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This criteria is applied to determine the minimum cross section area of the cable, so that cable can withstand the short circuit current.Failure to check the conductor size for short-circuit heating could result in permanent damage to the cable insulation and could also result into fire. In addition to the thermal stresses, the cable may also be subjected to significant mechanical stresses.
Citation preview
Sizing of power cables for circuit breaker
controlled feeders (part 1)
Posted May 10 2012 by Asif Eqbal in Cables, Low Voltage with 15 Comments Translate
Low voltage switchboard with circuit breakers (incomers, feeders)
The following three criteria apply for the sizing of cables for circuit breaker controlled feeders:
I. Short circuit current withstand capacity
This criteria is applied to determine the minimum cross section area of the cable, so that cable
can withstand the short circuit current.
Failure to check the conductor size for short-circuit heating could result in permanent damage to
the cable insulation and could also result into fire. In addition to the thermal stresses, the cable
may also be subjected to significant mechanical stresses.
II. Continuous current carrying capacity
This criteria is applied so that cross section of the cable can carry the required load current
continuously at the designed ambient temperature and laying condition.
III. Starting and running voltage drops in cable
This criteria is applied to make sure that the cross sectional area of the cable is sufficient to keep
the voltage drop (due to impedance of cable conductor) within the specified limit so that the
equipment which is being supplied power through that cable gets at least the minimum required
voltage at its power supply input terminal during starting and running condition both.
1. Criteria-1 Short circuit capacity
The maximum temperature reached under short circuit depends on both the magnitude and
duration of the short circuit current. The quantity I2t represents the energy input by a fault that
acts to heat up the cable conductor. This can be related to conductor size by the formula:
A = Minimum required cross section area in mm2
t = Operating time of disconnecting device in seconds
Isc = RMS Short Circuit current Value in Ampere
C = Constant equal to 0.0297 for copper & 0.0125 for aluminum
T2 = Final temp. C (max. short circuit temperature)
T1 = Initial temp. C (max. cable operating temperature normal conditions) T0 = 234.5 C for copper and 228.1 C for aluminum
Equation-1 can be simplified to obtain the expression for minimum conductor size as given
below in equation-2:
Now K can be defined as a Constant whose value depends upon the conductor material, its
insulation and boundary conditions of initial and final temperature because during short circuit
conditions, the temperature of the conductor rises rapidly. The short circuit capacity is limited by
the maximum temperature capability of the insulation. The value of K hence is as given in Table
2.
Boundary conditions of initial and final temperature for different insulation is as given under in
Table 1 below.
Table 1
Insulation material Final temperature T2 Initial temperature T1
PVC 160 C 70 C
Butyl Rubber 220 C 85 C
XLPE / EPR 250 C 90 C
Table 2
Material Copper Aluminum
Insulation PVC Butyl Rubber XLPE / EPR PVC Butyl Rubber XLPE / EPR
(K) 1 Second Current
Rating in Amp/mm2
115 134 143 76 89 94
(K) 3 Second Current
Rating in Amp/mm2
66 77 83 44 51 54
In the final equation-2 we have determined the value of constant K. Now the value of t is to
be determined. The fault current (ISC) in the above equation varies with time. However,
calculating the exact value of the fault current and sizing the power cable based on that can be
complicated. To simplify the process the cable can be sized based on the interrupting capability
of the circuit breakers/fuses that protect them.
This approach assumes that the available fault current is the maximum capability of the
breaker/fuse and also accounts for the cable impedances in reducing the fault levels.
The fault clearing time (tc) of the breakers/fuses per ANSI/IEEE C37.010, C37.013, and UL
489 are:
For medium voltage system (4.16 kV) breakers, use 5-8 cycles
For starters with current limiting fuses, use cycle
For low voltage breakers with intermediate/short time delay, use 10 cycles
For low voltage breakers with instantaneous trips, use 1 cycle
Alternatively let us consider that feeder is for any large motor which is being fed from LV 415V
or 400V switchgear having a circuit breaker with separate multifunction motor protection relay
(For this calculation it is assumed to be SIEMENS made 7SJ61).
