C I R E D 20th International Conference on Electricity Distribution Prague, 8-11 June 2009

Paper 0120

CIRED2009 Session 1 Paper No 0120

EFFECT OF DRY ZONE FORMATION AROUND UNDERGROUND POWER CABLES ON THEIR RATINGS

Ossama E. Gouda Ghada M. Amer Adel Z. El Dein Cairo University, Egypt Benha University, Egypt Valley University, Egypt Dr_gouda@yahoo.com dr_ghada11@hotmail.com azeinm2001@hotmail.com

ABSTRACT As it is known there are many factors affecting underground power distribution cables loadings. Such these factors are ambient temperature, cable depth laying, and number of cable parallel circuits and thermal resistivity of the soil. One important factor usually ignored is the formation of dry zones around the underground power cables due to cable loading. Dry zones are usually formed around underground power cables under loading condition due to the migration of soil moisture content. In this paper the effect of dry zone formation on the underground power cables ampacity is investigated. De-rating factor for the formation of dry zone around underground power cables is suggested and calculated for different types of natural backfill soils. IEC 60287-1-3 is taken as reference. Experimental work is done to study the dry zone phenomena of each type of soil.

INTRODUCTION The current ratings of buried cables are determined by the characteristics of surrounding soils and cable properties as given in IEC 60287 -1-3[1]. In this standard the soil thermal resistivity of the surrounding soil is supposed to be varied from 0.5 C0m/w to 1.2 C0m/w, but under loading the heat dissipated from underground power cables increases the soil thermal resistivity and this may lead to cable thermal failure and thermal instability of the soil around the underground cables[2], [3]. For this reason de-rating factors for cable loading taking the dry zone formation into consideration has to be considered during distribution cable network design. Several approaches have been adopted to establish current ratings of buried cables based on constant values of soil thermal conductivities [4 -7]. Mathematical models are suggested by many researches to study the drying out phenomena around underground power cables [8 - 14]. In this paper de-rating factor for underground power cables taking dry zone formation into account are calculated depending on IEC 60287 -1-3[1]. This paper also contains an experimental work carried out on different types of soils to investigate the formation of dry zone phenomena under loading by heat source simulating the underground cables. EXPERMINETAL STUDTY

1. Soil Samples Used in Testing

Several experiments are carried out on different types of

natural soils to study the dry out zone formation under different loadings conditions. Six types of natural soils are investigated for studying the drying out phenomena and the thermal behavior of the soil around the power cables. These types of soil can be classified in composition as given in table 1.

Table 1 Classification for investigated soil types Weight percentage (%) Soil

type Gravel Sand Silt Clay Classification

Sand1 1.5 88.5 10 - Very coarse sand, poor in gravel, moderately poor in silt

Sand2 2 88.5 9.5 - Moderately fine sand, poor in gravel, moderately poor in silt

Sand3 13 84 3 - Medium to coarse sand, some gravel and traces of silt

Sand4 8 92 - - Medium to coarse sand, some gravel

Silty sand 8 60 30 - Medium to coarse sand, some

gravel Clayey Silty sand

3 37 30 30 Medium to coarse sand, some gravel

2. Thermal Test for Studying the Drying Out

Phenomena in Sandy Soils 2.1 Experimental setup

Fig. 1 shows a sketch for the arrangement used in this test. The sample under testing is contained in a cylinder of material with a diameter of 100 mm. The height of the soil sample is 100mm. In the top part, a heat flux of known magnitude is introduced in a downward direction; this flux is measured by means of a calibrated heat flux meter. The bottom of the sample is in contact with a porous slab of sintered Pyrex glass with small pores (pores diameter 5 mm). This filter plate is glued on to a vessel of transparent plastic material completely filled with water a flexible tub connects the vessel with a leveling bottle, the water level in this bottle function as an artificial ground water table. The cylinder containing the soil sample has been sealed off by an o-ring against the top wall of the insulated level. By this arrangement the moisture tension and thus water content can be adjusted. A number of their couples are placed with the walls at the axis of the sample that provide a possibility of measuring the temperature distribution at different points of the soil sample.

2.2 Test results The temperature distribution at different points in the investigated samples, sand1, sand2, sand3, sand4, silty sand and clayey silty sand against distance are given in

C I R E D 20th International Conference on Electricity Distribution Prague, 8-11 June 2009

Paper 0120

CIRED2009 Session 1 Paper No 0120

Fig’s 2-7. The samples under testing are heated under the stated condition for heat flux density Qh and suction tension pf= ∞, as shown in figures there are two slopes for the temperature distance relationship with respect to time, i.e. there are two zones, zone1 near the heat source represents the cable and this is the drying out zone and zone2 which is usually start from the end of zone1 and it is known as the wet zone. The discontinuity in the curves indicates the separation between dry zone and moist zone. It is noticed also that the slope of each zone gives indication to the increase in the thermal resistivity that could be calculated as following [1]:

hQdZdT

⎟⎠⎞

⎜⎝⎛

=σ (1)

Where dZdT

is the temperature gradient C0/m

σ Is the soil resistivity C0m/W and Qh is the heat flux density w/m2 The velocity of the dry band formation can be calculated by using the relation:

21

21

ttXX

−−

= velocity of dry band X1> X2 (2)

Where X1 is the position of dry band at any point recorded at t1, and X2 is the position of dry band at any point recorded at t2.

