LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
electricalwith-tool

Ac Resistance Temperature

Computes the AC resistance of a power cable conductor at operating temperature by first correcting DC resistance from 20 deg C using R'(T) = R_20 * [1 + alpha_20 * (T - 20)], then applying the IEC 60287-1-1 skin effect factor ys to obtain R_ac = R_dc(T) * (1 + ys). Essential for cable thermal rating and power loss calculations in transmission and distribution systems.

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

Standards

IEC 60287-1-1IEEE 738

Tags

ac-resistancedeterministicelectricalskin-effecttemperaturetransmission-lines

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

4 inputs

Always given

Included directly in every task prompt.

3

  • Dc resistance 20c ohm per km

    dc_resistance_20c_ohm_per_km

    DC resistance of conductor at 20 deg C

    0.01 – 5 ohm/km

  • Operating temp c

    operating_temp_c

    Operating temperature of the conductor

    20 – 200 deg C

  • Frequency

    frequency_hz

    System frequency

    16.7 – 60 Hz

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Conductor material

    conductor_material

    Conductor material

    Derived from the archetype scenario. Hidden at hard difficulty.

    copperaluminium

Scored outputs

3 outputs

Dc resistance at temp ohm per km

dc_resistance_at_temp_ohm_per_km

DC resistance at operating temperature (ohm/km)

Scores if within ±3% of the reference value.

Skin effect factor

skin_effect_factor

Skin effect factor ys (dimensionless)

Scores if within ±5% of the reference value.

Ac resistance ohm per km

ac_resistance_ohm_per_km

AC resistance at operating temperature (ohm/km)

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

Standard 50 Hz copper, moderate temperature, all params given

Frequency hz restricted to: 50

medium

All inputs given

Any material and frequency, transmission-level conductors

hard

Some inputs hidden

Conductor material hidden, agent must infer from context and resistance value

Hidden inputs

  • Conductor materialconductor_material

Prompt replacement text

The installation uses {{ archetype.description }} practices ({{ 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
  • ac-resistance-temperature_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 transmission and conductor design.2 3## Problem4 5Calculate the AC resistance of a conductor at its operating temperature, accounting for the temperature correction of DC resistance and the skin effect factor per IEC 60287-1-1.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| DC resistance at 20 °C | {{ dc_resistance_20c_ohm_per_km }} | ohm/km |12{% if conductor_material is defined %}13| Conductor material | {{ conductor_material }} | - |14{% endif %}15| Operating temperature | {{ operating_temp_c }} | °C |16| System frequency | {{ frequency_hz }} | Hz |17{% if archetype_description is defined %}18 19### Installation Context20 21{{ archetype_description }}22{% endif %}23 24{% if tool_available %}25## Available Tool26 27A calculation tool is available at `/workspace/ac-resistance-temperature_calc.py`. Run it with:28 29```bash30python3 /workspace/ac-resistance-temperature_calc.py --help31```32 33You may use this tool to verify your calculations or compute values directly.34{% endif %}35 36## Required37 38Calculate the following:39 401. DC resistance at operating temperature (ohm/km)412. Skin effect factor ys (dimensionless)423. AC resistance at operating temperature (ohm/km)43 44## Applicable Standards45 46- IEC 60287-1-1 — Electric cables — Calculation of the current rating — Current rating equations and calculation of losses47- IEEE 738 — Standard for Calculating the Current-Temperature of Bare Overhead Conductors48 49## Constraints50 51- No internet access is available. Work from engineering knowledge and the provided tool.52- Use the IEC 60287-1-1 method:53 1. DC resistance at temperature: R_dc(T) = R_dc_20 * [1 + alpha_20 * (T - 20)]54 2. Temperature coefficient alpha_20: copper = 0.00393 /°C, aluminium = 0.00403 /°C55 3. Skin effect argument: xs^2 = 8 * pi * f * 1e-7 * ks / R_dc(T) where R_dc(T) is in ohm/m and ks = 1 for round stranded conductors56 4. Skin effect factor: ys = xs^4 / (192 + 0.8 * xs^4)57 5. AC resistance: R_ac = R_dc(T) * (1 + ys) — proximity effect yp = 0 for single isolated conductors58 59## Output Format60 61Show your step-by-step working in Markdown, including the temperature correction, skin effect calculation, and final AC resistance. At the end of your solution, include a JSON block with your final answers in exactly this format:62 63```json64{65 "dc_resistance_at_temp_ohm_per_km": <numeric_value>,66 "skin_effect_factor": <numeric_value>,67 "ac_resistance_ohm_per_km": <numeric_value>68}69```70 71Write your complete solution to `/workspace/output.md`.72

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.

Distribution copper

distribution_copper

Copper distribution cable at moderate temperature

sydney-urbanmelbourne-urban
Parameter ranges
dc_resistance_20c_ohm_per_km
0.1 – 2
operating_temp_c
30 – 70

Distribution aluminium

distribution_aluminium

Aluminium distribution cable at moderate temperature

brisbane-suburbanperth-suburban
Parameter ranges
dc_resistance_20c_ohm_per_km
0.08 – 1.5
operating_temp_c
30 – 70

Transmission copper

transmission_copper

Copper transmission conductor at elevated temperature

hunter-valley-transmissionlatrobe-valley-transmission
Parameter ranges
dc_resistance_20c_ohm_per_km
0.01 – 0.15
operating_temp_c
50 – 120

Transmission aluminium

transmission_aluminium

Aluminium transmission conductor at high temperature

queensland-overheadsouth-australia-overhead
Parameter ranges
dc_resistance_20c_ohm_per_km
0.02 – 0.2
operating_temp_c
60 – 200

Example task

hunter-valley-transmission-transmission-copper-preview — hard difficulty, some inputs hidden.

Copper transmission conductor at elevated temperature. hunter-valley-transmission. Required outputs: dc_resistance_at_temp_ohm_per_km, skin_effect_factor, ac_resistance_ohm_per_km

The model sees

Scenario context and visible inputs.

dc_resistance_20c_ohm_per_km
0.01 to 0.15 ohm/km
operating_temp_c
50 to 120 deg C
frequency_hz
16.7 to 60 Hz

Executable tool: ac-resistance-temperature_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Conductor material

    conductor_material

Stand-in text in the prompt

The installation uses {{ archetype.description }} practices ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "dc_resistance_at_temp_ohm_per_km": <number>,
  "skin_effect_factor": <number>,
  "ac_resistance_ohm_per_km": <number>
}
  • dc_resistance_at_temp_ohm_per_km · scored within ±3%
  • skin_effect_factor · scored within ±5%
  • ac_resistance_ohm_per_km · scored within ±3%