The instantaneous protection feature of this relay will be turned ON as and when any fault
occurs. However, the selected cable shall have the capacity to withstand the maximum fault
current for a finite duration (that is fault clearing time of the circuit breaker).
The minimum faults withstand duration necessary (for the instantaneous setting) for cable
is calculated as under:
Si. No. Parameters Time in
ms Source/Back up
1 Relay sensing/pickup time 20 SIEMENS 7SJ61 technical data
2 Tolerance/Delay time 10 SIEMENS 7SJ61 technical data
3 Breaker operating time 40
L&T make C-Power breaker have typical
opening
time of 40 ms and closing time of 60ms)
4 Relay overshoot 20 GEC handbook Network Protection & automation
Guide 5 Safety Margin 30
TOTAL TIME IN MILI
SECONDS 120
Therefore the cable selected for a circuit breaker controlled motor feeder in 415V or
400V switchgear shall be suitable to withstand the maximum rated fault current of 50kA for at
least 120msec. However taking allowance of 40 Mili seconds in the opening time of circuit
breaker due to aging, frequent number of operation, increase in contact resistance of circuit
breaker and finally to cover the variation due from manufacturer to manufacturer.
Hence the cable selected for a circuit breaker controlled motor feeder in 415V or 400V
switchgear shall be suitable to withstand the maximum rated fault current of 50kA for at least
(120+40) 160msec. Many consultants recommend for use operating time of disconnecting device
as 200msec also. Value of t more than 160 seconds is a conservative design.
A = (Isc x t)/K = (50000 x 0.16)/94 = 212.766mm2
Next standard cable size: = 240 mm2
Although it may appear that selection of minimum cross sectional area of cable conductor as
240 mm2 is only just large enough for the duty, the actual fault current in the motor circuit is
generally less than the switchboard fault withstand rating of 50kA, hence the selection of cable
of cross sectional area 240 mm2 in practice offers sufficient design margin.
The minimum cross sectional area of cable required for 415V or 400V switchgear motor feeder
from fault withstand point of view shall be 240mm2.
We have considered for circuit breaker controlled motor feeder and analyzed the duration of
short circuit/fault withstanding time in seconds for the same. Exactly the Same holds true for
Circuit breaker controlled (Please see the below figure) outgoing transformer feeder.
However operating time of disconnecting device is slightly different for circuit breaker
controlled incomer and tie feeders. Duration of fault withstanding/operating time of
disconnecting device for incomer and tie feeder is 1 and 0.5 second respectively. This is because
of additional presence of inverse definite minimum time delay protection relays along with
instantaneous protection. The inverse definite time delay protection has time settings greater than
0.5 for incomer feeders and about 0.5 for tie feeders.
For all different type of feeders the operating time of disconnecting device is indicated in figure
below:
Typical value of t (fault clearing time). All the connecting cables has to be sized for short circuit
duration (t) indicated in the diagram above
The final cable size shall be selected considering the other two criteria that is continuous
current carrying capacity & voltage drop criteria which would be continued in part-2 and part-3.
Sizing of power cables for circuit breaker
controlled feeders (part 2)
Posted May 13 2012 by Asif Eqbal in Cables, Energy and Power with 2 Comments Translate
Sizing of power cables for circuit breaker controlled feeders (part 2)
Continued from article Sizing of power cables for circuit breaker controlled feeders (part 1)
2. Criteria-2 Continuous current capacity (Ampacity)
This criterion is applied so that cross section of the cable can carry the required load current
continuously at the designed ambient temperature and laying condition. Ampacity is defined as
the current in amperes a conductor can carry continuously under the conditions of surrounding
medium in which the cables are installed. An ampacity study is the calculation of the temperature
rise of the conductor in a cable system under steady-state conditions.
Cable ampacity, if required to be calculated than it is calculated as per the following equation
givenin IEEE -399, section 13.
This equation is based on Neher-McGrath method where,
Tc allowable conductor temperature (C) Ta ambient temperature (either soil or air) (C) Td temperature rise of conductor due to dielectric heating (C) Tint temperature rise of the conductor due to interference heating from
adjacent cables (C)
Rac electrical ac resistance of conductor including skin effect, proximity and temperature effects (_/ft)
Rca effective total thermal resistance of path between conductor and surrounding ambient to include the effects of load factor, shield/sheath losses, metallic conduit losses,
effects of multiple conductors in the same duct etc (thermal- ft, C-cm/W).
From the above equation it is clear that the rated current carrying capacity of a conductor is
dependent on the following factors:
1. Ambient temperature (air or ground) 2. Grouping and proximity to other loaded cables, heatsources etc. 3. Method of installation (aboveground or below ground) 4. Thermal conductivity of the medium in which the cable is installed 5. Thermal conductivity of the cable constituents
However please note that while sizing a power cable we never calculate the ampacity. The above
equation is used to analyze the cable ampacities of unique installations. Standard ampacity tables
are available for a variety of cable types and cable installation methods and can be used for
determining the current carrying capacity of a cable for a particular application.
These standards provide tabulated ampacity data in manufacturers catalog for cables installed in
air, in ductbank, directly buried or in trays for a particular set ofconditions clearly defined.
It is because of this reason that we need to give the reference of manufacturers catalog from
where the ampacity values are picked up.
Now once the current carrying capacity of a cable is found from standard catalog; we convert
that rated capacity (Ampacity) into actual laying condition. The standard current ratings for
cables are modified by the application of suitable multiplying factors to account for the actual
installation conditions. Hence we define one more term here called ampacity deration factor.
Ampacity duration factor is defined as the product of various factors which accounts for the
fraction decrease in the ampacity of the conductor. Those factors and physical condition deriving
them are as follows:
1. K1= Variation in ambient air temperature for cables laid in air / ground temperature for cables laid underground.
2. K2 = Cable laying arrangement. 3. K3 = Depth of laying for cables laid direct in ground. 4. K4 = Variation in thermal resistivity of soil.
Ampacity Deration factor = Product of applicable multiplying factors among 1 to 4 listed above.
K = K1 x K2 x K3 x K4
Now from where do we get these multiplying factors to find the overall ampacity deration
factor? Againwe get these values from manufacturers catalog because manufacturer of the cable
is in best position to conduct thepractical experiments and test on the cables and find the
percentage/fractional decrease in current carrying capacity of the cable in various conditions.
For better understanding of the ampacity deration factor the following pictorial representation is
provided below.
Table for ampacity deration factor along with pictorial representation is provided below.
However readers to note that ampacity deration factor table provided in this article is to verified
from the manufacturers catalog which is intended to be used for project.
Rating factors for variation in ambient air temperature:
Air Temperature C 20 25 30 35 40 45 50 55
Rating
Factors
Conductor
Temp. 90C 1.81 1.41 1.10 1.05 1.00 0.95 0.89 0.84
Rating factors for variation in ground temperature:
Ground Temperature C 20 25 30 35 40 45 50
Rating
Factors
Conductor
Temp. 90C 1.12 1.08 1.04 0.96 0.91 0.87 0.82
Rating factors for multicore cables laid on open racks in air:
No. of
rocks
No of cables per rack
1 2 3 6 9
1 1.00 0.98 0.96 0.93 0.92
2 1.00 0.95 0.93 0.90 0.89
3 1.00 0.94 0.92 0.89 0.88
6 1.00 0.93 0.90 0.87 0.86
No. of
rocks
No of cables per rack
1 2 3 6 9
1 1.00 0.84 0.80 0.75 0.73
2 1.00 0.80 0.76 0.71 0.69
3 1.00 0.78 0.74 0.70 0.68
6 1.00 0.76 0.72 0.68 0.66
Rating factors for single core cable in trefoil circuits laid on open racks in air:
No. of
rocks
No of circuits per rack
1 2 3
1 1.00 0.98 0.96
2 1.00 0.95 0.93
3 1.00 0.94 0.92
6 1.00 0.93 0.90
Rating factors for groups of multicore cables laid direct in ground, in horizontal
formation:
Spacing
No. of cables in group
2 3 4 6 8
Cables touching 0.79 0.69 0.62 0.54 0.50
15 cm 0.82 0.75 0.69 0.61 0.57
30 cm 0.87 0.79 0.74 0.69 0.66
45 cm 0.90 0.83 0.79 0.75 0.72
60 cm 0.91 0.86 0.82 0.78 0.76
Rating factors for grouping of multicore cables laid direct in ground in tier
formation:
Spacing No. of cables
4 6 8
Cables touching 0.60 0.51 0.45
15 cm 0.67 0.57 0.51
30 cm 0.73 0.63 0.57
45 cm 0.76 0.67 0.59
60 cm 0.78 0.69 0.61
Rating factors for grouping of single core cable laid in trefoil circuits laid direct
in ground in horizontal formation:
Spacing
No. of circuits in group
2 3 4 6 8
Cables touching 0.78 0.68 0.61 0.53 0.48
15 cm 0.81 0.71 0.65 0.58 0.54
30 cm 0.85 0.77 0.72 0.66 0.62
45 cm 0.88 0.81 0.76 0.71 0.67
60 cm 0.90 0.83 0.79 0.76 0.72
Rating factors for depth of laying for Cables laid direct in the ground:
* Voltage Depth of laying 75 90 105 120 150 180 and above
1.1 kV
Rating factor up to 25 sq. mm. 1.00 0.99 0.98 0.97 0.96 0.95
Rating factor above 25 sq. mm and
up to 300 sq. mm 1.00 0.98 0.97 0.96 0.94 0.93
Rating factor above 300 sq. mm. 1.00 0.97 0.96 0.95 0.92 0.91
Rating factors for variation in thermal resistivity of soil:
(multicore cables laid direct in ground)
Nominal area of
conductor in sq. mm
Rating factors for value of Thermal Resistivity of Soil in C cm / Watt
100 120 150 200 250 300
25 1.14 1.08 1.00 0.91 0.84 0.78
35 1.15 1.08 1.00 0.91 0.84 0.77
50 1.15 1.08 1.00 0.91 0.84 0.77
70 1.15 1.08 1.00 0.90 0.83 0.76
Rating factors for variation in thermal resistivity of soil, three single core cables
laid direct in the ground:
(three cables in trefoil touching)
Nominal area of
conductor in sq. mm
Rating factors for value of Thermal Resistivity of Soil in C cm / Watt
100 120 150 200 250 300
25 1.19 1.09 1.00 0.88 0.80 0.74
35 1.20 1.09 1.00 0.88 0.80 0.74
50 1.20 1.09 1.00 0.88 0.80 0.74
Now let us apply the ampacity criteria for sizing the cable of a motor. The minimum required
size as per criteria-1 is already determined in part-1 of this article.
No. Input Required Source of Input
1 Rated kW of Load (Here we assume it as 160kW
Motor) Mechanical/Process Load list
2 Motor Data (PF and efficiency, Here we are
considering PF of 0.85 and motor efficiency of 95%)
From Motor Data sheet submitted by
manufacturer
3 Type of Cable to be used (Here we are considering
Aluminium, XLPE, 3 core cable)
Project technical specification (For
insulation and conductor material)
4
Electrical design ambient temperature (We are
considering electrical design ambient temperature of
50C)
Project technical specification
5 Laying condition From Electrical cable route layout
6 Cable ampacity and deration factors From reputed cable manufacturers
catalog
Rated Load current for 160kW motor = 160 x 1000/ (1.732 x 415 x 0.85 x motor efficiency)
Rated load current for motor = 275.66 Ampere
Now assuming that cable is laid in open racks in air the applicable ampacity deration factor will
be:
K = K1 X K2 (K3 and K4 will not be applicable in this case)
K1 = 0.89
K2 = 0.70 (assuming 3 Nos. of cable rack with number of cables/rack to be 6 and cables are laid
touching each other)
K = 0.89 x 0.70 = 0.623
Now K x Cable Ampacity should be greater than or equal to the required load current.
