optimization of high voltage cable dimension in scania

IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2019

Optimization of High Voltage Cable Dimension in Scania Electric Vehicle’s Systems

HERALDUS PANJI ARIKSON

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Optimization of High Voltage Cable Dimension in Scania Electric Vehicle’s Systems

Author

Heraldus Panji Arikson <[email protected]>

KTH Royal Institute of Technology

Program

MSc Electric Power Engineering

Place and Date

KTH Royal Institute of Technology, Stockholm, Sweden

Scania Tekniskt Centrum, Södertälje, Sweden

September 2019

Examiner

Hans Edin


Supervisors

Fadi Hanna

Scania

Nathaniel Taylor


With the increasing demand for electrified vehicles, the demand for electrical

components, including cables, is rising too. Thus, it is important to develop a method to

optimize the cable sizing to ensure the cable is technically robust and economically efficient.

The aim of this project is to study and evaluate different cables’ designs to find the optimum

dimension for “high voltage” class (automotive voltage class B) cables in the electrical

vehicle system. Three important technical aspects in evaluating the optimum cross-section

area (CSA) are the ampacity of the cable, short-circuit withstand capability and voltage drop.

In this project, the ampacity of a cable placed in air is calculated by the analytical

method based on IEC 60287 and by a finite-element simulation. These results are verified

against direct measurements using a dc source and load. In DC calculation, the similarity of

all three methods is high, within 96%. The formation of the cable also affects the ampacity

of the cable. For DC currents, the vertical formation has a higher ampacity than the

horizontal formation, by almost 2%. For AC currents, the trefoil formation has a higher

ampacity than the horizontal and vertical formation, by around 6-9%.

Calculations of short circuit withstand capability and voltage drop were performed to

ensure cable performance. The larger CSA corresponds to both higher short circuit capability

and lower voltage drop. In a short circuit, a duration around 0.5 s is critical since there is a

significant difference between short circuit withstand capability before and after this.

Voltage drop calculation is performed to ensure that the combination of CSA and length

does not exceed 3% voltage drop at the load end side of the circuit. The Voltage drop is not

found to be an important factor to consider. Based on those three factors, the optimization

process is described with a flowchart.

Efterfrågan på elfordon ökar, och därmed ökar också efterfrågan på den elektriska

komponenten. Därför är det viktigt att utveckla en metod för att optimera kabelstorleken så

att kabeln är tekniskt robust och ekonomiskt effektiv. Syftet med detta projekt är att

studera och utvärdera olika kablarnas konstruktioner för att hitta den optimala dimensionen

för högspänningsklass (spänningsklass B) i elfordonssystemet. Tre viktiga tekniska aspekter

vid utvärderingen av den optimala kabelstorleken är kabelns kapacitet,

kortslutningsförmåga och spänningsfall.

I detta projekt placeras kabeln i luften. Ampaciteten beräknas med hjälp av en

analytisk metod baserad på IEC 60287 och en simulering med finita element metoden.

Dessa resultat verifieras mot direkta mätningar med hjälp av en likströmskälla och elektrisk

belastning. För DC-beräkning är likheten för alla tre metoderna mycket hög. Bildningen av

kabeln påverkar också kabelns ampacitet. För DC-strömmar har den vertikala formationen

en högre ampacitet än den horisontella formationen för nästan 2%. För växelströmmar har

trefoilformationen en högre ampacitet än den horisontella och vertikala formationen med

6-9 %.

Kortslutningsförmågan och spänningsfallberäkningen utfördes för att säkerställa kabelprestanda. En större CSA innebär högre kortslutningsförmåga och lägre spänningsfall. Spänningsfallberäkning utförs för att begränsa kabellängden för att säkerställa ett maximalt 3% spänningsfall vid kretsens laständsida. Spänningsfallet är en viktig faktor att beakta. Med hjälp av dessa tre faktorer beskrivs optimeringsprocessen med ett flödesschema.

Contents ..................................................................................................................................2

......................................................................................................................3

List of Tables ...........................................................................................................................6

List of Figures ..........................................................................................................................7

Introduction ...............................................................................................................1

Study Literature Review .............................................................................................4

Cable Properties and Heat Sources ............................................................................8

Cable Components ............................................................................................................8

Heat Sources in the Cable ................................................................................................10

Conductor Losses (Wc) .............................................................................................10

Dielectric Losses (Wd)...............................................................................................12

Loss factor for sheath and screen (Ws) .....................................................................13

Thermal Resistance .........................................................................................................14

Thermal Resistance of the inner insulation (T1) ........................................................15

Thermal resistance between sheath and Armor (T2) ................................................15

Thermal Resistance of outer insulation (T3) .............................................................15

External Thermal Resistance (T4) .............................................................................15

Conductor Material .........................................................................................................16

Heat Transfer...................................................................................................................17

Ampacity, Short Circuit & Voltage Drop in the Cable ................................................18

Ampacity .........................................................................................................................18

Short Circuit Current ........................................................................................................19

Voltage Drop ...................................................................................................................20

Simulation Method and Experimental Setup ............................................................22

Simulation Set Up ............................................................................................................23

Experimental Set Up ........................................................................................................24

Result and Analysis ..................................................................................................27

Ampacity Calculation .......................................................................................................27

Losses Calculation .....................................................................................................27

AC Ampacity Result ...................................................................................................30

DC Ampacity Result...................................................................................................37

Conductor Material Comparison ...............................................................................44

Short Circuit Calculation ..................................................................................................46

Voltage Drop Calculation .................................................................................................49

Cable Optimization Process ......................................................................................52

Conclusion ...............................................................................................................54

Future Work.............................................................................................................56

Appendix ...................................................................................................................................57

Formula .................................................................................................................................57

Figure ....................................................................................................................................61

AC Ampacity ......................................................................................................................61

DC Ampacity ......................................................................................................................63

Voltage Drop .....................................................................................................................64

Matlab Code..........................................................................................................................66

Ampacity Calculation .........................................................................................................66

Short Circuit Calculation Code ...........................................................................................73

Voltage Drop Calculation Code ..........................................................................................74

Bibliography ..............................................................................................................................77

List of Tables

Table 1. Circuit Loading Multiplication Factors ............................................................................4

Table 2. Normalized Comparison of Copper and Aluminium Characteristic [17] ........................16

Table 3. Heat Dissipation Coefficient [14] ..................................................................................22

Table 4. Cable Section Material Properties ................................................................................23

Table 5. General Material Properties .........................................................................................27

Table 6. Loss Factor for Screen ..................................................................................................29

Table 7. Comparison of Temperature Development Calculation in AC Horizontal Formation.....31

Table 8. Comparison of Temperature Development Calculation in AC Vertical Formation .........33

Table 9. Comparison of Temperature Development Calculation in AC Trefoil Formation ...........34

Table 10. Comparison of Temperature Development Calculation in AC Multicore Cable ...........35

Table 11. AC Cable Ampacity .....................................................................................................37

Table 12. Comparison of Temperature Development Calculation for DC in Horizontal

Formation .................................................................................................................................39

Table 13. Comparison of Temperature Development Calculation for DC in Vertical Formation .41

Table 14. Comparison of Temperature Development Calculation for DC Multicore Cable .........42

Table 15. DC Cable Ampacity .....................................................................................................43

Table 16. Short Circuit Withstand Capability of a Cable .............................................................48

Table 17.Maximum Length of DC Application Cable ..................................................................50

List of Figures

Figure 1. Evolution of the global electric car stock from 2013 to 2017 [1]....................................1

Figure 2. Global EV stock in the New Policies and EV30@30 scenarios, 2017-30 [1] ....................2

Figure 3. Optimization Process for Cross Sections [8] ..................................................................6

Figure 4. Cable Layers for Single-core ..........................................................................................8

Figure 5. Two Core Cable Cross Sectional ....................................................................................9

Figure 6. Cable Heat Equivalent Circuit ......................................................................................10

Figure 7. Skin Effect in AC Conductor (b) compared to DC Conductor (a) ...................................11

Figure 8. Proximity Effect of Cable Conductor ...........................................................................12

Figure 9. A current Icx flows through the insulation material due to the capacitive and

resistive characteristics of the insulation material [20] ..............................................................13

Figure 10. Analogy of electrical and thermal conduction ...........................................................14

Figure 11. Power Triangle ..........................................................................................................21

Figure 12. External Natural Convection to a Cylinder Heat Flux .................................................23

Figure 13. Measurement Set Up for Cable Temperature Development in Ambient

Temperature .............................................................................................................................25

Figure 14. Cable Inside the Temperature Chamber Measurement Set Up .................................26

Figure 15. Simplified Measurement Diagram .............................................................................26

Figure 16. Copper Conductor AC to DC Resistance Ratio ...........................................................28

Figure 17. Aluminium Conductor AC to DC Resistance Ratio ......................................................28

Figure 18. 50 mm2 AC Cable Temperature Development in Horizontal Formation .....................30

Figure 19. 50 mm2 Three Cables Horizontal with 150 A in 20 oC Ambient (FEM Simulation) ......31

Figure 20. 50 mm2 AC Cable Temperature Development in Vertical Formation .........................32

Figure 21. 50 mm2 Three Cable Vertical with 150 A in 20 oC Ambient (FEM Simulation) ............32

Figure 22. 50 mm2 AC Cable Temperature Development in Trefoil Formation ...........................33

Figure 23. 50 mm2 Three Cable Trefoil with 150 A in 20 oC Ambient (FEM Simulation) ..............34

Figure 24. 4 mm2 Three-Cores AC Cable Temperature Development .........................................35

Figure 25. AC Three Phase Multicore Temperature Development (FEM Simulation)..................36

Figure 26. 70 mm2 DC Cable Temperature Development in Horizontal Formation .....................38

Figure 27. 70 mm2 Two Cables Horizontal with 150 A DC in 25 oC Ambient (FEM Simulation) ...38

Figure 28. 70 mm2 Cable Temperature Development Measurement with 150 A in Room

Temperature .............................................................................................................................39

Figure 29. 70 mm2 DC Cable Temperature Development in Vertical Formation .........................40

Figure 30. 70 mm2 Two Cables Vertical with 150 A DC in 25 oC Ambient (FEM Simulation) ........40

Figure 31. 4 mm2 Two-Cores Cable Temperature Development ................................................41

Figure 32. DC Multicore Temperature Development (FEM Simulation) .....................................42

Figure 33. Comparison of Conductor Material in AC Cable Application ......................................44

Figure 34. Comparison of Conductor Material in DC Cable Application ......................................44

Figure 35. Short Circuit Withstand Capability of 50 and 70 mm2 CSA .........................................46

Figure 36. Short Circuit Withstand Capability of 4 and 8 mm2 CSA.............................................47

Figure 37. Short Circuit Withstand Capability for 50 mm2 CSA given various initial conductor

temperature..............................................................................................................................47

Figure 38.Voltage Drop Percentage for 30, 50 and 70 mm2 in DC Application............................49

Figure 39. Voltage Drop for 4 mm2 Two-Core DC Application ....................................................50

Figure 40. Voltage Drop for 50 mm2 AC Cable with various power factor ..................................51

Figure 41. CSA Optimization Flow Chart ....................................................................................52

Figure 42. 70 mm2 AC Cable Temperature Development in Horizontal Formation .....................61

Figure 43. 70 mm2 AC Cable Temperature Development in Vertical Formation .........................61

Figure 44. 70 mm2 AC Cable Temperature Development in Trefoil Formation ...........................62

Figure 45. 4 mm2 Multicore AC Cable Temperature Development .............................................62

Figure 46. 50 mm2 DC Cable Temperature Development in Horizontal Formation .....................63

Figure 47. 50 mm2 DC Cable Temperature Development in Vertical Formation .........................63

Figure 48. 4 mm2 Multicore DC Cable Temperature Development ............................................64

Figure 49. 70 mm2 AC Cable Voltage Drop with Various pf ........................................................64

1

Introduction

In 2017, new electric car sales surpassed a record volume of 1 million units worldwide. This sale included battery electric vehicles (BEVs), plug-in hybrid electric vehicles (PHEVs) and fuel-cell electric vehicles (FCEVs). In 2009, The Electric Vehicles Initiatives (EVI) was established. EVI is a multi-governmental policy forum dedicated to accelerating the deployment of EVs worldwide. Governments consist of the largest and most rapidly growing EV markets worldwide, which are Canada, China, Finland, France, Germany, India, Japan, Mexico, Netherlands, Norway, Sweden, UK and USA. EVI promoted EV30@30, a campaign that setting the collective aspirational goal for all EVI members of a 30% market share for electric vehicles in the total of all vehicles (except two-wheelers) by 2030 [1].

Figure 1. Evolution of the global electric car stock from 2013 to 2017 [1]

Figure 1 displays the increase of EV stock globally since 2013 to 2017 both for Battery Electric Vehicle and Plug-in Hybrid Electric Vehicle around the world. Using New Policies and EV30@30 scenarios, Figure 2 shows a scenario where there will be a significant increase in EV global stock until 2030. With the increasing demand for electric vehicles, a lot of vehicle manufacturers are joining the competition to electrify their vehicles, including SCANIA. The increase of EVs thus increases the needs of on-board electrical components, including cable harness. To be able to compete in this market, the company should be able to innovatively provide both technically fine and affordable products. In the last years, the developing trends in the automotive industry are to provide convenience and safety for the passengers while also competing in terms of weight and energy saving. 10% of weight reduction contributes to 3-4% less fuel average for passenger vehicles or around 5% for heavy-duty vehicles such as trucks and buses [2].

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Figure 2. Global EV stock in the New Policies and EV30@30 scenarios, 2017-30 [1]

The automotive power supply system has great importance regarding the electrical functions and is one of the main factors to reduce manufacturing costs, including the cost of the cable harness [3]. The challenges in vehicle construction are to reduce weight, cut costs, increase efficiency and achieve ever greater functionality while maintaining an increasingly high level of quality. What these challenges mean for wire harnesses in vehicles is that an increasing number of conductors must be accommodated in a very tight space [4]. Cable, as the link between the power supply and the load, requires proper sizing to optimize its function. Correct sizing means to choose the optimum cross-sectional area dependent on various constraints such as ambient temperature, the thickness of insulation, current-carrying capacity, voltage drop allowance and other related things. Thus, it is important that proper cable size is employed in specific applications such as high current circuits for batteries and motors or relatively long cables in bus applications. Applying an improper cable size can cause melting, fire or even explosion.

