Calculating Generator Reactance
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| Combustion Engine Driven Generator: Source: Cummins |
Generator reactances are used for two distinctly different purposes. One use is to calculate the flow of the symmetrical short circuit current in coordination studies. A second use for generator, reactances are in specifications that limit the sub-transient reactance to 12% or less in order to limit the voltage distortion induced by non-linear loads. For either short circuit or harmonic distortion analyses, the stated reactances will need to be converted to a common base to make valid comparisons.
Typically, generator reactances are published in per-unit values on a specified base alternator rating. Where the generator set rating differs from the alternator base rating it will be necessary to convert the per-unit values from the alternator base rating to the generator set rating.
Related Article: Fundamentals of Generator Protection
For selecting circuit breakers with adequate AIC rating the maximum asymmetrical short circuit current to flow in the first half-cycle may be approximated from the generator sub-transient reactance (x"d ) and a factor to account for DC offset.
The flow of current in an AC circuit is controlled by impedance. When a short circuit fault occurs in a distribution system the fault current that flows is a function of:
- the internal voltage of the connected machines in the system (generators and motors)
- the impedance of those machines,
- the impedance to the point of the fault, mostly cable impedance,
- the impedance of the fault, if arcing.
The generator internal voltage and generator impedance determine the current that flows when the terminals of a generator are shorted. The effect of
armature reaction on the generator air gap flux causes
the current to decay over time from an initial high value
to a steady-state value dependant on the generator
reactances. Since the resistive component in generators is negligible, for practical purposes it may be
ignored and only the reactances need be considered.
Generator reactances, as determined by tests with
fixed excitation, are:
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| Generator Reactance | Source: Cummins |
Sub-transient reactance
Sub-transient reactance
With a generator operating at full voltage, a symmetrical
3-phase short circuit at its terminals will cause a large
amount of current to flow. This initial current is used to
determine the required interrupting rating of overcurrent
devices, circuit breakers, and fuses, located at the
generator(s). The initial instantaneous current value
(ISCSym) is controlled by the sub-transient reactance
(X"d) and is expressed by the voltage divided by the
sub-transient reactance, or:
ISCSym = EAC ÷ X"d
In per unit, assuming a 0.10 sub-transient reactance,
the initial symmetrical short circuit current expressed in
multiples of full load current:
ISCSym = 1.0 ÷ 0.10 = 10 = 1000% of full load current
Related Article: Major Component of Large Generators
Reactances, including the sub-transient, are expressed
with a plus or minus tolerance of 10%, typically.
Determination of the maximum current should use the
worst-case tolerance of minus 10%. The maximum
symmetrical current from the example above becomes:
ISCSym = 1.0 ÷ (0.10 – 10%) = 11.1 = 1110% of full load current
The peak current in the first half cycle will also include
a DC component, the magnitude of which depends on
the point in the cycle when the short circuit occurs.
A DC component offsets the symmetrical current
around the zero axis resulting in asymmetry. If the short
occurs at point where voltage is at its peak, the DC
component will be zero. If the short occurs at the point
where voltage is at zero, the DC component will be at
its maximum, and the peak current will be almost two
times the symmetrical current.
In practice the actual DC offset will likely range somewhere between zero offset and the maximum offset.
However, for the purpose of selecting the interrupting
rating of circuit breakers the assumption that the DC
offset will be at maximum is a safe and conservative
assumption (ISCSym x 2). Generally, circuit breaker
interrupting ratings are expressed in RMS Symmetrical
Amperes and are tested to achieve near maximum
offset at that symmetrical current magnitude. Select
breakers, then, based on the maximum allowable
generator symmetrical short circuit current.
Calculating per unit
sub-transient reactance
The
generator sets, however, have various base ratings, and so there is a need to convert from the alternator base to the generator set base. This conversion is accomplished using the following formula:
For example, suppose you want to find the subtransient reactance (X"d ) in Per-Unit for the 105°C rise,
480-volt alternator on a 750 kW DFHA generator set.
From the generator set specification sheet, S-1132,
the alternator data-sheet is ADS-311. ADS-311 shows
a sub-transient reactance of 0.16 P.U. based on the
125°C alternator base rating of 1300kVA. The base kVA
rating of the 750DFHA is 938 kVA. Using the formula,
calculate X"d on the generator set base as follows:
Limiting voltage distortion
It is becoming commonplace for consulting engineers
to limit sub-transient reactance in specifications to 0.12
per-unit or less to limit generator voltage distortion
caused by non-linear load induced harmonic currents.
The alternator source voltage distortion induced by
the harmonic (sub-cyclic) current distortion is directly related to the generator set sub-transient reactance.
The higher the reactance is, the higher the voltage
distortion. Reducing the source impedance (reactance)
reduces the voltage distortion. This calculation will
need to be used to check and compare suppliers’
submittals against specifications. In the example, while
a 125°C rise alternator may have been specified, 105°C
alternator would have to be supplied to meet a 0.12
per-unit or less sub-transient reactance requirement.
Summary
The sub-transient reactance of a generator set is used
to calculate the maximum available short circuit current
for selecting circuit breakers with adequate interrupting
rating. Since nearly all of the generator impedance is
reactance, addition of the DC component for the first few
cycles may almost double the symmetrical value of current. Specifications that limit the sub-transient reactance
(x"d ) to 12-per-unit or less limit the voltage distortion
caused by non-linear load currents. Calculation of the
available short circuit current using per-unit values may
require converting from the alternator base rating to the
generator set base rating using the formula provided.
Source:
- Title: Calculating generator reactances | Technical information from Cummins Power Generation
- Author: Timothy A. Loehlein | A graduate of the The University of Minnesota with a Bachelor of Electrical Engineering and a PE in Minnesota.
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