What is the Peek formula?

The Peek formula (1929) gives the empirical power loss due to corona on a transmission line conductor: P = 241/δ × (f+25) × √(r/d) × (V − Vc)² × 10⁻⁵ kW/km/phase, where δ is relative air density, f is frequency (Hz), r is conductor radius (cm), d is geometric mean spacing (cm), V is operating line-to-neutral voltage (kV, RMS), and Vc is the critical disruptive voltage.

What is critical disruptive voltage?

The critical disruptive voltage (Vc) is the minimum voltage at which corona begins. Using Peek: Vc = 21.2 × δ × r × ln(d/r) kV (line-to-neutral, RMS). Below this voltage, corona loss is zero.

What is relative air density (δ)?

δ = (3.92 × b) / (273 + t), where b is barometric pressure in cm Hg and t is temperature in °C. At sea level, standard conditions (76 cm Hg, 25 °C), δ ≈ 1.0. At higher altitudes, δ decreases and corona loss increases.

Why does conductor size matter?

Larger conductors have a lower electric field gradient at their surface for the same voltage, which raises the critical disruptive voltage and reduces or eliminates corona loss. Bundled conductors work on the same principle.

Is this formula accurate for all cases?

The Peek formula is a useful first-order estimate. It underestimates loss in wet or contaminated conditions and may not apply to bundled conductors directly. For precise design, field measurements or advanced EMT simulation are recommended.

Corona Loss Calculator

Compute corona discharge power loss per kilometer on a high-voltage transmission line using the Peek empirical formula.

Line Parameters

Line-to-Line Voltage (kV)

System Frequency (Hz)

Conductor Outer Radius, r (cm)

Typical ACSR: 0.6–2.0 cm

Geometric Mean Spacing, d (cm)

For equilateral spacing, d = phase spacing. For flat, d = ∛(D₁₂·D₂₃·D₁₃).

Relative Air Density, δ

Sea level ≈ 1.0. Use δ = (3.92·b)/(273+t) for altitude correction.

Air Density Helper (optional)

Barometric Pressure (cm Hg)

Temperature (°C)

Critical Disruptive Voltage

—

kV (line-to-neutral, RMS)

Operating Voltage V_n

—

kV (line-to-neutral, RMS)

Loss per Phase

—

kW / km

Total 3-Phase Loss

—

kW / km

Voltage Sensitivity (total 3-phase kW/km)

V_LL (kV)	Loss (kW/km)	vs. input

Summary

Corona discharge on high-voltage transmission lines wastes energy, causes radio interference, and degrades hardware. This calculator applies the Peek empirical formula to estimate corona power loss per kilometer per phase and total three-phase loss, given line voltage, conductor geometry, frequency, and relative air density. It also computes the critical disruptive voltage so you can see whether your design operates in the corona region.

How it works

Compute critical disruptive voltage: Vc = 21.2 × δ × r × ln(d/r) kV.
If operating voltage (line-to-neutral) is below Vc, corona loss is zero.
Above Vc, apply Peek: P = (241/δ) × (f+25) × √(r/d) × (V − Vc)² × 10⁻⁵ kW/km/phase.
Multiply by 3 for total three-phase loss per km.
Results update instantly as you change any input.

Use cases

Estimate energy waste from corona discharge on overhead HV lines.
Compare conductor sizes to find the most corona-efficient design.
Check whether a line voltage exceeds the critical disruptive voltage.
Evaluate the effect of altitude (lower air density) on corona losses.
Assist in transmission line design courses and power engineering studies.
Quick sanity-check during substation or line upgrade feasibility studies.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu