Parameters Affecting the Ampacity of HVDC Submarine Power Cables

Redy Mardiana Department of Electrical Engineering, The Petroleum Institute

PO Box 2533, Sas Al Nakhl, Umm Al Naar Abu Dhabi, United Arab Emirates

��������—This paper explains some parameters that affect the ampacity of HVDC submarine power cables. The parameters include ambient temperature, burial depth, and spacing distance between two cables. The analytical computation of cable ampacity is carried out in steady-state conditions. Internal, external, and mutual thermal resistances of power cables are taken into account in the calculation. The ampacity calculation is applied to a single conductor armored mass-impregnated polypropylene laminated paper (MI-PPLP) submarine cable. The HVDC system which has bipolar configuration with earth return is considered as a case study. The calculation results of cable ampacity are presented and discussed.

Keywords-submarine cable; ampacity cable; HVDC system;heat transfer.

I. INTRODUCTION

There is a trend towards the introduction of high-voltage direct current (HVDC) transmission technology that will facilitate such items as increased short-circuit capacity which accompanies the expansion of power systems and the longer distance of power transmission due to the remote locations of power supplies. When two or more power systems are separated by the sea, the HVDC submarine power transmission cables are applied to connect among them [1].

Oil-filled (OF) cables and mass-impregnated (MI) cables are major insulation types of the HVDC submarine cables. OF cables have the limit of transmission length because of the capacity of oil feeding equipment, while MI cables are suitable for the long HVDC transmission lines although MI cables have the lower design temperature than OF cables, leading to the increase of the conductor size [2].

Cable sizing is the first step to be considered when power systems are going to use the transmission cables. Cable sizing is closely related to the cable ampacity. In this paper, some parameters that affect the ampacity of HVDC submarine power cables are studied. The analytical techniques for the computation of cable ampacity in steady-state conditions through the use of assumptions that simplify the problem are presented. Single conductor armored mass-impregnated polypropylene laminated paper (MI-PPLP) cable which has been used in the submarine cable installations worldwide is therefore selected in the design [3]. It is thought that a work of this type will be useful not only as a guide to engineers entering the field and as a reference to more experienced, but particularly as a basis for setting up computation methods for the preparation of utility load capability.

II. HEAT TRANSFER IN DC CABLES

� ���� ���Rating of a power cable is generally expressed in term of

ampacity [4-6]. Ampacity is the current-carrying capacity of a cable. Ampacity in air or in an underground cable system is determined by the capacity of the installation to extract the heat from the cable and dissipate it in the surrounding medium. There are three physical mechanisms for heat transfer: • Conduction • Convection • Radiation

Fourier Law describes the heat transferred by conduction. In very simple terms, the heat flux is proportional to the ratio of temperature over space. In an underground cable installation heat conduction occurs everywhere except in the air space in the conduit. If the cable is installed in air heat conduction occurs only inside the cable, the heat transfer beyond the outer serving (outer jacket) is convection and radiation.

Convection of heat occurs in moving fluids (air, water, etc.) and obeys Newton's Law. The flow of heat is proportional to the temperature difference. In a submarine cable installation (the cable is not buried), convection takes place from the cable(s) to the sea water. If a submarine cable installation is buried, only conduction takes place.

The Stefan-Boltzmann Law describes the radiation of heat phenomenon as being proportional to the difference the temperatures at the power of four. In cables in air, radiation of heat occurs from the cable(s) to the air space. There is a practical distance, away from the heat source, beyond which the heating effects are not felt.

� ������������ ������������The heat sources in AC cable installations can be divided

into two generic groups: heat generated in conductors and heat generated in insulators. The losses in the metallic (conductors) elements are by far the most significant losses in a cable and they are caused by: (a) Joule losses due to impressed currents, circulating currents or induced (eddy current) losses; (b) Hysteresis losses in conductors that are also magnetic.

The following metallic components of a cable system will produce heat:

� Core conductors � Sheaths � Armors

The losses in those components are functions of the frequency (�) and the temperature (�) of operation and proportional to the square of the current (�).

Insulating or dielectric materials also produce heat. The heat produced in the insulating layers is only important under certain high voltage conditions. The following components could be considered: � Main insulation � Shields � Screens � Jackets � Beddings/servings

The dielectric loss when ac voltage is applied is given by:

2 tan( )� ��� �� (1)

where � is the capacitance, �� is the voltage applied and � is the dielectric loss angle.

The heat source in DC cable installations is generated only in conductors. Because when cable is energized by dc voltage, the power frequency becomes zero, therefore:

� No losses due to skin and proximity effects on conductor � No Dielectric Losses on Insulation � No Eddy Current Losses on Sheath � No Hysteresis Losses on Armor � No Circulation Current on Sheath, Armor and Conductor

Therefore, DC cables have lower losses than AC cables.

