Comparisons Between the <i>p--q</i> and <i>p--q--r</i> Theories in Three-Phase Four-Wire Systems

This paper presents a comparative analysis between results from applications of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-q</i> and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-q-r</i> theories in shunt active power filters for three-phase four-wire systems, discussing aspects related to the influence of the system voltage in the control methods that calculate the compensating currents. It is shown that in some cases, a preprocessing of the system voltage is required if the goal is to achieve sinusoidal compensated currents. On the other hand, when the goal is to compensate zero-sequence current, the need of energy storage elements in the active filter is discussed. In this case, if zero-sequence components are present simultaneously in the system voltage and load current, they produce zero-sequence power flow, and the control methods based on both theories must contain additional calculations to allow the elimination of energy storage elements in the active filter. A control strategy based on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-q</i> theory is proposed to eliminate the neutral current without the need of energy storage elements, with the advantage of avoiding the extra transformation from alphabeta0 to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pqr</i> coordinates that is needed in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-q-r</i> theory. Simulation results are presented for the purpose of comparing the performance of both control methods.