Circle Diagram of Induction Motor

What Is a Circle Diagram?

A circle diagram plots the approximate steady-state current locus of an electrical machine as its operating condition changes. Related graphical methods can be applied to transformers, alternators and synchronous motors. This article covers the classical Heyland diagram for balanced three-phase induction motors.

Importance of Circle Diagram

A phasor diagram shows the relationship between current and voltage at one operating point. The circle construction places a range of assumed operating points on one plane. With the chosen current and power scales, it can estimate output power, power factor, torque, slip, speed, copper loss and efficiency. These are graphical estimates rather than direct measurements.

Tests Used to Draw the Circle Diagram

The construction uses no-load and blocked-rotor test data from the induction motor. During the no-load test, the shaft runs without an external load at rated voltage. Measure line voltage, line current and total three-phase input power, commonly with the two-wattmeter method. The input includes stator copper, core, friction, windage and stray losses. Slip is small and is approximated as zero for the basic construction. The readings give the no-load current magnitude and power-factor angle.

During the blocked-rotor test, secure the rotor and apply a reduced voltage until the specified test current flows. Keep the test short to limit heating. The rotor slip is one, like a transformer with a short-circuited secondary. Measured voltage, current and input power give the blocked-rotor current phasor and combined series impedance. A separate stator-resistance value is needed to divide total copper loss between stator and rotor.

How to Draw Circle Diagram of Induction Motor

Choose consistent current and power scales before starting. Then use the measured phasors to construct the diagram shown below:

1. Plot the no-load current at its measured angle as line OA, where θ₀ is the no-load power-factor angle.
2. Plot the blocked-rotor current at its measured angle as line OC, where θ_B is the blocked-rotor power-factor angle. Scale the current to rated voltage if the construction method requires it.
3. Draw the perpendicular bisector of AC. Extend it to intersect line AE; this intersection is the circle centre.
4. For a selected operating point, plot the stator-current phasor from the origin to point B on the circle, using the chosen current scale.
5. AC is the output line in this construction. At operating point B, the vertical intercept MB represents output power when read with the selected power scale.
6. Read total copper loss from line GM at the same operating point.
7. To draw the torque line, divide total copper loss into stator and rotor components. In the labelled construction, DE represents stator copper loss and CD represents rotor copper loss; this locates point E.
8. AD is the torque line used to read developed torque from the chosen operating point.

Parts of a Circle Diagram

The parts of a circle diagram include:

• Maximum output power
• Maximum torque
• Maximum Input Power

Maximum Output Power

Maximum output occurs where a tangent to the circle is parallel to the output line. Draw a perpendicular from the circle centre to the output line and extend it to the circle at M.

Maximum Torque

Maximum torque occurs where a tangent to the circle is parallel to torque line AD. Draw a perpendicular from the centre to AD and extend it to the circle at N.

Maximum Input Power

Maximum input power occurs at the point whose tangent is horizontal. For the orientation shown, the highest point of the circle is marked R and its vertical ordinate extends towards S.

Conclusion of Circle Diagram

The circle diagram assumes constant machine parameters and a circular current locus. Test error, voltage scaling, saturation, rotor-parameter variation and drawing precision all affect the result. Use it for an estimate and state the scale and assumptions with every plotted value.

A hand-drawn circle diagram takes time and can add plotting error. Equivalent-circuit calculations or software are better when repeatability and numerical precision matter. For more practice with motor concepts and related topics, see these basic electrical questions.