)

=(nF

2+ 1) Rg m (T1h − T0)

Mm+m

2

(mRg

πMmRi2

)2T1h

2

p12

(A.7)

=(nF

2+ 1) Rg m

((p0p1

) 2nF+2 − 1

)T0

Mm+

m3Rg2 T1h

2

2π2M2mRi

4 p12

(A.8)2The hydrostatic work in the compressor can be neglected.3An assumption which holds for hydrogen, methane and natural gas in par-

ticular.4This corresponds to a worst case analysis.

A.2. HEAT EXCHANGERS AND RECOVERY 121

If necessary, a turbine can be used to expand the gas to its finalpressure p3 at the end of the pipeline. The turbine power can alsobe computed using equation A.8. For the arrangement depicted infigure A.1 (variant A), T3 and p3 are the temperature and pressureat the turbine inlet and T4 and p4 are the temperature and pressureat the turbine outlet. The turbine power is thus:

PPump2 =(nF

2+ 1) RgMm

m

((p3

p4

) 2nF+2

− 1

)T3+

m3Rg2 T3

2

2π2M2mRi

4 p32

(A.9)PPump1 and PPump2 represent the mechanical work applied to

respectively taken from the medium. Positive values indicate thatenergy is transferred to the fluid. The required electric power PF1,2or the delivered electric power of the motor/generator connected tothe compressor/turbine is given by its efficiency, which can differ foreach operation mode:

PF1,2 = 1

η1,2PosPPump 1,2 for PPump 1,2 ≥ 0

η1,2Neg PPump 1,2 otherwise(A.10)

A.2 Heat exchangers and waste heat re-covery

A.2.1 Use of compression waste heat

Variants A and B

In a first set of variants (figures A.1 and 5.9) the gas is compressedto the inlet pressure p1 from the pressure p0 (either the pressure ofthe gas from a production or storage process). During compression(or eventually expansion) the gas temperature will rise (respectivelyfall). To be used as a coolant in the interconnector, the gas should becooled down to nearly ambient temperature. This could even yieldenergy, if an adequate recovery process is available.


Interconnector

PPump1

PF1

Qw1

Pw1

PF1,tot

PF,tot

PQ

Qw2

Pw2

PPump2

PF2

PF2,tot

T0 T1h T1 T2 T3 T4

Figure A.1: Interconnector system layout and power flowfor waste heat recovery variant A.

The power PPump1 required to compress the gas in the inlet com-pressor for variant A has been calculated in equation A.8. A motordriving this compressor would need the power PF1 given in equationA.10.

The following definition applies:

β :=κ

κ− 1=nF2

+ 1 (A.11)

For simplicity, isobaric cooling of the gas in the heat exchanger isassumed. The extracted heat flow is:

Qw1A =(nF

2+ 1) mRg

Mm(T1hA − T1) (A.12a)

=(nF

2+ 1) mRg

Mm

((p1

p0

) 2nF+2

T0 − T1

)(A.12b)

The recovery process uses a cold source with the temperature TK1,thus the maximum efficiency of this recovery process corresponds to


the Carnot efficiency:

ηc1APos = 1− TK1

T1hA(A.13)

The main operation mode of the heat exchanger will be cooling downthe gas (i.e. Qw1 > 0) at temperatures exceeding the cold sourcetemperature (TK1):

Pw1A =ηRec1APos Qw1A if Qw1A ≥ 0 and TK1 ≤ T1

undefined otherwise(A.14)

The total recovery efficiency ηRec1APos is the product of the Carnotefficiency ηc1APos which describes the boundary imposed by the coldsource (i.e. independently of a particular recovery process) and theexergy efficiency of a particular recovery process ηEx1APos, which inturn describes its “intrinsic” performance.

ηRec1APos = ηc1APos ηEx1APos (A.15)

From this, the total power required at the interconnector entry is thecompressor power reduced by the amount of power recuperated fromthe gas compression.

PF1ATot = PF1A − Pw1A (A.16)

At the inlet, the situation is the same for both variants A and B.

Variant C

The concept of an interconnector system using cryogenic energytransmission is depicted in figure A.2. At the inlet of the inter-connector, the gas is cooled down to the temperature T1 by meansof a compressor which increases the gas pressure to p1hC , a heatexchanger and a valve which lets the gas expand to p1, which alsocauses it to cool down. Assuming adiabatic expansion of the gas, therequired pressure at the outlet of the heat exchanger p1kC becomes:

p1kC =(T1kC

T1C

)βp1C (A.17)


Interconnector

PPump1C

PF1C

Qw1C

Pw1C

PF1,totC

PF,totC

PQC

Qw2C

Pw2C

PPump2C

PF2C

PF2,totC

T0 T1hC T1kC T1C T2C T3C T4

Figure A.2: Interconnector system layout and power flowfor waste heat recovery variant C.

The cooling of the gas in the heat exchanger is assumed to be iso-baric, thus the compressor has to compress the gas to the pressurep1hC = p1kC . The gas temperature at the inlet of the heat exchangertherefore is:

T1hC =(p1hC

p0

) 1β

T0 (A.18)

In the heat exchanger, the heat flow Qw1C is extracted from the gas:

Qw1C =(nF

2+ 1) mRg

Mm(T1hC − T1kC) (A.19)

In an adequate heat recovery system the power Pw1C can be recu-perated. The normal operation mode of the heat exchanger is to cooldown the gas to a temperature superior or equal to the cold sourcetemperature.

Pw1C =ηRec1CPos Qw1C if Qw1C ≥ 0 and T1kC ≥ TK1



whereηRec1CPos = ηc1CPos ηEx1CPos (A.21)

and

ηc1CPos = 1− TK1

T1hC(A.22)

Finally, the inlet compressor has the mechanical power:

PPump1C =β RgMm

m

((p0

p1C

)−1β

− 1

)T0 +

m3Rg2

2π2M2mRi

4

T1hC2

p1hC2

(A.23)The motor power PF1C is again given by equation A.10.

A.2.2 Use of warm gas at the bus outlet

Variants A and B

The two system layouts shown in figures A.1 (variant A) and 5.9(variant B) will be discussed first. In both cases the gas enters theinterconnector at the temperature T1 and leaves it at the higher tem-perature T2. The task of the waste heat recovery system is twofold:make use of any temperature difference between the gas and the am-bient temperature and bring the gas to the pressure p4 required inthe distribution system or for its further processing at the receivingend.

