# Short Circuit Current Calculations

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1 Introduction Several sections of the National Electrical Code relate to proper overcurrent protection. Safe and reliable application of overcurrent protective devices based on these sections mandate that a short circuit study and a selective coordination study be conducted. These sections include, among others: 0.9 Interrupting Rating 0.0 Component Protection 240. Conductor Protection Equipment Grounding Conductor Protection Marked Short-Circuit Current Rating; (3) Meter Disconnect Industrial Control Panels (B) Air Conditioning & Refrigeration Equipment (A) Industrial Machinery Selective Coordination Health Care Facilities - Selective Coordination Essential Electrical Systems In Healthcare Systems Selective Coordination for Elevator Circuits Emergency Systems Legally Required Standby Systems Compliance with these code sections can best be accomplished by conducting a short circuit study as a start to the analysis. The protection for an electrical system should not only be safe under all service conditions but, to insure continuity of service, it should be selectively coordinated as well. A coordinated system is one where only the faulted circuit is isolated without disturbing any other part of the system. Once the short circuit levels are determined, the engineer can specify proper interrupting rating requirements, selectively coordinate the system and provide component protection. See the various sections of this book for further information on each topic. Low voltage fuses have their interrupting rating expressed in terms of the symmetrical component of short-circuit current. They are given an RMS symmetrical interrupting rating at a specific power factor. This means that the fuse can interrupt the asymmetrical current associated with this rating. Thus only the symmetrical component of short-circuit current need be considered to determine the necessary interrupting rating of a low voltage fuse. For listed low voltage fuses, interrupting rating equals its interrupting capacity. Low voltage molded case circuit breakers also have their interrupting rating expressed in terms of RMS symmetrical amps at a specific power factor. However, it is necessary to determine a molded case circuit breaker s interrupting capacity in order to safely apply it. See the section Interrupting Rating vs. Interrupting Capacity in this book. 0.6 now requires arc-flash hazard warning labeling on certain equipment. A flash hazard analysis is required before a worker approaches electrical parts that have not been put into a safe work condition. To determine the incident energy and flash protection boundary for a flash hazard analysis the short-circuit current is typically the first step. General Comments on Short Circuit Calculations Sources of short-circuit current that are normally taken under consideration include: - Utility Generation - Local Generation - Synchronous Motors - Induction Motors - Alternate Power Sources Short circuit calculations should be done at all critical points in the system. These would include: - Service Entrance - Transfer Switches - Panel Boards - Load Centers - Motor Control Centers - Disconnects - Motor Starters - Motor Starters Normally, short circuit studies involve calculating a bolted 3-phase fault condition. This can be characterized as all 3-phases bolted together to create a zero impedance connection. This establishes a worst case (highest current) condition that results in maximum three phase thermal and mechanical stress in the system. From this calculation, other types of fault conditions can be approximated. This worst case condition should be used for interrupting rating, component protection and selective coordination. However, in doing an arc-flash hazard analysis it is recommended to do the arcflash hazard analysis at the highest bolted 3 phase short circuit condition and at the minimum bolted three-phase short circuit condition. There are several variables in a distribution system that affect calculated bolted 3-phase short-circuit currents. It is important to select the variable values applicable for the specific application analysis. In the Point-to-Point method presented in this section there are several adjustment factors given in Notes and footnotes that can be applied that will affect the outcomes. The variables are utility source short circuit capabilities, motor contribution, transformer percent impedance tolerance, and voltage variance. In most situations, the utility source(s) or on-site energy sources, such as on-site generation, are the major short-circuit current contributors. In the Point-to-Point method presented in the next few pages, the steps and example assume an infinite available short-circuit current from the utility source. Generally this is a good assumption for highest worst case conditions and since the property owner has no control over the utility system and future utility changes. And in many cases a large increase in the utility available does not increase the short-circuit currents a great deal for a building system on the secondary of the service transformer. However, there are cases where the actual utility medium voltage available provides a more accurate short circuit assessment (minimum bolted short-circuit current conditions) that may be desired to assess the arcflash hazard. When there are motors in the system, motor short circuit contribution is also a very important factor that must be included in any short-circuit current analysis. When a short circuit occurs, motor contribution adds to the magnitude of the short-circuit current; running motors contribute 4 to 6 times their normal full load current. In addition, series rated combinations can not be used in specific situations due to motor short circuit contributions (see the section on Series Ratings in this book). For capacitor discharge currents, which are of short time duration, certain IEEE (Institute of Electrical and Electronic Engineers) publications detail how to calculate these currents if they are substantial. Procedures and Methods To determine the fault current at any point in the system, first draw a one-line diagram showing all of the sources of short-circuit current feeding into the fault, as well as the impedances of the circuit components. To begin the study, the system components, including those of the utility system, are represented as impedances in the diagram. The impedance tables include three-phase and single-phase transformers, cable, and busway. These tables can be used if information from the manufacturers is not readily available. It must be understood that short circuit calculations are performed without current-limiting devices in the system. Calculations are done as though these devices are replaced with copper bars, to determine the maximum available short-circuit current. This is necessary to project how the system and the currentlimiting devices will perform. Also, multiple current-limiting devices do not operate in series to produce a compounding current-limiting effect. The downstream, or load side, fuse will operate alone under a short circuit condition if properly coordinated. The application of the point-to-point method permits the determination of available short-circuit currents with a reasonable degree of accuracy at various points for either 3Ø or Ø electrical distribution systems. This method can assume unlimited primary short-circuit current (infinite bus) or it can be used with limited primary available current Cooper Bussmann

