Circle diagram construction

Reference notes

Use Next → on the narrator above to construct the induction-motor circle diagram from no-load and blocked-rotor test data, then read operating points off it.

What the circle diagram is

The circle diagram is a graphical solution of the induction motor's equivalent circuit. As load varies, the locus of the stator current vector in the complex plane traces (almost exactly) a circle. One circle, one chart, every operating quantity — current, power factor, input power, output power, torque, slip, efficiency — readable directly.

It predates SPICE and Python by about a century. Today it's largely superseded by computer calculations, but it remains the cleanest visualisation of how an induction motor's electrical behaviour evolves with load.

Build it from two tests

You only need the no-load (NL) test and the blocked-rotor (BR) test data from the previous induction lesson. From these:

• NL point — plot the no-load current I₀ as a phasor from the origin, at its no-load power-factor angle (almost 90° lagging — the motor is almost a pure reactor at no-load).
• SC point (blocked-rotor scaled to full voltage) — the BR test was run at reduced voltage; scale the current linearly to what it would be at rated voltage. Plot at its blocked-rotor power-factor angle.
• Draw the circle that passes through both points, with its centre on the horizontal line through I₀.

The radius is automatic — once you have the two points and the centre-line direction, the circle is determined.

Reading the circle

Any operating point sits on the circle. From its position:

• Stator current |I₁| and power factor cos θ — magnitude and angle of the phasor from the origin to the operating point.
• Input power P_in ∝ vertical projection of the operating point (because V is along the vertical axis, and P = V·I·cos θ).
• Output (mechanical) power P_mech ∝ vertical distance between the operating point and the "output line" (a chord drawn between the NL point and the SC point).
• Air-gap power P_g ∝ vertical distance between the operating point and the "torque line" — a parallel chord positioned just below the output line.
• Rotor copper loss = P_g − P_mech = vertical distance between the output line and the torque line at the operating point.
• Stator copper loss = vertical distance from the torque line down to the no-load line.
• Slip = (rotor Cu loss) / P_g = the 1 : s : (1−s) ratio applied to those vertical distances.
• Torque = P_g / ω_s (synchronous watts, divided by synchronous angular speed). Read directly off the air-gap line.
• Efficiency = P_mech / P_in — ratio of two vertical lengths.

Why this is still useful

• It shows at a glance how power factor improves and efficiency rises as load grows from no-load up to rated, and how both degrade as load is pushed further.
• The maximum-torque, maximum-power-factor, and maximum-power-output operating points all appear as specific tangent points on the circle — geometrically obvious.
• For a student, the circle diagram is one of the most enlightening single-page explanations of induction-machine behaviour ever invented.

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