The variants A and B only differ in the sequence of the compressorand heat exchanger. Adiabatic compression/expansion of the gas inthe compressor/turbine and isobaric change of temperature in theheat exchanger will be assumed in order to compute the recoveredpower PF2A,BTot in each variant.

Variant A

In variant A the gas passes the heat exchanger directly at the outletof the interconnector. The process is assumed to be isobaric. The


gas is cooled down to the temperature T3 such that the gas will leavethe outlet turbine at the temperature T4.

T3A =(p3A

p4

) 1β

T4 (A.24)

Thus the extracted heat flow becomes:

Qw2A =(nF

2+ 1) mRg

Mm(T2 − T3A) (A.25a)

=(nF

2+ 1) mRg

Mm

(T2 −

(p3

p4

) 2nF+2

T4

)(A.25b)

A recovery process working with the cold source temperature TK2

(respectively hot source temperature) will have the following Carnotefficiencies:

ηc2APos = 1− TK2

T2if TK2 is the cold source (A.26a)

ηc2ANeg = 1− T2

TK2if TK2 is the hot source (A.26b)

Depending on the temperature difference between the cold sourceand the gas, several cases must be considered separately:

• The gas is cooled down to a temperature higher or equal to thecold source temperature TK2 (Qw2A ≥ 0 and TK2 ≤ T3A < T2).This corresponds to a waste heat recovery process, which canbe utilised.

• The gas is heated up to a temperature lower or equal to thecold source temperature TK2 which takes to role of the hotsource (Qw2A < 0 and T3A ≤ TK2). The gas becomes thecold source of a process, which can also yield energy, providedthe recovery process allows for symmetrical operation. Such ascenario, however, is unlikely in the layout of an interconnector.


• All other cases are assumed to yield an undefined power to therecovery system.

Thus the recovered electric power becomes:

Pw2A =

ηRec2APos Qw2A if Qw2A ≥ 0 and TK2 ≤ T3A < T2

−ηRec2ANeg Qw2A if Qw2A < 0 and T3A ≤ TK2


The recovery efficiencies ηRec2APos,Neg are the product of the cor-responding Carnot efficiency ηc2APos,Neg and the exergy efficiencyof the recovery process ηEx2APos,Neg.

ηRec2APos = ηc2APos ηEx2APos (A.28a)ηRec2ANeg = ηc2ANeg ηEx2ANeg (A.28b)

The power PPump2A of the outlet compressor/turbine has beencalculated in equation A.9 and the resulting electric power PF2A atthe motor/generator in equation A.10. The recovered power at theinterconnector outlet becomes:

PF2ATot = Pw2A − PF2A (A.29)

Variant B

In variant B, the gas first passes a turbine at the outlet of the in-terconnector. The turbine is operated such that the desired outletpressure p3B = p4 is reached. Thus the mechanical power at theturbine is:

PPump2B =β Rg T2

Mmm

((p3B

p2

) 1β

− 1

)− m3Rg

2

2π2M2mRi

4

T22

p22

(A.30)

The electric power at the motor/generator can be computed usingequation A.10. The gas temperature at the outlet of the turbine is:

T3B =(p3B

p2

) 1β

T2 (A.31)


The temperature difference to a cold source TK2 can be used toextract some heat from the gas (T4 is the temperature the gas isrequired to have at the end of the interconnector system). The ex-tracted heat flow is:

Qw2B =(nF

2+ 1) mRg

Mm(T3B − T4) (A.32a)

=(nF

2+ 1) mRg

Mm

(T2 −

(p3B

p2

) 2nF+2

T2

)(A.32b)

The Carnot efficiency for this process with TK2 as a cold, respectivelyhot source temperature is:

ηc2BPos = 1− TK2

T3Bif TK2 is the cold source (A.33a)

ηc2BNeg = 1− T3B


Depending on the temperature difference between the cold sourceand the gas, several cases must be considered separately:

• The gas is cooled down to a temperature higher or equal to thecold source temperature TK2 (Qw2B ≥ 0 and TK2 ≤ T4 < T3B).This corresponds to a waste heat recovery process yielding en-ergy.

• The gas is heated up to a temperature lower or equal to thecold source temperature (which takes to role of the hot source)(Qw2B < 0 and T4 ≤ TK2). The gas becomes the cold sourceof a process, which can also yield energy, provided the recoveryprocess allows for symmetrical operation.

• All other cases are assumed to yield an undefined power to therecovery system.

Pw2B =

ηRec2BPos Qw2B if Qw2B ≥ 0 and TK2 ≤ T4 < T3B

−ηRec2BNeg Qw2B if Qw2B < 0 and T4 ≤ TK2



Where:

ηRec2BPos = ηc2BPos ηEx2BPos (A.35a)ηRec2BNeg = ηc2BNeg ηEx2BNeg (A.35b)

The overall recovered power at the bus outlet thus becomes:

PF2BTot = Pw2B − PF2B (A.36)

Variant C

The waste heat recovery in variant C (cryogenic energy transmission)is similar to variant B and can be modelled as an isobaric cooling ofthe gas in the heat exchanger (p3C = p4). The gas pressure and tem-perature at the bus outlet will, however, be different for both cases.The following quantities are computed in analogy to the computationfor variant B:

• Turbine mechanical power:

PPump2C =β Rg T2C

Mmm

((p3C

p2C

) 1β

− 1

)− m3Rg

2

2π2M2mRi

4

T2C2

p2C2

(A.37)

• Turbine outlet gas temperature

T3C =(p3C

p2C

) 1β

T2C (A.38)

• Extracted thermal power

Qw2C =(nF

2+ 1) mRg

Mm(T3C − T4) (A.39)


• Recuperated electric power:

Pw2C =

ηRec2CPos Qw2C if Qw2C ≥ 0

and TK2 ≤ T4 < T3C

−ηRec2CNeg Qw2C if Qw2C < 0 and T4 ≤ TK2


where

ηRec2CPos = ηc2CPos ηEx2CPos (A.41a)ηRec2CNeg = ηc2CNeg ηEx2CNeg (A.41b)

and

ηc2CPos = 1− TK2

T3Cif TK2 is the cold source (A.42a)

ηc2CNeg = 1− T3C


A.3 Efficiency of the overall interconnec-tor system

The comparison of different interconnector system layouts or oper-ation strategies requires a definition of the efficiency of the overallsystem. The following definitions are introduced for the efficienciesof the components of this system:

• ηsend is the efficiency of the inlet compressor / turbine sta-tion. The electric power Pel1 and the chemical power Pch passthrough the station. Its operation requires the electric powerPF1 while the power Pw1 can be recovered in the waste heatrecovery system.

