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This paper proposes a novel model for a PV cell with parameters variance dependency on temperature and irradiance included. The model relies on commercial available data, calculates the cell parameters for standard conditions and then extrapolates them for the whole operating range. An up-to-date review of the PV modeling is also included with series and parallel parasitic resistance values and dependencies discussed. The parameters variance is analyzed and included in the proposed PV model, where the self-heating phenomenon is also considered. Each parameter variance is compared to the results from different authors. The model includes only standard components and can be run on any SPICE-based simulator. Unlike other approaches that consider the internal temperature as a parameter, our proposal relies on air temperature as an input and computes the actual internal temperature accordingly. Finally, the model is validated via experiments and comparisons to similar approaches are provided.

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In this paper we study in detail a family of continued fraction expansions of any number in the unit closed interval [0, 1] whose digits are differences of consecutive non-positive integer powers of an integer m ≥ 2. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For this expansion, we apply the method of random systems with complete connections by Iosifescu and obtained the solution of its Gauss-Kuzmin type problem.

A new hybrid step-up converter suitable in applications where large conversion ratios are needed is presented. The topology is still simple, containing only one transistor and three diodes. A detailed dc and ac analysis is performed and all design equations are provided. Compared to other topologies of the same type, the proposed converter exhibits lower or equal current and voltage stresses. A state space model is provided including the conduction losses and based on it the audio susceptibility and the control to output function are derived. As the converter is still of second order with the control to output transfer function exhibiting a right half plane zero, controller design is practically the same like in a Boost topology. It is shown how the proposed converter can be used in a photovoltaic system for performing the maximum power point tracking algorithm using the perturb and observe method. All theoretical considerations are verified through simulation and finally validated by practical experiments.

Using the natural extension for θ-expansions, we give an infiniteorder-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion. (2010). Mathematics Subject Classifications

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We consider a family {T N : N ≥ 1} of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from T N , we solve its Gauss-Kuzmin-type problem by applying the theory of random systems with complete connections by Iosifescu. Mathematics Subject Classifications (2010). 11J70, 11K50