Unified Sensitivity Analysis of Powers and Distortion Quantities in Non-Sinusoidal Regime

Non‑sinusoidal operation is very common in modern power networks and affects both equipment and system‑level performance. Real situations involve significant changes in the quantities values of electrical networks and determining the limitations imposed by industrial equipment is particularly important. In this case sensitivity analysis can be extremely useful. This paper unifies two complementary approaches—sensitivity‑based evaluation of reactive/apparent (Q/Sa) power and sensitivity‑based evaluation of active power (P) and total voltage and current harmonic distortion (THDu, and THDi) where also included the power factor (KP) —into a single methodology. For these key quantities of nonsinusoidal regime P, Q, Sa, KP, THDu, and THDi new relations are introduced with respect to harmonic weightings of voltage (rk) and current (pk). Thus, the modification of one or several parameters simultaneously rk or/and pk is reflected in the calculated sensitivities. The second order sensitivities are used to analyze the values of key quantities when two set of harmonic weightings are changed. A compact algorithm based on MATLAB is provided and the errors between the values obtained by classical definition and by sensitivity relations are calculated. The obtained results validate the accuracy of proposed method and the harmonic mitigation solutions reflected by the values of THDu, and THDi is compliant with IEEE Std 519‑2022.