Analysis of a controllable LC-filter for compensation of specific harmonics

In this paper a recently proposed circuit to compensate harmonics is analysed. The circuit consists of an LC-filter which is connected in series with an electronic switch, which enables control of the system. The compensator is intended to be connected in parallel to a harmonic-generating appliance, such as line commutated converters. The system is analysed for the third harmonic by applying the principle of superposition. The circuit is considered to be excited by the undistorted grid voltage with the so called switch voltage superimposed on it. After fourier-series expansion of the switch voltage, linear circuit theory is applied. Based on the analysis, a mathematical relation between the harmonic and major control and circuit parameters is derived. The obtained formula´s can be used for purpose of control and design for a system with one zero current interval. The model has been verified by comparison with experimentally obtained results. The analysis led to following conclusions: 1) for control with a single dead time, the current amplitude is roughly proportional to cos (ωt₁), where t₁ is the firing instant with respect to the -/+ zero crossing of the phase voltage. 2) phase and amplitude cannot be controlled independently if one zero current interval is applied 3) for a phase angle of 90° the amplitude has a maximum, which is for many applications an acceptable combination.