Tomasz WĘGIEL SPACE HARMONIC INTERACTIONS IN PERMANENT MAGNET GENERATORS    Cracow University of Technology Publisher Cracow 2013

  The development of magnetic material engineering and production of high-performance magnets, enabling the excitation of magnetic fields comparable to those produced electromagnetically caused synchronous generators excited by permanent magnets (PM) to be seriously used in high-power applications. Interest in synchronous generators excited by PM is also associated with global trends to support local power systems with renewable energy sources, in which synchronous generators excited by permanent magnets are often used. Mathematical models of generators should be capable to, in a relatively simple manner, resolve various operational issues associated with the production of electrical energy. For this reason, both design and mathematical modelling techniques of these machines are continually developed and improved.
  The work presents the methodology of creating the so-called circuit mathematical models of synchronous machines excited by permanent magnets. These models include the term co-energy and dependences representing flux linkage that are defined for windings placed in a magnetic circuit with permanent magnet linear characteristics. The shape of the magnetic circuit is modelled using the function of unit permeance.
  The monograph presents the methodology to determine the distribution of magnetic field in the magnetic circuit of a machine with surface-mounted magnets on the rotor, which creates a chance of an analytical determination of energy dependences, inductances and characteristics of windings in a currentless state.
   In order to write the equations of mathematical models, Lagrange’s formalism was used, by defining a modified co-energy function for coils placed in the magnetic circuit, wherein a permanent magnet is located. This enabled the creation of mathematical models, very similar to conventional synchronous generators excited electro-magnetically.
In the monograph, a detailed analysis of a three-phase synchronous generator excited by permanent magnets mounted on the rotor surface is carried out. Particular attention was paid to such processing of equations with respect to models excited by permanent magnets, so as to create a possibility to determine the machine properties in states established on the basis of equations, without even having to use quantitative solutions. The theory of linear differential equations used here, with periodically variable coefficients allowed a precise determination of Fourier spectra with respect to winding currents and electromagnetic torque (both quantitatively and qualitatively) in steady state operating conditions.
   Analyses of space harmonic interaction in a steady state were presented for the generator operating with a three-phase resistive load and cooperating with a diode rectifier. The obtained satisfactory convergence between the results of calculations and measurements confirmed the initial assumption that the developed circuit models of generators excited by PM are sufficiently accurate and can be useful in the analyses and tests of operational issues at the final stages of the design process.