Cable Sizing - baixardoc

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Smart Brains Institute of Engineering Design & Research

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ELECTRICAL ENGINEERING DESIGN 1/17

CABLE SIZING CABLE RATING & SIZING The following factors are to be considered for sizing and rating a cable:

• Voltage Rating (rated operating & peak withstand)

• Short circuit rating

• Emergency overload rating

• Voltage drop

• Current carrying capability (ampacity) Voltage Rating The voltage rating of the cable insulation is based on the phase-to-phase voltage of the system in which the cable is to be used, system grounding/earthing (grounded or ungrounded) and the fault clearing time for ground/earth faults on a system by the protective devices. In case of systems where a ground/earth fault is not isolated promptly, the cable insulation is subject to extra stresses during the fault conditions, affecting the cable life. Therefore, such cables must have greater insulation thickness. Medium Voltage Power Cable Insulation Levels – ANSI based Projects An insulation level of 100, 133, or 173 percent must be specified when purchasing medium voltage power cables. These insulation levels correspond to the fault clearing time for the system voltage level being used.

• The 100-percent insulation level is generally applicable to electrical systems having relay protection such that ground faults will be cleared as rapidly as possible but, in any case, within 1-minute of occurrence. Usually, these are solidly grounded systems.

• The 133-percent insulation level applies to systems whose breaker clearing time is not within the 1-minute criterion but offering adequate assurance that the fault will be cleared within 1 hour. Usually, these are ungrounded or high resistance grounded systems.

• The 173-percent criterion applies to systems in which the fault clearing time is indefinite. The 133 percent insulation level is the most common and is recommended for ungrounded systems. In accordance with the NEMA/ICEA standards, the voltage rating, printed on the cable jacket, is the phase-to-phase voltage of the cable. For example, cable rated 15 kV is appropriate for 15 kV phase-to-phase, but is appropriate only for 8,660 volts phase-toground under normal operating conditions. For ungrounded or resistance grounded systems under fault conditions, the phase-to-ground voltage rises to 15 kV until the fault is cleared. The clearing time determines whether the insulation level should be 100, 133, or 173 percent. If a system were designed that has a line to neutral voltage of 15 kV, the phase-to-phase voltage of the system would be 26 kV, and a 15 kV rated cable would not be suitable, in which case, the next standard cable rating, 28 kV, should be selected. Medium Voltage Power Cable Voltage Ratings – IEC based Projects The voltage designation/rating U0/U should be per the relevant cable standard, for





e.g., 600/1000V, 1900/3300V etc. and should be appropriate for the type of system & earthing arrangements. To facilitate the selection of appropriate voltage rating of a cable, the systems are divided into three categories per IEC 60183.

• Category A, comprises those systems in which any phase conductor that comes in contact with earth/earth conductor, is disconnected within 1-minute.

• Category B, comprises those systems which, under fault conditions, are operated for short time with one phase earthed. This period should not exceed 1-hour.

• Category C, comprises those systems which do not fall into category A or B. Fault Current Rating 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. For e.g., XLPE/EPR insulated cables are designed to operate with a continuous conductor temperature of 90oC and a maximum of 250oC under short circuit. The corresponding figures for PVC are 70oC and 160oC respectively. 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. 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:

Minimum cable size is calculated from following formula:

⎟⎟⎠

⎞⎜⎜⎝

⎛++

×=⎟⎠⎞

⎜⎝⎛

234

23450176

1

2

2

lnT

Tt

A

I (Derived from IEC 60949 or 60724)

tIA ××=⇔ 007.0

I = short-circuit current in rms amperes t = duration of short circuit in seconds, (tc)A = cable conductor cross sectional area in circular mils or mm2 (use actual mm2

instead of nominal size) C = Constant equal to 0.0297 for copper & 0.0125 for aluminum

T1 : Initial operating temperature (Max. permissible continuous conductor temperature)

(T1 = 90 OC for XLPE insulated conductor)

T2 :Maximum permissible temperature at short circuit

(T2 = 250 OC for XLPE insulated conductor)





