Current Carrying Capacity The Current Carrying Capacity (Current Rating) 4-1 The Fundamentals : In the first place the current carrying capacity is determined by the max. permissible conductor temperature and the ambient conditions as far as they are relevant for the dissipation of heat. With mass- impregnated paper-insulated cables the permissible difference between the temperature reached under full- load conditions and the no-load temperature has also to be taken into account. Inadmissibly high conductor temperatures and excessive temperature differences will speed up the ageing process. The current carrying capacity of H.T. Cables has to be calculated with particular care. The cable is heated up by the ohmic losses occurring in the conductors and-if the cable is operated with a.c. – in the metallic covering. The dielectric losses are negligible with Protodur cables up to U o / U = 5.8 / 10 kV, mass-impregnated cables up to
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Current Carrying Capacity
The Current Carrying Capacity (Current Rating)
4-1 The Fundamentals:
In the first place the current carrying capacity is determined by the max.
permissible conductor temperature and the ambient conditions as far as they are
relevant for the dissipation of heat. With mass-impregnated paper-insulated cables
the permissible difference between the temperature reached under full-load
conditions and the no-load temperature has also to be taken into account.
Inadmissibly high conductor temperatures and excessive temperature differences
will speed up the ageing process. The current carrying capacity of H.T. Cables has
to be calculated with particular care.
The cable is heated up by the ohmic losses occurring in the conductors and-
if the cable is operated with a.c. – in the metallic covering. The dielectric losses are
negligible with Protodur cables up to Uo/ U = 5.8 / 10 kV, mass-impregnated
cables up to Uo /U = 5.8/10 kV, mass-impregnated cables up to Uo/U = 34.7/60 kV
and protothen cables up to Uo/U = 64 / 110 kV operating voltage. Under steady-
state conditions the heat dissipated is equal to the sum of all the losses in the cable.
The heat flows by conduction to the surface of the cable and, if this is arranged in
free air, is transferred to the surrounding air by convection and radiation. With
cables buried in the ground the heat generated by losses flows from the surface of
the cable by thermal conduction via the ground into the atmosphere. Whilst the
cable itself is heated up. The difference between conductor temperature and
ambient temperature is nearly proportional to the total losses. The law of heat flow
is analogous to ohm’s law, with the heat flow (ohmic losses) V, corresponding to
electric current I, the difference in temperature corresponding to voltage U and
the total thermal resistance S corresponding to electrical resistance R:
Thus - V S analogous to U = I R. (1)
The heat flow is the sum of all losses generated in the cable. To reach the
surrounding air from its point of origin the heat flow must overcome the thermal
resistance Sk of the cable and the thermal resistance of the air SL or of the ground
SE caused by the transfer of heat from the surface of the cable to the surrounding
media.
In accordance with the analogy existing between the heat flow and the
electric current (equation 1) an equivalent circuit diagram (Fig. 1) may be drawn
for the heat losses flowing from the cable and the temperature rise they produce.
The heat transfer by radiation and convection, if the cable is installed in free air, is
represented by two resistors connected in parallel to each other and in series with
the remaining thermal resistances of the cable. The heat losses due to the current
(ohmic losses) are developed in the conductor, in the metal sheath and in the
armour (see also equation 6). They are represented by electric currents fed in at
these points. As a result of the heat losses, the conductor temperature L is
increased by and the surface temperature of the cable o by a as compared
with the ambient temperature u.
Fig. (1) Equivalent Circuit Diagrams for the Heat Flow in a Cable.
With the equation for the ohmic losses
V = n I2 RW 10-3, W/m (2)
we obtain from equation (1) the current carrying capacity for operation with a.c. or
three-phase current with the cable installed in free air, for example:
I = √ Δϑ 105
n RW (SK' + S L)
A
(3)
where
= given temperature rise of the conductor with respect to the
surroundings, C.
n = number of current carrying conductors,
RW = effective resistance of a conductor at operating
temperature /km.
SK'
= fictitious thermal resistance of the cable, C cm/W
SL = thermal resistance of the air, C cm/W.
The effective resistance (a.c. resistance) RW is arrived at as follows:
RW = R + R /km, (4)
Where R = d.c. resistance at operating temperature, /km.
The extra resistance:
R = R [y + y1 + (1 + y + y1) ( + 1)], /km (5)
indicates the measurable increase in the conductor resistance due to current-
dependent a.c. losses. These losses are produced in the conductor by the skin and
proximity effects (y and y1), inductive currents and eddy currents and reversal of
magnetic polarity in the armour (1). By introducing these factors into equation (1)
we obtain for the temperature rise of the conductor:
The component resistance are those of the insulation Sis and of the inner and outer
protective coverings SCi and SCa. (The thermal resistance of the metallic
components can be assumed to be negligible.)
