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Chapter 1: AC Machine Fundamentals Torque Produced: A fixed magnetic flux density vector Bs produced by a ‘stator’ and moving magnetic flux density vector Br existing on a ‘rotor’. The torque produced by the interaction of these 2 fields is given by: T = k Bs × Br [1-1] (vector product) Note that one can use a permanent magnet, or an electrical magnet (coil with magnetic core fed from a DC source) to produce these flux densities. Br = µ 0 H (i ) Bs α i Br N α Bs i T S (Remember Gauss’ Law of “maximum flux density”) Losses: The losses in an AC machine can be divided in 4 basic categories: • Electrical losses Also called ‘Copper’, or ‘Joules’, or ‘Resistive’ losses (I2R losses). These are the heating losses due to resistive effects in windings. We also have to include the resistive losses in the excitation windings. AC machine fundamentals 1 • Core Losses When the core sees an alternating flux, it follows a hysteresis loop. The area of the loop is proportional to the energy lost in that cycle. Therefore the hysteresis losses are proportional to the frequency of the supply. A conducting material placed in a changing field sees a voltage induced by that field ( e = − dΦ ). Hence a current will flow in the circuit (called an dt ‘eddy current’). This circuit has a resistance, and therefore some resistive losses in the core are going to result. These losses are called ‘eddy current losses’ and are proportional to the square of the frequency. • Mechanical losses These are associated with the mechanical motions. “Friction and Windage” are mechanical losses due to mechanical friction of the mechanical parts (bearings), and the fluid losses due to the air flow resistance. Note that there would also be a component called “Stiction” at start, but this is not considered when the machine rotates. • Stray losses Unfortunately, when one adds the 3 losses above, the result comes lower than the actual losses. The difference is called “Stray Losses”. Since the source of these losses is unknown, one cannot measure them as such. However in practice they can be approximated as 1% of full load. The diagram below shows the power-flow diagram of a GENERATOR, which transforms Mechanical Power to Electrical Power Mechanical >>>>> Power Transformation in the Air Gap >>>>> Electrical Power Output 3 phase Power Input (mechanical on the shaft): 3 V I cos Torque x Speed of the “Prime Mover” Joules Losses Core losses (hysteresis,eddy) Mechanical Losses (friction, windage) Stray Losses AC machine fundamentals 2 Performance Indices: The EFFICIENCY of a generator is given in % by: η G= Electrical Power Out × 100 Mechanical Power In + Excitation Power [1-2] (Note that the total input power must take into consideration the power used by the excitation power of the generator). The VOLATGE REGULATION of a generator is defined in % as: σ G= No Load Voltage − Full Load Voltage × 100 Full Load Voltage AC machine fundamentals 3 [1-3]