The Induction Motor

-->

The Induction Motor

The theory of the induction motor is well known [10], so only the basics will be described here. Fig. IM-1 shows a cross-section view of a three-phase induction motor, with the stator and rotor coils represented by concentrated windings. Voltage equations can be written for the stator and rotor phases in terms of self and mutual-inductances. As the rotor moves in figure IM-1, the mutual inductances between the rotor and stator coils will change, because the angle between the axes of the rotor and stator changes. To eliminate the time-varying inductances, the equations are frequently transformed to q-d-0 variables in the arbitrary reference frame. For this simulation, we used a stationary reference frame, which has the advantage of eliminating some terms from the voltage equations. 

-->

The simulation of the induction motor, is conveniently accomplished by solving for the flux linkages per second in terms of the voltages applied to the machine.  The derivatives of the stator flux linkages are given by equations IM1 to IM3.  In these equations and the following equations, the superscript "s" indicates the stationary reference frame.  The subscript "s" indicates stator quantities, and omega sub b is the base radian electrical frequency. 

 

-->

Fig. IM-2 shows the Graphic Modeller simulation of the induction motor.  As noted above, the model for the induction motor requires voltages as inputs.  Thus one block consists of a three-phase source that provides a balanced set of three-phase voltages.  The induction motor block is a compound block that contains another level, and will be described in the next paragraph.  The final block in the model is the load torque, which by suitable choice of constants allows constant power, constant torque, horsepower squared, and horsepower cubed loads.  For convenience there are also two strip plot recorders that plot the stator and rotor phase currents.  Double clicking them, after a simulation run, will plot the appropriate variables.
 

-->

Induction motor simulation in Graphic Modeller

-->

Double clicking on the induction motor block reveals the next level of detail as shown in Fig. IM-3.  Compound blocks can be used to allow multiple levels in a model.  That has the advantage of keeping the amount of blocks to a reasonable number at any given level of the model.  In this case, the compound block was used so the model could be used as a tool by undergraduates who are not concerned with the simulation equations.  More advanced undergraduate and graduate students, on the other hand can go down a level to understand the theory behind the simulation.

Since the inputs and outputs to the compound block are phase voltages and currents, they must be transformed to the stationary reference frame.  Thus, the leftmost blue block contains the equations to transform the phase voltages to the stationary reference frame, and the q-d-0 stationary reference frame currents to phase currents.  The center green block contains ACSL code representing equations IM-1 through IM-16, and is thus the actual simulation of the electrical portion of the induction motor.  This block also contains constants for the parameters of the machine, which can be changed by the user to represent other machines.  The purple box contains the code for equation IM-17 and determines the speed and position of the rotor as a function of time.  The last block (the right blue one) is another transformation.  In this case the rotor q-d-0 currents are transformed to phase currents in the rotor reference frame.