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IEC 60909 Fault Calculations

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Discussion

To calculate system faults, we can use the guidance given in IEC 609096 "Short-circuit currents in three-phase a.c. systems. For faults far from the generator faults in three phase systems, each type of fault the symmetrical short-circuit current I"_k is given by:

The Formulae

	Three-Phase System	Single-Phase System	D.C. System
Three phase short circuit	$I_{k}^{"} = \frac{c U_{n}}{\sqrt{3} Z_{1}}$	-	-
Line-to-line short circuit	$I_{k 2}^{"} = \frac{c U_{n}}{Z_{1} + Z_{2}} = \frac{c U_{n}}{2 Z_{1}} = \frac{\sqrt{3}}{2} I_{k}^{"}$	$I_{k}^{"} = \frac{c U_{n}}{2 Z_{1}}$	$I_{k}^{"} = \frac{c U_{n}}{2 Z_{1}}$
Line-to-line-earth short circuit	$I_{k E 2 E}^{"} = \frac{\sqrt{3} c U_{n} Z_{2}}{Z_{1} Z_{2} + Z_{1} Z_{0} + Z_{2} Z_{0}} = \frac{\sqrt{3} c U_{n}}{Z_{1} + 2 Z_{0}}$	-	-
Line-earth short circuit	$I_{k 1}^{"} = \frac{\sqrt{3} c U_{n}}{Z_{1} + Z_{2} + Z_{0}} = \frac{\sqrt{3} c U_{n}}{2 Z_{1} + Z_{0}}$	$I_{k}^{"} = \frac{c U_{n}}{Z_{1} + Z_{0}}$	$I_{k}^{"} = \frac{c U_{n}}{Z_{1} + Z_{0}}$

Note:

for most components (except synchronous machines), we can take Z₂ as equal to Z₁.
for single-phase line to line is equivalent to line-neutral, and for d.c. positive to negative

Source Impedance

Source impedance Z_Q, is given by:

$Z_{Q} = \frac{c U_{n}}{\sqrt{3} I_{k}^{"}}$

Symbols

c          - voltage factor
I"_k                  - initial symmetrical three phase short-circuit current (r.m.s.)
                  - I"_k1        line-to-earth
                        - I"_k2 line-to-line
                        - I"_kE2E    line-to-line-earth
U_n          - nominal system voltage, line-to-line (r.m.s.)
                        - positive-negative voltage for d.c. systems
Z₁          - positive sequence short -circuit impedance
Z₂     - negative sequence short circuit impedance
Z₀    - zero sequence short circuit impedance

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IEC 60909 Fault Calculations

The Formulae

Source Impedance

Symbols

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