basic electrical characteristics carl landinger hendrix wire & cable
TRANSCRIPT
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When Electric Current Flows in a Path
There is a voltage (electrical pressure) driving the current
An electric field eminates from the current path
A magnetic field surrounds the current Except for superconductors, there is some
resistance/impedance to the current flow There is a loop path to-from the source
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A Cable Carrying Current has a Magnetic Field Associated with the Current Flow
CONDUCTOR
INSULATION
MAGNETIC FIELD FLUX LINES EXTEND OUT TO INFINITYNOTE THAT ANY COVERING OR INSULATION DOES NOTALTER THE MAGNETIC FIELD LINES
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Two Cables Carrying Current Will Have Magnetic Fields Interacting With Each Other
Cable #1 Cable #2
MAGNETIC FIELD (FLUX) FROM EACH CABLE LINKS THE ADJACENT CABLETHIS CAUSES A FORCE TO EXIST BETWEEN THE CABLES.IF THE CURRENTS ARE TIME VARYING, A VOLTAGE IS INDUCEDINTO THE ADJACENT CABLE.
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Force on Adjacent Current Carrying Conductors
I1 d I2
DC: F = 54101 2
7
.I xI x
d
lbs./ft.
For RMS Symmetrical current Single Phase Symmetrical
AC: F = 10 8101 2
7
.I xI x
d
lbs./ft.
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Force on Adjacent Current Carrying Conductors
A B Cd d
I I
I
RMS Symmetrical Current3 Asymmetrical Fault
A or CMaximum
34 9102 7
.I x
d
F = lbs./ft.
BMaximum
F = 37 5102 7
.I x
d
lbs./ft.
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Force on Adjacent Current Carrying Conductors
A Cd dI I
I
RMS Symmetrical Current3 Asymmetrical Fault
34 9 10 10
0 5
4 2 7.
.
x x = 689 lbs./ft.
Assume: I = 10,000 Amps/Phase, d = 6in. (0.5 ft.)
Maximum Force on A or C Phase is:
This is no small amount of force!
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Resistivity Vs Conductivity Resistivity is a property of every material Resistivity is a measure of a material to resist the flow
of DC current Resistivity is stated as per unit volume or weight at a
specific temperature Conductivity is a measure of a material to conduct DC
current and is the reciprocal of resistivity Materials having a low resistivity make good
conductors. Materials with high resistivities are insulators.
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Percent Conductivity The conductivity of conductor grade annealed copper
was established as the standard and given as 100% (IACS)
Other materials are stated as a percentage of being as conductive of this standard
Aluminum is approximately 61% as conductive as annealed copper on a volume basis. However, it is over twice as conductive on a weight basis.
It is possible to exceed 100% i.e. silver is 104.6% Metal purity and temper effect conductivity
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Relationship Between Resistance and Volume Resistivity
l = lengthheight = h
current flow w = width Area = w X h
Resistance = Volume Resistivity x LengthArea
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Temperature Coefficient of Resistance
RT2 = RT1[1 +
where:RT2 = DC resistance of conductor at desired or
assumed temperatureRT1 = DC resistance of conductor at “base” temperatureT2 = Assumed temperature to which dc resistance is
to be adjustedT1 = “Base” temperature at which resistance is known
and Temperature coefficients of resistanceat the base temperature for the conductor
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Temperature Coefficient of Resistance (Continued)
For the range of temperatures in which most conductors operate the formula reduces to
RT2 = RT1[1 +
values for
Conductor 0°C 20°C 25°C61.2% Aluminum 0.00440 0.00404 0.00389100.0% Copper 0.00427 0.00393 0.00378
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Effective AC Resistance
“Effective” ac resistance is required for voltage drop calculations
“Effective” ac resistance includes– Skin effect
– Proximity effect
– Hysteresis and Eddy current effects
– Radiation loss
– Shield/sheath loss
– Conduit/pipe loss
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Alternating Current Resistance
For the general case when calculating impedance for voltage drop or system coordination;
Rac = Rdc(1 + YCS + YCP) + RWhere: YCS is the multiple increase due to skin effect YCP is the multiple increase due to proximity effect R is the apparent increase due to shield loss, sheath
loss, armor loss, ………..