� �� � �������� ��� ����������!�������� ������������The technique known as the Neher-McGrath method for

ampacity calculations is based on a thermal-electrical analogy method [7]. The basic idea is to subdivide the study area in cable layers. Then one substitutes the heat sources by current sources and the thermal resistances by electrical resistances. Each layer has its own thermal resistance. Figure 1 shows the typical construction of a submarine dc cable, while Figure 2 shows the correspondence between the cable installation components and the electric circuit elements for steady state ampacity calculations.

To find the ampacity we first note that the potential of every node in the circuit is analog to the temperature of the regions between the layers. Thus, the potential difference (��)between the terminals of the circuits and the innermost current source represents the temperature rise of the core (�conductor) of the cable with respect to the ambient temperature (�ambient). Only conductors generate Joule losses, �c.

From Figure 2, we can compute ∆� as follows:

� �1 2.���"����� �#� ��� � � �$� #� � � ! ! ! ! ! � �! !�! !! (2)

where !� is thermal resistance of layer �, !�$� is external thermal resistance of medium beyond the cable materials (e.g. air, soil), and !# is mutual thermal resistance.

To derive an expression from where the ampacity can be computed directly, the heat sources (electrical losses) �� is expressed as �2%"�. The conductor losses are computed usingthe dc resistance and the current. Thus, the ampacity of a cable can be expressed as:

� �1 2.���"����� �#� ���

"� � �$� #

� ��% ! ! ! ! !

�

�! !! !! (3)

where o

o

Normal operating temperature of conductor ( C)

Ambient temperature ( C)���"�����

�#� ���

��

�

�

From expression (3) one can compute the ampacity of a cable. Of paramount importance for cable rating is the accurate calculation of the thermal resistances ! and the dc resistance %"� of the core of the cable. The %"� considers the temperature dependency of the resistances.

The temperature at the conductor is highest, and the temperature of the insulation nearest the conductor limits the ampacity. Ambient soil temperature is the temperature at the burial depth of the cable in the absence of any non-native heat sources. These temperatures are usually established during a route thermal survey.

Construction:1 -Conductor (key-stone type) 6 -Plastic jacket 2 -Conductor shielding 7 -Tape armor bedding 3 -Insulation (mass-impregnated paper) 8 -Optical fiber 4 -Insulation shielding 9 -Steel wire armor 5 -Lead sheath 10 -Serving

Figure 1. Typical construction of submarine DC cable.

Figure 2. Thermal-electrical equivalent of heat transfer in a DC cable.

III. THERMAL RESISTANCE

� ���������!&��#���%�� ������������������In the Neher-McGrath method, the thermal resistances are

either computed from basic principles or from heuristics. One can appreciate, from Figure 1, that some of the internal layers of a cable can be considered as tubular geometries. The following expression is used for the computation of the thermal resistance of layer- of tubular geometries:

ln2

�����

����

�!�

��

�� � �

� � (4)

where

2

Thermal resistance (K. m/W)Thermal resistivity (K.m/W) Diameter (mm )

!

����

�

Equation (4) is applicable for most internal to the cable layers (!'(�!)(*(�!�). For complicated geometries and for the layers external to the cable, such as three-core cables, duct banks, etc., heuristics are used. If the layer is metallic conductor (e.g. sheath, armour), the thermal resistivity is very small, so that the thermal resistance for metallic conductor is

generally neglected (! �� 0). The term ���

����

����

�����

��ln in equation

(4) is called the geometrical factor because it is a function of the shape and dimensions of the particular geometry. There are a number heuristics used in the calculation of thermal resistances. For example, there are expressions for: equally or unequally loaded cables, touching or not touching cables, flat or triangular formations, trefoils, backfills, duct banks, etc.

� �$�������!&��#���%�� ������������� �"��������The external thermal resistivity of a cable buried

underground is commonly computed assuming that the surface of the earth in the neighborhood of the cable installation is an isothermal. This assumption allows for the application of the image method to compute the external thermal resistance (!�$�). The following expression is the results from the image method:

� �

2 2

4

0.8

2

2 4ln .ln

2

1.02 .24

6.71 10100

0.2 Load Factor 0.8 Load FactorLoss Factor

�� $�$�

� $

$ �

��

+ + ��! +,� �

�

+,+,

��

�

��

� � �� �� �� � � � �� �� � � �� �

�

��

� � ��

(5)

where

2

External thermal resistance (K. m/W)Soil thermal resistivity (K.m/W)

Depth of buried cable (m) Diameter serving cable (mm )

�

�

!

+�

����

�

The thermal resistance of the layers external to the cable (!�$�) must also include the duct when present, and the air inside. The duct itself is of tubular geometry and it very easy to model, however, the treatment of the air inside of a duct is a complex matter. The heat transfer is dominated by convection and radiation and not by conduction. There exist simple formulas, which have been obtained experimentally and that work fine for the conditions tested.

