Assessing the Effect of Smart Reinforcement Al- ternatives on the …essay.utwente.nl/74878/1/Groen_MA_EEMCS.pdf · 2018-04-17 · April19,2018 MASTER THESIS Assessing the Effect

April 19, 2018

MASTER THESIS

Assessing the Effect of Smart Reinforcement Al-ternatives on the Expected Asset Lifetime ofLow Voltage Networks

Marius Groen

Faculty of Electrical Engineering,Mathematics and Computer Science (EEMCS)Chair: Computer Architectures for Embedded Systems (CAES)

Exam committee:Prof.dr.ir. G.J.M. Smit (UT)V.M.J.J. Reijnders MSc (UT)Dr.ir. M.E.T. Gerards (UT)Prof.dr. J.L. Hurink (UT)

Abstract

Trends in the current energy transition in the Netherlands may require a large amount of lowvoltage electricity networks to be reinforced in the coming years. However, cable reinforcementis expensive and labor intensive for underground electricity cables as used in the Netherlands.This study, performed in context of project GridFlex Heeten, assesses alternatives to cablereinforcement to increase the grid capacity of low voltage networks and the effect of thesealternatives on the expected lifetime of cables and transformers.

The considered alternatives are online tap changer transformers (OLTCs), centralized neighbor-hood storage, and smart control of flexible devices using the Profile Steering approach. In a casestudy of the network of Heeten the effect of the mentioned alternatives on the grid capacity andthe asset lifetime is compared to cable reinforcement. Photovoltaic systems, electric vehicles,heat pumps, and batteries are simulated for different penetration levels.

The result of this case study is that an OLTC or centralized neighborhood storage is a validalternative to cable reinforcement, especially if temporary overloading of cables is allowed.Furthermore, we show that the lifetime expectancy of the cables of the network is 26 timesgreater than the economical lifetime in the current state. However, we also show that the networkis operated close to its power quality limits and may therefore require cable reinforcement in thecoming years. We also show that the effect on the expected transformer lifetime is negligible forthis particular network.

We also show that the decentralized energy management approach Profile Steering does improvepower quality. However, the Profile Steering heuristic does not completely negate the voltageissues of the network in the case study. Nevertheless, the positive results of voltage controlin the low voltage network using e.g. OLTCs suggest a more affordable, sustainable, and lesslabor intensive alternative to cable reinforcement to cope with the challenges of the energytransition.

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Dankwoord & Acknowledgement

Na een aantal maanden afstuderen en een aantal jaren studie die vooraf gingen aan het documentdat voor u ligt wil ik een aantal mensen in het bijzonder bedanken voor de tijd en energie die zein mij geïnvesteerd hebben.

Allereerst wil ik de vakgroep CAES bedanken, waar ik zowel mijn Bacheloropdracht heb uitgevo-erd als mijn Masterscriptie. Ik heb erg genoten van de sociale activiteiten als de vaste koffiepauzes(al dan niet met taart of seizoenslekkernijen), lunchwandelingen, vrijdagmiddagborrels, uitjes enetentjes.

Ook wil ik de mensen uit het Energiehok, het kantoor waar ik gewerkt heb, bedanken voor hetverdragen van mijn flauwe humor, het meerdere malen per dag uitlenen van hun koffiepasjes enhet meedenken over verschillende onderwerpen. De mensen in deze ruimte maakten dat ik metplezier naar de universiteit kwam.

Ik wil Victor Reijnders bedanken als mijn dagelijks begeleider en voor de kans om dit onderzoekte doen. Verder wil ik de andere commissieleden, namelijk Johann Hurink, Gerard Smit en MarcoGerards bedanken voor het doorlezen van dit document en hun waardevolle suggesties. In hetbijzonder wil ik Johann Hurink bedanken voor de suggestie om slimme netverzwaringsmethodeste vergelijken wat betreft levensduur van assets. Ook wil ik Gerwin Hoogsteen niet onvermeldlaten voor zijn altijd behulpzame houding, vakkennis en voor het geregeld sparren.

Verder wil ik Piet Soepboer en Tjeerd Broersma van Enexis en Jacco Heres van Allianderbedanken voor hun tijd en het meedenken vanuit hun rol als netbeheerder. Suzanne Verhoeckxen Erik van Aert van IEO Transformers wil ik bedanken voor het verschaffen van de benodigdeparameters voor de transformator die ik nodig had.

Ten slotte wil ik mijn ouders bedanken voor hun steun tijdens mijn studie, God voor demooie kansen die ik in mijn leven krijg en Alinda Blotenburg voor haar steun in mijn ‘groene’ambities.

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Contents

1 Introduction 91.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Problem Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Background and Related Work 112.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Low Voltage Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.2 Network Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.3 Smart Reinforcement Methods . . . . . . . . . . . . . . . . . . . . . . . . 132.1.4 Loss of Lifetime Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.1 Reliability Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 Thermal Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Economical Evaluation of an OLTC Transformer . . . . . . . . . . . . . . 152.2.4 Profile Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.5 DEMKit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Loss of Lifetime Modeling 173.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Transformer Loss of Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Transformer Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.2 An Overview of Transformer Thermal Models . . . . . . . . . . . . . . . . 183.2.3 Description of the IEEE Clause 7 Model . . . . . . . . . . . . . . . . . . . 193.2.4 Transformer Loss of Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Cable Loss of Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.1 Cable Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.2 Cable Thermal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3.3 IEC 60287 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.4 Olsen et al. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.5 Cable Loss of Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.4.1 Transformer Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . 313.4.2 Cable Thermal Model Performance . . . . . . . . . . . . . . . . . . . . . . 323.4.3 Cable Model Accuracy vs. Computation Time . . . . . . . . . . . . . . . 33

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Simulations 374.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 Data and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

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4.1.2 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2.1 Heeten Current State versus Pilot . . . . . . . . . . . . . . . . . . . . . . 404.2.2 Pushing the Network to its Limit . . . . . . . . . . . . . . . . . . . . . . . 424.2.3 Smart Reinforcement versus Cable Reinforcement . . . . . . . . . . . . . . 46

4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5 Conclusion and Discussion 535.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6 Recommendations 55

Appendices 57

A Reliability Modeling 59

References 60

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Chapter 1

Introduction

1.1 Motivation

The wish for a more sustainable society in the Netherlands drives many changes. One of them isto move away from fossil fuels for the production of electricity, heating of our houses, and ourmobility. Very often, electrical energy is seen as the ideal energy carrier for more sustainablealternatives. Heat pumps, for instance, allow us to move away from gas powered boilers and useelectricity from sustainable sources to heat our houses. Furthermore, decentralized productionof electricity gains popularity and new devices using electricity start to find their way to ourhouseholds. For instance, we more often produce our own renewable energy using solar panelsand sometimes charge electric vehicles at home, rather than fueling them at a petrol station.However, the electricity network has not been designed with these use cases in mind and partsof the network may get overloaded in the near future.

In the electricity network within a neighborhood (low voltage grid) the maximally allowedtransported power is often limited by either the allowed current or the allowed voltage drop overthe cable. If power is transported through a cable, current will flow through the conductor whilstthe conductor has a certain electrical resistance. This causes an increase in cable temperaturedue to losses and introduces a voltage drop over the length of the cable. For low voltage cables,the conductor temperature should be below 55°C for PVC insulated cables and the voltageis allowed a tolerance of ±10% with respect to the nominal voltage of 230V [1] for 10 minuteaverage values.

When either the operation below maximum current or the operation within the voltage tolerancecannot be guaranteed, the electricity network of the corresponding part has to be reinforced.Traditionally, this means that the cables are to be replaced by cables with larger conductors. Thisis expensive (approximately €135 per meter, including labor) and labor intensive. Furthermore,acquiring sufficient qualified personnel is seen as one of the biggest challenges of the energytransition for distribution system operators (DSOs), who are responsible for replacing thesecables (see interviews in [2]). Therefore, other ways to reinforce an electricity network or topostpone reinforcement gain interest. These methods are called smart reinforcement methodsin this work and concern any approach that allows for more grid capacity without replacingcables.

Examples of smart reinforcement methods are smart control of flexibility, centralized neighbor-hood storage, and online tap changing transformers, which are treated in more detail in Section2.1.3. Smart control could compromise on comfort to reduce network usage. The other methodsallow more power flow through the existing infrastructure, which may impact the lifetime of thecables and of transformers. What these methods have in common, is that they more effectively

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use existing infrastructure, instead of simply replacing it. This study aims to assess whether thesemethods significantly impact the lifetime of the cables and transformers in a low voltage networkand whether these methods are proper alternatives to traditional reinforcement. This may helpdistribution system operators to determine the most sustainable, feasible, and affordable solutionto support the energy transition in the low voltage network.

1.2 Problem Statement

The problem statement of this study is as follows: Assess the effect of smart reinforcementmethods on the lifetime of cables and transformers in the low voltage network.

1.3 Problem Context

This study is part of project GridFlex Heeten, which has set itself the goal to experiment withnovel pricing schemes to stimulate local production and usage of electricity in neighborhoodthe Veldegge of the village Heeten. Besides the University of Twente, partners are Enexis B.V.,Energy Cooperation Endona, Enpuls B.V., Dr. Ten B.V., and ICT Automatisering NederlandB.V. As DSO in this area, Enexis has made the topology available of the low voltage networkof the Veldegge. In this work, this low voltage network of 47 houses is often referred to as thenetwork of Heeten.

1.4 Scope

The scope of this study is constrained to the low voltage network, including the distributiontransformer feeding the network. Components under study are the transformer, and the outgoingfeeders of the transformer. Loss of lifetime is not considered for cable joints nor cables connectinghouseholds to the feeder cable. Furthermore, the cable rating models in IEC 60853 [3] areconsidered out of scope, as they are not available to us. IEC 60853 is for instance used by DSOsto assess temporary overloading of medium and high voltage cables.

The performance and technical feasibility of the smart reinforcement methods themselves isnot the subject of this study, however the potential of these methods and their effect on assetlifetime is. Therefore, for most methods perfect control is assumed. For example, for centralizedneighborhood storage it is assumed that it is able to always inject or draw current from thenetwork and that sufficient storage capacity is available.

Furthermore, the loss of lifetime modeling is constrained to extruded cables (i.e. not the olderGPLK cables) and oil-immersed distribution transformers. The approach is limited to a discretetime simulation case study in the network of Heeten, whereby load-flow analysis is used.

1.5 Structure

The structure of this thesis is as follows: in Chapter 2 the background and related work for thisstudy is presented. In Chapter 3 the approach to model loss of lifetime of transformers andcables is assessed, followed by simulations in Chapter 4. In Chapter 5 one can find the conclusionand discussion. Finally, in Chapter 6 recommendations for future work are presented.

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Chapter 2

Background and Related Work

2.1 Background

In this section the relevant background for this study is treated. First, low voltage networks andtheir relevant components is explained, second the network planning process is considered, fol-lowed by smart network reinforcement methods. The background is concluded by an introductionon loss of lifetime modeling for distribution transformers and low voltage cables.

2.1.1 Low Voltage Network

A schematic representation of a low voltage network is presented in Figure 2.1. Here, the slack busis the connection to the medium voltage electricity network that drives the low voltage network.In the Netherlands, medium voltage often has a nominal voltage of 10kV. The transformeris a distribution transformer, which transforms medium voltage to a low voltage level (230Vnominally). Feeder cables run underground from the transformer through the streets in aneighborhood. Households are connected via connection cables and a cable joint to the feedercable.

Slack Bus (MV)

Transformer

LV

joint

Feeder 1

joint joint joint...

joint

Feeder 2joint

joint joint...

...

Figure 2.1: Schematic Representation of an LV Network

Distribution transformers in the Netherlands are often oil-immersed transformers, see Figure 2.2for a transformer with cutout parts. The three coils inside the transformer convert the voltagefrom medium voltage to low voltage. These coils heat up due to losses and are cooled by the oiland heat convection at the interface of the casing with the ambient air. Typically, distribution

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Figure 2.2: Example of a Distribution Transformer [4]

transformers have cooling mode ONAN, meaning that the transformer is cooled using naturaloil using natural convection with air (Oil-Natural-Air-Natural).

Low voltage electricity cables in the Netherlands are typically underground three phase, fourwire cables laid at a depth of 60cm [5]. An example of such cable can be found in Figure 2.3.In Figure 2.3, (1) is the aluminium conductor, (2) and (3) are the insulation, (4) is the innerfiller, (5) is the inner sheath, (6) is the outer filler, (7) is the copper screen, and (8) is the outersheath. Insulation is used to electrically isolate the conductors, sheaths serve as the mechanicalprotection of the cable, the screen for grounding, and fillers are used to assure that no air ispresent within the cable, as air is a poor conductor of heat.

Standardized cables are made of aluminium for relatively new networks. The sizes of theconductors include 50mm2, 95mm2, 150mm2, and 240mm2. The cables are often referred to asthe number of conductors times the cross-sectional area of one conductor and Al or Cu stand forthe aluminium or copper material of the conductors. An example is 4x95Al for an aluminiumcable having four 95mm2 conductors.

To limit the amount of power transported, fuses are installed at the beginning of each feederto prevent overloading of the cables and/or transformer, e.g. in case of a short circuit in theunderground cable.