Note: The presence of enclosing metallic, magnetic and non-magnetic conduit or raceway will increase these factors as well
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Alternating Current ResistanceWhen Calculating for Ampacity Determination
Rac = Rdc(1 + YCS + YCP) Where; YCS is the multiple increase due to skin effect YCP is the multiple increase due to proximity effect Shield loss, sheath loss, armor loss, …are handled as
separate heat sources introduced at their location in the thermal circuit.
Note; The presence of enclosing metallic, magnetic and non-magnetic conduit or raceway will increase all of these factors.
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Insulation Thickness
Cables are voltage rated phase to phase based on a grounded WYE three phase system unless stated– Thus, unless otherwise noted, the insulation thickness
is designed for a voltage equal to the cable voltage rating divided by 1.732
– For a 15kV cable the insulation thickness is designed for; 15 kV/1.732 = 8.66 kV
– Cables used on other systems must be selected accordingly
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Insulation Thickness
For an ungrounded 15 kV delta system the voltage to the neutral point varies from 15 kV/1.732 depending on load balance. For this case, it is common to select insulation thickness based on 1.33 x 15 kV or 20 kV as long as a fault to GRD. is cleared within 1 hour.
This is the origin of the 133% insulation level The insulation thickness for a 20 kV cable is 215
mils/ICEA, 220 mils/AEIC
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Insulation Thickness When a phase to ground fault occurs on an
ungrounded delta system, full phase to phase voltage appears across the insulation – For 15 kV this is equivalent to a 15 X 1.732 = 26 kV cable.
– If such a fault is to be allowed to exist for more than 1 hour, it is common to select insulation thickness based on this voltage.
– This is the origin of the 173% level
– the 173% level is not common and the values are not widely published
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Insulation ResistanceNo insulation is perfect. If the conductor is made into one electrode, and the shield over the insulation, or made shield such as water is used as the other electrode, and a Direct Current Voltage E, applied across the electrodes, a current I, will flow. Using Ohms Law, E = I/R, an insulation resistance can be calculated.
EI
..
R = insulation resistance (ohms) = E/I
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Typical DC Leakage Current With Constant Voltage Applied
IG = charging currentIA = absorbtion currentIL = leakage currentIT = total current
IL
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Insulation Resistance ConstantIf one uses a 100 to 500 volt DC source to measure the resistance
from conductor to shield, or a made shield such as water, of a 1,000 foot length of insulated cable at a temperature of 60°F, the following formula describes the relationship between the insulation thickness, the resistance reading obtained, and a constant which is peculiar to the insulation;
R = (IRK) Log10(D/d)Where; R is the resistance in megohms-1,000 feet
D is the diameter over the insulation d is the diameter under the insulation
IRK is the insulation resistance constant
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Insulation Resistance Constants Non Rubber Like Materials
Impregnated Paper 2,640Varnished Cambric 2,460Crosslinked Polyethylene 0-2 kV 10,000Crosslinked Polyethylene > 2 kV 20,000Thermoplastic Polyethylene 50,000Composite Polyethylene 30,00060°C Thermoplastic PVC 50075°C Thermoplastic PVC 2,000
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Insulation Resistance Constants Rubber Like Materials
Ethylene Propylene Rubber Type I 20,000
Ethylene Propylene Rubber Type II, 0-2kV 10,000
Ethylene Propylene Rubber Type II, >2kV 20,000
Code Grade Synthetic Rubber 950Performance Natural Rubber 10,560
Performance Synthetic Rubber 2,000
Heat Resistant Natural Rubber 10,560
Heat Resistant Synthetic Rubber 2,000
Ozone Resistant Synthetic Rubber 2,000
Ozone Resistant Butyl Rubber 10,000
Kerite 4,000
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Insulation Resistance Constant Important Notes
If the measurement is not made at 60° F but at a temperature not less than 50 or more than 85°F, correction factors must be used to correct to 60°
If the measurement is made on a length other than 1,000 feet, correction to an equivalent 1,000 foot length is necessary
Insulation Resistance Constants (IRK) are published for different classes of insulations. These are minimums and actual values obtained from test measurements should exceed these values or there is an indication of a problem in the material or test
Using IRK to determine the condition of cables in the field is difficult and subject to error
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Cable Average Electrical Stress
G ave = Voltage to Ground Insulation thickness (mils)
G ave = volts/mil
T
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Cable Radial Electrical Stress at Any Point in the Insulation
G x = Vgrd Volts/Mil X Ln(R2/R1)
.
