LIVEdataset aec-bench@releasetasks 552models 18disciplines 5last submission … · built …

electricalwith-tool

Static Thermal Rating

Determines the continuous current-carrying capacity (ampacity) of bare overhead conductors by solving the IEEE 738 steady-state heat balance equation: convective and radiative cooling must equal solar heat gain plus ohmic heating. Accounts for wind speed, solar radiation, conductor emissivity, and temperature-dependent air properties to rate transmission and distribution lines.

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

Standards

CIGRE TB 601 IEEE 738

How this task is generated

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

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
04
Task prompt
The model responds with the declared outputs.

Parameters

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

Inputs

9 inputs

Always given

Included directly in every task prompt.

Show 7 inputs

Conductor diameter
conductor_diameter_mm
Outer diameter of the bare overhead conductor
5 – 50 mm
Conductor resistance ohm per km
conductor_resistance_ohm_per_km
AC resistance of conductor at 25 deg C
0.02 – 1.5 ohm/km
Max conductor temp c
max_conductor_temp_c
Maximum allowable conductor operating temperature
50 – 150 deg C
Ambient temp c
ambient_temp_c
Ambient air temperature
-10 – 50 deg C
Wind speed
wind_speed_m_s
Wind speed perpendicular component
0 – 15 m/s
Wind angle
wind_angle_deg
Angle between wind direction and conductor axis (0 = parallel, 90 = perpendicular)
0 – 90 deg
Solar radiation
solar_radiation_w_m2
Total solar radiation intensity on surface normal to conductor
0 – 1200 W/m2

Derived from scenario

Sampled from the scenario and inferable from its description.

Emissivity
emissivity
Conductor surface emissivity (0 = shiny new, 1 = fully weathered)
Derived from the archetype scenario. Hidden at hard difficulty.
0.2 – 0.9
Absorptivity
absorptivity
Conductor surface solar absorptivity (0 = fully reflective, 1 = fully absorbing)
Derived from the archetype scenario. Hidden at hard difficulty.
0.2 – 0.9

Scored outputs

4 outputs

Convective cooling w

convective_cooling_w_m

Convective heat loss per unit length (W/m)

Scores if within ±5% of the reference value.

Radiative cooling w

radiative_cooling_w_m

Radiative heat loss per unit length (W/m)

Scores if within ±5% of the reference value.

Solar heat gain w

solar_heat_gain_w_m

Solar heat gain per unit length (W/m)

Scores if within ±5% of the reference value.

Ampacity

ampacity_a

Steady-state ampacity (A)

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

Low wind, no solar, all params given including emissivity and absorptivity

Solar radiation w m2 restricted to: 0

Wind angle deg restricted to: 90

medium

All inputs given

Full weather conditions, all params given

hard

Some inputs hidden

Emissivity and absorptivity hidden, agent must infer from conductor age and conditions

Hidden inputs

Emissivityemissivity
Absorptivityabsorptivity

Prompt replacement text

The line uses {{ archetype.description }} in the {{ archetype.site_context }} corridor

Task bundle

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

/workspace

instruction.md
static-thermal-rating_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 overhead transmission line design and thermal rating.2 3## Problem4 5Calculate the steady-state thermal rating (ampacity) of a bare overhead conductor using the IEEE 738 heat balance method. The ampacity is the maximum current the conductor can carry continuously without exceeding its maximum allowable temperature.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Conductor outer diameter | {{ conductor_diameter_mm }} | mm |12| AC resistance at 25°C | {{ conductor_resistance_ohm_per_km }} | ohm/km |13| Maximum conductor temperature | {{ max_conductor_temp_c }} | °C |14| Ambient air temperature | {{ ambient_temp_c }} | °C |15| Wind speed | {{ wind_speed_m_s }} | m/s |16| Wind angle to conductor axis | {{ wind_angle_deg }} | degrees |17| Solar radiation intensity | {{ solar_radiation_w_m2 }} | W/m² |18{% if emissivity is defined %}19| Conductor emissivity | {{ emissivity }} | - |20{% endif %}21{% if absorptivity is defined %}22| Conductor absorptivity | {{ absorptivity }} | - |23{% endif %}24{% if archetype_description is defined %}25 26### Line Conditions27 28{{ archetype_description }}29{% endif %}30 31{% if tool_available %}32## Available Tool33 34A thermal rating calculation tool is available at `/workspace/static-thermal-rating_calc.py`. Run it with:35 36```bash37python3 /workspace/static-thermal-rating_calc.py --help38```39 40You may use this tool to verify your calculations or compute values directly.41{% endif %}42 43## Required44 45Calculate the following:46 471. Convective heat loss per unit length (W/m) — using the maximum of natural and forced convection482. Radiative heat loss per unit length (W/m)493. Solar heat gain per unit length (W/m)504. Steady-state ampacity (A) — from the heat balance equation51 52## Applicable Standards53 54- IEEE 738 — Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors55- CIGRE TB 601 — Guide for Thermal Rating Calculations of Overhead Lines56 57## Constraints58 59- No internet access is available. Work from engineering knowledge and the provided tool.60- Use the IEEE 738 steady-state heat balance: qc + qr = qs + I²R, solved as I = sqrt((qc + qr - qs) / R)61- Evaluate air properties (density, viscosity, thermal conductivity) at the film temperature: Tfilm = (Tc + Ta) / 262- Air density at sea level: rho = P × M / (R_gas × T_K) where P = 101325 Pa, M = 0.0289644 kg/mol, R_gas = 8.31447 J/(mol·K)63- Dynamic viscosity via Sutherland's law: mu = 1.458e-6 × T_K^1.5 / (T_K + 110.4) Pa·s64- Thermal conductivity of air: kf = 2.424e-2 + 7.477e-5 × Tf - 4.407e-9 × Tf² W/(m·°C)65- Natural convection: qcn = 3.645 × rho^0.5 × D^0.75 × (Tc - Ta)^1.25 W/m66- Forced convection (low Re): qc1 = Kangle × [1.01 + 1.35 × NRe^0.52] × kf × (Tc - Ta) W/m67- Forced convection (high Re): qc2 = Kangle × 0.0754 × NRe^0.6 × kf × (Tc - Ta) W/m68- Use qc = max(qcn, qc1, qc2)69- Wind angle factor: Kangle = 1.194 - cos(phi) + 0.194 × cos(2phi) + 0.368 × sin(2phi)70- Reynolds number: NRe = D × rho × Vw / mu71- Radiative cooling: qr = pi × D × sigma × epsilon × (Tc_K^4 - Ta_K^4) where sigma = 5.6704e-8 W/(m²·K⁴)72- Solar heat gain (perpendicular incidence): qs = alpha × Qse × D73- AC resistance at conductor temperature: R(T) = R(25°C) × [1 + 0.00403 × (T - 25)] where 0.00403 /°C is the temperature coefficient for aluminium74- Convert resistance from ohm/km to ohm/m before computing ampacity75 76## Output Format77 78Show your step-by-step working in Markdown, including air property calculations, each heat balance component, and the final ampacity derivation. At the end of your solution, include a JSON block with your final answers in exactly this format:79 80```json81{82  "convective_cooling_w_m": <numeric_value>,83  "radiative_cooling_w_m": <numeric_value>,84  "solar_heat_gain_w_m": <numeric_value>,85  "ampacity_a": <numeric_value>86}87```88 89Write your complete solution to `/workspace/output.md`.90