V-VMvKsas 0,6/1 kV - 4x240 Alsvm sas70Artikelnummer: 520.15.0332.004

Volgens NEN 3616

Kabelopbouw Hoofdafmetingen en gewichtGeleider (1): Geleider: (hoogte) 16,0 mmIsolatie (2): Isolatie:Geslagen aders (3): Nom. dikte 2,2 mmVulmantel (4): rubber Diameter (hoogte) 20,6 mmBinnenmantel (5): Samenslag: 45 mmVulmantel (6) Slaglengte: 1,5 mAardscherm (7): Binnenmantels: 52 mm

Aardscherm: 53 mmBuitenmantel (8) PVC (grijs) Buitenmantel: 59 mm

* kleuren volgens NEN3616: rood - geel- blauw - geel/blauw Gewicht per meter: 6,2 kg

Mantelstempeling

Electrische gegevensToegekende spanningen U0/U: 0,6/1 kV

Verpakking (voorbeelden) GeleiderHaspeltype: DW4220A (hout) Gelijkstroomweerstand bij 20 °C, max. 0,125 Ω/kmFlensdiameter: 2200 mm Wisselstroomweerstand bij 55 °C 0,143 Ω/kmKerndiameter: 1250 mm Bruto breedte: 1360 mmlengte: 500 m Capaciteit (alleen als richtwaarde) 0,76 µF/kmTotaal gewicht ca.: 3,5 ton * praktische waarden kunnen afwijken

Aardscherm0,268 Ω/km

Leginstructies Kabel Continu toelaatbare stroom belasting

10,6 kN (Berekend aan de hand van NEN1010, 1 circuit)Minimale buigstraal tijdens leggen 0,71 mMinimale buigstraal na installatie 0,59 mMinimum kabellegteperatuur -5 oC 425 A

370 A

Bedrijfsreactantie bij 50 Hz 0,073 Ω/km

Prysmian Netherlands Datasheet 26-jan-16

Prysmian Netherlands B.V. – Schieweg 9, 2627 AN Delft – Postbus 495, 2600 AL Delft

T. 088 - 808 44 44 F. 088 - 808 45 67 E. [email protected] W www.prysmiangroup.nl

De informatie in deze documentatie is onderhevig aan wijzigingen zonder voorafgaande kennisgeving. Hoewel de informatie die wordt aangeboden in dit document met grote zorg is samengesteld en wordt onderhouden, kan Prysmian Netherlands B.V. geen enkele garantie geven dat de beschikbare informatie volledig en/of juist is. Prysmian Netherlands B.V. kan dan ook geen aansprakelijkheid aanvaarden voor eventuele gevolgen, zoals schade of gederfde winst op welke wijze dan ook als gevolg van het gebruik, het vertrouwen op of acties ondernomen naar aanleiding van informatie in dit document.

PRYSMIAN NL - V-VMvKsas 0,6/1 kV - 4x240 Alsvm sas70 NEN 3616 datum meterstempeling

In lucht, Tl = 20 °C, géén directe zonnestraling

In grond, 0,7 m diep, Tg = 15 °C, T geleider = 55oC, g= 0,75 Km/W

Gelijkstroomweerstand bij 20 °C, max.

Maximale trekkracht (met trekkous)

koperdraden in S-vorm met koperband tegenspiraal

aluminium sectorvormig massiefPVCSamenslag *

PVCrubber

(5) (6) (1) (2) (4) (3) (7) (8)

Pagina 1 van 1

Figure 2.3: Example of a Low Voltage Cable [6]

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2.1.2 Network Planning

The amount of power that can be transported over a cable is limited by physical constraintsand norms on power quality. Power quality concerns the bounds of certain parameters of anelectricity network. Operating a network outside these bounds may decrease the lifetime ofcertain devices and cause inconvenience to the connected users. The DSOs are incentivizedto keep the network within these bounds. In the Netherlands, the norm on power quality isNEN-EN 50160 [1] and according to NEN-EN 50160 the maximum allowed voltage drop is ±10%at the end user for 10 minute average values.

Reference [7] presents an optimization procedure for low voltage network planning. In thisprocedure, the power transported is limited by the rated transported power for each cable andtransformer. Furthermore, the maximum allowed voltage drop in the low voltage network is setto ±5% instead of the full range of ±10%. This is done to allow for ±5% voltage drop in themedium voltage grid, which feeds the low voltage network. This way, DSOs can guarantee thatthe total voltage drop at the connected users remains in the range of ±10% with respect to thenominal voltage.

Note from the network planning optimization procedure that the maximum current rating andthe maximum voltage drop of ±5% in the low voltage network are the most important limitingfactors for the allowed power flow. Based on these parameters the maximum power flow isdetermined and fuses are installed to prevent overloading and to disconnect a feeder in case of ashort circuit situation.

In industry, the current rating of low voltage cables is often determined using the IEC 60287standard [8]. The rated current IR according to IEC 60287 is based on the thermal aging ofthe insulation, i.e. the cable should be able to allow IR to flow for its entire economical lifetime(e.g. 40 years). DSOs prevent accelerated aging of cables by choosing a cable with an IR greaterthan the peak current of a network. Because of this conservative approach, the actual lifetime ofunderground low voltage cable is often much higher than 40 years.

Of course, voltage drop and maximum current are not the only factors at stake. Other factorsinclude the voltage unbalance, voltage dips, harmonic distortion, and flicker. Voltage unbalanceis considered in this study, the others are treated as outside the scope. Voltage unbalance isthe difference in voltage over one of the three phases in a three phase network and should beminimized. Voltage unbalance is caused by unequal loading of the phases, e.g. due to an unequaldistribution of single phase loads. The voltage unbalance factor (VUF) according to NEN-EN50160 [1] is used as a performance indictor for the unbalance and should remain below 2%according to the norm for 10 minutes average values.

Note that the older GPLK cables (outside the scope of this study) suffer from mechanical agingby repeatedly heating up and cooling down, this is less so for modern extruded cables [4].

2.1.3 Smart Reinforcement Methods

Smart reinforcement methods improve network capacity by means other than replacing cables.Some assets in the network can improve the allowed voltage drop and smart control of deviceshelps to keep the maximum current within limits.

For instance, centralized neighborhood storage can be used to limit the voltage drop caused byphotovoltaic generation or in times of large demand [9]. Another option for voltage control is toreplace transformers with on load tap changer transformers (OLTCs). These transformers arecapable of changing the voltage imposed on the feeder, often using discrete steps [7].

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Smart control of devices in a local context, e.g. using decentralized energy management, mayalso help to keep the power flow within bounds [10]. Energy management often also involvesbatteries installed in households to balance local demand and supply of electricity.

2.1.4 Loss of Lifetime Modeling

IEEE Std. C57.91 [11] presents a widely used estimation method for expected lifetime oftransformers. It assumes a single dominant aging mechanism based on the temperature of theinsulation material. The method uses the Arrhenius reaction rate theory to relate the temperatureof the transformer to expected life. Arrhenius is also used for cable lifetime assessments (e.g. in[12]).

As the temperature inside a transformer is not uniformly distributed, the temperature of theso-called hottest spot of the insulation is used. For cables, the conductor temperature is used asthe hottest spot temperature. (2.1) Presents Arrhenius reaction rate theory, in which L is theinsulation life, B an empirical constant, θHS the hottest spot temperature of the asset in K, andC the so-called life scaling parameter.

L = C eBθHS (2.1)

Parameter C is defined in (2.2), where Lnom is the nominal insulation lifetime of an asset andθHS,nom its corresponding nominal hottest spot temperature.

Lnom = C eB

θHS,nom (2.2)

In this study we consider discrete time simulation. Therefore, from this point we denote θHS(i)as the hottest spot temperature of an asset in time interval i instead of θHS . For each timeinterval a cumulative amount of asset lifetime expectancy is lost. This loss of lifetime is denotedby Llost and calculated by (2.3). In this equation, Llost is the loss of lifetime up to time intervaln in seconds, ∆t the time interval in seconds, and Faa(i) the so-called aging acceleration factorof time interval i. The latter is defined in (2.4).

Llost =n∑i=1

(Faa(i) ∆t) (2.3)

Faa(i) = eB/θHS,nom−B/θHS(i) (2.4)

Using the aging acceleration factor Faa(i) for the considered time intervals, the equivalent lossof lifetime Llost,eq can be determined. The equivalent loss of lifetime is defined as presented in(2.5), where Tsim is the total simulation time in seconds. The equivalent loss of lifetime is ameasure for how much longer or shorter the expected lifetime of the asset is with respect to thenominal asset life. For instance, an Llost,eq of 50% means that the expected lifetime is twice thenominal life.

Llost,eq =LlostTsim

· 100% (2.5)

Note that for high and medium voltage cables, the effect of electrical field stresses should beconsidered, as described in [12]. However, the effect of the field stresses is often considerednegligible for low voltage cables [13]. Therefore, we consider lifetime assessment for low voltagecables using thermal degradation only.

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2.2 Related Work

In this section, we present work related to this study. First, the broader scope of loss of lifetimemodeling is treated, namely reliability modeling. Second, studies on usage of thermal limits forcables instead of current ratings are presented. These studies are followed by an economicalevaluation of the on load tap changer transformer, one of the methods used in this work. Thesection is concluded by a decentralized energy method called Profile Steering and the DEMKittoolkit.

2.2.1 Reliability Modeling

Loss of asset lifetime is often considered in network adequacy studies concerning the reliabilityof assets. Network adequacy is based on certain performance indicators, e.g. its reliability,robustness, availability, etc. Reliability is the cumulative probability that an asset is up andrunning after a time T .

In [12], a model is presented for high voltage cables including accessories, considering thermaland electric field stresses. The model relates asset temperature and electric field to the reliabilityof the network. However, a constant value for the cable temperature and for the electric fieldis considered and therefore the model cannot be used to assess the cumulative aging effect ofdifferent loading profiles. Of course, the model can be used to assess the expected lifetime of anetwork in the planning stage under the assumption of constant values.

In [14], a reliability model for transformers is proposed considering thermal stresses, stress dueto local weather, and outages caused by overloading the current protection, i.e. the installedfuses. Also, it provides a starting point to model the cumulative aging effect the cable modelin [12] did not provide. To extend the loss of lifetime modeling approach used in this work toreliability assessments of the thermal failure mode, we refer the reader to Appendix A.

2.2.2 Thermal Limits

Previous research [15] presents an approach called electrothermal coordination for overheadlines, which uses temperature as a limit instead of current. This way, some cables can be safelyoverloaded for a short period of time using the thermal inertia of the system. This can be ofuse during maintenance on other cables, or when rerouting certain cables in case of a faultsomewhere else. The proposed method is intended for overhead lines, in which case it takesapproximately 30 minutes before a load change of 20% reaches a constant value as a response toa step change in the load profile (i.e. its steady state value).

Reference [16] uses electrothermal coordination for the Danish underground transmission grid.In this case, the thermal inertia is larger, as the heat capacity of soil is relatively high. Therefore,the cables can be overloaded for a period of several hours, compared to 30 minutes for overheadcables. This indicates that limiting the power flow by means of a constant current based onIEC 60287 is conservative for underground cables. Of course, dehydration of the soil should beprevented if temporary overloading of cables is allowed.

2.2.3 Economical Evaluation of an OLTC Transformer

Nijhuis et al. [7] show an economical evaluation of an on load tap changer distribution transformer.In a case study typical rural, sub-urban, and urban low voltage networks are considered fordifferent scenarios of the penetration of photovoltaic generation over 40 years. For the rural and

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sub-urban networks, the on load tap changer transformer allows for a lower net present value forthe investment costs for reinforcement. Overloading based on current rating only occurs in thecase of a sub-urban network in the scenario of high penetration. Note that the costs of cables inthis evaluation seem to not consider the installation costs of cables, which would make the casefor an OLTC transformer to postpone conventional grid reinforcements even stronger.

Different control strategies for the OLTC transformer are investigated in [7]. The two relevantones are control based on voltage at the output of the transformer and control based on thevoltage at the end of each low voltage feeder. The other strategies control based on measuredcurrent at the transformer. Using the first control strategy, only the voltage drop of the mediumvoltage network can be mitigated, the latter strategy allows to also compensate for the voltagedrop within the low voltage network. However, the latter requires communication between themeters and the transformer, which introduces extra costs and makes the system more vulnerableto communication faults and unauthorized control of the asset. Based on a maximum of ±5%voltage drop in the medium voltage network, the allowed voltage drop in the low voltage networkis [7]:

• ±5% without OLTC

• ±10% with OLTC, using local measurements at the transformer

• ±19% with OLTC, using measurements at the end of each feeder

2.2.4 Profile Steering

The Profile Steering heuristic developed at the University of Twente [17] is an optimizationalgorithm to steer devices such as electric vehicles, heat pumps, and batteries, that offer flexibilityin their electricity consumption to match supply and demand of energy. The method steersthe load profile of the devices such that the global objective profile is met as much as possible.Participants can be rewarded for the improvement they make to realize the objective profilebased on the Euclidian distance between the objective and realized profile.

Profile Steering was extended to support local power flow constraints [10]. However, voltageconstraints are not explicitly taken into account in the current implementation. In [18], theprofile steering approach is used to minimize loss of lifetime of a distribution transformer underhigh penetration of electric vehicles in a low voltage network. The authors show that the ProfileSteering approach is close to the optimal solution and far below the greedy charging approachnormally used to charge an electric vehicle.

2.2.5 DEMKit

DEMKit is a decentralized energy management toolkit written in Python to simulate smartgrids [19, 20]. It focuses on residential areas and micro-grids and uses a bottom-up approachby modeling individual devices. Smart control is added to each of these devices and groupcontrollers steer a group of devices towards a certain objective. Furthermore, the devices can beconnected to a model of a physical electricity network to allow for cyberphysical system (CPS)modeling. This network model supports load-flow simulations using a forward-backward sweep.In this work we extend this network model in DEMKit with thermal and loss of lifetime modelsand use it to perform simulations.

Page 16

Chapter 3

Loss of Lifetime Modeling

3.1 Introduction

This chapter presents the modeling approach for the implementation in the DEMKit toolkit.First, loss of lifetime modeling for distribution transformers is discussed, followed by loss oflifetime modeling for underground low voltage cables. Section 3.4 presents tests for these modelson the performance of the models which gives insight in the results of this study.