Fig 1 Arrangement used in drying out experiments

Table2 gives the thermal resisitivities of different soil types under testing when loading by 728 w/m2 at suction tension Pf = ∞. From this table it is noticed that for sand1 the dry band is partially formed after 3 hours, 3.5 hours for sand2, 2 hours for sand3, 2.7 hours for sand4, 4 hours for silty sand and 3 hours for clayey silty sand and

finally the dry zones reached to steady state after time between 24 to 48 hours for the different soils under testing. Also it is noticed that the velocity of dry band formation decreases with time until reaching to very small value at steady state. But it is noticed that the time and the velocity of dry band formation depend on the loading w/m2 and the pf values. Table 2: The Thermal resisitivities and velocity dry band

of different soil types under testing

Soil type

Qf w/m2 pf

Time in

hours

σ for dry zone

C0m/w

σ for wet zone

C0m/w

Velocity of dry band formation

cm/hrs

1 0.137 0.137 3 1.136 0.471

0.45 between 1 to 3 hours

5 1.2 0.543 0.1 between 5 to 9 hours

24 1.67 0.766 Sand1 728 ∞

48 1.64 0.749

0.00416 between 24

and 48 hours

1 0.188 0.188 3.5 1.089 0.484

0.36 between 1 to 3 hours

6 1.244 0.6 0.016 between 6 to 24 hours

24 1.648 0.763 Sand2 728 ∞

48 1.737 0.686

0.0041 between 24 to

48 hours

2 0.549 0.374 4 0.869 0.549

0.25 between 2 to 4 hours

6 1.010 0.597 0.2 between 4 to 6 hours

24 1.751 0.789 0.033 between 6 and 24 hours

Sand3 728 ∞

48 1.537 0.795 0.0085

between 24 and 48 hours

1 0.477 0.12 5 0.986 0.670

0.6 between 1 to 3 hours

24 1.770 0.784 0.2 between 3 to 5 hours Sand4 728 ∞

48 1.654 0.534 0.0041

between 24 to 48 hours

1 0.223 0.223

4 1.098 0.4995

1.66 between 1 to 4 hours

6 1.226 0.554 0.15 between 4 to 6 hours

24 1.590 0.883 0.055 between 6 and 24 hours

Silty Sand 728 ∞

48 1.609 0.732 0.012 between

24 and 48 hours

3 0.565 0.283 6 0.8360 0.481

0.2 between 3 to 6 hours

24 1.694 0.824 0.38 between 6 to 24 hours

Clayey Sand 728 ∞

48 1.648 0.549 0.01 between 24 to 48 hours

DE-RATING FACTOR DUE TO THE DRY BAND FORMATION

By de-rating factor we mean the ratio between current ampacity of the cable with dry band formation and the cable ampacity assuming there is no dry band is formed. IEC 60287-1-3 [1] gives formula to calculate the current ampacity taking the dry band into consideration. To use

C I R E D 20th International Conference on Electricity Distribution Prague, 8-11 June 2009

Paper 0120

CIRED2009 Session 1 Paper No 0120

this formula the ratio between the dry and moist zones resisitivities of the backfill soil (υ) and the difference between the critical temperature of boundary between the moist and dry zones C0 and ambient temperature (θx-θa) have to be obtained. Table 3 gives these values for the soil under testing when Qh equals 728w/m2. Some tests are carried out by varying Qh to be 468 w/m2 and 344 w/m2 respectively but it is noticed that there is no essential variation in (θx-θa) and also in (υ).

Fig 2 Temperature versus distance for sand1 when pf= ∞

and Qh =728 w/m2

Table 3 θx-θa and υ for soil samples under testing. Type of soil θx θa υ = θx-θa

Sand1 63 25 2.179 38 Sand2 65 27 2.16 38 Sand3 58 22 2.21 36 Sand4 76 22 2.257 34

Silty sand 57 21 2.1962 38 Clayey silty

sand 60 18 2.055 42

From the so many tests carried out on different soils used as backfill materials it is noticed that the critical temperature for dry band formation depends on the soil components but its independent on the cable loading. Also the ratio between the dry and wet thermal resisitivities depend on the soil type and independent on the cable loading but it is noticed that the time required to form the dry band around underground power cables depends on the cable loading, soil type and soil moisture content. The ampacity of cable loading can be calculated by IEC 60287-1-3 equations [1] without and with dry band formation for different distribution cables. IEC 60287-1-3 are listed below: The current carrying capacity of a buried cable is:

Where:

, the difference between the conductor temperature and the ambient temperature Co,

n Number of load carrying conductors in the cable (they

are of equal size and carrying the same load), Dielectric loss per unit length for the insulation surrounding the conductor per phase, Alternating current resistance per unit length of the conductor at its maximum operating temperature ( ,

Thermal resistance per unit length per core between conductor and sheath (Com/w),

Fig 3 Temperature versus distance for sand2 when pf= ∞

and Qh =728 w/m2.

