## What is a Circle Diagram

A **circle diagram** is a graphical representation of the performance of an electrical machine. It is commonly used to illustrate the performance of transformers, alternators, synchronous motors, and induction motors. It is very useful to study the performance of an electric machine under a large variety of operating conditions. The diagrammatic representation of a circle diagram makes it much easier to understand and remember compared to theoretical and mathematical descriptions.

## Importance of Circle Diagram

The diagram provides information which is not provided by an ordinary phasor diagram. A phasor diagram gives relation between current and voltage only at a single circuit condition. If the condition changes, we need to draw the phasor diagram again. But a circle diagram may be referred to as a phasor diagram drawn in one plane for more than one circuit conditions. On the context of induction motor, which is our main interest, we can get information about its power output, power factor, torque, slip, speed, copper loss, efficiency etc. in a graphical or in a diagrammatic representation.

## Test Performed to Compute Data Required for Drawing Circle Diagram

We have to perform no load and blocked rotor test in an induction motor. In no load test, the induction motor is run at no load and by two watt meter method, its total power consumed is calculated which is composed of no load losses only. Slip is assumed to be zero. From here no load current and the angle between voltage and current required for drawing circle diagram is calculated. The angle will be large as in the no load condition induction motor has high inductive reactance.

In block rotor test, rotor is blocked which is analogous to short circuiting secondary of a transformer. From this test, we need to calculate short circuit current and the lag angle between voltage and current for drawing circle diagram. Also, we need rotor and stator copper loss.

## How to Draw Circle Diagram of Induction Motor

A circle diagram is commonly used to represent an induction motor. To draw a circle diagram like the one below:

- The no-load current and the no load angle calculated from no load test is plotted. This is shown by the line OA, where Ɵ
_{0}is the no load power factor angle. - The short circuit current and the angle obtained from block rotor test is plotted. This is shown by the line OC and the angle is shown by Ɵ
_{B}. - The right bisector of the line AC is drawn which bisects the line and it is extended to cut in the line AE which gives us the centre.
- The stator current is calculated from the equivalent circuit of the induction motor which we get from the two tests. That current is plotted in the circle diagram according to the scale with touching origin and a point in the circle diagram which is shown by B.
- The line AC is called the power line. By using the scale for power conversion that we have taken in the circle diagram, we can get the output power if we move vertically above the line AC to the periphery of the circle. The output power is given by the line MB.
- The total copper loss is given by the line GM.
- For drawing the torque line, the total copper loss should be separated to both the rotor copper loss and stator copper loss. The line DE gives the stator copper loss and the line CD gives the rotor copper loss. In this way, the point E is selected.
- The line AD is known as torque line which gives the torque developed by induction motor.

## Parts of a Circle Diagram

The parts of a circle diagram include:

- Maximum output power
- Maximum torque
- Maximum Input Power

### Maximum Output Power

When the tangent to the circle is parallel to the line then output power will be maximum. That point M is obtained by drawing a perpendicular line from the center to the output line and extending it to cut at M.

### Maximum Torque

When the tangent to the circle is parallel to the torque line, it gives maximum torque. This is obtained by drawing a line from the center in perpendicular to the torque line AD and extending it to cut at the circle. That point is marked as N.

### Maximum Input Power

It occurs when tangent to the circle is perpendicular to the horizontal line. The point is the highest point in the circle diagram and drawn to the center and extends up to S. That point is marked as R.

## Conclusion of Circle Diagram

This method is based on some approximations that we have used in order to draw the circle diagram and also, there is some rounding off of the values as well. So although there is some error to this method, it can still give us a good approximation of the results.

The main downside to a circle diagram is that although it is easy to interpret and read, it can be