The general modeling approach for each asset is as follows:

1. Estimate its losses

2. Estimate its hottest temperature from the losses

3. Estimate its loss of lifetime based on the hottest spot temperature

3.2 Transformer Loss of Lifetime

This section presents an approach to model transformer loss of lifetime. Only distributiontransformers are considered, i.e. medium to low voltage transformers, with ONAN or ONAFcooling modes (natural convection or forced air cooling). First, Section 3.2.1 considers the lossesin transformers, second an overview of available thermal models is given in Section 3.2.2, followedby a detailed description of the thermal model presented in IEEE Std C57.91 Clause 7 in Section3.2.3. The section concludes with the loss of lifetime model for transformers based on the hottestspot temperature in Section 3.2.4.

3.2.1 Transformer Losses

First, we consider the losses in a transformer. These losses are input to the thermal model whichis presented in Section 3.2.2. Two types of losses manifest in distribution transformers [11]: loadlosses (or copper losses) and no-load losses (or iron losses). The load losses are the Joule lossesof the windings of the transformer and vary with the load, whereas no-load losses are caused bythe magnetic excitation of the core. The latter are considered constant as long as overexcitationdoes not occur. The losses can be estimated using (3.1), in which Ploss are the losses of thetransformer in W, PNL,R are the no-load losses at rated load in W, L is the load in VA, LR isthe rated load in VA, and PL,R are the load losses at rated load in W.

Page 17

Ploss = PNL,R +

(L

LR

)2

PL,R (3.1)

3.2.2 An Overview of Transformer Thermal Models

Here we present an overview of four thermal models for transformers. Based on this overview wechoose to use the thermal model found in Clause 7 of IEEE Std. C57.91 [11] and describe thismodel in more detail in Section 3.2.3. The goal of a thermal model for transformers is to estimatethe hottest spot temperature of the transformer based on the losses of transformer.

We present four thermal models, of which two are given in the transformer loading guide IEEEStd. C57.91-2011 [11] (in Clause 7 and Annex G respectively). The other two models arethermo-electric equivalent models (TEE). The first of these models is by Susa et al. [21] and thesecond is by Swift et al. [22]. The sections below present an overview of these models, followedby the approach considered in this work. For further reading the reader is referred to [23].

3.2.2.1 IEEE Models

The IEEE models of the IEEE Loading Guide [11] are solutions to a relatively simple linearsystem. Therefore, the required computational power is low compared to the TEE models,which contain nonlinear terms. The model presented in Annex G is said to estimate the hottestspot temperature more accurately under transient conditions [11]. However, the loading guidedoes note that the model of Annex G might not be equally valid for all transformer types.Furthermore, the model of Annex G requires parameters that are difficult to obtain such asbottom oil temperature, whereas the parameters of Clause 7 are easily obtainable from heat runtests.

In general, the IEEE models conservatively predict of the hottest spot temperature, i.e. theactual lifetime time of a transformer can be assumed higher than the predicted outcome of thesemodels [11].

3.2.2.2 TEE Models

The thermo-electric equivalent models of Susa et al. and Swift et al. are both systems of twononlinear differential equations and are similar to each other. Both models have originally beendesigned for a different class of transformers, namely power transformers, i.e. high voltage tomedium voltage transformers. The model of Swift et al. is validated for a 250MVA powertransformer in [24], which is three orders of magnitude larger than the considered distributiontransformer in this study. The model of Susa et al. is validated for power transformers, howeveralso for an ONAN distribution transformer of 2500kVA, which better resembles the distributiontransformer used in this study (only one order of magnitude higher).

The model of Swift et al. uses difference equations to solve the nonlinear differential equations.The disadvantage of this is that it requires relatively short simulation time steps for stability, atleast shorter than the time constant of the windings (which is about 5 minutes). The model ofSusa et al. requires knowledge of the bottom oil temperature, whereas the model by Swift et al.does not. The performance of the Susa et al. model is comparable to that of the IEEE Annex Gmodel [21].

Page 18

3.2.2.3 Approach

The heat run test by the supplier of the transformer used in this study was conducted accordingto IEC 60076:2. This test does not include the rating of bottom oil temperature, which isnecessary for the IEEE Annex G and of Susa et al. models presented before. Therefore, weonly consider the IEEE Clause 7 model and the model by Swift et al. as candidates for thisstudy. We present a simulation comparison between these models in Section 3.4.1. Based onthis comparison, we choose to only use the IEEE Clause 7 model in this study. The followingsection explains his model in more detail.

3.2.3 Description of the IEEE Clause 7 Model

This section shows a detailed description to the IEEE Std C57.91 Clause 7 model, referred to asIEEE Clause 7. This thermal model for transformers used the losses presented in Section 3.2.1as an input and calculates the hottest spot temperature of the transformer. The hottest spottemperature serves as an input to the transformer loss of lifetime model in Section 3.2.4.

The IEEE Clause 7 model is described in the IEEE Guide for Loading Mineral-Oil-ImmersedTransformers and Step-Voltage Regulators [11]. The model is a discrete time model and isoriginally intended for 24h load cycles. For the purpose of this work, the tap position of thedistribution transformer is assumed to be set to the default tap position. The equations andparameters presented in this section are to be found in [11].

3.2.3.1 Required Parameters

The required parameters for IEEE Clause 7 are listed in Table 3.1. Inputs for this model are theambient temperature (θA [°C]) and the losses as calculated in Section 3.2.1.

Symbol Unit DescriptionLR VA Rated load of the transformer

PNL,R W No-load losses (core) at rated loadPL,R W Load losses (windings) at rated load

∆θTO,R °C Top-oil temperature rise over ambient at rated load∆θHS|A,R °C Winding hottest spot temperature rise over ambient at rated load

Mcc kg Weight of the core and coil assemblyMT kg Weight of the tank and fittings directly in contact with the oilVoil L Volume of oil in the transformer

Table 3.1: Required Parameters for the IEEE Clause 7 Model

3.2.3.2 Model Description

Here we describe the IEEE Clause 7 model. The hottest spot temperature of a transformerdepends on the ambient temperature, the temperature rise between the oil in the top of thetransformer, and the temperature rise between the hottest spot in the windings of the coilsand the oil, as described in (3.2). In this equation θHS is the hottest spot temperature, θA isthe ambient temperature, ∆θTO is the top-oil temperature rise over ambient temperature, and∆θHS is the winding hottest spot temperature rise over top-oil temperature, all in °C.

θHS = θA + ∆θTO + ∆θHS (3.2)

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Top-Oil Temperature Rise To estimate the top-oil temperature rise ∆θTO at time step t,(3.3) is used. Parameter ∆θTO,t−1 is the top-oil temperature rise over ambient temperature forthe previous time step, ∆θTO,∞ the top-oil temperature rise that would be reached if the loadand ambient temperature would be applied for an infinite amount of time, ∆t the length of thetime step of the simulation in seconds, and τTO the oil time constant in seconds.

∆θTO,t = ∆θTO,t−1 + (∆θTO,∞ −∆θTO,t−1)

(1− e−

∆tτTO

)(3.3)

Parameter ∆θTO,∞ is estimated using (3.4), where ∆θTO,R is the rated top-oil rise, K is theratio of the transformer load to rated load, R the ratio of load loss at rated load to no-load loss,and n an empirically derived coefficient. The IEEE Loading Guide sets n equal to 0.8 for ONANand ONAF cooling modes.

∆θTO,∞ = ∆θTO,R

(K2R+ 1

R+ 1

)n(3.4)

Oil Time Constant The oil time constant τTO used in (3.3) is temperature dependent andis estimated using (3.5), where τTO,R is the oil time constant under rated conditions.

τTO = τTO,R

∆θTO,∞∆θTO,R

− ∆θTO,t−1

∆θTO,R(∆θTO,∞∆θTO,R

) 1n −

(∆θTO,t−1

∆θTO,R

) 1n

(3.5)

The oil time constant under rated conditions τTO,R is defined in (3.6), in which C is the thermalcapacity of the transformer in J/K and PT,R the total losses at rated load in W.

τTO,R =C ∆θTO,RPT,R

(3.6)

The thermal capacity C for ONAN and ONAF cooling modes is estimated using (3.7), whereMcc is the weight of the core and coil assembly in kg, MT the weight of the tank and fittingsdirectly in contact with the oil in kg, and Voil the volume of oil in L.

C = 1440 (0.1323Mcc + 0.0882MT + 0.3513Voil) (3.7)

Winding Hottest Spot Temperature Rise Finally, the winding hottest spot temperaturerise over top-oil temperature ∆θHS used in (3.2) is estimated in a similar way as the top-oil temperature rise, see (3.8). Here, ∆θHS,t−1 is the winding hottest spot rise over top-oiltemperature for the previous time step, ∆θHS,∞ is the hottest spot rise that would be reachedif the current inputs would be applied for an infinite amount of time, ∆t is the time step inseconds, and τw is the winding time constant in seconds. We set the winding time constant τw to5 minutes, which is a proper value when unknown according to the IEEE Loading Guide.

∆θHS,t = ∆θHS,t−1 + (∆θHS,∞ −∆θHS,t−1)(

1− e−∆tτw

)(3.8)

The value ∆θHS,∞ can be estimated using (3.9), in which ∆θHS,R is the hottest spot temperaturerise over top-oil at rated load, and m an empirically derived exponent equal to 0.8 for ONANand ONAF transformers according to the IEEE Loading Guide.

Page 20

∆θHS,∞ = ∆θHS,RK2m (3.9)

The hottest spot temperature at rated conditions is estimated using (3.10). In this equation∆θHS|A,R is the winding hottest spot temperature rise over ambient temperature at rated loadand ∆θTO,R the top-oil temperature rise at rated load, both in °C.

∆θHS,R = ∆θHS|A,R −∆θTO,R (3.10)

Now the hottest spot temperature rise ∆θHS and the top-oil temperature rise ∆θTO are known,their respective values are inserted in (3.2) to estimate the hottest spot temperature of thetransformer. The hottest spot temperature serves as an input to the loss of lifetime model inSection 3.2.4.

3.2.4 Transformer Loss of Lifetime

In section 3.2.1 we presented the calculation of losses in transformers, Section 3.2.3 showed amethod to calculate the hottest spot temperature based on the losses, and this section presentsthe method to calculate the equivalent loss of lifetime of the transformer based on the hottestspot temperature.

We estimate equivalent loss of lifetime Llost,eq of the transformer using the hottest spot tempera-ture and the loss of lifetime modeling approach presented in Section 2.1.4. The aging accelerationfactor Faa(i), defined in (2.4), is required for each time interval to calculate Llost,eq. For (2.4) weuse B = 15000 and θHS,nom = 383.15 K for (2.4) as recommended by the IEEE Loading Guide[11]. This finalizes the approach to model loss of lifetime of transformers based on the hottestspot temperature.

3.3 Cable Loss of Lifetime

This section presents an approach to model loss of lifetime for underground low voltage cables.First, Section 3.3.1 assesses cable losses, followed by an overview of thermal models in Section3.3.2, third we describe the IEC 60287 thermal model in Section 3.3.3 and the Olsen et al.thermal model in Section 3.3.4. Lastly loss of lifetime is treated in Section 3.3.5. Similar tothe transformer models, the cable losses are an input to the thermal models and the conductortemperature of the cable is an input to the loss of lifetime model.

The cable models introduced here consider low voltage cables with sector shaped conductors.The network of Heeten uses a V-VMvKhsas 4x95Al cable, with 4 aluminium conductors of95mm2 and a copper screen of 35mm2, and signal/support conductors of 6mm2. With respectto thermal modeling, we choose to ignore the support cables to keep the problem tractable.Furthermore, the use of support conductors is uncommon in the Netherlands for relatively newnetworks. In Heeten, the support conductors feed the public lighting (usually fed by a separatecable). Therefore, we model a 4x95Al cable without the support conductors (V-VMvKsas).Figure 3.1 shows a cross-section of this cable.

3.3.1 Cable Losses

Three types of losses may manifest in electricity cables: joule losses, dielectric losses, and screenlosses. We estimate Joule losses by means of (3.11), where subscript i denotes the conductor

Page 21

Data sheet V-VMvKsas 0,6/1kV

KON TT date: 11.01.2016 subject to technical alteration page: 1 / 1

Conductor, Al

Insulation, PVC

Inner bedding, rubber

Inner sheath

Outer bedding, rubber

Concentric conductor, Cu

Sheath, PVC, grey

Cable type Dim. V-VMvKsas 0,6/1kV

Standard - based on NEN 3616

Conductor - aluminium

Form of conductor - solid sector, shaped

Cross section, conductor mm² 4x240

Maximum permissible pulling force kN 28,8

Screen mm² 70

Insulation - PVC

Thickness of insulation, medium value mm 2,20

Inner filler - EPDM

Pitch of twist of stranded cores approx. mm 1150

Thickness of inner filler, medium value mm 1,3

Inner sheath - PVC

Thickness of inner sheath, medium value mm 1,60

Sheath - PVC

Thickness of outer sheath, medium value mm 3,00

Colour of the sheath - grey

Outer diameter, approx. mm 61,8

Minimum bend radius during installation mm 618

Weight, approx. kg/km 6400

Figure 3.1: V-VMvKsas 4x95Al Cable [25]

(ranging 1 to 4). Of conductor i, PJ,i are the Joule losses, Vdrop,i the complex voltage drop andI∗i the complex conjugate of the current. The voltage drop and current are calculated by meansof a load-flow simulation.

PJ,i = |Re (Vdrop,i · I∗i ) | (3.11)

DEMKit, the toolkit used in this work, calculates the voltage drop Vdrop,i based on a 4x4impedance matrix of the cable. This includes the effect of mutual impedances between theconductors. However, it currently does not include the effect of the increase in resistance once aconductor heats up.

Dielectric losses are caused by repolarization of the insulation dielectric because of the alternatingelectric field in the cable. According to [8], dielectric losses can be neglected below 6kV for PVCinsulation. Furthermore, current through the grounding screen of the cable introduces screenlosses. Based on parameters used in [26] we neglect these losses, because the authors of [26]estimate the effect of screen losses compared to Joule losses to be a factor of 8.12E-5. This factoris orders of magnitude below the expected accuracy of the model. Therefore, this study onlyconsiders Joule losses.