The fictitious thermal resistance of the cable is obtained from equations (3)
and (6):
Sk' =
Sis + (1 + λ ) SCi
1 + λ + λ1
+ SCa ,∘C cm /W
(8)
By substituting the thermal resistance of the soil SE for the thermal resistance of the
air SL in equation (3) the current carrying capacity IE of the cable for burial in the
ground is obtained.
For the special case of operation with d.c. it is necessary to substitute the d.c.
resistance R at operating temperature for RW and the actual thermal resistance of
the cable SK for SK'
in equation (3).
The thermal resistance of the cable SK and the effective resistance RW
depend mainly on the values of the components of the cable and its design. The
permissible temperature rise and the thermal resistance of the surroundings SE
or SL are determined by the ambient conditions at the place of installation of the
cable. Generally acceptable values may be agreed upon for the conditions which
are most important i.e. ambient temperature, arrangement of cables, mode of
operation etc. With the help of these the current carrying capacity may be
calculated and planning work is made easier. The values in tables are based on the
standard conditions incorporated in VDE 0255, VDE 0265 and VDE 0271. These
correspond to the climatic conditions prevailing in Central Europe as well as the
methods of laying and the operating conditions most common in Germany.
In the following, these conditions are called “normal” and are indicated by
the index “n” added to the symbol.
With installation in free are the current carrying capacity is:
I n = √ Δ ϑ 105
n RW (Sk' + SLn )
A
(9)
For burial in the ground
I n = √ Δ ϑ 105
n RW (Sk' + SEn )
A
(10)
applies
It must be remembered that for normal conditions several current carrying
capacity values, which depend on the methods of laying and operation, are given
for one and the same cable (six values each for a single-core cable 0.6/1 kV with
copper and aluminum conductors). The extent to which the current carrying
capacity depends on the ambient conditions makes it impossible to arrive at a
“rated current carrying capacity” similar to the rated voltage.
The current carrying capacity is determined by:
(1) Conductor resistance and losses due to the current (ohmic losses),
(2) Thermal resistance of the cable,
(3) Conductor temperature and ambient temperature (temperature difference),
(4) Installation conditions (in free air or in the ground).
(1) Conductor resistance and losses due to the current (ohmic losses):
Certain planning problems can only be solved with knowledge of the ohmic
losses. These losses for cables in the ground are shown in tables for permissible
current In. For operating currents I (other than current rating under conditions In)
the losses may be calculated as follows:
V = V n ( II n )
2
, W/m (11)
(2) Thermal Resistance of the Cables:
The fictitious thermal resistance SK'
required for carrying out special
planning work may be easily obtained for a single cable according to equation
(12):
SK' =
Δϑ n 102
V n
− SEnC cm/W (12)
where
n = temperature rise under normal conditions (see table 1).
Vn = losses depending on the current under standard conditions.
SEn = thermal resistance of the soil at E = 100 C cm/W
The thermal resistance of the soil SEn may be taken from Fig. 6 or calculated as
shown on page 109.
(3) a. Conductor Temperature:
The conductor temperature has been fixed with regard to the life of the cable
and is stated in VDE specifications for nearly all of cables. Please refer to table 1
for a summary.
(3) b. Ambient Temperature:
Measuring the ambient temperature is not possible in every case; it has to be
estimated quite often. The value used for planning should be exceeded only on a
few days during the year or a few hours during the day.
The following ambient temperature values may be taken as a basis, unless
higher values have been established by measurements or experience:
Unheated cellars 20C
Normal conditioned rooms
(unheated during the summer) 25C
Factories, workshops etc. 30C
The aforementioned ambient temperatures are valid under the conditions
prevailing in Central Europe.
Temperatures of above 30C are normally reached in rooms, which are not
sufficiently protected against solar radiation, or badly ventilated or contain
machinery with high heat losses etc.
Table 1: Permissible Conductor Temperature of Mass-impregnated Cables (with
Paper Insulation and Metal Sheath) and Protodur Cables.
Type of CableRated
Voltage
Uo/U
kV
Permissible
Conductor
Temperature
C
Temperature Rise at the
Conductor
Max. Permissible
Temperature ifference1)1)
in the Grounded
at 20C
degC
in Air
at 30C
degC
in the
Ground
degC
in Air
degC
Mass-impregnated Cables
Belted Cables
0.6/1
3.5/680 60 50 65 55
5.8./10 65 45 35 45 35
Single-core
Cables,
H.S.L. Cables
and
H-type Cables
0.6/1
3.5/680 60 50 65 55
5.8/10 70 50 40 55 45
8.7/15
11.6/2065 45 35 45 35
17.3/30 60 40 30 40 30
Protodur Cables
All Types
0.6/1
3.5/670 50 40 55 55
5.8/10 65 45 35 50 50
8.7/15
11.6/2060 40 30 45 45
17.3/30 55 35 25 40 40
Conversion factors for ambient temperatures higher or lower than those
shown may be taken from table 2.
Under certain conditions the heat generated by the losses in the cables may
lead to an increase in the ambient temperature. This applies to cables in tunnels in
particular (see page 94).
1)1) These values have not been fixed for plastic-insulated cables (protodur cables), but it is recommended that they should not be exceeded in consideration of the longitudinal of the cables.
(3) c. Temperature Rise:
The permissible temperature rise of a cable is determined by the permissible
conductor temperature and the ambient temperature – other sources of heat
excluded – (see page 80 and table 1). In cases where the ambient temperature of
cable installation differs from the normal 20C underground or 30C in air, for
example with low outside temperatures over an extended period or due to heating
wires running parallel to the cable route, the permissible current I is calculated as
follows:
I = I n √ (Δϑ / Δϑ n) A (13)
For direct burial = n + 20 - u C (14)
For installation in free air = n + 30 - u C (15)
where
In = Current rating under normal conditions
n = Temperature rise under normal conditions
= actual ambient temperature
= permissible temperature rise according to equations (14) and (15)
With mass-impregnated paper-insulated cables the temperature variation
may not exceed the max. permissible values shown in table 1, which means that
the load may not be increased even at lower ambient temperatures.
The temperature rise within the conductor for any current I, with the ambient
temperature remaining constant and the change in resistance with changing
conductor temperature being neglected, is calculated as follows:
Δϑ = Δϑ n ( II n )
2∘C
(16)
(4) a. Installation in free Air (Thermal Resistance of the Air):
Installation “in free air” is taken as the normal condition for determination of
the current carrying capacity of a cable. By “in free air” is meant that the heat
losses are freely dissipated from the surface of the cable to the surroundings by
natural convection and radiation under exclusion of outside sources of heat,
without the surrounding media being media being heated up noticeably (infinite
heat capacity of the surroundings).
The pre-conditions are:
The clearance between the cables and walls, floor or ceiling must be at least
2 cm. With cables arranged in flat formation in one layer the clearance between
them should not be less than twice the diameter of the cables. Several layers of
cables arranged in flat formation should be installed with a vertical clearance of at
least 30 cm.
Protection against direct solar radiation etc. Sufficiently large or ventilated
rooms such that the ambient temperature is not increased by the heat generated by
the losses in the cables.
If the cable is installed touching a wall or directly on the floor, the current
carrying capacity has to be reduced by 0.95. Rating for grouping of cables are
given in tables 4 and 5. In these tables the reduction by 0.95 for direct installation
on a wall has been taken into account where necessary.
The thermal resistance of the air for a cable installed in free air may be
determined according to page 104. As a rule, however, knowledge of the same is
not required for planning.
With cables of very small diameter the thermal resistance of the air is
considerably greater than the thermal resistance of the soil. The current rating of
cables with a small diameter in free air is therefore lower than in the ground. With
increasing diameter of the cable the thermal resistance of the air decreases faster
than that of the soil. The result is that the ratio of current rating for installation in
free air and in the ground increases together with the diameter of the cable and that
with large diameters the current carrying capacity in free air is greater than that for
installation in the ground. Tests have confirmed that this is actually the case.
(4) b. Direct Burial in the Ground (Thermal Resistance of the Soil):
In the ground, cables are normally embedded in sand or riddled soil and
covered with bricks. This method of laying forms the basis for the current rating
values, whereby the depth of laying h is assumed to be 70 cm and the thermal
resistivity of the soil E to be 100C. cm/W. The equation for the thermal resistance
of the soil SE of, for example, a multicore cable with diameter d (see page 111)
shows that SE increases with increasing h and E, whilst the current rating
decreases:
SE =σ E
2 πln ( 4 h
d ) C cm/W (17)
The influence of the depth of laying is small. With increasing depth the
ambient temperature and normally also the thermal resistivity decrease as the
deeper layers of the ground normally contain more moisture and stay more
uniformly moist than the upper layers. For the normal depths of laying for L.T. and
medium tension cables (70 to 120 cm) a conversion of the current rating values is
not necessary if the ambient temperature is taken as being 20C and the thermal
resistivity of the soil as being 100C cm/W.