T0 = 234.5° C for copper and 228.1° C for aluminum On medium voltage systems, the fault current at the load will not be significantly different than at the source due to the system impedance. Cable impedances have little effect on reducing the fault levels. However, in case of low voltage systems or when the loads are far from the source the cable impedances have a major effect in reducing the fault levels at the load end. Sizing - Recommendations The short circuit capacity need not be calculated for every cable. Generally, low voltage branch circuit feeders are not sized for short circuit withstand current. It is conventional to calculate the minimum cable size required for each switchboard or system and then ensure that all cables are of at least this size. Different sizes may be selected in line with the different types of protection applied. Generally short circuit capacity will be of greatest concern on high voltage systems. ANSI based projects The fault current (I) in the above equation varies with time. However, calculating the exact value of the fault current and sizing the 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. ½ cycles

• For low voltage breakers with intermediate/short time delay, use 10 cycles

• For low voltage breakers with instantaneous trips, use 1 cycle These are recommended values, and can be modified based on specific project data. In case the short circuit data at different voltage levels are available based on an ETAP study, the same can be used for sizing the cables. IEC based projects For fuse protected equipment the value of I2t can be calculated from the fuse characteristic directly. For low voltage fuses maximum allowable operating time is 5 seconds for fixed equipment and 0.4 seconds for socket outlets and portable equipment. These are voltage dependant. Operating time for the fuse at the expected current should be considered. For circuit breaker fed circuits with instantaneous protection, it is conventional to assume t = 0.2 seconds. The current is assumed to be the switchgear short circuit rating, however, in some cases this can lead to cables with large cross sectional area, which practically, cannot be accommodated. In these circumstances the actual or future projected fault current produces more prudent results. For circuit breaker fed circuits without instantaneous protection, protection operating times of 1 second are normally assumed. It should be noted that if inverse definite minimum time delay relays have time settings greater than 0.5, then longer operating





times are required. Again the current is assumed to be the switchgear short circuit rating. Most cable manufacturers produce graphs of conductor short circuit capacity. Short Circuit Rating of Shield/Screen In case of shielded power cables during ground/earth fault conditions, the shield/screen can be damaged if exposed to excessive fault currents. The shield must be large enough to carry the fault current for a sufficient length of time to permit the system protective devices to operate. The suitability of the shield can be calculated using,

I = Fault current flowing through the shield in amperes A = Area of shield in circular mils or mm2/1974 (use actual mm2 instead of nominal size) K = Constant based on temperature limits of jackets and metallic portion of shield T = duration of fault in seconds When the ground/earth fault current is greater than the short circuit current, it will also be necessary to re-check that the phase conductor is still protected against damage by the ground/earth fault current. Emergency Overload Rating Conductor operating temperature affects the life of the insulation. The life of the cable insulation is approximately halved and the thermally caused service failure doubled for

every 8° to 10°C rise in temperature. Sustained operation over the normal operating temperature or ampacities should not be allowed. Overloading for short periods of time can be considered, provided the following conditions are met for ANSI/IEC based projects. ANSI Based Projects The changes in cable temperature are not instantaneous based on variation in load. During overload conditions, the cable may be overloaded for short periods of time. The ICEA has established maximum emergency overload temperatures for various

insulations. For e.g., 130°C for XLPE and 130°/140°C for EPR rated at 90°/105°C continuous rating. Warning, cable expansion may be a problem at elevated temperatures, particularly for XLPE which has a high coefficient of expansion. For exceptionally long cable lengths providing expansion loop may be considered. Operations at the emergency overload temperature should not exceed 100 hours/year or more than 500 hours during the life of the cable. Refer to IEEE 141, Table 12-5 for uprating factors for short time overloads for various types of insulated cables. This uprating factor multiplied by the nominal current rating of a cable for a particular installation will give the emergency or overload current rating for the particular installation. IEC based Projects For IEC cable current capability, the following definitions apply: In = the nominal current or current setting of the protective device Ib = the design current (full load current of the circuit).





