Results of phase splitter simulation at steady-state mode.
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
\n'}],latestNews:[{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"},{slug:"oiv-awards-recognizes-intechopen-s-editors-20201127",title:"OIV Awards Recognizes IntechOpen's Editors"},{slug:"intechopen-joins-crossref-s-initiative-for-open-abstracts-i4oa-to-boost-the-discovery-of-research-20201005",title:"IntechOpen joins Crossref's Initiative for Open Abstracts (I4OA) to Boost the Discovery of Research"},{slug:"intechopen-hits-milestone-5-000-open-access-books-published-20200908",title:"IntechOpen hits milestone: 5,000 Open Access books published!"},{slug:"intechopen-books-hosted-on-the-mathworks-book-program-20200819",title:"IntechOpen Books Hosted on the MathWorks Book Program"}]},book:{item:{type:"book",id:"7218",leadTitle:null,fullTitle:"OCT - Applications in Ophthalmology",title:"OCT",subtitle:"Applications in Ophthalmology",reviewType:"peer-reviewed",abstract:"I am very proud and excited to introduce to you this book, which provides many interesting indications on how to better understand and handle the world of optical coherence tomography (OCT). 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Mouzakis",authors:[{id:"107011",title:"Associate Prof.",name:"Dionysios",middleName:"E.",surname:"Mouzakis",fullName:"Dionysios Mouzakis",slug:"dionysios-mouzakis"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"69158",title:"Induction Electrical Machine Simulation at Three-Phase Stator Reference Frame: Approach and Results",doi:"10.5772/intechopen.88906",slug:"induction-electrical-machine-simulation-at-three-phase-stator-reference-frame-approach-and-results",body:'\nThe induction motor (IM) plays a very important role in industrial sectors and transport, primarily due to its robustness and low cost. There are some authors, who devote their publications to problems of mathematical modeling of IM [1, 2, 3, 4, 5, 6]. The author wishes to offer its own version of a mathematical model (MM) of the IM, suitable for unbalanced modes of simulation purposes.
\nWriting the equations of the MM of a three-phase IM in a three-phase stator reference frame (SRF) is useful in the analysis, comparing the calculated and actual curves of currents and phase voltages, suitable without additional transformation of equations for the consideration of modes of IM operation at asymmetrical characteristics of feed or parameters of IM. Simulation results for the coordinates\n
It can be argued—subject to review only, the fundamental spatial harmonics of the magnetic field in the air gap is symmetrical in a construction three-phase IM, powered by non-sinusoidal voltages asymmetrical system—that simulation results will be correct, but the same one in two-phase orthogonal coordinates will not.
\nThe suggested MM of a three-phase IM is based on a three-phase electrical machine MM at SRF coordinate system axis \n
Traditionally, the rotor parameters are given to the stator winding. Detailed components of the system (Eq. (1)) are described in Eqs. (2)–(7). The form of Eq. (1) as much as possible is unified with published equations (Eq. (1)) of a three-phase transformer MM [7]:
\nVoltages at the terminals of phase magnetization branches (derived from flux linkage of mutual induction)
\nMutual inductance of IM windings defined as
\n\n\n
\n\n
Per-phase magnetizing currents:
\nIn the expressions (Eq. (4)), \n
Flux linkages of IM rotor phases:
\nThe electromagnetic torque of IM equation is
\nThe equation of motion for the IM shaft in the case of single-mass mechanical part:
\nwhere \n
In the general case, Eq. (9) can be written as
\n\n\n
\n\n
The angle of rotation of the IM rotor shaft, radian
\n\n\n
It is interesting to know the energy performance of the electric machine in the transition process. For IM in the absence of power from the rotor instantaneous value of the active power consumption is calculated as
\nThe instantaneous reactive power consumption
\nThe instantaneous value of useful shaft power of IM
\nThe abovementioned equations (Eqs. (1)–(15)) of IM MM may be supplemented by the expressions (Eq. (16)), which allow to go to the description of the rotor phase currents at frequency of \n
Such a representation of the rotor currents demonstrates the nature of changes in the transition processes (see \nFigure 1\n, which shows the results of the rotor phase current simulation in the case of balanced power supply sinusoidal voltages for IM type AE92-4, 4-pole, 40 kW). In \nFigure 1\n, curve 1 is \n
The results of the rotor phase current simulation for IM type AE92-4.
\n\nFigure 2\n shows the applicability of the developed MM for the simulation of electromagnetic and electromechanical processes in IM with its power supply from the power semiconductor converter—autonomous voltage inverter.
\nThe results of simulation for traction IM type DTA-350M (6-pole, 350 kW) under power supply from autonomous voltage inverter condition.
In the process of the computer model of the IM according to the equations (Eqs. (1)–(12)), development using OrCAD—computer-aided design system—intended primarily for the design and simulation of electronic and electrical devices [8], there was the task of ensuring the embedded model of IM in an electrical power supply circuit, including converters, by simple connection of virtual terminals. That is, relative to the model of the electrical circuit that is attached to this circuit, the IM model should also have the properties of electric circuits: one can apply a potential difference to the terminals, providing a bidirectional electric current in the connecting circuits, including a pass-through current between them. Another task is the formation of such structure of the computer model which will be used perhaps as a universal template, which records the values of variables (parameters of IM), asked simultaneously for all equations. The resulting computer model is suitable for the description of both the squirrel-cage and wound rotor IM in any of four quadrants. The winding phases can be connected in a triangle scheme, wye, independently joined with each of its voltage to have any other wiring of each other or of power source. The developed computer model gives the user access to the beginning and the end of a winding of each of the three phases of the stator and the rotor. This property is particularly important when considering the asymmetric modes of operation or when powered by the special circuitry of semiconductor converters [9].
