This paper presents control strategies for cascaded H-bridge multilevel active power filters (APFs). A current loop controller is implemented using a proportional-resonant (PR) regulator, which achieves zero steady-state error at target frequencies. The power balancing mechanism for the dc-link capacitor voltages is analyzed and a voltage balancing controller is presented. To mitigate the picket-fence effect of the conventional FFT algorithm under asynchronous sampling conditions, the Hanning Windowed-FFT algorithm is proposed for reference current generation (RCG). This calculates the frequency, amplitude and phase of individual harmonic components accurately and as a result, selective harmonic compensation (SHC) is achieved. Simulation and experimental results are presented, which verify the validity and effectiveness of the devised control algorithms.