� �$�������!&��#���%�� ����������������� ��� ��When a cable is exposed in air, convection and radiation

occur simultaneously from cable to air space. The external thermal resistance (!�$�) which includes convection and radiation heat transfers can be computed using the following formula,

2 21 2 1 2

1( )

( )( )

�$�� � �

��

�

�

!� & &

-.&�

& � � � �

�

��

�

�

�

(6)

where 2

2

-8 -2 -4

Convection heat transfer coefficient (W/m .K)

Radiation heat transfer coefficient (W/m .K)Thermal conductivity (W/m.K))

Nusselt number

Boltzman Constant, 5.67 10 (Wm K ) Emissity num

�

"

�

&&-.��

�

�

��

� ��

1

2

ber Outer serving temperature (K) Ambient temperature (K)

��

��

In case of natural convective heat transfer, the value of convective heat transfer coefficient (&�) must be calculated beforehand. Equation (7) shows the formula to derive the convective heat transfer coefficient at a predefined temperature:

� �

� �

31 2

2

1 214

2

0.53 .

��

� � �

��

�

/ � � �0

�

� �

. 0 1-.&�

�

�

�

�

�

�

(7)

where 2

-3

-6 2

1

2

Convection heat transfer coefficient (W/m .K)

28.15 10 (W/m.K) 18.4 10 (m /s) Prandtl number = 0.7035 Outer serving temperature (K) Ambient temperature (K)

�

�

&-�1��

�

� �

� ����

� 2������!&��#���%�� �������������� �"��������When multiples cables are installed in the ground, there is

a mutual heating effect of the other cables or cable pipes in a system of equally loaded, identical cables or cable pipes. For several loaded cables placed underground, we must deal with superimposed heat fields. The principle of superposition is applicable if we assume that each cable acts as a line source and does not distort the heat field of the other cables. Therefore, in the following subsections, we will assume that the cables are spaced sufficiently apart so that this assumption is approximately valid. The mutual thermal resistance (!#) is expressed by the following formula.

� �ln2

�#! ,�

�� (8)

where ,� is a geometry factor. The axial separation of the cables should be at least two cable diameters. The distances needed to compute factor , are defined in Figure 3. These are center-to-center distances. For cable 3,�

' ' ' '1 2

1 2

3 3 3- 3

3 3 3- 3

" " " ",

" " " " � � � �

� � �� � � � � �� �� � � � � �� �� � � � � �

� � � �3- 3 � � � �3- 3 " """"3- 3

�" ""� � � �� � � �3 3

" """" (9)

IV. WALL TEMPERATURE AND DC RESISTANCE

� �����!�#3��������The wall temperature is the temperature at the boundary

between two layers. The wall temperature, especially the outer

serving temperature, must be calculated when the convection and/or radiation heat transfer takes place. To find the wall temperatures, we can use

. ln2

����� ���� �����

����

�� � ��

��

� � � �

� � (10)

where Heat Loss (W/m)

Temperature at inner media (K)Temperature at outer media (K)

����

�����

���

���

� ���%�� �������������"������The operating dc resistance of a cable is a function of the

temperature. The temperature variation is described by:

� �6

2020

1.02 10 1 ( 20)"�%�

� � ��� (11)

where o

20o

20

o

2

Resistivity at 20 C ( .m)

Temperature coefficient at 20 C (/K)

Operating temperature ( C)Cross section (mm )�

�

�

�

� �

�

�

�

The value of resistivity and temperature coefficient can be obtained from the Table 1:

Table 1: Resistivity and temperature coefficient

When a conductor is energized by dc voltage, there are no skin and proximity effects in cables; hence, the above equation is very simple and accurate formula adequate for the ampacity calculation.

V. SIMULATION AND RESULTS

� �4���#�1���#������As a case study of cable ampacity calculation, a 500-kV

HVDC system is considered. The HVDC system as depicted in Figure 4 is assumed to be bipolar configuration with earth return and it has one cable per-pole. The cable is assumed to be a single conductor with mass-impregnated polypropylene laminated paper (MI-PPLP) insulation. The conditions to calculate the cable ampacity are given as follow: a. Normal operating temperature of conductor : 85oC b. Ambient temperature : 30oC c. Load Factor : 100% d. Conductor : Copper e. Thermal soil resistivity : 1.2 oC.m/W f. Insulation: MI - PPLP g. Thermal insulation resistivity: 6.0 oC.m/W h. Maximum allowed temperature: 85 oC.

Figure 3. Illustration of the development of an equation for the external thermal resistance of a single cable buried under an isothermal plane.

i. Type of installations: � Cables in air (tunnel) � Cables is directly buried

j. Minimum thickness of insulation: 22 mm. k. Minimum thickness of metallic sheath (lead alloy): 3.5 mm. l. Submarine armoring, diameter of steel wire: 6 mm m. Thickness of armor bedding (plastic) = 6 mm n. Minimum thickness of outer serving (extruded Poly-

propylene yarn): 3 mm.

