SUPER-HIGH FREQUENCY MODELS AND BEHAVIOR OF IMs
Voltage strikes and restrikes produced during switching operations of induction motors fed from standard power grid may cause severe dielectric stresses on the stator IM windings, leading, eventually, to failure. In industrial installations high dielectric stresses may occur during second and third pole circuit breaker closure. The second and the third pole closure in electromagnetic power circuit breakers has been shown to occur within 0 to 700 μs . For such situations, electrical machine modeling in the frequency range of a few KHz is required. Steep fronted waves with magnitudes up to 5 p.u. may occur at the machine terminals under certain circuit breaker operating conditions. On the other hand, PWM voltage source inverters produce steep voltage pulses which are applied repeatedly to induction motor terminals in modern electric drives. In IGBT inverters, the voltage switching rise times of 0.05 to 2 μs, in presence of long cables, have been shown to produce strong winding insulation stresses and premature motor bearing failures. With short rise time IGBTs and power cables longer than a critical lc, repetitive voltage pulse reflection may occur at motor terminals. The reflection process depends on the parameters of the feeding cable between motor and inverter, the IGBTs voltage pulse time tr, and the motor parameters. The peak line to line terminal overvoltage (VpK) at the receiving end of an initially uncharged transmission line (power cable) subjected to a single PWM pulse with rise time tr  is
where the critical cable length lc corresponds to the situation when the reflected wave is fully developed; Vdc is the d.c. link voltage in the voltage source inverter and Γm is the reflection coefficient (0 < Γm < 1). Z0 is the power cable and Zm – the induction motor surge impedance. The distributed nature of a long cable L-C parameters favor voltage pulse reflection, besides inverter short rising time. Full reflection occurs along the power cable if the voltage pulses take longer than one-third the rising time to travel from converter to motor at speed u* ≈ 150 to 200 m/μs. The voltage is then doubled and critical length is reached  (Figure 21.1).