About Harmonic Distortion & K-Factor Calculator
The harmonic distortion calculator takes a measured harmonic spectrum (the fundamental plus the magnitude of each harmonic order) and returns the total harmonic distortion (THD), the true RMS, and the transformer K-factor. THD is defined as the RMS of all harmonics above the fundamental divided by the fundamental, expressed as a percentage; a pure 60 Hz sine has THD = 0.
The K-factor weights each harmonic by the square of its order to capture the extra eddy-current heating that harmonics cause in a transformer, following IEEE C57.110. A pure fundamental gives K = 1. Enter each harmonic order and magnitude (in amps for current or volts for voltage) and the tool computes THD, true RMS, the K-factor, and the recommended K-rated transformer, with IEEE 519 compliance guidance.
How It Works
- Enter the harmonic spectrum: one row per harmonic order h (h = 1 is the fundamental) with its RMS magnitude.
- The calculator sums the squares of the harmonics above the fundamental to get the harmonic RMS, then divides by the fundamental for THD.
- It computes the true RMS as the square root of the sum of all squared magnitudes including the fundamental.
- It evaluates the K-factor as sum(I_h(pu)^2 * h^2) / sum(I_h(pu)^2), where I_h(pu) = I_h / I_1, and maps it to the next standard K-rated transformer.
Worked Example
A nonlinear load draws a spectrum of I1 = 100 A, I3 = 30 A, I5 = 20 A, I7 = 10 A. The harmonic RMS is sqrt(30^2 + 20^2 + 10^2) = sqrt(1400) = 37.42 A, so THD = 37.42 / 100 = 37.4%. The true RMS is sqrt(100^2 + 1400) = sqrt(11400) = 106.77 A. For the K-factor the per-unit magnitudes are 1.0, 0.3, 0.2, 0.1: the numerator is 1*1 + 0.09*9 + 0.04*25 + 0.01*49 = 3.30 and the denominator is 1 + 0.09 + 0.04 + 0.01 = 1.14, so K = 3.30 / 1.14 = 2.89. A K-4 rated transformer is recommended.
Formulas
- Total harmonic distortion
THD = sqrt( sum_{h>=2} I_h^2 ) / I_1 * 100%- True RMS
I_rms = sqrt( sum_{h>=1} I_h^2 )- Transformer K-factor (IEEE C57.110)
K = sum( I_h(pu)^2 * h^2 ) / sum( I_h(pu)^2 ), I_h(pu) = I_h / I_1- Reference checks
pure fundamental: THD = 0, K = 1 | THD relative to true RMS: THD = sqrt(I_rms^2 - I_1^2) / I_1
Standards & References
- IEEE 519 (Harmonic Control in Electric Power Systems)
- IEEE C57.110 (transformer loading with nonsinusoidal currents)
- UL 1561 (K-rated dry-type transformers)
Frequently Asked Questions
What is total harmonic distortion (THD)?
THD is the ratio of the RMS of all harmonic components above the fundamental to the fundamental, expressed as a percentage. It measures how far a waveform departs from a pure sine. A clean 60 Hz sine has THD = 0, while heavily distorted nonlinear loads can exceed 40 percent current THD.
What is the transformer K-factor and why does it matter?
The K-factor weights each harmonic by the square of its order, reflecting that eddy-current losses grow with frequency squared. It quantifies the extra heating harmonics cause in a transformer. A pure fundamental gives K = 1; the more high-order harmonic current present, the larger the K-factor, and the higher the K-rated transformer needed.
How do I choose a K-rated transformer?
Select a standard K-rating (K-4, K-13, K-20, K-30) at or above the computed K-factor. For example a K-factor of 2.9 calls for a K-4 unit, while a K-factor of 5 calls for K-13. K-rated transformers have design features (larger neutrals, transposed windings, reduced flux density) that tolerate the additional harmonic heating.
What does IEEE 519 limit?
IEEE 519 sets limits on voltage and current distortion at the point of common coupling. Current limits are expressed as total demand distortion (TDD) and depend on the short-circuit-to-load ratio I_sc/I_L; for instance systems with I_sc/I_L below 20 are limited to about 5 percent TDD. Voltage THD is commonly limited to 5 percent for systems at or below 69 kV.