Aluminum, XLPE, 3C x 300 Sq mm cable has ampacity in air = 461 Amperes (From
Manufactures catalog)
Applying ampacity deration factor = 461 * 0.623 = 287.203 Amperes which is greater than
required load current of 275.6 Amperes.
Hence cable size selected on the basis of continuous current requirement is single run of 3C x
300 Sq mm, Aluminum, XLPE.
Conclusion:
A motor rated 160kW controlled by air circuit breaker fed from main PCC of fault rating 50kA
and connected through Aluminum XLPE cable requires a cable size of 3C x 240 Sq mm
minimum because of short circuit rating, however selected size because of continuous current
requirement is 3c x 300 Sq mm.
The third and final criteria of voltage drop will be discussed in part-3 of this article
Sizing of power cables for circuit breaker
controlled feeders (part 3)
Posted May 17 2012 by Asif Eqbal in Cables, Energy and Power with 3 Comments
Translate
Sizing of power cables for circuit breaker controlled feeders (technical article by mr. Asif Eqbal)
Continued from article Sizing of power cables for circuit breaker controlled feeders (part 2)
3. Criteria Starting and running voltage drops in cable
This criterion is applied so that the cross sectional area of the cable is sufficient to keep the
voltage drop (due to impedance of cable conductor) within the specified limit so that the
equipment which is being supplied power through that cable gets at least the minimum required
voltage at its power supply input terminal during starting and running condition both.
Cables shall be sized so that the maximum voltage drop between the supply source and the load
when carrying the design current does not exceed that which will ensure safe and efficient
operation of the associated equipment. It is a requirement that the voltage at the equipment is
greater than the lowest operating voltage specified for the equipment in the relevant equipment
standard.
So before starting with calculation for voltage drop let us first analyze that what is the
permissible voltage drop as per relevant standards and guidelines and what is the possible logic
behind selecting these values as the permissible values.
Indian standard 1255- CODE OF PRACTICE FOR INSTALLATION AND MAINTENANCE
OF POWER CABLES UP TO AND INCLUDING 33 kV RATING in its clause 4.2.3.4
mentions the permissible value for different cross sectional sizes of Aluminium conductor in
volts/kM/Ampere for cables from voltage grade of 1.1kV till 33kV. Since we calculate voltage
drop in terms of percentage of source voltage, this clause is not very widely used in basic as well
as detailed engineering fraternity.
Its complex unit requires to be multiplied by cable length and ampacity. However one can
definitely check for any cable size and length, what value is obtained in terms of percentage?
IEEE standard 525 Guide for the Design and Installation of Cable Systems in Substations in its annexure C, clause number C3 mentions that Voltage drop is commonly expressed as a
percentage of the source voltage. An acceptable voltage drop is determined based on an overall
knowledge of the system. Typical limits are 3% from source to load center, 3% from load center
to load, and 5% total from source to load. These values are indicated diagrammatically below.
6.6kV substation layout
dV1 is the drop from source (Transformer) to load center (PCC) which should be less than or equal to 3%. Feeder connecting source to load center is also known as primary feeder.
dV2 is the drop from load center (PCC) to individual loads which should be less than 3%. Feeder connecting load center to individual loads is also known as secondary feeder.
dV2 = dV1 + dV2 is the total drop from source (Transformer) to load which should be less than or equal to 5%
So far we have understood:
1. What are primary and secondary feeders?
2. What are the permissible values of voltage drop in cables for different types of feeder?
3. What are the governing standards for permissible voltage drop values?
Now before proceeding further some fundamental question that should be asked is:
Even though all the electrical equipments are rated for negative tolerance of 10% in voltage,
and system voltage variation allowed is also 10% on negative side than why do we design the
cable from source to load for a voltage drop of 5% maximum, what is wrong if the cable is
also designed for voltage drop of 10%?