2 Three-Phase Short Circuits Basic Point-to-Point Calculation Procedure Step. Determine the transformer full load amps (F.L.A.) from either the nameplate, the following formulas or Table : Step 2. Find the transformer multiplier. See Notes and 2 3Ø Faults Multiplier = Ø Line-to-Line (L-L) Faults See Note 5 & Table 3 00 *% Z transformer * Note. Get %Z from nameplate or Table. Transformer impedance (Z) helps to determine what the short circuit current will be at the transformer secondary. Transformer impedance is determined as follows: The transformer secondary is short circuited. Voltage is increased on the primary until full load current flows in the secondary. This applied voltage divided by the rated primary voltage (times 00) is the impedance of the transformer. Example: For a 480 Volt rated primary, if 9.6 volts causes secondary full load current to flow through the shorted secondary, the transformer impedance is 9.6/480 =.02 = 2%Z. * Note 2. In addition, UL (Std. 56) listed transformers 25kVA and larger have a ± 0% impedance tolerance. Short circuit amps can be affected by this tolerance. Therefore, for high end worst case, multiply %Z by.9. For low end of worst case, multiply %Z by.. Transformers constructed to ANSI standards have a ±7.5% impedance tolerance (twowinding construction). Step 3. Determine by formula or Table the transformer letthrough short-circuit current. See Notes 3 and 4. Note 3. Utility voltages may vary ±0% for power and ±5.8% for 20 Volt lighting services. Therefore, for highest short circuit conditions, multiply values as calculated in step 3 by. or.058 respectively. To find the lower end worst case, multiply results in step 3 by.9 or.942 respectively. Note 4. Motor short circuit contribution, if significant, may be added at all fault locations throughout the system. A practical estimate of motor short circuit contribution is to multiply the total motor current in amps by 4. Values of 4 to 6 are commonly accepted. Step 4. Calculate the "f" factor..732 x L x I3Ø f = C x n x E L-L 2 x L x I f = L-L C x n x EL-L Ø Line-to-Neutral (L-N) Faults 2 x L x See Note 5 & Table 3 I f = L-N C x n x EL-N Where: L = length (feet) of conductor to the fault. C = constant from Table 4 of C values for conductors and Table 5 of C values for busway. n = Number of conductors per phase (adjusts C value for parallel runs) I = Available short-circuit current in amperes at beginning of circuit. E = Voltage of circuit. Note 5. The L-N fault current is higher than the L-L fault current at the secondary terminals of a single-phase center-tapped transformer. The short-circuit current available (I) for this case in Step 4 should be adjusted at the transformer terminals as follows: At L-N center tapped transformer terminals, I L-N =.5 x I L-L at Transformer Terminals. At some distance from the terminals, depending upon wire size, the L-N fault current is lower than the L-L fault current. The.5 multiplier is an approximation and will theoretically vary from.33 to.67. These figures are based on change in turns ratio between primary and secondary, infinite source available, zero feet from terminals of transformer, and.2 x %X and.5 x %R for L-N vs. L-L resistance and reactance values. Begin L-N calculations at transformer secondary terminals, then proceed point-to-point. Step 5. Calculate "M" (multiplier) or take from Table 2. Step 6. M = + f Calculate the available short circuit symmetrical RMS current at the point of fault. Add motor contribution, if applicable. I S.C. sym. RMS = I S.C. x M Step 6A. Motor short circuit contribution, if significant, may be added at all fault locations throughout the system. A practical estimate of motor short circuit contribution is to multiply the total motor current in amps by 4. Values of 4 to 6 are commonly accepted. Calculation of Short-Circuit Currents at Second Transformer in System Use the following procedure to calculate the level of fault current at the secondary of a second, downstream transformer in a system when the level of fault current at the transformer primary is known. H.V. UTILITY CONNECTION I S.C. primary MAIN TRANSFORMER I S.C. primary I S.C. secondary 3Ø Transformer (I S.C. primary and f = I S.C. primary x V primary x.73 (%Z) I S.C. secondary are 00,000 x V transformer 3Ø fault values) Ø Transformer (I S.C. primary and I S.C. secondary are Ø fault values: I S.C. secondary is L-L) f = IS.C. primary x V primary x (%Z) 00,000 x V transformer M = + f I S.C. secondary = V primary x M x I S.C. primary V secondary I S.C. secondary Procedure for Second Transformer in System Step A. Calculate the "f" factor (I S.C. primary known) Step B. Step C. Calculate "M" (multiplier). Calculate the short-circuit current at the secondary of the transformer. (See Note under Step 3 of "Basic Point-to- Point Calculation Procedure".) 2005 Cooper Bussmann 93

