A Mathematical Model of the “Network–Nonlinear Load” System with an Active Power Filter in the Mode of Compensation of Higher Harmonics

A mathematical model is presented that provides a description of electromagnetic processes in the “network–load–active power filter” system. In particular, by specifying the shape of the load-current and the network-voltage parameters, it is possible to determine the quality indicators of electric power at the common connection point: the quality indicators of the network voltage and currents in network and load sections. The model also makes it possible to calculate the instantaneous values of currents in the power circuit of the most active filter, thus enabling the power loss in the filter to be estimated. The mathematical model is based on the spectral method of analysis of periodic nonsinusoidal processes and the use of switching functions. It is a feature of the model that it enables an analysis of electromagnetic processes with various structures of the active power filter by only making minimal changes. It is also possible to take into account distortions of the network voltage shape and use various algorithms for compensation of higher harmonics. Electromagnetic analysis has been performed for a “network–nonlinear load” system in which harmonics are compensated by an active power filter based on a two- and three-level converter and by using passive first- and third-order PWM harmonic filters. The simulation was carried out for three algorithms of active power-filter operation in a distorted network, which provide maintaining of a constant active power consumption, a sinusoidal shape of the mains current, and a power factor equal to 1.