Well answer to this lies in the fact that there is a rule of thumb that 2 percent of voltage is lost at
terminations and other points like cable joints in a circuit between the power source and the load.
Such voltage loss are not indicated and accounted for in cable sizing calculation. The cable
sizing calculation only considers the voltage drop in cable conductor from source to load. It is
prudent to make certain that the designed voltage drop does not exceed 5% to avoid problems
after installation.
It is much more costly to remove and replace an existing cable or piece of equipment that is
under rated versus the cost of equipment and cables designed with a degree of extra size and
avoid problems due to inadequate voltage at the load.
The NEC recommends or requires a maximum voltage drop of 5%, but realistically connection
impedances, deterioration of terminals due to heat and age, etc; add resistance to the total circuit.
Top
Difference between voltage drop and voltage dip?
A voltage dip is a decrease in the magnitude of a supply voltage having the duration of some
cycles to seconds. A voltage dip is a power quality problem which occurs due to:
Sudden change in the load, such as suddenly switching ON the large inductive load or any
temporary fault in the utility side of the system and impedance of source (Transformer)
Voltage dip is a sort of transient negative side fluctuation of bus voltage which is experienced by
all other loads connected to that bus, however it is caused by switching ON of any one single
load of large magnitude. It is mainly experienced as a decrease in bus voltage due to starting of
large motor. Since bus voltage decreases so other loads connected to that bus experience a
fluctuation of voltage. We often come across this phenomenon at our home also when due to
sudden switching ON of refrigerator or an air condition the voltage fluctuates.
Even in case of utility the addition of a large load will normally be scheduled with the utility so
they can project the time of day that a load, such as an office or industrial plant, is turned on.
Whereas the voltage drop is the drop in supply voltage before it reaches to the load. It is totally
because of impedance of the connecting cable. It is because of this reason that for checking the
adequacy of transformer MVA capacity and suitability of its percentage impedance that we
conduct voltage dip calculation after sizing of transformer. Same can also be done by motor
starting studies.
Now let us come back to the original topic that is voltage drop and its calculation. As we already
know about the permissible values of voltage drop so let us calculate and derive an expression
for the same in terms of impedance of cable, cable length and source voltage.
Let us consider a reference phasor as V. Direction of V as X axis and perpendicular to V as Y
axis. Approximation OC = OF which is almost equal to OE as EF can be neglected because EF
Vd = VS + (IRCos + IX Sin) (VS2 (IXCos IRSin)2 (Equation -6)
Equation-6 is the final expression for voltage drop where:
VS = the supply voltage
I = the load current
R = the resistance of cable conductor in Ohms/kM
X = the reactance of cable conductor in Ohms/kM
The above equation for voltage drop is recommended for exact calculation as per IEEE-241,
Recommended Practice for Electric Power Systems in Commercial Buildings, clause number
3.6.1 and IEEE-141, Recommended Practice for Electric Power Distribution for Industrial
Plants, clause number 3.11.1
Many consultants recommend the use of above formula for exact calculation of voltage drop in
cables meant for power plants. However as per IEEE-525, Guide for the Design and Installation
of Cable Systems in Substations, equation number C.2b of Annexure C recommends the use of
following formula:
Vd = IRCos + IXSin (Equation-7)
Since cable length is usually expressed in meters so before substituting in above expression
proper unit conversion should be done.
Sometimes multiple runs of cable are used so number of runs should come as division factor in
above expression for equivalent resistance. Multiplying factor of 3 is to be taken for 3 phase system.
