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Parabolic carrier Pulse Width Modulation (PWM) method is considered as one of the direct current control methods for the Voltage Source Converters (VSCs). This method has an excellent dynamic response. Besides, it offers a constant switching frequency by employing a pair of parabolic PWM carriers. However, it suffers from some drawbacks and limitations. The major drawback of this method is its sensitivity to the inductance variations. In other words, in grid-connected applications, the exact value of grid inductance should be known to achieve a proper performance. Moreover, it is essential that during each switching cycle, the voltage at the point of common coupling remains constant. In grid connected applications such as active power filter, these drawbacks may lead to operation at variable or non-expected frequencies. Therefore, this paper provides suggestions to deal with the situation. In this paper, by applying the conventional method, the aforementioned problems are examined in a grid-connected active power filter. It is shown analytically that by using the proposed method, the problem of sensitivity to inductance is overcome and the necessity for a constant voltage at the point of common coupling in a switching period will be solved as well. The simulation and experimental results are presented. [ABSTRACT FROM AUTHOR]