Circle diagram
Graphical locus of input voltage and current for electrical machines.
The circle diagram, also known as a Heyland, Ossanna, or Sumec diagram, is a graphical representation of the performance of an electrical machine in terms of the locus of the machine's input voltage and current. It is notable for providing a visual method to analyze induction motor behavior, particularly by plotting the real and imaginary parts of the current phasor as a circle in the complex plane.
- First conceived by
- Alexander Heyland (1894) and Bernhard Arthur Behrend (1895)
- Improved by
- Johann Ossanna (1899) and Josef Sumec (1910)
- Sumec contribution
- Incorporated rotor resistance
- Heyland diagram assumptions
- Stator input voltage, rotor resistance and rotor reactance constant; stator resistance and core loss zero
- Data sources
- No load test and blocked rotor test
Lore & Background
The circle diagram was first conceived by Alexander Heyland in 1894 and Bernhard Arthur Behrend in 1895, and subsequently improved by Johann Ossanna in 1899 and Josef Sumec in 1910. Sumec's contribution was to incorporate the rotor resistance. The Heyland diagram is an approximate representation of a circle diagram applied to induction motors, assuming that stator input voltage, rotor resistance and rotor reactance are constant and that stator resistance and core loss are zero. The theory begins with Steinmetz's analysis of an induction motor as a real transformer attached to a varying resistance.
Reader's Guide
The circle diagram obtains its name because the real and imaginary parts of the current phasor form a circle in the complex plane. Further information can be obtained through additional geometric constructions on the same plot. The appropriate scale identifies current with power, multiplying the current by the phase voltage and the number of phases. A complete diagram includes parameters such as stator resistance and leakage reactance, rotor resistance and leakage reactance referred to the stator and rotor slip, core and mechanical losses, magnetization reactance, impressed stator voltage, no load current, blocked rotor current, operating current, no load angle, blocked rotor angle, maximum output power and related slip, maximum power factor, maximum torque and related slip, efficiency, slip, power factor, and PF angle at operating current. The line AB represents rotor power input, which divided by synchronous speed equals starting torque. In practice, the circle diagram is drawn from data obtained from no load and either short-circuit or 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.
Frequently Asked Questions
What is the Circle diagram?
The Circle diagram (also called the Heyland, Ossanna, or Sumec diagram) is a graphical tool that maps an electrical machine's input voltage and current by plotting the real and imaginary parts of the current phasor as a circular locus in the complex plane. It gives engineers a quick visual way to read off induction motor performance without grinding through lengthy algebra.
Who created the Circle diagram?
Alexander Heyland first proposed the concept in 1894, and Bernhard Arthur Behrend followed with his own version in 1895. Johann Ossanna refined the method in 1899, and Josef Sumec added further improvements in 1910, building on the earlier work.
What assumptions does the Heyland version of the diagram rely on?
The Heyland formulation treats stator input voltage, rotor resistance, and rotor reactance as fixed constants while assuming stator resistance and core losses are zero. These simplifications are what allow the current phasor to trace a clean circular path rather than a more complicated curve.
What did Sumec add to the Circle diagram?
Josef Sumec's 1910 refinement explicitly incorporated rotor resistance into the model in a way the earlier Heyland and Ossanna versions did not fully capture. This made the graphical method more faithful to real motor behavior where rotor resistance effects are hard to ignore.
What test data is needed to construct the Circle diagram?
Two standard laboratory measurements feed the construction: the no-load test and the blocked-rotor test. Together they supply the parameters required to draw the circular locus and read off performance values at any chosen operating point.
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