Inefficiency arises as a consequence of oversizing the conductor. On a positive note, the oversized conductor would ensure a better safety condition for power transmission because with the larger conductor size a higher current is allowed in the cable. For the same length, the resistance value will also be lower than the smaller cable, thus the voltage drop and power loss will be smaller. Nevertheless, there are also many designs and economical downsides to cable oversizing. Large cable takes a lot of space. Compared to static power system cable that usually has wide space which can be utilized, the dynamic electric vehicle does not offer this possibility. The cable should be fit in a more limited space. Thus, having a large cable is not an advantage in terms of system design. Larger cables also increase the total weight of the vehicle. Generally, the heavier vehicle consumes more power. More importantly, larger cable requires more conductor material, which corresponds to higher initial costs of the component. In terms of system design, vehicle total weight and initial costs, the large cable is a disadvantage.

Damage can also occur when the cable is under-sized. Compared to the larger cable, under-sizing conductor certainly offer a better option in terms of easier cable-in-truck system design, lighter weight and lower initial costs. However, under-sizing cable compromises the safety aspects of the vehicle itself. Lower cables mean higher resistance. Higher resistive loss is a major disadvantage for a cable because it will increase the temperature rise of the conductor for the same current flowing in the conductor. The smaller conductor will reach the maximum allowable temperature for the lower current

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compared to the larger conductor. In other words, a smaller conductor causes lower ampacity. The higher resistive loss also means more power required to supply the device, thus decreasing the efficiency of the system. For a specific application, like battery, lower efficiency causes higher usage rate of the battery and will reduce the lifecycle of the component. To minimize the cost, weight and space, while also ensuring the reliability and safety of the system, the optimization process should be implemented.

Therefore, this project is aimed to evaluate different cables’ designs to find the optimum dimension requirement for Voltage Class B cable in the hybrid electrical vehicle system. Steady-state maximum current or ampacity in various geometries and cable formations will be the main focus. The cross-section area then will also be evaluated with their short circuit withstand capacity and voltage drop.

Trucks and busses will require higher current flowing from the charging component compared to light-weight vehicles. Therefore, investigation of the cable performance is very critical for heavy-duty vehicle. To find the optimum cross-section area, an algorithm needs to be developed to evaluate the optimum favorable cable dimension.

The scope of the project will only be discussed voltage class B cable in the electric vehicle system. As defined in ISO6469-3:2008, Voltage class B is the voltage with a maximum working rms voltage of >30 V and ≤ 1000 V in an AC system, or >60 V and ≤1500 V in a DC system. The analysis of the cable connectors on both ends will not be included in this project. This project will focus on the optimization of cable material, geometry and configuration. Aluminium is an alternative for conductor material to be considered beside copper in this project. Other complications that arise as the result of choosing aluminium such as special crimping technique will not be included as it is a different topic to address. Analysis of the insulation dimension will also not be included in this project due to broad aspect that it can cover and lack of knowledge on the respective field.

In this project, analytical calculation, finite element method simulation and

measurement are used in combination to find cable ampacity. The reason for using these

three methods is to validate the results of calculation and simulation by conducting

measurement experiments. It could be used to explain the phenomena seen in the

simulation. Simulation offers flexibility to test any type of geometry and formation without

actually building it. The program Comsol Multiphysics is used for the finite element

simulation. Comsol is a finite element analysis, solver and multiphysics simulation software.

It allows computation of physics-based simulation and coupled systems of partial

differential equations (PDEs). Comsol is used because it offers simple physics simulation to

calculate the temperature development in the cable. The analytical method calculation is

developed in Matlab based on IEC 60287 [14, 15], which is the International Electrotechnical

Commission's standard that defines the procedures and equations to be used in

determining the current carrying capacity of cables. The standard is applicable to all ac

cables and to dc cables up to 5kV.

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Study Literature Review

There are several works that have been carried out before as the foundation of this project. The previous works presented guidance on cable design [5-9], calculated the rise of the conductor temperature as the function of current or ampacity [3, 10-16], voltage drop analysis [3, 5, 7], short circuit assessment [5, 8, 12] and alternative material consideration [2, 17].

In [5] , by Brandon R. Meier and Badrul Chowdhury, a simple method for conductor sizing is explained. It covers conductor loading, ambient temperature, proximity effect, minimum ampacity, fault current capability and voltage drop. However, it does not explain the heat source of the cable, which is the main factor for determining the current loading of the cable. The calculation also more appropriate for a cable with constant low frequency such as power system since it does not take frequency into consideration. The six consideration factors to choose proper sizing are:

a. Circuit Loading. Determine the load of the corresponding circuit is the first step to properly select a conductor. The base ampacity (𝐼𝑏𝑎𝑠𝑒) for circuit loading is the minimum current carrying capability of the conductor. Multiplication factors are applied to account for margin to the actual operation of load to cover potential overload or inrush. Typical multiplication factors are provided in Table 1. 𝐼 is the continuous current that may be available from nameplate information of motors, transformer, chargers, etc. Continuous operation is defined as operation for three or more hours [18].

Table 1. Circuit Loading Multiplication Factors

Load Multiplication Factors [19]

Motor 𝐼𝑏𝑎𝑠𝑒 = 1.25 x 𝐼

General-Purpose Transformer 𝐼𝑏𝑎𝑠𝑒 = 1.25 x 𝐼

Heaters 𝐼𝑏𝑎𝑠𝑒 = 1.1 x 𝐼

Chargers 𝐼𝑏𝑎𝑠𝑒 = 1.25 x 𝐼

Motor Control Centers 𝐼𝑏𝑎𝑠𝑒 = ∑ 𝐼 + 25% Largest Motor

b. The dc resistance of a conductor changes as a result of the ambient temperature

(𝑀𝐴𝑀𝐵). These dc resistance changes affect the value of the ampacity in the conductor. If the ambient temperature increases, the dc resistance increases. Higher dc resistance means higher conductor losses.

c. Proximity Effect (𝑀𝑃𝐸). There will be additional heating effects when multiple conductors are close to each other, due to the induction of magnetic fields. A derating factor needs to be applied to account for the increase of the total resistance. Conductor impedance depends on many factors involving conductor itself, conductor spacing and frequency, etc.; therefore, quantifying the electromagnetic field with different configurations is complicated.

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d. Minimum Circuit Ampacity (𝐼𝑎𝑚𝑝) is the minimum ampacity of the circuit taking

account of the ambient temperature and proximity effect. e. Fault Current Capability. The heat generated in the cable is proportional to the

square of the current. Due to a very short time of the event before the short circuit is interrupted, the amount of the heat transferred is usually very small. However, in the case when a sustained short circuit happens, the amount of heat transferred from the conductor will increase considerably, and the cable must be dimensioned to preserve its integrity in the worst case.

f. Excessive voltage drop has many negative effects on the electrical systems such as decreased motor torque and reduced pull torque of ac solenoids. General industry practice is to prevent drop exceeding 3 % to the load, or 5 % overall. Voltage drop is found as the product of current and impedance of the circuit (V = IZ). Based on this, the amount of voltage drop can be determined, if the power factor is known.

Another cable sizing method is presented in [7], which includes a study about the effect of cable length on the dynamic performance of an induction motor is also presented. The approach is different compared to [5]; there are four steps to calculate proper techno-economical cable size for a consumer, which are:

1. Determine Cross-Sectional Area Calculation Based on Short Circuit Withstand Capacity Minimum cross-sectional area of cable is determined by the fault current that is flowing,

𝑆 = 𝐼 √𝑡

𝐾

(1)

where 𝑆 is the nominal CSA of conductor [mm2], 𝑡 is the fault clearing time [s], 𝐼 is the fault current [A], and 𝐾 is factor taking account of the resistivity, temperature coefficient, heat capacity, and initial and final temperatures.

2. Determine Effective Current Carrying Capacity (Thermal Ampacity) This is the maximum current the cable can carry under specified conditions without exceeding the conductor permissible steady-state temperature. In this article, derating or correction factors are applied such as grouping of cables rating (𝐶𝑔) and

ambient temperature factor (𝐶𝑎). 3. Cable Size Selection According to Load Current

In this step, the current flowing in the related conductor is calculated. After considering the derating factors to both load current and short circuit, a larger CSA is chosen.

4. Verification of Cable Size According to Permissible Voltage Drop During Steady-State Operating Condition and Motor Start-Up

This paper [7] provides the main factors to consider when assessing the cable size, and focus heavily on length effect on the voltage drop of the cable. Assessing cable length is important in order to limit the voltage drop in the far end of the cable. In [7], as the cable length increases motor starting current decreases and motor terminal voltage dip increases. Motor starting time also increases with the increase in the length of the cable.

In [8], a simulation-based method to optimize multi-voltage power supply system is presented using an electrical-thermal model to determine ampacity and voltage drop in the cable. There are rating functions that are developed for cable and converter. The factors of

6

evaluation are cost, weight and power loss. Weight and cost of cables are determined by the density of the material. From [8], reducing the conductor size is the main factor to reduce the weight and costs of the cable harness.

This same work [8] developed an algorithm to optimize the cable cross-section area as can be seen in Figure 3. It compares the calculated temperature T as the result of current flowing to the maximally allowed temperature (𝑇𝑚𝑎𝑥) and if it meets the requirement, it also compares the minimum voltage (𝑈𝑚𝑖𝑛) requirement. The optimum CSA (𝐴𝑜𝑝𝑡) should

be reached after implementing this process.

Figure 3. Optimization Process for Cross Sections [8]

In [6], the object of the study is a similar automotive power cable. It researched the problem that may arise due to the use of common shielding in the multicore cable. The focus of the research was about the optimization of cable configuration and material to shielding effectiveness and magnetic compatibility. Temperature development in the cable is a problem in various formations tested in [6]. The temperature development is evaluated in [6] using simulation in Comsol, with variation of the geometry of the AC Cable and DC Cable, the twisting of the cable, shielding material, shielding connection and cable separation.

Aluminium conductors in automotive industry cables are studied in [2, 17]. In [2], the weight reduction of chosen cables is approximately 1.78 kg per truck and 9.67 kg per bus with 40% reduction, thus leading to fuel consumption decrease and environmental advantages.

In [3, 11], different ways of modeling the cable are presented. [11] developed a mathematical model to predict the rise of temperature for a given current in the case of electrical and thermal transient, based on the geometrical subdivision of the structure in several meshes, using Finite Elements Method. [11] studied several methods such as eigenvector (analytical), Runge Kutta, Euler and Crank-Nicolson (numerical methods). From the comparison with the experiment, the results show the maximum error is around 4%.

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All the investigated methods in [3] lead to the same results. Experimental data was also used to validate the result of the model. The three developed models are a direct solution using heat transfer equation, thermal equivalent approach and solution with power flow. The cable was treated as being in free air, with its ampacity restricted by the surrounding ambient temperature. Thus, [3] analyzed cable ampacity in different ambient temperatures and also the heating time to reach pseudo steady state. However, in the calculation and experiment, [3] only used small conductor areas of 0.5 mm2 in free air. Conductor size variation to ampacity and voltage drop that has been simulated in [3] is from 1.5 mm2 to 4 mm2.

In this project, optimization factors affecting cable dimension are derived from the above references. Calculation of factors such as ampacity, voltage drop and short-circuit heating is based directly on the references, and an optimization method is developed using these factors.

8

Cable Properties and Heat Sources

Cable Components

The essential parts of the cables are electrical conductor and insulation. Even though the high voltage of automotive cable is similar to low voltage in the power system, the cable has some differences. During vehicle operation the AC voltage frequency in the cable is not as stationary as in a power system cable in which it is either 50 or 60 Hz: instead, it can go up to more than 600 Hz, depending upon the application. Physically, the automotive cable needs to be more flexible because of the limited space that it has compared to the distribution cable. In most automotive cables, there is no armor layer because it will make the cable difficult to bend. Armor is a steel layer in the cable that provides mechanical protection for the cable. Most of the cables also have a screening layer to reduce the electromagnetic interference. These are some components in the automotive cables (Figure 4):

1. Conductor (Copper or Aluminium), in this project bare stranded 2. Coverage (Tape) 3. Insulation 4. Shielding, tin plated copper braid 5. Wrapping (Tape) 6. Sheath, Outer Insulation

Figure 4. Cable Layers for Single-core

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Figure 5. Two Core Cable Cross Sectional

For multicore cable (Figure 5) shows:

1. Inner Insulation 2. Fillers 3. Shielding 4. Wrapping (tape) 5. Sheath, Outer Insulation 6. Conductor

The two figures above are indicative of single-core and multicore cables for most of the automotive cables. The conductor usually is made from either copper or aluminium due to their high electrical conductivity. The tape is typical of higher voltage cables where it smooths the electric field [20]; it will be ignored in this work. The insulation (both inner and outer) provide protection for the conductor and to prevent short circuit. There are several materials for insulation such as XLPE, PVC, Silicone Rubber, etc. In this project, the inner insulation and the fillers are made of RADOX 155S (extruded and electron beam crosslinked polyolefin copolymer) and outer insulation is RADOX Elastomer (extruded irradiation cross-linked copolymer). Shielding material is tin plate copper braid.

