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This paper compares the popular control methods for two dominant types of active power filters (APFs). With the equivalent transformation of their control diagrams, the recently proposed current-source control method for series active power filter (SAPF) is revealed to have the same control structure as the traditional voltage-source control method therefore have same compensation performances. Similarly, two kinds of popular control methods for parallel active power filter (PAPF) are also compared and found to have the similar control structure. The recently proposed PAPF control scheme without harmonics detection is revealed as a reduced version of the traditional control scheme with harmonics detection. Therefore both have same basic control principles regarding load current harmonics compensation. A general expression of the control methods for PAPF is then proposed in the form of both a control diagram and a set of equations based on current detection. With a particular set of filter gains of the three detected currents, each particular control scheme can be specifically identified and described by the general expression. Subsequently the 64 possible sets of filter gains are examined by the proposed necessary conditions to locate practically valid control schemes. Finally 4 valid control schemes come out and among which some are schemes that have never been reported before. With the comprehensive comparison of the control methods and the proposed general expression in this paper, the essential relationships of the control methods are revealed, some misinterpretations from previous publications are clarified, and some new control schemes are obtained.