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9: Synchronous machine and winding models

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    Introduction

    The objective here is to develop a simple but physically meaningful model of the synchronous machine, one of the major classes of electric machine. We can look at this model from several different directions. This will help develop an understanding of analysis of machines, particularly in cases where one or another analytical picture is more appropriate than others. Both operation and sizing will be of interest here.

    Along the way we will approach machine windings from two points of view. On the one hand, we will approximate windings as sinusoidal distributions of current and flux linkage. Then we will take a concentrated coil point of view and generalize that into a more realistic and useful winding model.

    • 9.1: Relating Rating to Size
      It is possible, even with the simple model we have developed so far, to establish a quantitative relationship between machine size and rating, depending (of course) on elements such as useful flux and surface current density.
    • 9.2: Winding Inductance Calculation
      The purpose of this section is to show how the inductances of windings in round- rotor machines with narrow air gaps may be calculated.
    • 9.3: Physical Picture- Current Sheet Description
      Consider this simple picture. The ‘machine’ consists of a cylindrical rotor and a cylindrical stator which are coaxial and which have sinusoidal current distributions on their surfaces: the outer surface of the rotor and the inner surface of the stator.
    • 9.4: Continuous Approximation to Winding Patterns
      Now let’s try to produce those surface current distributions with physical windings.
    • 9.5: Classical, Lumped-Parameter Synchronous Machine
      Now we are in a position to examine the simplest model of a polyphase synchronous machine.
    • 9.6: Balanced Operation
      Now, suppose the machine is operated in this fashion: the rotor turns at a constant velocity, the field current is held constant, and the three stator currents are sinusoids in time, with the same amplitude and with phases that differ by 120 degrees.
    • 9.7: Reconciliation of Models
      We have determined that we can predict its power and/or torque characteristics from two points of view : first, by knowing currents in the rotor and stator we could derive an expression for torque vs. a power angle:
    • 9.8: Per-Unit Systems
      Before going on, we should take a short detour to look into per-unit systems, a notational device that, in addition to being convenient, will sometimes be conceptually helpful.
    • 9.9: Normal Operation
      The synchronous machine is used, essentially interchangeably, as a motor and as a generator. Note that, as a motor, this type of machine produces torque only when it is running at synchronous speed.
    • 9.10: Salient Pole Machines- Two-Reaction Theory
      So far, we have been describing what are referred to as “round rotor” machines, in which stator reactance is not dependent on rotor position.

    This page titled 9: Synchronous machine and winding models is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James Kirtley (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform.