A 4160 V, 2500 hp, 2 pole, 3 phase, Y-connected, 3580 rpm, 60 Hz squirrel-cage i
ID: 2085761 • Letter: A
Question
A 4160 V, 2500 hp, 2 pole, 3 phase, Y-connected, 3580 rpm, 60 Hz squirrel-cage induction motor is driving a boiler-feed pump. The motor parameters are: X,= X2= 0.72 ohm/phase, Xv= 3 ohm/phase, neglect all resistances. Open-circuit transient time constant= 3.6 sec Short-circuit time constant= 0.12 sec The motor is operating fully loaded at rated voltage and draws 2160 kVA at 0.9 power factor from the mains. Compute the transient reactance and draw the constant voltage behind transient reactance model. Compute the current and E (magnitude and phase angle). Determine the time required after interruption of the normal supply for the residual voltage to decay to 25 percent of the normal bus voltage. Note that when the normal source is tripped, flux linkages are "trapped" with the closed rotor circuits of the operating motors, producing a voltage at the terminals (often called the residual voltage) which may require an appropriate time to decay to zero. Determine the speed to which the motor decelerates in this interval (computed in part c). The inertia of the motor and the pump impeller is 76 kg.m2 and the load torque varies as the square of the speed. (Neglect all losses are neglected. 1 hp=746 W.)
Explanation / Answer
In electrical engineering and mechanical engineering, a transient response or natural response is the response of a system to a change from equilibrium. The transient response is not necessarily tied to "on/off" events but to any event that affects the equilibrium of the system. The impulse response and step response are transient responses to a specific input (an impulse and a step, respectively).
DAMPING:
The response can be classified as one of three types of damping that describes the output in relation to the steady-state response.
An underdamped response is one that oscillates within a decaying envelope. The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here damping ratio is always <1.
A critically damped response is the response that reaches the steady-state value the fastest without being underdamped. It is related to critical points in the sense that it straddles the boundary of underdamped and overdamped responses. Here, damping ratio is always equal to one. There should be no oscillation about the steady state value in the ideal case.
An overdamped response is the response that does not oscillate about the steady-state value but takes longer to reach than the critically damped case. Here damping ratio is greterthan 1 it is the response of a system with respect to the input as a function of time.
properties:
Rise time
Rise time refers to the time required for a signal to change from a specified low value to a specified high value. Typically, these values are 10% and 90% of the step height.
Overshoot
Overshoot is when a signal or function exceeds its target. It is often associated with ringing.
Settling time
Settling time is the time elapsed from the application of an ideal instantaneous step input to the time at which the output has entered and remained within a specified error band.
Delay-time
The delay time is the time required for the response to reach half the final value the very first time
Peak time
The peak time is the time required for the response to reach the first peak of the overshoot.
Steady-state error
the steady-state error of a system as "the difference between the desired final output and the actual one" when the system reaches a steady state, when its behavior may be expected to continue if the system is undisturbed.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.