Tech Brief
This issues Tech Brief covers two
topics. Both relate to the
interrupting rating of switchgear,
X/R ratio and asymmetrical
short-circuit current.
by Baldwin Bridger, P.E.
Powell Electrical Manufacturing Co. (retired)
X/R Ratio
W
hat is X/R (“X over R”) ratio, and why is it important? First, X/R ratio is simply the ratio of
the system reactance to the system resistance,
looking back towards the power source from any point in a
power circuit, assuming that a short circuit is applied to the
system at that point. It is another way of stating the power
factor of the source system. Mathematically, if power factor
is equal to cosine theta, then X/R is equal to tangent theta.
Note that this is the power factor of the system up to that
point. It has absolutely no relationship to the power factor
of any load on the system. Since generators, transformers,
and transmission lines are generally quite highly inductive,
the X/R ratio is generally significantly above unity in any
utility or industrial power system.
Why is the X/R ratio important? Its importance is that
it affects the level of short circuit current a circuit breaker is
required to interrupt. When a short circuit occurs, the rms
value of the symmetrical fault current is determined by the
system source voltage and the total system impedance to the
point of fault. However, almost all faults involve significant
asymmetry in at least one phase. This asymmetry is treated
www.netaworld.org in analysis as a dc component which must be combined
with the ac symmetrical component to give a new current
value, the rms asymmetrical value. It is the value of the rms
asymmetrical current at the moment of contact parting
which a circuit breaker must interrupt. See PTB #22 for
further information.
This dc component of a fault current decays rather rapidly,
reaching an insignificant value in a matter of three to five
cycles of the power frequency. However, this rate of decay
is determined by the X/R ratio of the circuit at the point
of fault. The higher the X/R ratio, the more slowly the dc
component decays.
Circuit breakers are tested using power sources with an
X/R ratio prescribed by industry standards. For power circuit
breakers, both low- and high-voltage, the ANSI standards
require the X/R ratio to be 6.6 or higher, corresponding
to a power factor of 15 percent or less. For a given level of
symmetrical fault current and a given circuit breaker contact
parting time, this X/R ratio establishes the value of asymmetrical fault current the breaker is required to interrupt.
A higher X/R ratio, with its slower decay rate, will result in
a higher asymmetrical fault current at contact parting time.
If the X/R ratio is too high, the asymmetrical fault current
may exceed the breaker’s interrupting capability.
Winter 2009-2010 NETA WORLD
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Since the X/R ratio of a system is inherent in its design
and cannot be changed easily, what can be done about a
high X/R? The approach taken by the ANSI standards is to
establish multiplying factors for the symmetrical fault current. These factors vary with the system X/R ratio and the
speed of the circuit breaker. For high-voltage circuit break-
ers (over 1000 V), information about the values and use of
these factors is found in §5 of ANSI/IEEE C37.010-1979.
For low-voltage power circuit breakers, this information is
found in §10 of ANSI/IEEE C37.13-1990.
Short Circuit Currents –
Crest, rms Symmetrical and rms Asymmetrical
T
he figure below shows a typical short circuit current
wave form and defines the various component parts
of this wave. At the moment of initiation of a short
circuit the ac current wave, which is normally symmetrical
about the zero axis, BX is offset by some value, creating a
waveform which is symmetrical about another axis, CC′.
The degree of asymmetry is a function of several variables,
including the parameters of the power system up to the point
of the short circuit and the point on the ac wave at which
the short circuit was initiated. In a three-phase circuit, there
is usually one phase which is offset significantly more than
the other two phases.
current is equal to the initial peak value of the ac current,
the resulting waveform is said to be fully offset or to have
100 percent dc component. It is possible, in some power
systems, to have an offset in excess of 100 percent which
may result in a waveform that has no current zeros for one
or more cycles of the ac power frequency.
The ac component of the short-circuit current will also
decay at a rate dependant on the system parameters. In
general, the closer the fault is to generators or other large
rotating machinery, the faster the decay will be.
In the figure, 1MC is the crest, or peak value of the short
circuit current. It is the maximum instantaneous current
in the major loop of the first cycle of short-circuit current.
The rms symmetrical value of the short circuit current at
any instant, such as EE′, is the rms value of the ac portion of
the current wave. Its value is equal to the ac portion divided
by the square root of 2, and it is shown graphically by the
distance from CC′ to DD′. The rms asymmetrical value of
the short circuit current is the rms value of the combined
ac and dc waves, and it is calculated by the formula:
———————
(IAC)2
I = —— + (IDC)2
√ 2
It is convenient to analyze this asymmetrical waveform
as consisting of a symmetrical ac wave superimposed on a
dc current. CC′ represents the dc current, and the value of
that current at any instant is represented by the ordinate
of CC′. The dc component of the current normally decays
rapidly and reaches an insignificant value within 0.1 second
in most power systems. The rate of decay is a function of
the system parameters. When the initial value of the dc
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NETA WORLD Winter 2009-2010
Baldwin Bridger, PE, is recently retired Technical Director of Powell
Electrical Manufacturing Co., Houston, Texas. He has worked as an engineer and engineering manager in the design of low- and medium-voltage
switchgear since 1950, first at GE and since 1973 at Powell. He is a Fellow
of IEEE and a past president of the IEEE Industry Applications Society.
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