Performing short-circuit calculations requires an understanding of various system components and their interaction.

It's very important to understand the meaning of the term "short-circuit fault." Basically, a short-circuit fault in a power system is an abnormal condition that involves one or more phases unintentionally coming in contact with ground or each other. Thus, short-circuit protection is necessary to protect personnel and apparatus from the destructive effects of the resulting excessive current flow, which is caused by the relatively low impedance of the short-circuit fault connection.

To provide the required protection, we must determine the extent of short-circuit current at various points of our power distribution system. This determination requires a calculation.

In Part one of this three-part series, we'll discuss specific parameters needed to perform short-circuit calculations of industrial and commercial power systems according to the ANSI/IEEE 141 standard, Recommended Practice for Electric Power Distribution for Industrial Plants (Red Book).

Sources of fault current

Where does fault current come from? Basically, it comes from rotating electric machinery, usually in the form of synchronous generators, synchronous motors and condensers, induction machines, and electric utility systems. The magnitude of fault current from these sources is limited by the impedance of the machine itself as well as the impedance between the machine and the fault itself.

Because a synchronous generator has a prime mover and an externally excited field, its fault current will continue unless interrupted by some switching means.

Synchronous motors and condensers supply current to a fault in much the same way as synchronous generators; however, their fault current diminishes as their magnetic fields decay. Induction motor fault current is generated by inertia that is driving the motor in the presence of a field flux, which is produced by induction from the motor's stator.

The basics

A balanced 3-phase fault implies that all three phases of the power system are simultaneously short-circuited to each other through a direct or "bolted" connection. Although the probability of this happening is small, relative to the probability of other types of unbalanced faults occurring (e.g., phase-to-ground and phase-to-phase faults), we nevertheless use a balanced 3-phase fault for a short-circuit study for the following reasons.

* Often, a 3-phase fault produces the largest short-circuit current magnitude; thus, this worst-case result is then used as the basis to select the short-circuit capabilities of switchgear from manufacturers' tables.

* Short-circuit calculations are simplest for a balanced 3-phase fault because symmetry of the fault connection permits us to consider only one of the three phases.

The other types of unbalanced short-circuit faults are important in selecting the time-current characteristics and settings of phase-overcurrent and ground-fault protective devices to provide selective coordination. This coordination assures service continuity and minimizes damage to switchgear and load equipment. However, unbalanced fault calculations are more difficult to perform for industrial and commercial power systems and require a knowledge of the method of symmetrical components.

Symmetrical RMS current versus short-circuit duty

In Fig. 1, we see a 3-phase synchronous generator, previously unloaded, that has been subjected to a balanced, 3-phase fault across its accessible terminals. In general, an asymmetrical short-circuit current waveform is produced by a balanced, 3-phase fault.

Fig. 2 shows a typical asymmetrical short-circuit waveform (bottom) for one phase of the 3-phase synchronous generator. The diagram also shows that this waveform is a combination of two components: a unidirectional (DC) component (upper left waveform) and a symmetrical (AC) component (upper right waveform). The DC component approximately decays exponentially with a time constant equal to [X.sub.EQ]/[R.sub.EQ], where [X.sub.EQ] and [R.sub.EQ] are the equivalent inductive reactance and resistance at the fault location, respectively. The DC component eventually decays to zero, and the amplitude of the symmetrical AC component eventually decays to a constant amplitude in the steady-state. The sum of these two components at any time instant is equal to the total asymmetrical short-circuit current at that instant.

The root mean-square (rms) value of the asymmetrical short-circuit current waveform is the basis for the selection of the short-circuit capabilities of circuit breakers and fuses. Calculation of the precise rms value of an asymmetrical current at any time after the inception of a short-circuit may be very involved. Accurate decrement factors to account for the DC component at any time are required, as well as factors for the rate of change of the apparent reactance of the generators. This precise method may be used, if desired; however, simplified methods have evolved whereby the DC component is accounted for by simple multiplying factors. These multiplying factors convert the rms value of the symmetrical AC component (symmetrical rms current) into rms current of the asymmetrical waveform, including the DC component (asymmetrical rms current or short-circuit current duty).

Types of networks to calculate symmetrical rms current

In order to utilize AC circuit theory in calculating symmetrical rms current, three types of networks are used to represent the power system over three time intervals of the fault-on time period.

* First-cycle (momentary) network.

* Contact-parting (interrupting) network.

* Approximately 30 cycle network.

These networks only differ from one another by the assignments of constant reactances for the machines.

First-cycle (momentary) network. This network is used to calculate the first-cycle (momentary) symmetrical rms current. Here, the rotating machine sources of short-circuit current are represented, for the most part, by their subtransient reactances, according to the entries in the first column of Tables 4-1 and 4-2 of the 1993 edition of the IEEE Red Book (or Tables 24 and 25 of the 1986 edition).

Contact-parting (interrupting) network. This network is used to calculate the contact-parting (interrupting) symmetrical rms current for circuit breaker minimum contact-parting times of 1.5 to 4 cycles after the inception of the short-circuit fault. Here, the rotating machine sources of short-circuit current are represented by different constant reactances than the first-cycle (momentary) network, according to the entries in the second column of Tables 4-1 and 4-2 of the 1993 edition of the IEEE Red Book (or Tables 24 and 25 of the 1986 edition).

Approximately 30 cycle network. This network is often a minimum-source representation to investigate whether minimum short-circuit currents are sufficient to operate current-actuated relays. Minimum-source networks might apply at night or when production lines are down for any reason. Some of the source circuit breakers may be open and all motor circuits may be off. In-plant generators are represented with transient reactance or a larger reactance that is related to the magnitude of decaying generator short-circuit current at the desired calculation time.

In Part 2 (December 1995 issue), we'll use a simple example that shows the necessary steps needed to determine the appropriate reactances and resistances of the power system apparatus for the first-cycle (momentary) and contact-parting (interrupting) networks.

In Part 3 (April 1996 issue), we'll explain how to construct the networks, impose the fault connection, and use basic AC circuit theory to reduce the networks to equivalent reactance and resistance values. These equivalent reactance and resistance values can then be used to calculate symmetrical rms short-circuit currents and equivalent short-circuit [X.sub.EQ]/[R.sub.EQ] ratios.


Asymmetrical short-circuit current: A fault current whose waveform is asymmetrical to the zero axis. The peak positive current at any of the waveform loops will be greater than 1.414 times the rms symmetrical current.

Symmetrical short-circuit current: A fault-current whose waveform is symmetrical about the zero axis. In other words, the positive peak current has the same value as the negative peak current. These peak (maxium) currents are always equal to 1.414 times the rms symmetrical current.

rms current: Current which, while flowing through a given ohms resistance, will produce heat at the same rate as a DC ampere.

Reactance: An opposition to the flow of electrical current in a circuit. It is usually expressed in ohms and consists of inductive and capacitive parts.

Sub-transient reactance: The value of reactance that determines the amount of short-circuit current during the first half cycle after the fault occurs.

Dr. Frank J. Mercede, P.E. is a Consulting Power Engineer from Rosemont, PA, who provides training and engineering services to utility and industrial clients.