Short Circuit Impedance Calculation | IEC60909

Short circuit impedance calculation techniques based on IEC 60909 with correction factors for synchronous generators, power supply units, and transformers.

Determining the current paths whether ‘non-meshed’ or ‘meshed’ and the proximity of the fault, ‘far from’ or ‘near’ generators are prerequisites in the calculation of short circuit currents in IEC 60909. Prior to this is the determination of the impedances of the electrical equipment. For many, the short circuit impedance calculation is a straightforward process but in IEC 60909, the determination of impedances for certain equipment requires a slightly different approach. This is especially useful in the calculation of short circuit currents prescribed in the standard.

Network Feeders

Network feeders are usually represented by the initial symmetrical short circuit MVA, S_kQ”, or the initial symmetrical short circuit current, I_kQ”. With the nominal voltage at point Q (U_nQ shown in the figure), the impedance can be calculated using,

If the short circuit R_Q/X_Q ratio is available, the reactance X_Q can be calculated using,

If no short circuit R_Q/X_Q ratio information is available, the resistance R_Q and reactance X_Q can be approximated using the following relationship,

For networks operating at a nominal voltage greater than 35kV, setting the impedance equal to the reactance is usually sufficient.

It is also possible to use the above techniques in cases where the short circuit is fed through a transformer by introducing the transformation ratio such that

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Synchronous Generators

For synchronous generators, the following information is usually available.

1. Rated Apparent Power, S_rG
2. Rated Voltage, U_rG
3. Rated Power Factor, cos φ_rG
4. Per unit Subtransient Reactance, x”_d

The generator reactance can be determined from x”_d using

To determine R_G, the following approximations are fairly accurate.

R_G = 0.05X”_d, when U_rG ≥ 1kV and S_rG ≥ 100MVA

R_G = 0.07X”_d, when U_rG ≥ 1kV and S_rG ≤ 100MVA

R_G = 0.15X”_d, when U_rG < 1kV

The generator subtransient impedance can be calculated using

Correction Factor for Generators (K_G)

The voltage correction factors presented in our introductory discussion on IEC 60909 were intended to account for the system pre-fault conditions. Generally, voltage variation in power systems falls within ±5% to ±10% of the system nominal voltages. The calculation of maximum short-circuit current using applicable voltage factors, however, may not be sufficiently applicable to generators or power station units especially considering their subtransient behavior, i.e., equivalent voltage source cVn is used instead of substransient voltage E”. Accordingly, IEC 60909 introduced impedance correction factors specifically for generators and power station units.

The impedance correction factor for generators directly connected to the system can be calculated using,

where

Z_GK is the generator corrected impedance

Z_G is the generator subtransient impedance

K_G is the generator impedance correction factor

C_max is the voltage correction factor

U_rG is the generator rated voltage

x”_d is the generator per unit subtransient reactance

φ_rG is the phase angle between I_rG and U_rG/ 3

Correction Factor for Power Supply Unit (K_PSU)

For generators with a dedicated transformer, a single correction factor is applied to the sum of their impedances. It is as if the generator and its dedicated transformer are treated as one unit.

where

Z_PSU is the power supply unit corrected impedance

Z_G is the generator subtransient impedance in ohms

Z_rTHV is the transformer rated impedance referred to the HV side in ohms

t_r is the transformer rated voltage ratio, V_HV/V_LV

K_PSU is the power supply unit impedance correction factor

C_max is the voltage correction factor

U_nQ is the nominal system voltage

U_rG is the generator rated voltage

x”_d is the generator per unit subtransient reactance

x_T is the transformer per unit reactance

φ_rG is the phase angle between I_rG and U_rG/ 3

Two-Winding Transformers

The impedance of two-winding transformers are calculated as follows:

where

Z_T is the transformer positive sequence impedance

u_kr is the transformer short circuit voltage at rated current

U_rT is the transformer rated voltage

S_rT is the transformer rated apparent power

R_T is the transformer positive sequence resistance

P_krT is the transformer total winding losses at rated current

I_rT is the transformer rated current

X_T is the transformer positive sequence reactance

Correction Factor for Transformers (K_T)

As with synchronous generators, transformer impedance correction factor can be calculated using,

where

Z_KT is the transformer corrected impedance

Z_T is the transformer positive sequence impedance

K_T is the transformer impedance correction factor

C_max is the voltage correction factor

x_T is the transformer per unit reactance

U_rT is the transformer rated voltage

S_rT is the transformer rated apparent power

X_T is the transformer reactance in ohms

It is important to note that the short circuit impedance calculation presented in this article are chosen based on the author’s perspective on the topic. The readers are encouraged to review the calculations prescribed in IEC 60909.

References

IEEE Std 551-2006 [The Violet Book]: Recommended Practice for Calculating AC Short Circuit Currents in Industrial and Commercial Power Systems. (2006). S.I.: IEEE.

BS EN 60909-0:2001: Short-circuit currents in three-phase a.c. systems Part 0: Calculation of currents (2002).

Kaskci, I. (2002). Short Circuit in Power Systems: A Practical Guide to IEC 60909. Weinheim, Germany: Wiley-VCH Verlag-GmbH.