title: Circle diagram
text: # Circle diagram
  
  The circle diagram (also known as Heyland diagram or Heyland circle) is the graphical representation of the performance of the electrical machine drawn in terms of the locus of the machine's input voltage and current. It was first conceived by Alexander Heyland [de] in 1894 and Bernhard Arthur Behrend in 1895. A newer variant devised by Johann Ossanna [de] in 1899 is often named Ossanna diagram, Ossanna circle, Heyland-Ossanna diagram or Heyland-Ossanna circle. In 1910, Josef Sumec [d] further improved the diagram by also incorporating the rotor resistance, then called Sumec diagram or Sumec circle.
  
  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. Another common circle diagram form is as described in the two constant air-gap induction motor images shown here, where,
  
  * $R_s,$ $X_s:$ Stator resistance and leakage reactance
  * $R_r^',$ $X_r^',$ s: Rotor resistance and leakage reactance referred to the stator and rotor slip
  * $R_c,$ $X_m,$ : Core and mechanical losses, magnetization reactance
  * $V_s,$ Impressed stator voltage
  * $I_0$ = $OO^',$ $I_{BL}$ = OA, $I_1$ =OV: No load current, blocked rotor current, operating current
  * $Φ_0,$ $Φ_{BL}$ : No load angle, blocked rotor angle
  * $P_{max},$ $s_{Pmax},$ $PF_{max},$ $T_{max},$ $s_{Tmax}:$ Maximum output power & related slip, maximum power factor, maximum torque & related slip
  * $η_1,$ $s_1,$ $PF_1,$ $Φ_1,:$ 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.
  
  