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

Line Capacitance

Calculates per-phase overhead line capacitance from conductor radius and geometric mean phase spacing. The reduced transposed-line method also estimates three-phase charging Mvar per 100 km and surge impedance from an explicit inductance input.

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

Standards

IEC 60909

Tags

chargingdeterministicelectricalline-capacitancesurge-impedancetransmission-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

7 inputs

Always given

Included directly in every task prompt.

6

  • Conductor radius

    conductor_radius_m

    Physical conductor radius

    0.001 – 0.05 m

  • Phase spacing ab

    phase_spacing_ab_m

    Spacing between phase A and phase B

    0.2 – 30 m

  • Phase spacing bc

    phase_spacing_bc_m

    Spacing between phase B and phase C

    0.2 – 30 m

  • Phase spacing ca

    phase_spacing_ca_m

    Spacing between phase C and phase A

    0.2 – 50 m

  • Nominal voltage

    nominal_voltage_kv

    Line-to-line nominal voltage

    1 – 765 kV

  • Inductance mh per km

    inductance_mh_per_km

    Per-phase line inductance

    0.1 – 3 mH/km

Hidden at higher difficulty

Visible in easier tasks and withheld in one or more harder tiers.

1

  • Frequency

    frequency_hz

    System frequency

    Hidden at hard difficulty.

    16.7 – 60 Hz

Scored outputs

4 outputs

Geometric mean distance

geometric_mean_distance_m

Geometric mean distance between phases

Scores if within ±3% of the reference value.

Capacitance nf per km

capacitance_nf_per_km

Per-phase capacitance per kilometre

Scores if within ±3% of the reference value.

Charging mvar per 100km

charging_mvar_per_100km

Three-phase charging reactive power per 100 km

Scores if within ±3% of the reference value.

Surge impedance ohm

surge_impedance_ohm

Surge impedance from L and C

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

Distribution line with all geometry visible

Frequency hz restricted to: 50

medium

All inputs given

Distribution or transmission capacitance calculation

hard

Some inputs hidden

Frequency hidden in system context

Hidden inputs

  • Frequency hzfrequency_hz

Prompt replacement text

Use the system frequency implied by {{ archetype.description }}.

Frequency hz restricted to: 50

Task bundle

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

/workspace

  • instruction.md
  • line-capacitance_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 capacitance.2 3## Given4 5| Parameter | Value | Unit |6|-----------|-------|------|7| Conductor radius | {{ conductor_radius_m }} | m |8| Phase spacing A-B | {{ phase_spacing_ab_m }} | m |9| Phase spacing B-C | {{ phase_spacing_bc_m }} | m |10| Phase spacing C-A | {{ phase_spacing_ca_m }} | m |11| Nominal line voltage | {{ nominal_voltage_kv }} | kV |12{% if frequency_hz is defined %}13| System frequency | {{ frequency_hz }} | Hz |14{% endif %}15| Line inductance | {{ inductance_mh_per_km }} | mH/km |16 17## Constraints18 19- Use `GMD = (Dab x Dbc x Dca)^(1/3)`.20- Use `C = 2 pi epsilon0 / ln(GMD / conductor_radius)`.21- Convert F/m to nF/km.22- Charging Mvar is for 100 km of three-phase line.23- Surge impedance is `sqrt(L / C)` using H/m and F/m.24 25## Output Format26 27Include a JSON block with exactly these keys:28 29```json30{31 "geometric_mean_distance_m": <numeric_value>,32 "capacitance_nf_per_km": <numeric_value>,33 "charging_mvar_per_100km": <numeric_value>,34 "surge_impedance_ohm": <numeric_value>35}36```37 38Write your complete solution to `/workspace/output.md`.39

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 line

distribution_line

Medium-voltage distribution overhead line

rural-feederurban-distribution
Parameter ranges
conductor_radius_m
0.004 – 0.015
phase_spacing_ab_m
0.5 – 3
phase_spacing_bc_m
0.5 – 3
phase_spacing_ca_m
1 – 6
nominal_voltage_kv
11 – 66
inductance_mh_per_km
0.6 – 1.6

Transmission line

transmission_line

High-voltage transmission overhead line

132kv-overhead330kv-overhead
Parameter ranges
conductor_radius_m
0.01 – 0.04
phase_spacing_ab_m
3 – 15
phase_spacing_bc_m
3 – 15
phase_spacing_ca_m
5 – 30
nominal_voltage_kv
110 – 500
inductance_mh_per_km
0.6 – 1.5

Example task

132kv-overhead-transmission-line-preview — hard difficulty, some inputs hidden.

High-voltage transmission overhead line. 132kv-overhead. Required outputs: geometric_mean_distance_m, capacitance_nf_per_km, charging_mvar_per_100km, surge_impedance_ohm

The model sees

Scenario context and visible inputs.

conductor_radius_m
0.01 to 0.04 m
phase_spacing_ab_m
3 to 15 m
phase_spacing_bc_m
3 to 15 m
phase_spacing_ca_m
5 to 30 m
nominal_voltage_kv
110 to 500 kV
inductance_mh_per_km
0.6 to 1.5 mH/km

Executable tool: line-capacitance_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Frequency hz

    frequency_hz

Stand-in text in the prompt

Use the system frequency implied by {{ archetype.description }}.

The model must produce

The scored JSON answer schema.

{
  "geometric_mean_distance_m": <number>,
  "capacitance_nf_per_km": <number>,
  "charging_mvar_per_100km": <number>,
  "surge_impedance_ohm": <number>
}
  • geometric_mean_distance_m · scored within ±3%
  • capacitance_nf_per_km · scored within ±3%
  • charging_mvar_per_100km · scored within ±3%
  • surge_impedance_ohm · scored within ±3%