Fig 4 Temperature versus distance for sand3 when pf= ∞

and Qh =728 w/m2.

C I R E D 20th International Conference on Electricity Distribution Prague, 8-11 June 2009

Paper 0120

CIRED2009 Session 1 Paper No 0120

Fig 5 Temperature versus distance for sand4 when pf= ∞ and Qh =728 w/m2.

Thermal resistance per unit length of bedding between sheath and armour (Com/w),

Thermal resistance per unit length of the external serving of the cable (Com/w),

Thermal resistance per unit length between the cable surface and the surrounding soil (Com/w),

Ratio of losses in the metal sheath to total losses in all conductors in that cable, and

Ratio of armouring losses to conductors total losses in that cable.

And the modified equation for cable rating calculation is:

Where:

, the difference between the critical temperature and ambient temperature Co,

The ratio between the thermal resistivities (of dry and moist zones)

θx-θa and υ are taken from table 3 for different types of sands and their thermal resistivity plotted in Fig’s from 2 to 7 and tabulated in table 2. A computer program to calculate the de-rating factor for 11, 33, 66 and 132 kV cables using the tested soils as backfill materials is used. Fig 8 shows sample of dry band formed around the directly buried three cables 33kV. Table 4 gives sample of the obtained results. It is concluded that de-rating factor due to dry zone formation is ranged between 0.88 and 0.98 depending on the backfill soil and cable ratings. The cables depth and spacing are taken as 1 m and 0.4 m respectively for cables higher than 33 kV and for cables rated less than 33 kV the laying depth is taken as 0.8m. Fig. 8 shows the surface temperature distribution around 33 kV cables. The dry zones are formed at 63, 65, 58, 56, 57 C0 and 60 C0 respectively depending on the soil type.

Fig 6 Temperature versus distance for silty sand when pf=

∞ and Qh =728 w/m2.

Table 4 gives summary of the calculated results to

determine the cables under study de-rating factor with dry zone formation. From the tabulated results it is clear that soil type's sand 2 and sand1 have higher de-rating factor than the others.

Fig 7 Temperature versus distance for Clayey

Silty sand when pf= ∞ and Qh =728 w/m2. They have approximately the same dry to moist thermal resistivity and same difference between critical and ambient temperature as given in table 3, also they have approximately the same components as given in table 1 , there are little differences in weight percentage of gravel and silt. Sand 4 has the lowest de-rating factor, the reason may be due to it has the highest value of dry to moist thermal resistivity as given in table 3 and also it does not contain any amount of clay or silt as given in table 1.Silty sand and clayey silty sand have also good de-rating factors but they may cause corrosion for cable sheathing due to the high amounts of silt.

Fig. 8 temperature distribution within and around the

directly buried three cables (33kV), three phases, three cores in flat formation

Figure 8 gives the temperature distribution around 33kV, three phases' three core cables when loaded by 1106A and directly buried in soil type sand1. The spacing between each phase is 0.4 m and the buried depth is 1 m. It is noticed that there is dry band zone formed at temperature 63oC.

C I R E D 20th International Conference on Electricity Distribution Prague, 8-11 June 2009

Paper 0120

CIRED2009 Session 1 Paper No 0120

Table 4 De-rating factor of single-core cables in flat configuration

CONCLUSIONS From the experimental study and analysis carried out in this paper, it is concluded that: 1-The dry zones formation around underground

cables decreases cables capacity by factor defined in this paper by de-rating factor depending on the soil type 2- From the so many tests carried out it is noticed that drying out phenomena in backfill soil started at different temperatures with different velocities depending on the soil type and the weight percentage of silt 3- The time required for dry zone formation around buried cables is longer for the sand samples contain silt than samples do not contain silt. While the velocity of dry zone movement around the cables buried in sand contain silt is slower than that do not contain silt REFERENCES For a Conference citation:

[1] IEC publication 60287-1-3 “Calculations of the continuous current rating of cables (100% load factor”, 1982.

[2] Koopmans G., Gouda O.E. “Transport of heat and moisture in soils with hysteretic moisture potential” 4th. International conference on numerical methods in thermal problems. 15-18 July 1985, Swansea, U.K.

