Analysis of the Ampacity Characteristic of Single-Core AC Cable Laid in Water

DING Shuchun, JIAN Ganyang, LIU Gang, LEI Chenghua

School of Electric Power, South China University of Technology, Guangzhou, 510640, China

Email: shuchunding@163.com Abstracts-Cable conductor temperature is an important parameter

to determine the cable ampacity. On the other hand, the

surrounding condition has a tremendous influence on cable

conductor temperature. In order to improve the operating current

of cable, this article derivates the calculation formulae for the

ampacity of single-core AC cable laid in water, by analyzing the

operating current characteristics of the single-core AC cable laid

on water. The further correctness of the theoretical analysis is

demonstrated by the comparison of the experimental statistics of

conductor temperature of the single-core AC cables respectively

immersed in water and in air without being exposed to the sunlight.

It also draw a conclusion that AC cable laid on water can maximize

the cable ampacity, and provide important theoretical basis to

maximize the cable ampacity.

Key words-110kV cable; ampacity; external thermal resistance;

core temperature; water; test

I. INTRODUCTION

Improving the carrying capacity of cable, reducing the operating core temperature, extending the service life of cable and improving the circuit reliability are urgent need to address the problem[1-3]. Cable laid in different surrounding conditions has carrying capacity of a large range [4], which depends on the cable laying conditions and status of site [5-6]. Carrying capacity of cable at home and abroad is generally according to IEC60287 standard calculation [7]. However, the standard for cable laid in water does not give a formulae for calculating cable ampacity, so we could not get characteristic of cable set in water directly from the IEC60287 standard, Therefore, this article is about when the 110kV high voltage cable is under the same carrying capacity-1000A,and about how to derive the external thermal resistance of core AC cable laid on water based on the similar surrounding condition of AC cables which immersed in water and in air without being exposed to the sunlight. This leads to the formula for cable’s core temperature and cable ampacity . The further correctness of the theoretical analysis is demonstrated by the comparison of the experimental statistics of conductor temperature of the single-core AC cables respectively

immersed in water and in air without being exposed to the sunlight. It also make a conclusion that AC cable laid on water can maximize the cable ampacity, and provide important theoretical basis to improve the carrying capacity of cable, which can reduce conductor temperature of the single-core AC cables and prolong the service life of cable and improve the reliability of circuit operation.

II. DERIVATION OF THE THERMAL RESISTANCE OF AC SINGLE-CORE CABLE LAYING IN THE WATER

Because of the similar surrounding ambient conditions of AC cable immersed in water and air without being exposed to the sunlight-air and water are fluids, we can derivate the calculation formulae for external thermal resistance of single-core AC cable laid in water by the calculation formulae for one’s immersed in air without being exposed to the sunlight [8].

The recent distance between the cable surface and the wall surface is S ≥ 0.3De, De ≤ 0.15m.

A. The Calculation of External Thermal Resistance 4T of

Single-core AC Cable Immersed in Air Without Being Exposed to the Sunlight

The calculation formulae for external thermal resistance of single-core AC cable laid in air without being exposed to the sunlight is as follows[5]:

4 1/4

1( )e s

TD hπ θ

=⋅ ⋅ ⋅ Δ

(1)

Where, h is heat sinking factor

ge

Zh ED

= + (2)

De — out diameter, m. According to the reference : Z=0.21, E=3.94, G=0.60[3] When the out diameter of cable is 0.15m, h=4.5955,Kcal / m • Time • ℃

sθΔ — temperature rise of conductor surface above ambient

temperature, K

Calculation of 1/ 4( )sθΔ [5]:

978-1-4244-6255-1/11/$26.00 ©2011 IEEE

12 1 3 1 2

1 2

[ (1 ) (1 )]1

eA

D h TK T T

nπ λ λ λ

λ λ⋅

= + + + + ++ +

(3)

So

1/4 1/41 1/4( ) [ ]

1 ( )d

s nA sK

θ θθθ+

Δ + ΔΔ =

+ Δ (4)

Made the initial Value of 1/ 4( )sθΔ 2 and substituted into

the type, iterated repeatedly until the difference between two adjacent values less than 0.001; There,

dθΔ — The factor of Calculation of dielectric loss, Dimension with temperature, when ignore the dielectric, dθΔ is 0. ∆θ—permissible temperature rise of conductor above ambient temperature, K

B. Derivate the Calculation of the External Thermal

Resistance 4T ′ of Single—core AC Cable Laid on

Waters

Because of the similar surrounding ambient conditions of AC cables immersed in water and in air without being exposed to the sunlight [9-10], the external thermal resistance of single core cable around water can be similar to the type formula (1):

4 1/4

1( )e s

TD hπ θ

′′ ′=

⋅ ⋅ ⋅ Δ (5)

Where, the differences with formula (1) are heat sinking

factor h′ and 1/4( )sθ ′Δ ;

This paper considers that the cable is laid in still water. At this point, the water heat sinking factor is the thermal conductivity coefficient. The thermal conductivity coefficient of water in a saturated atmosphere or thermal conductivity line is shown in table 1[11].

