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This article focuses on modeling of an Axial Flux Permanent Magnet Generator (AFPMG). The authors analyzed selected variants of disk generators, including coreless stator constructions and with iron core ones, also taking into account the Permanent Magnet (PM) arrangement in order to show the way to obtain the optimal machine characteristics based on analytical equations. In addition to the full model, which takes into account the higher harmonics of the magnetic field distribution, the paper presents a simplified mathematical model developed for generator operation cases such as standalone, connected to a 3-phase power grid and loaded with a diode rectifier. The analytical and finite-element method (FEM) calculations were performed as well as laboratory tests to confirm the correctness of presented model assumptions.

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Purpose To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions. Design/methodology/approach The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions. Findings Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic. Research limitations/implications Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist. Practical implications Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time. Originality/value Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

Single-phase short-circuits are most often faults in electrical systems. The analysis of this damage type is taken for backup power supply systems, from small power synchronous generators. For these hybrid installations, there is a need for standard protection devices, such as fuses or miniature circuit breaker (MCB) analysis. Experimental research mentioned that a typical protective apparatus in low-voltage installations, working correctly during supplying from the grid, does not guarantee fast off-switching, while short-circuits occur during supplication from the backup generator set. The analysis of single-phase short-circuits is executed both for current waveform character (including sub-transient and transient states) and the carried energy, to show the problems with the fuses and MCB usage, to protect circuits in installations fed in a hybrid way (from the grid and synchronous generator set).