Iz = the current carrying capacity of the conductors, under particular installation conditions. I2 = the current causing the effective operation of the protective device. Relationship between In, Ib, Iz, and I2 In must be greater than or equal to Ib Iz must be greater than or equal to In I2 must not exceed 1.45Iz HRC (high rupturing capacity) fuses, cartridge fuses, mccbs (molded case circuit breakers) and mcbs (miniature circuit breakers), must comply with the requirement that the fusing current does not exceed 1.45Iz and the current carrying capacity of any conductor in the circuit is not less than the nominal rating of the protective device. A HRC fuse is often referred to as having a fusing factor of 1.5, but this is in an open test rig, and when installed in an enclosure, its fusing factor can be considered to be 1.45. Voltage Drop 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. Designing the system so that buses operate at nominal voltage plus or minus 10 percent has its problems, it is also not practical (or necessary) to calculate the voltage at every load. The approach should be to establish a set of maximum allowable cable voltage drops, and then allow for these drops in the design. Naturally, when choosing the allowable cable voltage drops, it is necessary to review the system to ensure that the allowable drops are sufficient for the worst-case loads. However, cable should not be oversized (beyond acceptable voltage drop) to compensate for bad system design. The system should be corrected if the total voltage drop at the load is excessive when cable voltage drop is acceptable. The voltage-drop in a circuit, V'D, line to neutral, is given by the following Approximation (IEEE 141 - 1993, Chapter 3):

Where, I = current flowing in the conductor, in amperes. R = total line resistance for one conductor, in ohms. X = total line reactance for one conductor, in ohms.

cosφ= load power factor, in per unit.

sinφ = load reactive factor, in per unit. Es= Sending end voltage





The voltage-drop obtained from the formula above is in one conductor, one way (i.e., line-to-neutral voltage drop). However, the line-to-line voltage-drop, VD in a three phase ac system is computed by multiplying the formula above by √3:

where, R = conductor resistance per 1000 feet(meters), in ohms. X = conductor reactance per 1000 feet(meters), in ohms. l = total length of circuit, in feet/meters. and VD can be expressed as; VD = (%VD)*(VL) where (%VD) = Percentage of the Voltage-Drop . (VL) = Nominal Bus Voltage

Rearranging, gives the circuit length as;

This formula is used in determining the maximum feeder cable lengths. When using the formulae to calculate the voltage drop in a cable supplying a motor load, it is necessary to perform the calculation for motor starting and running conditions. The value at full load is based on practical and economic considerations and that at starting to ensure that motor starting torque is sufficient to accelerate the driven equipment. Resistance data are usually tabulated in the form of dc resistance per 1000 feet of conductor at some given temperature, such as 20°C or 25°C, for different sizes and cable construction (stranded, solid, coated, uncoated, etc.). This resistance must then be corrected for the proper cable operating temperature, skin effect, installation in magnetic conduit, and, for large cables, proximity effect. (The skin effect causes an increase in apparent resistance for ac operation.) Because most cables carry current that is less than their rated ampacity, their actual operating temperatures will be less than their rated operating temperature. To be on the safe side and to simplify things, the resistance is usually corrected for the cable’s rated maximum operating temperature. This yields the worst case resistance.





Voltage Drop Study - Recommendations Normally the limits of cable voltage drop are established individually for each project and are given in the project Electrical Design Criteria. The values are usually based on Client requirements and National Standards, where applicable. Typical LV cable voltage drop values, as a percentage of the nominal circuit voltage, are as follows:

• Motor Feeders at motor full load current 5% at starting 15%

• Power distribution feeders 2%

• Lighting distribution feeders 1%

• Lighting sub-circuits 2%

Cable Ampacity 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, whether calculated or taken from an ampacity table is based on the following equation,

This equation is based on Neher-McGrath method where, Tc’ – allowable conductor temperature (oC) Ta’ – ambient temperature (either soil or air) (oC) ΔTd – temperature rise of conductor due to dielectric heating (oC) ΔTint – temperature rise of the conductor due to interference heating from adjacent cables (oC) Rac – electrical ac resistance of conductor including skin effect, proximity and temperature effects (μΩ/ft) R’ca – 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-Ωft, oC-cm/W). From the above equation it is clear that the rated current carrying capacity of a conductor is dependent on the following factors,

• Ambient temperature (air or ground)

• Grouping and proximity to other loaded cables, heat sources etc.

• Method of installation (aboveground or below ground)

• Thermal conductivity of the medium in which the cable is installed

• Thermal conductivity of the cable constituents





Cable Ampacity Study – Standard Tables 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 for cables installed in air, in ductbank, directly buried or in trays for a particular set of conditions clearly defined. If the actual design conditions in a project are different from those defined in these tables, rating factors have to be applied to obtain the correct rating of the cables. The standards below provide the rating factors for variations in ambient or ground temperature, depth of laying, thermal resistivity of soil and mutual heating due to cables installed together. Manufacturers are another source of ampacities.

