CHAPTER 6
Voltage Regulation: Using equation (6-18):
SHORT CIRCUIT CURRENTS Today’s high capacity power systems require that the short circuit capabilities of system cables be considered. Calculations can be used to determine an installed cable’s ability to withstand various short circuit conditions or the cable size needed to withstand a given short circuit condition.
Conductor Formula The usual form of the equation used to calculate the conductor’s short circuit current (I SC) is presented in ICEA for copper and aluminum conductors.2 The equations for calculating short circuit currents for copper and aluminum conductors are presented on the following pages. The accompanying figures graphically depict the relationship between conductor size and short circuit current duration for copper and aluminum conductors with thermoset or thermoplastic insulation. For these equations and curves to be valid, the conductor must be allowed to return to or below the rated maximum operating temperature (T 1) before another short circuit is encountered. The short circuit current equations may be simplified after designating the conductor metal and the values of T1 and T2 as follows: (6-31) where: I SC = sho short rt circ circuit uit cur curren rentt in amps amps A
= co cond nduc ucto torr area area in in cmil cmil
F C = t
conductor condu ctor short short circui circuitt factor factor from from Table Table 6-1 6-1
= dur durati ation on of short short circ circuit uit in in second secondss
TABLE 6-1 CONDUCTOR CONDUCT OR SHORT CIRCUIT FACTOR FACTORS S, F C Insulation
Copper
Aluminum
Thermoset (XLPE, EPR)
0.0678
0.0443
0.0719
0.0470
0.0529
0.0346
T1=105°C, T2=250°C Thermoset (XLPE,EPR) T1=90°C, T2=250°C Thermoplastic (PVC, PE) T1=75°C, T2=150°C
Calculation can be made for any value T 1 and T2 by using (6-32) or (6-33) 2
ICEA P-32-382, “Short Circuit Characteristics of Insulated Cable” – Fourth Edition, 1999.”
SOUTHWIRE 6-14
ELECTRICAL CHARACTERISTICS
) s p m A f o s d n a s u o h T ( t n e r r u C t i u c r i C t r o h S
Conductor Size
Figure 6-15 Allowable Short Circuit Currents for Copper Conductor and Thermoset Insulation
Curves based on: (6-32)
where: I SC = short circuit current in amps A
= conductor area in cmil
t
= duration of short circuit in seconds
T 1
= maximum operating temperature of the conductor (105°C)
T 2
= maximum short circuit temperature rating of the conductor (250°C)
SOUTHWIRE 6-15
CHAPTER 6
) s p m A f o s d n a s u o h T ( t n e r r u C t i u c r i C t r o h S
Conductor Size Figure 6-16 Allowable Short Circuit Currents for Copper Conductor and Thermoset Insulation
Curves based on:
(6-32)
where: I SC = short circuit current in amps A
SOUTHWIRE 6-16
= conductor area in cmil
t
= duration of short circuit in seconds
T 1
= maximum operating temperature of the conductor (90°C)
T 2
= maximum short circuit temperature rating of the conductor (250°C)
ELECTRICAL CHARACTERISTICS
) s p m A f o s d n a s u o h T ( t n e r r u C t i u c r i C t r o h S
Conductor Size Figure 6-17 Allowable Short Circuit Currents for Copper Conductor and Thermoplastic Insulation
Curves based on:
(6-32)
where: I SC = short circuit current in amps A
= conductor area in cmil
t
= duration of short circuit in seconds
T 1
= maximum operating temperature of the conductor (75°C)
T 2
= maximum short circuit temperature rating of the conductor (150°C)
SOUTHWIRE 6-17
CHAPTER 6
) s p m A f o s d n a s u o h T ( t n e r r u C t i u c r i C t r o h S
Conductor Size Figure 6-18 Allowable Short Circuit Currents for Aluminum Conductor and Thermoset Insulation
Curves based on:
(6-33)
where: I SC = short circuit current in amps A
SOUTHWIRE 6-18
= conductor area in cmil
t
= duration of short circuit in seconds
T 1
= maximum operating temperature of the conductor (105°C)
T 2