Shielding is used to prevent electrical interference by reducing electromagnetic waves, whether from the protected circuit to other circuits or from other circuits to the protected circuit [9]. The shield works as a blockade between the source of the electromagnetic fields and the areas which need protection from it. In order to reduce the electromagnetic field, thus, a high conductivity material is used in the shielding, such as copper [6]. Shielding also protects the inner insulation and conductor better from damage from outside the cable [9]. The shielding used in this project is tin plate copper braid. Tin is the cheapest coating option for ordinary usage. It has a good corrosion protection and it facilitates the application of solder. Tin’s application is limited to 120 because above this it will oxidize, turning black and corroded [9]. Most of the automotive wires are stranded in order to give flexibility and to improve reliability. For multicore cable, fillers are used to give a cable a smoother construction by supporting the cable outer layer. Filler also gives the inside of the cable a cleaner appearance and strengthens the cable.

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Heat Sources in the Cable

Heat is generated due to losses in the power cable. Heat in the cable is the limiting factor for a conductor to carry the current. In general, there are four types of losses in the power cable, which are:

1. Conductor Losses (𝑊𝑐) 2. Dielectric Losses (𝑊𝑑 ) 3. Sheath Losses (𝑊𝑠) 4. Armor Losses (𝑊𝑎)

The losses in the cable can be described using heat equivalent circuit as can be seen in Figure 6. As can be seen in the figure, each layer of the cable is represented by a thermal resistance. In this project, the cable has no armor (𝑊𝑎 = 0), thus it will not be presented in the picture or discussion. Armored cable is mainly used for underground cable or fixed to outdoor wall mounting because armor provides mechanical protection for the cable. The armor reduces the risk of damage to a cable. However, it also increases the cable weight and thus reduces the flexibility of the cable so it will be more difficult to bend, which is a downside for this project’s application.

Figure 6. Cable Heat Equivalent Circuit

Conductor Losses (𝑊𝑐)

The main source of heat in the cable is the resistive losses coming from the conductor of the cable. The formula of the resistive or conductor loss is

𝑊𝑐 = 𝐼2𝑅

(2)

where 𝐼 is the current flowing in the conductor [A] and 𝑅 is the resistance of the conductor at a certain temperature [Ω]. The resistance value of the cable is temperature dependent. Thus, dc resistance per unit length of the conductor at operating temperature is given by

𝑅′ = 𝑅𝑜[1 + 𝛼20(𝜃 − 20)] (3)

11

where

𝑅𝑜 : the dc resistance of conductor at 20 [Ω/m]; 𝛼20 : the temperature coefficient [1/K] at 20 . For copper conductor: 3.93 x 10-3, and for aluminium is 4.03 x 10-3 𝜃 : the maximum operating temperature [], usually determined by the insulation.

The resistance value usually is given by the manufacturer. In this project, the values of conductor resistivity (𝜌) at 20 for copper conductor is 1.7241 x 10-8 and for aluminium conductor is 2.8264 x 10-8. If AC current flowing through a conductor, there are two other factors that differentiate it from the DC link with regard to the effective resistance, i.e. the power loss in (2). The “AC resistance” of a conductor at maximum operating temperature is given by (4) where 𝑦𝑠 and 𝑦𝑝 are factors for skin and proximity effects.

𝑅𝑎𝑐 = 𝑅𝑑𝑐(1 + 𝑦𝑠 + 𝑦𝑝) (4)

a. Skin Effect (𝑦𝑠)

When direct current flows through the conductor, the current is uniformly distributed across the conductor area or current density is the same in all points. However, when alternating current flows in a conductor, it tends to avoid the center of the conductor and flows with higher current density in the peripheral part of the conductor. Thus, the effective total area of current flowing is smaller. Since the resistance is inversely proportional to the effective area of the cable, it will then increase the resistance of the cable, which means higher loss.

Figure 7. Skin effect in AC Conductor (b) compared to DC Conductor (a)

The calculation of skin effect factor (𝑦𝑠) can be seen in the appendix, formula (22), (23), (24) and (25). It depends on the frequency of the AC power, diameter and the experimental skin effect coefficient value that depends on the type of conductor and material. In this study, both stranded copper and aluminium skin effect coefficient value is 1, according to IEC 60287.

The reverse way to understand the skin effect is by considering skin depth. Skin depth is the depth at which the intensity of the material falls to about 37% of its value at the surface. Skin depth is calculated using this formula:

𝛿 = √

𝜌

𝑓 ∙ μ𝑜 ∙ μ𝑟 ∙ π

(5)

12

where μ𝑟 is the relative permeability of the material, μ𝑜 is the permeability of free space (4π 10-7 H/m) and 𝜌 is the resistivity of the material. Since the permeability and conductivity of the material are fixed, the skin depth depends on the frequency.

b. Proximity Effect (𝑦𝑝)

The proximity effect is unequal distribution of alternating current over the cross-section of a conductor caused by current in another conductor. It occurs whenever parallel conductors carry alternating current [21]. If the conductors carry the current in the same direction, the magnetic field of the halves of the adjacent conductors are canceling each other which pushes the current to flow more on the away side of the conductor [22]. When the conductors carry the current in the opposite direction, the magnetic fields of the far-off halves of the conductors cancel each other, thus more current flow in the near half side of the conductor [22]. The illustration can be seen in Figure 8. Due to these phenomena, the effective area of the current flow is less, which results in an increase of the wire resistance, and therefore to more power losses in the cable.

DC currents are uniformly distributed and thus there is no proximity effect in the circuit. Frequency, diameter, structure and material are factors affecting the proximity effect. Proximity effect is higher with increasing frequency and diameter. Proximity effect is higher in the material made of higher ferromagnetic material and in solid conductors compared to stranded conductors [22]. The proximity effect factor 𝑦𝑝 for three-core cables

and for three single-core cables, circular conductor can be calculated using formula (26).

Figure 8. Proximity effect of Cable Conductor

Dielectric Losses (𝑊𝑑 )

The dielectric loss is the loss in the insulation material. The cable insulation with the conductor and earthing sheath forms a cylindrical capacitor. The resistive current is flowing through the cable insulation from the conductor to the earthed sheath. This phenomenon can be described by the following figure.

13

Figure 9. A current 𝐼𝑐𝑥 flows through the insulation material due to the capacitive and resistive characteristics of the insulation material [20]

The insulation resistance R is the representative of various losses, which are conductive losses, dipole losses and partial discharge losses. In dc cable with a static electric field, there is no dielectric loss. Hence, it is unnecessary to calculate the dielectric loss for d.c. cable [14].

𝑊𝑑 = 𝜔 𝐶 𝑈𝑜2 tan 𝛿 (6)

Here, 𝐶 is the capacitance per unit length [F/m], 𝑈𝑜 is the operating voltage to earth [V] and tan 𝛿 is the loss factor of the insulation at power frequency and operating temperature.

Dielectric loss is also voltage dependent, thus only important to a certain voltage level related to the insulation material being used [14]. The amount of loss increases quadratically as the voltage level is increased. The dielectric loss should be taken into consideration if the value of 𝑈𝑜 equal to or greater than 6000 V [14]. Since the operating voltage applied in this case is less than 1000 V, the dielectric losses factor can be neglected.

Loss factor for sheath and screen (𝑊𝑠)

Generated magnetic fields induce a current that flow in the earthing sheath. Loss factor in the screen (𝜆1) consists of losses caused by circulating currents (𝜆1

′ ) and eddy currents (𝜆1

′′).

𝜆1 = 𝜆1′ + 𝜆1

′′ (7)

Circulating current (𝜆1′ ) loss is due to magnetically induced currents. The AC current flowing

in the conductor will induce a voltage in the shield as a parallel metal ‘loop’. Likewise, parallel cables will influence each other in all metal loops. Depending on the bonding type of the cable, this induced voltage can cause a current to flow in that loop and this induced current can again influence all other metal loops in the surrounding. If the induced voltage in a certain loop cause a current flowing, there will be losses in the resistance of the metal [20]. In contrast to circulating current, eddy current losses (𝜆1

′′) occur for all types of bonding, although they are relatively small. Alternating magnetic fields due to AC current in the cable cause eddy currents in the earthing sheaths [20].

14

Formula (7) expresses the loss in terms of the total power loss in the conductor and indicates which type of loss need to be considered for each particular case [14]. For example, the formula for single-core cables applies to single circuits only and the effects of earth return paths are neglected. For single-core cable with screen bonded at both ends, only loss due to circulating current in the screen needs to be considered. The formula to calculate this loss is presented in Appendix for certain type of formation (29), (31), (32), (33), (38), (39) and (40). Sheath or screen losses are very much dependent on the formation of the cable, bonding arrangement, frequency, sheath and conductor resistance and current in the conductor [23].

Thermal Resistance

When there is a current flowing in the cable, heat is generated in the conductor. The heat can be transferred through the cable by conduction, convection and radiation. Heat produced is then transferred to the surrounding through a medium. This medium has thermal resistance properties which limit the amount of heat that can be released. The schematic of this thermal resistance can be seen in Figure 10. Thermal conductivity indicates how fast heat will flow in a given material [24]. Heat flow can be illustrated as electrical current in the thermal part of the equivalent circuit.

Figure 10. Analogy of electrical and thermal conduction

The thermal equivalent circuit of Ohm’s law can be described as

𝜃1 − 𝜃2 = 𝑊.𝑇 (8)

Here, 𝜃1 − 𝜃2 is the temperature difference [], 𝑊 is the heat flow through thermal resistance per unit cable length [W/m] and 𝑇 is the thermal resistance of material through which current flows per unit cable length.

Metal components of the cable (conductor and shielding) are assumed as a very good heat conductor so the thermal resistance of this material is neglected. The calculation of the ampacity requires a thermal resistance value from the cable properties. For standard circular single-core cable, the thermal resistance calculation is as following

𝑇𝑐𝑠 =

Δ𝜃

𝑊𝑐𝑠=

𝜌𝑐𝑠

2 𝜋ln (

𝑟𝑠𝑟𝑐

)

(9)

Here, 𝑟𝑠 is the outer radius of the material and 𝑟𝑐 is the inner radius of the material. From this value, the thermal resistance of other components can be derived.

15

Thermal Resistance of the inner insulation (𝑇1)

𝑇1 is the thermal resistance between conductor and sheath/shielding. This thermal resistance will be different for single-core and multicore cable. Thermal Resistance between one single-core cable conductor and sheath (𝑇1) is given by

𝑇1 =

𝜌T

2 𝜋ln [1 +

2𝑡1𝑑𝑐

] (10)

With

𝜌T : the thermal resistivity of inner insulation [K.m/W]

𝑑𝑐 : the diameter of conductor [mm]

𝑡1 : the thickness of insulation between conductor and sheath [mm]

Thermal resistance between sheath and Armor (𝑇2)

𝑇2 is not applicable in this project because the cable does not have armor so there is no bedding. Therefore, the value of 𝑇2 is equal to zero. Since earthing sheath is a metal part, thermal resistance is neglected. The 𝑇2 notation will still be kept like IEC nomenclature.

Thermal Resistance of outer insulation (𝑇3)

Since the layout of the cable is concentric cylindrical layers, (9) is applicable to this part. The thermal resistance of the outer insulation is influenced by thermal resistivity of the insulation material, thickness of the insulation material and the diameter of all the outer cover.

𝑇3 =

𝜌T

2 𝜋ln [1 +

2𝑡3𝐷𝑎

] (11)

With 𝜌T : the thermal resistivity of outer insulation [K.m/W] 𝐷𝑎 : diameter of all layer before the outer insulation [mm] 𝑡3 : thickness of outer insulation [mm]

External Thermal Resistance (𝑇4)

Heat transfer from the cable will goes through from the conductor to the

surrounding. Thus, the external thermal resistance (surrounding) becomes very important.

In this part, the formation of the cable decides which constant that will be used. Several

possibilities are a stand-alone cable, three cables in horizontal formation, three cables in

vertical formation, three cables in trefoil, two cables in horizontal formation and two cables

in vertical formation. Those configurations are also varied with distance between each

cable. This constants account for the thermal proximity effect of the cable.

For general purpose, the thermal resistance for cable in air and protected from solar

radiation is as follows

𝑇4 =

1

𝜋 𝐷𝑒∗ ℎ (∆𝜃𝑠)

14

(12)

Where

16

ℎ =

𝑍

(𝐷𝑒∗)𝑔

+ 𝐸 (13)

ℎ is the heat dissipation coefficient, using the appropriate values of constant 𝑍, 𝐸 and 𝑔 given in table 2 in IEC60287-2-1, 𝐷𝑒

∗ is the external diameter of cable [m] and ∆𝜃𝑠 is the excess of cable surface temperature above ambient temperature. It can be calculated through series of iterative formula or using graphical method provided in IEC60287-2-1 section 5.7.

Conductor Material

The standard choice for electrical conductors for automotive wiring is stranded copper cable. Copper properties of low electrical resistance, high thermal conductivity, physical strength, ease of processing and proven termination techniques are the reasons for choosing copper. However, driven by the need to improve fuel economy and exhaust emission of vehicles which directly related to vehicle weight, alternatives material is being investigated [17]. Aluminium, once again, being investigated as a viable option in this project.

Aluminium has been a key material in engineering for more than 200 years. Aluminium is the lightest of all ordinary metals with a specific mass of 2700 kg/m3. For the same value of electrical conductivity, the weight of aluminium conductor is less than half of the weight of copper conductor. This weight reduction impacts the decrease in fuel consumption and thus CO2 emission [2]. One of the most important facts about aluminium is its plentiful available resource. As a consequence, aluminium price is relatively stable and cheaper compared to copper

On the other hand, copper is the most widely used conductor for electrical purposes. Copper has excellent electrical and thermal conductivity which is very good for power cable so that it can carry high current load. Lower resistivity also means that the total voltage drop, for the same length and cross-section area, will be lower than other metallic conductors [17]. High thermal conductivity material causes easier dissipation for heat. Due to high tensile strength, copper conductor is substantially strong to sustain and withstand mechanical loads and ensure much tension which is beneficial during the installation [2]

The comparison of aluminium and copper properties can be seen in the Table 1Table 2. It displays key properties in order to get a full picture of comparison between aluminium and copper.

