Hassane Bouzahir

Chaotic behavior in a switched dynamical system

We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator) which is a Scilab (scientific laboratory) package. The followed approach takes into account the hybrid nature of the circuit.

Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.

Comparison of methods in estimating Weibull parameters for wind energy applications

Purpose The purpose of this study is to select the most accurate and the most efficient method in estimating Weibull parameters at Agadir region in Morocco. Design/methodology/approach In this paper, Weibull distribution is used to model the wind speed in hourly time series format. Since several methods are used to adjust the Weibull distribution to the measured data, in reporting and analyzing the easiest and the most effective method, seven methods have been investigated, namely, the graphical method (GM), the maximum likelihood method (MLM), the empirical method of Justus (EMJ), the empirical method of Lysen (EML), the energy pattern factor method (EPFM), Mabchour’s method (MMab) and the method of moments (MM). Findings According to the statistical analysis tools (the coefficient of determination, root mean square error and chi-square test), it was found that for five months, the MLM presents more efficiency, and for four months, EMJ is ranked first and it is ranked second for February. To select only one method, the selected methods (MLM and EMJ) were compared by calculating the error in estimating the power density using Weibull distribution adjusted by those methods. The average error was found to be −0.51 and −4.56 per cent for MLM and EMJ, respectively. Originality/value This investigation is the first of its kind for the studied region. To estimate the available wind power at Agadir in Morocco, investors can directly use MLM to determine the Weibull parameters at this site.

Estimation of electricity production for a Moroccan wind farm

In this paper, an estimation of the available and produced power in three wind farms (Akhfennir, Tarfaya and Fem El oued) in Southern Morocco is studied. Wind characteristics are analyzed. The Weibull distribution is used to model the wind speed at these wind parks, Fem El oued is the more windy park and where wind speed is more uniform. The monthly estimated available power density is more important in Fem El Oued, so, the investment in terms of increasing the number of wind turbines in this park can be profitable. The average usable power is estimated, Fem El oued has the lowest production because there is less number of wind turbines.

Design optimization of a wind farm layout for maximum wind energy capture: A new constructive approach:

Wind energy is becoming an attractive source of clean energy. However, this type of power source is subject to power reductions due to losses in wind energy conversion system and to frequent changes in wind velocity. For that reason, the important phase of a wind farm design is solving the wind farm layout optimization problem, which consists in optimally positioning the turbines within the wind farm so that the wake effects are minimized and therefore the expected power production is maximized. This problem has been receiving increasing attention from the scientific community. In this article, a mathematical optimization scheme is employed to optimize the locations of wind turbines with respect to maximizing the wind farm power production. To formulate the mathematical optimization problem, we used Jensen’s wake model. We calculate the wake loss and express the expected wind farm power as a differentiable function in terms of the locations of the wind turbines. Furthermore, we develop a new constructive approach to find the best solution to the wind turbines placement problem. Finally, our results are compared with those in some other ealier studies.

Optimization of Design of Wind Farm Layout for Maximum Wind Energy Capture: A New Constructive Approach

Wind energy is becoming an attractive source of clean energy. However, this type of power source is subject to power reductions due to losses in wind energy conversion system and to frequent changes in wind velocity. For that reason, the important phase of a wind farm design is solving the Wind Farm Layout Optimization Problem (WFLOP), which consists in optimally positioning the turbines within the wind farm so that the wake effects are minimized and therefore the expected power production is maximized. This problem has been receiving increasing attention from the scientific community. In this paper, a mathematical optimization scheme is employed to optimize the locations of wind turbines with respect to maximizing the wind farm power production. To formulate the mathematical optimization problem, we used Jensen’s wake model. We calculate the wake loss and we express the expected wind farm power as a differentiable function in terms of the locations of the wind turbines. In this paper Furthermore, we develop a New Constructive Approach (NCA) to find the best solution to the wind turbines placement problem. Lastly, our results are compared with those in some other ealier studies.

Some Stochastic Functional Differential Equations with Infinite Delay: A Result on Existence and Uniqueness of Solutions in a Concrete Fading Memory Space

This paper is devoted to existence and uniqueness of solutions for some stochastic functional differential equations with infinite delay in a fading memory phase space.

Simulation of Piecewise Hybrid Dynamical Systems in Matlab

DC-DC converters are widely used in industrial, commercial, residential and aerospace environments. These circuits are typically controlled by PWM (Piece Wise Modulation) or other similar techniques to regulate the tension and the current given to the charges. The controller decides to pass from one configuration to another by considering that transitions occur cyclically or in discrete time. In order to make the analysis possible, most of mathematical treatments use some techniques that are based on averaging or discretization. Averaging can mean to wrong conclusions on operation of a system. Discrete models do not give any information on the state of the system between the sampled instants. In addition, they are difficult to obtain. In fact, in most cases, a pure analytic study is not possible. Another possible approach to analyze these converters can be done via some models of hybrid dynamical systems. DC-DC converters are particularly good candidates for this type of analysis because of their natural hybrid structure. The nature of commutations of these systems makes them strongly nonlinear. They present specific complex phenomena such as fractals structures of bifurcation and chaos.