If a short circuit is applied to the terminals of a synchronous generator, the short-circuit current starts out at a high value and decays to a steady-state value some time after the inception of the short circuit.

Since a synchronous generator continues to be driven by its prime mover and to have its field externally excited, the steady-state value of short-circuit current will persist unless interrupted by some switching means.

An equivalent circuit consisting of a constant driving voltage in series with an impedance that varies with time is used to represent this characteristic. The varying impedance consists primarily of reactance.

Xd"= subtransient reactance; determines current during Þrst cycle after fault occurs. In about 0.1 s reactance increases to

Xd'= transient reactance; assumed to determine current after several cycles at 60 Hz. In about 0.5 to 2 s reactance increases to

Xd = synchronous reactance; this is the value that determines the current ßow after a steadystate condition is reached.

Because most short-circuit interrupting devices, such as circuit breakers and fuses, operate well before steady-state conditions are reached, generator synchronous reactance is seldom used in calculating fault currents for application of these devices.

Synchronous generator data available from some manufacturers includes two values for direct axis subtransient reactanceÑfor example, subtransient reactances Xdv"(at rated voltage, saturated, smaller) and Xdi" (at rated current, unsaturated, larger).

Because a shortcircuited generator may be saturated, and for conservatism, the Xdv" value is used for short-circuit current calculations.


Causes of phase-voltage unbalance
Most utilities use four-wire grounded-wye primary distribution systems so that single-phase distribution transformers can be connected phase-to-neutral to supply single-phase loads, such as residences and street lights. Variations in single-phase loading cause the currents in the three-phase conductors to be different, \ producing different voltage drops and causing the phase voltages to become unbalanced.

Normally the maximum phase-voltage unbalance will occur at the end of the primary distribution system, but the actual amount will depend on how well the single-phase loads are balanced between the phases on the system.

Perfect balance can never be maintained because the loads are continually changing, causing the phase-voltage unbalance to vary continually. Blown fuses on three-phase capacitor banks will also unbalance the load and cause phase-voltage unbalance.

Industrial plants make extensive use of 480Y/277 V utilization voltage to supply lighting loads connected phase-to-neutral. Proper balancing of single-phase loads among the three phases on both branch circuits and feeders is necessary to keep the load unbalance and the corresponding phase-voltage unbalance within reasonable limits.

Measurement of phase-voltage unbalance
The simplest method of expressing the phase-voltage unbalance is to measure the voltages in each of the three phases:

The amount of voltage unbalance is better expressed in symmetrical components as the negative sequence component of the voltage:

percent unbalance = maximum deviation from average/ average X 100%

voltage unbalance factor = negative-sequence voltage/ positive-sequence voltage


Conductor current–carrying capacity, or ampacity, is determined by the maximum safe operating temperature of the insulation used on the conductor. Heat generated as a result of current flow is dissipated into the environment.

Thus, for a given installation context (open-air, buried in earth, or enclosed), ampacity increases with increasing conductor size and with maximum permissible insulation temperature.

If more than three conductors are placed in a conduit, the resultant increase in temperature requires that the conductors be derated to maintain safe operating conditions.

Because heat dissipation from a conductor in free air is much greater than that from the same conductor enclosed in conduit or directly buried, its corresponding allowable ampacity is also greater.

Conversely, if the ambient temperature around a conductor is higher than 30ºC (86ºF), the temperature upon which all standard ampacity tables are based, the permissible ampacity must be reduced.

Ampacity tables for conductors in free air, for cable types not shown in Table below, and derating factors for high ambient temperatures are all found in the NEC.

Physical Properties of Bare Copper Conductors

Source: Except for millimeter dimensions, this table was extracted from NFPA 70-1999, the National Electrical Code. © 1999, National Fire Protection Association, Quincy, MA 02269.

Note: This extracted material is not the complete and official position of the National Fire Protection Association on the referenced subject, which is represented only by the standard in its entirety.
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