Filter & compensation design

This page designs the passive filter branches that bring harmonic distortion back inside its limits, and re-checks whether they are safe to add. It is studyOptions.enablePassiveFilterDesign in engines/passive-filter.js, which selects single-tuned, C-type or second-order high-pass branches, sizes each one from the measured harmonic current in the target order, and reports the branch impedance and the shunt ratio at that order. The design is then verified by feeding the branches into the same Z(h) model used by the resonance scan and comparing the per-order content and the THD before and after, with the limit verdicts taken from the four-standard harmonic limit source. The page also shows the series-reactor recommendation (study "reactor") and its resonance re-check.

Once harmonics are over the limit there are only two options — reduce the source or filter the current — and a filter is a piece of equipment that has to be specified, priced and checked. A wrongly tuned branch does not just fail to help: it adds a new resonance, amplifies a non-target order and can destroy its own capacitors. The value of this page is that the deliverable is a specification (C, L, kvar, tuned order, quality factor) together with the evidence that the distortion target is met and that nothing else got worse.

Input: the measured per-order harmonic currents and content from the harmonic study, the target orders (for example 5, 7, 11, 13), the branch type, the quality factor, the tuning margin and the external Ssc → chain: the tuning order is h_r = n·(1 − δ) with δ defaulting to 6% tuning margin, the reactance percentage is p = 1/h_r², and from the base-frequency capacitive reactance Xc come C = 1/(ω1·Xc), L = p·Xc/ω1 and R = Xc/(h_r·Q); the branch rating follows the measured harmonic current, with the fundamental current at least K_i times the harmonic current (K_i default 1.5, which keeps the branch rms at about 1.20 of the fundamental, inside the common 1.35 ceiling), kvar = 3·Uph·I1 rounded up to the next standard step → the designed branches are added to the same Z(h) model as extra branches, the per-order amplification ratio is re-read and multiplied by the measured values to obtain the after-content and after-THD → those are judged against the harmonic limit source → the resonance re-check verifies that a new parallel anti-resonance does not land on a dominant order that is not a design target → output: the branch list with C, L, kvar, tuned order and shunt ratio, a summary with the THD before and after, whether the target is met and which limit set was used, and notes. Linkage: capacitor kvar or detuning changes the system resonance and therefore the filter selection; the target orders decide the number and rating of branches; cable earth capacitance changes the system impedance and hence the shunt ratio; and because the branches themselves change the system impedance, the result is visible both as a lower THD on the harmonics page and as a moved resonance point on the resonance page. Approximations, all disclosed: the branch equations follow PSCAD / IEEE passive-filter design practice for the three types, including the 6% tuning margin; the kvar rating is rounded up to standard steps; the design is verified through the same linear frequency-domain model rather than by a nonlinear or time-domain simulation.