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In this research, we discuss the construction of the analytic solution of the homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves a local fractional order derivative, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L2 [0, l], the solution is constructed in the form of a Fourier series including the exponential function. The illustrative examples present the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.
The main topic of the paper is the large signal averaged model of a switch-mode flyback power converter. The use of the large-signal averaged models of switching converters allows for fast simulation of power systems. The known averaged models of a flyback are based on the state-space averaging or switch-averaging approach. The model presented in the paper is derived with the use of the separation of variables approach and include parasitic resistances of all converter components. The limitations of the model accuracy are discussed. The calculations based on the averaged model are compared with detailed full-wave simulations and measurements results.
Small-signal transmittances: input-to-output and control-to-output of BUCK converter power stage working in CCM or DCM mode are discussed. Ideal converter case and converter with parasitic resistances are considered separately. Derivations of small-signal transmittances, based on different approaches to finding the converter averaged models, are presented and the results are compared. Apart from theoretical considerations, some results of numerical calculations are presented.
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