Table 2. Normalized Comparison of Copper and Aluminium Properties [17]

Properties Copper Aluminium

Resistivity 1 1,58

Density 1 0,3

Cost (Raw Materials) 1 0,72

Thermal Conductivity 1 0,4

Thermal Expansion 1 1,38

Melting Point 1 0,7

17

Heat Transfer

Heat transfer science seeks to predict the energy transfer which may take place between material bodies as a result of a temperature difference [24]. Similar to current which flows from the higher to lower potential, heat transfer happens between media with different temperatures. Heat transfer is characterized by the following mechanisms:

a. Conduction Heat transfer mechanism is different in different media. For gas, it happens due to collisions of the molecules; for a fluid, through oscillations of each molecule in a cage formed by the neighbors; while in metals, mainly by electrons carrying heat [25]. Energy transferred by conduction is proportional to the normal temperature gradient.

𝑞 = −𝑘𝐴

𝜕𝑇

𝜕𝑥

(14)

Here, 𝑞 is the heat transfer rate, 𝜕𝑇 𝜕𝑥⁄ is the temperature gradient in the direction of the heat flow, 𝑘 is the thermal conductivity of the material [24].

b. Convection Heat convection takes place through the net displacement of a fluid, which transports the heat content in a fluid through the fluid’s own velocity. The convection terms also refer to the heat dissipation from a solid surface to a fluid [25]. The convection effect can be described as

𝑞 = ℎ 𝐴(𝑇𝑤 − 𝑇∞) (15)

with ℎ is the convection heat-transfer coefficient, 𝑇𝑤 is the surface temperature and 𝑇∞ is the temperature of the fluid.

c. Radiation In contrast to the mechanism of conduction and convection where energy is transferred through a material or medium, in radiation the heat may also be transferred into regions where perfect vacuum exists. The heat transferred through electromagnetic radiation as a result of temperature difference [24]. When two bodies exchange heat by radiation, the net heat exchange is then proportional to the difference in 𝑇4, thus

𝑞 = 휀 𝜎 𝐴(𝑇14 − 𝑇2

4) (16)

with 𝜎 is the proportionality constant (Stefan-Boltzmann constant) and 휀 is the emissivity (absorptive power) which lies between 0 to 1.

18

Ampacity, Short Circuit & Voltage

Drop in the Cable

Ampacity

Ampacity, also known as current-carrying capacity, is the amount of current that can continuously flow through a conductor under certain conditions without exceeding a certain temperature rating [12]. Ampacity is related to electrical and thermal characteristics of a cable. The main source of heat in the cable is the resistive losses coming from the conductor of the cable due to the resistance properties. Controlling the amount of current flowing in the conductor is essential to keep the heat of the cable within the acceptable level.

IEC 60287 [14, 15] is an analysis method to calculate the maximum continuous current flowing in the conductor. IEC 60287 is a parametric study of the major factors affecting ampacity. IEEE std. 60835 is a similar study. Both are based on Neher-McGrath method [16] published in 1957. It is applied to a steady-state conditions, continuous current operation with 100% load factor, to produce the maximum conductor temperature assumed that the ambient surrounding is constant [12]. It is applicable to all AC voltage and DC voltage up to 5 kV.

The ampacity of an AC cable can be derived from the temperature rise above the ambient temperature as follow

∆𝜃 = (𝐼2𝑅 + 0.5 𝑊𝑑)𝑇1 + [𝐼2𝑅(1 + 𝜆1) + 𝑊𝑑]𝑛 𝑇2 + [𝐼2𝑅(1 + 𝜆1 + 𝜆2) + 𝑊𝑑]𝑛 (𝑇3 + 𝑇4) (17)

where

𝐼 : current flowing in one conductor [A]; ∆𝜃 : conductor temperature rise above the ambient temperature [K]; 𝑅 : ac resistance per unit length of the conductor at maximum operating temperature

[Ω/m]; 𝑊𝑑 : dielectric loss per unit length for the insulation surrounding the conductor [W/m]; 𝑇1 : thermal resistance per unit length between one conductor and the sheath [K.m/W]; 𝑇2 : thermal resistance per unit length of the bedding between sheath and armor [K.m/W]; 𝑇3 : thermal resistance per unit length of the external serving of the cable [K.m/W]; 𝑇4 : thermal resistance per unit length between cable surface and surrounding [K.m/W]; 𝑛 : number of load-carrying conductors in the cable (equal size and carrying the same load); 𝜆1 : the ratio of losses in the metal screen to total losses in all conductors in that cable; 𝜆2 : the ratio of losses in the armoring to total losses in all conductors in that cable;

From the formula (17), ampacity rating for an AC cable application is obtained as follows

19

𝐼 = [

∆𝜃 − 𝑊𝑑 [0,5 𝑇1 + 𝑛 (𝑇2 + 𝑇3 + 𝑇4)]

𝑅𝑇1 + 𝑛𝑅(1 + 𝜆1)𝑇2 + 𝑛𝑅 (1 + 𝜆1 + 𝜆2)(𝑇3 + 𝑇4)]

0.5

(18)

and the ampacity rating of a DC cable application is as follows

𝐼 = [

∆𝜃

𝑅′(𝑇1 + 𝑛𝑇2 + 𝑛𝑇3 + 𝑛 𝑇4) ]0.5

(19)

In the above, 𝑅′ is the DC resistance per unit length of the conductor at maximum

operating temperature [Ω/m]. The differences between AC and DC cable ampacity calculation are the losses. In AC, the conductor losses are dependent on the frequency which causes proximity effect and skin effect in the cable. It causes AC conductor resistance that could be significantly higher than DC resistance. Sheath and screen losses also not applicable in DC application while it increases total losses in the AC application [14].

Short Circuit Current

As mentioned, heat generated in the cable is proportional to the square of current flowing within the conductor. In the normal operation, the steady state current in the cable can flow for long periods in which the cable may reach close to the steady state temperature for the given current. However, during short circuit, the current flowing will be significantly higher, possibly by several or many times. Cables and other equipment are protected from effects of short-circuit by a protection device which will interrupt the current flow according to its setting. One of the most important factors for setting short circuit interruption is the total clearing time or time required to interrupt the short circuit. Since a short circuit is usually interrupted either instantaneously or in a very short time, the amount of heat transferred from the conductors outward to the insulation and other material is small [26]. Therefore, it is important to assess the integrity of the cable insulation. Based on [5], the short circuit capability of a cable can be assessed using

𝐼 = 𝐴 (1.97exp (3)) [0.0297 log (

𝑇2 + 234𝑇1 + 234)

𝑡]

1/2

(20)

where

𝐼 : short circuit current [A] 𝐴 : conductor area [mm2] 𝑡 : total clearing time [s] 𝑇1 : conductor insulation temperature [ ] 𝑇2 : maximum short circuit temperature []

From (20), there are several factors affecting how much short circuit current are allowed in the circuit, which are

a. Clearing time (𝑡)

20

Clearing time is the total time required for the system to clear the circuit from the fault (short circuit current). Extremely high current should be interrupted as soon as possible compared to the lower fault current.

b. Conductor Area (𝐴) Since larger CSA means lower resistance, the larger conductor has a better short circuit withstand capacity than the smaller one. It allows higher current flowing in the cable for the same clearing time.

c. Conductor Insulation Temperature (𝑇1) Basically, conductor insulation temperature is equal to the ampacity temperature limit. The inner insulation of the cable is exposed to the heat generated by the conductor inside. Conductor Insulation Temperature is the limit of temperature that the insulation can withstand in steady state condition. The lower the operating temperature would allow higher gap from the cable to reach the maximum short circuit temperature, thus improve short circuit capability.

d. Maximum short circuit temperature (𝑇2) Ampacity is dealing with the steady state condition which means the temperature limitation is specified for the cable to sustain this temperature for as long as possible. Meanwhile, due to thermal resistance, the cable will not be deteriorated instantaneously if the temperature goes above the ampacity temperature limit. Thus, the maximum short circuit temperature is the extreme temperature limit allowable in the cable for relatively short transient time. In this project, the insulation can withstand 250 up to 5 seconds. The higher the short circuit temperature limit, the higher short circuit limit for the cable.

Voltage Drop

Voltage drop is the amount of voltage loss that occurs through certain electrical circuit due to circuit impedance. Important factors affecting voltage drops [7] are

a. Material The lower electrical resistivity is the better material for a conductor because it will provide lower total resistance; thus, lower voltage drops. In general, copper has lower resistivity than aluminium.

b. Conductor CSA Larger cross section area means lower total resistance. Therefore, increasing the size of the cable means reducing the voltage drop in the circuit.

c. Length Since the total resistance is proportional to the length of the circuit, so the longer the circuit, the bigger the total resistance. To provide better voltage at the end side of the circuit, the limitation of the length should be considered.

d. Frequency Frequency affects the total resistance and reactance in the circuit. For AC cable with large CSA, higher frequency cause skin effect and proximity effect which leads to the current flowing in smaller effective area in the conductor. The smaller area, the higher resistance of the cable, thus higher voltage drops.

21

e. Amount of current flowing The higher the design current, the higher the voltage drop.

Power factor (𝑝𝑓) also affects the voltage drop in the system. Power factor (𝑝𝑓) is defined as the ratio of the average true or active or effective power in watts to the apparent power in volt-amperes (VA), which is the product of the voltage and current magnitudes in an ac circuit [27]. It is described in Figure 11. A pure resistive load has a 𝑝𝑓 of 1. Power factor gives a measure of how effective the real power utilization in the system is. It also represents a measure of distortion of the line voltage and the line current and phase shift between them. In voltage drop calculation, as can be seen in equation (21), the power factor defines how much resistance and reactance of the circuit affecting the total voltage drop.

Figure 11. Power Triangle

Excessive voltage drop is a disadvantage in a power system. In the vehicle, there are a lot of voltage sensitive items of equipment such as inverter and the induction motor. General practice is to limit the voltage drop to a maximum 3% [18]. If the power factor is known, the total voltage drop calculation can be simply put as follow

𝑉𝐷 = 𝐼 ∙ 𝐿(𝑅 cos𝜙 + 𝑋 sin𝜙) (21)

where

𝑉𝐷 : voltage drop in the circuit [V] 𝐼 : current flowing in the conductor [A] 𝐿 : length of the conductor [m] 𝑅 : line resistance for one conductor [Ω] 𝑋 : line reactance for one conductor [Ω] 𝜙 : angle whose cosine is the load pf

Total voltage drop then should be normalized with the supply voltage or voltage at the source to get the percentage of voltage drop along the cable.

22

Simulation Method and Experimental

Setup

Ampacity is a function of temperature as a factor of current flowing in the

conductor. The final conductor temperature limits the cable ampacity. If the final conductor

temperature is set to be higher, then the rise of conductor temperature will be higher too.

Thus, more current is allowed to flow in the conductor. The limitation on the temperature

conductor depends on the insulation thermal ability. In this project, the term ampacity

related to the cable ability to deliver current until the conductor temperature reaches 100

.

The main differences between AC and DC cable applications are the losses. Skin

effect, proximity effect and screen losses happen in AC application while not in the DC

application. All these losses depend on the frequency of the AC power. In this project, the

AC frequency applied is 700 Hz. The AC extra losses calculated in the 6.1.1 will be

implemented to calculate the temperature rise of the conductor given certain current

flowing. For an AC Cable, three conductors are used for three phase current. The

alternatives are three-single conductor in horizontal formation, three-single conductor in

vertical formation, three-single conductor in trefoil formation and three-core cable.

The formation of the cable influences the heat dissipation of the cable. The analytical

method based on IEC 60287 explains this using a heat dissipation coefficient (ℎ). The heat

dissipation coefficient, using the appropriate values of constants 𝑍, 𝐸 and 𝑔 given in Table 3.

These constants depend on the formation of the cable that are taken directly from IEC

60287-2-1 with some appropriation.

Table 3. Heat Dissipation Coefficient [14]

Number Formation Z E g

1 Two Cables Touching, Horizontal 0.29 2.35 0.5

2 Two Cables Touching, Vertical 1.42 0.86 0.25

3 Three Cables Touching, Trefoil 0.94 0.79 0.2

4 Three Cables Touching, Horizontal 0.62 1.95 0.25

5 Three Cables Touching, Vertical 1.61 0.42 0.2

6 Single Cable, Multicore 1.69 0.63 0.25

23

Simulation Set Up

In Comsol, the physics modules used for modeling formations of more than one

cable are Magnetic Fields, Heat Transfer in Solids and Laminar Flow. These modules are

coupled using the multiphysics menu. Thus, the heat transfer from each cable will be

influenced by the formation of the cables. Since the space around the cable is tight, it is

modelled as a closed off-air domain that represents the space around the cables with a box

surrounding the cable with ambient temperature.

For a single cable (single phase, multicore), the physic modules implemented are

simpler. The airflow around the cable is modeled using convective heat flux from the heat

transfer physic module. The boundary condition ‘External natural convection to long

horizontal cylinder’ is applied to the outer layer of the cable, shown in Figure 12. This model

doesn’t need the non-isothermal flow multiphysics module and laminar flow physics

module, it is a lot less computationally demanding. Both models are running as a transient

simulation with a sufficiently long time, around 10-50 thousand seconds depending on the

conditions, to model pseudo-steady state condition.

Figure 12. External Natural Convection to a Cylinder Heat Flux

Some materials such as copper, aluminium and air are available in the Comsol

library, but others need to be imported manually into comsol user defined library. Radox

155 and REMS properties were imported manually from the manufacturer’s datasheet.

These two are the material of inner and outer insulation for all types of cable. Thin plate

copper braid is the material for cable shielding.

Table 4. Cable Section Material Properties

Material Properties Radox 155 REMS Tin Plate Copper

Electrical Conductivity 4.5 x10-19 [S/m] 8.07 x10-19 [S/m] 7.24 x106 [S/m]

Density 1200 [kg/m3] 1350 [kg/m3] 8960 [kg/m3]

Thermal conductivity and heat capacity for Radox and REMS are temperature

dependent properties. Thermal conductivity and heat capacity data for both materials at

certain temperatures were provided by the supplier, so the Comsol interpolation function

was used to define material property from reading experimental data.

