Comparisons Between the p--q and p--q--r Theories in Three-Phase Four-Wire Systems

This paper presents a comparative analysis between results from applications of the
p-q
and the
p-q-r
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
p-q
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
pqr
coordinates that is needed in the
p-q-r
theory. Simulation results are presented for the purpose of comparing the performance of both control methods.