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MATHEMATICAL MODEL OF A VOLTAIC SOLAR POWER PLANT

In many countries, including Armenia.Solar power plants, are constructed according to the scheme of voltaic solar power plants that directly convert solar energy into electrical energy. The schemes and methods of research and calculation of such solar power plants are not sufficiently developed. That is solution to these issues is relevant. Mathematical models and software and computing complexes are effective tools for research and calculation. The developed schemes and mathematical model of a voltaic power plant based on a voltage inverter and a resonant parallel-series filter operating in parallel with the network are presented. The intensity of solar radiation is an argument for the processes taking place and, with the existing approach, is expressed by the magnitude of the generated direct current. Voltage and power are considered derived quantities. In the schemes and mathematical model, a transformation is performed in which solar panels are presented as a voltage source, where the independent variable is voltage, which linearly depends on solar radiation, and the function is the generated current and load power. Using the model, the following was studied: ensuring a sinusoidal shape of the output voltage, the frequency spectra and distortion coefficients of the output voltage shape were calculated, the functions of the transient process when connecting a solar power plant to the network, the load characteristics of the generation and transmission of active and reactive power to the network were determined. The developed mathematical model of a voltaic solar power plant is an adequate tool for research and calculation of power plant parameters. Studies conducted on the model confirm the possibility of generating and transmitting active and reactive power to the network, linearly related to the intensity of solar radiation, while ensuring the sinusoidal shape of the output voltage and satisfactory quality of the transient process. To increase the overloadability, stability and controllability of power (both active and reactive) of voltaic solar inverter power plants, it is advisable to use buffer batteries at the inverter input and/or synchronous compensators at the inverter output, as well as parallel operating synchronous generators of traditional power plants with low communication resistances.

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INVESTIGATING THE MEASUREMENT ERRORS OF THE COMPONENTS OF THE COMPLEX RESISTANCE OF MUTUAL INDUCTION BY THE PHASE METHOD

A microcontroller measurer of the complex resistance components of mutual induction (MI) of magnetically coupled coils is considered for the case when, due to the effects of “capacitance” and “eddy currents”, an active component arises in the EMF of the secondary coil, the 90° phase shift angle between this electromotive force and the current of the primary coil is violated (“phase defect”). At the same time, corrective terms ("admixture" and "frequency correction") appear in the resistance MI. These phenomena increase with an increase in the frequency and value of the supply current of the coils, when using ferromagnetic cores. Balanced AC bridges are used in well-known resistance component MI measurers; their disadvantages are listed. The developed measurer uses the phase method using a temporary separation of the measurement channel. The measuring circuit (MC) is powered by the current of a controlled generator of sinusoidal signals. In the MC, the measured parameters are converted into the phase shift angle between the two output voltages. These voltages are supplied to the analog inputs of a programmable microcontroller (MCC), in which angle is measured by the discrete counting method. During the measurement process, the MCC sets the frequency of the MC power generator, controls the position of the electronic switch of the measurement channel, measures angle and determines the values of the components of the MI complex resistance according to the specified algorithms. A method of theoretical investigation of measurement errors has been developed. The errors are caused by the inaccuracy and instability of the parameters of the MC and MCC elements appearing in the algorithms for determining the measured values. The method of error calculation is accompanied by a numerical example. The results of calculation of measurement errors are presented.

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THE PROBLEM OF OBSERVING THE MAXIMUM OF A SUPERPOSITION WAVE FIELD

The well-known Laue condition determining the intensity maximums of diffracted on an ideal crystal structure plane wave is discussed. Initially the consideration is performed for the near observation region and after that by means of applying the corresponding approximation the expression of superposition field is presented as a sum of plane waves. So, the description of the superposition field for the far observation region is made. It is proved that the Laue conditions, which are restrictions imposed on the values of the scattering wave vector, is more correctly to be considered as a pair of two conditions. The first condition relates to the wave vector of an incident wave and the second condition relates to the wave vector of an observation direction. In other words, to observe the maximums, it is not enough when only the difference (the scattering wave vector) of these two vectors satisfies the Laue condition. To observe the maximums, it is necessary that each of these vectors separately, i.e. the wave vector of the incident wave and the wave vector of the observation direction satisfy the Laue condition. It is shown that such a doubling of the maximum conditions leads to a decrease in the number of the observed maximums compared to the condition imposed only on the scattering wave vector. Within the framework of the previously developed method, a number of formerly known results related to the kinematic theory of diffraction of a plane wave by an ideal crystal structure were reproduced. It is assumed that the generation of secondary waves of each atom of the crystal is provoked by the presence in the volume of the crystal of a primary field, which in Fraunhofer formulation is considered in the form of a plane and time-harmonic wave. The intensity distribution, as well as the positions of the maxima of the diffraction pattern, was studied depending on the spatial parameters of the crystal lattice.

