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An analytical model has been developed for calculating magnetic field in a multiphase synchronous electric machine with fractional toothed windings. For this, a harmonic analysis of the distribution functions of the magnetic field of excitation and the magnetic field of the armature reaction was carried out, taking into account the presence of higher harmonic components in the function of the magnetomotive force of permanent magnets, variable magnetic conductivity of the air gap, polyharmonic mode of operation of a multiphase electric machine and a non-sinusoidal law of variation of spatial winding functions. As a result of the analysis, the substantiation is given that in the investigated electric machine a nine-phase winding can extract with the greatest efficiency the harmonic components of the first and third order of a rotating magnetic field to create flux linkage and induce an electromotive force (as well as create a magnetomotive force with prevailing spatial harmonics of the first and third order). In the investigated electric machine, the amplitudes of the working harmonics of the induction of the modulated magnetic field of the armature reaction can be increased due to the modulation of the inoperative harmonics of the magnetomotive force of the armature response by the stator teeth to the first and third order. To check the developed provisions, a magnetostatic vector model of the magnetic field of the investigated electric machine was created. The simulation results confirmed the high efficiency of the developed analytical model for calculating the magnetic field in a synchronous electric machine with fractional toothed windings. The use of such a model will make it possible to reveal most reliably the influence of the geometricparameters of the magnetic circuit and the multiphase winding circuit on the nature of the change in the functions of the magnetic field in the air gap with the lowest time costs in the process of optimizing an electric machine.

As a result of the study of a two-dimensional finite element model of the magnetic field of a synchronous electric machine with fractional tooth windings, typical magnetic fluxes (fundamental, edge effect, scattering) in its magnetic system have been identified. The analysis of the degree of influence of magnetic fluxes of the edge effect and scattering on the magnitude of the main magnetic flux is carried out and equivalent circuits of the magnetic circuit of the studied synchronous electric machine with fractional tooth windings are constructed for different positions of the stator teeth relative to the rotor poles. An analytical model has been developed to determine the main magnetic flux through the coil of the working winding of a synchronous electric machine with fractional toothed windings. A feature of the proposed model is taking into account the dependence of the main magnetic flux through the coil of the working winding on the coordinate of the rotor position, the magnetic fluxes of the edge effect and scattering. The developed model allows solving the problem of quantitative determination of the value of the main magnetic flux through the coil of the working winding with high accuracy. In addition, the proposed model makes it possible to determine the influence of the main geometrical parameters of the magnetic circuit on the nature of the change in the main magnetic flux through the coil of the working winding with the least amount of time. The developed analytical model can be applied in the process of optimizing a synchronous electric machine with fractional tooth windings.

A system for vector control of current in the circuit of a polyphase electric machine has been developed. For this, on the basis of the analysis of electromagnetic processes in a multiphase semiconductor converter of electrical energy, its discrete mathematical model was created, which takes into account the redistribution of electromagnetic energy by individual spatial harmonic components depending on the number of phases. Using this mathematical model and the scheme of injection of higher current harmonics, which provides a polyharmonic mode of operation of a semiconductor converter, a method for independent control of the spatial harmonic components of the input current of the converter has been developed. The formation in each of the phases of polyharmonic currents, conjugated in shape and phase with the voltage supplying the converter, is carried out by means of control actions in the form of voltage vectors of a semiconductor switch, the implementation of which is carried out by the method of multiphase space-vector modulation. To check the developed provisions, a simulation model of a nine-phase semiconductor converter of electrical energy with a vector control system was created. The results of the study of the model confirmed the adequacy of the developed technical solutions, the use of which will ensure the most complete realization of the own advantages of a multiphase electric machine in order to generally improve the weight, size and energy indicators of the autonomous power supply system.

The autonomous power supply system (APSS) from synchronous magnetoelectric generator and active voltage rectifier (AVR) maximally meets the requirements of the minimum specific mass and the complete coordination of the primary electric power source with the load. With multiphase (m > 3) execution of the electric machine, it is possible to obtain a trapezoidal electromotive force (EMF) and increase the specific power conversion provided that the EMF and the current at the output of the m-phase generator are fully matched. Therefore, the aim of the work is to synthesize the space-vector modulation (SVM) algorithm of the active voltage rectifier to fully match the primary source of electrical energy with the load under the condition of a trapezoidal EMF of the generator. Synthesis of the PVM algorithm for the m-phase AVR is based on the use of a vector-matrix mathematical apparatus. Using the example of a nine-phase system, a SVM algorithm has been developed, the feature of which is the transformation of the generalized voltage vector m-phase coordinate system into (m – 1)/2 voltage vectors with different angular velocities in two-phase orthogonal stationary αβ coordinate systems. At the same time, based on the developed PVM algorithm, it is possible to independently control the (m – 1)/2 voltage vectors in the corresponding αβ planes, providing a signal similar to the EMF of the generator at the input terminals of the AVR. In order to confirm the theoretical propositions, an imitation model of the space-vector modulation unit for the realization of trapezoidal signals at the terminals of a nine-phase AVR has been developed. The efficiency of the developed algorithm is confirmed by the results of simulation modelling. As a result of the evaluation of the energy parameters (operating power) of the phase of power supply system direct current, it is established that the application of the developed space-vector modulation algorithm for the active voltage rectifier in order to fully match the trapezoidal shape of the EMF and the current at the output of the m-phase generator will increase the power of the APSS by 14 % compared to a power supply system of direct current with a sinusoidal form of the EMF and the current of the generator phase. It is established that the developed measuring device can be used to establish the presence of defects like "delamination". The influence of the depth of the defect placement on the measured parameters is shown.