Of much greater importance is the thermal resistivity of the soil, which
depends on a large number of factors. There is especially the drying-out of the soil
caused by a continuous load according to the rating tables, which leads to an
increase in the thermal resistance of the soil in the course of time. Therefore the
values in tables (e.g. table 6) for direct burial are to be reduced to 75% if the
current load is constant all the time. This is not necessary, if the possibility of the
soil drying out has been taken into account by calculating with a sufficiently high
value for the soil thermal resistivity (table 3).
4-2 Calculating the Load Current:
The load current is the result of operating voltage U in kV and load to be
transmitted P in kW:
For d.c.:I = P
UA
(18)
For single-phase a.c.: I = P / (U cos ) A (19)
For three-phase current: I = P / (√3 U cos ) A (20)
0
Examples:
1) 3 Protodur cables type NYFGBY 3 x 185 sm 3.5/6 kV laid directly in the ground,
clearance 7 cm, covered with bricks; public utilities load; thermal resistivity of the
1)1) With regard to the max. permissible temperature difference for mass-impregnated paper-insulated cables (see page 83) it is not possible in every case to increase the current rating at low ambient temperature.
Table 3 Multi-core Cables
Rated
Voltage
Uo/U
kV
Cross- sectional
Area of
Conductors
mm2
Thermal Resistivity of the Soil E
degC-cm/W
701)1) 100 120 150 200 250 300
Rating Factor
Twin-core Plastic (P.V.C.) and Paper-insulated Cables
0.6/1
up to 25 1.09 1 0.95 0.88 0.80 0.73 0.69
35 – 95 1.11 1 0.94 0.87 0.78 0.71 0.66
120 – 240 1.12 1 0.94 0.86 0.78 0.70 0.65
300 – 500 1.13 1 0.93 0.86 0.77 0.69 0.65
3- and 4-core Plastic (P.V.C.) and Paper-insulated Cables
0.6/1
up to 25 1.11 1 0.94 0.87 0.78 0.72 0.67
35 – 95 1.13 1 0.93 0.86 0.76 0.70 0.64
120 – 240 1.14 1 0.93 0.85 0.76 0.69 0.63
300 – 500 1.15 1 0.92 0.85 0.75 0.68 0.63
3-core Plastic (P.V.C.) –insulated Cables
3.5/6
and
5.8/10
up to 25 1.11 1 0.94 0.87 0.78 0.72 0.67
35 – 95 1.13 1 0.93 0.86 0.76 0.70 0.64
120 – 240 1.14 1 0.93 0.85 0.76 0.69 0.63
300 – 500 1.15 1 0.92 0.85 0.75 0.68 0.63
3-core Paper-insulated Cables (Belted, H-type and H.S.L. Cables)
3.5/6
and
5.8/10
up to 25 1.09 1 0.95 0.88 0.80 0.73 0.69
35 – 95 1.11 1 0.94 0.87 0.78 0.71 0.66
120 – 240 1.12 1 0.94 0.86 0.78 0.70 0.65
300 – 500 1.13 1 0.93 0.86 0.77 0.69 0.65
3-core Cables with Paper Insulation (H.S.L. and H-type cables) and Plastic (P.V.C.) – insulated Cables
8.7/15
11.6/20
17.3/30
up to 25 1.08 1 0.96 0.9 0.81 0.75 0.7
35 – 95 1.09 1 0.95 0.89 0.79 0.73 0.67
120 – 240 1.1 1 0.95 0.88 0.79 0.72 0.66
300 – 500 1.11 1 0.94 0.88 0.78 0.71 0.66
Table 3 (Continuation) Single-core Cables
1)1) The factor in this column may be used only if the thermal resistivity of the soil has been actually measured.