3 Three-Phase Short Circuits System A Available Utility Infinite Assumption 500 KVA Transformer, 480V, 3Ø, 3.5%Z, 3.45%X,.56%R I f.l. =804A 25' - 500kcmil 6 Per Phase Service Entrance Conductors in Steel Conduit 2000A Switch One-Line Diagram Fault X Step. I f.l. = 500 x 000 = 804A 480 x.732 Step 2. Multiplier = 00 = Step 3. I S.C. =804 x = 5,540A I S.C. motor contrib = 4 x,804* = 7,26A I total S.C. sym RMS = 5, ,26 = 58,720A Fault X2 Step 4. Use I S.C.sym Fault X to calculate f f =.732 x 50 x 49,803 = ,85 x 480 Step 5. M = = Step 6. I S.C.sym RMS = 49,803 x.77 = 35,445A I sym motor contrib = 4 x,804* = 7,26A KRP-C-2000SP Fuse Step 4. f =.732 x 25 x 5,540 = ,85 x 6 x 480 I total S.C. sym RMS = 35, ,26 = 42,66A (fault X 2 ) Fault X 400A Switch Step 5. M = = LPS-RK-400SP Fuse Step 6. I S.C.sym RMS = 5,540 x.9663 = 49,803A 50' kcmil Feeder Cable in Steel Conduit I S.C.motor contrib = 4 x,804* = 7,26A I totals.c. sym RMS = 49, ,26 = 57,09A (fault X) Fault X 2 Motor Contribution M 2 *Assumes 00% motor load. If 50% of this load was from motors, I S.C. motor contrib. = 4 x,804 x.5 = 3608A System B Available Utility One-Line Diagram Fault X Infinite Assumption Step. 000 KVA Transformer, 480V, 3Ø, 3.5%Z I f.l.= 203A I f.l. = 000 x 000 = 203A 480 x.732 Step 2. Multiplier = 00 = Fault X2 Step 4. f =.732 x 20 x 33,25 = x,424 x 480 Step 5. M = = kcmil 4 Per Phase Copper in PVC Conduit 600A Switch KRP-C-500SP Fuse Fault X 400A Switch Step 3. I S.C. = 203 x = 34,370A Step 4. f =.732 x 30 x 34,370 = ,706 x 4 x 480 Step 5. M = = Step 6. I S.C.sym RMS = 33,25 x.905 = 30,059A Fault X3 Step A. f = 30,059 x 480 x.732 x.2 = ,000 x 225 Step 6. I S.C.sym RMS = 34,370 x.9664 = 33,25A Step B. M = = LPS-RK-350SP Fuse Step C. I S.C. sym RMS = 480 x.4286 x 30,059 = 29,73A /0 2 Per Phase Copper in PVC Conduit Fault X KVA transformer, 208V, 3Ø.2%Z Fault X Cooper Bussmann