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INTEGRATED PHOTOVOLTAIC AND THERMAL SOLAR ENERGY CONVERTER

The utilization of solar energy is essential to curb climate change, reduce dependence on finite fossil fuel reserves, and achieve energy independence. The leading existing technologies for the use of solar radiation are the photovoltaic (PV) conversion of light directly into electricity and the thermal conversion of solar rays into heat. The main problem with solar energy is efficiently collecting this energy and cost-effectively converting it into other useful forms. The existing solar energy systems are still expensive. The other problem is the decreased efficiency of PV modules at high working temperatures. It is well known, that in PV solar cells, mostly made of silicon, most of the absorbed solar radiation (about 80%) is not converted into electricity but contributes to increasing the temperature of solar cells, then reducing the electrical efficiency of cells. This is the inherent drawback feature of solar cells - degradation in performance due to temperature. Aiming to reduce the cost of solar converters and to increase solar energy trans-for¬mation efficiency, a new type of Photovoltaic and Thermal (PVT) hybrid solar energy converter is developed in the research laboratory “Photovoltaic Semiconductor Devices” at National Polytechnic University of Armenia. Different innovative approaches are used in developing PVT converters. The prototype of a new type of PVT converter is prepared and tested. The new PVT converter has several advantages in comparison with general PV modules and PV module-based PVT collectors. The production of the developed new PVT collectors is cheap and can be realized using standard off-the-shelf technologies.

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INVESTIGATING THE ERRORS OF A DIGITAL METER OF RC-TWO-POLE PARAMETERS

A device for an invariant measurement of the electrical parameters of RC-two-pole poles based on the phase method is described. The device implements a structural-algorithmic method of increasing the accuracy of measurements with time division of the measurement channel. A programmable microcontroller (MCC) is used to control the measurement process and to process the measurement results, which allows to minimize the number of parameter and signal transformations and increase the measurement accuracy. In the measuring circuit (MC), two sample resistors are connected in series with the two-pole under study: the main and additional (switchable). The reference voltage is formed in the feedback circuit of the operational amplifier. The MC is powered by a current generator of a sinusoidal signal of a programmable frequency. The MC has two output voltages, the phase shift angle between which is an informative parameter. The output voltages of the MC are supplied to the analog inputs of the MC. In the MCC, the angle is converted into a time interval, which is measured by the discrete counting method by quantizing it with pulses of the MCC clock generator. By analyzing the MC, algorithms for determining the measured parameters are obtained. The parameters of the IC elements are calculated, at which the required measurement ranges of the investigated object parameters are provided. The main content of the article is devoted to the development of the methodology of theoretical calculation of measurement errors. The errors are caused by inaccuracy and instability of the parameters of the MC and MCC elements appearing in the obtained algorithms. The calculation technique is accompanied by numerical example applied to specific measurement ranges. It is shown that in the total errors of measurement the private error caused by the inaccuracy and instability of resistances of sample resistors used in the MC, is predominant.

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A METHOD OF PIECE-QUADRATIC INTERPOLATION OF A TABLED FUNCTION WITH A CONTINUOUS FIRST DERIVATIVE BASED ON LINEAR COMBINATION OF CENTRAL-SYMMETRIC PARABOLAS