24

In the magnetic fields interface, the “coil” feature was added for each conductor.

The current flowing in the conductor then added into the coil setting. In 3 phase AC system,

the currents are equal in magnitude and displaced in phase from each other by 120o. Thus,

the two other phases are multiplied by 𝑒−𝑗2𝜋/3and 𝑒𝑗2𝜋/3. For the mesh setting, the

“extremely fine” element size of physics-controlled mesh was chosen. Laminar flow physics

was implemented in the air domain inside the box in multi-cable configurations.

Incompressible flow and gravity were put as the physical model in laminar flow setting.

Experimental Set Up

Measurements to observe temperature development of the cable due to DC current

flow were conducted in the laboratory. Measurements were done for 4 mm2 two-core

cable, and for 50 mm2 and 70 mm2 paired single-core cables. Equipment used in the testing

were thermocouples, thermal measurement equipment, temperature chamber, power

source, electrical load and related cables.

The cable measurements were done in two ambient temperature conditions: the

room temperature (25) and the chamber temperature (40). Figure 13 shows the

standard set up to measure the cable temperature development in ambient temperature.

Thermocouples were put inside the cable conductor, on the cable surface and in the air near

the cable. The power source was connected into the electrical load through the cable. The

load was set to control the current flowing in the conductor. The temperature development

was observed on a computer that was connected with the thermocouples using

temperature measurement equipment and its software. The setup of the measurement can

be seen in these pictures. Figure 14 shows the standard set up to measure the cable

temperature development inside a climate chamber. This climate chamber set the initial

ambient temperature for the cable that will be observed. Figure 15 is the simplified

measurement diagram of how measurement in Figure 14 conducted.

25

Figure 13. Measurement Set Up for Cable Temperature Development in Ambient Temperature

26

Figure 14. Cable Inside the Temperature Chamber Measurement Set Up

Figure 15. Simplified Measurement Diagram

27

Result and Analysis

In this chapter, the results of ampacity, short circuit analysis and voltage drop

calculation will be presented to evaluate the proper sizing for each cable application. All

calculations are done for a cable placed in air.

Ampacity Calculation

In order to cross-validate the results, various methods are implemented to analyze

the ampacity of the cable. As in [12], analytical calculation method based on IEC 60287 is

implemented in Matlab script. The results are compared with Finite Element Method

simulation in Comsol and direct testing in Scania Technical Centre. Several sensitivity

analyses are also presented for various factors affecting the ampacity such as the material,

cross-section area, formation, frequency and temperature.

Almost all the properties of the cable were built based on the 70 mm2 automotive

screened cable. When changing the size of the cable, some related properties are adjusted

accordingly. All the cables that are analyzed in this study are shielded cables. Specifically, for

this project, the evaluated areas are 50 and 70 mm2 for single-core cable and 4 mm2 for

multicore cable. DC Cable is applied for all three CSA while AC Cable application is mainly for

50 mm2 cable.

Table 5. General Material Properties

Material Properties Value

Copper Resistivity 1.81 x10-8 [Ω·m]

Copper Constant Mass Temperature Coefficient 3.93 x10-3

Copper Relative Permeability 0.99

Aluminium Resistivity 2.82 x10-8 [Ω·m]

Aluminium Constant Mass Temperature Coefficient 4.03 x10-3

Aluminium Relative Permeability 1

Screen Resistivity 1.39x10-7 [Ω·m]

Losses Calculation

As described in 3.2, there are four main types of losses in the cable and the

conductor loss is the main heat source in the cable. From (4), the difference between AC

and DC cable losses are skin effect and proximity effect. A detailed description of both can

be seen in 3.2.1. Both effects are related to the frequency, material and CSA.

28

Figure 16. Copper Conductor AC to DC Resistance Ratio

In Figure 16, the resistance is higher with higher frequency. In the calculation above,

the conductor final temperature is set at 100 for two single-core copper cable tighten

together. As can be inferred from (22) formula, the skin effect and proximity effect are also

dependent on the dc resistance (𝑅′) which are related to CSA. For the same length, the

larger CSA has the smaller dc resistance. Resistance is inversely proportional to skin and

proximity effect factor. Thus, the skin and proximity effect are higher in larger conductor.

This phenomenon can also be explained with the skin depth as in (26) formula. Comparing

Figure 16 and Figure 17, Skin and proximity effect for the same conductor size are higher in

copper conductor rather than aluminium conductor due to copper lower electrical

resistivity. However, it does not necessarily mean that aluminium conductor has a lower

total resistance.

Figure 17. Aluminium Conductor AC to DC Resistance Ratio

100

105

110

115

120

125

130

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Per

cen

tage

Frequency

AC to DC Resistance Ratio in Various CSA

4

10

30

50

70

100

102

104

106

108

110

112

114

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Per

cen

tage

Frequency

AC to DC Resistance Ratio in Various CSA

4

10

30

50

70

29

Table 6. Loss Factor for Screen

Cable Formation Loss factor for screen 𝜆1

4 mm2 10 mm2 30 mm2 50 mm2 70 mm2

3 Cores 7.52x10-4 0.0047 0.0419 0.1070 0.1886

3 Single-core Trefoil 3.55x10-3 2.04x10-2 0.1540 0.3583 0.5795

3 Single-core Flat 8.42x10-3 0.0503 0.3966 0.9064 1.3972

The formula to calculate the loss factor for sheath and screen can be seen in (29),

(33) and (38). Only three cores and three single-core cables are calculated because the loss

is only applied for AC cable application. The results in Table 6 are calculated for maximum

conductor temperature at 100 , copper conductor material and 700 Hz frequency. The

results show that the higher the CSA, the higher loss factor for sheath and screen. Three

single-core cables in flat formation have a higher loss factor compared to trefoil formation

or a three-core cable. These loss factors were used in the ampacity calculation as the ratio

to total conductor losses in that cable. The higher loss factor corresponds to the higher total

loss in the cable, thus higher temperature increases for the same current.

30

AC Ampacity Result

In this part, temperature development of three single-core cables laid in horizontal,

vertical and trefoil formation is presented. Three-cores cable with 4 mm2 CSA is also

presented.

Figure 18. 50 mm2 AC Cable Temperature Development in Horizontal Formation

31

Figure 19. 50 mm2 Three Cables Horizontal with 150 A in 20 oC Ambient (FEM Simulation)

Table 7. Comparison of Temperature Development Calculation in AC Horizontal Formation

Method AC Current [A] Conductor Temperature []

T ambient = 20 T ambient = 40

Analytical Method (IEC)

100 47.4 68

150 74.8 96.1

FEM Simulation (Comsol)

100 35.7 57.6

150 53.6 77.4

32

Figure 20. 50 mm2 AC Cable Temperature Development in Vertical Formation

Figure 21. 50 mm2 Three Cable Vertical with 150 A in 20 oC Ambient (FEM Simulation)

33

Table 8. Comparison of Temperature Development Calculation in AC Vertical Formation




100 45.2 65.8

150 70.5 91.7


100 34.3 55.1

150 49 70.8

Figure 22. 50 mm2 AC Cable Temperature Development in Trefoil Formation

34

Figure 23. 50 mm2 Three Cable Trefoil with 150 A in 20 oC Ambient (FEM Simulation)

Table 9. Comparison of Temperature Development Calculation in AC Trefoil Formation




100 44.2 64.9

150 68.7 90.3


100 35.5 56.4

150 52.1 73.8

35

Figure 24. 4 mm2 Three-Cores AC Cable Temperature Development

Table 10. Comparison of Temperature Development Calculation in AC Multicore Cable




20 36.2 57

30 53 75.4

40 77.5 101.2


20 40.2 62

30 60.4 84.2

40 89.3 116

36

Figure 25. AC Three Phase Multicore Temperature Development (FEM Simulation)

There are significant differences between the analytical method based on IEC 60287

calculation and the FEM simulation in Comsol. The absolute difference between both

methods ranges from 4 up to 37 . The IEC analytic method tends to overestimate the

cable loss in the screen factor calculation as described in [28]. In [10], the analytical method

produces optimistic results when it applies to a different condition than the designated

environment. In other work [29], the FEM Comsol Simulation was found to slightly

underestimate the heat transfer calculation. The gaps between both calculations is

significant at higher frequency. At zero frequency, the results show a very close value.

Graphics and pictures for other areas can be seen in Figure 42, Figure 43, Figure 44 and

Figure 45.

From Figure 18, Figure 20 and Figure 22, the ampacities of the cables are

summarized in Table 11. Three cables in trefoil have higher ampacity compared to

horizontal and vertical formation. Since the cables implemented are identical, this

difference happened due to the formation. Cables in trefoil formation have a better heat

dissipation coefficient which represents this formation’s ability to release heat into the

ambient. The ampacity is taken from the hottest conductor out of the three. In a three-

phase system, this conductor is the limiting factor for the cable delivering more current.

37

Table 11. AC Cable Ampacity

CSA [mm2] Type Formation Ampacity [A]

Ta = 20 Ta = 40 Ta = 60 Ta = 80

4 Multicore 47 39 31 20

50 Single-Core

Horizontal 185 155 121 79

Vertical 194 163 127 83

Trefoil 197 165 129 84

70 Single-Core

Horizontal 199 167 130 85

Vertical 207 174 136 89

Trefoil 219 184 143 94

The maximum ampacity difference between the presented formations is up to 20 A.

For the 50 mm2 and 70 mm2 CSA, the maximum ampacity difference due to cable formation

is stable around 6 % and 9% for all ambient temperature. Horizontal formation has the

lowest ampacity due to the limitation of the cable in the middle. Heat flow is proportional to

the surface area according to (14), (15) and (16) equations. In horizontal formation, the

middle cable is trapped by other conductors in the left and right so that the effective area to

release the heat is decreasing.

Vertical formation has a better heat dissipation than the horizontal one because the

limitation factor, the conductor on the top, has a wider effective surface area to dissipate

heat. Trefoil cable formation also has a better heat dissipation than the horizontal one

because the heat is dissipated more balance by all three conductors. Table 6 shows that the

loss factor for the screen in trefoil formation is smaller than the flat formation which affect

the total loss in the system. However, for cable installation in a complex and tight place such

as truck chassis, the formation of the cable might be changing along the line, in which case it

is important to consider the lowest ampacity as the cable ampacity.

Heated air rises because it is less dense compared to the colder air around, as can be

seen in Figure 19, Figure 21 and Figure 23. In Figure 19, the middle cable is the hottest one

because it has the smallest area to dissipate the heat since it is blocked by other cables.

Figure 25 is the example of temperature development simulation result performed by

Comsol for multicore cable. It applied convective heat flux from the heat transfer physic

module which is simpler than more than one cable formation. The outer layer of the cable is

simulated using ‘external natural convection to long horizontal cylinder’ boundary

condition. Thus, it will assume an isothermal outer environment of the cable.

DC Ampacity Result

a. Two Cables Touching Horizontally

38

Figure 26. 70 mm2 DC Cable Temperature Development in Horizontal Formation

Figure 27. 70 mm2 Two Cables Horizontal with 150 A DC in 25 Ambient (FEM Simulation)

39

Figure 28. 70 mm2 Cable Temperature Development Measurement with 150 A in Room Temperature

Table 12. Comparison of Temperature Development Calculation for DC in Horizontal Formation

Method DC Current [A] Conductor Temperature []



150 40.9 56.6

200 51.2 67.3


150 40.4 55.3

200 51.7 67.2

Experiment 150 39.3 47.9

200 51.4 55.1

40

Figure 29. 70 mm2 DC Cable Temperature Development in Vertical Formation

Figure 30. 70 mm2 Two Cables Vertical with 150 A DC in 25 Ambient (FEM Simulation)

41

Table 13. Comparison of Temperature Development Calculation for DC in Vertical Formation




150 40.2 55.8 200 50.2 66.5


150 39.9 54.9 200 50.3 65.9

Figure 31. 4 mm2 Two-Cores Cable Temperature Development

42

Figure 32. DC Multicore Temperature Development (FEM Simulation)

Table 14. Comparison of Temperature Development Calculation for DC Multicore Cable




20 37.1 52.7

30 49.8 66

40 67.3 84.3


20 40.4 56.4

30 55.7 72.8

40 76.3 94.7

Experiment

20 36.4 46.5

30 47.7 55.3

40 70.2 69.2

Different from AC calculation, the temperature development calculation for DC cable

application is almost identical in all three methods. At the room temperature (25 oC), the

difference between the calculated value in analytical method compared to the

measurement is very small, around 0.2 oC to 2.5 oC or less than 5%. FEM simulation also

provides a close result with the absolute temperature difference around 0.2 to 2.4 oC (1% to

4% error), similar to analytical method. The analytical method showed this consistency for

various CSA. For temperature development of multicore cable, the analytical method has a

better approach than FEM simulation: the simulation has an absolute 8 oC temperature

difference, around 15%, at 30 A. However, the temperature development is not linear, and

this error value reduces at the higher or lower currents.

43

At 40 ambient temperature setting, measurements made in the chamber showed

a worse deviation from calculation and simulation than was seen at room temperature. In

two-cables formation with 50 and 70 mm2 CSA, the absolute error for the analytical method

and also FEM Simulation is around 5 to 12 , i.e. 15-20% relative error. For the 4 mm2 CSA

multicore cable, FEM simulation has a worse error, around 20-30 %. This error is likely

caused by the temperature setting in the chamber where it has a fan that took the heat

away so that it can keep the chamber temperature steady at designated 40 . Even though

the fan has been covered with an internal box, the indirect fluid may still be affecting the

cable. See the last row of Table 12, the 25 and 40 ambient temperature difference for

70 mm2 cable with 200 A current flowing is only 3.7 oC. In Table 14, the 4 mm2 multicore

cable with 40 A current has a higher conductor temperature (70 to 69.2 ) in 25

ambient temperature than the 40 chamber temperature.

Table 15. DC Cable Ampacity

CSA [mm2] Type Formation Ampacity [A]

Ta = 25 Ta = 40 Ta = 60 Ta = 80

4 Multicore 53 46 36 24

50 Single-Core Horizontal 280 245 192 126

Vertical 284 249 195 128

70 Single-Core Horizontal 347 304 238 157

Vertical 353 309 243 160

Ampacity of the cables from Figure 26, Figure 29 and Figure 31, are summarized in

Table 15. Similar to AC simulation, the cable in the horizontal formation has a lower

ampacity compared to the vertical formation which means it has a higher loss in the cable.

In vertical formation, the limitation factor is the upper cable where the heat from the lower

cable goes up and increases the amount of heat that needs to be released. For the

horizontal cable, both conductors are heated equally. Vertical formation has a slightly better

heat dissipation coefficient.

The difference in the ampacity is not as big as in an AC cable application. For the 50

mm2 CSA, the ampacity difference between horizontal and vertical is around 3 A or 1.5 %.

For 70 mm2 CSA, the ampacity different is 5 A or 1.7%. Considering the complexity of the

cable routing, it is good to consider the lowest ampacity as the main ampacity.

Figure 28 is an example of typical result shows in the computer when performing the

temperature development measurement. There are three curves which represent three

different temperature measurement. The red one is the temperature development inside

the conductor, the orange represent the temperature development at the jacket of the

cable while the other one is the ambient temperature. Ambient temperature was generally

stable at 25 while other two parameter rose up as the current increased.

Figure 32 is the example of temperature development simulation result performed

by Comsol for dc multicore cable. It applied convective heat flux from the heat transfer

physic module which is simpler than more than one cable formation. The outer layer of the

cable is simulated using ‘external natural convection to long horizontal cylinder’ boundary

condition. Thus, it will assume an isothermal outer environment of the cable.

44

Conductor Material Comparison

Figure 33. Comparison of Conductor Material in AC Cable Application

Figure 34. Comparison of Conductor Material in DC Cable Application

Figure 33 and Figure 34 show the comparison between copper and aluminium as

conductor material in both AC and DC application. For AC application, although the skin

45

effect has greater impact on copper conductor, the overall resistance of the copper

conductor is still lower than aluminium conductor. This applied to 700 Hz, with 70 mm2 CSA.

For smaller CSA, the skin effect would be reduced as can be seen in Figure 16. To reach 100

from 20 ambient, the copper allowed 199 A while aluminium allowed 182 A.

For DC application, the skin effect is not relevant. The ampacity of the 70 mm2 cable

in 25 ambient temperature is 347 A for copper and 277 A for aluminium. Even more,

from Figure 34, copper at 60 ambient has higher ampacity than aluminium at 25

ambient if the conductor temperature set above 140 .

46

Short Circuit Calculation

The important variables for maximum short circuit current evaluation are the cross-

section area of the cable, the conductor operating temperature, the maximum short circuit

temperature and clearance time. Since the insulation material is crosslinked thermoplastic

polymer (RADOX), it can withstand short circuit temperature up to 250 for 5 seconds.

The conductor temperature is the temperature when the conductor is operated at its

ampacity, which is 100 in this case.

Figure 35. Short Circuit Withstand Capability of 50 and 70 mm2 CSA

Figure 35 and Figure 36 shows cable short circuit withstand capability from 0.1 to 5

seconds for various CSA. The larger the CSA, the higher the short-circuit current that is

allowed for the same clearance time. The larger the CSA, the longer fault duration the cable

can withstand. For duration less than about 0.5 s, a small change in duration such as 0.1 s

can make a substantial change to the maximum permitted short-circuit current. Figure 37

shows the short circuit withstand capability given various initial conductor temperature

conditions. The higher the initial conductor temperature, the lower the cable short circuit

withstand capability due to a smaller temperature gap to reach maximum short circuit

temperature, 250 .

47

Figure 36. Short Circuit Withstand Capability of 4 and 8 mm2 CSA

Figure 37. Short Circuit Withstand Capability for 50 mm2 CSA given various initial conductor temperature

Short circuit withstand capability of a cable does not change linearly with time. From Figure

35 and Figure 36, after 0.5 seconds there is a big decrease in how much short circuit current

are able to be handled by the cable. From 0.1 s to 0.5 s, the short circuit current is

decreased by more than 50%. Another 50% reduction is happened from 0.5 s to 2 s. It is

48

crucial to check on how much the short circuit current can flow in the cable and how long it

takes for the protection system to isolate the fault. Those two criteria are the reason behind

choosing the correct CSA. The summary from short circuit withstand capability figure can be

seen in the table below.

Table 16. Short Circuit Withstand Capability of a Cable

duration [s]

Short Circuit Withstand [kA]

Cross-Section Area

4 mm2 8 mm2 20 mm2 50 mm2 70 mm2

0.1 2.6 5.2 13.1 32.7 45.8

0.25 1.65 3.3 8.2 20.7 29

0.5 1.1 2.3 5.8 14.6 20.5

2 585 [A] 1.1 2.9 7.3 10.2

5 370 [A] 741 [A] 1.8 4.6 6.4

49

Voltage Drop Calculation

Voltage drop in the cable depends on three important factors. From equation (21),

the cable impedance, cable total length and the current flowing in the conductor are factors

to consider for correct sizing of the cable. For AC application, the power factor also affects

the composition of resistance and reactance in total impedance. Frequency also is relevant

in AC cable application because it changes the resistance value due to skin and proximity

effects.

Figure 38.Voltage Drop Percentage for 30, 50 and 70 mm2 in DC Application

The chosen ampacity as the current flowing in the calculation is the highest between

those three formations in AC or two formations in DC. In the calculation, the voltage that is

used as base voltage for AC is 650 Vrms and for DC is 660 V. Figure 38 shows the cable length

effect to the voltage drop of 30, 50 and 70 mm2 cable. Each cable has the current flowing in

its conductor as much as the ampacity from 25 room temperature to 100 so that the

resistance value is at 100 . The maximum length for those cables to keep the voltage drop

below 3% is presented in Table 17.

50

Table 17.Maximum Length of DC Application Cable

Formation CSA [mm2] Maximum Length [m]

Single-Core

70 83

50 74

30 60

Two-Cores 4 31

Figure 39. Voltage Drop for 4 mm2 Two-Core DC Application

Figure 39 shows the voltage drop magnitude for 4 mm2 two-Core DC cable on its

ampacity. Depending on the type of voltage applied in the cable, the 3% voltage drop limit

can be varied. For the same 660 V, the maximum 4 mm2 two-core cable length to limit the

voltage drop is 31 m in order that the voltage drop magnitude is not more than 19.8 V. A

difference when calculating DC and AC cable application is that the equation (21) is

multiplied by 2 in a DC application to account for the conductor length from the source to

the load (+) and from the load back to the source (-), whereas for three phase AC application

the equation should be multiplied by √3.

Voltage drop of 50 mm2 AC cable at various power factor is described in Figure 40.

For 50 mm2 AC cable, the worst voltage drop happens when the pf = 0.55. This means that

for this cable, pf value of 0.55, the impedance is at the highest compared to other pf values.

For 50 mm2 AC cable, at 0.55 pf, the maximum length should be 61 meters while if the pf

value is 1, the maximum length can go up to 105 meters. The reactance value affects the

total impedance due to this power factor. In the automotive power system, the power

51

factor would vary depending on the application. Thus, it is important to consider all the

possible pf when assessing maximum length of the AC cable.

Figure 40. Voltage Drop for 50 mm2 AC Cable with various power factor

52

Cable Optimization Process

This chapter elaborates steps that need to be taken to obtain the smallest possible cable cross-section area from technical point of view. The optimization process is explained step by step with this flow chart.

Figure 41. CSA Optimization Flow Chart

CSA Optimization Flow Chart in Figure 41 describes steps to choose the smallest CSA that is still technically reliable. These steps would save the initial investment cost of the cable. Cable CSA optimization process is divided into three important steps, which are

53

A. Choosing CSA based on the current flowing in the conductor

1. As described in Figure 41, the first step is collecting all the data and the standard

required to calculate the temperature development which are initial CSA (An),

current flowing in the circuit, frequency, ambient temperature, maximum

conductor temperature, short circuit profile in the circuit (current and duration).

2. For certain initial CSA, current and ambient temperature, calculate the final

conductor temperature.

3. If the final conductor temperature (𝜃) is lower than the standard maximum

conductor temperature (𝜃𝑚𝑎𝑥), decrease the cable CSA until the final conductor

temperature is equal to or slightly lower than the maximum conductor

temperature.

4. Otherwise, if the final conductor temperature is higher than the standard

maximum conductor temperature, increase the cable CSA until the final

conductor temperature is equal to or slightly lower than the maximum conductor

temperature.

5. If the final conductor temperature is equal to maximum conductor temperature,

continue to the next step.

B. Short-Circuit Evaluation

6. Calculate short circuit capability for related cable.

7. Compare the short circuit current (Isc) and time in the related cable protection

setting to the calculated short circuit capability (SCC).

8. If the short circuit or fault current in the cable is higher than the cable short circuit

capability, increase the cable CSA.

9. If the short circuit or fault current in the cable is lower than or equal to the cable

short circuit capability, continue to the next step.

C. Voltage Drop Calculation

10. Calculate the voltage drop for the cable with its specific length.

11. If the cable voltage drop is more than 3%, increase the cable CSA.

12. If the voltage drop is less than 3%, then the cross-section area is the most optimal

CSA for this circuit.

54

Conclusion

Ambient temperature, maximum permitted conductor temperature, and total losses

generated in the cable are factors affecting the ampacity. Cable sections can be located

through different ambient temperatures; thus, it is important to choose the highest ambient

temperature the cable has to go through in order to cover the weakest link in the cable. The

highest temperature was set to 100 in this study, to maximize the temperature rise while

not unduly reducing the cables’ expected lifetime.

In three-phase AC power applications with three cables, trefoil is the best formation

to maximize cable ampacity. For example, for 50 mm2 CSA with 700 Hz frequency, trefoil

cable formation ampacity in 20 ambient temperature is 197 A. For the same parameter,

horizontal formation ampacity is 185 A and the vertical formation is 194 A. On average, the

ampacity difference due to cable formation is around 6 to 9%. In trefoil formation, the heat

is evenly distributed in all three cables. Meanwhile, in horizontal and vertical formation, the

cable in the middle or the top will continuously receive higher heat than the others, and so

will wear out faster than the other two cables. Therefore, trefoil formation is the most

recommended formation for three-cables AC application.

In two-cables DC application, the vertical formation has a better ampacity than the

horizontal one. For example, in 70 mm2 CSA, the vertical formation ampacity in 25

ambient temperature is 353 A while the horizontal formation ampacity is 347 A. On average,

the ampacity difference between horizontal and vertical formation is less than 2%. For DC

application, heat distribution is better in the horizontal formation than the vertical

formation. Both left and right conductors are exposed to the same amount of heat. In the

vertical formation, the conductor in the upper position receives higher heat compared to

lower conductor. Thus, in DC current application, vertical formation provides higher

ampacity.

There are significant differences between the analytical method based on IEC 60287

calculation and the FEM simulation in Comsol. The absolute difference between both

methods ranges from 4 up to 37 . The IEC analytic method tends to overestimate the

cable loss in the screen factor calculation. Different from AC calculation, the temperature

development calculation for DC cable application is almost identical in all three methods. At

the room temperature (25 ), the difference between the calculated value in analytical

method compared to the measurement and simulation is very small, around 0.2 to 2.5

or less than 5%. Further investigation needs to be done to get deeper understanding.

Short-circuit withstand capability of a cable depends on the CSA, maximum short

circuit temperature, conductor temperature and time required to clear the fault. 500 ms is

the critical time for the short circuit calculation because there is a significant difference

between short circuit withstand capability before and after this time. The protective device

55

that protects the cable should be able to clear the fault faster than the maximum permitted

clearance time for the short circuit current in the cable.

Voltage drop calculation is assessed to limit the cable length so that the voltage at

the load end side does not vary unreasonably much. In DC application, voltage drop only

depends on the total resistance and length of the cable while in AC, it depends on total

impedance and power factor. For automotive cable applications, voltage drop is not a

significant factor.

56

Future Work

The following is an indication of future works that can be done to complement the

work done in this project. Since the gap between the IEC analytical method and the

simulation result for AC application was substantial, the cable should be tested directly in

the laboratory. In order to observe the influence of frequency on the skin effect, proximity

effect and screen losses, a three-phase current generator and frequency controller are

required. The testing result would verify which method is the best option to calculate

temperature development in AC application.

The cable designs tested in this project were based on actual and standard cable

layouts that can be implemented in a vehicle right now. It is recommended to simulate

other various types of formation and cable design to deepen the understanding of the cable

formation and design effect. Various cable designs that can be investigated are shaped-

conductor, DC four-core cables, AC six-core cables, etc. Many types of cable formation,

especially if the multicables for the same phase will be used, can also be simulated such as

trefoil with circular arrangement of the cable, six horizontal cables, rectangular or square

shaped formation of the cable, etc.

Study of the Voltage Class B insulation part might also be required. The insulation

material and its thickness affect the cable thermal resistance and the safety standards of

the cable. The insulation’s ability to withstand high temperature is also critical because it is

the limiting factor of the cable’s ampacity which is also related to cable expected lifetime.

The insulation material and thickness will also affect other mechanical properties of the

cable such as bending ratio and total weight.

57

Appendix

Formula

The calculation of skin effect factor (𝑦𝑠) is given by the following equations:

For 0 < 𝑥𝑠 ≤ 2.8

𝑦𝑠 = 𝑥𝑠

4

192 + 0.8 𝑥𝑠4

(22)

For 2.8 < 𝑥𝑠 ≤ 3.8 𝑦𝑠 = −0.136 − 0.0177𝑥𝑠 + 0.0563𝑥𝑠

2 (23)

For 𝑥𝑠 > 3.8 𝑦𝑠 = 0.354𝑥𝑠 − 0.733 (24)

where

𝑥𝑠2 =

8𝜋𝑓

𝑅′10−7𝑘𝑠

(25)

𝑓 : the supply frequency [Hz] 𝑘𝑠 : experimental skin coefficient value depends on the type of cabling. In this study, stranded copper and aluminium cable is 1.

