Martin P. Calasan

Simple Sensorless Control for High-Speed Operation of Switched Reluctance Generator

High-speed operation of the switched reluctance generator (SRG) in discontinuous conduction mode (DCM) as well as in continuous conduction mode (CCM) is considered in this paper. Very simple control method of SRG that enables stable SRG operation in CCM without using the rotor position information is proposed. Although the conventional SRG power converter can be used to implement this sensorless method, two more suitable converter topologies are also proposed. These topologies are based on diode bridge rectifiers and do not contain switch components. The output power of SRG is controlled by regulating the dc excitation current. The simulation results show that the proposed control method provides much more output power of SRG at high speeds than conventional control in DCM, and the same power as conventional control in CCM. Experimental results confirm validity and effectiveness of the proposed control method.

On the exact analytical solution of some families of equilibrium critical thickness transcendental equations

The problem of finding an exact analytical closed-form solution of some families of transcendental equations, which describe the equilibrium critical thickness of misfit dislocation generation in epitaxial thin films, is studied in some detail by the Special Trans Functions Theory (STFT). A novel STFT mathematical approach with an analytical closed-form solution is presented. Structure of the STFT exact solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. The proposed STFT analytical approach shows qualitative improvement in theoretical sense (a novel gradient coefficient genesis), and, in accuracy when compared to the conventional analytical and numerical methods.

The retardation method for bearings loss determination

A new method for determining bearings losses of a synchronous generator, based on measurement of the speed change during mechanical and electrical braking, is described in this paper. During the mechanical and electrical braking, the total braking torque of the hydrogenerator is made up of the torques defined by single losses. In this paper, the torque-speed curve is represented by the corresponding equations which describe all the torques occurring during mechanical or electrical braking. Based on the proposed equations, speed change is obtained and compared with the speed response, which is measured in the hydro power plant Djerdap (in Serbia). Also, obtained results for unknown losses are compared with calculated values. The proposed method has the most economical use when applied to large synchronous machines.

Concerning current STFT estimations to the RC diode circuit

The subject of the theoretical analysis presented in this article is obtaining formulae for current in the RC diode nonlinear circuit by using the Special trans functions theory (STFT). Namely, the modified Lambert nonlinear functional equation which describes the current in RC diode circuit is solved analytically in closed form (a novel special tran function, tranLD(R, C, T, i (0)), and, also, is solved by using an advanced iterative procedure within STF theory. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT.

Concerning an analytical solution of some families of Kepler’s transcendental equation

The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.

Review of marine current speed and power coefficient — Mathematical models

The knowledge of the mathematical models of ocean currents and of power coefficients is necessary for a complete marine current generator systems modeling. Review of these models is the topic of this paper. For any of the listed marine current mathematical models, simulation results of marine current velocity as a function of time is presented. Also, using the mathematical model of ocean currents based on the first order Stockes model, the time-dependence of the marine current speed, as a function of the ocean depth, across horizontal and vertical axis, is presented. On the other hand, as the marine current turbines are similar in many aspects to wind turbine technologies, mathematical models of the wind power coefficients are used for mathematical description of the marine power coefficients. The experimental results of the marine power coefficient are fitted using the proposed mathematical equation. All mentioned mathematical models are implemented, and simulation results obtained, using the software package MATLAB.

On an exact analytical solution in Weibull probability distribution domain

The variation in wind speed are best described by the Weibull probability distribution function. In this paper, the problem of finding an exact analytical closed-form solution of some families of transcendental equations, which describe the Weibull probability distribution, is studied in some detail, by the Special Trans Functions Theory (STFT). A novel STFT mathematical approach by an analytical closed-form solution is presented. Structure of the STFT exact solutions, numerical results and graphical simulations confirm the validity and base principle of the STFT.

Obtaining an analytical STFT closed form solution to the solar cell junction ideality factor using the maximum power point characteristics

The problem of finding an analytical closed form solution of the solar cell junction ideality factor n is studied in some detail, by the Special Trans Functions Theory (STFT). The novel mathematical method just as the structure of the theoretical derivation is presented, while proofs and numerical results confirm the validity and base principle of the STFT. In addition, the obtained results are compared with the calculated values of other methods for alternative proving its significance. Undoubtedly, the proposed novel STFT analytical approach implies qualitative improvement of the conventional analytical and numerical methods.

The special trans functions theory for Mott's semiconductor conductivity equation

The electrical conductivity in semiconductors vs. temperature (Motts equation) can be described by some nonlinear functional equations of the transcendental type. In this paper, the problem of finding the exact analytical closed-form solution for Motts equation is studied, in some detail, by the Special Trans Functions Theory - STFT. The numerical results and graphical presentations confirm validity of direct application of the STFT to the theoretical analysis electrical conductivity in semiconductors. Undoubtedly, proposed analytical STFT approach implies the qualitative improvement of the conventional methods.

Experimental Testing and Analytical Solution by Means of Lambert W-Function of Inductor Air Gap Length

Abstract In this paper the exact analytical closed form solutions for inductor air gap length have been presented. To be specific, in a mathematical sense, the dependence between the air gap length, inductance and other constructional parameters of inductor is nonlinear, i.e. transcendental. In this paper that nonlinear equation is solved in two manners – by using the Lagrange inversion theorem of the Lambert W function or by using its asymptotic formula and by using Special Trans Functions Theory. The numerical results obtained by using these methods, are mutually compared in terms of the calculation error. In order to prove the validity of the mathematical dependence between the inductance, air gap length, and the other constructional parameters, two inductors have been created. The measured results of inductance and air gap length are compared with the corresponding results obtained by the calculations. Very good agreement is shown between the measured and the calculated value of both the air gap length and the inductance value.