Red band needle blight, or Dothistroma needle blight is one of the most common and harmful diseases of pine. The causative agents of the disease are pathogenic micromycetes Dothistroma septosporum (Dorogin) M. Morelet and Dothistroma pini Hulbary. Dothistroma needle blight was firstly detected in Belarus in 2012 year, but till now information about this disease in the republic is fragmentary. The article presents the results of a survey of different pine trees, carried out in the period 2016–2020 years in botanical and dendrological gardens, forest nurseries and mini-arboretums at forestry enterprises, urban stands, nurseries of decorative plants, garden centers, for the presence of Dothistroma needle blight. The species identification of the causative agent of the disease was carried out by mycological and molecular genetic methods. In this study, Dothistroma needle blight was revealed on individual trees of Pinus mugo, P. nigra and P. ponderosa in the stands of the Central Botanical Garden of the NAS of Belarus, the dendrological garden of the Glubokoe experimental forestry enterprise, in the nurseries of decorative plants in the Grodno and Minsk regions. In the collected samples of needles, the invasive species Dothistroma septosporum was identified. The frequency of occurrence of the pathogen was 4.8–7.2 %, the proportion of observation sites in which this disease was detected at 60 %. The detection of Dothistroma needle blight on pine trees, mainly on planting material imported from abroad, indicates a transboundary route of D. septosporum entering the country. Analysis of literature data indicates the potential danger of Dothistroma needle blight for pine stands in the republic, which in turn requires the organization of regular monitoring of the disease and the development of methods to limit the spread of D. septosporum in the republic.

Different pines species are heavily infected with fungal pathogens all over the world, some of them are alien species for European region. The potential invasion of alien species into forests, forest nurseries, urban greeneries causes great concern among Belarusian phytopathologists. In this regard, in recent years local scientists have been monitoring the phytosanitary state of natural and managed plantations to identify alien species. The aim of this investigation was to monitor the phytosanitary state of conifers in botanical and dendrological gardens, urban plantations and tree nurseries in the Republic of Belarus, and assessment of the incidence of alien pathogens of pines. There were used light microscopy and molecular genetic techniques. As a result of our research the brown spot needle blight fungus, Mycosphaerella dearnessii was for the first time noted in the region of the Republic of Belarus in a consignment of imported plants of pines Pinus mugo, Pinus nigra, Pinus ponderosa. The disease was revealed both on young and adult plants in botanical gardens and nurseries. In the forests, urban greeneries Mycosphaerella dearnessii is currently not identified. The fungus affects not only the old, but also young needles, strongly inhibiting the growth of trees. Based on the investigation results we suppose that this disease can be dangerous for pinetums in our country.

One of the ways to combat the penetration and spread of dangerous pathogens of fungal plant diseases on the territory of the republic may be the selection of domestic varieties resistant to fungal phytopathogens and a reduction of the import of planting material. Over the past decades, the Central Botanical Garden of the National Academy of Sciences of Belarus (CBG) has been working on the development of new cultivars of coniferous plants for landscaping purposes. The purpose of this study was to study of the composition of the mycobiota of needles and shoots of ornamental forms of Scotch pine of the CBS breeding.The article presents the results of the survey of Pinus sylvestris L. cultivars of CBG selection, carried out in the period 2020–2021 years in The Central Botanical Garden of NAS (Belarus, Minsk). As a result, it was found that among the 18 of Pinus sylvestris L. cultivars of CBG selection, the most stable were 'Woshodjaschaia' and 'Minchanka', the least stable were 'Karolina' and 'Chupa Chups'.The species composition of the mycobiota of needles and shoots includes such dangerous pathogens as fungi from the genus Lophodermium, causing premature falling of needles, as well as Cyclaneusma minus, causing premature yellowing and falling of needles, and Gremmeniella abietina, the causative agent of scleroderriosis or pine shoot cancer. Among the less dangerous fungi, conditionally pathogenic species have been identified – Alternaria alternara, Auerobasidium pullulans, Cladosporium spp., Phoma spp., as well as the endophyte fungus Sydowia polyspora.

The article presents the results of the mitochondrial DNA (30 837 n. r.) sequencing of the phytopathogenic fungi Phoma sp.1 – causative agent of Phoma blight of the pine and spruce plants cultivated in the forest nurseries. Annotation of the Phoma sp.1 mitochondrion showed 43 coding loci. Potential open reading frames (orf89, orf87, orf76 and orf108) and gene introns (cox3, nad1) are described. A comparative single genes analysis in the NCBI GenBank database showed, that Phoma sp.1 belongs to the Didymella spp., which can have Phoma anamorph. It has been shown that mitohondrial genes can be used as DNA markers for the diagnosis of Phoma and phoma-like fungi. Analysis of the mitochondrial synthenia of Phoma sp.1 and a related species (including phoma-like fungi), revealed significant structural rearrangements in mtDNA during phylogenesis.