Constant air-gap induction motor equivalent circuit
Thecircle diagram (also known asHeyland diagram orHeyland circle) is the graphical representation of the performance of theelectrical machine[1][2][3] drawn in terms of the locus of the machine's input voltage and current.[4] It was first conceived byAlexander Heyland [de] in 1894 and Bernhard Arthur Behrend in 1895. A newer variant devised byJohann Ossanna [de] in 1899 is often namedOssanna diagram,Ossanna circle,Heyland-Ossanna diagram orHeyland-Ossanna circle.In 1910,Josef Sumec [d] further improved the diagram by also incorporating the rotor resistance, then calledSumec diagram orSumec circle.
The circle diagram can be drawn foralternators,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 fromno load and eithershort-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.
^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.