In engineering practice, one often has to deal with reference and experimental data, in particular, with tabularly specified functional dependencies. Such functions characterize the properties of materials, as well as physical and technical objects. The dielectric properties of materials are represented by functional dependences of the electric polarization of a substance or electric displacement on the strength of the electric field. Such functions are called polarization curves of dielectrics. Their significant nonlinearity is manifested in ferroelectrics. The magnetic properties of materials are represented by functional dependences of the magnetization of a substance or magnetic induction on the strength of the magnetic field. Such functions are called magnetization curves. Their essential nonlinearity is manifested in ferro- and ferrimagnets. The properties of technical objects are largely determined by the properties of materials, designs, geometric dimensions of parts, elements and assemblies. Information about the properties of standardized materials and products from them can be contained in reference books in graphical or tabular form in cases of non-linearity of the corresponding functional dependencies. In the course of technical calculations, they need to be smoothly interpolated. A method of piecewise-quadratic interpolation of a tabularly given function with a continuous first derivative is proposed based on the linear combination of modified (centrally symmetric) parabolas, which does not require the use of logical operations in calculations to determine a partial segment of the grid of argument values. A method for weighted minimization of the oscillatory effect for non-uniform grids of argument values is proposed. Computational experiments with the reference main magnetization curve of electrical steel show the high numerical stability of the proposed method with respect to the effect of oscillation and the technical flexibility in its application for solving practical problems of processing tabularly specified functional dependencies on essentially non-uniform grids of argument values, including those with a small number of tabular points.

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DESIGNING AN ELECTROMAGNET WITH A STRAIGHT ARM USING MACHINE LEARNING METHODS

The studied electromagnet is used in switching devices as a drive, in high-speed trains on a magnetic cushion as a magnetic suspension, etc. In the previous works of the authors, an electromagnet with a forward arm was studied, in particular, a mathematical model of the system was developed, the forward and reverse problems of the magnetic circuit were formulated and solved, the methods of calculating the control coil and the methodology of optimal design of this electromagnet using the genetic algorithm were described, an automatic system was developed, including all stages of design of an electromagnet by the classical method: setting the input values of the parameters (electromagnetic force between the poles of the cores and the armature, magnetic induction in the air gap, ambient temperature, etc.), determining the dimensions and choosing the materials of the magnetic wire and coil, calculating the magnetic flux, electromagnetic force, etc. The problem of this research is to design a database and to train them using machine learning algorithms, to estimate and analyze the predicted values of electromagnet parameters. The database, compiled with the calculation data obtained as a result of the design of an electromagnet with a straight arm, includes the results of one million design options. The training of the compiled database was carried out using the algorithms of the machine learning package Regression Learner in the MatLab program environment: Regression Trees (Fine Tree, Medium Tree), Linear Regression Models (Linear, Interactions Linear, Robust Linear), Support Vector Machines - SVM (Linear), Neural Network (Narrow, Bilayered, Trilayered). The results of training and the characteristics of forecasting are presented and analyzed in the work.

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A DC TO AC CONVERTER WITH A HIGH FREQUENCY LEVEL

Two block diagrams of DC-AC converters with a voltage curve of a given frequency close to the sinusoidal shape without a high-frequency section and with a high-frequency section are considered. In the converter circuit without a high-frequency link, an autonomous voltage inverter (AVI) is used, and in the converter circuit with a high-frequency link, a high-frequency AVI (AVI HF) and a direct frequency converter with quasi-single-band modulation (DFC QF) are used. In both of these converter circuits, for electromagnetic isolation between the DC voltage source and the load, a power transformer is envisaged, to match the input and output voltages. To improve, ensure and obtain on the load the output voltage curve close to the sinusoidal shape, filters are used, which is the simplest way of improvement without a selective elimination of distorting harmonics of non-sinusoidal periodic voltage with multiple switching of valves, without pulse-width modulation, and so on with the complication of voltage inverter and DFC control systems. At the same time, in the first converter circuit, one filter is used: connected between the output of the inverter and the input of the output transformer, and in the second converter circuit, two filters are used, one of which is connected between the output of the AVI HF and the high-frequency transformer, and the other - between the output of the DFC with the QF load. Since the output voltages of AVI and DFC are non-sinusoidal periodic functions, using the methods of harmonic analysis and switching functions, mathematical descriptions of the output voltages of AVI and DFC are obtained in the form of a trigonometric Fourier series. A numerical assessment of the weight and size parameters of transformers and filters in relative units is carried out. It is shown that the use of a converter with a high-frequency link based on AVI HF and DFC with QF allows to significantly reduce the mass and dimensions of power electromagnetic elements.

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