Synchronous Machine Winding Layout & Flux Animation Tool

This paper describes the development and application of a tool created in MathCAD® to illustrate the internal workings of a synchronous machine on video. Upon receiving a set of parameters and preferences, the tool creates an interactive animation of the currents, magnetic flux, and physical rotation of the machine. The tool even recommends the best settings to obtain a movie that loops to simulate continuous rotation in a fast or slow motion. This enables the student to see what a finite element program might reveal about a synchronous machine but requires only the same MathCAD® readily available on a university-wide license. The program has an attractive level of sophistication. For example, its inputs are the following: physical dimensions, number of poles and slots, air gap width, frequency, positive and negative sequence inputs, appropriate motor or generator sign convention, power and torque output, resistances, reactances, simulation time and time step, and calculation density. The tool then builds and displays an appropriate physical cross-section diagram of the stator created from the given dimensions, showing a correct number of slots with their windings properly pitched. It calculates a complete lumped parameter d-q model, displaying its particulars on request. The tool then creates the rotor from the given dimensions, with windings appropriately placed, pitched, and skewed. The rotor has a calculation burden appropriate for the animation. The program calculates flux linkage, illustrating it as an animated distribution of arrows similar to the manner in which finite element programs show this. The density of the points for flux linkage analysis and the information that their arrow distribution shows is another usercontrolled option, based on assigned permeabilities and calculated topology. Calculations are based on a Biot-Savart model of the magnetic, consistent with Maxwell's equations. The program updates these with every time step as the machine rotates. A plotting algorithm, specially developed to illustrate the results, shows an animated illustration of the machine's currents, magnetic fluxes, and rotation. The tool calculates a companion phasor diagram to help explain the machine's state and the interaction of its voltages, currents, and lumped parameter model of internal behaviors. This collaborating phasor diagram can be displayed next to the animated cross section illustration of the machine. Animation controls, as with all inputs and controls, are available on a graphical user interface. P ge 24150.2 The tool is intended not to replace finite element analysis, but to provide an illustration of appropriate results gained at no extra cost to the college student who is already using MathCAD®. It is appropriate for use in classroom and instructional settings and likely pertains to the college undergraduate or graduate levels. In presenting this paper, we will show the animation, we will provide assessment data from use with students, and we will provide a link for download of the tool. We have employed this program in college classroom demonstrations, but not for student use on projects yet. Student reaction, taken anecdotally so far and not rigorously sampled, enthusiastically supports the program’s value for illustrating machine behavior and for gaining familiarity with the output of a finite element program. Faculty reaction to this program has likewise been quite enthusiastic, reinforcing with comments its value as a means to illustrate elementary synchronous machine functions without the price tag of a finite element software package. The Overall Objective The objective of this Animation Tool is to assist the studying engineer in understanding the electrical and magnetic interactions of a 3 phase synchronous machine. This educational motive is achieved by permitting a simple way to enter Synchronous Machine (S/M) parameters and immediately see interactive results all in the familiar software environment of MathCAD®. A visual depiction of an axial cutaway view of a S/M is automatically produced and is accompanied by a corresponding phasor diagram. To further enhance S/M understanding, the tool visually depicts changes to electrical and magnetic parameters as the user gradually advances through full electrical cycles or utilizes the incorporated assisted animation tool. It was the desire to learn that prompted the development of this tool, and it is the desire to inform that keeps it going, hopefully in an enjoyable way. Classroom objectives obtained from the tool may include an understanding of winding layout in conjunction with various pole, slot, and pitch combinations. Numerous arrangements could be presented quickly to permit efficient use of classroom time to illustrate the basics of S/M physical layout. Once animated, objectives may focus on how a three phase system produces a balanced, rotating magnetic field. Students can see how the stator-produced rotating field interacts with the rotor magnetic field to yield a range of power output levels. The phasor diagram provides performance feedback as the user changes machine parameters, thus permitting another set of related objectives. A variety of classroom objectives can be drawn to ultimately result in enhanced student understanding of the 3 phase S/M. Here, we have only touched on the most basic objectives, but I believe many more will be extracted as the reader explores the details.