Electrical Power Quality & Data-Center Distribution
Harmonic THD, True Power Factor & K-Factor Formula
Calculate IEEE 519 Current Total Harmonic Distortion (THD_I), Total RMS Current, True Total Power Factor PF_disp / SQRT(1 + THD_I^2), and UL 1561 Transformer Eddy-Current K-Factor.
Stop reading cos(phi_1) meters alone on nonlinear VFD and rectifier loads!
Old induction-disc and fundamental-phase meters measure only 60/50 Hz Displacement Power Factor PF_disp = COS(phi_1). Six-pulse variable-frequency drives (VFDs), EV fast chargers, and switch-mode server PSUs draw heavy 5th and 7th harmonic currents (I_5, I_7) that produce ZERO net real watts while inflating Total RMS Current I_rms = SQRT(I_1^2 + I_5^2 + I_7^2)! Under IEEE Std 519, Current Total Harmonic Distortion is THD_I = SQRT(I_5^2 + I_7^2) / I_1, collapsing True Power Factor to PF_true = PF_disp * (I_1 / I_rms) = PF_disp / SQRT(1 + THD_I^2)! Worse yet, transformer winding eddy-current heating scales with harmonic order SQUARED (h^2: 25x at h=5, 49x at h=7!), quantified by UL 1561 Transformer K-Factor = (I_1^2 * 1^2 + I_5^2 * 5^2 + I_7^2 * 7^2) / I_rms^2!
Verify on a 6-Pulse VFD Feeder—Fundamental_Current I_1 = 80 A (B2), 5th_Harmonic I_5 = 48 A (B3), 7th_Harmonic I_7 = 36 A (B4 -> Harmonic RMS = SQRT(48^2 + 36^2) = 60 A), and Displacement_PF = 0.95 (B5): Current THD_I is 60 / 80 = 0.7500 (75.00% in E2); Total Feeder RMS Current is SQRT(80^2 + 60^2) = 100.00 A (E3); True Total Power Factor drops from 0.95 to 0.95 * (80 / 100) = 0.7600 (E4); and Transformer K-Factor jumps to (6,400*1 + 2,304*25 + 1,296*49) / 10,000 = 12.75 (requiring a K-13 rated transformer in E5)!
| IEEE 519 / UL 1561 Metric (I1=80A, I5=48A, I7=36A, Displacement PF=0.95) | Formula | Verified Output |
|---|---|---|
| Current Distortion Ratio THD_I | SQRT(I_5^2 + I_7^2) / I_1 | 0.7500 (75.00%; 0.0000 Linear) |
| Total Feeder RMS Current (A) | SQRT(I_1^2 + I_5^2 + I_7^2) | 100.00 A (+25% Thermal Amps) |
| True Total Power Factor PF_true | PF_disp * (I_1 / I_rms) | 0.7600 (0.9500 Linear) |
| UL 1561 Transformer K-Factor | (I1^2*1 + I5^2*25 + I7^2*49) / Irms^2 | 12.75 (Specify K-13; 1.00 Linear) |
UL 1561 Transformer Harmonic K-Factor Formula
Validate I_1 > 0, non-negative harmonic currents I_5, I_7 >= 0, and 0 < PF_disp <= 1!
=LET(i_f1, B2, i_h5, B3, i_h7, B4, pf_d, B5, IF(OR(i_f1 <= 0, i_h5 < 0, i_h7 < 0, pf_d <= 0, pf_d > 1), "Invalid Harmonic Spectrum", LET(sm_2, (i_f1 ^ 2) + (i_h5 ^ 2) + (i_h7 ^ 2), wt_k, (i_f1 ^ 2) * 1 + (i_h5 ^ 2) * 25 + (i_h7 ^ 2) * 49, ROUND(wt_k / sm_2, 2))))Active Harmonic Filter / Pure Sinusoidal Verification (I_5 = 0, I_7 = 0)
Install an active harmonic filter zeroing B3 = 0 and B4 = 0: THD_I drops to 0, RMS current drops to 80 A, True PF restores to 0.95, and K-Factor equals 1.00!
=IF(ISTEXT(E5), E5, ROUND(B5 * (B2 / E3), 4))Try the example
Use the original values or change them to test your understanding.