To be conservative, we use the maximum Joule losses of the different conductors in the cable tomodel the conductor temperature used to estimate loss of lifetime.

3.3.2 Cable Thermal Models

Section 3.3.1 shows the calculation of cable losses in this study, which serves as an input to thethermal model. The goal of a thermal model is to estimate the conductor temperature of thecable, such that loss of lifetime can be estimated using the approach which we present in Section3.3.5.

In this section we present an overview of thermal models for underground cables as well as achoice for the model to be used in this work. The output a thermal model is the conductortemperature. The following properties are desirable for the underground cable model:

• Dynamic, i.e. it also models high current ramping and small time intervals

Page 22

• Able to model four conductor, low voltage cables in standard conditions

• Scalable algorithms which can be incorporated in the load flow simulator of DEMKitshould result

3.3.2.1 Types of Cable Models

Different types of models are considered in literature. In industry, cable ratings are based on thesteady state or duty cycle rating of norms IEC 60287 [8] and IEC 60853 [3]. Steady state ratingsare defined as the steady state current a cable can carry before violating certain constraints(such as maximum temperature of 90°C of the conductor for XLPE cables or 45°C for the jacketof a cable to prevent soil dehydration [4]). Duty cycle ratings are intended for loads that can bedescribed by an equivalent daily duty cycle. They are used to model the effect of periodic peakloads on the cable and for planned overloading of cables. The thermal inertia of the cable is alsotaken into account for duty cycle ratings.

Dynamic models also consider the thermal inertia of a cable, sometimes including dynamicmeteorological conditions. These models work well for relatively small time steps, i.e. minutesversus hours for duty cycle models. Two types of dynamic models can be found: FiniteElement/Difference Models (FEM/FDM) and Thermo-Electric Equivalent (TEE) models. FEMand FDM are often used for nonstandard cases, for instance to model cables crossing a street.However they are computationally expensive [16, 27]. TEE models require less computationalpower, but are only valid for standard cases [16]. Below, an overview of relevant models availableis given.

3.3.2.2 Rating Models

The steady state model of IEC 60287 [8] is often used in the Netherlands to determine themaximum loading capacity of a cable and does not consider the thermal inertia of the system.Though IEC 60287 is not available to us, we found its thermal model in [26]. IEC 60853 isconsidered out of scope as the norm is not available to us and the model can not be found inother literature.

3.3.2.3 Finite Element/Difference Models

An example of a Finite Element Model can be found in [27]. Using FEM, the continuous spaceof an underlying problem is divided into smaller finite parts solved peace by peace. Tools usedfor these methods are e.g. ANSYS [27] and Comsol [16]. FEM/FDM has an advantage if anonstandard situation has to be modeled (e.g. crossing cable ducts) be it computationallyslow.

3.3.2.4 Thermo-Electric Equivalent Model

Thermo-electric equivalents (TEEs) model thermal behavior using the analogy of an electriccircuit. For instance, an electrical current source is equivalent to heat losses. In [16] a TEEmodel is constructed for an underground, single conductor, high voltage cables in close vicinityof other cables. Though our work focuses on three phase low voltage cables, an argument couldbe made that these cables can also be modeled as single phase cables, especially when sectorshaped conductors are considered. The model is a dynamic model and requires a computationally

Page 23

intensive initialization step for each cable. However, each simulation time step the algorithm isrelatively fast.

3.3.2.5 Preferred Model

We consider the TEE model by Olsen et al. [16] to be the best candidate for the undergroundcable model. It is a dynamic model and able to model underground cables in standard conditionswith relatively small computational power (compared to FEM/FDM) and can be incorporatedwith relative ease in a typical load flow simulator. One risk of using this model is the assumptionthat four conductor, three phase underground cables can be modeled as a single phase cablewithout loosing too much accuracy. For comparison, the IEC 60287 steady state model is alsoimplemented. In the following two sections these two models are explained in more detail.

3.3.3 IEC 60287 Model

This section presents a description of the IEC 60287-1-1:2006 [8] thermal model, referred to asthe IEC 60287 model. This relatively simple model estimates the temperature of a low voltagecable as if the temperature follows load changes instantly. The version of the model presentedhere neglects dielectric and screen losses.

3.3.3.1 Required Parameters

Parameters required by the IEC 60287 model are T1 (the thermal resistance between conductorand sheath), T2 (the thermal resistance between sheath and screen), T3 (the thermal resistance ofthe jacket), and T4 (the thermal resistance of the soil), all in K·m/W. Inputs are the (undisturbed)soil temperature and Joule losses per conductor.

3.3.3.2 Model Description

The IEC 60287 model is described using a single equation, presented in (3.12). In this equation,θc,i is the conductor temperature in °C for conductor i, θs the soil temperature in °C, WL,i theJoule losses per unit length of conductor i in W/m, n the number of conductors in the wire, andT1-T4 are the thermal resistances in K·m/W. Often, T2 is neglected and we therefore we set it tozero.

θc,i = θs +WL,i (T1 + n (T2 + T3 + T4)) (3.12)

The thermal resistances T2, T3, T4 are multiplied by the number of conductors in the cablebecause the area for heat conduction per conductor to the ambient is as n times smaller thanfor a single conductor cable, hence the n times larger resistances. We use the highest conductortemperature as the conductor temperature of the cable.

3.3.4 Olsen et al. Model

Here we present a description of the Olsen et al. thermal model. Opposed to the IEC 60287model presented in Section 3.3.3, the model proposed and verified by Olsen et al. in [28] considersthe time constants involved in the heating or cooling of an underground cable, whilst not addingtoo much computational complexity. Olsen et al. verified the model to operate within 2°C of a

Page 24

4868 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 4, NOVEMBER 2013

II. THERMAL MODELING OF TRANSMISSION CABLES

A. Choice of Thermal ModelThe thermal models of [1] are, as stated, concerned with over-

head lines; but as the thermal conditions of OHL and under-ground cables are very different, another thermal model is nec-essary for this study.Different methodologies for temperature calculations on ca-

bles have already been developed, where the most commonare: finite element modeling (FEM, see, e.g., [7]), finite differ-ence modeling (FDM, see, e.g., [8]), thermoelectric equivalents(TEE, see, e.g., [9]) and the step response method (e.g., [10]).It is clear from the ETC-application, that the thermal model

to be selected must be fast, since the temperature has to be cal-culated for a large number of cables, and accurate, because thereliability of the entire transmission system depends on accuraterating calculations. Based on these two requirements, the TEEmethod was chosen for thermal modeling.Compared to 2-D and, in particular, 3-D FEM simulations,

performed with commercially available FEM software, TEEscan model the dynamic thermal behavior of transmission ca-bles both with a sufficient accuracy and fast [11]. The accu-racy of TEEs was proven in [6], where the modeled temperatureof cables in a large scale experimental setup was compared tomeasurements.

B. Design of Thermal ModelThe following briefly summarizes dynamic temperature cal-

culations by TEE.1) Calculating the Thermal Parameters: TEEs utilize the re-

semblance between heat flowing in a thermal system and currentflowing in an electric system. Thus thermal resistances of mate-rials can be modeled by electric resistances, as well as thermalcapacitances can be modeled by electric capacitances. The heatgenerated in conductor, dielectric, screen, etc. is resembled bycurrent sources in the electric analogy.When modeling the heat flowing through a resistance, with a

current, the voltage drop will be equal to the temperature differ-ence on the two sides of the thermal resistance. Fig. 1 shows thesimplest case of a TEE for a directly buried cable.In the figure, the thermal parameters of each subcomponent

(conductor, insulation, metal screen, jacket and surroundingsoil) are lumped together into few components. As explained in[6] and [11], such a coarse division of the thermal parameters,as seen in Fig. 1, will result in deviations between the modeleddynamic temperature and the temperature of a cable in oper-ation where the thermal parameters are continuously spreadover the entire material. It was therefore suggested in [6] thatthe different subcomponents should be divided into multiplethermal zones. Such a division into zones is shown in Fig. 2where the insulation for illustrative purposes is divided intothree.Throughout this paper, the assumption is made that all

metal parts of the thermal network can be considered as beingisotherms. This is a valid assumption due to the high thermalconductivity of metals as compared to dielectric materials.The thermal resistances used for modeling the different sub-

components are calculated by using adapted versions of theguidelines given by IEC standard 60287-1 [12], as shown in thefollowing.

Fig. 1. Thermoelectric Equivalent, TEE, of a single phased cable withoutarmor. are joule losses in the conductor, the sum of and are thedielectric losses and are the screen losses. The ’s are the thermal capaci-tances and the ’s are the thermal resistances of the respective subcomponents.

Fig. 2. Cable design used for thermal modeling. and illustrate the outerradius of Zone 1 and 2, respectively.

The thermal resistance of zone “ ” in the insulation is calcu-lated as given in (1) and the thermal resistance of zone “ ” inthe jacket is calculated as given in (2):

(1)

where is the thermal resistivity of the dielectric mate-rial, is the radius of zone is the conductor radius andis the total number of zones in the insulation:

(2)

where is the thermal resistivity of the jacket material,is the radius of zone is the screen outer radius and is

the total number of zones in the jacket.The thermal resistance, , of zone “ ” in the surrounding

soil is calculated as given in (3):

(3)

where is the thermal resistivity of the surroundings,the burial depth, the radius of zone is the outer radius

of the cable itself), the distance from zone to the imageof the cable itself above ground, is the distance from thecable under investigation, , to cable is the distance fromcable to the image of cable above ground, is the number of

Figure 3.2: Original Olsen et al. Model for Single Core Cables, adapted from [16]4868 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 4, NOVEMBER 2013

II. THERMAL MODELING OF TRANSMISSION CABLES

A. Choice of Thermal ModelThe thermal models of [1] are, as stated, concerned with over-

head lines; but as the thermal conditions of OHL and under-ground cables are very different, another thermal model is nec-essary for this study.Different methodologies for temperature calculations on ca-

bles have already been developed, where the most commonare: finite element modeling (FEM, see, e.g., [7]), finite differ-ence modeling (FDM, see, e.g., [8]), thermoelectric equivalents(TEE, see, e.g., [9]) and the step response method (e.g., [10]).It is clear from the ETC-application, that the thermal model

to be selected must be fast, since the temperature has to be cal-culated for a large number of cables, and accurate, because thereliability of the entire transmission system depends on accuraterating calculations. Based on these two requirements, the TEEmethod was chosen for thermal modeling.Compared to 2-D and, in particular, 3-D FEM simulations,

performed with commercially available FEM software, TEEscan model the dynamic thermal behavior of transmission ca-bles both with a sufficient accuracy and fast [11]. The accu-racy of TEEs was proven in [6], where the modeled temperatureof cables in a large scale experimental setup was compared tomeasurements.

B. Design of Thermal ModelThe following briefly summarizes dynamic temperature cal-

culations by TEE.1) Calculating the Thermal Parameters: TEEs utilize the re-

semblance between heat flowing in a thermal system and currentflowing in an electric system. Thus thermal resistances of mate-rials can be modeled by electric resistances, as well as thermalcapacitances can be modeled by electric capacitances. The heatgenerated in conductor, dielectric, screen, etc. is resembled bycurrent sources in the electric analogy.When modeling the heat flowing through a resistance, with a

current, the voltage drop will be equal to the temperature differ-ence on the two sides of the thermal resistance. Fig. 1 shows thesimplest case of a TEE for a directly buried cable.In the figure, the thermal parameters of each subcomponent

(conductor, insulation, metal screen, jacket and surroundingsoil) are lumped together into few components. As explained in[6] and [11], such a coarse division of the thermal parameters,as seen in Fig. 1, will result in deviations between the modeleddynamic temperature and the temperature of a cable in oper-ation where the thermal parameters are continuously spreadover the entire material. It was therefore suggested in [6] thatthe different subcomponents should be divided into multiplethermal zones. Such a division into zones is shown in Fig. 2where the insulation for illustrative purposes is divided intothree.Throughout this paper, the assumption is made that all

metal parts of the thermal network can be considered as beingisotherms. This is a valid assumption due to the high thermalconductivity of metals as compared to dielectric materials.The thermal resistances used for modeling the different sub-

components are calculated by using adapted versions of theguidelines given by IEC standard 60287-1 [12], as shown in thefollowing.

Fig. 1. Thermoelectric Equivalent, TEE, of a single phased cable withoutarmor. are joule losses in the conductor, the sum of and are thedielectric losses and are the screen losses. The ’s are the thermal capaci-tances and the ’s are the thermal resistances of the respective subcomponents.

Fig. 2. Cable design used for thermal modeling. and illustrate the outerradius of Zone 1 and 2, respectively.

The thermal resistance of zone “ ” in the insulation is calcu-lated as given in (1) and the thermal resistance of zone “ ” inthe jacket is calculated as given in (2):

(1)

where is the thermal resistivity of the dielectric mate-rial, is the radius of zone is the conductor radius andis the total number of zones in the insulation:

(2)

where is the thermal resistivity of the jacket material,is the radius of zone is the screen outer radius and is

the total number of zones in the jacket.The thermal resistance, , of zone “ ” in the surrounding

soil is calculated as given in (3):

(3)

where is the thermal resistivity of the surroundings,the burial depth, the radius of zone is the outer radius

of the cable itself), the distance from zone to the imageof the cable itself above ground, is the distance from thecable under investigation, , to cable is the distance fromcable to the image of cable above ground, is the number of

Figure 3.3: Original Olsen et al. TEE [16]

measured cable for most of the time in a period of four months [28]. Furthermore, it was foundto deviate only 1.5°C compared to an elaborate FEM simulation in [29].

In the following sections we first present the TEE model by Olsen et al. for underground singleconductor high voltage cables in Section 3.3.4.1, followed by a modification to support fourconductor low voltage cables in Section 3.3.4.2. Furthermore, we assess the thermo-electricequivalent model of the considered low voltage cable in Section 3.3.4.3, followed by the equationsand usage of the modified Olsen et al. model for low voltage four conductor cables in Section3.3.4.4. Concluding, we present the cable parameters used in this study in Section 3.3.4.5.

3.3.4.1 Original Model

The original model of Olsen et al. considers single conductor high voltage cables as schematicallyrepresented in Figure 3.2. The figure shows the conductor, insulation (Insulating Dielectric),screen, and sheath (Jacket). Figure 3.3 shows the corresponding thermo-electric equivalent.In the TEE, T1, T3, and T4 are the insulation resistance, the jacket resistance, and the soilresistance respectively in K·m/W. Furthermore, CC is the conductor capacitance, the sum ofCd1 and Cd2 is the capacitance of the insulation, Cs is the capacitance of the screen, Cj isthe capacitance of the jacket, and Csoil is the capacitance of the soil. All capacitances are inJ/(K·m). Furthermore, Wc are the Joule losses of the conductor, the sum of Wd1 and Wd2 arethe dielectric losses, and Ws are the screen losses, in W/m.

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3.3.4.2 Modification for Four Conductor Cables

For four conductor low voltage cables we extent the original model of Olsen et al. Because theOlsen et al. model uses the circular symmetry of rings, it is preferable to design a four conductormodel using ring shaped components. To achieve this, we make a single conductor equivalent(SCE) of the four conductor cable. Figure 3.4 shows the proposed methodology to make an SCEof the four conductor cable used in this study.

In the first step we combine the four conductors to one circular conductor with its radius equalto the inner radius of the insulation. Furthermore, we model the insulation as a ring, with athickness equal to the thickness of the insulation.

In the second step we simplify the other cable components. The dark grey material in thebottom picture of Figure 3.4 is PVC, the yellow color is EPDM rubber. We simplify the innerbedding to ring 3 with the same thickness as the minimum thickness of the original bedding.Furthermore, we reduce the inner sheath, outer bedding, screen, and outer sheath to ring 4 madeof PVC with a thickness equal to the sum of the thicknesses of these parts.

Note that the conductor area of the SCE model is larger than the sum of the area of the originalfour conductors. This is not an issue as the resistance of the conductor is assumed to be zero,and the cross-sectional area (an input for the capacitance) is already known for this cable. Notethat for the insulation ring, it is probable that we underestimate the thermal resistance becausewe expect that heat conducts worse at the corners of the segment shaped conductors. This effectmay be a source of inaccuracy and is left for future work due to time constraints.

Also note that this SCE is not validated empirically. However, we compare the results of theSCE with expected values in Section 3.4.2.

3.3.4.3 Low Voltage Cable TEE

In Figure 3.5 we present the thermo-electric equivalent circuit of the SCE described in theprevious paragraph. In this TEE,Wc is the conductor loss per meter in W/m and the parametersCc, Cins, Cfill, Cscr, Csh, and Csoil are the thermal capacitances in J/(K·m) of the conductor,insulation, filler, screen, sheath and soil respectively. The thermal resistances in K·m/W of theinsulation, filler, sheath and soil are given by the parameters Tins, Tfill, Tsh, and Tsoil. Thethermal resistance of the conductor and screen is assumed to be zero as metals conduct heatorders of magnitude better than PVC and EPDM rubber. Furthermore, θc is the conductortemperature in °C.

Note that we have removed the dielectric and screen losses compared to the TEE by Olsen et al.(see Figure 3.5). The reason is that we consider these losses negligible for low voltage cables (seeSection 3.3.1).

The conductor losses per meter Wc in this TEE are defined in (3.13), where WL,i are the joulelosses of conductor i. We choose to scale the losses with the number of conductors in the cableinstead of scaling the thermal resistances and capacitances as is done by the authors of themodel of IEC 60287 (see (3.12)). The reader can verify the validity of this approach using theequations in the following paragraph. Note that the capacitance of the four conductor cablewould scale inversely with the number of conductors with respect to the single core model.

Wc = 4 · max1≤i≤4

(WL,i) (3.13)

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Conductor, Al

Insulation, PVC


Inner sheath



Sheath, PVC, grey







Screen mm² 70

Insulation - PVC


Inner filler - EPDM



Inner sheath - PVC


Sheath - PVC








Conductor, Al

Insulation, PVC


Inner sheath



Sheath, PVC, grey







Screen mm² 70

Insulation - PVC


Inner filler - EPDM



Inner sheath - PVC


Sheath - PVC






1 2 3 4 5

Figure 3.4: Cable Cross Section for Thermal Resistance Modeling

# Name Material ⇢T [Km/W] Radius [mm] T [Km/W]1 Conductor Aluminium 0 15.5 -2 Insulation PVC 5.0 17.1 0.07823 Filler EPDM 6.0 18.4 0.07004 Sheath PVC 5.0 22.1 0.14585 Soil Soil 0.75 600 0.3941

Table 3.2: Material Properties for Resistance Modeling

Part Material cT [J/(m3K)] Area [mm2] C [J/(K m)]Conductor Aluminium 2.5 · 106 4x95 950Insulation PVC 0.68 · 106 163.9 111.4Filler EPDM 2.0 · 106 145 290Screen Copper 3.45 · 106 35 120.8Sheath PVC 0.68 · 106 470.8 320.1Soil Soil 1.9 · 106 3.14 · 106 5.97 · 106

Table 3.3: Material Properties for Thermal Capacitance Modeling

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Figure 3.4: Making a Single Conductor Equivalent (SCE) of a Four Conductor Cable

Page 27

Wc Cc Cins

Tins

Cfill

Tfill

Cscr Csh

Tsh

Csoil

Tsoilθc

Figure 3.5: Low Voltage Cable TEE

W C1

T1

C2

T2

C3

T3

C4

T4θ1 θ2 θ3 θ4

Figure 3.6: Generic 4 Layer Cable TEE

3.3.4.4 Usage of the TEE

In the following section we describe the usage of the TEE for low voltage four conductor cables.Olsen et al. presents a method to solve the TEE of the original model for the conductortemperature in [16]. Based on this, we present a method to solve the TEE of the modified model.To simplify the nomenclature of the TEE, we introduce a generic 4 layer TEE in Figure 3.6.Compared to the low voltage cable TEE in Figure 3.5, parameter C1 is the sum of Cc and Cins,C3 is the sum of Cscr and Csh, W is Wc, and θ1 is θc.

For the generic 4 layer TEE, the set of differential equations is given in (3.14). The solution to theset of differential equations is given in (3.15), where for layer i, θi(t) is the temperature at timet, θi(∞) the steady-state temperature rise (see (3.16)), λi an eigenvalue of the matrix in (3.14),~vi a corresponding eigenvector, W the conductor losses, and c1, c2, c3, c4 are constants based onthe boundary conditions presented in (3.17). In (3.17), the value θi(t− 1) is the temperaturerise of layer i of the previous time interval of the simulation. Note that this approach assumesthat the matrix in (3.14) has no repeated eigenvalues.

θ′4θ′3θ′2θ′1

=

−(

1T4C4

+ 1T3C4

)1

T3C40 0

1T3C3

−(

1T3C3

+ 1T2C3

)1

T2C30

0 1T2C2

−(

1T2C2

+ 1T1C2

)1

T1C2

0 0 1T1C1

− 1T1C1

θ4

θ3

θ2

θ1

+

000WC1

(3.14)

θ4(t)θ3(t)θ2(t)θ1(t)

= c1 ~v1 · eλ1t + c2 ~v2 · eλ2t + c3 ~v3 · eλ3t + c4 ~v4 · eλ4t +

θ4(∞)θ3(∞)θ2(∞)θ1(∞)

(3.15)

θ4(∞)θ3(∞)θ2(∞)θ1(∞)

=

T4 ·W

θ4(∞) + T3 ·Wθ3(∞) + T2 ·Wθ2(∞) + T1 ·W

(3.16)

Page 28

[~v1 ~v2 ~v3 ~v4

]·

c1

c2

c3

c4

=

θ4(t− 1)θ3(t− 1)θ2(t− 1)θ1(t− 1)

−θ4(∞)θ3(∞)θ2(∞)θ1(∞)

(3.17)

The absolute temperature is obtained by adding the (modeled) undisturbed soil temperature tothe temperature rise of the first ring used in this model, as presented in (3.18).

θc(t) = θs + θ1(t) (3.18)

To assure adequate accuracy, we extent the approach by slicing the layers to multiple layersfollowing the example of Olsen et al. for the original single conductor model [16]. Olsen et al.model a cable with an insulation thickness of 20mm, a sheath of 5.9mm, and a laying depth of0.7m. Olsen et al. use ten rings to model the insulation, three for the sheath, and 100 for thesoil. This means that every 1 to 2mm in the problem is modeled as a resistance-capacitance pairfor the cable parts and once every 7mm for the soil.

For the 4x95Al cable, the insulation thickness is 1.6mm, the thickness of the filler is 1.3mm, thethickness of the sheath is 3.7mm, and the laying depth of the cable is 0.6m. We set the values ofthe number of rings to 2 for the insulation, 2 for the filler, 4 for the sheath, and 75 for the soil.We present the trade-off between accuracy and computational effort in Section 3.4.3 which weused to determine the number of rings.

3.3.4.5 Cable Parameters

This section introduces the cable parameters for the low voltage four conductor model. Notethat resistances and capacitances do not require scaling using the number of conductors, as wescale the losses with the number of conductors in (3.13).

For the resistances for the TEE of the 4x95Al cable used in this study, we use Figure 3.7 whichshows the corresponding cross-section. The materials are numbered 1 to 5, which corresponds tothe numbers used in Table 3.2. As mentioned, the aluminium conductor is modeled as a singleconductor with zero thermal resistance. We calculate the thermal resistance T of a ring using(3.19) [16], in which the subscript i denotes the ring, ri the outer radius of ring i with respect tothe center of the cable and ρT,i the thermal resistivity. The source of the thermal resistivities ρTin Table 3.2 is IEC 60287 [8]. Furthermore, we model the thermal resistance of the soil as a ringwith a radius equal to the laying depth of the cable and the thermal resistivity is assumed to be0.75 K·m/W for typical Dutch soil, as Dutch soil is often quite humid [4].

Ti =ρT,i2π

ln

(riri−1

)(3.19)

The thermal capacitances in J/(K·m) of the materials are calculated by multiplying the specificheat of the material by the cross-sectional area. For the aluminium conductor and the screenthe cross-sectional area is known, for the other parts the thermal capacitance is calculated aspresented in (3.20), in which cT,i is the specific heat of material i in J/(m3K) and r its radiuswith respect to the center of the cable in meters.

Ci = cT,i · π ·(r2i − r2

i−1

)(3.20)

Page 29

1 2 3 4 5

Figure 3.7: Cable Cross-Section of the 4x95Al SCE

# Name Material ρT [K·m/W] Radius [mm] T [K·m/W]1 Conductor Aluminium 0 15.5 -2 Insulation PVC 5.0 17.1 0.07823 Filler EPDM 6.0 18.4 0.07004 Sheath PVC 5.0 22.1 0.14585 Soil Soil 0.75 600 0.3941

Table 3.2: Material Properties for Resistance Modeling

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Part Material cT [J/(m3K)] Area [mm2] C [J/(K·m)]Conductor Aluminium 2.5 · 106 4x95 950Insulation PVC 0.68 · 106 163.9 111.4Filler EPDM 2.0 · 106 145 290Screen Copper 3.45 · 106 35 120.8Sheath PVC 0.68 · 106 470.8 320.1Soil Soil 1.9 · 106 3.14 · 106 5.97 · 106

Table 3.3: Material Properties for Thermal Capacitance Modeling

Table 3.3 lists the material properties used for thermal capacitance modeling. For the specificheat of the aluminium, copper, and the soil, we use [16], for PVC we use [30], and for EPDM weuse [31].

3.3.5 Cable Loss of Lifetime

In Section 3.3.1 we presented a calculation method of cable losses, which serves as an input tothe thermal models of IEC 60287 and Olsen et al. in Section 3.3.3 and Section 3.3.4 respectively.We use the conductor temperature based on the thermal models to estimate the loss of lifetimeof cables in this section.

The aging acceleration factor Faa(i), defined in (2.4), is required for each time interval to calculatethe equivalent loss of lifetime Llost,eq. For (2.4) we require a value for B and for θHS,nom (thelatter is the nominal conductor temperature in case of a cable). Parameter θHS,nom= 55°C forthe 4x95Al cable. Furthermore, in loss of lifetime assessments (see e.g. [12]), the parameter Bis often written as presented in (3.21), where ∆W is the activation energy of the material inJ/mol and R̄ the gas constant in J/(mol·K).

B =∆W

R̄(3.21)

In [32] a value for ∆W is measured of 73.84 kJ/mol and in [33] a value of 71.2 kJ/mol is usedfor new PVC. Based on these values we choose a value of ∆W = 72 kJ/mol. This finalizes theapproach to model loss of lifetime of cables based on the conductor temperature.

3.4 Model Testing

In this section three tests on the developed thermal models used to model transformer and cableloss of lifetime are presented. The purpose of this section give the reader some insight in theknown accuracy issues and how to interpret the results of this study. First, the IEEE Clause 7model and the transformer model by Swift et al. is compared, second the performance of thethermal models for underground cables is assessed, followed by a tradeoff between accuracy andcomputation time for the Olsen et al. cable model.

3.4.1 Transformer Model Comparison

In this section a comparison is made of the IEEE Clause 7 model and the model by Swift et al.presented in Section 3.2.2.

