## Drive operating envelopes and induction machines, Electrical Engineering

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Solve using data from the DC machine data sheet, using the "hot" resistance value for all calculations. Note that the value of K on the sheet is for rated (100%) field flux.  Assume that the machine can safely handle as much current as the power converter can deliver to it.  In addition, assume that all power  semiconductors are ideal with zero voltage drop when they are on.

1. Consider a 2 hp, 850 rpm dc machine connected to a single-phase, fully-controlled thyristor bridge as shown in Fig. 2.9-4 (pg. 53), assuming that the series inductance is large enough to justify the assumption of infinite output inductance.  The amplitude of the ac voltage source is 210 Vrms, the maximum thyristor current is 10 A and the phase control angle α can be varied over the full range from 0 to π rad.  Assume that the maximum machine speed is 2000 rpm in either direction (i.e., ± 209.4 rad/s).

a)  Plot the complete boundary envelope (i.e., capability curve) of the drive system's torque-speed operating capabilities on a set of T-ω axes, with torque T on the y-axis [in N-m] and speed ω on the x-axis [in rad/s].  Assume that the field flux is constant at its rated (100%) value.  In addition, assume that the maximum armature current is determined by the maximum thyristor current rather than the rated machine current based on its rated power.  Similarly, assume that the maximum applied armature voltage amplitude is determined by the maximum positive and negative rectifier output voltage (@α = 0 and α = π) rather than the rated machine voltage.  What are the torque, speed, machine shaft power, and phase control angle α at the four corners of the operating envelope?

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