• ηtrans is the efficiency of the transmission device itself. Thechemical power Pch is conserved while the ohmic losses PVaffect the electrical transmission. A fraction PQ of these lossesis, however, taken over by the chemical medium.

A.3. OVERALL EFFICIENCY 131

• ηrec is the efficiency of the receiving end turbine/compressorstation. The electric and chemical power are not affected byits operation which enables the recovery of the electric powerPw2 − PF2.

The following definitions for ηsend, ηtrans and ηrec are proposed:

ηsend =Pel1 + Pch

Pel1 + Pch + PF1 − Pw1(A.43a)

ηtrans =Pel1 − PV + PQ + Pch

Pel1 + Pch(A.43b)

ηrec =Pel1 − PV + Pch − PF2 + Pw2

Pel1 − PV + PQ + Pch(A.43c)

These definitions clearly facilitate the introduction of an overall sys-tem efficiency ηtot for the transmission system.

ηtot = ηsend ηtrans ηrec

=Pel1 − PV + Pch − PF2 + Pw2

Pel1 + Pch + PF1 − Pw1(A.44)

Appendix B

Example: a coaxialenergy interconnector

A coaxial energy interconnector as described in figure B.1 is con-sidered. Two cylindrical conductors are separated by an electricallyinsulating layer and thermally insulated from the surroundings.

The cross sectional area of each conductor is:

Ac = π kf(R2

2 −R12)

(B.1)

Therefore the following outer radius for the internal conductor be-comes:

R2 =

√R1

2 +Acπ kf

(B.2)

The inner radius of the outer conductor thus is:

R3 = R2 + wi (B.3)

and its outer radius is:

R4 =

√R3

2 +Acπ kf

(B.4)

133

134 APPENDIX B. EXAMPLE

R1

R2

R3

R4

wi wt

Figure B.1: A coaxial energy interconnector.

The specific d.c. resistance of this coaxial conductor is:

R′

dc =2ρc20

kf Ac(1 + αc (Tc − 293)) (B.5)

The ks factor for skin effect losses of a hollow conductor is ap-proximately [21]:

ks =d′c − d

′i

d ′c + d′i

(d′c + 2 d

′i

d ′c + d′i

)2

(B.6)

where

d′c =

√kf dc + (1− kf ) di2 (B.7)

and di and dc are the inner, respectively outer diameter of the con-ductor.

In a coaxial conductor, the value of ks is thus different for theinner and the outer conductors. In the following, its mean value willbe used:

135

ks =ks1 + ks2

2(B.8)

where

ks1,2 =d

′

c1,2 − d′

i1,2d

′c1,2 + d

′i1,2

d ′

c1,2 + 2 d′

i1,2d

′c1,2 + d

′i1,2

2

(B.9a)

d′

c1,2 =√kf dc1,2 + (1− kf ) di1,2

2 (B.9b)

and

di1 = 2R1 (B.10a)dc1 = 2R2 (B.10b)di2 = 2R3 (B.10c)dc2 = 2R4 (B.10d)

The proximity effect losses are computed using a formula adaptedfrom [29]:

yp =Acρc

kp2π Ra

√12ω µ0 µrc ρc (B.11a)

=√ω µ0 µrc

2 ρc

π(Ra

2 −Ri2)kf

2π Ra

(1 +

RcenterRshield

)(B.11b)

136 APPENDIX B. EXAMPLE

Appendix C

Illustration examplesfor the interconnectordimensioning

C.1 Example 1: Dimensioning of an in-terconnector for energy distribution

In this first example, a scenario for the lowest distribution layer isconsidered. The situation shown in figure C.1 represents three resi-dential housing estates. Each of those has been defined by its electricand chemical power requirements and the thermal power will resultfrom the layout process.

The system described consists of three interconnectors. Theapplication of the layout procedure presented in section 7.1 yieldsthe inner radius, transmission voltage and conductor overall cross-sectional area summarised in table C.1.

The thermal power available at each hub is given by the inter-connector layout and can either be used directly or converted in a

137

138 APPENDIX C. ILLUSTRATION EXAMPLES

HUB HUB HUB

Interconnector ii

1 km

Interconnector i

1 km

Interconnector iii

1 km

Pth = 1 kWPel = 57 kWPch = 76 kWPth = 4.9 kW

Pel = 55 kWPch = 77 kWPth = 3.1 kW

Pel = 58 kWPch = 75 kWPth = 1.4 kW

Figure C.1: System considered in example 1.

waste heat recovery process. The calculation of the overall efficiencyat maximum electric power ηTotBAMax assumes that a share of thisenergy (50% of the Carnot efficiency) is re-usable.

The following remarks apply to the resulting layout and systemperformance shown in table C.1:

• The losses are unacceptably high: for the consumers at theend of interconnector i, the combined transmission efficiency is76% for a transmission length of only 3 km. This is absurdly lowbecause of the underlying assumption that the gas is heated upand cooled down three times, i.e. once in each interconnectori-iii, over this short distance.

• The low transmission voltages and huge conductor cross-sectional areas are unusual for this kind of application andrepresent an excessive use of material.

This example illustrates that the application of the interconnectorprinciple to end-user distribution under the assumption that waste-heat can be re-used and that hubs are available at both line ends leadsto an inefficient layout. In further steps, these assumptions and thelayout procedure could be revised for distribution applications.

C.2. EXAMPLE 2: REGIONAL DISTRIBUTION 139

Line i ii iiiPelAMax 74.8 kW 130 kW 205 kWPchAMax 74.6 kW 152 kW 228 kWPV AMax 16.9 kW 17.4 kW 17.9 kWUin 143.6 V 242 V 372 VRi 2.84 mm 3.76 mm 4.44 mmAcTot 1300 mm2 1340 mm2 1370 mm2

ηTotBAMax 86.5 % 92.5 % 95.0 %

Table C.1: Layout of the interconnectors for example 1.

