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

Line Inductance

Calculates per-phase line inductance for a reduced transposed three-phase overhead line model. The template computes geometric mean distance from phase spacings, equivalent GMR for simple bundled conductors, and inductance using L = 0.2 ln(GMD/GMR) mH/km.

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

Standards

IEC 60909IEEE 738

Tags

deterministicelectricalgmdgmrline-inductancetransmission-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

6 inputs

Always given

Included directly in every task prompt.

5

  • Conductor gmr

    conductor_gmr_m

    Geometric mean radius of one subconductor

    0.001 – 0.05 m

  • Phase spacing ab

    phase_spacing_ab_m

    Spacing between phase A and phase B

    0.2 – 20 m

  • Phase spacing bc

    phase_spacing_bc_m

    Spacing between phase B and phase C

    0.2 – 20 m

  • Phase spacing ca

    phase_spacing_ca_m

    Spacing between phase C and phase A

    0.2 – 40 m

  • Bundle spacing

    bundle_spacing_m

    Spacing between subconductors in the bundle

    0.1 – 0.8 m

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Bundle count

    bundle_count

    Number of subconductors in each phase bundle

    Derived from the archetype scenario. Hidden at hard difficulty.

    singletwothreefour

Scored outputs

3 outputs

Geometric mean distance

geometric_mean_distance_m

Geometric mean distance between phases

Scores if within ±3% of the reference value.

Equivalent gmr

equivalent_gmr_mm

Equivalent bundle GMR

Scores if within ±5% of the reference value.

Inductance mh per km

inductance_mh_per_km

Per-phase inductance per kilometre

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

Single-conductor line with all dimensions given

Bundle count restricted to: single

Bundle spacing restricted to: 0.45

medium

All inputs given

Single or two-conductor bundle

Bundle count restricted to: single, two

hard

Some inputs hidden

Bundle count inferred from transmission-line context

Hidden inputs

  • Bundle countbundle_count

Prompt replacement text

Use the conductor arrangement implied by {{ archetype.description }}.

Bundle count restricted to: two, three, four

Task bundle

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

/workspace

  • instruction.md
  • line-inductance_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 calculating overhead line parameters.2 3## Problem4 5Calculate the geometric mean distance, equivalent bundle GMR, and per-phase inductance for a reduced transposed three-phase line.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Conductor GMR | {{ conductor_gmr_m }} | m |12| Phase spacing A-B | {{ phase_spacing_ab_m }} | m |13| Phase spacing B-C | {{ phase_spacing_bc_m }} | m |14| Phase spacing C-A | {{ phase_spacing_ca_m }} | m |15{% if bundle_count is defined %}16| Bundle count | {{ bundle_count }} | - |17{% endif %}18| Bundle spacing | {{ bundle_spacing_m }} | m |19{% if archetype_description is defined %}20 21### Site Context22 23{{ archetype_description }}24{% endif %}25 26{% if tool_available %}27## Available Tool28 29A line inductance calculation tool is available at `/workspace/line-inductance_calc.py`. Run it with:30 31```bash32python3 /workspace/line-inductance_calc.py --help33```34{% endif %}35 36## Required37 38Calculate:39 401. Geometric mean distance, `GMD = (Dab x Dbc x Dca)^(1/3)`412. Equivalent bundle GMR in mm423. Per-phase inductance, `L = 0.2 x ln(GMD / GMR_eq)` mH/km43 44## Constraints45 46- For a single conductor, `GMR_eq = GMR`.47- For two subconductors, `GMR_eq = sqrt(GMR x bundle_spacing)`.48- For three subconductors, `GMR_eq = (GMR x bundle_spacing^2)^(1/3)`.49- For four subconductors, `GMR_eq = 1.09 x (GMR x bundle_spacing^3)^(1/4)`.50 51## Output Format52 53Show your working in Markdown. At the end, include a JSON block with exactly these keys:54 55```json56{57 "geometric_mean_distance_m": <numeric_value>,58 "equivalent_gmr_mm": <numeric_value>,59 "inductance_mh_per_km": <numeric_value>60}61```62 63Write your complete solution to `/workspace/output.md`.64

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 single

distribution_single

Single-conductor distribution line

urban-distributionrural-feeder
Parameter ranges
conductor_gmr_m
0.003 – 0.015
phase_spacing_ab_m
0.6 – 2
phase_spacing_bc_m
0.6 – 2
phase_spacing_ca_m
1.2 – 4

Transmission single

transmission_single

Single-conductor transmission line

132kv-overhead220kv-overhead
Parameter ranges
conductor_gmr_m
0.006 – 0.02
phase_spacing_ab_m
3 – 8
phase_spacing_bc_m
3 – 8
phase_spacing_ca_m
5 – 16

Bundled transmission

bundled_transmission

Bundled high-voltage transmission line

330kv-overhead500kv-overhead
Parameter ranges
conductor_gmr_m
0.006 – 0.025
phase_spacing_ab_m
5 – 15
phase_spacing_bc_m
5 – 15
phase_spacing_ca_m
8 – 30
bundle_spacing_m
0.3 – 0.6

Example task

330kv-overhead-bundled-transmission-preview — hard difficulty, some inputs hidden.

Bundled high-voltage transmission line. 330kv-overhead. Required outputs: geometric_mean_distance_m, equivalent_gmr_mm, inductance_mh_per_km

The model sees

Scenario context and visible inputs.

conductor_gmr_m
0.006 to 0.025 m
phase_spacing_ab_m
5 to 15 m
phase_spacing_bc_m
5 to 15 m
phase_spacing_ca_m
8 to 30 m
bundle_spacing_m
0.3 to 0.6 m

Executable tool: line-inductance_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Bundle count

    bundle_count

Stand-in text in the prompt

Use the conductor arrangement implied by {{ archetype.description }}.

The model must produce

The scored JSON answer schema.

{
  "geometric_mean_distance_m": <number>,
  "equivalent_gmr_mm": <number>,
  "inductance_mh_per_km": <number>
}
  • geometric_mean_distance_m · scored within ±3%
  • equivalent_gmr_mm · scored within ±5%
  • inductance_mh_per_km · scored within ±3%