4 Single-Phase Short Circuits Short circuit calculations on a single-phase center tapped transformer system require a slightly different procedure than 3Ø faults on 3Ø systems.. It is necessary that the proper impedance be used to represent the primary system. For 3Ø fault calculations, a single primary conductor impedance is only considered from the source to the transformer connection. This is compensated for in the 3Ø short circuit formula by multiplying the single conductor or single-phase impedance by.73. However, for single-phase faults, a primary conductor impedance is considered from the source to the transformer and back to the source. This is compensated in the calculations by multiplying the 3Ø primary source impedance by two. 2. The impedance of the center-tapped transformer must be adjusted for the halfwinding (generally line-to-neutral) fault condition. The diagram at the right illustrates that during line-to-neutral faults, the full primary winding is involved but, only the half-winding on the secondary is involved. Therefore, the actual transformer reactance and resistance of the half-winding condition is different than the actual transformer reactance and resistance of the full winding condition. Thus, adjustment to the %X and %R must be made when considering line-to-neutral faults. The adjustment multipliers generally used for this condition are as follows:.5 times full winding %R on full winding basis..2 times full winding %X on full winding basis. Note: %R and %X multipliers given in Impedance Data for Single Phase Transformers Table may be used, however, calculations must be adjusted to indicate transformer kva/2. 3. The impedance of the cable and two-pole switches on the system must be considered both-ways since the current flows to the fault and then returns to the source. For instance, if a line-to-line fault occurs 50 feet from a transformer, then 00 feet of cable impedance must be included in the calculation. The calculations on the following pages illustrate Ø fault calculations on a singlephase transformer system. Both line-to-line and line-to-neutral faults are considered. Note in these examples: a. The multiplier of 2 for some electrical components to account for the single-phase fault current flow, b. The half-winding transformer %X and %R multipliers for the line-to-neutral fault situation, and c. The kva and voltage bases used in the per-unit calculations. Short Circuit Primary Secondary L 2 N L N 50 Feet Primary Secondary Short Circuit A B C L Short Circuit L Cooper Bussmann 95

5 Single-Phase Short Circuits Cooper Bussmann

6 Impedance & Reactance Data Transformers Table. Short-Circuit Currents Available from Various Size Transformers (Based upon actual field nameplate data or from utility transformer worst case impedance) Voltage Full % Short and Load Impedance Circuit Phase kva Amps (Nameplate) Amps / ph.* / ph.** / ph.** * Single-phase values are L-N values at transformer terminals. These figures are based on change in turns ratio between primary and secondary, 00,000 KVA primary, zero feet from terminals of transformer,.2 (%X) and.5 (%R) multipliers for L-N vs. L-L reactance and resistance values and transformer X/R ratio = 3. ** Three-phase short-circuit currents based on infinite primary. UL listed transformers 25 KVA or greater have a ±0% impedance toler - ance. Short-circuit amps shown in Table reflect 0% condition. Transformers constructed to ANSI standards have a ±7.5% impedance tolerance (two-winding construction). Fluctuations in system voltage will affect the available short-circuit current. For example, a 0% increase in system voltage will result in a 0% greater available short-circuit currents than as shown in Table. Impedance Data for Single-Phase Transformers Suggested Normal Range Impedance Multipliers** X/R Ratio of Percent For Line-to-Neutral kva for Impedance (%Z)* Faults Ø Calculation for %X for %R * National standards do not specify %Z for single-phase transformers. Consult manufacturer for values to use in calculation. ** Based on rated current of the winding (one half nameplate kva divided by secondary line-to-neutral voltage). Note: UL Listed transformers 25 kva and greater have a ± 0% tolerance on their impedance nameplate. This table has been reprinted from IEEE Std (R99), IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems, Copyright 986 by the Institute of Electrical and Electronics Engineers, Inc. with the permission of the IEEE Standards Department.. Impedance Data for Single-Phase and Three-Phase Transformers- Supplement kva Suggested Ø 3Ø %Z X/R Ratio for Calculation These represent actual transformer nameplate ratings taken from field installations. Note: UL Listed transformers 25kVA and greater have a ±0% tolerance on their impedance nameplate Cooper Bussmann 97