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.

Light distribution

light_distribution

Light distribution line with small new ACSR conductor (recently strung, minimal weathering)

regional-australiarural-new-zealand

Parameter ranges

conductor_diameter_mm: 5 – 15
conductor_resistance_ohm_per_km: 0.5 – 1.5
max_conductor_temp_c: 50 – 80
wind_speed_m_s: 0.5 – 5
emissivity: 0.23 – 0.3
absorptivity: 0.23 – 0.3

Medium subtransmission

medium_subtransmission

Subtransmission line with medium ACSR conductor aged in service (10+ years weathered surface)

sydney-western-corridormelbourne-northern-ring

Parameter ranges

conductor_diameter_mm: 15 – 30
conductor_resistance_ohm_per_km: 0.1 – 0.5
max_conductor_temp_c: 75 – 100
wind_speed_m_s: 0.5 – 8
emissivity: 0.7 – 0.9
absorptivity: 0.7 – 0.9

Heavy transmission

heavy_transmission

High-voltage transmission line with large ACSR conductor aged in service (10+ years weathered surface)

hunter-valley-transmissionqueensland-powerlink

Parameter ranges

conductor_diameter_mm: 25 – 50
conductor_resistance_ohm_per_km: 0.02 – 0.15
max_conductor_temp_c: 80 – 150
wind_speed_m_s: 0.5 – 15
emissivity: 0.7 – 0.9
absorptivity: 0.7 – 0.9

Example task

sydney-western-corridor-medium-subtransmission-preview — hard difficulty, some inputs hidden.

Subtransmission line with medium ACSR conductor aged in service (10+ years weathered surface). sydney-western-corridor. Required outputs: convective_cooling_w_m, radiative_cooling_w_m, solar_heat_gain_w_m, ampacity_a

The model sees

Scenario context and visible inputs.

conductor_diameter_mm: 15 to 30 mm
conductor_resistance_ohm_per_km: 0.1 to 0.5 ohm/km
max_conductor_temp_c: 75 to 100 deg C
ambient_temp_c: -10 to 50 deg C
wind_speed_m_s: 0.5 to 8 m/s
wind_angle_deg: 0 to 90 deg
solar_radiation_w_m2: 0 to 1200 W/m2

Executable tool: static-thermal-rating_calc.py

The model must infer

Inputs withheld at this difficulty.

Absorptivity
absorptivity
Emissivity
emissivity

Stand-in text in the prompt

The line uses {{ archetype.description }} in the {{ archetype.site_context }} corridor

The model must produce

The scored JSON answer schema.

{
  "convective_cooling_w_m": <number>,
  "radiative_cooling_w_m": <number>,
  "solar_heat_gain_w_m": <number>,
  "ampacity_a": <number>
}

convective_cooling_w_m · scored within ±5%
radiative_cooling_w_m · scored within ±5%
solar_heat_gain_w_m · scored within ±5%
ampacity_a · scored within ±3%

Static Thermal Rating

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Convective cooling w

Radiative cooling w

Solar heat gain w

Ampacity

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Light distribution

Medium subtransmission

Heavy transmission

Example task

The model sees

The model must infer

The model must produce