Slobodan N. Vukosavi}

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, 2010.

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Recezenti: Prof. dr M Prof. dr

ELECTRIC MACHINES

Electromechanical energy conversion. Modeling of electromechanical systems. Magnetic circuits, magnetic flux and magnetomotive forces. Electromagnetic torque. Winding turns and sections. Concentrated and distributed windings.

Electromotive forces and magnetomotive forces of windings.DC current machines. Induction machines. Synchronous machines. Coordinate

transformations, dynamic model of electric machines.Steady state operation, equivalent circuits and mechanical characteristics. Power losses. Copper and

iron losses. Mechanical losses. Machines power supply and controls. Transient phenomena in electric machines.

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PREFACE

This textbook is intended for engineering students taking their first course in electrical machines. It is also recommended for students preparing a capstone project where they need to understand, model, supply, control and specify electric machines. The book is primarily written for Electrical Engineering students. At the same time, it can be used as a valuable reference for other engineering disciplines involved with electric actuators, electric generators and drives. The book is self-contained and it comprises questions and answers and solved problems wherever the learning process requires an overview.

This book comes out of the fifteen years of authors experience teaching Electrical Machines at the Department of Electrical Engineering, University of Belgrade. Introductory Chapters are suited for second year students with a rather limited background in mathematics, physics, engineering fundamentals, circuit theory and electromagnetics. Prerequisites do not include spatial derivatives and field theory. Necessary background includes elementary electrostatics and magnetics, DC and AC current circuits and some elementary skill with complex numbers and phasors.

The scope of this textbook is the set of basic knowledge and skills in Electrical Machines the prospective engineers should acquire. The approach starts with basic functionality and the role of electrical machines in their typical applications, their electrical and mechanical connections and characteristics. Mathematical models of electrical machines are developed by using coordinate transforms. Before applying Clarke and Park transforms, the need for them is emphasized and the benefits are discussed, along with available options. The

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effort of applying transforms is justified by obtaining a more intuitive, concise and easy-to-use model. Steady state operation is described by equivalent circuits and mechanical characteristics. Design and construction of practical machines is discussed in the extent needed to understand the principles of operation, the power losses and cooling, and the problems of power supply and control of electric machines. Details such as the slot shape and the disposition of permanent magnets are discussed as far as they affect the machine parameters and performance. The book covers DC machines, induction machines and synchronous machines. Design of magnetic circuits, windings and mechanical elements are left out of the scope.

The authors wishes to thank the reviewers, Prof. Milo Petrovi and Prof. Dragutin Salamon for their valuable comments and suggestions. In addition the author would like to thank Prof. Joef Varga, renown expert in design of electrical machines. Particular contributions of Assistant Prof. Petar Mati and Prof. Mili R. Stoji made a significant improvements in this book consistency and value. The author owes special thanks to assistants Nikola Popov, Dragan Mihi, and Igor Cvetkovi for their help and devoted efforts in technical preparation of this manuscript.

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1 .............................................................................................. 1 1.1 .................... 1

1.1.1 ..................................... 1 1.1.2 .................................. 2 1.1.3 ......... 2 1.1.4 ............................................................... 3 1.1.5 ............................................... 3 1.1.6 .......................................... 4 1.1.7 .................................................. 5

1.2 .............................. 6 1.3 ............................. 11

1.3.1 ................. 13 1.4 ..................................... 15

1.4.1 ................. 16 1.4.2 ............................................................ 16 1.4.3 .......................................... 16 1.4.4 ........... 17 1.4.5 ..................................................... 18

1.5 ............................ 18 1.5.1 ................................................... 20 1.5.2 ....... 21

2 ............................. 27 2.1 ................................................................... 27 2.2 ......................... 29 2.3 ................ 30 2.4 ............................................................ 32 2.5 .......................................................... 34 2.6 ................................................................ 35 2.7 ............ 36 2.8 ..................................................... 37 2.9 .................................................... 41 2.10 ............................................................... 42

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2.11 ............... 43 2.11.1 , .............. 43 2.11.2 , ..... 45 2.11.3 .............................................................. 46 2.11.4 ................................................... 48 2.11.5 ...... 50 2.11.6 .................................... 51

2.12 .................. 52 2.12.1 .................................................. 53 2.12.2 ...................................................... 55 2.12.3 - ................................... 58

2.13 ................................................................. 60 2.13.1 .......................................... 61

62 62 63

2.13.2 ............................................................ 64 2.13.3 ........ 64 2.13.4 ......................................... 65 2.13.5 ....................................... 69 2.13.6 ........................... 70

2.14 ........................................... 72 2.14.1 ........................................ 72 2.14.2 .................................. 73 2.14.3 ............................. 75 2.14.4 .................... 75 2.14.5 ....... 77

2.15 ............................................ 80 2.15.1 .............................. 81 2.15.2 ...................................................... 82 2.15.3 ..................................................................... 83 2.15.4 ...................................... 85 2.15.5 ................................. 87 2.15.6 ................................................. 89 2.15.7 ...... 92 2.15.8 , .................... 94

2.16 ................................. 98 2.16.1 ......................................... 99

100 2.16.2 ............................................................. 102

102 103

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103 103

2.16.3 ............................................................ 104 2.16.4 .............................................. 105 2.16.5 ................................. 106 2.16.6 ....................................................... 108 2.16.7 .......................................... 112 2.16.8 .................................................... 113 2.16.9 ..................................................... 116 2.16.10 ............................................ 119 2.16.11 ........................ 120 2.16.12 ................................................ 121 2.16.13 ............................. 122 2.16.14 . 124 2.16.15 ......................... 126

2.17 ........... 127 2.17.1 .......... 129 2.17.2 ........................ 130 2.17.3 ........................................ 132 2.17.4 ............. 135 2.17.5 ....................... 136 2.17.6 ..................................................... 138

139 140

2.17.7 .................................................... 141 2.17.8 ...... 142 2.17.9 ... 143 2.17.10 .... 146 2.17.11 .......................................................... 150 2.17.12 ................................... 152

152 153 153

2.18 ............................... 154 2.18.1 .. 155 2.18.2 .. 158 2.18.3 .................................. 160

161 163 166

2.18.4 ..... 170 2.18.5 ........ 172