ONE TYPICAL EXTREMUM IN ELECTRICAL PROBLEMS

The aim of this work is to attract attention of teachers, scientific personnel, engineers and students to one peculiarity of extremum seeking in different electrical problems. This feature lies in the fact that in many parts of electrical engineering extremum seeking comes to analysis one and the same mathematical structure (T-structure), but differences lie only in many symbols (designation).In one problems this structure appear in finale, the most simple form, but in others – T-structure is “veiled”, and as a rule  we need  elementary algebraic transformation to detect it.

Taking into account high frequency of this structure appearing in electrical problems, in the first part of article the authors  carried out the investigation of extremum characteristics of T-structure and show the results in easy algorithms. To determine the typical T-structure there were taken five problems-examples for extremum seeking  from different parts of electrical engineering. The first and the second examples belong to the theory of electrical circuits.

In the first example the problem of maximum active load power obtaining was considered, in the second we see the solution of problem for inductive coupled circuit adjustment in order to obtain the hump current. In the third example the band active filter, built on operating amplifier, is analyzed. According to these methods, taken in the first part of article, the frequency is determined, on which amplifier provides maximum  amplification factor. The forth example deals with analysis of efficiency of transformer. According to algorithm, the optimal efficiency of transformer’s load and also equation for its maximum was determined in this article. In the fifth example the mechanical characteristics of induction motor is analyzed. It is indicated how, on the basis of algorithms article, to obtain equations for critical slip and motor moment, and also the simple development of formula Klossa.

The methods of contrastive analysis of equations for calculation of extreme parameters in different electrical problems were used in this article. And as a result, it was determined that there is the same T-structure in equations, and this allow to develop the single approach for extreme parameters determination. It was shown that looking of extreme parameters in many electrical problems leads to analysis of the single mathematical T-structure. On the basis of T-structure analysis was obtained the single algorithm of extremum seeking. These five examples from different fields of electrical engineering present, first, typicalness of T-structure, the second, the simplicity obtaining of extreme parameters on the base of algorithm.

extremum, electrical problems, mathematical structure

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