\nThe tasks are solved by combining two approaches in the IM computer model development: circuit for electrical parts and the method of block diagrams for the magnetic and mechanical parts. The computer model of IM is packed into a hierarchical block with a specified list of variables (parameters of IM). Within a single OrCAD project, using the copy operation, one can get the required number of hierarchical blocks (models of IM), for each of which it is possible to set unique parameter values. Sensors and signal inputs in the IM model used controlled sources of currents and voltages. Such voltage source is controlled by current (VSCC) and by voltage (VSCV), and current source is controlled by voltage (CSCV). A graphical image of the computer model of phase A windings of the stator and the rotor of IM, composed of Eqs. (1)–(7), is shown in \nFigure 3\n.
\nThe graphical image of the computer model of phase A windings of the stator and the rotor of IM.
VSCC1 performs a function of the phase current of the stator \n
The rest of the equations of a three-phase IM mathematical model is implemented by the author in the computer model in the form of block diagrams [11]. \nFigure 4\n shows a part of the model, where one obtains instantaneous value of \n
The block diagram for obtaining instantaneous values of complete phase inductance of the stator winding from the main magnetic flux in relative units \n\n\nL\nμ\n\n∗\n\n.
Signal \n
where \n
\n\nFigure 5\n shows the piecewise linear approximation by five points of \n
The piecewise linear approximation by five points of \n\n\nL\nμ\n\n∗\n\n\n\nΨ\n\nμ\nΣ\nm\n\n\n∗\n\n\n\n for IM type AGV250.
In \nFigure 6\n there is the model part corresponding to the abovementioned (Eqs. (1)–(3)) equations. \nFigure 7\n shows a part of the IM model, designed to determine the rotation electromotive force in each phase. Model rotor speed \n
The block diagram that implements the calculation of the instantaneous value of the amplitude of the representing vector of the flux linkage of mutual induction.
Part of the IM model, designed to determine the rotation electromotive force in each phase.
Block diagrams corresponding to equations (Eq. (2)).
Block diagrams, which form the signals of electromagnetic torque \n\n\nT\nem\n\n\n, angular speed \n\n\nω\nr\n\n\n, and the angle of rotation of rotor \n\n\nΘ\nr\n\n\n.
A good example of functionality for previously provided MM under unbalanced supply voltage maybe modeling of electromechanical phase splitter, made on the basis of a three-phase IM.
\nElectromechanical phase splitters are used in Russia and India [12] onboard of electric trains and electric locomotives for transform AC single-phase voltage in three-phase voltage to feed auxiliary electric drives with IM loaded by fans and air compressors. \nFigure 10\n is a schematic diagram of the rotary phase splitter, where \n
Schematic diagram of the rotary phase splitter.
Phase splitters are IM with a symmetrical or nonsymmetrical stator winding and no load (or low load) on the shaft. Phase splitter can be considered as combined single-phase IM and three-phase synchronous generator. In accordance with the terminology, adopted in India, the phase splitter is called the ARNO converter [12].
\nOn contemporary freight AC electric locomotives of family “Ermak” in Russia, IM of NVA-55 type (4-pole, 55 kW) is used as a phase splitter. To drive the fans and compressor, the same type of IM is used. Let us make simulation of the phase splitter start without connecting electrical loads to check for phase splitting effect. Define \n
The simulated results of phase splitter start are shown in \nFigures 11\n and \n12\n, where the graphs are 1, 2, 3—line voltages between phases A-B, B-C, C-A— and 4, rotor speed. Start-up capacity \n
Results of phase splitter start simulation.
Results of phase splitter simulation at steady-state mode.
\n\nFigure 12\n shows the results of simulation of phase splitting in steady state (at average rotor speed of phase splitter 1500 rotation per minute). In \nFigure 12\n curves 6–8 are the phase currents A, B, and C. \nTable 1\n presents the numerical results at steady-state mode. Obviously, the phase splitting effect is clearly demonstrated by the results of simulation.
\nPhase-to-phase voltages (V) | \nPhase currents (A) | \n||||
---|---|---|---|---|---|
\nA-B\n | \n\nB-C\n | \n\nC-A\n | \n\nA\n | \n\nB\n | \n\nC\n | \n
444 | \n380 | \n408 | \n131.9 | \n113.9 | \n22.1 | \n
Splitted | \nObtained from a single-phase transformer secondary winding | \nSplitted | \nWithout any connected electrical loads | \n
Results of phase splitter simulation at steady-state mode.
The proposed mathematical model of a three-phase IM and the method of its computer implementation confirmed their adequacy and effectiveness to address some of the problems of analysis and design of electrotechnical complexes and systems, having IM in its composition.
\nIn conclusion, the author would like to identify ways of improving the suggested mathematical model of a three-phase IM [13, 14]. Priority for criticism might be the lack in the mathematical model accounting for the skin effect in the conductors of the rotor winding. In fact, this is a notable disadvantage since in some cases, the current displacement in the rotor is able to accelerate the transitional process of IM start-up in several times [15, 16].
\nThere are two types of problems whose solution requires a mathematical model accounting for the skin effect in the conductors of the IM rotor winding: the correct description of transient processes at direct start-up and correct account of the losses in the rotor winding in the case of feeding from the source of non-sinusoidal voltage or current. When deciding tasks of the first type, the author sometimes puts active resistance and leakage inductive resistance of the rotor, which change depending on the slip. The solution of tasks of the second type requires the coordination of the complex resistance components of the rotor values to current frequency in it. The second approach is more versatile as it can be used for solution of both types of the abovementioned tasks. According to the author, to implement the second approach, the best way is to create the computer implementation of the mathematical model of a three-phase IM in the original coordinates.
\n.
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