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# Modelling of Power Factor Correctors on the Basis of an Averaging Method

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G.A. Belov, G.V. Malinin, A.V. Serebryannikov

A power factor correctors (PFC) concern essentially nonlinear non-stationary discrete systems that complicates their analysis and calculation. Modelling of PFC with use of existing standard programs, for example, in the environment of MatLab-Simulink, leads to slowly working models that complicates their use for the analysis and synthesis of systems. At the same time it appears, that at neglect some details of processes of power part of PFC, such as high-frequency pulsations of an entrance current and target pressure, probably considerable simplification of model and subsequent research of PFC with its use. Such approach is based on the averaging method which application is possible, as frequency of switchings of the power transistor in PFC, reaching hundreds kilohertz, on three order exceeds frequency of a power line. In work models of PFC which is based on such approach, for two groups of schemes are proved: 1) PFC, working in a mode of a continuous current of a power throttle, with a two-planimetric control system; 2) PFC with unlocking of the power transistor at zero of a current of a throttle. The contour of regulation of a current contains pulse-width modulator (PWM) and is discrete by the nature. It is known, that the analysis of a contour of regulation of a current of the pulse converter an averaging method in schemes of the first group we will admit, if the sufficient stock of its stability is provided. Stability of a contour of regulation of a current is necessary for checking taking into account its step-type behaviour, for example by means of linear pulse structural model, or on linearized difference equations describing processes in this contour. In offered model of PFC restriction of average value of a current of the throttle, considering restriction of instant value of this current available in the real scheme, realised by deenergizing of the power transistor is provided at achievement of a threshold of restriction by instant value of a current. Instant value of a current in model is supervised implicitly. In the second scheme the average nonlinear differential equation describing change of target pressure, is shown by variable replacement to the linear equation, that essentially simplifies model and accelerates calculations. Dynamic models of PFC proved in work differ limiting simplicity, but correctly reflect all their basic operating modes, including at the big indignations on a power line and loading, allowing to define the curve changes averaged during switchings in time of the basic variables characterising a condition of system. Real experimental samples of proof-readers of a power factor allow to replace these models at their designing, accelerating and reducing the price of process of creation of modern electronic and electrotechnical equipment. Models are convenient for definition of power characteristics of PFC, such as efficiency and a power factor, and also indicators of quality of processes of regulation of an entrance current and target pressure. Parameters both linear, and nonlinear blocks of models are easily reconstructed. Numerical values of some parameters are resulted only as an example.
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