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 R_m):

        r₁ = 0.018                                x₁ = 0.085                         x_m = 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 w_e =13 = 1.0, 0.5, and 0.1 pu. Determine the maximum torque T_max, the corresponding slip frequency at maximum torque, wow = 1³ - WrMT (in pu) where co_rm', is the rotor speed in pu at maximum torque, and the stator current amplitude I_nn' 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).

Iimr-m[in pu] cosimr-in [in pu]

Generating (T_e < 0)
T_max__g [in pu]

IimT-g[in pu] womT-g [in pu]

b) Find the "voltage boost" that would be required at w_e =13 = 0.5 and 0.1 pu in order to hold the maximum motoring torque T_max__m constant at its value for w_e = 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 T_max__g when this same boost voltage is applied.

13 = 0.5 pu                              V₀₅ =___________ x 0.5 pu            T_max g = ___________  pu

(3 = 0.1 pu                               V01 =__________ x 0.1 pu            T_max g = ___________  pu