The calculation of proximity effect factor (𝑦𝑝) is given by the following equations:

𝑦𝑝 =

𝑥𝑝4

192 + 0.8 𝑥𝑝4(𝑑𝑐

𝑠)

2

[

0.312 (𝑑𝑐

𝑠)

2

+1.18

𝑥𝑝4

192 + 0.8𝑥𝑝4 + 0.27

]

(26)

𝑥𝑝2 =

8𝜋𝑓

𝑅′10−7𝑘𝑝

(27)

𝑑𝑐 is the diameter of the conductor [mm], 𝑠 is the distance between the conductor axes [mm] and 𝑘𝑝 is the experimental proximity coefficient value depends on the type of cabling.

In this study, the value is 1 for stranded copper conductor and solid aluminium conductor while 0.8 for stranded aluminium conductor.

The calculation of capacitance for cylindrical conductors is given by a

𝐶 =

휀

18 ln (𝐷i

𝑑c)10−9

(28)

where

휀 : relative permittivity of the insulation 𝐷i : external diameter of the insulation (excluding screen) [mm] 𝑑c : diameter of conductor, including screen if any [mm]

58

The Calculation of Loss Factor for Screen Losses

For two single-core cables and three single-core cables (triangle) with screen bonded at both ends, the loss factor is given by

𝜆1′ =

𝑅𝑠

𝑅

1

1 + (𝑅𝑠

𝑋 )2 (29)

where

𝑅𝑠 : resistance of the screen per unit length of cable at maximum operating

temperature [Ω/m];

X : reactance per unit length of screen of cable [Ω/m];

𝑋 = 2 𝜔 10−7ln (2𝑠

𝑑) (30)

𝑠 : the distance between conductor axes in the electrical section being considered [mm] 𝑑 : mean diameter of the screen [mm] 𝜆1

′′ : 0, eddy current is ignored.

For three single-core cables in flat formation, with the middle cable equidistant from the outer cables, without transposition and with the sheaths bonded at both ends, the loss factor for the outer cable carrying the lagging phase is

𝜆11′ =

𝑅𝑠

𝑅[0.75𝑃2

𝑅𝑠2 + 𝑃2

+0.25𝑄2

𝑅𝑠2 + 𝑄2

+2 𝑅𝑠𝑃 𝑄𝑋𝑚

√3(𝑅𝑠2 + 𝑃2)(𝑅𝑠

2 + 𝑄2)]

(31)

For the other outer cable, the loss factor is

𝜆13′ =

𝑅𝑠

𝑅[0.75𝑃2

𝑅𝑠2 + 𝑃2

+0.25𝑄2

𝑅𝑠2 + 𝑄2

−2 𝑅𝑠𝑃 𝑄𝑋𝑚

√3(𝑅𝑠2 + 𝑃2)(𝑅𝑠

2 + 𝑄2)] (32)

For the middle cable, the loss factor is

𝜆12′ =

𝑅𝑠

𝑅

𝑄2

𝑅𝑠2 + 𝑄2

(33)

In this formula:

𝑃 = 𝑋 + 𝑋𝑚 (34)

𝑄 = 𝑋 −𝑋𝑚

3 (35)

where

59

𝑋 = 2 𝜔 10−7ln (2𝑠

𝑑)

(36)

is the reactance of screen per unit length of cable for two adjacent single-core cable [Ω/m];

𝑋m = 2 𝜔 10−7ln(2)

(37)

is the mutual reactance per unit length of cable between the sheath of an outer cable and the conductors of the other two when the cables are in flat formation. Eddy current loss 𝜆1

′′ is ignored.

For two core unarmored cable where the cores are contained in a common metallic sheath, circulating current loss (𝜆1

′ ) is negligible and the loss factor for round conductors is

𝜆1′′ =

16 𝜔210−14

𝑅 𝑅𝑠(𝑐

𝑑)2

[1 + (𝑐

𝑑)

2

] (38)

where

c : distance between the axis of one conductor and the axis of the cable [mm] d : mean diameter of the sheath [mm]

For a three-core unarmored cable where the cores are contained in a common metallic sheath, circulating current loss (𝜆1

′ ) is negligible and the loss factor for round conductors is

- for 𝑅𝑠 less than or equal to 100 𝜇Ω/m

𝜆1′′ =

3 𝑅𝑠

𝑅 [(

2𝑐

𝑑)

2 1

1 + ( 𝑅𝑠𝜔 107)

2 + (2𝑐

𝑑)

4 1

1 + 4 ( 𝑅𝑠𝜔 107)

2]

(39)

- for 𝑅𝑠 greater than 100 𝜇Ω/m

𝜆1′′ =

3.2 𝜔2

𝑅 𝑅𝑠(2𝑐

𝑑)

2

10−14

(40)

Calculation of Thermal Resistance of the Inner Insulation (𝑇1)

For two core belted cables with circular conductors

𝑇1 =

𝜌T

2 𝜋𝐺

(41)

where

G : Geometry factor that depends on the thickness of insulation between conductors

(𝑡), thickness of insulation between conductors and sheath (𝑡1) and diameter of the

conductor (𝑑𝑐). The value is given on IEC60287-2-1, Figure 2.

For three core belted cable with circular conductors

60

𝑇1 =𝜌i

2 𝜋𝐺 + 0.031(𝜌𝑓 − 𝜌i)𝑒

0.67𝑡1𝑑𝑐 (42)

where

𝜌i : thermal resistivity of the insulation [K.m/W];

𝜌i : thermal resistivity of the filler material [K.m/W]

The geometric factor is given in figure 3 of the IEC60287-2-1

Calculation of External Thermal Resistance (𝑇4)

𝐾𝐴 = 𝜋 𝐷𝑒

∗ ℎ

(1 + 𝜆1 + 𝜆2)[𝑇1

𝑛+ 𝑇2(1 + 𝜆1) + 𝑇3(1 + 𝜆1 + 𝜆2)]

(43)

Then

(Δ𝜃𝑠)𝑛+11/4

= [Δ𝜃 + Δ𝜃𝑑

1 + 𝐾𝐴(Δ𝜃𝑠)𝑛1/4

]

0.25

(44)

Set the initial value of (∆𝜃𝑠)1

4 = 2 and reiterate until (Δ𝜃𝑠)𝑛+11/4

− (Δ𝜃𝑠)𝑛

1

4 ≤ 0.001. If Δ𝜃𝑑 =

0 if dielectric losses are neglected.

61

Figure

AC Ampacity

Figure 42. 70 mm2 AC Cable Temperature Development in Horizontal Formation

Figure 43. 70 mm2 AC Cable Temperature Development in Vertical Formation

62

Figure 44. 70 mm2 AC Cable Temperature Development in Trefoil Formation

Figure 45. 4 mm2 Multicore AC Cable Temperature Development

63

DC Ampacity

Figure 46. 50 mm2 DC Cable Temperature Development in Horizontal Formation

Figure 47. 50 mm2 DC Cable Temperature Development in Vertical Formation

64

Figure 48. 4 mm2 Multicore DC Cable Temperature Development

Voltage Drop

Figure 49. 70 mm2 AC Cable Voltage Drop with Various pf

66

Matlab Code

Ampacity Calculation

%% AMPACITY CALCULATION BASED ON IEC60287-1-1 and IEC60287-2-1

clear all

clc

%% PARAMETRIC SWEPT

A_con = [50]; %cross section [mm2]

T_start = [25 40 60 80];%ambient temperature [degC]

s_con_axis = [0]; %separation of cable [mm]

material = [1 2]; %1=COPPER, else = ALUMINIUM

T_con = [20:160]; %Temperature end variable[deg C]

%% CONTROL VARIABLE

TR1Factor = 1; %Factor to calculate T1

%1 = single-core - AC & DC

%2 = 2 core belted cables - multicore DC

%3 = 3 core belted cables - multicore AC

n = 1; %number of conductors in a cable, so either 1, 2 or 3

f = 0;

formationtype = 2; %Factor to Calculate T4

%1 = DC touching horizontal %2 = DC touching vertical

%3 = DC space horizontal %4 = DC space vertical

%6 = AC touching horizontal %7 = AC touching vertical

%8 = AC space horizontal %9 = AC space vertical

%5 = AC touching trefoil %10 = single cable (multicore)

%%space mean = 1 D

typeofssloss = 3; %Sheat Screen Losses

%1 = AC-3ph-Trefoil,

%2 = AC-3ph-Flat,

%3 = AC-3cores,

%% LOOP

for cc = 1:length(material);

for aa = 1:length(A_con);

for bb = 1:length(T_start);

for dd = 1:length(s_con_axis);

for ee = 1:length(T_con);

%% GENERAL

omega = 2*pi*f;

T_0 = T_start(bb)*1; %Ambient Temperature

T_end = T_con(ee); %Max Conductor Temperature

if T_end > T_0

dT = T_end-T_0;

else

dT = 0;

end

u0 = 4*pi*10^(-7); %Permeability of free space

%% GEOMETRY

Acon = A_con(aa)*10^(-6); %cross section [m2]

rcon = sqrt(Acon/pi); %radius of conductor [m]

dcon = 2*rcon; %diameter of conductor [m]

t_ins1mm = 1.77; %thickness of inner insulation [mm]

t_ins1 = t_ins1mm*10^(-3); %thickness of inner insulation [m]

67

d_ins1 = dcon+(2*t_ins1); %diameter of insulation [m]

t_smm = 0.55; %thickness of shield [mm]

t_s = t_smm*10^(-3); %thickness of shield [m]

if n == 1; %mean diameter of the screen [m]

d_s = d_ins1+(2*t_s);

elseif n == 2;

d_s = (2*d_ins1)+(2*t_s);

elseif n == 3; %use equilateral triangle

d_s = 2*((d_ins1/sqrt(3))+0.5*d_ins1) + (2*t_s);

end

d_cc = d_ins1/sqrt(3); %distance between axes of conductor and

axes of cable for 3 core cable

t_ins2mm = 1.2; %thickness of outer insulation [mm]

t_ins2 = t_ins2mm*10^(-3); %thickness of outer insulation [m]

d_ins2 = d_s+(2*t_ins2); %diameter of outer insulation [m]

d_cable = d_ins2;

if n == 1;

s_cab = s_con_axis(dd)*10^(-3); %separation between cable [m]

s_ax = d_cable+s_cab; %distance between cable axes [m]

else

s_ax = d_ins1; %1 core axes to another is the same for

2 or 3 cores, diameter of the insulation 1

end

%% MATERIAL

copper = material(cc)*1; %1=COPPER, else = ALUMINIUM

if copper == 1

%R20hub = 0.000259; %ohm/m, for 70mm2

%p = R20hub*70e-6; %resistivity of copper [Ohm.m]

%Rdc20 = p/Acon; %DC resistance of conductor at 20deg C per unit

length

Rdc20 = 0.000368; %for 50mm2

%Rdc20 = 0.00509; %for 4mm2

alpha20 = 3.93e-3; %constant mass temperature coefficiet at

20deg C per kelvin, provided by IEC60287-1-1

ur = 0.999994; %relative permeability

else

p = 2.8264*10^(-8); %resistivity of aluminium, from IEC60287-1-

1 [Ohm.m]

Rdc20 = p/Acon; %DC resistance of conductor at 20deg C per

unit length [Ohm/m]




end

Rdc_max = Rdc20*(1+alpha20*(T_end-20)); %dc resistance per unit length at

max operating temperature

p_shield = 1.38e-7; %Resistivity of tin plate copper braid [Ohm.m]

R_s = p_shield/Acon; %Resistance of shield

%% LOSSES

%Skin Effect and Skin Depth Calculation

68

ks = 1; %given in IEC60287-1, table 2. Stranded copper and aluminium both

ks and kp equal to 1

xs = sqrt(8*pi*f*power(10,-7)*ks/Rdc_max);

if 0 < xs <= 2.8

ys = (xs^4)/(192 + 0.8*(xs^4));

elseif 2.8 < xs <= 3.8

ys = -0.136 -0.0177*xs+0.0563*(xs^2);

else

ys = 0.354*xs - 0.733;

end

%Proximity Calculation -- Only for AC, thus only take yp for 3-core cable

or 3 single-core cables

xp = xs; %formula exactly the same but using kp instead of

ks. kp equals to 1, same with ks

ypfactor = 0.312*(dcon/s_ax)^2+1.18/(xp^4/(192+0.8*xp^4)+0.27);

yp = xp^4/(192+0.8*xp^4)*((dcon/s_ax)^2)*(ypfactor);

%AC Resistance

Rac_max = Rdc_max*(1+ys+yp);

ACtoDC = Rac_max/Rdc_max*100;

%Dielectric Losses Calculation - Not applicable

Wd = 0; %dielectric loss

%for single-core cable with sheaths bonded at both ends, only loss due to

%circulating current in the sheaths need to be considered. IEC

%Sheath and Screen Losses Factor Calculation

if typeofssloss == 1 %AC trefoil 3 Cables

edy_loss = 0; %lambda1"

X = 2*omega*10^(-7)*log(2*s_ax/d_s); %reactance per unit length

of cable

circ_loss = (R_s/Rac_max)*(1/(1+(R_s/X)^2));%lambda1'

elseif typeofssloss == 2 %AC Flat Formation

edy_loss = 0;

X = 2*omega*10^(-7)*log(2*s_ax/d_s); %reactance per unit length of

cable

Xm = 2*omega*10^(-7)*log(2);

P = X+Xm;