Figure 3.8 presents a simulation comparison for a cyclic load of 2p.u. for 4 hours and 1p.u.for 20 hours, where per unit is with respect to the rated load of the transformer. We use the

Page 31

Table 3.4: Transformer Parameters of the Comparison

Symbol Value DescriptionLR 2500 kVA Rated load of the transformer

PNL,R 16 kW No-load losses (core) at rated loadPL,R 2211 W Load losses (windings) at rated load

∆θTO,R 48 °C Top-oil temperature rise over ambient at rated load∆θHS|A,R 72.5 °C Winding hottest spot temperature rise over ambient at rated load

Mcc 2829 kg Weight of the core and coil assemblyMT 1030 kg Weight of the tank and fittings directly in contact with the oilVoil 1227 L Volume of oil in the transformer

parameters of the transformer found in [21], as presented in Table 3.4. In Figure 3.8, θHS is themodeled the hottest spot temperature and θTO the top oil temperature for the IEEE Clause 7and Swift et al. model. Figure 3.8 shows that the model of Swift et al. approaches the steadystate value quicker than the Clause 7 model, while the same time constants for the oil and thewindings have been used for both models. Note that this does not imply that the model bySwift et al. performs better, only that the response is different for the two models.

The IEEE Loading Guide [11] and Swift et al. in [22] note that there are some known accuracyissues with the estimation of the top oil temperature of the Clause 7 model. However, Swift etal. used parameter estimation to fit the model parameters to the transformer in their validation[22], which does not necessarily mean that parameters from a datasheet give accurate results aswell for the Swift et al. model. Therefore we choose to only use the IEEE Clause 7 model inthis study.

0 2 4 6 8 10 12 14 16 18 20 22 2440

60

80

100

120

140

160

Time [h]

Tempe

rature

[°C]

θHS IEEE θHS SwiftθTO IEEE θTO Swift

Figure 3.8: Simulation Comparison of IEEE Clause 7 and Swift et al. Models

3.4.2 Cable Thermal Model Performance

This section assesses the performance of the thermal models used in this study. To assureadequate accuracy of the cable thermal models, we conducted a test at rating conditions. Therating conditions should result in a nominal conductor temperature of 55°C. The rating conditionsare as follows: the current per phase is 200A, the soil resistivity 0.75 Km/W, the soil temperatureis 15°C, and the laying depth 0.6 meters. The thermal resistances presented in Table 3.2 are

Page 32

used for the IEC 60287 model (Section 3.3.3) and for the Olsen et al. single conductor equivalent(SCE) model (Section 3.3.4), which we refer to as the Olsen et al. model from this point.

For the thermal resistances of IEC 60287 in (3.12), T1 is set to the resistance of the insulation,T2 to zero, T3 to the sum of the resistances of the filler and sheath, and T4 as the resistance ofthe soil. Note that T2 to T4 are multiplied by the number of conductors, where T1 is not. This isdifferent from the Olsen et al. model, in which effectively speaking all resistances are multipliedby the number of conductors.

Model Conductor [°C] Jacket [°C]IEC 60287 49.36 36.51Olsen et al. 52.56 36.51Expected 55.00 N/A

Table 3.5: Cable Thermal Model Performance

Table 3.5 presents he resulting temperatures of the test at rating conditions. For the Olsen et al.model the steady state value is given, as defined θi(∞) in (3.16). The conductor temperatureis the maximum conductor temperature of the cable, and the jacket temperature or sheathtemperature is the temperature of the outer sheath of the cable which touches the soil.

The difference of the conductor temperature of Olsen et al. with the expected temperatureis relatively small, taking the inaccuracy into account of manual calculation of the thermalresistances based on the dimensions of cable in the datasheet. The IEC 60287 model however,has a larger deviation. This is probably caused by a correction that is required for the insulationresistance T1, as the so-called geometric factor used in [34]. Because IEC 60287 is not availableto us, we use the steady state temperature of the Olsen et al. model instead of the temperaturefrom the IEC 60287 model from this point.

When the load changes each time interval, the dynamic and steady state temperatures are oftenquite different. An example of this difference is presented in Figure 3.9. Here, the conductortemperature θc and jacket temperature θj of the Olsen et al. model are plotted for a duty cycleload of 200A for 16 hours and 0A for 4 hours under the same conditions as the test above. Notethat even at the end of the peak from t=4h to t=20h the dynamic temperature does not reachthe steady state temperature. This means that the thermal inertia of the cable and soil has apositive effect in decreasing the maximum temperature of the soil. This effect can be modeledusing the Olsen et al. model.

In this section we showed the known issues of the thermal models for cables. Furthermore,we chose to use the steady state temperatures of the Olsen et al. instead of the IEC 60287temperatures in the remainder of this study. Moreover, we showed the effect of the thermalinertia of underground cables of decreasing the maximum conductor temperature.

3.4.3 Cable Model Accuracy vs. Computation Time

This section presents a trade-off between accuracy of the Olsen et al. model and the requiredcomputation time of the model.

To determine an adequate amount of rings for the Olsen et al. model, we model a cable andvary the number of rings of the soil from 10, 25, 50, 75, 100, and 200. Only the number of ringsof the soil are varied, because the time constants (τi = TiCi) of the rings of the soil are largecompared to the time constants of the rings modeling the cable itself. It is assumed that themodel accurately models the conductor temperature for 200 rings. However, we consider thecomputation time for 200 rings too large.

Page 33

0 2 4 6 8 10 12 14 16 18 20 22 24

20

30

40

50

60

Time [h]

Tempe

rature

[°C]

θc Steady State θc Dyn. θj Steady State θj Dyn.

Figure 3.9: A Comparison of Olsen et al. Steady State and Dynamic Ratings

Rings θmax [°C] ∆θmax Comp. Time [ms] Speed Up200 43.94 0 11220 1.00100 43.76 0.18 5355 2.1075 43.64 0.30 4355 2.5850 43.37 0.57 3689 3.0425 42.41 1.53 2341 4.7910 38.69 5.25 1754 6.40

Table 3.6: Effect of the Number of Rings on the Accuracy and Computation Time

The corresponding results are presented in Figure 3.10. The colored lines indicate the conductortemperature for different number of rings. The dashed lines indicate the load profile of the cable,the maximum value is equivalent to a current of 200A. Note the effect of increasing the numberof rings and that the values for 50 rings and above are relatively close to each other.

Furthermore, Table 3.6 shows the difference in the maximum conductor temperature andcomputation time with respect to the case of 200 rings. In the table, θmax is the maximumtemperature reached in the simulation, and Speed Up the speed up factor with respect to asimulation using 200 rings. Based on these results we choose the value of 75 for the number ofrings. In this case we underestimate the maximum temperature by 0.3°C, while the computationtime is 2.58 times faster with respect to 200 rings.

In another attempt to speed up the Olsen et al. model, we tried difference equations to solvethe system of differential equations. The fastest implementation however was twice as slow asthe approach used by Olsen et al.

3.5 Conclusion

In this chapter we introduced loss of lifetime models for distribution transformers and lowvoltage underground cables. For both assets, we used the heat losses to model the hottest spottemperature and used the hottest spot temperature to estimate the loss of lifetime.

Page 34

0 2 4 6 8 10 12 14 16 18 20 22 24

20

30

40

Time [h]

Tempe

rature

[°C]

20010075502510

40

60

80

100

120

140

Powe

r[k

VA

]

Figure 3.10: The effect of increasing the number of rings for Olsen et al. (dashed line denotesthe load profile of the cable in kVA)

We chose to use the thermal model of IEEE Std. C57.91 Clause 7 [11] for transformers andshowed an overview of alternatives for the thermal model of a transformer. Furthermore, wepresented the cable thermal model of IEC 60287 [8] and modified the Olsen et al. model [16] tomodel four conductor cables instead of single conductor cables. Furthermore, we presented knownissues for the Olsen et al. and IEC 60287 models in Section 3.4.2 and made a trade-off betweenaccuracy and required computation time for the Olsen et al. model in Section 3.4.3.

Page 35

Page 36

Chapter 4

Simulations

This chapter presents the simulation results of this study. The effect of smart reinforcementmethods on the loss of lifetime of cables and distribution transformers is simulated using casestudies for the network of neighborhood the Veldegge in Heeten. The following cases areconsidered:

• The current state of the network compared to the state as envisioned in the GridFlexHeeten project (Section 4.2.1)

• Pushing the network to its limits (Section 4.2.2)

• A comparison between smart reinforcement options and cable reinforcement (Section 4.2.3)

First, the methodology for the simulations is assessed in Section 4.1, followed by the simulationresults for each of the cases. The chapter is concluded in Section 4.3.

The considered network of Heeten has three feeders, connecting 47 households in total using onetransformer. The network is relatively new and is installed in 2010. The transformer is ratedat 250kVA and is originally manufactured in 1984. The cables are 4x95Al and each feeder isprotected by a 125A-gG fuse (i.e. a slow type fuse).

The feeders supply power to 24, 22, and 1 house(s) respectively. The feeder supplying a singlehousehold is neglected in this work as one household will not have a significant effect on the lossof lifetime of the feeder and a minor impact on the loss of lifetime of the transformer.

4.1 Method

This section presents the method used for this study. In Section 4.1.1 we present the input dataand parameters used in the simulations and in Section 4.1.2 we show the simulation settingsused in DEMKit.

4.1.1 Data and Parameters

This study uses DEMKit to perform load-flow analysis and to model loss of lifetime of the assets.In this section the used parameters and data for DEMKit are presented. Demand profiles, sizesof PV systems, and electric vehicle arrival times, departure times, and energy requirements aregenerated by the Artificial Load Profile Generator (ALPG) developed at the University of Twente[35]. The ALPG generates demand profiles based on modeled activities of occupants.

Page 37

Table 4.1: Transformer Parameters for the IEEE Clause 7 Model

Symbol Value DescriptionLR 250 kVA Rated load of the transformer

PNL,R 238 W No-load losses (core) at rated loadPL,R 2213 W Load losses (windings) at rated load

∆θTO,R 40.26 °C Top-oil temperature rise over ambient at rated load∆θHS|A,R 56.11 °C Winding hottest spot temperature rise over ambient at rated load

Mcc 787 kg Weight of the core and coil assemblyMT 103 kg Weight of the tank and fittings directly in contact with the oilVoil 203 L Volume of oil in the transformer

• The following input parameters have been used for the occupants in the ALPG. Of thehouseholds, 18 are dual worker families without children who work full-time, 3 are retiredfamilies of two people, 7 households are dual worker families who both work full-time andhave children, and 18 households are single worker families who work full-time and havechildren. Activities are chosen from a normal distribution. The probability of a familyouting is between 10 and 20% per day. The probability of a person having an activityoutside the neighborhood is between 20-30% per day for both weekdays and weekends.

• The photovoltaic systems are dimensioned in such a way that the PV production isenough to fulfill the yearly energy consumption of the currently installed appliances in thehousehold (i.e. excluding electric vehicles and heat pumps). We assume PV panels with anarea of 1.65m2, an STC (standard test conditions) rated peak power of 300Wp, and that asystem of 1kWp on average results in a yearly yield of 875kWh. Using these assumptions,the average installed peak power is 4.1kWp or roughly 14 panels for a household with aPV installation. PV production profiles are based on data from DSO Régie de Wavre [36].

• In this study we assume all electric vehicles to be charged using a single phase chargingstation. The maximum single phase load we expect from charging stations depends on thegrid connection of the household. In the network of Heeten 35% of the connections is 1x40A(single phase) and 65% of the connections is 3x25A (three phase). The maximum load forthe 1x40A connection is 5750W (i.e. 25A, single phase) and the maximum load for the3x25A connection is 3680W (i.e. 16A, single phase). Electricians use these values to assureselectivity of the protection fuses in a household in case of a short circuit. Furthermore, theelectric vehicles are assumed to drive a distance chosen from a Gaussian distribution witha mean of 25km and a standard deviation of 10km. The driving distances are transformedto a required charge using 1kWh per 5km on average. Some variance is included, includingseasonal effects on the efficiency of the battery, see [20].

• Heat pumps in the simulation have a coefficient of performance (CoP) of 4.5, a maximumcharging rate of 16A single phase (3680W), and have a buffer with a capacity of 10kWhthermal. The profiles of the Flex Street use case are used for the heat demand of thehouseholds [37].

• Batteries have a capacity of 5kWh and their charge and discharge rate is assumed to belimited to the inverter connected to the battery. Therefore, a charge and discharge rate of16A single phase is used.

• As the transformer is manufactured in 1984 and its parameters were not available, pa-rameters of a similar transformer by the same manufacturer have been used. These aresummarized in Table 4.1, see Section 3.2.3 for more information.

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4.1.2 Simulation Settings

All houses are connected as if they would have a single phase connection, and the phases areevenly distributed over the houses. Power quality constraints according to NEN-EN on thevoltage use 10 minute averaged values [1], therefore we use a simulation time step of 10 minutes.The length of the simulation is one year.

If we use devices with a given penetration level in the simulations, the devices are randomlydistributed over the households. We assure reproducibility of the results using a given randomseed to the (pseudo)random number generator in DEMKit. Note that this means that only theexact case is reproducible and that if e.g. a house receives a photovoltaic system for a penetrationlevel of 10%, this does not necessarily mean the same house also receives a photovoltaic systemfor a penetration level of 20%. The penetration levels of photovoltaic systems, electric vehicles,heat pumps, and batteries can be varied.

In some cases we use Profile Steering to control devices, see Section 2.2.4. In the context of thiswork we consider single commodity Profile Steering without power limits. This means that theDEM approach does not actively control phase balance and is not aware of power limits of thenetwork. Furthermore, perfect predictions are used to predict e.g. photovoltaic production andelectric vehicle arrival times. The objective profile for Profile Steering is a zero profile, such thatPS flattens the load profile given the available flexibility.

4.2 Cases

In this section we show the results of the simulations. In Section 4.2.1 the current state of thenetwork is simulated and compared to the envisioned state of the pilot of the GridFlex Heetenproject. In Section 4.2.2 the network is pushed to its limit by increasing the penetration ofphotovoltaic systems, electric vehicles, and heat pumps. In Section 4.2.3 smart reinforcement iscompared with cable reinforcement for a case that requires up to twice the current capacity ofthe network.

