What is the definition of short-circuit impedance?
Short-circuit impedance, also called impedance voltage, is an important design parameter of a transformer [1]. Thus, it is crucial to understand this parameter. In this brief post we introduce three ways of definition of short-circuit impedance.
Definition 1
Short-circuit impedance (reactance and resistance) is a percentage (%) voltage drop in the transformer at full-load current with respect to the open-circuit voltage.
Definition 2
Short-circuit impedance is inverse proportional to the short-circuit current (expressed in p.u. of the full-load current) when neglecting any other impedance in the system.
Definition 3
Short-circuit voltage, in % or p.u., corresponds to the short-circuit impedance, in % or in p.u. It is a voltage to be supplied to the primary winding of the transformer to cause the rated current to flow on the secondary side of the transformer when the secondary winding is short-circuited ¹
¹ Also applicable vice versa, i.e. primary winding short-circuited and secondary winding supplied with voltage.
Notation
- Short-circuit impedance: zk, z_sc [% or p.u.]
- Short-circuit reactance: xk, x_sc [% or p.u.]
- Short-circuit voltage: uk, u_sc [% or p.u.]
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Design with high short-circuit impedance
Transformer design with high short-circuit impedance is characterized by:
- low volt/turn ratio
- many turns
- shorter windings
- larger diameter of windings
- higher load losses
- high stray flux
Design with low short-circuit impedance
Transformer design with low short-circuit impedance is characterized by:
- high volt/turn ratio
- less turns
- taller windings
- smaller diameter of windings
- high short-circuit current and forces
- lower load losses
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Extreme values of short-circuit impedance, both too low and too high value, are not optimal from design point of view and increase the manufacturing cost [2]. Moreover, extreme values of impedance pose technical challenges to the system:
- very low zk ⇒ high short-circuit currents and dynamic forces, risk for VFD with fuseless protection concept
- very high zk ⇒ high voltage drop at load, reduced input power factor, high stray flux leading to possible hot spots, difficulty to detect faults in multi-winding transformers
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References
[1] VFD transformers: Impedance requirements, MB Drive Services, September 2020, available online, https://mb-drive-services.com/transformer-short-circuit-impedance/
[2] Transformer design and cost drivers, MB Drive Services, March 2022, available online, https://mb-drive-services.com/transformer-design-and-cost-drivers/
