# The Art of Protecting Electrical Systems, Part 5

05/15/2006

This fifth part in our series describes typical electrical system faults and the changes in transient voltage and power factor they produce.

When a short circuit occurs, generators—whether utility or on-site—do not stop generating instantly, even if the drivers are immediately shut down. Because the only thing limiting the initial current a generator can deliver to its shorted terminals is its internal impedance, initial current flow may be 20 or more times the rated load current.

Under fault conditions, generator impedance increases rapidly as a result of increased generator winding temperatures, voltage imbalance and changes in machine speed. As a result, the fault current decreases to a steady-state condition within a few cycles.

Similarly, electric motor-driven equipment does not stop instantly. The inertial energy stored in operating systems causes the motors to continue rotating anywhere from several seconds to several minutes. Motors become driven machines and generate power.

Current is highest at the time the fault occurs because machines are operating at normal speed. As a rule of thumb, an induction motor’s initial fault current approximates its locked rotor current. However, the current decreases rapidly as the equipment speed decreases. Figure 4.4 shows the increase in reactance measured from the time of fault.

To simplify short-circuit calculations, the decrease in generator and motor fault current is treated as an increase in reactance. Industry standards divide reactance of rotating machines under short-circuit conditions into three values:

%%POINT%% Sub-transient reactance (X“d). During the first cycle after a fault, the subtransient reactance determines the fault current.

%%POINT%% Transient reactance (X’d). From 0.1 seconds up to

%%POINT%% Steady-state or synchronous reactance (Xd). Machine reactance for time in excess of

Specific values for various machines and how to use these values will be discussed under short-circuit calculations. At this point, it is sufficient to understand that all rotating machines produce maximum fault current at the instant of fault, and this fault current decreases to a steady-state condition in a short period of time.

Inductors and capacitors can affect current flow. Inductive reactance in series with the fault current decreases current flow by the amount of impedance. Capacitors may cause large current increases, depending on whether the capacitor was charged or discharged at the instant of fault.

## Changes in transient voltages

When low-impedance, high-current faults occur, there is an instantaneous voltage dip in the entire system. The amount of drop is determined to a great degree by the system’s inherent capacity. For example, at the instant of fault, a large utility network may be able to maintain substantial voltage except under general network failure.

On the other hand, at the inception of a low-impedance fault in long radial systems (such as rural areas) voltage may drop to almost zero. If the fault persists, however, there is a voltage recovery. This occurs because of increased utility and system resistance and reactance, which reduce the current flow.

At the instant a major fault occurs there is an instantaneous increase in current. One theory is that the rapidly changing current causes a corresponding increase in the magnetic field surrounding all current-carrying components. When the current flow is suddenly interrupted, this magnetic field collapses and generates a transient voltage in the system.

The transient voltage, therefore, depends on the amount of fault current involved and the manner in which it is interrupted. If not controlled, these transients may be damaging to some system components.

Another theory, mostly used for analysis of long-line distribution and transmission systems, sets up a simple series circuit consisting of a resistance, a reactance and a capacitance. The capacitance represents the transmission or distribution line, while the resistance and reactance represent the power source impedance (see Figure 4.5).

As indicated, when a line-to-ground fault occurs, it is paralleled across the capacitance. With the system short circuited, if the resistance is small in relation to the reactance, fault current will lag the system voltage by close to 90 degrees. If the short is interrupted at zero current, condenser voltage does not return to normal until there have been several oscillations. These may approach twice the normal system peak voltage.

## Changes in power factor

Under load conditions, most systems have operating power factors between 80% and 90%. In general, short circuits “short-out” more resistance than reactance, thereby sharply increasing system X/R ratio. The result is a significant drop in power factor.

(Power factor is the cosine of the angle between voltage and current. X/R ratio is the tangent of this angle. A low power factor means the system has a large X/R ratio.)