7 Conductors & Busways "C" Values Table 4. C Values for Conductors Copper AWG Three Single Conductors Three-Conductor Cable or Conduit Conduit kcmil Steel Nonmagnetic Steel Nonmagnetic 600V 5kV 5kV 600V 5kV 5kV 600V 5kV 5kV 600V 5kV 5kV / / / / , Aluminum / / / / , Note: These values are equal to one over the impedance per foot and based upon resistance and reactance values found in IEEE Std (Gray Book), IEEE Recommended Practice for Electric Power Systems in Commerical Buildings & IEEE Std (Buff Book), IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems. Where resistance and reactance values differ or are not available, the Buff Book values have been used. The values for reactance in determining the C Value at 5 KV & 5 KV are from the Gray Book only (Values for 4-0 AWG at 5 kv and 4-8 AWG at 5 kv are not available and values for 3 AWG have been approximated). Table 5. C Values for Busway Ampacity Busway Plug-In Feeder High Impedance Copper Aluminum Copper Aluminum Copper Note: These values are equal to one over the impedance per foot for impedance in a survey of industry Cooper Bussmann

8 Voltage Drop Calculations Ratings of Conductors and Tables to Determine Volt Loss With larger loads on new installations, it is extremely important to consider volt loss in mind, otherwise some very unsatisfactory problems are likely to be encountered. The actual conductor used must also meet the other sizing requirements such as full-load current, ambient temperature, number in a raceway, etc. How to Figure Volt Loss Multiply distance (length in feet of one wire) by the current (expressed in amps) by the figure shown in table for the kind of current and the size of wire to be used, by one over the number of conductors per phase. Then, put a decimal point in front of the last 6 digits you have the volt loss to be expected on that circuit. Example 6 AWG copper wire in 80 feet of iron conduit 3 phase, 40 amp load at 80% power factor. Multiply feet by amperes: 80 x 40 = 7200 Multiply this number by number from table for 6 AWG wire threephase at 80% power factor: 7200 x 745 = Multiply by x = #/phase Place decimal point 6 places to left. This gives volt loss to be expected: 5.364V (For a 240V circuit the % voltage drop is x 00 or 2.23%). 240 These Tables take into consideration reactance on AC circuits as well as resistance of the wire. Remember on short runs to check to see that the size and type of wire indicated has sufficient ampere capacity. How to Select Size of Wire Multiply distance (length in feet of one wire) by the current (expressed in amps), by one over the number of conductors per phase. Divide that figure into the permissible volt loss multiplied by,000,000. Look under the column applying to the type of current and power factor for the figure nearest, but not above your result you have the size of wire needed. Example Copper in 80 feet of steel conduit 3 phase, 40 amp Ioad at 80% power factor Volt loss from local code equals 5.5 volts. Multiply feet by amperes by 80 x 40 x = #/phase Divide permissible volt loss multiplied by,000,000 by this number: 5.5 x,000,000 = Select number from Table, three-phase at 80% power factor, that is nearest but not greater than 764. This number is 745 which indicates the size of wire needed: 6 AWG. Line-to-Neutral For line to neutral voltage drop on a 3 phase system, divide the three phase value by.73. For line to neutral voltage drop on a single phase system, divide single phase value by 2. Open Wiring The volt loss for open wiring installations depends on the separation between conductors. The volt loss is approximately equal to that for conductors in nonmagnetic conduit offers a method to calculate conductor ampacity. Installation in Conduit, Cable or Raceway NEC Tables 30.6 through 30.9 give allowable ampacities (currentcarrying capacities) for not more than three conductors in a conduit, cable, or raceway. Where the number of conductors exceeds three the allowable ampacity of each conductor must be reduced as shown in the following tables: Installation in Conduit, Cable or Raceway per 30.5(B)(2)(a) The Number of Percentage of Values Conductors In One In Tables 30.6 And Conduit, Raceway 30.8 Or Cable 4 to 6 80% 7 to 9 70% 0 to 20 50% 2 to 30 45% 3 to 40 40% 4 and over 35% Conditions Causing Higher Volt Loss The voltage loss is increased when a conductor is operated at a higher temperature because the resistance increases. If type RH, RHW, THW, or THWN wire (75 C wire) is loaded to near its full rating, or if room temperature is 5 C higher than normal, add the following percentages to get the volt loss. Conditions Causing Higher Volt Loss Direct Single Or Three Phase Power Factor Wire Size Current 00% 90% 80% 70% 60% 4 to 4 AWG 5.0% 5.0% 4.8% 4.7% 4.7% 4.6% 2 to 3/0 AWG 5.0% 5.0% 4.2% 3.8% 3 5% 3.3% 4/0 AWG to 500 kcmil 5.0% 5.0% 3.% 2.6% 2.4% 2.0% 600 kcmil to 000 kcmil 5.0% 5.0% 2.5% 2.2%.6%.3% If type RHH, THHN or XHHW wire (90 C. wire) is loaded to near its full rating or if room temperature is 30 C higher than normal, add twice the above percentages to get the volt loss. Room Temperature Affects Ratings The ampacities (carrying capacities) of conductors are based on a room temperature of 86 F or 30 C. If room temperature is higher, the ampacities are reduced by using the following multipliers; (for volt, insulated conductors not more than 3 conductors in raceway or direct buried, Table 30.6). Room Temperature Affects Ratings Room Ampacity Multiplier Temperature TW THW, THWN THHN, XHHW* C F (60 C Wire) (75 C Wire) (90 C Wire) Cooper Bussmann 99