So we get two different formulas for voltage drop from two standards of same code IEEE. However the
formula mentioned in equation number -6 can be approximated as formula given in equation-7, if the
vertical component of voltage drop Vdy is negligible as compared to supply voltage.
That is we are neglecting the vertical component of both the inductive drop and resistive drop.
So approximating VS-Vdy almost equal to VS the formula in equation-6 will be reduced to
formula in equation-7.
Resistance of cable conductor
Resistance of cable conductor is calculated from resistivity value of conductor material at 20 C,
which is a standard temperature for testing adopted by all cable manufacturers. Resistivity is
concerted into resistance by following formula:
Rdc = X L / A
Where:
= Resistivity at 20 C L= 1 kM length
A = Cross sectional area of conductor.
This resistance is DC resistance at 20C. It is converted to DC resistance at 90 C by the following
conversion formula:
Rt = R20 (1 + T)
Where:
R20 = Resistance at 20 C
= Coefficient of linier expansion of Aluminium T = Temperature at which resistance is to be calculated
For sizing of cables for AC system the resistance of conductor to be selected should be AC
resistance at 90 C and not DC resistance. DC resistance is selected for sizing of cables for DC
system like battery, battery charger etc.
A conductor offers a greater resistance to a flow of alternating current than it does to direct
current. When the term ac resistance of a conductor is used, it means the DC resistance of that conductor plus an increment that reflects the increased apparent resistance in the conductor. This
increment is mainly caused by:
Skin effect
This results in a decrease of current density toward the center of a conductor. A longitudinal
element of the conductor near the center is surrounded by more magnetic lines of force than is an
element near the rim.
Thus, the counter-emf is greater in the center of the element. The net driving emf at the center
element is thus reduced with consequent reduction of current density. In simple terms the current
tends to crowd toward the outer surface.
Proximity Effect
In closely spaced ac conductors, there is a tendency for the current to shift to the portion of the
conductor that is away from the other conductors of that cable. This is called proximity effect.
The flux linking the conductor current in one conductor is distorted by the current in a nearby
conductor which in turn causes a distortion of the cross-sectional current distribution.
The above mentioned two factors are for increased resistance is generally expressed as the
AC/DC resistance ratio. There are other magnetic effects can also cause an additional increase in
AC/DC resistance ratios. However we are not going to discuss them in this article. ac/dc ratio is
determined by skin effect factor and proximity effect factor.
Rac = (AC/DC) ratio x Rdc
For frequencies higher than 60 hertz, a correction factor for the values of resistance is applied as
follows:
x = 0.027678 f/Rdc
Where:
f = frequency in hertz
Rdc = conductor DC resistance at operating temperature, in ohms per 1000 feet. The inductance
of a multi-conductor cable mainly depends on the thickness of the insulation over the conductor.
Inductive reactance of cable conductor
The inductive reactance of an electrical circuit is based on Faradays law. That law states that the induced voltage appearing in a circuit is proportional to the rate of change of the magnetic flux
that links it. The inductance of an electrical circuit consisting of parallel conductors, such as a
single-phase concentric neutral cable may be calculated from the following equation:
XL = 2 f (0.1404 log S/r + 0.153) x 10-3
Where:
XL = Ohms per 1000 feet
S = Distance from the center of the cable conductor to the center of the neutral
r = Radius of the center conductor
S and r must be expressed in the same unit, such as inches.
Please note that we do not do any calculation for finding inductive reactance or resistance of cable. It is
cable manufacturers job to do it and place the values in tabulated form in catalog. We directly select
the values from catalog as has been done above.
Now, in technical articles part-2 and part-1 we had considered the sizing of cable for DOL motor
feeder rated at 160kW supplied by 415V. Minimum required area was calculated as 3CX240 Sq
mm Al, XLPE, however due to continuous current requirement the cable cross section required
was calculated as 3CX300 Sq mm.