R1
X
R2
Maximum Stress X = R1
Minimum Stress X = R2
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STRESS GRADIENT IN #2-7 STRAND175 MIL CABLE AT 7.2 kV ac
Maximum Stress = 60.7 V/milMinimum Stress = 29.2 V/mil
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STRESS GRADIENT IN 1/0-19 STRAND345 MIL CABLE AT 20.2 kV ac
Maximum Stress = 105 V/milMinimum Stress = 36.0 V/mil
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The Formula for Calculating Per Foot Capacitance For Fully Shielded Cable Is:
C DD
oi
oc
7 354
10
.
log
x 10-12
–where, is the dielectric constant of the covering
–Doc is the diameter over the conductor (or semi conducting shield, if used)
–Doi is the diameter over the covering (or insulation in the case of shielded cables)
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Shunt Capacitive Reactance For single conductor shielded primary cables the shunt capacitance
may be calculated by
where:
= dielectric constant of the insulation
Doi =diameter over insulation
Dui = diameter under insulation
The capacitive reactance may then be calculated as:
CLog
DD
oi
ui
7354
10
µµfarad/1000 ft
Xj fcc
1
2
where:f = frequency in Hzj = a vector operator
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The Formula for Calculating Charging Current, Per Foot, For A Fully Shielded Cable Is:
i = 2fce
i = Charging currentf = 60Hze = Voltage Phase to grdc = Capacitance
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Example of Charging Current, per Foot, For Fully Shielded Cable
ix
Log
2 607 354 2 3
1566105610
. .
.
.
x 10-12 x (14.4 x 103) = 0.539 milliamps/ft
= 2.3Doc = 1.056 inchDoi = 1.566 inche = 14.4 kV to ground
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Power Factor Vs Dissipation Factor A Cable is Generally a CapacitorIc
ab
Ir
Ic should be >>>Ir
Power Factor = Ir
I Ir c( ) ( )2 2 = Cos (b) always < 1.0
Dissipation Factor = Ir/Ic = Tan (a) ranging from 0 to For the normal case where Ic>>>Ir;
Ic Ir Ic ( ) ( )2 2
So, Power Factor and Dissipation Factor are often thought to be the same, but they are very different.
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Dielectric Power Dissipation (Dielectric Loss)
Ic It
Power DissipationP = E (Ir) = E (It) cos = E(Ic) tan
BUT;
Ic = 2fCEP = 2fCE2(Tan )
Ir E
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Inductive Reactance
L LogGMD
GMRX 01404 1010
3. henries to neut. per 1000 ft.
Where:GMD = Geometric mean distance (equivalent conductor spacing) between the current carrying cables.
GMR = Geometric mean radius of one conductor - inches
At 60 Hz: 2(frequency) = 377orXL = j0.05292 Log10 GMD/GMR ohm to neut. per 1000 ft.
j is a vector operator
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Geometric Mean Distance
Equilateral TriangleGMD =A=B=C
Right TriangleGMD = 1.123 A
Unequal triangleGMD = AxBxC3
A C
B A
CB BA
C
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Geometric Mean Distance
A B
C
Symmetrical FlatGMD = 1.26 A
A B
C
Unsymmetrical FlatGMD = AxBxC3
A
FlatGMD = A
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Effective Cross Sectional Area of Sheath/shield (A)
T y p e o f S h i e l d / S h e a t h F o r m u l a t o C a l c u l a t e ( A ) W i r e s / B r a i d n d s 2 H e l i c a l T a p e , n o l a p 1 . 2 7 n w b H e l i c a l T a p e , l a p p e d 4
1 0 0
2 1 0 0b d
Lm ( )
C o r r u g a t e d T a p e , L C S 1 2 7 5 0. [ ( ) ] d B bi s T u b u l a r 4 b d m
B-Tape Lap (mils) n-Number of wires/tapesb-Tape Thickness (mils) L-Tape overlap, %dis-Dia over Ins. Shield (mils)dm-Mean sheath/shield Dia. (mils)ds-Dia. of wires (mils)w-Tape width (mils)