The algorithm of 1/4( )sθ ′Δ is derived from the algorithm

of 1/ 4( )sθΔ , it only change h to h’. We can make a conclusion

that h’ << h by comparing h=4.5955, Kcal / m • Time • ℃and

the value in table 1.We know that the range of 1/ 4( )sθΔ is

0—1.6[4] [6] by looking up the IEC60287 standard. When compared with the range of h, it is so small that can be neglected.

TABLE.Ⅰ WATER THERMAL CONDUCTIVITY IN AN ATMOSPHERIC

PRESSURE OR SATURATION LINE

Temperature

T(℃)

Heat Sinking Factor

h’×10^2

(Kcal / m • Time • ℃)

10 50.47

20 51.85

30 53.14

40 54.34

50 55.29

60 56.23

70 56.92

80 57.61

90 58.13

100 58.56

110 58.81

120 59.07

130 59.16

140 59.16

150 59.07

III. COMPARE AND ANALYSE THE AMPACITY CHARATERISTICS OF SINGLE-CORE AC CABLE

LAID IN WATER

For the single-core AC cable laid in free air without forced convection, the calculate formulae for the ampacity can be derived from the temperature rise above ambient temperature formulae (6) as the following formulae [5]:

2 21 1 2

21 2 3 4

( 0.5 ) [ (1 ) ]

[ (1 ) ] ( )d d

d

I R W T I R W T

I R W T T

θΔ = + ⋅ + + λ + ⋅

+ + λ + λ + ⋅ + (6)

0.51 2 3 4

1 1 2 1 2 3 4

[0.5 ( )]{ }

(1 ) (1 )( )dW T T T T

IRT R T R T T

θΔ − + + +=

+ + λ + + λ + λ + (7)

The calculation formulae for the temperature rise above ambient temperature and the ampacity of single-core AC cable laid in water can be derived by analog (6)(7), based on the derivation of external thermal resistance of single-core AC cable laid in water.

2 21 1 2

21 2 3 4

( 0.5 ) [ (1 ) ]

[ (1 ) ] ( )d d

d

I R W T I R W T

I R W T T

θ ′

′

Δ = + ⋅ + + λ + ⋅

+ + λ + λ + ⋅ + (8)

0.51 2 3 4

1 1 2 1 2 3 4

[0.5 ( )]{ }

(1 ) (1 )( )dW T T T T

IRT R T R T T

θ ′′

′

Δ − + + +=

+ + λ + + λ + λ + (9)

Above formulas show that only heat sinking factor changes among those environment factors. When only heat sinking factor changes and the others are unaltered , the change process of permissible temperature rise of conductor

above ambient temperature ∆θ can be described as the follows: h T4 θΔ

As h’ ≫ h, it can be concluded that when the 110kV high voltage cable which is under the same carrying capacity-1000A and in two different installation environment, arrives stable state, permissible temperature rise of conductor

is higher than ambient temperature show θΔ ≫ θ ′Δ . So

when the maximum temperature of cable allowing steady-state operation remains the same, I ′ ≫ I

This shows that carrying capacity of cable increased greatly when laid in water.

IV. CASE STUDY OF THE AMPICATY CHARATERISTICS OF SINGLE-CORE AC CABLE

LAID IN WATER

The ampacity of cable will be different as the environment changes [12-13].

A. Conductor Temperature Analysis of Cables Laid in Different Environment when Loading the Same Current.

The conductor temperature of cable is different when cable is located in different environment, air and water, even though the loading current is the same. In the conducted experiment, the cable was located as Fig.1, and the thermal couples were located in cable as Fig.2. The measured temperature is shown in Fig.3.

Figure 1. The method of locating the cable

Figure 2. The located method of thermal couples

Figure 3. The measured conductor temperature in different environment

When loading current was 1000A with the initial condition of room temperature, the corresponding conductor temperature of cross-linked polyethylene cable until 80 minutes later was as the left part of Table 1. As Fig.3 has shown, the conductor temperature of cable when cable was in water was 14℃ lower than in air after the temperature reached the steady state. Then the loaded current shifted to 1380A and last for 60 minutes more. The corresponding conductor temperature was as the right part of Table 1. As Fig.3 has shown, the conductor temperature of cable when cable was in water 24℃ lower than in air after the temperature reached the steady state. Therefore, we can conclude that the conductor temperature of cable when cable was in water was greatly lower than in air after the temperature reached the steady state.

B. Lording Current Analysis of Cables in Different Environment When the Conductor Reaches the Same Temperature

The loading current of cable is different when cable is located in different environment, air and water, even though the conductor temperature is the same. Exchanging the axis of Fig.3, we can conclude that the ampacity of cable when it was located in water was approximately 20% larger than in air. So the experiment data in this paper demonstrates the proposed ampacity property analysis. We can draw a conclusion that the ampacity of AC power cable can be enlarged by placing it in the water.

V. CONCLUSION

(1)This article derivates the calculation formulae for the ampacity of single-core AC cable laid in water according to IEC60287 standard by the method of comparison and analogism, and analyzes the ampacity characteristic of the single-core AC cable by comparison. The further correctness of the theoretical analysis is demonstrated by the comparison

of the experimental statistics of conductor temperature of the single-core AC cables respectively immersed in water and in air without being exposed to the sunlight. (2)Consequence of analysis shows that the carrying capacity of the single-core AC cable laid in water will increase about 38% than one’s in air. It provides an important theoretical basis to maximize the cable ampacity.

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