CABLE SIZING PROCEDURE

1) PROCEDURE

The size of the cable is selected based on the following considerations.

a) Short circuit withstand capacity (SC Ampacity).

b) Effective current carrying capacity (Thermal Ampacity). c) Voltage drop during steady state operating conditions and motor start-up.

Short circuit withstand capacity is to be checked for HT cables and for LT incomer feeders

only.For LT breaker controlled motor feeders ,the cable impedance reduces short circuit current

considerably,hence, short circuit withstand capacity is not required to be checked for the rated

fault level of the LT motors.

For HT feeders & LT incomer feeders ,the minimum cable size which satisfies the above three

conditions is selected. For other LT feeders , minimum cable size which meets b) & c) is selected.

3.0 STEPS FOR CABLE SIZING

Following steps are to be followed to conclude proper techno-economical cable size for a

consumer.

3.1 Step-1 (Applicable for HT cables and LT incomer cables only)

The cross sectional area where calculated shall not be less than the value determined by

the following formula.

S = I√t

K





Where,

S = Nominal cross sectional area of the conductor in mm²

I = Value of fault current in Amperes.

t = Fault clearing time in seconds (This is generally taken as 0.2

seconds for motor & transformer feeders,0.6 seconds for plant

feeders, 1.0 seconds for incoming feeder.)

K = Factor taking account of the resistivity, temperature co-efficient,

heat capacity of the conductor material, initial and final temperature. Value of

`K’ (as per BS 7671) shall be taken as 94 for XLPE insulated Aluminium

Cables , 143 for XLPE insulated copper cables and 76 for PVC insulated

Aluminium cables.

Wherever the application of the formula results in a non-standard size, a conductor of the

next higher standard cross section area shall be used.

Short circuit duration for cables must be commensurate with the tripping time of the

protective devices associated with the feeder.

3.2 Step-2 - Effective Current Carrying Capacity (Thermal Ampacity)

The current carrying capacity of a cable corresponds to the maximum current that it can

carry under specified conditions without the conductors exceeding the permissible limit

of steady state temperature for the type of insulation concerned. Derating factor or

correction factor (C) shall be applied where the installation conditions differ from those

for which values of current carrying capacity are defined. Derating factors generally

considered are as follows:

a) In Ground Installation (direct burial)

C = Cs X Cg X Cd X Ct

Where,

Cs = Rating factor for variation in Ground temperature.

Cg = Rating factor for Grouping of cables.

Cd = Rating factor for Depth of laying.

Ct = Rating factor for Thermal resistivity of soil.

b) Above Ground Installation

C = Ca X Cg

Where

Ca = Rating factor for variation in Ambient air temperature.

Cg = Rating factor for Grouping of cables.

c) Values of different derating factors for calculating ‘C’ shall be taken as per

manufacturer catalogues. The value of ‘C’ thus calculated is multiplied by the





cable continuous current obtained from the standard tables gives the derated

current carrying capacity of cable.

d) In case cables are laid partially in air and ground , take the lowest derating factor

for calculation.

e) Prepare derated current rating chart for each size cable after multiplying the

cable ampacity with the applicable derating factor ‘C’.

3.3 Step-3 (Cable size according to load current)

a) Calculate load current for a consumer using following formulas

(i) I = KW for 3 ph AC loads

√3 * V* pf *effn

(ii) Iload = KW for 1 Ph AC load

V*pf*effn

(iii) Iload = KW for DC

V*effn

Where I = Load current of the electrical consumer ( in Amp)

KW = Output kW (name plate) rating of the load . In case of battery charger

maximum load considering normal load + boost charging to be considered

.V = Line to line voltage in case of 3ph AC/ Line to phase in case of 1 ph AC / DC

voltage in case of DC ( in kV and name plate voltage rating of the consumer

,not

the switchgear bus voltage) in kV

pf = power factor in case of AC voltage at rated load

effn = Efficiency (≤1) of the equipment at rated load.

b) Select the cable size from the calculated chart (cl 3.2 e)

c) Compare the cable size as per short circuit (step-I) and according to load Current

(step-3). Select the higher cable size.

3.4 Step-4 –Verification of cable size according to permissible voltage drop during

steady state operating conditions & motor start up.

a) For three phase circuits.

% Voltage drop can be computed using the formula

% Vd = √3 * I * L * (Rac * Cos∅ + X * Sin∅) * 100 / (N * V)

Where,

Vd = Voltage drop in percentage

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