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electricalwith-tool

Three Phase Fault Current

Computes initial symmetrical (Ik'') and peak (ip) short-circuit currents for a radial network using the IEC 60909-0 simplified method. Sums source, transformer, and cable impedances in series referred to the system voltage level, then applies the voltage factor c and peak factor kappa to determine fault currents for switchgear rating and protection coordination.

with-tool: The model is given an executable Python calculator script.

Standards

AS 3851IEC 60909-0:2016

Tags

deterministicelectricalfault-currentiec-60909short-circuit

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

8 inputs

Always given

Included directly in every task prompt.

7
Show 7 inputs

  • System voltage

    system_voltage_kv

    Nominal system voltage at the fault location

    0.4 – 33 kV

  • Source fault level

    source_fault_level_mva

    Upstream source fault level (short-circuit power)

    50 – 2000 MVA

  • Transformer rated power

    transformer_rated_power_mva

    Transformer rated apparent power

    0.1 – 100 MVA

  • Transformer impedance percent

    transformer_impedance_percent

    Transformer short-circuit impedance (uk%)

    4 – 12 %

  • Cable resistance ohm per km

    cable_resistance_ohm_per_km

    Cable resistance per unit length

    0.05 – 1.5 ohm/km

  • Cable reactance ohm per km

    cable_reactance_ohm_per_km

    Cable reactance per unit length

    0.06 – 0.15 ohm/km

  • Cable length

    cable_length_m

    Cable route length from transformer to fault point

    5 – 500 m

Optional

Used only when the sampled task needs this part of the contract.

1

  • Voltage factor c

    voltage_factor_c

    IEC 60909 voltage factor c for maximum fault current

    Derived from the archetype scenario. Optional input. Hidden at hard difficulty.

    1 – 1.1

Scored outputs

6 outputs

Source impedance ohm

source_impedance_ohm

Source impedance referred to system voltage (ohm)

Scores if within ±3% of the reference value.

Transformer impedance ohm

transformer_impedance_ohm

Transformer impedance referred to system voltage (ohm)

Scores if within ±3% of the reference value.

Cable impedance ohm

cable_impedance_ohm

Cable impedance magnitude (ohm)

Scores if within ±3% of the reference value.

Total impedance ohm

total_impedance_ohm

Total short-circuit impedance at fault point (ohm)

Scores if within ±3% of the reference value.

Initial symmetrical current ka

initial_symmetrical_current_ka

Initial symmetrical short-circuit current Ik'' (kA)

Scores if within ±3% of the reference value.

Peak current ka

peak_current_ka

Peak short-circuit current ip (kA)

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

easy

All inputs given

LV system, short cable, all parameters given including voltage factor

medium

All inputs given

Any voltage level and archetype, all parameters given

hard

Some inputs hidden

Voltage factor hidden, agent must determine c from IEC 60909 Table 1

Hidden inputs

  • Voltage factor cvoltage_factor_c

Prompt replacement text

The installation is a {{ archetype.description }} ({{ archetype.site_context }})

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • three-phase-fault-current_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior electrical engineer specializing in power systems protection and short-circuit analysis.2 3## Problem4 5Calculate the three-phase short-circuit currents at a specified fault location in a radial network using the IEC 60909-0 simplified method.6 7The network consists of an upstream source, a single transformer, and a cable run to the fault point.8 9## Given10 11| Parameter | Value | Unit |12|-----------|-------|------|13| Nominal system voltage (Un) | {{ system_voltage_kv }} | kV |14| Upstream source fault level (Sk) | {{ source_fault_level_mva }} | MVA |15| Transformer rated power (Sn) | {{ transformer_rated_power_mva }} | MVA |16| Transformer impedance (uk%) | {{ transformer_impedance_percent }} | % |17| Cable resistance | {{ cable_resistance_ohm_per_km }} | ohm/km |18| Cable reactance | {{ cable_reactance_ohm_per_km }} | ohm/km |19| Cable length | {{ cable_length_m }} | m |20{% if voltage_factor_c is defined %}21| Voltage factor c | {{ voltage_factor_c }} | - |22{% endif %}23{% if archetype_description is defined %}24 25### Installation Context26 27{{ archetype_description }}28{% endif %}29 30{% if tool_available %}31## Available Tool32 33A fault current calculation tool is available at `/workspace/three-phase-fault-current_calc.py`. Run it with:34 35```bash36python3 /workspace/three-phase-fault-current_calc.py --help37```38 39You may use this tool to verify your calculations or compute values directly.40{% endif %}41 42## Required43 44Calculate the following:45 461. Source impedance referred to system voltage (ohm)472. Transformer impedance referred to system voltage (ohm)483. Cable impedance magnitude (ohm)494. Total short-circuit impedance at the fault point (ohm)505. Initial symmetrical short-circuit current Ik'' (kA)516. Peak short-circuit current ip (kA)52 53## Applicable Standards54 55- IEC 60909-0:2016 — Short-circuit currents in three-phase a.c. systems, Calculation of currents56- AS 3851 — The calculation of short-circuit currents in three-phase a.c. systems57 58## Constraints59 60- No internet access is available. Work from engineering knowledge and the provided tool.61- Use the IEC 60909-0 simplified method for a radial network:62 - Source impedance: Zs = c * Un^2 / Sk (assumed purely reactive)63 - Transformer impedance: Zt = (uk% / 100) * Un^2 / Sn (assumed purely reactive)64 - Cable impedance: Zc = sqrt(Rc^2 + Xc^2) where Rc = r * L/1000 and Xc = x * L/100065 - Total impedance: sum R and X components separately, then Zk = sqrt(R_total^2 + X_total^2)66 - Initial symmetrical current: Ik'' = c * Un / (sqrt(3) * Zk), result in kA67 - Peak current: ip = kappa * sqrt(2) * Ik''68 - Kappa factor: kappa = 1.02 + 0.98 * exp(-3 * R/X)69- All impedances are referred to the system voltage level.70- Un is in kV, Sk and Sn are in MVA, impedances are in ohm.71 72## Output Format73 74Show your step-by-step working in Markdown, including each impedance calculation, the total impedance, and the fault current derivations. At the end of your solution, include a JSON block with your final answers in exactly this format:75 76```json77{78 "source_impedance_ohm": <numeric_value>,79 "transformer_impedance_ohm": <numeric_value>,80 "cable_impedance_ohm": <numeric_value>,81 "total_impedance_ohm": <numeric_value>,82 "initial_symmetrical_current_ka": <numeric_value>,83 "peak_current_ka": <numeric_value>84}85```86 87Write your complete solution to `/workspace/output.md`.88

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Lv commercial

lv_commercial

Low-voltage commercial distribution board

sydney-commercialmelbourne-commercial
Parameter ranges
system_voltage_kv
0.4
source_fault_level_mva
150 – 500
transformer_rated_power_mva
0.5 – 2
transformer_impedance_percent
4 – 6
cable_length_m
5 – 50

Lv industrial

lv_industrial

Low-voltage industrial motor control centre

hunter-valley-industrialgladstone-industrial
Parameter ranges
system_voltage_kv
0.4
source_fault_level_mva
200 – 750
transformer_rated_power_mva
1 – 5
transformer_impedance_percent
5 – 6.5
cable_length_m
10 – 100

Mv distribution

mv_distribution

Medium-voltage distribution switchboard

perth-substationbrisbane-substation
Parameter ranges
system_voltage_kv
11
source_fault_level_mva
250 – 1000
transformer_rated_power_mva
5 – 30
transformer_impedance_percent
6 – 10
cable_length_m
50 – 500

Mv heavy industrial

mv_heavy_industrial

Medium-voltage heavy industrial switchgear

pilbara-miningbowen-basin-mining
Parameter ranges
system_voltage_kv
22 – 33
source_fault_level_mva
500 – 2000
transformer_rated_power_mva
10 – 100
transformer_impedance_percent
7 – 12
cable_length_m
100 – 500

Example task

perth-substation-mv-distribution-preview — hard difficulty, some inputs hidden.

Medium-voltage distribution switchboard. perth-substation. Required outputs: source_impedance_ohm, transformer_impedance_ohm, cable_impedance_ohm, total_impedance_ohm, initial_symmetrical_current_ka, peak_current_ka

The model sees

Scenario context and visible inputs.

system_voltage_kv
11 to 11 kV
source_fault_level_mva
250 to 1000 MVA
transformer_rated_power_mva
5 to 30 MVA
transformer_impedance_percent
6 to 10 %
cable_resistance_ohm_per_km
0.05 to 1.5 ohm/km
cable_reactance_ohm_per_km
0.06 to 0.15 ohm/km
cable_length_m
50 to 500 m

Executable tool: three-phase-fault-current_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Voltage factor c

    voltage_factor_c

Stand-in text in the prompt

The installation is a {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "source_impedance_ohm": <number>,
  "transformer_impedance_ohm": <number>,
  "cable_impedance_ohm": <number>,
  "total_impedance_ohm": <number>,
  "initial_symmetrical_current_ka": <number>,
  "peak_current_ka": <number>
}
  • source_impedance_ohm · scored within ±3%
  • transformer_impedance_ohm · scored within ±3%
  • cable_impedance_ohm · scored within ±3%
  • total_impedance_ohm · scored within ±3%
  • initial_symmetrical_current_ka · scored within ±3%
  • peak_current_ka · scored within ±3%