Rated
Voltage
Uo/U
kV
Cross- sectional
Area of
Conductors
mm2
Thermal Resistivity of the Soil E
degC-cm/W
701)1) 100 120 150 200 250 300
Rating Factor
3 Unarmoured Cables in Flat Formation or in Trefoil Formation
0.6/1
3.5/6
5.8/10
up to 25 1.12 1 0.94 0.85 0.76 0.70 0.65
35 – 95 1.14 1 0.94 0.84 0.74 0.68 0.62
120 – 240 1.15 1 0.93 0.83 0.74 0.67 0.61
300 – 500 1.16 1 0.92 0.83 0.73 0.66 0.61
8.7/15
11.6/20
17.3/30
up to 25 1.11 1 0.94 0.87 0.78 0.72 0.67
35 – 95 1.13 1 0.93 0.86 0.76 0.70 0.64
120 – 240 1.14 1 0.93 0.85 0.76 0.69 0.63
300 – 500 1.15 1 0.92 0.85 0.75 0.68 0.63
1 Separately Installed D.C. Cable with Plastic Insulation (P.V.C.)
0.6/1
up to 25 1.09 1 0.95 0.88 0.80 0.73 0.69
35 – 95 1.11 1 0.94 0.87 0.78 0.71 0.66
120 – 240 1.12 1 0.94 0.86 0.78 0.70 0.65
300 – 500 1.13 1 0.93 0.86 0.77 0.69 0.65
1 Separately Installed D.C. Cable with Paper Insulation
8.7/15
11.6/20
17.3/30
up to 25 1.08 1 0.95 0.89 0.80 0.75 0.7
35 – 95 1.1 1 0.95 0.88 0.78 0.73 0.67
120 – 240 1.11 1 0.94 0.87 0.78 0.72 0.66
300 – 500 1.12 1 0.93 0.87 0.77 0.71 0.66
Grouping in Air:
1)1) The factor in this column may be used only if the thermal resistivity of the soil has been actually measured.
Table 4: Multi-core Cable in Three-phase Systems and Single-core Cables in D.C.
Systems. These factors are valid only under the condition that the
ambient temperature is not perceptibly increased by the heat generated
by the cable.
Distance from the wall 2cm
Clearance between cables = diameter d
Number of Cables
1 2 3 6 9
Rating Factor
Cable laid on the ground in flat formation
0.95 0.90 0.88 0.85 0.84
Cables laid on troughs (circulation of air is restricted)
Number of
troughs
1 0.95 0.90 0.88 0.85 0.84
2 0.90 0.85 0.83 0.81 0.80
3 0.88 0.83 0.81 0.79 0.78
6 0.86 0.81 0.79 0.77 0.76
Cables laid on racks in flat formation
Number of
racks
1 1 0.98 0.96 0.93 0.92
2 1 0.95 0.93 0.90 0.89
3 1 0.94 0.92 0.89 0.88
6 1 0.93 0.90 0.87 0.86
Cables arranged on structures or on the wall
1 0.93 0.90 0.87 0.86
Arrangements for which a reduction of the current rating is not necessary
Distance form the wall
2cm
Clearance between cables
= 2d
Any number of cables
Grouping in Air:
Table 5: Single-core Cables in Three-phase Systems. These factors are valid only
under the condition that the ambient temperature is not perceptibly
increased by the heat generated by the cable.
Distance from the wall 2 cm
Clearance between cable = diameter d
Number of System
1 2 3
Rating Factors
Cables laid on the ground in flat formation
0.92 0.89 0.88
Cables laid on troughs (circulation of air is restricted)
Number of
troughs
1 0.92 0.89 0.88
2 0.87 0.84 0.83
3 0.84 0.82 0.81
Cables laid on racks in flat formation
Number of
racks
1 1 0.97 0.96
2 0.97 0.94 0.93
3 0.96 0.93 0.92
6 0.94 0.91 0.90
Cables arranged on structures or on the wall
0.94 0.91 0.89
Touching the wall 0.89 0.86 0.84
Current rating under normal conditions according to table 6 for a single cable: In =
370 A.
Permissible conductor temperature according to table 6 : 70 C.
Rating factors:
For higher ambient temperature according to table 2:0.89
For higher thermal resistivity of the soil according to
Table 3 0.85
For grouping according to table 0.75
The permissible load current for 3 cables is therefore:
I = 3.370. 0.89. 0.85. 0.75 = 630 A.
The transmission power (complex PS) of the cable connection is:
PS = I √3 U 10-3
= 630 √3 6 10-3
= 6.55 MVA
2) 5 MVA at an operating voltage of 10 kV have to be transmitted by Protodur
cables.
Ambient conditions:
Cables laid in flat formation in the ground, clearance 7 cm covered with
bricks; continuous load; thermal resistivity of non-dried-out soil 100C cm/W
ambient temperature 25C.
Load Current:
I = PS 103 / (√3 U) = 5 103 / (√3 10) = 290
Estimate: 2 cables installed parallel will be required.
Table 6: Three-and Four-core Cables for 0.6/1 kV, e.g. NYY, NYCY, NYCWY,
NYKY, YTY, Three-core Cables for 3.5/6kV and 5.8/10 kV, e.g.
NYFGbY, NYSEY, NYHFGbY.
NominalCross-sectional
Areamm2
Rated Voltage Uo/U in kV0.6/1 3.5/6 5.8/10
Permissible Conductor Temperature70C 70C 65C
Three-and Four-core Three-core Three-coreAmbient Temperature and Installation
20C 30C 20C 30C 20C 30CGround Air1)1) Ground Air Ground Air