# The Art of Protecting Electrical Systems, Part 4: System Analysis

04/18/2006

Editor’s Note: Protective equipment must withstand changes caused by short circuits in electrical systems. This fourth article in our series discusses aspects of short circuit calculations

Engineers designing protection for electrical systems must consider the many changes that take place when a short circuit occurs. Protective equipment must be able to withstand the effects of short circuits, minimize damage and restore service as quickly as possible.

The changes that occur during faults—many of which are interdependent—have not been brought to the attention of engineers. This article introduces some of the fundamental ideas. Later articles will consider these concepts in detail as they apply to specific equipment and applications.

Most common fault calculations are based on balanced, three-phase short circuits. Such calculations determine the maximum fault current at specific places in the system. They are made primarily to determine if the installation conforms to applicable code requirements.

More than 25 types of faults must be considered. They usually are calculated using the symmetrical-components method, which will be discussed in future articles. These faults include three phase to ground; single-phase to ground; phase to phase; double-line to ground; three phase to ground through an impedance; one line open and the other two shorted; and three-phase to ground with impedance in one phase.

However, since the great majority of low-voltage systems, as well as a significant number of medium-voltage systems, are solidly grounded, this discussion is directed toward such systems. Upcoming articles will cover ungrounded, resistance-grounded and transformer-grounded systems.

What is a fault current?

A fault current is a current flowing out of its normal path. In a fault caused by incorrect wiring (crossed phases), all current flow is confined to the circuit conductors, but in the wrong phases. Because such faults occur on system start-up or after system modifications only, they will not be considered here.

The greatest number of faults occur because of insulation failure. This is generally caused by:

%%POINT%%Physical damage, by personnel or machinery

%%POINT%%Accelerated aging from sustained over-temperatures

%%POINT%%Use of insulation unsuitable for the environment

%%POINT%%Over-voltage, possibly from lightning or switching surges

%%POINT%%Poor installation methods, e.g., damage to insulation in splicing, excessive stress on insulation when pulling cable or too short a radius on cable bends

%%POINT%%Normal end of life

%%POINT%%Damage by animals and birds

%%POINT%%Infestations of insects, especially bees and wasps

%%POINT%%Deformation of bus structures by magnetic stress during a fault

%%POINT%%Flooding and other water damage

Current takes a different path during insulation breakdown. It may use the ground, system neutral or the phase conductors, but the majority of current does not pass through the faulted circuit’s load impedance.

At a given voltage, current flow in any circuit is determined by the circuit’s impedance. Total impedance includes that of the utility, of the facility being considered (system impedance) and of the load.

Under Normal operating (nonfault) conditions, utility impedance may be ignored because it is a very small portion of the total. System impedance does have an effect, but its value is so slight that it seldom is considered except in voltage-drop and low-flow studies. Prior to a fault, therefore, currents in all parts of a system are determined primarily by load impedance.

Utility and system impedance values have been omitted.) The 50-foot, 480Y/277-volt, three-phase, four-wire branch circuit is composed of four #12 AWG copper conductors in steel conduit. At the end of the circuit, a single-phase load is connected from phase A to neutral. The current is 16 amperes. Using Ohm’s Law, total impedance at this point in the circuit is:

Z = E / I = 277 / 16 = 17.3 ohms

where: Z = Impedance, E = Voltage and I = Current

In contrast, in a circuit with the load shorted out—representative of the condition extant with a fault—the approximate line-to-neutral AC impedance of a 50-foot branch circuit is 0.1 ohms, about 0.57% of total impedance.

Larger conductors have a correspondingly smaller impedance. For example, a 50-foot circuit of 500 kcmil has a line-to-neutral impedance of approximately 0.0028 ohms (0.02% of total impedance).

Impedance at fault point

The instant a fault occurs, part or all of the load impedance in the faulted circuit is placed in parallel with the fault impedance. At this point, the circuit is said to be shunted or bypassed. The impedance at the fault (fault impedance) may approach zero-commonly known as a bolted-fault condition. Under these conditions, only the utility and system impedances control current flow. Their total is only a small fraction of the load impedance.

If we assume an unlimited utility power source (zero impedance) and ignore changes in power factor, current in the 500-kcmil circuit described would approximate 99,000 amperes at 277 volts:

I = 277 / 0/0028 = 98,928 amperes

Fault impedance can vary from near zero to several hundred ohms. In typical bolted three-phase faulted circuits, impedance is considered to be zero.

There are many possible causes of fault impedance. The most common cause of high fault impedance in phase-to-phase faults is arcing at the point of fault. When insulation fails and a fault results between two or more conductors, the magnetic force surrounding the conductors tends to alternately pull them tighter and force them apart.

In addition, the increased current raises the temperature of the conductor, causing it to expand, further increasing conductor movement. If the conductors are confined in a conduit, or are otherwise prevented from free movement, a sustained arc may be drawn.

As the conductors move, the arc length changes and impedance again varies. The fault current increases and decreases accordingly. Fault impedance alone may restrict the fault current to 0.5 amperes or less, and the fault-return path may limit it even more.

When such arcing faults are not interrupted quickly, the enclosure may be destroyed. This can ionize the air, produce additional faults and start a fire. Some of the most serious damage from electrical faults results directly or indirectly from arcs.

In other instances, what starts as an arcing fault between conductors quickly turns into a welded fault with little or no impedance. Moving conductors often collide, and the arc that was the cause of low fault impedance can weld the conductors solidly.

Fault-current return path

When a fault occurs, current not only flows to the fault, but it must return to the source to complete the circuit. This is considered to be the transformer next upstream from the fault. Just as the fault may have high or low impedance, the fault-current path also may have high or low impedance.

When faults occur between two of more phases and/or between any phase and neutral, system impedance is that of the conductors and other components and is usually quite low. However, when the fault is between one conductor and ground, and does not directly involve another phase, a quite different set of conditions controls current flow.

In many systems, the ground-return path has substantial impedance. Consider just a couple of the more common examples:

Joints between lengths of conduit and conduit terminations are not thought of as electrical connections, and no special procedures are required when working with them. However, experience shows that these threaded joints often are not drawn wrench-tight, i.e., have only been tightened by hand. All conduit joints must be tight to avoid high impedance.

Aluminum conduit oxidizes readily and this oxide has high resistance. Often, aluminum conduit threads will be oxidized before the conduit is installed, so even tight connections may have significant resistance. Obviously, this also can occur with steel conduit systems. This emphasizes the fact that threads on all conduit connections must be clean.

The only ground-fault return path may be the conduit, and it is expected to carry all or most of the fault current. It may restrict the current to values so low they cannot be detected as fault currents, and overcurrent devices will not operate quickly enough to protect the system.

Conduit and conductors heated by this current flow can cause other, more serious, faults. If the fault current is low enough, the fault may be allowed to persist almost indefinitely. This will impress a sustained voltage on conduit and enclosures, expose personnel to shock and perhaps result in sever injury or death.

In many older systems, all equipment grounds are connected to the building steel. While the resistance of such grounds is usually quite low, there may be wide spacing between phase conductors and the ground-return path with drop cable to equipment. This spacing causes very high reactance and results in high impedance.

The above conditions and many other similar situations have caused such serious problems that the National Electrical Code (NEC) requires use of separate equipment grounding conductors for many applications. In addition, there is a growing trend for using equipment grounding conductors for most, if not all, applications even when not mandated.

The next article in the series will discuss typical faults and describe resulting changes in transient voltages and power factor.

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