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Short-circuit study — network, transformer, cables (IEC 60909)

Computes Ik3, ip and Ik1 step by step, from the MV network to the end of the circuit, with the IEC 60909 method of impedances: upstream network, transformer with KT, two cable sections, motors at the main board. Checks Icu and the magnetic threshold.

Inputs

V
MVA
kVA
%
W
Parallel transformers
Material
m
Cable 1: conductors per phase
A
kA
m
Cable 2: conductors per phase
A

Result

Checks —
Ik3 max at the main board —
Peak ip at the main board —
Ik3 max at the end of cable 2 —
Peak ip at the end of cable 2 —
Ik3 min at the end of cable 2 —
Ik1 min at the end of cable 2 —
Network impedance —
Transformer impedance —
Cable 1 impedance —
Cable 2 impedance —
R/X at the main board —
Formula and method 
IMPEDANCES, REFERRED TO THE LV SIDE

  Z_Q = c_Q × Un² / S″kQ          c_Q = 1.10    X_Q = 0.995·Z_Q    R_Q = 0.1·X_Q
  Z_T = uk × Un² / Sr             R_T = Pk × Un² / Sr²
  K_T = 0.95 × c_max / (1 + 0.6·x_T)    x_T = X_T / (Un² / Sr)
  R_c = ρ·L / (S·n)               X_c = 0.08 mΩ/m × L / n
  Z_M = (1/5) × Un / (√3 × ΣIr)   X_M = 0.922·Z_M    R_M = 0.42·X_M

  Variables:
    ρ    1/54 (Cu) · 1/34 (Al)  Ω·mm²/m at 20 °C
    n    conductors per phase; parallel transformers divide Z_T
    ΣIr  motors at the main board, in parallel with the source (I_LR / Ir = 5)


CURRENTS

  Ik3 max = c_max × Un / (√3 × |Zk|)               c_max = 1.05, cables at 20 °C
  ip      = κ × √2 × Ik3 max                       κ = 1.02 + 0.98·e^(−3R/X)
  Ik3 min = c_min × Un / (√3 × |Zk,80°C|)          c_min = 0.95, no motors
  Ik1 min = √3 × c_min × Un / |2·Z(1) + Z(0)|      Dyn transformer, TN system

  Z(0): network absent, transformer R(0) = R and X(0) = 0.95·X,
  cable Z(0) = 4·Z(1) (neutral of the same section as the phase).


CHECKS

  Ik3 max at the main board  ≤  Icu of the breaker
  Ik1 min at the end         ≥  magnetic threshold Im (with a 20 % margin: release tolerance)

Reference: IEC 60909-0:2016 IEC 60364-4-41

∼MV networkS″kQTransformerSr, uk, PkCable 1S, L, nMain boardIk3 max, ip≤ IcuMΣIrCable 2S, L, nFaultIk3 max, ipIk3 minIk1 min ≥ ImZk = Z_Q + K_T·Z_T + Z_c1 + Z_c2

This study follows the short-circuit current step by step, like a calculation note: MV network, transformer, cable to the main board, then cable to the circuit under study. It shows the share of each element in the impedance and gives the currents at both points of the circuit.

Data to collect:

  1. Upstream network: short-circuit power S″kQ, given by the utility. For a minimum calculation, enter the minimum value.
  2. Transformer: rated power, uk and load losses Pk, from the nameplate or the test report. The secondary no-load voltage is taken equal to Un.
  3. Cables: material, section, length and conductors per phase of each section. Length 0 if the main board is at the transformer terminals.
  4. Motors at the main board: sum of their rated currents. IEC 60909-0 allows them to be neglected if this sum does not exceed 1 % of Ik3.
  5. Thresholds to check: Icu of the breaker at the main board and magnetic threshold of the circuit. A field left empty removes the check.

Results: Ik3 max and ip size the breaking capacity and the busbar withstand. Ik3 min and Ik1 min check tripping. The impedances show which element limits the current.

Limits: radial LV network, far from generators (Ik″ = Ik). κ is computed from the R/X of the equivalent impedance, including with motors. The neutral has the section of the phase; a reduced PE or neutral conductor lowers Ik1. For a meshed network, a generator set or a selectivity study, use network calculation software. This study uses the IEC 60909-0 resistivities (1/54 and 1/34): its results at the end of a cable differ slightly from those of the simplified calculator.

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Reference standards