Conductor Ampacity Calculator: Ambient & Dynamic Line Rating

Thermal balance

For one metre of bare conductor, solve $I^2R(T)+q_s=q_c+q_r$. The thermal rating is $I_{max}=\sqrt{\max(0,q_c+q_r-q_s)/R(T_{limit})}$. Negative heat headroom gives zero ampacity and a warning, rather than an invalid square root.

Convection uses the maximum of the natural, low-wind and high-wind branches of IEEE Std 738-2012 (including Cor 1-2013), following the open LineRate implementation (attached s4, pp.1–3). Air density, viscosity and conductivity use film temperature and elevation. Empirical correlation coefficients take SI numerical values; the viscosity correlation retains the source's 273 K rounding. For a transient conductor briefly below ambient, convection is extended as signed heat exchange with the same magnitude correlations.

Radiation uses $q_r=\pi D\epsilon\sigma[(T+273.15)^4-(T_a+273.15)^4]$, with $\sigma=5.670374419\times10^{-8}$ W/(m² K⁴). Absolute temperatures are explicitly converted to kelvin; differences are in K. Resistance is linear between 25 and 75 °C, with extrapolation explicitly limited by the tool's validity range. The manufacturer provides AC resistance at 75 °C (60 Hz); the 25 °C value is estimated using the entered aluminium coefficient at 20 °C unless overridden.

Open solar heating

For horizontal conductor axis and solar elevation $h$, the beam projection is $s=\sqrt{1-[\cos h\cos(\Delta z)]^2}$. The derived isotropic-sky cylinder model is $G_{eff}=DNI\,s+(\pi/2)[DHI+a_g(DNI\sin h+DHI)]$ and $q_s=\alpha D G_{eff}$. The diffuse factors follow integration over an isotropic hemisphere, as in a CIGRE 207 style projection, rather than a standard's solar table. CIGRE TB 601 (2014) uses a different diffuse-sky convention; this tool does not claim to implement its complete model. Effective-flux mode is $q_s=\alpha DG_{eff}$; using GHI is the approximation in NREL/PR-6A40-91599 (2024), attached s2 p.5.

Transient and example day

Integrate $C' dT/dt=I^2R(T)+q_s-q_c-q_r$ with adaptive Dormand–Prince ode45, relative tolerance 10⁻⁶, and $C'=m_{Al}c_{Al}+m_{St}c_{St}$. Each current-step starts at its previous-current equilibrium. The 24-hour scenario starts at midnight equilibrium; its 145 plotted samples are interpolated only for playback. The entire ODE is independent of the playing hour.

Solar declination is the sinusoidal day-of-year approximation; east/north/up solar direction components are derived from latitude and local solar hour. Below-horizon solar heating is zero. Illustrative DNI is scaled by the square root of the positive solar altitude sine, DHI by that sine; effective-flux mode scales its flux by that sine. The ambient profile has the entered daily maximum at hour 15 and peak-to-peak swing; wind is weakest at solar noon. These profiles are authored scenarios, not weather data.

Sag

Derive the parabolic length excess $w^2L_r^2/(24H^2)$ and first-order elastic strain $H/(EA)$. Solve

Then $f=wL^2/(8H)$ and clearance $=h_{support}-f-D/2$. Enter ruling span $L_r=\sqrt{\sum L_i^3/\sum L_i}$. These equations are derived here from cable geometry and linear elasticity; a bisection solve recovers the reference state. Sag above 8% of either inspected or ruling span is rejected.

The effective thermal expansion input uses µm/(m·K) so its full value is readable (default 19). It is explicitly converted to 1/K before the elastic thermal state equation. Mechanical screening uses the hottest sample over the complete current-step transient, including the initial state of a cooling step. The clearance screen takes the minimum over the complete transient clearance vector.

• One horizontal, unbundled bare conductor; level supports and level ground. Current is RMS per conductor; table AC resistance is for 60 Hz.
• Nexans Drake ACSR and Greeley AAAC data were retrieved on 2026-10-27. Diameter, area, mass and AC resistance at 75 °C are manufacturer values. Drake constituent masses are separately rounded and differ slightly from total mass; constituent masses set thermal capacity, total mass sets gravity load.
• Default emissivity/absorptivity 0.8 are screening choices consistent with NREL 91599, not immutable material properties. Default 900 J/(kg K) aluminium/alloy and 480 J/(kg K) steel heat capacities are constant approximations. Review them for the conductor and temperature.
• Default 75 GPa effective modulus and 19 × 10⁻⁶/K thermal expansion are editable ACSR screening assumptions. They are not catalogue guarantees. When selecting AAAC, review values nearer 69 GPa and 23 × 10⁻⁶/K, along with actual stringing tension.
• Surroundings radiate at ambient air temperature. Dry conductor: no rain/evaporation, icing, wind mechanical load, solar obstruction, bundle wake interaction or internal temperature gradient.
• The example-day weather is explicitly synthetic; there is no live weather feed. Local solar time is used, not civil clock time.
• The diagram adjusts vertical scale to make sag readable. Drawing readouts use SI units; input and result-card units can be switched to US units.

Screening only. A qualified engineer must check thermal ratings, mechanical strength, sag and surveyed clearances before operational or design use. Installation work belongs to qualified personnel.

Named thermal basis: IEEE Std 738-2012, incorporating Cor 1-2013 (DOI 10.1109/IEEESTD.2013.6692858); CIGRE TB 601 (2014) is the related methodology, not an assertion of complete implementation. Check against the standard in force. The independent radiation regression values are from CIGRE TB 207 (2002) as published in LineRate.

The tool limits ambient weather to −40…60 °C, calculated conductor temperatures to at most 150 °C, elevation to 0…3000 m, and Reynolds number to 50,000. The steady solver searches up to 250 °C only to detect out-of-range loading; results are withheld above the valid range. Linear resistance extrapolation must remain positive at −40 °C. Very low wind is handled by natural convection; wind uncertainty and local sheltering are not quantified.

The reported ampacity is a thermal limit only. Clearance can govern at a lower temperature; check the clearance warning and the entered clearance requirement separately. This is not an emergency-duration rating, clearance certificate, forecast-based dispatch tool or full sag-tension design. Excludes creep, stress-strain nonlinearity, permanent stretch, ACSR load transfer/knee point, annealing, unequal support levels, insulator movement, lateral blowout, ice, wildfire, connector limits and bundle interactions.

FERC Order No. 881 (2021) is regulatory context reviewed on 2026-10-27. Its AAR framework includes updated ambient forecasts and absence of solar heating at night; the fixed-sun ambient-only comparison here is a sensitivity calculation, not compliance with Order 881 or a transmission provider's tariff. Actual rating procedures and applicable clearance rules must be supplied and checked by the responsible engineer.

The Reynolds-number validity check covers present weather, ambient-only reference weather (including its example-day comparison), every ambient/wind sensitivity sample and the angle sweep. Present and example-day thermal simulations additionally use conservative bounds: the coldest applicable air temperature for film properties, paired with the maximum applicable wind speed. A bound above 50,000 rejects the calculation even if a less conservative paired-weather evaluation could pass. No out-of-range chart is used as a valid result.