Q = X-(Xm/3);

helper1 = 0.75*P^2/(R_s^2+P^2);

helper2 = 0.25*Q^2/(R_s^2+Q^2);

helper3 = 2*R_s*P*Q*Xm/(sqrt(3)*(R_s^2+Q^2)*(R_s^2+P^2));

circ_loss = R_s/Rac_max*(helper1+helper2+helper3);

circ_loss2 = R_s/Rac_max*(helper1+helper2-helper3);

circ_loss3 = R_s/Rac_max*(Q^2/(R_s^2+Q^2));

else typeofssloss == 3; %AC - 3 cores 1 cable

if R_s <= 100*10^(-6);

helper4 = (R_s/omega*10^7)^2;

helper5 = (2*d_cc/d_s)^2*(1/(1+helper4));

helper6 = (2*d_cc/d_s)^4*(1/(1+4*helper4));

edy_loss = 3*R_s/Rac_max*(helper5+helper6);

circ_loss = 0;

else

edy_loss = 3.2*omega^2/(Rac_max*R_s)*(2*d_cc/d_s)^2*10^(-14);

circ_loss = 0;

end

end

lambda1 = circ_loss+edy_loss; %lambda1, loss factor for sheath and screen

69

lambda2 = 0; %idk lambda2

%% T1, T2, T3 Calculation

rho_155 = 4.31; %resistivity of RADOX 155

rho_elastomer = 4.1; %resistivity of RADOX Elastomer

rho_t1 = rho_155; %thermal resistivity of the inner insulation [K.m/W]

rho_i1 = rho_155; %thermal resistivity of the insulation, for 3 core

[K.m/W]

rho_f1 = rho_155; %thermal resistivity of the filler material [K.m/W]

Gt1perdc = t_ins1/dcon; %Geometry Factor

if TR1Factor == 1;

T1 = (rho_t1/(2*pi))*log(1+2*t_ins1/dcon);

elseif TR1Factor == 2;

if Gt1perdc <= 0.1;

G = 0.5; %taken from IEC60287-2-1, figure 2

elseif 0.1 < Gt1perdc <= 0.4

m = 2 %gradient area 1

G = m*(Gt1perdc-0.1)+0.5;


m = 1.1667 %gradient area 2

G = m*(Gt1perdc-0.4)+1.1;

elseif 0.7 < Gt1perdc <= 1.2;


G = m*(Gt1perdc-0.7)+1.45;



G = m*(Gt1perdc-1.2)+1.8;

elseif Gt1perdc > 1.8


G = m*(Gt1perdc-1.8)+2.1;

end

T1 = rho_t1*G/(2*pi)

elseif TR1Factor == 3;

if Gt1perdc <= 0.1;

G = 0.5; %taken from IEC60287-2-1, figure 3


m = 3 %gradient area 1

G = m*(Gt1perdc-0.1)+0.5;



G = m*(Gt1perdc-0.3)+1.1;



G = m*(Gt1perdc-0.7)+1.6;



G = m*(Gt1perdc-1.3)+2.1;

elseif Gt1perdc > 1.9


G = m*(Gt1perdc-1.9)+2.4;

end

T1 = rho_i1*G/(2*pi)+(0.031*(rho_f1 - rho_i1)*exp(0.67*t_ins1/dcon));

end

%T2 Calculation

T2 = 0;

%T3 Calculation

70

rho_t3 = rho_elastomer; %thermal resistivity of outer insulation

T3 = rho_t3/(2*pi)*log(1+2*t_ins2/d_s);

%% T4 Calculation

if formationtype == 1;

Z_iec = 0.29; E_iec = 2.35; g_iec = 0.5;

elseif formationtype == 2;

Z_iec = 1.42; E_iec = 0.86; g_iec = 0.25;

elseif formationtype == 4

Z_iec = 0.75; E_iec = 2.8; g_iec = 0.3;


Z_iec = 0.94; E_iec = 0.79; g_iec = 0.2;


Z_iec = 0.62; E_iec = 1.95; g_iec = 0.25;

elseif formationtype == 7;

Z_iec = 1.61; E_iec = 0.42; g_iec = 0.2;

elseif formationtype == 9; %8 in the IEC

Z_iec = 1.31; E_iec = 2; g_iec = 0.2;

else %3, 8, 10

Z_iec = 1.69; E_iec = 0.63; g_iec = 0.25;

end

heatc = (Z_iec/d_cable^g_iec)+E_iec; %heat coefficient IEC

K_A = pi*d_cable*heatc*(T1/n+T2+T3); %neglect the AC losses

dThetas = 2 %initial number given, remember that dThetas always in

the power of 1/4

diff_dThetas = 1000 %random

iterasi = 0

while diff_dThetas > 0.001

dThetas_1 = power(dT/(1+K_A*dThetas),0.25)

diff_dThetas = dThetas_1 - dThetas

dThetas = dThetas_1

iterasi = iterasi + 1

end

T4 = 1/(pi*d_cable*heatc*(dThetas));

%% AMPACITY DC

%DC & AC show the same result in f = 0

huy = Wd*(0.5*T1+n*(T2+T3+T4))

I_DC_compare_end (ee) = sqrt(dT/((Rdc_max*T1)+(n*Rdc_max*(T2+T3+T4))));

I_AC_compare_end (ee) = sqrt((dT-

0)/(Rac_max*T1+n*Rac_max*(1+lambda1)*T2+n*Rac_max*(1+lambda1+lambda2)*(T3+T

4)));

%collecting per variation

I_T_end (ee) =

sqrt((dT)/(Rac_max*T1+n*Rac_max*(1+lambda1)*T2+n*Rac_max*(1+lambda1+lambda2

)*(T3+T4)));

I_CSA (aa) =


)*(T3+T4)));

I_T_amb (bb) =


)*(T3+T4)));

%material variation

if (cc) == 1;

I_CSA_cop = I_CSA;

I_T_amb_cop = I_T_amb;

71

I_T_end_cop = I_T_end;

else

I_CSA_al = I_CSA;

I_T_amb_al = I_T_amb;

I_T_end_al = I_T_end;

end

%I as function of Tambient, combined with T in conductor. Figure 5

%could be copper or aluminium

if (cc) == 1 %for copper

if (bb) == 1 %20 deg C

I_T_end20_cop = I_T_end

elseif (bb) == 2 %40 deg C






end

else

if (bb) == 1 %20 deg C

I_T_end20_al = I_T_end







end

end

end

end

end

end

end

%% GRAPHICS

figure(1)

plot(A_con, I_CSA_cop, 'r-o',A_con,I_CSA_al,'b-*')

legend('copper','aluminium')

xlabel('Cross Section [mm2]')

ylabel('Cable Ampacity [A]')

title('Single-core Cable';'Ambient Temperature = 20 C'; ' Max Conductor

Temperature = 90 C')

grid on

figure(2)

plot(T_start, I_T_amb_cop,'r-o', T_start, I_T_amb_al, 'b-*')


xlabel('Ambient Temperature [deg C]')

ylabel('Cable Ampacity [A]')

title('Single-core Cable';'Conductor Cross Section Area = 70mm2'; ' Max

Conductor Temperature = 90 C')

grid on

figure(4)

plot(I_T_end_cop,T_con,'r-o', I_T_end_al,T_con,'b-*')

72


ylabel('Conductor Temperature [deg C]')

xlabel('Continuous Current Applied [A]')

title('Single-core Cable';'Cross Section Area = 70mm2'; 'Tamb = 20 degC')

grid on

%main, many plot

figure(5)

plot( I_T_end20_cop, T_con, 'g', I_T_end40_cop, T_con, 'b',

I_T_end60_cop, T_con, 'y', I_T_end80_cop, T_con, 'r', 'LineWidth',1.2)

ylabel('Conductor Temperature [deg C]')

xlabel('Continuous Current Applied [A]')

title('Single-core Cable';'Two Cables Touching, Vertical';'Cross Section

Area = 50 mm2')

hleg = legend('25','40', '60', '80');

htitle = get(hleg,'Title');

set(htitle,'String','Ambient Temperature [deg C]')

grid on

73

Short Circuit Calculation Code

%% SHORT CIRCUIT CAPABILITY

clear all

clc

Tscmax1 = 250;

T_01 = 100;

t_cl1 = [0.05:0.01:5];

A_con1 = [20 30 50 70]; %cross section [mm2]

for dd = 1:length(A_con1)

for cc = 1:length(t_cl1);

t_c = t_cl1(cc)*1;

A_con = A_con1(dd)*(1973.52524139); %convert the unit to per mil

Isc(cc) = A_con*sqrt(0.0297*log((Tscmax1+234)/(T_01+234))/t_c);

%CSA variation

if (dd) == 1 %20

ISC20 = Isc

elseif (dd) == 2 %30

ISC30 = Isc


ISC50 = Isc


ISC70 = Isc

end

end

end

figure(1)

plot( t_cl1, ISC20, 'r', t_cl1, ISC30, 'b', t_cl1, ISC50, 'k', t_cl1,

ISC70, 'y')

legend('CSA = 20','CSA = 30', 'CSA = 50', 'CSA = 70')

ylabel('Maximum Short Circuit Current[A]')

xlabel('clearance time [s]')

title('Short Circuit Withstand Capability')

grid on

74

Voltage Drop Calculation Code

%% AC VOLTAGE DROP CALCULATION

clear all

clc

long = [0:1:150];

A_con = 50; %cross section [mm2]

T_end = 120; %Temperature end variable in matlab [deg C]

f = 700;

pf = [1 0.85 0.7 0.55 0.4 0.1];

material = 1; %1=COPPER, 2 = ALUMINIUM

I_con = 200;

s_con_axis = [0]; %separation of cable [mm]

%% CONTROL Variable

n = 1; %number of conductor in a cable

%% for LOOP start

for aa = 1:length(pf);

for bb = 1:length(long);

%% GENERAL

Vbaseac = 650;

Vbasedc = 900;

omega = 2*pi*f;

costheta = pf(aa)*1;

degree = acosd(costheta);

sintheta = sind(degree);

leng = long(bb)*1;

%% GEOMETRY

Acon = A_con*10^(-6); %cross section [m2]

rcon = sqrt(Acon/pi); %radius of conductor [m]

dcon = 2*rcon; %diameter of conductor [m]

t_ins1mm = 2.1; %thickness of inner insulation [mm]

t_ins1 = t_ins1mm*10^(-3); %thickness of inner insulation [m]

d_ins1 = dcon+(2*t_ins1); %diameter of insulation [m]

t_smm = 0.5; %thickness of shield [mm]

t_s = t_smm*10^(-3); %thickness of shield [m]

if n == 1; %mean diameter of the screen [m]

d_s = d_ins1+(2*t_s);

elseif n == 2;

d_s = (2*d_ins1)+(2*t_s);

elseif n == 3; %use equilateral triangle

d_s = 2*((d_ins1/sqrt(3))+0.5*d_ins1) + (2*t_s);

end

d_cc = d_ins1/sqrt(3); %distance between axes of conductor and

axes of cable for 3 core cable

t_ins2mm = 1.2; %thickness of outer insulation [mm]

t_ins2 = t_ins2mm*10^(-3); %thickness of outer insulation [m]

d_ins2 = d_s+(2*t_ins2); %diameter of outer insulation [m]

d_cable = d_ins2;

if n == 1;

75

s_cab = s_con_axis*10^(-3); %separation between cable [m]

s_ax = d_cable+s_cab; %distance between cable axes [m]

else

s_ax = d_ins1; %1 core axes to another is the same for

2 or 3 cores, diameter of the insulation 1

end

%% MATERIAL

copper = material*1; %1=COPPER, else = ALUMINIUM

if copper == 1

R20hub = 0.000259; %ohm/m, for 70mm2

p = R20hub*70e-6; %resistivity of copper [Ohm.m]


unit length [Ohm/m]




else

p = 2.8264*10^(-8); %resistivity of aluminium, from IEC60287-1-

1 [Ohm.m]


unit length [Ohm/m]




end

Rdc_max = Rdc20*(1+alpha20*(T_end-20)); %dc resistance per unit length at

max operating temperature

R_s = 0.0037; %ohm/m. Shielding tin copper braid, from COROPLAST

%% LOSSES

%Skin Effect and Skin Depth Calculation

ks = 1; %given in IEC60287-1, table 2. Stranded copper and aluminium both

ks and kp equal to 1

xs = sqrt(8*pi*f*power(10,-7)*ks/Rdc_max);

if 0 < xs <= 2.8

ys = (xs^4)/(192 + 0.8*(xs^4));

elseif 2.8 < xs <= 3.8

ys = -0.136 -0.0177*xs+0.0563*(xs^2);

else

ys = 0.354*xs - 0.733;

end

%Proximity Calculation -- Only for AC, thus only take yp for 3-core cable

or 3 single-core cables

xp = xs; %formula exactly the same but using kp instead of

ks. kp equals to 1, same with ks

ypfactor = 0.312*(dcon/s_ax)^2+1.18/(xp^4/(192+0.8*xp^4)+0.27);

yp = xp^4/(192+0.8*xp^4)*((dcon/s_ax)^2)*(ypfactor);

%AC Resistance

Rac_max = Rdc_max*(1+ys+yp);

ACtoDC = Rac_max/Rdc_max*100;

X = 2*omega*10^(-7)*log(2*s_ax/d_s); %reactance per unit length of

cable

%% RESULT

76

%aa = pf variation

if aa == 1;

Vd_ac1 = I_con*sqrt(3)*leng*(Rac_max*costheta+X*sintheta); %AC Voltage

Drop

drop_ac1(bb) = Vd_ac1/Vbaseac*100;

elseif aa == 2;


Drop

drop_ac85 (bb)= Vd_ac85/Vbaseac*100;

elseif aa == 3;


Drop


elseif aa == 4;


Drop


elseif aa == 5;


Drop


elseif aa == 6;


Drop


end

end

end

%% GRAPH

figure(1)

plot(long, drop_ac1, 'r', long, drop_ac85, 'b',long, drop_ac7, 'k',long,

drop_ac55, 'g',long, drop_ac4, 'y',long, drop_ac01, 'm');

legend('pf 1','pf 0.85','pf 0.7','pf 0.55','pf 0.4','pf 0.1')

grid on

77

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