Free Tool · Neher-McGrath · IEEE 835 / NEC 310 · Soil 3-Zone Model

Cable Ampacity Calculator

Neher-McGrath ampacity calculation for MV/HV underground cables (IEEE Std 835). Enter soil thermal resistivities using the 3-zone model, installation type, burial depth, and load conditions — output includes rated ampacity, operating temperature, CYMCAP trigger flags, and DC string sizing (NEC 690). Universal MV/HV — not solar-specific. See note below.

ⓘ Universal MV/HV — applies to any underground cable installation. Solar context: includes DC cable sizing per NEC 690 with bifacial I_mp gain basis.

ground surface depth d Cu/Al T₁ cond→insul T₂ insul→jacket T₃ jacket→soil T₄ soil→ambient T_c − T_a = I² · R_ac · (T₁ + T₂ + T₃ + T₄)
Cross-links: Soil Resistivity IEEE 81 · Grounding Grid IEEE 80 · BESS Grid Connection
Cable Parameters
Installation Conditions

3-Zone soil thermal resistivity

3-zone: 24"×24" dry-out centered on cable (90% compaction, 0% moisture) + recompacted zone to surface + native zone. For bore: 2-zone model (dry-out + native).

Zone ρ (°C·cm/W) Description
1 Dry-out 24"×24", 90% compaction
2 Recompacted Backfill to surface
3 Native Undisturbed soil

Default 0.65 — owner approval needed to reduce

AC/DC Crossing Configuration
Adjacent heat source (AC or DC crossing)
DC String Sizing (NEC 690)
Enable DC string sizing
Ampacity Results
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A
Rated Ampacity I_z
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°C
Operating Temp T_c
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Utilization I_d/I_z
Configuration
Installation—
Burial depth—
Soil effective ρ—
Parallel cables—
Thermal
Thermal resistance R_th—
Skin/proximity factor k_s—
Load factor L_f—
Temperature Check
Ambient T_a—
Limit (rated)—
Actual T_c—
Status—
Methodology
Neher-McGrath (IEEE Std 835)
T_c − T_a = I² × R_ac × (T_1 + T_2 + T_3 + T_4)

Solve iteratively for I, accounting for temperature-dependent resistance and load factor L_f. T_1–T_4 are thermal resistances from conductor to ambient.

IEC 60287 Relationship
I = √[(T_d − T_a) / (ρ_eff × R_th × k_p)]

IEC 60287-1-1 Eq. 1 is the steady-state form. Use CYMCAP for full 3D thermal field in complex geometries (trench fill, crossings, bundle effects).

DC String (NEC 690)
I_z = I_base × f_t | ΔU = 2·ρ·L·I_mp / S

NEC 2023 Table 310.17 base ampacity × ambient correction (Table 310.15(B)(1)). Voltage drop ≤ 2% per PV design practice. Bifacial gain: add 10–15% to I_mp.

Related Tools

Soil Resistivity — IEEE 81 Earthing Grid — IEEE 80 BESS Grid Connection Cable Sizing — EN 60364-5-52

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FAQ
The Neher-McGrath method (IEEE Std 835) solves a simplified thermal circuit representing heat flow from the conductor through insulation and sheath to the surrounding medium (soil, conduit, air). The key equation is: T_c − T_a = I² × R_ac × (T_1 + T_2 + T_3 + T_4), where T_1–T_4 are thermal resistances between conductor and ambient. The iterative solution accounts for load cycling via the load factor L_f. This method underpins IEC 60287 and is the industry standard for MV/HV underground cable ampacity.
The 3-zone model divides the soil around a buried cable into: (1) dry-out zone — 24"×24" (610 mm) centered on the cable, 0% moisture, 90% compaction — typically ρ = 90–150 °C·cm/W for dry sandy soil; (2) recompacted zone — backfilled to surface, ρ = 70–100 °C·cm/W; (3) native zone — undisturbed soil, ρ = 40–80 °C·cm/W in wet clay. The effective trench thermal resistivity is the depth-weighted average. For directional drilling (bore), a 2-zone model (dry-out + native) is used.
CYMCAP is required when: (1) any cable operates above 90°C (or above rated temp) — full thermal field resolution needed; (2) two or more parallel cables cross two or more other cables at any angle — mutual heating effects are 3D; (3) AC/DC crossings are present — harmonic currents in DC return paths induce voltages on adjacent AC cable sheaths. A justification waiver is required for flags marked "waiver: true" in the output.
The load factor L_f (default 0.65) accounts for the fact that cables rarely carry rated current continuously. A lower load factor allows higher cyclic ampacity because the soil has time to cool between peak loads. Neher-McGrath corrects the ampacity iteratively: I_corr = √[(T_d − T_a) / (R_th × k_s − L_f × R_th × I²)]. Owner approval is required to reduce below 0.65.
NEC 2023 Table 310.17 gives ampacity for single-conductor cables in free air (90°C XLPE). Apply ambient temperature correction (Table 310.15(B)(1)): at 45°C ambient, f_t = 0.87. Voltage drop is limited to ≤ 2% for DC strings per PV system design practice. For bifacial panels, add 10–15% to I_mp to account for rear-side irradiance gain.
IEC 60287-1-1 Equation 1 is the steady-state form of the same Neher-McGrath circuit: I = √[(T_d − T_a) / (ρ_eff × R_th × k_p)]. IEC 60287 Tables 1–3 provide tabulated values for T_1 (conductor-to-sheath), T_2 (jacket), and T_3 (external) for standard cable constructions. CYMCAP extends IEC 60287 by solving the full 3D heat equation for complex geometries (trench fill, multiple cables, crossing configurations).