Steinmetz system design under unbalanced conditions

Abstract

This paper studies and develops general analytical expressions to obtain three-phase current symmetrization under unbalanced voltage conditions. It proposes two procedures for this symmetrization: the application of the traditional expressions assuming symmetry conditions and the use of optimization methods based in the general analytical equations. Specifically, the paper applies and evaluates these methods to analyze the Steinmetz system design. Several graphics evaluating the error introduced by assumption of balanced voltage in the design areplotted and an example is studied to compare both procedures. In the example the necessity to apply the optimization techniques in highly unbalanced conditions is demonstrated.

Steinmetz Circuit Influence on the Electric System Harmonic Response

“…This is done by considering that the currents injected by the three-phase nonlinear load are a set of positive-sequence ( and where ) since (4) or if they are a set of negative-sequence ( and where ) since (5) where are the phases corresponding to the sequence (e.g., with , ). The consideration about the injected current sequence is correct because the supply voltages are balanced and the Steinmetz circuit consumes symmetrical currents.…”

“…1. Therefore, the procedure to design the Steinmetz circuit determines the analytical expression of the unbalance factor and forces this factor to be zero [4].…”

“…There are different studies on the Steinmetz circuit design under sinusoidal balanced or unbalanced conditions. Some of these studies propose analytical expressions and optimization techniques for its characterization [4].…”

Characterization of Harmonic Resonances in the Presence of the Steinmetz Circuit in Power Systems

“…where the typical limit λ LC = (√3)/2 can be obtained from (4) by imposing τ 1 = 0 (Jordi et al, 2002;Sainz & Riera, submitted for publication). Supply voltage unbalance is considered in (Qingzhu et al, 2010a(Qingzhu et al, , 2010b by applying optimization techniques for Steinmetz circuit design, and in (Jordi et al, 2002;Sainz & Riera, submitted for publication) by obtaining analytical expressions for the symmetrizing reactances.…”

“…Supply voltage unbalance is considered in (Qingzhu et al, 2010a(Qingzhu et al, , 2010b by applying optimization techniques for Steinmetz circuit design, and in (Jordi et al, 2002;Sainz & Riera, submitted for publication) by obtaining analytical expressions for the symmetrizing reactances. However, the supply voltage balance hypothesis is not as critical as the pure Steinmetz circuit inductor hypothesis.…”