Severe faults tend to produce lower power factors than lesser faults. The location of the fault is also a factor. In general, the closer to the service entrance and the larger the conductors, the lower the power factor (the higher the X/R ratio). This is true because the X/R ratio of 250 kcmil, and larger cables, is significantly higher than the X/R ratio of smaller cables.

Previous articles in this series established that UL, NEMA, ANSI and similar bodies have established standardized short-circuit power factors and corresponding X/R ratios for the testing of electrical equipment. These short-circuit power factors are different for each level of short-circuit rating, being higher for large fault ratings.

Severe shot circuits in most 600-volt and less power systems commonly have short-circuit power factors in the range of 15% to 25%; lesser faults have values around 50%. Medium and high voltage systems may have short-circuit power factors of 5% or less.

When applying equipment it is important to know the system’s X/R ratio, because systems may have X/R ratios exceeding the test standards. If not compensated for during design, equipment failure may result.

## Short-circuit power factor

Utility system X/R ratio at point of service varies widely and may be influenced most by the X/R ratio of the nearest utility transformer. When performing system analysis, these values can be obtained from the utility.

Transformers are a significant source of reactance and for many systems are the largest factor in the overall short-circuit X/R ratio. Traditional substation transformers have X/R ratios that range from 5:1 for 112.5 kVA to 12:1 for 2,000 kVA and larger.

Because the trend today is to use lower impedance transformers, these ratios are changing. They may be higher or lower, depending on transformer design. Whenever possible, values should be obtained from the manufacturer.

On-site generation, especially when generation is at utilization voltage, must be carefully considered. Generator X/R ratios may be 15:2 or higher.

Reactance coils or high-reactance busway are sometimes recommended to reduce available short-circuit current. Some of this equipment has X/R ratios of 20:1 or higher.

Introducing capacitive reactance to the system may lower the net reactance, which is considered to be inductive. Capacitance lowers the X/R ratio.

Short-circuit power factor is important because it determines the multiplier used to obtain the asymmetrical current. (How these multipliers are derived was covered in the previous article in this series.)

## Effect of temperature changes

Increased current flow raises the temperature of all system components and therefore increases their resistance. Heating is minimal at the instant of fault, but if the fault continues for more than a cycle or two, it will significantly reduce fault current.

The effect that increased temperature has on system components must be considered. For example, it softens many insulations, increases oxidation and shortens insulation life; expansion followed by contraction stresses system components; and it may cause fusing of contacts and small conductors, especially operating coils and overload heater elements.

Insulation temperature is a significant limiting factor. Organic insulations have maximum rated temperatures for both sustained and transient conditions and exceeding these values can prematurely age the insulation and shorten life. Higher temperatures can result in immediate failure.

## Magnetic-field changes

A magnetic field surrounds all components carrying current. In addition to affecting the transient voltage, this field also causes magnetic stress to all components. The effect of this stress is readily visible when considering various bus structures. Less well-known, but just as important, is the effect magnetic stress has on wire and cable, motor windings, transformer windings and similar components.

Other factors being equal, the strength of the magnetic field varies almost directly with the square of the instantaneous peak current. Most systems are alternating current, and the magnetic field reverses with each change in polarity. If fault currents are permitted to continue for one or more cycles, the damage caused by magnetic stress is compounded by the alternating fields, which cause flexing of components. For example, UL, ANSI and NEMA standards for bus structure and busway only require short-circuit testing for three cycles, yet some protective schemes may permit fault currents to persist for as much as 12 cycles.

All of these factors are interdependent. Conductor heating may soften insulation and cause it to lengthen. At the same time, magnetic stress is moving the conductors in the conduit. The combined effect may cause significantly more insulation damage than any single factor. A very low short-circuit power factor causes a significant increase in the peak asymmetrical current, which of itself increases the magnetic stress. At the same time the current’s increased rate of change also increase magnetic stress.

The next article in this continuing series will elaborate on equipment short-circuit ratings, including interrupting and withstand. Adequacy requirements for labeling will be discussed, and an overview of short-circuit calculations will be given, preparatory to an in-depth discussion of such calculations.

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