= maximum short circuit temperature rating of the conductor (250°C)
ELECTRICAL CHARACTERISTICS
) s p m A f o s d n a s u o h T ( t n e r r u C t i u c r i C t r o h S
Conductor Size Figure 6-19 Allowable Short Circuit Currents for Aluminum Conductor and Thermoset Insulation
Curves based on:
(6-33)
where:
I SC
= short circuit current in amps
A
= conductor area in cmil
t
= duration of short circuit in seconds
T 1
= maximum operating temperature of the conductor (90°C)
T 2
= maximum short circuit temperature rating of the conductor (250°C)
SOUTHWIRE 6-19
CHAPTER 6
) s p m A f o s d n a s u o h T ( t n e r r u C t i u c r i C t r o h S
Conductor Size
Figure 6-20 Allowable Short Circuit Currents for Aluminum Conductor and Thermoplastic Insulation
Curves based on:
(6-33)
where: I SC = short circuit current in amps A
SOUTHWIRE 6-20
= conductor area in cmil
t
= duration of short circuit in seconds
T 1
= maximum operating temperature of the conductor (75°C)
T 2
= maximum short circuit temperature rating of the conductor (150°C)
ELECTRICAL CHARACTERISTICS
Metallic Shield Formula The same general equation (6-32) may be applied to copper metallic shields. For this equation to be valid, the shield temperature must be allowed to return to or below the maximum rated shield temperature (T1) before another short circuit is encountered. However, the determination of the area (A) of the shield is more involved than for a conductor. (6-34) where: F S = shield short circuit factor from Table 6-2
TABLE 6-2 SHIELD SHORT CIRCUIT FACTORS F S Insulation
Jacket
T1
Thermoset (XLPE, EPR)
Thermoplastic (PVC, PE, LSZH, CPE) Thermoset (Hypalon)
85°C
Thermoplastic (PVC, PE)
Thermoplastic (PVC, PE, LSZH, CPE)
70°C
T2
FS (Copper)
200°C
0.0630
350°C
0.0890
200°C
0.0678
NOTES: (A) T1 is the shield temperature resulting from the maximum conductor operating temperature. (B) T2 is the maximum short circuit shield temperature. (C) T1 and T2 are from ICEA P-45-482. 3 (D) Calculations can be made for any value of T 1 and T2 by using equation (6-32).
Equations for Calculation of Shield Areas The equations for calculating the area of the shield are taken from ICEA. 3 For overlapped tapes, ICEA used the concept of effective tape shield area to compensate for the contact resistance between the tape laps that can increase the shield resistance. While in service, the contact resistance will likely increase as the cable ages and is exposed to heat and moisture. ICEA states that under these conditions the contact resistance may approach infinity, where (6-35) could apply. Helically Applied Tape Shield Tape Overlapped (6-35) Tape Not Overlapped (6-36) Tubular Shields (6-37) Wire Wrap (Concentric) or Braided Shields (6-38) Longitudinally Applied Corrugated Tape (6-39)
3
ICEA P-45-482, “Short Circuit Characteristics of Metallic Shields and Sheaths on Insulated Cable” – Fourth Edition, 1999.
SOUTHWIRE 6-21
CHAPTER 6
where: A = effective cross-sectional area of metallic shield in cmils b
= tape or tube thickness in mils
Dc
= diameter of core over semiconducting insulation shield in mils
L
= overlap of tape in percent
d m N d s B w
= mean diameter of shield in mils = number of wires = diameter of wire in mils = tape overlap in mils = width of tape in mils
Typical Calculation A given circuit has protection devices that are guaranteed to operate within 1 second (60 Hz). What are the maximum conductor and shield short circuit currents when using an EPR insulated 500 kcmil copper cable that has a semiconducting insulation shield diameter of 1.305 inches, with a 5 mil, 1.5 inches wide, 1/4 (25%) overlap copper tape shield and a PVC jacket? The continuous operating temperature of the cable is 105ºC.
Conductor Short Circuit Current Using equation (6-34):
Shield Short Circuit Current Using equation (6-35):
Using equation (6-34):
SOUTHWIRE 6-22
