Variable Frequency Operation of Induction Machine
A 500 Hp, 2300 Volt, 60 Hz, three phase, 4 pole induction machine has the following per-unit parameters (ignore Rm):
r1 = 0.018 x1 = 0.085 xm = 3.8
r2 = 0.013 x2 = 0.085
a) Assume that the machine is excited with a stator voltage amplitude that is directly proportional to the excitation frequency so that V1 = 13 pu. Consider three excitation frequencies we =13 = 1.0, 0.5, and 0.1 pu. Determine the maximum torque Tmax, the corresponding slip frequency at maximum torque, wow = 13 - WrMT (in pu) where corm', is the rotor speed in pu at maximum torque, and the stator current amplitude Inn' at this maximum torque operating point. Find these quantities for both motoring (positive torque) and generating (negative torque) operation at the three excitation frequencies. (Note: All per-unit variables, including frequency, are normalized by their rated values at 60 Hz).
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Exc. Freq, /3 [in pu] Motoring (Te > 0)
Tmax_m [in pu]
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1.0 pu
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0.5 pu 0.1 pu
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Iimr-m[in pu] cosimr-in [in pu]
Generating (Te < 0)
Tmax_g [in pu]
IimT-g[in pu] womT-g [in pu]
b) Find the "voltage boost" that would be required at we =13 = 0.5 and 0.1 pu in order to hold the maximum motoring torque Tmax_m constant at its value for we = 13 = 1.0 pu operation. The voltages should be expressed as fractional values of the voltage that would be applied if the stator voltage is scaled in direct proportion to the excitation frequency (as in part a above). Also find the resulting maximum torque in the generating mode Tmax_g when this same boost voltage is applied.
13 = 0.5 pu V05 =___________ x 0.5 pu Tmax g = ___________ pu
(3 = 0.1 pu V01 =__________ x 0.1 pu Tmax g = ___________ pu