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Table 4.2: Additional simulation results Heeten current state vs. pilot

Current State Pilot StateLc,steady 3.85% 3.79%

Lc,dyn 3.83% 3.78%θj,steady 21.74 °C 19.36 °Cθj,dyn 19.33 °C 17.24 °CθHS,t 39.68 °C 39.27 °C

Lt 1.50·10−5 1.44·10−5

4.2.1 Heeten Current State versus Pilot

The current state of the network in Heeten is simulated and compared to the state as envisionedin the pilot. Roughly 33% of the houses have installed photovoltaic systems in this network. Inthe GridFlex pilot, electrical energy is shared and used locally as much as possible. To achievethis, 24 houses get a battery with a capacity of 5kWh. The batteries in the simulation arecontrolled using the Profile Steering approach.

Figure 4.1 shows box plots of the simulation results. The 1% percentiles P1 and P99, 5%percentiles P5 and P95, and median P50 are shown. Furthermore, the minimum and maximumvalues are presented by the disconnected marks in each of the figures. For the voltage, voltageunbalance factor (VUF), current, and temperatures the values are presented for the worst casenode or cable segment in the network for a 10 minute average value. The conductor temperaturesteady state is the estimated temperature using the steady state thermal model for cables, and theconductor temperature dynamic uses the model by Olsen et al. for cables (for more information,see Section 3.3.2 and 3.4.3). The slack bus power is the total power transported to/from thenetwork. The dashed line in Figure 4.1a indicates the -5% threshold for the voltage.

Figure 4.1a shows that the network is primarily limited by the minimum voltage. As argued inSection 2.1.2, the voltage drop allowed in the planning process of the network is assumed tobe ±5% (i.e. 218.5V for the minimum voltage). Though the minimum mark of the minimumvoltage exceeds the threshold, the limit is only violated 2 times in the simulated year in thecurrent state. No other thresholds are violated. The state as envisioned in the pilot performsbetter regarding slack bus power. The median is slightly shifted to the right and the maximumand minimum power is decreased by approximately one third. Furthermore, the distribution ofthe maximum phase current is shifted to the left, however, the maximum value is still relativelyhigh. There is no large difference in the conductor temperature.

Table 4.2 shows additional simulation results for this case. Lc, Lt are the equivalent lossof lifetime of cables and transformer respectively, θj and θHS,t the maximum jacket and themaximum transformer hottest spot temperature respectively, and subscripts steady and dynindicate usage of steady state or dynamic thermal models. The equivalent loss of lifetime of thecables is approximately 3.8% for both cases. This means that theoretically, the mean time tofailure of the cables in this network is about 26 times larger than the economical lifetime of thecables considering thermal degradation. This value can be expected if the network is planned tosupport a maximum current according to IEC 60287 (see Section 2.1.2).

The maximum temperature of the jacket stays well below 45 °C, a threshold to limit soildehydration (see Section 3.3.2.1). Furthermore, the 250kVA transformer is only loaded lightly.The maximum temperature is well below 110 °C, the temperature the transformer could sustainfor its entire economical lifetime. This makes the effect of thermal loss of lifetime of thetransformer negligible.

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Figure 4.1: Simulation results Heeten current state (C) vs. pilot (P)

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Table 4.3: Additional simulation results increasing the photovoltaic penetration level

PV 0% 33% 100% 150% 200%Lc,steady 3.86% 3.85% 4.04% 4.54% 5.79%

Lc,dyn 3.83% 3.83% 4.00% 4.41% 5.27%θj,steady 19.70 °C 19.70 °C 20.19 °C 25.12 °C 31.93 °Cθj,dyn 17.63 °C 17.61 °C 18.73 °C 21.51 °C 25.57 °CθHS,t 39.52 °C 39.68 °C 47.64 °C 58.52 °C 72.43 °C

Lt 1.53·10−5 1.50·10−5 2.27·10−5 5.37·10−5 2.21·10−4

4.2.2 Pushing the Network to its Limit

In this section we push the network of Heeten to its limit by increasing the number of photovoltaicsystems, electric vehicles, and heat pumps independently. All of these are incremented in separatecases, such that the effect of a certain technology on the network can be assessed. First, weincrease the penetration of photovoltaic systems, second the electric vehicle penetration, followedby a case increasing the heat pump penetration.

4.2.2.1 Increasing the Photovoltaic Penetration

The photovoltaic penetration level is increased with the following steps: 0%, 33%, 100%, 150%,and 200%. 33% is the current state of the network, 100% is the case in which all houses have PVsystems installed large enough to compensate their current yearly demand. The cases 150% and200% are included to assess the case of overproduction and the possibility of future householdsalso compensating the yearly consumption of e.g. a heat pump or electric vehicle. For example,200% would generate twice the yearly amount of energy as demanded in the current situation.In terms of installed photovoltaic capacity, the range is approximately 0, 52 kWp, 189 kWp,284 kWp, and 379 kWp respectively. Note that the latter two are rather unrealistic extremesfor a neighborhood with the current technology (it probably will not fit on the rooftops) andlegislation.

Figure 4.2 shows the simulation results. Note that the 100% case is not expected to resultin any grid violations. The 150% case does exceed the +5% voltage threshold in 18 intervals.The 200% case exceeds this threshold in 2638 intervals. Furthermore, it is interesting to notethat the voltage unbalance nearly does not vary for increasing PV penetration. However, itshould be noted that, except for the 33% case, the systems are always evenly distributed overthe phases. Considering the maximum phase current, the network does exceed the currentlyinstalled 125A feeder fuse for the cases 150% and 200%, indicated by the dashed line. However,the expected conductor temperature remains below 40 °C for all of the cases, as shown by thedynamic conductor temperature. Note that the minimum slack bus power does drop significantlyand even though this is not an issue in this network, this effect may become an issue in anearlier stage in other networks. Note that we do not show the minimum voltage, as the minimumvoltage is already shown in Section 4.2.1.

In terms of loss of lifetime, the cables and transformers are only loaded lightly, see Table 4.3.The loss of lifetime for cables is 5.27% and for the transformer it is negligible. Note that forincreasing cable loss of lifetime, the difference in steady state and dynamic thermal modelsslightly manifests. Soil dehydration is not an issue for these cases, having a maximum value forthe jacket temperature of 21.51 °C.

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Figure 4.2: Simulation results increasing the photovoltaic penetration level

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Table 4.4: Additional simulation results increasing the electric vehicle penetration level

EV 0% 10% 20% 35% 50% 75% 100%Lc,steady 3.86% 4.21% 4.33% 4.92% 6.95% 15.51% 18.05%

Lc,dyn 3.83% 4.16% 4.27% 4.76% 6.22% 11.05% 12.73%θj,steady 19.70 °C 22.84 °C 22.83 °C 24.82 °C 32.03 °C 43.82 °C 44.04 °Cθj,dyn 17.63 °C 18.79 °C 18.89 °C 19.88 °C 23.25 °C 28.67 °C 29.51 °CθHS,t 39.52 °C 39.53 °C 39.53 °C 39.54 °C 44.71 °C 55.46 °C 68.18 °C

Lt 1.53·10−5 1.65·10−5 1.75·10−5 2.17·10−5 3.25·10−5 9.11·10−5 4.25·10−4

4.2.2.2 Increasing the Electric Vehicle Penetration

The electric vehicle penetration level is increased with the following steps: 0%, 10%, 20%, 35%,50%, 75%, and 100%. In the 100% case each house has one electric vehicle. Note that in anextreme future scenario, the actual penetration level may exceed the 100% case if multiplevehicles would be owned per household. We did not simulate this scenario however.

Figure 4.3 shows the simulation results. The dashed lines in the minimum voltage plot indicatethe -5% threshold and -10% threshold (218.5V and 207V respectively). Note that for 10% EVpenetration, the -5% threshold is already violated for 95% of the intervals, while 10% penetrationwould be 4 or 5 electric vehicles in this network of 46 houses. Also note that for penetrations50% and higher, the -10% threshold is also violated. It can also be seen that the voltageunbalance increases significantly with the amount of electric vehicles, approaching the powerquality threshold of 2% [1] for higher penetrations. The minimum voltage is further decreaseddue the voltage unbalance. For instance, the 1% and 5% percentiles of the minimum voltageare lower for the 75% than the 100% case and the distribution of the voltage unbalance isshifted more to the right for the 75% case. This can be explained by a better balance when eachhousehold has an electric vehicle. This effect counterintuitively decreases the number of -10%voltage violations from 656 to 282 for the 75% and 100% cases respectively.

The two dashed lines in the maximum phase current plot indicate the feeder fuse thresholdof 125A and the IEC 60287 steady state current rating of 200A of the cable (using thermalresistivity of soil 0.75 K·m/W and soil temperature 15 °C). It can be seen that for penetrations35% and higher the fuse threshold is violated and the IEC 60287 threshold for penetrations 75%and 100%, while the conductor temperature remains well below 50 °C. Note that for this casethe difference between steady state and dynamic thermal models clearly manifests. While thesteady state approach predicts thermal violations, the dynamic model shows that the conductortemperature remains below 50 °C even for 100% EV penetration, because of the high thermalcapacity of the system. The dashed line in the temperature plots is the 55 °C value a cablecould sustain for its entire economical lifetime.

Table 4.4 presents the additional simulation results. The equivalent loss of lifetime of the cablefor 100% EV penetration is 12.73% using the dynamic model, which would imply that the meantime to failure of the cables is approximately 8 times the economical lifetime. The steady statethermal model would give a loss of lifetime of 18.05%. Furthermore, it can be seen that therisk of soil dehydration is low, with a maximum jacket temperature of 29.51 °C. Note that themaximum steady state jacket temperature is very close to 45 °C, which could be interpretedas a risk if only steady state temperatures would be considered. The effect of the load on thetransformer loss of lifetime remains insignificantly small.

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Figure 4.3: Simulation results increasing the electric vehicle penetration level

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Table 4.5: Additional simulation results increasing the heat pump penetration level

HP 0% 10% 20% 35% 50% 75% 100%Lc,steady 3.86% 3.87% 3.88% 3.90% 3.94% 3.99% 4.02%

Lc,dyn 3.83% 3.84% 3.86% 3.87% 3.91% 3.95% 3.97%θj,steady 19.70 °C 19.70 °C 19.70 °C 20.16 °C 20.32 °C 20.32 °C 20.36 °Cθj,dyn 17.63 °C 17.63 °C 17.64 °C 17.70 °C 17.72 °C 17.76 °C 17.81 °CθHS,t 39.52 °C 39.53 °C 39.53 °C 39.53 °C 39.54 °C 39.55 °C 39.55 °C

Lt 1.53·10−5 1.54·10−5 1.54·10−5 1.55·10−5 1.57·10−5 1.59·10−5 1.62·10−5

4.2.2.3 Increasing the Heat Pump Penetration

The heat pump penetration level is increased with the following steps: 0%, 10%, 20%, 35%,50%, 75%, and 100%. Figure 4.4 shows the simulation results. It can be seen that no violationsoccur except for voltage violations. The number of -5% voltage violations increases from 4 to 56intervals for 10% and 100% penetration respectively. The maximum voltage unbalance increasesfrom 0.8% to 1.0%. Furthermore, the maximum phase current increases by 30A, however, it isstill below the 125A feeder fuse threshold. The temperature of the conductor remains below20°C.

Table 4.5 presents the additional simulation results. It can be seen that the effect of the heatpump for the loss of lifetime of cables the heat pumps is relatively small. The jacket temperatureincreases by approximately 5°C when the penetration is increased from 0% to 100%. The loss oflifetime of the transformer is considered negligible for all heat pump penetrations.

4.2.3 Smart Reinforcement versus Cable Reinforcement

In this case study, smart reinforcement options are compared with cable reinforcement. Asmentioned in Section 1.4, perfect control is assumed for the smart reinforcement methods.Centralized neighborhood storage and online tap changer transformers are assumed to perfectlycontrol the voltage level for both feeders such that a voltage drop of ±19% can be tolerated (seeSection 2.2.3 for the motivation).

From the previous cases it can be seen that increasing the penetration of electric vehicles posesthe biggest challenge in the network of Heeten. Therefore, the case of 50% EV penetration and100% penetration are used in this comparison. First, the voltage control reinforcement options(i.e. online tap changer transformers and centralized neighborhood storage) are assessed. Second,the effect of decentralized energy management using Profile Steering is considered. Two methodsare assessed: DEM using the flexibility of the electric vehicles only and using DEM and addinga battery of 5kWh to each household for extra flexibility.

Two cable sizes are used for the cable reinforcement options, 4x150Al and 4x240Al (4x150mm2

and 4x240mm2 aluminium conductors respectively). The conductor temperature and cable lossof lifetime for the 4x150Al and 4x240Al cable are not modeled in this case study due to timeconstraints and the fact that for each different cable a separate model with proper thermalresistances and capacitances would have to be made. Furthermore, it has already been shownthat cable loss of lifetime is not an issue for 4x95Al cables, therefore it would also not be anissue for cables with smaller electrical resistance under the same conditions.

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Figure 4.4: Simulation results increasing the heat pump penetration level

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4.2.3.1 Voltage Control versus Cable Reinforcement

To verify whether voltage control is a valid option for reinforcement, at least the followingconditions must all be met after simulation:

1. The voltage drop does not exceed ±19% (see Section 2.2.3)

2. The equivalent loss of lifetime of the cable does not exceed 100%

3. The risk of soil dehydration is not substantial

Note that usually, the loss of lifetime or the power rating of the transformer should also beconsidered, however it is already shown that both parameters do not form an issue for 50%nor 100% EV penetration in this network. Furthermore, a transformer upgrade is relativelyaffordable in comparison with cable reinforcement.

