Review of AC chargers topologies with active power factor correction are considered in the paper. Single and double-stage charger topologies are highlighted and the feasibility of using the first group of converters is substantiated because of its smaller size and simpler structure. Among single-stage converters, the advantages of modular converters based on SEPIC topologies are emphasized because of minimal dynamic losses, a simple algorithm, and circuit implementation of power factor correction at the boundary condition mode (BCM) of input current and small dimensions. The operation of modular converters is analyzed on the example of a two-cell converter and the principle of improving the shape of the input current under the condition of shifting control pulses of each cell is shown. As a result, the functional dependence of the electricity quality parameters (power factor PF and the total harmonic distortion THD) on the pulse ratio of each converter cell is established. Since it is difficult to comply BCM in real converters, and in continuous mode the shape of the input current is distorted, such converters operate in the discontinuous conduction mode (DCM) of input current. Based on the analysis of equivalent circuits in three intervals of operation of the SEPIC converter - interval of increase of input current, interval of decrease of input current and interval of zero pause - its mathematical model was created. It is shown that the increase of relative zero current interval duration significantly worsens the value of the power factor PF and the total harmonic distortion THD. As a result, the PF and THD parameters are functions of duty cycle and the relative zero current interval duration and have a complex relationship. Therefore, in order to estimate the number of converter cells that provide the required PF and THD values, it is advisable to derive these dependencies in analytical form, based on the use of a Double Fourier series. The obtained dependencies simplify the selection of the number of cells of the converter for a given range of duty cycle and the relative zero current interval duration. PF and THD dependencies for two, three and four cells are constructed on the basis of the derived formulas.