Spring 2014, EECE 549: Assignment 3: Induction Machine Modeling Due on Monday, March 3

rd (in class)

Develop a Simulink model for the 500-hp induction machine (IM) from the reference book (p. 165). Use

the Arbitrary Reference Frame (ARF) so that you can change the speed ω. Try to use a MATLAB script

file to store and load model parameters. Also implement a balanced 3-phase sinusoidal voltage source

(VS) with variable amplitude to supply the IM with the rated (nominal) voltages. Determine the system’s

eigenvalues and comment about numerical stiffness. Choose an ode solver with the settings (error

tolerances and step-size limits) that you think produces trustable results and is numerically efficient.

Comment on your choice.

1) Assume a short-circuited (or squirrel-cage) rotor. In this part you will simulate the start-up transient

assuming zero initial conditions and no mechanical load. Run the model up to 2 sec (roughly to steady-

state). Use different speed for the reference frame: (a) stationary reference frame ω = 0; (b) rotor

reference frame ω = ωr; and (c) synchronous reference frame ω = ωe = ωb. In each case, plot variables:

qdsv , qdsi , qdri , asi , and, m (all on one page using the subplot command). Comment on the

frequency of currents, voltages, and flux linkages as viewed in different frames of reference. Which

reference frame resulted in the most numerically efficient solution? (Hint: use a variable time step

solver and compare the number of time steps).

2) The same model can also be implemented directly as a coupled circuit model in abc variables. Write a

MATLAB code to implement this model and show the start-up transient similar to part 1 using the

same ode solver. Compare the results and numerical efficiency with the model in part 1.

3) For all subsequent studies, use your qd model from part 1 in Simulink. In this part, set the initial

condition for no-load steady-state (hint: run the model until it is in steady-state. Save the final states

and use them as initial states for the next run. You can access the initial and final state settings from

Configuration Parameters in Simulation menu of your Simulink model file). Then, simulate this load

change: the machine starts from no load; at t = 0.1 s, a constant mechanical load of Tm = 1,980 Nm is

applied; at t = 0.6 s, the mechanical torque is reversed to Tm = −1,980 Nm. Run the model to t = 1.2 s

and plot stator current ias, electromechanical torque Te, rotor speed ωrm, slip frequency ωs, input real

and reactive powers Pe and Qe (book p. 139), and mechanical output power Pm. Explain the results and

the flow of real and reactive powers.

4) Incorporate magnetic saturation into your model. Use the synchronous reference frame. Start the

machine with 70% of the rated voltage. Then, at t = 3.5 s step the voltage up to 100% of the rated value

and continue to run the model till t = 5 s. Plot ias, Te, ωrm, and ωs with and without saturation. On one

plot compare iqs and ids with and without saturation showing the time interval from 3.45 to 3.65

seconds. Comments on the effect of saturation. Are the ac currents distorted due to saturation similar to

what you have seen in transformer?

5) Assume that you have a wound-rotor induction machine and can connect a three phase variable

resistors rr to the rotor terminals. In this part, you will change the steady-state torque-speed

characteristic by adjusting the rotor resistance to an optimal value (see eq. 4.9-22 [correct the typo in

this equation] and Fig. 4.9-3). a) Determine the additional rotor resistance as a function of speed

rrr such that the motor can accelerate using maximum torque. Plot the resulting steady-state

torque-speed characteristic and compare it with the machine with shorted rotor circuit; b) Repeat the

start-up transient study of part 1 and compare the results. Plot and compare ωrm, instantaneous real

power Pe, and the total energy spent during the entire transient upstartE . Which method is more

energy efficient? c) Assume that a motor like this can be realized using a double-cage rotor, NEMA

design type C. Sketch the qd equivalent circuit of the model in this part. Also sketch a model with two

rotor circuits and compare the two models (compare the equivalent circuits, no simulation is needed).

6) Suppose that you have a variable transformer to control the induction motor speed by changing just

the applied voltage magnitude. Considering the steady-state torque-speed characteristic of the motor,

how effective this technique of controlling motor speed is? For what type of motors would this

technique work? Using your model, try to obtain a transfer-function from the input voltage magnitude

to torque Te at an operating point corresponding to nominal speed and torque. Explain your method and

the order of the transfer function. If you had a hardware motor-load system, how would you go about

extracting this transfer-function?