C.2 Example 2: Dimensioning of an in-terconnector for regional energy dis-tribution

This second example presents a system of three interconnectors andthree hubs, where two hubs are load centres and one hub feeds energyinto this system (and can therefore represent the interface to a highernetwork layer) as shown in figure C.2. The size of the loads and thedistance between the hubs suggest that this application can representa system which corresponds to a part of a current MV network.

As in the first example, the electrical and chemical loads weregiven whereas the thermal powers are an output of the layout process.The resulting interconnector layouts are shown in table C.2.

The application of the interconnector principle is favourable inthis context because:

• The resulting voltage levels are in line with current practice,which indicates that the interconnector solution will lead to alayout which can be compared to current solutions.

• The overall transmission efficiencies (evaluated on the samebasis as example 1) are all above 99%, a reasonable value inthis context.


HUB HUB

HUB

Interconnector ii

30 km

Interconnector i

50 km

Interconnector iii

60 km

Pth = 100 kW

Pel = 200 MWPch = 210 MW

Pel = 68 MWPch = 89 MWPth = 2.8 MW

Pel = 130 MWPch = 120 MWPth = 2 MW


Within the framework of this work and assuming a reasonable useof the thermal power, the size range of the interconnectors consideredin this example is the most promising for further investigation.

C.3 Example 3: Dimensioning of an in-terconnector for bulk energy trans-mission

In this final example the application of the interconnector principleto bulk energy transmission is considered: a generator is connectedto a load centre via a 300 km line as shown in figure C.3.

The interconnector layout has been performed in the same wayas for the two preceding examples and its result is shown in tableC.3. The high transmission voltage and the inner diameter exceeding30 cm represent a challenge for the implementation of such intercon-nector links. The use of several parallel systems of the size rangepresented in example 2 may represent a solution to this issue.

C.3. EXAMPLE 3: BULK TRANSMISSION 141

Line i ii iiiPelAMax 100 MW 30 MW 100 MWPchAMax 139 MW 49.6 MW 74.4 MWPV AMax 1.69 MW 0.803 MW 1.45 MWUin 96.4 kV 36.5 kV 135 kVRi 12.6 cm 7.54 cm 10.2 cmAcTot 2590 mm2 2060 mm2 1860 mm2

ηTotBAMax 99.1 % 98.7 % 99.0 %


HUB

Interconnector i

300 km

Pth = 2.36 MWPel = 740 MWPch = 496 MWPth = 9.2 MW


Line iPelAMax 750 MWPchAMax 496 MWPV AMax 11.3 MWUin 1078 kVRi 33.2 cmAcTot 1740 mm2

ηTotBAMax 98.9 %


Appendix D

Heat exchangers layout

Though it is not the goal of this work to perform an in-depth studyof the heat exchanger layout, a simple approximation of the requiredexchanger volume is useful to assess the feasibility of waste heatrecovery. This chapter illustrates how the standard method from [30](VDI) has been adapted. Table D.1 indicates the correspondence inthe nomenclature, which depends on the selected waste heat recoveryvariant.

δTK and δTH can be regarded as design values indicating the

VDI Variant A Variant Bϑ1′ T2 T3B

ϑ1′′ T3 T4

ϑ2′ TK + δTK TK + δTK

ϑ2′′ T2 − δTH T2 − δTH

M1 m m

Table D.1: Variables used in the VDI heat exchanger layoutguideline.

143

144 APPENDIX D. HEAT EXCHANGERS LAYOUT

RTP

RTS

wTP wTS

Figure D.1: Cross section of the heat exchanger pipe model.

residual temperature difference between the cold respectively hotsource and the chemical energy carrier at the outlet of a heat ex-changer.

The VDI layout procedure is based on the dimensionless variablesΘ, Φ1, Φ2, Ψ1, Ψ2 and W1

W2. With two of these quantities known, the

remaining four can be computed:

Φ1 =ϑ1′ − ϑ1

′′

ϑ1′ − ϑ2

′ (D.1)

Φ2 =ϑ2′′ − ϑ2

′

ϑ1′ − ϑ2

′ (D.2)

The mass flow on the secondary side can be computed from theenergy balance:

M2 =cp1cp2

M1ϑ1′ − ϑ1

′′

ϑ2′′ − ϑ2

′ (D.3)

The required heat exchanger surface is given by:

k A‖ = Ψ1 W1 (D.4)

where k is of empirical nature. Table D.2 contains values taken from[30], valid for the concentric arrangement shown in figure D.1(“fieldtube heat exchanger”).

145

Inner medium outer medium kGas (1 bar) Gas (1 bar) 10 . . . 35Gas (200 bar) Gas (1 bar) 20 . . . 60Gas (200 bar) Gas (200 bar) 150 . . . 500Gas (200 bar) Liquid 200 . . . 600Liquid Gas Liquid 300 . . . 1400

Table D.2: Empirical values for k (from [30])

Medium Typical flow velocityLiquid 0.5 . . . 2 [m/s]Gas (low pressure) 10 . . . 25 [m/s]Gas (100 bar) 8 . . . 15 [m/s]

Table D.3: Realistic values for flow velocities in a heat ex-changer from [31].

In the case of a counterflow heat exchanger:

Θ =Φ1 − Φ2

ln(

1−Φ21−Φ1

) (D.5)

and

Ψ1 =Φ1

Θ(D.6)

From this, A‖ can be derived.The size of the heat exchanger will be approximated based on

a given flow velocity (as a design parameter). Realistic values havebeen taken from [31] and are shown in table D.3.

