I = E/Z,
is the basic relationship used in determining I, the short-circuit current, where E is the driving voltage of the source, and Z is the impedance from the source to the short circuit including the impedance of the source.
Most industrial systems have multiple sources supplying current to a short circuit since each motor can contribute. One step in short-circuit current calculation is the simplification of the multiple-source system to the condition where the basic relationship applies.
Type of short circuit
In an industrial system, the three-phase short circuit is frequently the only one considered, since this type of short circuit generally results in maximum short-circuit current. Line-to-line short-circuit currents are approximately 87% of three-phase short-circuit currents.
Line-to-ground short-circuit currents can range in utility systems from a few percent to possibly 125% of the three-phase value. In industrial systems, line-to-ground short-circuit currents higher than three phase are rare except when bolted short circuits are near the wye windings with a solidly grounded neutral of either generators or two winding, delta-wye, core-type transformers.
Assuming a three-phase short-circuit condition also simplifies calculations. The system, including the short circuit, remains symmetrical about the neutral point, whether or not the neutral point is grounded and regardless of wye or delta transformer connections. The balanced three-phase short-circuit current can be calculated using a single-phase equivalent circuit that has only line-to-neutral voltage and impedance.
In calculating the maximum short-circuit current, it is assumed that the short-circuit connection has zero impedance (is "bolted") with no current-limiting effect due to the short circuit itself. It should be recognized, however, that actual short circuits often involve arcing, and variable arc impedance can reduce low-voltage short-circuit current magnitudes appreciably.
Fault Calculation Detailed Procedure
A significant part of the preparation for a short-circuit current calculation is establishing the impedance of each circuit element and converting impedances to be consistent with each other for combination in series and parallel. Sources of impedance values for circuit elements are nameplates, handbooks, manufacturers' catalogs, tables included in this chapter, and direct contact with the manufacturer.
Two established consistent forms for expressing impedances are ohms and per unit (per unit differs from percent by a factor of 100). Individual equipment impedances are often given in percent, which makes comparisons easy, but percent impedances are rarely used without conversion in system calculations. The per unit form of impedance is used because it is more convenient than the ohmic form when the system contains several voltage levels. Impedances expressed as per unit on a defined base can be combined directly, regardless of how many voltage levels exist from source to fault.
To obtain this convenience, the base voltage at each voltage level must be related according to the turns ratios of the interconnecting transformers.
In the per-unit system, there are four base quantities: base apparent power in voltamperes, base voltage, base current, and base impedance. The relationship of base, per unit, and actual quantities is as follows:
per-unit quantity (voltage, current, etc.) = actual quantity/ base quantity
Usually a convenient value is selected for base apparent power in voltamperes, and a base voltage at one level is selected to match the transformer rated voltage at that level. Base voltages at other levels are then established by transformer turns ratios.
Base current and base impedance at each level are then obtained by standard relationships. The following formulas apply to three-phase systems, where the base voltage is the line-to-line voltage in volts or kilovolts and the base apparent power is the three-phase apparent power in kilovoltamperes or megavoltamperes:
Impedances of individual power system elements are usually obtained in forms that require conversion to the related bases for a per-unit calculation. Cable impedances are generally expressed in ohms. Converting to per unit using the indicated relationships leads to the following simplified formulas, where the per-unit impedance is Z pu:
Z pu = actual impedance in ohms ((base MVA) / (base k V)2
= actual impedance in ohms (base kVA) / (base k V)2(1000)
Transformer impedances are in percent of self-cooled transformer ratings in kilovoltamperes and are converted using the following:
Z pu = percent impedance (base kVA) / kVA rating (100)
= percent impedance (10) (base MVA) / kVA rating
Xpu = per-unit reactance (base kVA) / kVA rating
The procedure for calculating industrial system short-circuit currents consists of the following steps:
a) Step 1: Prepare system diagrams
b) Step 2: Collect and convert impedance data
c) Step 3: Combine impedances
d) Step 4: Calculate short-circuit current
Step 1: Prepare system diagrams
A one-line diagram of the system should be prepared to show all sources of short-circuit current and all significant circuit elements.
Impedance information may be entered on the one-line diagram after initial data collection and after conversion. Sometimes it is desirable to prepare a separate diagram showing only the impedances after conversion. If the original circuit is complex and several steps of simplification are required, each may be recorded on additional impedance diagrams as the calculation progresses.
The impedance diagram might show reactances only or it might show both reactances and resistances if a vector calculation is to be made. For calculation of a system X/R
ratio, as described later for high-voltage circuit breaker duties, a resistance diagram showing only the resistances of all circuit elements shall be prepared.
Step 2: Collect and convert impedance data
Impedance data, including both reactance and resistance, should be collected for important elements and converted to per-unit on bases selected for the study.
Since resistance is not constant but varies with temperature, consideration should be given to the choice of resistance values for study purposes.
For calculations of maximum short-circuit currents to select electric power system equipment, a fully loaded industrial power system is recommended because it has the largest number of motors connected and contributing to short-circuit current. Consequently, ÒhotÓ or rated load resistance values are usually accepted for these calculations.
These ÒhotÓ resistance values are also acceptable as conservative impedance data for load flows and similar calculations where probable maximum voltage drops and losses are desired results. This multiple usage provides a simplification of data preparation.
There is a concern that system operations at less than full load could reduce equipment and component temperatures, thus lowering resistances and increasing maximum short-circuit currents calculated using impedances.
This does not happen in most cases for industrial systems because the reduction in connected motors, at the reduced load and thus in motor contribution to the calculated short-circuit current, more than offsets the possible increase due to reduced resistance and increased X/R ratio.
In addition, for industrial systems where relatively high values of short-circuit current are expected, the short-circuit point reactance is generally much larger than the resistance and, due to the quadrature relationship of X and R, a possibly justifiable reduction in ÒhotÓ resistance values usually makes no significant difference in fault point impedance.
The effect of reduced resistance at reduced temperature should be examined in particular cases not covered by the general procedures of this chapter. For example, the calculation of the short-circuit current of an individual generator just being energized, before it takes load, should use ambient temperature resistance and
X/R ratios for a conservative result.
For industrial plant office buildings, and for other facilities with largely non-motor loads, full load might be applied without delay at start-up and calculations should account for pre-start-up temperatures of components and their resistances.
For a low-voltage short circuit at the end of a feeder from a substation to a non-motor load, where the resistance of the feeder circuit is significant in determining short-circuit current magnitude, it may be appropriate to assume a no-load feeder conductor temperature and resistance to calculate a maximum current.
Step 3: Combine impedances
The third step is to combine reactances or vector impedances, and resistances where applicable, to the point of fault into a single equivalent impedance, reactance, or resistance. The equivalent impedance of separate impedances in series is the sum of the separate impedances. The equivalent impedance of separate impedances in parallel is the reciprocal of the sum of the reciprocals of the separate impedances.
Step 4: Calculate short-circuit current
The final step is to calculate the short-circuit current. Calculation details are influenced by the system nominal voltage or voltages and the results desired.
It should be noted that nominal system voltages according to ANSI C84.1-1989 are as follows:
a) Low voltage = less than 1000 V
b) Medium voltage = equal to or greater than 1000 V and less than 100000 V
c) High voltage equal to or greater than 100000 V and equal to or less than 230000 V
IEEE high-voltage circuit breaker standards, IEEE Std C37.010-1979 and IEEE Std C37.5- 1979, deÞne high-voltage circuit breakers as those rated above 1000 V, so these standards cover calculating short-circuit currents for circuit breaker applications in both medium- and high-voltage systems. The results of these calculations are also usable when applying medium- and high-voltage fuses.
Three basic networks of selected impedances used for the results most commonly desired:
a) First-cycle duties for fuses and circuit breakers
b) Contact-parting (interrupting) duties for medium- and high-voltage circuit breakers
c) Short-circuit currents at operating times for time-delayed relaying devices
The three networks have the same basic elements except for the impedances of rotating machines. These depend on the purpose of the study. Where interrupting equipment applications are the purpose of the calculation, the differing impedances are based on standard application guides.
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