Course description This course explains the theory behind the operation of the main power electrical machine typologies of widespread use in industry and power plants. Building upon the principles of electric circuit theory and magnetic circuit theory, the following topics are examined in depth: single-phase/three-phase transformers, rotating magnetic field, single-phase/three-phase induction machines, wound field and permanent magnet synchronous machines, DC machines. Prerequisites Courses of Mathematical Analysis, Physics (mechanics, electromagnetism), and Electrical Engineering (electrical circuit theory). Course topics OUTLINES OF ELECTROMAGNETISM* Maxwell equations. Electrical integral laws: electrostatic potential, Faraday-Neumann-Lenz law. Application to electrical circuits: Ohm law, voltage balance. Magnetic integral laws: Gauss law for magnetism, Ampere law. Application to magnetic circuits: Hopkinson law, magneto-motive force balance. INTRODUCTORY NOTES ON ELECTRICAL MACHINES Classification of electrical machines, nominal values, power losses, efficiency, cooling. TRANSFORMERS Elements on the single-phase transformer structure. Study of the magnetic field in both core and windings. Leakage fluxes and leakage inductances. Operating equations and equivalent circuit. No-load and short-circuit tests and relative characteristic curves. Calculation of on-load voltage regulation and efficiency. Parallel connection and operation of single-phase transformers*. Autotransformers. Transformer with three and more windings*. Three-phase bank and three-phase transformers. Wye, delta and zig-zag winding connections. Angular shift. Equations of the three-phase transformer. Three-phase equivalent circuit. Three-phase transformers with unbalanced load: shift of the star-center potential*. Equivalent circuits of direct, reverse, and zero sequence*. Current and voltage harmonics in three-phase transformers*. ROTATING MAGNETIC FIELD Theory of the rotating magnetic field with p pole pairs generated by a three-phase current system. Generalities about windings for alternating current (AC) machines. Distribution and step factors. Magnetic circuits in rotating machines and magneto-motive force (MMF). Leakage inductances in rotating machines. INDUCTION MACHINES Elements on the induction machine structure. Induction machine locked-rotor operation and equations. Operating principle of the induction motor. Slip. Induction machine equations embedding rotor rotation and equivalent circuit. Calculation of machine electromagnetic torque. Analysis of induction machine operating ranges and circle diagram. Wound-rotor induction motor starting*. Single and double cage rotor motor theory; deep bars rotor*. Single-phase induction motor*. SYNCHRONOUS MACHINES Elements on the synchronous machine structure. No-load and loaded synchronous generator operation. Armature reaction. Synchronous reactance and simplified equivalent circuit. Calculation of the electromagnetic torque and notes on static stability. Round-rotor machines and Potier diagram*. Operation in parallel with an infinite power network. No-load and short-circuit characteristics and current characteristics. Operation with island load and external characteristics. Synchronous motors. "V" characteristics. Salient-pole-rotor synchronous machine: double reaction (Blondel) theory, direct and quadrature synchronous reactance*. DC MACHINES Structure: magnetic circuit, windings, collector. Electro-motive force induced in the rotor winding and neutral plane. No-load characteristic curve. On-load operation, armature reaction and rotor current reversal plan. Calculation of the electromagnetic torque. Hints on commutation*. Compensator winding*. Types of excitation*. Characteristic curves of dynamos*. Direct current electric motors and their characteristic curves*. Hints on speed regulation*. *Optional topic

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