Circle diagram

The circle diagram (also known as Heyland diagram or Heyland circle) is the graphical representation of the performance of the electrical machine[1][2][3] drawn in terms of the locus of the machine's input voltage and current.[4] It was first conceived by Alexander Heyland in 1894 and Bernhard Arthur Behrend in 1895. A newer variant devised by Johann Ossanna in 1899 is often named Ossanna diagram, Ossanna circle, Heyland-Ossanna diagram or Heyland-Ossanna circle. In 1910, Josef Sumec further improved the diagram by also incorporating the rotor resistance, then called Sumec diagram or Sumec circle.

For the chart with marked sectors of a circle, see Pie chart.
For other circle diagrams, see Smith chart and Nyquist plot.

Constant air-gap induction motor equivalent circuit

The circle diagram can be drawn for alternators, synchronous motors, transformers, induction motors. The Heyland diagram is an approximate representation of a circle diagram applied to induction motors, which assumes that stator input voltage, rotor resistance and rotor reactance are constant and stator resistance and core loss are zero.[3][5][6] Another common circle diagram form is as described in the two constant air-gap induction motor images shown here,[7][8] where,

  • Rs, Xs: Stator resistance and leakage reactance
  • Rr', Xr', s: Rotor resistance and leakage reactance referred to the stator and rotor slip
  • Rc, Xm, : Core and mechanical losses, magnetization reactance
  • Vs, Impressed stator voltage
  • I0 = OO', IBL = OA, I1 =OV: No load current, blocked rotor current, operating current
  • Φ0, ΦBL : No load angle, blocked rotor angle
  • Pmax, sPmax, PFmax, Tmax, sTmax: Maximum output power & related slip, maximum power factor, maximum torque & related slip
  • η1, s1, PF1, Φ1,: Efficiency, slip, power factor, PF angle at operating current
  • AB: Represents rotor power input, which divided by synchronous speed equals starting torque.

The circle diagram is drawn using the data obtained from no load and either short-circuit or, in case of machines, blocked rotor tests by fitting a half-circle in points O' and A.

Beyond the error inherent in the constant air-gap assumption, the circle diagram introduces errors due to rotor reactance and rotor resistance variations caused by magnetic saturation and rotor frequency over the range from no-load to operating speed.

Constant air-gap induction motor circle diagram

See also

References
  1. Behrend, Bernhard Arthur Behrend (1921). The Induction Motor and Other Alternating Current Motors, their Theory and Principles of Design. McGraw-Hill. p. ix. OL 7033483M.
  2. Heyland, Alexander Heinrich [in German] (1894). "A Graphical Method for the Prediction of Power Transformers and Polyphase Motors". ETZ. 15: 561–564. Retrieved 2013-01-04.
  3. Terman, Frederick Emmons; Freedman, Cecil Louis; Lenzen, Theodore Louis; Rogers, Kenneth Alfred (January 1930). "The General Circle Diagram of Electrical Machinery". Transactions of the American Institute of Electrical Engineers. American Institute of Electrical Engineers. 49.
  4. Bhattacharya, S. K. (2008-08-27). Electrical Machines (2008 ed.). Tata McGraw-Hill Education. p. 359. ISBN 978-0-07-066921-5.
  5. Heyland, Alexander Heinrich [in German] (1906). A Graphical Treatment of the Induction Motor. G. H. Rowe, R. E. Hellmund (translators). McGraw Publishing Company. Retrieved 2013-01-10.
  6. "The Asynchronous Motor Model" (PDF). Phase to Phase BV. 2006. pp. 5–6. Archived from the original (PDF) on 2014-08-10. Retrieved 2013-01-10.
  7. Alger, Philip L.; et al. (1949). "'Induction Machines' subsec. of sec. 7 - Alternating-Current Generators and Motors". In Knowlton, A. E. (ed.). Standard Handbook for Electrical Engineers (8 ed.). McGraw-Hill. pp. 710–711.
  8. Fernandez, Francis M. "Construction of Circle Diagram" (PDF). College of Engineering Trivandrum. Archived from the original (PDF) on 2014-08-08. Retrieved 2013-01-10.
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