The top three entries of Figure 4.5 show the simulation results for the 50% EV penetrationcase. The top three entries are simulated using three cable sizes, 4x95Al (original), 4x150Al,and 4x240Al. The dashed lines in the minimum voltage plot are the -5% and -10% voltagethresholds. The -19% threshold is not visible, as its value of 186.3V is off the chart. In themaximum current plot, the original fuse rating of 125A and IEC 60287 rating of 200A of the4x95Al cable are displayed using dashed lines.

It can be seen that the minimum voltage does not exceed -19%, however it does violate the -10%threshold for 50 intervals for 4x95Al cables. Referring to Section 2.2.3, this would imply thatan online tap changer transformer can be used if additional voltage measurement devices areinstalled at the end of the feeders.

As observed in the case presented in Section 4.2.2.2 the cable loss of lifetime and risk of soildehydration are no issues for 50% EV penetration, so condition 2 and 3 are also met. Thismeans that for the case of 50% EV penetration, an online tap changer transformer or centralizedneighborhood storage are both valid options to increase the network capacity without replacingthe 4x95Al cables. Note that the feeder fuses should also be replaced to at least allow a currentof 200A.

Figure 4.5a shows that increasing the cable size to 4x150Al or 4x240Al does not completelyeliminate the -5% voltage violations (4572 and 474 violations respectively). The -10% voltageviolations are completely eliminated however. So, an argument could be made that in this case,the current options for cable reinforcement are not sufficient to support 50% EV penetration inthis network. This would mean the low voltage network should either be redesigned or voltagecontrol should be applied to mitigate voltage violations.

Figure 4.6 show the simulation results of the 100% EV penetration case. Note that condition 1,the -19% voltage condition, is met. The number of voltage violations for 4x150Al and 4x240Alare 15952 and 730 respectively. Furthermore, the cable loss of lifetime and risk of soil dehydrationare already shown to be no issue in Section 4.2.2.2 and therefore conditions 2 and 3 are alsomet. Therefore, voltage control is a valid option for smart reinforcement for the 100% EVcase. However, the current exceeds the IEC 60287 rating of the 4x95Al cable, which requirestemporary overloading of the cables to be allowed by the DSO.

4.2.3.2 Decentralized Energy Management versus Cable Reinforcement

As mentioned, another smart reinforcement approach is power control. In this case a DecentralizedEnergy Management (DEM) approach is considered with and without local storage in thehouseholds and is compared to cable reinforcement. At least the following conditions should bemet after simulation for the DEM approach to be a valid reinforcement option:

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Figure 4.5: 50% EV penetration simulation results DEM vs. cable reinforcement

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1. The voltage drop does not exceed ±5% (see Section 2.2.3)

2. The equivalent loss of lifetime of the cable does not exceed 100%

3. The risk of soil dehydration is not substantial

Figure 4.5 shows the simulation results of the 50% EV penetration case. DEM indicatesthe approach without local storage and DEM+B the approach with batteries installed inevery household. It can be seen that the voltage condition of -5% is not met for either cablereinforcement nor for the DEM approach. This means that DEM is not a valid alternative forcable reinforcement in this case. What is interesting to note is that considering the minimumvoltage, smart charging the electric vehicles has the same effect as an upgrade from 4x95Al to4x150Al.

The effect of the DEM approaches is primarily visible in the maximum current and slack buspower. While cable reinforcement only decreases the losses of the cables, the DEM approachreduces the maximum current by 50A for the case without batteries and approximately 70A forthe case with batteries. The slack bus power is reduced by approximately 25kVA and 50kVArespectively for DEM without and including batteries.

Figure 4.6 shows the simulation results of the 100% EV case. The DEM approach performsslightly better than an upgrade from 4x95Al to 4x150Al considering the minimum voltage.Furthermore, the reduction of voltage unbalance is similar for DEM reinforcement and cablereinforcement to 4x150Al. The maximum current is reduced by 36A for DEM without batteriesand 62A for DEM with batteries. The slack bus power is reduced by approximately 60kVA and80kVA respectively for DEM without and including batteries.

4.3 Conclusion

In this chapter the simulation results of this study were presented. Case studies were simulatedin DEMKit of the current state of the network of Heeten and the envisioned pilot state of theGridFlex Heeten project. Furthermore the network we pushed to its limits by increasing thepenetration of photovoltaic systems, electric vehicles, and heat pumps. Lastly, a comparisonstudy of smart reinforcement and cable reinforcement methods is conducted. It was shown thatfor the network of Heeten, the minimum voltage is the limiting factor.

Furthermore, we found the expected cable lifetime to be higher than the economical life. Evenin the most extreme case the expected cable lifetime was 8 times greater than the economicallife, compared to 26 times in the current state. We found the transformer loss of lifetime to benegligible for this low voltage network for all case studies. Also, the risk of soil dehydration wasvery small for even the most extreme case.

The contribution to the GridFlex Heeten pilot can be found in the reduction of the minimum andmaximum power transported to/from the network and the maximum current in the network. Noimprovement in voltage and negligible improvement in cable loss of lifetime is observed.

A penetration of 100% for photovoltaic systems can be supported by the current low voltagenetwork. Electric vehicles cause the greatest issues and the introduction of only 4-5 electricvehicles would require reinforcement of the network. For higher penetrations of electric vehicles,serious upgrades are required and 4x240Al cables may not result in a sufficient solution. Voltagecontrol using online tap changer transformers or centralized neighborhood storage seems to bethe best option to cope with this issue, especially if temporary overloading of cables is allowed.Heat pumps seem to form less of an issue compared to electric vehicles.

Furthermore, decentralized energy management (DEM) including and excluding local storage

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has been investigated. Though the voltage improved, it was not enough to mitigate all voltageviolations such that DEM could be used as an alternative for cable reinforcement in the consideredlow voltage network.

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Chapter 5

Conclusion and Discussion

5.1 Conclusion

In this study alternatives to cable reinforcement of low voltage networks have been assessed tosupport the energy transition in an affordable and sustainable matter. The problem statement isto assess the effect of these smart reinforcement options on the expected asset lifetime of cablesand transformers.

The identified smart reinforcement options are online tap changer transformers (OLTCs),centralized neighborhood storage, and decentralized energy management (DEM). Loss of lifetimeof cables is modeled using IEC 60287 and a dynamic thermal model. Loss of lifetime fortransformers is modeled using the model of IEEE Std. C57.91 (Clause 7).

Case studies have been simulated to assess the current state of a network in Heeten. The networkwas also pushed to its limit by increasing penetrations of photovoltaic systems, electric vehicles,and heat pumps. Furthermore, the effectiveness of the identified smart reinforcement methodsto postpone cable reinforcement was assessed.

We showed that for the network of Heeten the minimum voltage is the biggest limitation ofthe amount of power the network could transport. Furthermore, we saw that large penetrationlevels of electric vehicles introduced problems even the biggest cable size currently availablecannot solve. Large penetrations of photovoltaic systems and heat pumps seem to form less of anissue in the considered network. The problem observed for large penetrations of electric vehiclescan be solved using an OLTC or centralized neighborhood storage, especially if temporaryoverloading of cables is allowed. Decentralized energy management primarily contributes to thereduction of maximum power and current transported through the network and less to decreasevoltage violations and is therefore not considered as a valid alternative to reinforce the networkof Heeten.

Concluding, smart reinforcement using e.g. an online tap changer transformer is a properalternative for cable reinforcement in neighborhood the Veldegge in Heeten and may evenoutperform conventional reinforcement while saving on costs, materials, and labor.

5.2 Discussion

The original problem statement of this work is different from the current focus. The originalproblem was to make a reliability model for assets in the low voltage network with a load profileas an input to assess the effect of decentralized energy management on the reliability of thenetwork. An important assumption was that reliability of the assets in a low voltage network is

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mostly determined by thermal aging of the components. However, we realized that low voltagenetworks are operated far below the thermal limits of the assets and that this assumption doesnot hold. The validity of this realization manifests in the results presented in this work, namelythat the equivalent loss of lifetime of a current network is 4% of the economical life. Thatmotivates the shift in focus to the effect of smart reinforcement on the loss of lifetime of cablesand transformers. The originally envisioned approach to model the reliability of low voltageconsidering the thermal failure mode is presented in Appendix A.

At the start of this study the norms IEC 60287 and IEC 60853 were not available to us andtheir relevance to this work was not well understood. We assumed it to be feasible to find theapproach of IEC 60287 in previous research. At some point we thought we had achieved this,however tests documented in Section 3.4.2 showed that the deviation from the expected resultswas too high. Probably this issue is caused by a misinterpretation of the thermal resistance ofthe insulation of section shaped cables, which may be compensated for in IEC 60287 using ageometric factor. However, using the steady state values of the single core equivalent model afairly accurate estimation could be made of the conductor temperature as a replacement to theIEC 60287 model. Furthermore, at the earlier stages of this study it was not well understood thatthe model in IEC 60853 could be used as a dynamic model as well. Using IEC 60853 could haveprevented the design of the single core equivalent of the Olsen et al. model. Furthermore, IEC60853 is validated extensively and used in industry to model the effect of temporary overloading,which would have made a comparison study of the single core equivalent and IEC 60853 modelinteresting to pursue.

According to NEN-EN 50160 [1] the minimum voltage at the end user is allowed to be -15% withrespect to the nominal voltage to cope with temporary events such as blackout or maintenancein another part of the network. Therefore, it is assumed that the extra 5% slack in minimumvoltage cannot be used in the network planning phase and is therefore not mentioned in thisstudy. However, it is imaginable that DSOs also use this to allow a very small number ofminimum voltage violations in the network planning phase. This would mean that the networkwould be able to transport more power before reinforcement would be required. The minimumvoltage may only be in the -10% to -15% range for 5% of the 10 minute average intervals in oneweek.

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Chapter 6

Recommendations

For future research, the thermal cable models could improve using IEC 60287, using its approachto model sector shaped conductor cables. Furthermore, a comparison of the cable thermalmodels using IEC 60853 would be interesting. Moreover, this work is a case study of the networkof Heeten. For future work stochastic load-flow analysis for multiple low voltage networks andpenetrations of new technology, demand profiles, and phase distribution is recommended. Thisway, the findings in this work can either be disproved or guaranteed to be valid for other networksas well.

Regarding Profile Steering, this study used single commodity Profile Steering with perfectpredictions and without limits. The results for this case study could increase by switchingto three commodities for the phases to reduce unbalance. Furthermore, the results could bemore realistic if predictions would be used instead of perfect knowledge of future demand andproduction. For instance, using the approach in [38] for electric vehicles. This reference showsthat the results with and without predictions may be similar. The current Profile Steeringlimits consider the current through a phase of the feeder, while in this work preventing voltageviolations is the real challenge. The implementation of voltage limits would be interesting ifProfile Steering is used to postpone grid reinforcements in low voltage networks. Combined withmulticommodity Profile Steering and knowledge of the phase distribution, Profile Steering maybecome a valid alternative for cable reinforcement. Another interesting issue to attend is toguarantee power quality in Profile Steering if all new technologies that offer flexibility (electricvehicles, heat pumps, and batteries) in a neighborhood would be controlled using Profile Steering.Voltage unbalance may also be decreased if controlled devices of the same type would be steeredto match their load profiles more.

For DSOs it may be interesting to explore the possibilities of thermal limits in low voltagenetworks, for instance by limiting the 95 percentile of the IEC 60287 jacket temperature to 45 °Cto increase the current rating of a feeder. Of course, the risk of soil dehydration and acceleratedthermal aging of the cables should be well understood if such an approach is to be applied innetwork planning. Expertise in temporary overloading of underground medium voltage cablecould provide insight in these matters. Furthermore, it would be interesting to perform threephase, stochastic load-flow analysis to a substantial amount of low voltage networks. This canbe combined with the case of 100% EV penetration to assess the effect of this possible extremeoutcome of the energy transition in low voltage networks to assure conservative and future proofgrid reinforcement. Moreover, combining thermal limits and online tap changer transformersin grid planning may be a better approach for low voltage network reinforcement in generalthan conventional cable reinforcement in terms of maximum capacity, costs, material usage, andlabor.

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Page 56

Appendices

Page 57

Appendix A

Reliability Modeling

This appendix shows how to extent the loss of lifetime models to model the reliability of anasset considering its thermal aging failure mode. To achieve this, the results of this work arecombined with [14]. The reliability of the thermal aging failure mode of an asset can be foundusing the cumulative failure probability, as presented in (A.1), where Ra is the aging reliabilityand Pa is the aging failure probability.

Ra = 1− Pa (A.1)

The cumulative failure probability distribution function of the failure mode of the asset atconstant hottest spot temperature is given in (A.2) [14]. L(θHS) is the loss of insulation lifetimefor a constant hottest spot temperature as given in (2.1), t the time variable, and β the Weibullshape parameter of a Weibull distribution.

Pa(t|θHS) = 1− e−(

tL(θHS)

)β(A.2)

The loss of insulation lifetime Llost (see (2.3)) can be seen as the equivalent operation time underthe reference temperature θ0 [14]. Therefore, the cumulative failure probability of asset as afunction of total loss of insulation lifetime is derived as presented in (A.3). L(θ0) is the nominalinsulation life. With this equation, the relation is made between the hottest spot temperatureprofile and the reliability of an asset.

Pa(t|θHS(t)) = Pr (t > T |θHS(t))

= Pr (t > Llost(t)|θ0)

= 1− e−(Llost(t)

L(θ0)

)β(A.3)

In [39] a validated value for β is found for transformers, β = 5.8718. In [40] a value of β =3.21417 for power cables is found, whereas in [41] a value of β = 3.4559 is given. Assuming βdoes not vary with insulation material of the cable, β = 3.3 is considered to be a proper value.Note however, that β has a large impact on the results of (A.3). The reliability of the asset canbe found by combining (A.1) and (A.3).

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