Since the primary and secondary mass flows as well as the flowvelocities are known, the radii RTP and RTS and finally the totalvolume of the exchanger can be calculated (εFT is a “fill factor” for

146 APPENDIX D. HEAT EXCHANGERS LAYOUT

the exchanger):

Vtot = εFTA‖

2RTP(RTS + wTS)2 (D.7)

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List of symbols

Symbol Unit Description

A0 m2 Cross sectional area at the pump inlet of gas ductA1 m2 Cross sectional area at the pump outlet of gas ductAc m2 Cross sectional area of the electrical conductor of

the energy interconnector (per phase or pole)AcTot m2 Cross sectional area of the electrical conductor of

the energy interconnector (all phases or poles)Ageom m2 Geometrical cross sectional area of the individual

electrical conductor (per phase)AgeomTot m2 Total geometrical cross sectional area of the elec-

trical conductor (all phases or poles)Ai m2 Cross sectional area of the inner conduit of the

energy interconnector

c1Pa2

m KCoefficient (1) for gas flow differential equation

c2WK

Coefficient (2) for gas flow differential equation

c3Pa2

KCoefficient (3) for gas flow differential equation

c4Wm

Coefficient (4) for gas flow differential equation

c5 Coefficient (5) for gas flow differential equation

cmMJ

kgKSpecific heat of the chemical medium

eD

Relative roughness of the pipeF N Forcef Friction factorfe s−1 Electrical frequencyg m/s2 Acceleration due to gravityh m Laying depth

151

152 LIST OF SYMBOLS


I A Electric current intensity (r.m.s.)Itot A Sum of the current intensities of all conductors

forming the energy interconnectorJ A/m2 Electric current density in the conductor (r.m.s.)JMax A/m2 Maximum admissible electric current density

(r.m.s.)JNom A/m2 Electric current density at the nominal pointkf Filling factor of the electrical conductorks Factor for the determination of skin effect lossesLtot m Total length of the energy interconnector

M1, M2 kg/s Primary (1) and secondary (2) mass flow rate in aheat exchanger

Mm kg/mol Molar mass of the chemical mediumm kg/s Mass flow ratem1 kg/s Coolant mass flow rate at the inlet of the energy

interconnectorm2 kg/s Coolant mass flow rate at the end of the energy

interconnectorms kg Coolant mass stored in the energy interconnectornc Number of connections to the main grid of a con-

sumer or areanF Number of degrees of freedom for ideal gasesnph Number of phases of the interconnectorPch W Chemical power throughput of the energy inter-

connectorPchAMax W Maximum transmissible chemical power (for

gaseous carriers)PchAPMax W Chemical power corresponding to the maximum

electric power (for gaseous carriers)PchAMin W Minimum transmissible chemical power (for

gaseous carriers)PchLMax W Maximum chemical power of an interconnector

with a liquid energy carrierPchMax W Maximum chemical power in the context of both

liquid and gaseous carriersPCM W Thermal power flow from the electrical conductor

to the chemical mediumPel W Electric powerPel1 W Electric input power to the energy interconnectorPelAMax W Maximum transmissible electric power (with

gaseous carriers)

153


PelchAMax W Electric power corresponding to the maximumchemical power (for gaseous carriers)

PelchAMin W Electric power corresponding to the minimumchemical power (for gaseous carriers)

PelLMax1 W Maximum electric power of an interconnector witha liquid energy carrier (corresponding to theminimum chemical power)

PelLMax2 W Maximum electric power of an interconnector witha liquid energy carrier (corresponding to themaximum chemical power)

PelMax W Maximum electric power in the context of bothliquid and gaseous carriers

PFTot W Overall net power needed to transport the chemi-cal medium across the energy interconnector

PF1A,PF1C

W Pump/compressor power at the inlet to transportthe chemical medium across the energy inter-connector (for recovery variant A, C)

PF2 W Pump/compressor power at the outlet to trans-port the chemical medium across the energyinterconnector

PF2A,PF2B ,PF2C

W Pump/compressor power at the outlet to trans-port the chemical medium across the energyinterconnector (for recovery variant A, B, C)

PF1Tot W Power needed at the inlet to transport the chemi-cal medium across the energy interconnector

PF1ATot W Power needed at the inlet to transport the chem-ical medium across the energy interconnector(for recovery variant A)

PF2Tot W Power needed at the outlet to transport the chem-ical medium across the energy interconnector

PF2ATot,PF2BTot

W Power needed at the outlet to transport the chem-ical medium across the energy interconnector(for recovery variant A, B)

PPump1 W Inlet pump/compressor mechanical power (for re-covery variants A and B)

PPump1C W Inlet pump/compressor mechanical power (for re-covery variant C)

PPump2A,PPump2B ,PPump2C

W Outlet pump/compressor mechanical power (forrecovery variant A, B, C)

PQ W Heat absorption rate by the chemical mediumPR W Heat induced by friction in the chemical medium

154 LIST OF SYMBOLS


Pth W Thermal transmitted powerPU W Thermal power flow from the interconnector to the

surrounding soilPV W Electrical loss power in the interconnectorPV AMax W Losses corresponding to the maximum transmissi-

ble electric power (for gaseous carriers)PV chAMax W Electrical losses corresponding to the maximum

chemical power (for gaseous carriers)PV chAMin W Electrical losses corresponding to the minimum

chemical power (for gaseous carriers)Pw1 W Recovered electric power at the inletPw1A,Pw1C

W Recovered electric power at the inlet (for recoveryvariant A, C)

Pw2 W Recovered electric power at the outletPw2A,Pw2B ,Pw2C

W Recovered electric power at the outlet (for recoveryvariant A, B, C)

P′

W/m Specific powerp Pa Pressurep0 Pa Pressure of the chemical medium at the inlet of

the pumpp1 Pa Pressure of the chemical medium at the inlet of

the energy interconnectorp1C Pa Pressure of the chemical medium at the inlet of

the energy interconnector (for variant C)p1kC Pa Pressure of the chemical medium in the inlet waste

heat recovery system (for variant C)p2 Pa Pressure of the chemical medium at the outlet of

the energy interconnectorp2C Pa Pressure of the chemical medium at the outlet of

the energy interconnector (for variant C)p2Min Pa Minimum outlet pressure required for the inter-

connector operationp3 Pa Pressure of the chemical medium in the outlet

waste heat recovery systemp4 Pa Pressure of the chemical medium after the outlet

waste heat recovery systempi Pa Pressure at the entry of a small mass elementpMax Pa Maximum admissible pressure in the intercon-

necotr

pKINkg m

sKinetic momentum

155


po Pa Pressure at the end of a small mass elementQ J Heat

Q W Heat flow (thermal power)

Qw1 W Thermal power extracted from the medium at theinlet

Qw1A,Qw1C

W Thermal power extracted from the medium at theinlet (for variant A, C)

Qw2 W Thermal power extracted from the medium at theoutlet

Qw2A,Qw2B ,Qw2C

W Thermal power extracted from the medium at theoutlet (for variant A, B, C)

R Ω Electrical resistance

R′ Ω

mSpecific electrical resistance

Re Reynolds constantRa m Outer radius of the electrical conductor of the en-

ergy interconnector

Rac′Ωm

Alternating current specific electrical resistanceper unit length

Rdc′ Ω

mDirect current specific electrical resistance per unit

length

RgJ

mol KGas constant of the chemical medium

RI′ Ω

mAlternating current specific electrical resistance

per unit length, including proximity effect andshield losses

Ri m Inner radius of the electrical conductor of the en-ergy interconnector

RthE K/W Thermal resistance of the soilRthI K/W Thermal resistance of the insulatorRthM K/W Thermal contact resistance between conductor and

chemical medium

R′

thE Km/W Specific thermal resistivity of the soil

R′

thI Km/W Specific thermal resistivity of the insulator

R′

thM Km/W Specific thermal resistivity between conductor andchemical medium

r1 Ratio of the maximum transmissible electric powerPelAMax to the minimum transmissible elec-tric power PelchAMin

156 LIST OF SYMBOLS


r2 Ration of the maximum transmissible chemicalpower PchAMax to the maximum transmissi-ble electric power PelAMax

s Degree of self-sufficiency of a consumer or an areaT (x) K Temperature of the chemical medium along the

energy interconnectorT0 K Temperature of the chemical medium at the inlet

of the chemical medium pumpT1 K Temperature of the chemical medium at the inlet

of the energy interconnectorT1c K Temperature of the chemical medium at the in-

let of the energy interconnector (for recoveryvariant C)

T1h K Temperature of the chemical medium in the inletwaste heat recovery system

T1hC K Temperature of the chemical medium in the inletwaste heat recovery system (for recovery vari-ant C)

T1kC K Temperature of the chemical medium in the outletwaste heat recovery system (for recovery vari-ant C)

T2 K Temperature of the chemical medium at the outletof the energy interconnector

T2c K Temperature of the chemical medium at the end ofthe energy interconnector (for recovery variantC)

T3 K Temperature of the chemical medium in the outletwaste heat recovery system

T3A,T3B ,T3C

K Temperature of the chemical medium in the outletwaste heat recovery system (for recovery vari-ant A, B, C)

T4 K Temperature of the chemical medium after theoutlet waste heat recovery system

Tc K Temperature of the electrical conductorTcAve K Average temperature of the electrical conductorTK K Cold source temperatureTK1 K Cold source temperature at the interconnector in-

letTK2 K Cold source temperature at the interconnector

outletTU K Temperature of the soilTi K Temperature at the entry of a small mass element

157


To K Temperature at the end of a small mass elementt s Time∆U J Internal energy differenceUin V d.c. input voltage of the energy interconnectorUinMax V Maximum d.c. input voltage of the energy inter-

connectorV m3 Volumev m/s Flow velocity of the chemical mediumv0 m/s Flow velocity of the chemical medium before the

pump (at the interconnector entry)v1 m/s Flow velocity of the chemical medium at the inlet

of the energy interconnectorv1h m/s Flow velocity of the chemical medium in the inlet

waste heat recovery systemv2 m/s Flow velocity of the chemical medium at the outlet

of the energy interconnectorv3 m/s Flow velocity of the chemical medium in the outlet

waste heat recovery systemvi m/s Flow velocity at the entry of a small mass elementvo m/s Flow velocity at the end of a small mass elementW J Work

W1, W2 W/K Primary and secondary specific heat capacity flowWR J Work of the friction force in the mediumwi m Thickness of electrical insulation layerwm J/kg Specific energy of the chemical mediumwT m Thickness of thermal insulation layerx m Position on the energy interconnectorxs Constant for the determination of the skin effect

lossesX Normalised position on the energy interconnectoryp Loss factor for skin effect lossesys Loss factor for proximity effect losses

α1 Coefficient for the determination of αLKα2 Coefficient for the determination of αLKαc K−1 Temperature coefficient of the electrical conductor

αLKW

m2KHeat transfer coefficient between conductor and

chemical medium

β Intermediary result“β := κ

κ−1

”∆p Pa Pressure difference∆pM Pa Intermediary result

158 LIST OF SYMBOLS


∆pR Pa Pressure drop due to friction∆Q J Heat difference∆QR J Heat produced by friction in the medium∆t s Time interval∆TLK K Temperature difference between the conductor and

the chemical medium in the energy intercon-nector

∆WR J Work by the medium due to the friction pressuredrop

δTH K Temperature difference between the hot sourceand the working fluid temperature at the out-let of the heat exchanger.

δTK K Temperature difference between the cold sourceand the medium temperature at the outlet ofthe heat exchanger.

η1 Efficiency of the inlet pump/compressorη1Neg Efficiency of the inlet pump/compressor for nega-

tive PPump1η1ANeg ,η1CNeg

Efficiency of the inlet pump/compressor for nega-tive PPump1A,C (for recovery variant A, C)

η1Pos Efficiency of the inlet pump/compressor for posi-tive PPump1

η1APos,η1CPos

Efficiency of the inlet pump/compressor for posi-tive PPump1A,C (for recovery variant A, C)

η2Neg Efficiency of the outlet pump/compressor for neg-ative PPump2

η2ANeg ,η2BNeg ,η2CNeg

Efficiency of the outlet pump/compressor for neg-ative PPump2A,B,C (for recovery variant A,B, C)

η2Pos Efficiency of the outlet pump/compressor for pos-itive PPump2

η2APos,η2BPos,η2CPos

Efficiency of the outlet pump/compressor for pos-itive PPump2A,B,C (for recovery variant A,B, C)

ηc Carnot efficiencyηc1Neg Carnot efficiency of inlet waste heat recovery sys-

tem for negative Qw1

ηc1ANeg ,ηc1CNeg

Carnot efficiency of inlet waste heat recovery sys-tem for negative Qw1A,C (for recovery vari-ant A, C)

ηc1Pos Carnot efficiency of inlet waste heat recovery sys-tem for positive Qw1

159


ηc1APos,ηc1CPos

Carnot efficiency of inlet waste heat recovery sys-tem for positive Qw1A,C (for recovery vari-ant A, C)

ηc2Neg Carnot efficiency of outlet waste heat recovery sys-tem for negative Qw2

ηc2ANeg ,ηc2BNeg ,ηc2CNeg

Carnot efficiency of outlet waste heat recoverysystem for negative Qw2A,B,C (for recoveryvariant A, B, C)

ηc2Pos Carnot efficiency of outlet waste heat recovery sys-tem for positive Qw2

ηc2APos,ηc2BPos,ηc2CPos

Carnot efficiency of outlet waste heat recoverysystem for positive Qw2A,B,C (for recoveryvariant A, B, C)

ηel Electrical efficiencyηpump Pump efficiencyηRec1Neg Efficiency of inlet waste heat recovery system for

negative Qw1

ηRec1ANeg ,ηRec1BNeg ,ηRec1CNeg

Efficiency of inlet waste heat recovery system fornegative Qw1A,B,C (for recovery variant A,B, C)

ηRec1Pos Efficiency of inlet waste heat recovery system forpositive Qw1

ηRec1APos,ηRec1CPos

Efficiency of inlet waste heat recovery system forpositive Qw1A,C (for recovery variant A, C)

ηRec2Neg Efficiency of outlet waste heat recovery system fornegative Qw2

ηRec2ANeg ,ηRec2BNeg ,ηRec2CNeg

Efficiency of outlet waste heat recovery system fornegative Qw2A,B,C (for recovery variant A,C)

ηRec2Pos Efficiency of outlet waste heat recovery system forpositive Qw2

ηRec2APos,ηRec2CPos

Efficiency of outlet waste heat recovery system forpositive Qw2A (for recovery variant A, C)

ϑ1′, ϑ1

′′,ϑ2′, ϑ2

′′K Primary (1) and secondary (2) inlet (′) and outlet

(′′) temperatures used in the heat exchangerlayout

κ Isentropic heat exponent (ratio of specific heats)

λ WmK

Heat conductivity

λ1 Factor for armour lossesλ2 Factor for shield losses

λcWmK

Thermal conductivity of the electrical conductor

160 LIST OF SYMBOLS


λEWmK

Thermal conductivity of the soil

λIWmK

Thermal conductivity of the insulator material

µ0VsAm

Permeability of vacuum

µM Ns/m2 Viscosity of the chemical mediumµrc Relative permeability of the electrical conductorρ Ωm Electrical resistivity of the electrical conductorρc20 Ωm Electrical resistivity of the electrical conductor at

20 degrees CelsiusρmM kg/m3 Mass density of the chemical medium

Γ, Γ1, Γ2 Intermediate resultΘ Intermediate resultΥ Intermediate resultΞ Intermediate resultΦ1, Φ2 Intermediate results used in the heat exchanger

dimensioningΨ1, Ψ2 Intermediate results used in the heat exchanger

dimensioning

Abbreviations

a.c. Alternating currentCHP Combined heat and powerch Chemicald.c. Direct currentel ElectricHVAC High voltage a.c.HVDC High voltage d.c.max Maximalmin MinimalMV Medium voltagePDE Partial differential equationr.m.s. Root mean squaresim. Result of a numerical simulationth ThermalT&D Transmission and distribution

List of Figures

4.1 Illustration of the “Vision of Future Energy Networks”multi-energy network framework. . . . . . . . . . . . . 15

4.2 Illustration of the Energy Hub concept. . . . . . . . . 17

5.1 Illustration of the Energy Interconnector with electricand chemical power transmission as well as waste heatreuse. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2 Transmittable chemical vs. electric power for an in-terconnector with a liquid chemical energy carrier fordifferent outlet temperatures T2 (example, Uin is keptconstant). . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.3 Cross-section and longitudinal view of the basic inter-connector model. . . . . . . . . . . . . . . . . . . . . . 28

5.4 Thermal model for the energy interconnector. . . . . . 335.5 Example for a temperature T (x) and pressure p(x)

profile of a gaseous medium along the interconnector. . 375.6 Profiles of the electrical losses in the conductor PV ′

and the heat flows at the interface with the soil PU ′

and the medium PCM′ (example). . . . . . . . . . . . 39

5.7 Profiles of the friction losses PR′, heat transfer fromthe electrical conductor PCM ′ and heat absorbed bya gaseous medium (example). . . . . . . . . . . . . . . 40

161

162 LIST OF FIGURES

5.8 Contour of the electric current density J in function ofthe mass flow rate m and the inlet pressure p1 (example). 41

5.9 Interconnector system layout and power flow for wasteheat recovery variant B. The figure also illustrates thenaming convention used for temperatures and pres-sures at the inlet and outlet of the interconnector. . . 42

5.10 Auxiliary power requirements and possible waste heatrecovery at the inlet and outlet of an interconnectorin dependence upon gas mass flow (example). . . . . . 44

5.11 Power flows for the overall interconnector system in-cluding auxiliary power. . . . . . . . . . . . . . . . . . 45

5.12 Contour lines of the electrical, chemical and totaltransmission efficiency (example). . . . . . . . . . . . . 47

5.13 Mass element in the pipe. . . . . . . . . . . . . . . . . 495.14 Comparison between simulated (numerical) and calcu-

lated (analytical) temperature and pressure profiles independance upon normalised current density (example). 60

5.15 Comparison between simulated (numerical) and calcu-lated (analytical) specific power profiles in dependanceupon normalised current density (example). . . . . . . 61

5.16 Permissible current density vs. mass flow rate for aninterconnector with low temperature energy transmis-sion (example with T1 = 253 K and T2 = 293 K). . . . 63

6.1 Nomenclature for the maximum and minimum electricand chemical powers. . . . . . . . . . . . . . . . . . . . 67

6.2 Operational area for an interconnector with a gaseouschemical medium for different outlet temperatures T2

(example). Parameter is the outlet temperature T2 [K]. 696.3 Maximum and minimum permissible outlet tempera-

ture in function of the operating point (example). . . . 696.4 Operational area for an interconnector with a gaseous

chemical medium for different inlet temperatures T1

(example). . . . . . . . . . . . . . . . . . . . . . . . . . 706.5 Operational area at different input voltages (example). 71