9 Voltage Drop Calculations Copper Conductors Ratings & Volt Loss Conduit Wire Ampacity Direct Volt Loss (See explanation prior page.) Size Type Type Type Current Three-Phase Single-Phase T, TW RH, RHH, (60 Cycle, Lagging Power Factor.) (60 Cycle, Lagging Power Factor.) (60 C THWN, THHN, 00% 90% 80% 70% 60% 00% 90% 80% 70% 60% Wire) RHW, XHHW THW (90 C (75 C Wire) Wire) Steel 4 20* 20* 25* Conduit 2 25* 25* 30* * 40* Non- 4 20* 20* 25* Magnetic 2 25* 25* 30* Conduit * 40* (Lead Covered Cables or Installation in Fibre or Other Non Magnetic Conduit, Etc.) * The overcurrent protection for conductor types marked with an (*) shall not exceed 5 amperes for 4 AWG, 20 amperes for 2 AWG, and 30 amperes for 0 AWG copper; or 5 amperes for 2 AWG and 25 amperes for 0 AWG aluminum and copper-clad aluminum after any correction factors for ambient temperature and number of conductors have been applied. Figures are L-L for both single-phase and three-phase. Three-phase figures are average for the three-phase Cooper Bussmann

10 Voltage Drop Calculations Aluminum Conductors Ratings & Volt Loss Conduit Wire Ampacity Direct Volt Loss (See explanation two pages prior.) Size Type Type Type Current Three-Phase Single-Phase T, TW RH, RHH, (60 Cycle, Lagging Power Factor.) (60 Cycle, Lagging Power Factor.) (60 C THWN, THHN, 00% 90% 80% 70% 60% 00% 90% 80% 70% 60% Wire) RHW, XHHW THW (90 C (75 C Wire) Wire) Steel 2 20* 20* 25* Conduit * 35* Non- 2 20* 20* 25* Magnetic * 35* Conduit (Lead Covered Cables or Installation in Fibre or Other Non Magnetic Conduit, Etc.) * The overcurrent protection for conductor types marked with an (*) shall not exceed 5 amperes for 4 AWG, 20 amperes for 2 AWG, and 30 amperes for 0 AWG copper; or 5 amperes for 2 AWG and 25 amperes for 0 AWG aluminum and copper-clad aluminum after any correction factors for ambient temperature and number of conductors have been applied. Figures are L-L for both single-phase and three-phase. Three-phase figures are average for the three-phase Cooper Bussmann 20

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