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Projective geometry in the electrical circuit theory with variable and nonlinear loads.

Author: Penin Alexandru
Degree:doctor habilitat of engineering
Speciality: 05.09.12 - Power electronics, energy conversion devices and systems
Scientific consultant: Anatolie Sidorenko
doctor habilitat, professor, Institute of the Electronic Engineering and Nanotechnologies
Institution: Institute of the Electronic Engineering and Nanotechnologies


The thesis was presented on the 9 February, 2017
Approved by NCAA on the 23 March, 2017


Adobe PDF document3.18 Mb / in russian


electrical circuit, multi-port, voltage converter, load, volt-ampere and regulation caracteristic, normalized parameters, projective tranformations, cross ratio


The review contains Introduction, 4 Chapters, General conclusions and recommendations, 92 references, 72 pages, 56 figures. The 45 scientific works were published, including two monographs, two books chapters, 20 research articles in international scientific journals, 4articles in national journals, 8 abstracts in proceedings/books of international or national conferences and 8 national patents.

Field of research: electric circuit theory, power electronics.

The aim and objectives of the work consists in: the research of interference's „mechanism” of circuit’s elements using projective geometry, disclose of supplementary properties of the circuits and elaboration the calculation method of regime parameters.

The scientific novelty and originality of the research consists in: offered method of the analysis of circuits on the basis of projective geometry; justification of determination of regime parameters in a relative type; justification and a formulation of the new scientific direction. The New scientific direction: group characteristics of changeable operating regimes of circuits, which are invariant to a type of the regime parameters and sections of circuits.

The theoretic value of the research consists in: the application of a new mathematical apparatus in the electric circuit theory for interpretation of changes or “kinematics” of electric circuits’ regimes; determination of regime parameters in a relative type; recalculation formulas of regime parameters; generalization of the equivalent generator.

The practical value of the research consists in: the convenient recalculation algorithms of loads’ currents; the simplified equivalent circuits of an initial network.

Implementation of scientific results consists in: development of original technical solutions (patents) for transfer of measuring signals via communication lines; elaboration of parametrical sources of load current; linearization of regulation characteristics of voltage converters.