Cross-Order Distortion Descriptor (CDD) for Paired Voltage and Current Harmonic Spectra: Separating THD-Determined and Order-Dependent Parts

In power-quality studies of power electronic converters, total harmonic distortion (THD) summarizes voltage and current spectra separately, obscuring their joint organization across harmonic orders. We develop the Cross-Order Distortion Descriptor (CDD), a magnitude-only descriptor of paired per-order root-mean-square (RMS) voltage and current spectra. In its exact factorization, the fundamental-related part is fixed by the fundamental RMS product and the two THD values, whereas the harmonic–harmonic part additionally depends on κ∈[0,1], the complement of the normalized same-order spectral overlap, which approximately locates a record below the THD-imposed ceiling. In the pair with the largest separation in κ among 2500 simulated diode-bridge rectifier supply spectra with equal voltage THD and nearly equal current THD, κ=0.96 and 0.34 accompany different conduction intervals; reversing the third-harmonic phase, with voltage magnitudes unchanged, reverses that ordering. In induction-motor records, the harmonic–harmonic part of CDD rises by 11.8% through κ at a nearly unchanged scale under illustrative error scenarios, whereas photovoltaic-inverter tests approximately double both THD values at nearly constant κ. In capacitor records, κ nearly follows joint spectral concentration; in data-center and capacitor records, harmonic–harmonic contributions stay small at low voltage THD, as the bounds require. CDD characterizes paired harmonic spectra, separating THD-determined and order-dependent contributions.