LIST OF FIGURES 163

6.6 Optimal transmission voltage (example). . . . . . . . . 726.7 Total transmission efficiency with optimal transmis-

sion voltage (example). . . . . . . . . . . . . . . . . . . 726.8 Limitation of the operating area by the ratings of the

compressors (example). In this example, the ratingsare chosen in order not to limit the operation range. . 79

6.9 Transmissible power for constant r1 and r2 (example). 816.10 Maximum input voltage for constant r1 and r2 (ex-

ample). . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.1 Maximum permissible electric power per interconnec-tor length unit in dependence of r1 and r2 (using hy-drogen). This data is computed once for a given setof material and constrained parameters and providesthe basis for a layout based on scaling laws. . . . . . . 87

7.2 Maximum permissible electric power per interconnec-tor length unit for r2 = 0.84. . . . . . . . . . . . . . . 89

7.3 Ri/Ltot3/5 in dependence of r1 and r2 (using hydrogen). 90

7.4 Inner radius for an interconnector with PelAMax =200 MW, PchAMax = 240 MW and Ltot = 50 km forvarious inlet temperatures (error bars: effect of a±25% variation of PelAMax, PchAMax and Ltot). . . . . 93

7.5 Inlet Voltage for an interconnector with PelAMax =200 MW, PchAMax = 240 MW and Ltot = 50 km forvarious inlet temperatures (error bars: effect of a±25% variation of PelAMax, PchAMax and Ltot). . . . . 94

7.6 Minimum and maximum transmissible powers for aninterconnector with different gaseous chemical carriers(example). . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.7 Minimum and maximum transmissible powers for aninterconnector with different liquid chemical carriers(example). . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.8 Inner radius of an interconnector in function of thefriction factor for constant maximum chemical power(example). . . . . . . . . . . . . . . . . . . . . . . . . . 98

164 LIST OF FIGURES

7.9 Maximum chemical and electric power at constantr1, r2 for various thermal resistances of the outer in-sulation (example). . . . . . . . . . . . . . . . . . . . . 101

7.10 Inner radius for a hydrogen interconnector for variousapplications and assumptions previously introducedfor the material and design parameters (error bars:result of a 25% variation in the specifications of theapplication). . . . . . . . . . . . . . . . . . . . . . . . . 104

7.11 Transmission voltage (d.c.) for a hydrogen intercon-nector for various applications and assumptions previ-ously discussed for the material and design parameters.105

7.12 Conductor cross-sectional area for a hydrogen inter-connector for various applications and with the as-sumptions introduced for the material and design pa-rameters. . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.13 Inner radius for a hydrogen interconnector for “smallscale” applications and with the assumptions intro-duced for the material and design parameters. . . . . . 107

7.14 Transmission voltage for a hydrogen interconnector for“small scale” applications and with the assumptionsintroduced for the material and design parameters. . . 108

7.15 Conductor cross-sectional area for a hydrogen inter-connector for “small scale” applications and with theassumptions introduced for the material and designparameters. . . . . . . . . . . . . . . . . . . . . . . . . 109

7.16 Efficiency ηTotBAMax for a hydrogen interconnectorfor “small scale” applications and with the assump-tions introduced for the material and design parameters.110

7.17 Inner radius of an interconnector for various chemicalcarriers (application: MVDC). . . . . . . . . . . . . . 111

7.18 Transmission voltage of an interconnector for variouschemical carriers (application: MVDC). . . . . . . . . 112

7.19 Conductor cross-sectional area of an interconnectorfor various chemical carriers (application: MVDC). . . 112

LIST OF FIGURES 165

A.1 Interconnector system layout and power flow for wasteheat recovery variant A. . . . . . . . . . . . . . . . . . 122

A.2 Interconnector system layout and power flow for wasteheat recovery variant C. . . . . . . . . . . . . . . . . . 124

B.1 A coaxial energy interconnector. . . . . . . . . . . . . 134

C.1 System considered in example 1. . . . . . . . . . . . . 138C.2 System considered in example 2. . . . . . . . . . . . . 140C.3 System considered in example 3. . . . . . . . . . . . . 141

D.1 Cross section of the heat exchanger pipe model. . . . . 144

166 LIST OF FIGURES

List of Tables

6.1 Sign table for dPVdp2

. pdz and pfp are the zeros of dPVdp2

and d2PVdp2

2respectively. They have no special meaning

in this context. . . . . . . . . . . . . . . . . . . . . . . 77

7.1 Temperature range for waste heat recovery equipmentor “direct” heat consumers. . . . . . . . . . . . . . . . 92

7.2 Examples of the ampacity of XLPE cables with copperconductor [28]. The maximum current depends on thetype of burying. . . . . . . . . . . . . . . . . . . . . . . 99

7.3 List of the investigated “generic” applications (nc:number of connections for the consumer, s degree ofself-sufficiency). . . . . . . . . . . . . . . . . . . . . . . 103

C.1 Layout of the interconnectors for example 1. . . . . . . 139C.2 Layout of the interconnectors for example 2. . . . . . . 141C.3 Layout of the interconnectors for example 3. . . . . . . 141

D.1 Variables used in the VDI heat exchanger layoutguideline. . . . . . . . . . . . . . . . . . . . . . . . . . 143

D.2 Empirical values for k (from [30]) . . . . . . . . . . . . 145D.3 Realistic values for flow velocities in a heat exchanger

from [31]. . . . . . . . . . . . . . . . . . . . . . . . . . 145

167

168 LIST OF TABLES

Curriculum vitae

1979 Born in Vevey, Switzerland

1985-1989 Primary school in Rougemont, Switzerland

1989-1994 Secondary school in Chateau-d’Oex, Switzerland

1994-1998 College in Bulle, Switzerland

1998-2003 Studies in electrical engineering and information tech-nology, ETH Zurich

2003-2008 Research assistant at the Power Systems and HighVoltage Laboratories, ETH Zurich

Since 2008 Technology consultant at the AREVA T&D Technol-ogy Centre in Stafford, United Kingdom

in copyright - non-commercial use permitted rights ......patrick favre-perrod dipl. el.-ing. eth...

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