Now let us check the running and starting voltage drop for the same using exact equation-6 as
well as approximated equation-7.
Resistance of conductor of 3CX300 mm Sq Al, XLPE cable = 0.128 Ohms/kM (From manufacturers catalog)
Reactance of conductor of 3CX300 mm Sq Al, XLPE cable = 0.071 Ohms/kM (From manufacturers catalog)
Cable length = 150Mtr (assumed for this calculation) Running power factor of motor = 0.85 Starting power factor of Motor = 0.3 Starting current of motor = 6 times rated current
Assuming a drop of 1.5% in the cable for incomer feeder, that is from (source) to load center
(PCC) which we have not calculated here for sake of simplicity and space limitation.
Modifying equation-6 for proper units:
L = length of cable = 150 Mtr
N = Number of parallel runs of cable = 1
Substituting the values all the values in the above equation:
Running voltage drop = 2.52% from load center (PCC) to Motor.
Total running voltage drop from source to load = dV1 + dV2 = 1.5% + 2.52% = 4.02% which is < 5%.
Starting voltage drop = 11.4% from load center (PCC) to Motor.
Hence total starting voltage drop from source to load = dV1 + dV2 = 1.5% + 11.4% = 12.9% which is <
15%.
As any motor is capable of starting properly if voltage available at its supply terminal is 85 to 80% of
rated voltage, hence the selected cable size of single run of 3CX300 Sq mm Aluminum, XLPE insulated
conductor is sufficient in all conditions of running and starting for motor rated at 160kW supplied by
415V and situated at 150Mtrs from the load center.
Now we can verify the above obtained result by the approximate formula so that we can analyze
the amount of approximation involved in using that formula.
Modifying equation-7 for proper units:
L = length of cable = 150 Mtr
N = Number of parallel runs of cable = 1
Substituting the values all the values in the above equation
Running voltage drop = 2.5% from load center (PCC) to Motor.
Total running voltage drop from source to load = dV1 + dV2 = 1.5% + 2.5% = 4.0% which is < 5%.
Starting voltage drop = 11.05% from load center (PCC) to Motor.
Hence total starting voltage drop from source to load = dV1 + dV2 = 1.5% + 11.05% = 12.55% which is <
15%.
Hence we can see that even the approximate formula does give accuracy till one place of decimal
and can be used. We can do a small case study by varying the cable length from 50 Mtrs to 150
Mtrs in steps of 15 Mtrs and analyze the difference in voltage drop by the use of two formulas.
No. Cable Length Exact Formula Approximate Formula
Running Starting Running Starting
1 50 2.35% 5.20% 2.35% 5.18%
2 65 2.56% 6.35% 2.61% 6.29%
3 80 2.80% 7.47% 2.86% 7.39%
4 95 3.10% 8.60% 3.12% 8.50%
5 110 3.30% 9.70% 3.37% 9.60%
6 125 3.63% 10.00% 3.63% 10.70%
7 140 3.90% 12.10% 3.88% 11.81%
8 150 4.02% 12.90% 4.05% 12.55%
Hence we can observer that voltage drop only after one place of decimal as obtained by exact
formula is on lesser side where as approximate formula till the route length of 100 Mtrs gives
voltage drop on higher side. For route length above 100 Mtrs both the formulas almost converge
to give same value of running voltage drop.
Hence it is advisable to go for exact formula as far as possible however the approximate formula
also gives the fairly accurate result.
With the completion of third and final criteria of voltage drop we come to the end of sizing of
power cables for breaker controlled motor feeders supplied by 415V supply. With this
methodology readers can develop a formulated excel sheet for sizing of power cables for circuit
breaker controlled feeders.
References:
1. Electrical power cable engineering, edited by William A Thue, Publishers: MARCELD
EKKER INC. NEW YORK
2. IEEE Red book
3. IEEE Grey book
4. IEEE-525
5. IEEE-835
6. Indian standard-1255 (second revision)