# Calculating Generator Reactances

**Topics:**Circuit breaker, Fuse, Short circuit

**Pages:**6 (1368 words)

**Published:**August 28, 2013

Calculating generator reactances

>Whitepaper By Timothy A. Loehlein, Technical Specialist-Electrical

Generator reactances are used for two distinctly different purposes. One use is to calculate the flow of 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. 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: 1. the internal voltage of the connected machines in the system (generators and motors),

2. the impedance of those machines, 3. the impedance to the point of the fault, mostly cable impedance, 4. and the impedance of the fault, if arcing. The generator internal voltage and generator impedance determines 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: Name Importance Symbol Range1 EffectiveTime

Sub-transient reactance X"d .09 – .17 0 to 6 cycles Determines maximum instantaneous current and current at time molded case circuit breakers usually open. Transient reactance X'd .13 – .20 6 cycles to 5 sec. Determines current at short time delay of circuit breakers. Synchronous reactance Xd 1.7 – 3.3 after 5 sec. Determines steady state current without excitation support (PMG). Zero sequence reactance Xo A factor in L-N short circuit current. .06 – .09

Negative sequence reactance X2 .10 – .22 A factor in single-phase short circuit current. 1

Reactances shown are typical per unit values for generators ranging from 40 to 2000 kW.

Power topic #6008 | Page 2

Sub-transientreactance

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=E AC÷X"d

GENERATOR SHORT CIRCUIT CURRENTS

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%offullloadcurrent

FIGURE1 – Symmetrical current

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=...

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