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Artificial Intelligence for Renewable Energy Systems


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      (1.18)image

      where xlax, xlay, and xlaz indicate leakage reactance between phase a (of winding set abc) with each phase of other winding set xyz.

      Phenomenon of mutual coupling is due to the sharing of same slot by stator winding conductor of different phase. This is signified by the term of common mutual leakage reactance (xlm). Value of xlm is dependent on displacement angle (α) and winding pitch, resulting in the variation in harmonic coupling of windings. By neglecting xlm, some variation is noted in the voltage harmonic distortion [13] with no change in transient effect. A detailed procedure for the determination of slot reactance is available [24] together with the standard method to evaluate the machine parameters [25, 26].

Schematic illustration of the circuit representation of a six-phase synchronous machine.

      (1.19)image

      (1.20)image

      (1.21)image

      (1.22)image

      (1.23)image

      (1.24)image

      (1.25)image

      Current in terms of flux is written as follows:

      (1.27)image

      (1.28)image

      (1.29)image

      (1.30)image

      (1.31)image

      ψmq and ψmd are defined using state variables as follows:

      (1.33)image

      (1.34)image

      where

      (1.35)image

      (1.36)image

      (1.37)image

      Developed electromagnetic torque (Te) and rotor dynamic equations for the machine can be expressed as follows:

      (1.38)image

      where

      (1.39)image

      the developed torque associated with the first winding set abc, and

      the developed torque associated with the second winding set xyz.

      where Te is overall developed electromagnetic torque and Tl is the prime mover torque. In the mathematical modeling, both motoring and generating mode is possible. In this chapter, generating mode is considered, where mechanical input torque Tl is fed from prime mover to generate the electrical output power, resulting the flow of current from machine to connected utility grid.

      Input voltages vabcs and vxyzs in stationary frame coordinate are transformed directly to images in rotor reference frame by using the transformation matrix [20, 22] images associated with each winding sets abc and xyz, respectively. The voltages applied to the damper windings are not shown, because voltages are zero due to short-circuited windings.