The installation for buried cable is shown in Figure 5.

� %�������Figure 6 show the current-carrying capacity (ampacity) of

a cable as a function of conductor cross sections. The ambient temperature is varied. For the same ambient temperature, the cable installed in air has higher ampacity compared to the buried cable. Therefore, the cable ampacity is determined by the buried cable installation. Hereafter, the analysis is focused on the ampacity of buried cable.

Figure 7 show the ampacity of a buried cable as a function of ambient temperature. The conductor cross section is varied. The higher is the ambient temperature, the lower is the ampacity. The maximum ambient temperature that can be achieved by MI-PPLP insulation can be higher than 60oC.

Figure 8 show the cable ampacity as a function of burial depth (+). The conductor cross section is varied. In this case, the ambient temperature is kept constant at 30oC and the spacing distance (�) is assumed to be larger than 5 meters. From the figure, the deeper is the burial depth the lower is the

ampacity. After a certain burial depth (i.e., 3 meters), the cable ampacity is nearly constant.

Figure 4. HVDC system with bipolar configuration and ground return.

Figure 5. Buried cable installation.Figure 6. Cable ampacity as a function of conductor diameter and ambienttemperature; (top) cable in air, (bottom) buried cable.

Figure 7. Cable ampacity as a function of ambient temperatures andconductor cross sections.

Cross section (mm2)

Cross section (mm2)

Figure 9 show the ampacity of a cable as a function of spacing distance between two cables. The diameter of conductors is varied. From the figure, the larger is the spacing distance, the higher is the ampacity. In this simulation, the ambient temperature is constant at 30oC and the burial depth is assumed to be 2 meters. After a certain spacing distance (i.e., 8 meters), the ampacity is nearly constant. In the other word, when the cable separation is larger than 8 meters there will be no temperature impacts from the other cables and, therefore,the mutual temperature resistance can be neglected in the ampacity calculation.

Figure 10 show the cable ampacity as a function of load factor. In this simulation, the ambient temperature is constant at 30oC, the burial depth is assumed to be 2 meters and spacing distance is assumed to be larger than 5 meters. The conductor cross section is varied. It can be seen from the figure that the ampacity is reduced when the load factor is increased.

VI. CONCLUSIONS

Some parameters that affect the ampacity of HVDC submarine power cables have been explained. The parameters being concerned were ambient temperature, burial depth, and spacing distance between two cables. The analytical computation of cable ampacity was carried out in steady-state conditions. The ampacity calculation was applied to a single conductor armored mass-impregnated polypropylene laminated paper (MI-PPLP) submarine cable. From the simulation results the following conclusions can be drawn: � The cable ampacity is determined by the buried cable

installation rather than the cable installation in air. � The higher is the ambient temperature, the lower is the

cable ampacity. � The deeper is the burial depth the lower is the ampacity.

The ampacity is nearly constant after 3 meters depth. � When the cable separation is larger than 8 meters there

will be no temperature impacts from the other cables and the mutual temperature resistance can be neglected.

� The ampacity is reduced when the load factor is increased.

REFERENCES

[1] J. Ueda, T. Ishida, and T. Yoshizumi, “Development of the 500-kV DC Converter System”, Hitachi Review, Vol. 47, No. 5, pp. 203-207, 1998.

[2] Y. Maekawa, K. Watanabe, S. Maruyama, Y. Murata, and H. Hirota, 2002, “Research and Development of DC +/- 500kV Extruded Cables”, CIGRE Session Paper 21-203, 2002.

[3] R. Hata, “Solid DC submarine cable insulated with polypropylene laminated paper (PPLP)”, SEI Technical Review, No. 62, pp. 3-9, June 2006.

[4] Increased Power Flow Guidebook— Underground Cables, EPRI, Palo Alto, CA: 2003. 1001818.

[5] George J. Anders, "Rating of Electric Power Cables: Ampacity Computations for Transmission, Distribution, and Industrial Applications, IEEE Press / McGraw Hill, 1997.

[6] F. Leon, “Calculation of underground cable ampacity”, Proc. CYME Int. T & D, pp. 1-6, 2005.

[7] J.H. Neher and M.H. McGrath, “The Calculation of the Temperature Rise and Load Capability of Cable Systems”, AIEE Transactions Part III - Power Apparatus and Systems, Vol. 76, pp. 752-772, October 1957.

Figure 8. Cable ampacity as a function of burial depths and conductor crosssections.

Figure 9. Cable ampacity as a function of spacing distance and conductorcross sections.

Figure 10. Cable ampacity as a function of load factor and conductor crosssections.