[3] Gouda O.E., “Formation of the dried out zone around underground cables loaded by peak loadings”. Modeling, Simulation & Control, ASME Press, vol. 7, No. 3, 1986, pp. 35-46.

[4] J. Hegyi and A. Klestoff “Current-Carrying Capability for Industrial Underground Cable Installations “, IEEE. Transactions on Industry Applications, Vol. 24, No.1 January-February 1988, pp.99-105.

[5] M.A. Hanna, A.Y. Chikhani and M.M.A. Salama , “Thermal Analysis of Power Cables in Multi-Layered Soil “ Part 3: Case of Two Cables in a Trench, IEEE Transactions on Power Delivery, Vol. 9, No. 1, January 1994, pp. 572-578.

[6] G. J. Anders, H. S. Radhakrishna, “Power Cable Thermal Analysis with Consideration of Heat and Moisture Transfer in the Soil”, IEEE Transactions on Power Delivery, Vol. 3, No. 4, October 1988, pp. 1280-1288.

[7] G. J. Anders, A.K.T. Napieralski, and W. Zamojski “Calculation of the Internal Thermal Resistance and Ampacity of 3-Core Unscreened Cables with Fillers “IEEE Transactions on Power Delivery, Vol. 13, No. 3, July 1998, pp.-699-705.

[8] Francisco de León, and George J. Anders “Effects of Backfilling on Cable Ampacity Analyzed With the Finite Element Method” IEEE Transactions on Power Delivery, Vol. 23,No. 2, April. 2008, pp. 537-543.

Type of soil  

Sand1  

Sand2  Sand3  Sand4 Silty sand 

Clayey silty sand 

Moist  thermal resistivity (Com/w) 

 0.766 

 0.763 

0.7898  0.784  0.732 

 0.8241 

Dry thermal resistivity (Com/w) 

 1.67 

 1.648 

 1.7513   

1.77  

1.609  

1.694 

Drying out zone 

temperature C0 

 63 

 65 

58  56  57  60 

132 kV cable Ampacity without dry 

band formation Amp. 

687  688  678  680  699  666 

Ampacity with dry band 

formation Amp. 

643  652  615  609  634  615 

De‐rating factor 

0.935  0.9477 0.9071  0.895 

0.907 0.9234 

66 kV cable 

Ampacity without dry band .Amp. 

841  842  830  832  858  814 

Ampacity with dry 

band .Amp. 

767  777  734  726  758  734 

De‐rating factor  

0.912  0.9228 0.8843 

0.872 0.8834  0.9017 

33 kV cable Ampacity without dry band, Amp. 

1106  1108  1092  1095  1127  1082 

Ampacity with dry 

band, Amp. 

1024  1037  980  970  1010  979 

De‐rating factor  

0.925  0.9359 0.897  0.8858 

0.8962  0.9048 

11 kV cable Ampacity without dry band, Amp. 

674  675  666  668  686  656 

Ampacity with dry 

band, Amp. 

639  647  613  607  631  612 

De‐rating factor  

0.948  0.9585 0.920  0.908  0.9198  0.9329 

C I R E D 20th International Conference on Electricity Distribution Prague, 8-11 June 2009

Paper 0120

CIRED2009 Session 1 Paper No 0120

[9] Charis Demoulias, DimitrisP. Labridis, Petros.S. Dokopoulos, and Kostas Gouramanis “Ampacity of Low-Voltage Power Cables Under Non-sinusoidal Currents” IEEE Transactions on Power Delivery, Vol. 22,No. 1,January 2007, pp. 584-594

[10] Carlos Garrido, Antonio F. Otero, and José Cidrás “Theoretical Model to Calculate Steady-State and Transient Ampacity and Temperature in Buried Cables” IEEE Transactions on Power Delivery, Vol. 18, No. 3, July 2003, pp. 667-678.

[11] Michael R. Yenchek, and Gregory P. Cole, “Thermal Modeling of Portable Power Cables”, IEEE Transactions on Industry Applications, Vol. 33, No. 1, January/February 1997, pp. 72-79.

[12] G.J. Anders, and A. Napieralski and Z. Kulesza “Calculation of the Internal Thermal Resistance and Ampacity of 3-Core Screened Cables with Fillers” IEEE Transactions on Power Delivery, Vol. 14, No. 3, July 1999, pp. 729-734.

[13] Neil P. Schmidt “Comparison between I.E.E.E. and CIGRE Ampacity Standards” IEEE Transactions on Power Delivery, Vol. 14, No. 4, October 1999, pp. 1555-1562.

[14] GJ.Anders, M. Chaaban, N. Bedard and R.WD. Ganton “New Approach to Ampacity Evaluation of Cables in Ducts Using Finite Element Technique” IEEE Transactions on Power Delivery, Vol. PWRD-2, No. 4, October 1987, pp. 969-975.