## Circle diagram of induction motor

To understand the **circle diagram of induction motor** we should first know what is the circle diagram; The circle diagram is a graphic representation of the performance of the machine and it’s drawn in terms of the locus of the input voltage and current. And it’s based on the approximate equivalent circuit.

Before deepen in steps of drawing the diagram it’s important to know:

#### Importance of circle diagram:

A picture is worth 1000 words, that’s the importance of the circle diagram in a simple description. But we use the circle diagram because:

- It is a phasor diagram drawn for than more one circuit condition in one plan; The phasor diagram provides us with the between voltage and current at only a single circuit condition.
- It provides us with the power output, power factor, speed, slip, torque, efficiency, and copper loss of the induction motor in a graphical representation.
- The diagram is also easier to remember and understand compared to the theoretical and mathematical description.

#### Test performed to compute data required for drawing circle diagram:

To draw the** circle diagram of induction motor** we do three tests:

**No load test:**

In this test, the motor runs at the rated supply voltage without any load so there would be no losses.

We assume the slip =0, the supply line voltage is V0, and the line current is I0;

We perform this test to calculate the angle between voltage and current which would be large because we have a high inductive reactance at no load.

**Φ0= P0/(√(3 ) V0I0).**

**Blocked rotor test:**

In this test, we block the rotor and apply a reduced supply voltage to obtain the rated current at the terminal of the motor, the angle between the voltage and current, also the rotor and stator copper loss.

**Φsc= Psc / √(3 ) VscIsc.**

**ISN ( current drawn when applying the rated voltage at blocked rotor condition)= Isc.V0/Vsc.**

**PSN (power input of the rated voltage in blocked rotor condition) = Psc (V0/Vsc)^2.**

**Resistance test:**

In resistance test, we apply the voltmeter-ammeter method to calculate the per phase equivalent stator resistance.

### Construction of circle diagram:

All the above information lights up our way to draw the **circle diagram** we apply the Kirchhoff’s current law at the approximate equivalent circuit to have:

**I1= I0+I’2.**

From this equation we start to draw;

The no-load current lags the voltage V1 by the angle Φ0 which ranges between 60 to 80 degrees; The get the no-load current and the no-load angle from the no-load test as we say.

At no load we have:

I0=V1/Zn1.

While: Zn1= (R0 ||jX0).

And also, we have no load loss:

P0=V1I0 cos Φ0.

When we refer the rotor current to the stator we have:

Of course, I’2 lags the voltage V1 and the angle between them will be:

While;

If we combine the above two equations we will have:

We also need to know:

- Rs: stator resistance.
- Xs: stator leakage reactance.
- R’r: rotor resistance referred to the stator and rotor slip.
- X’r: leakage reactance referred to the stator and rotor slip.
- Rc: core and mechanical losses.
- Xm: magnetization reactance.
- Vs: impressed stator voltage.
- I0 (no load current) =OO’.
- IBL ( blocked rotor current) =OA.
- I1 ( operating current) =OV.
- Φ0: no load angle.
- ΦBL: blocked rotor angle.
- Pmax: maximum output power.
- SPmax: slip related to maximum power.
- Tmax: maximum power factor.
- STmax: slip related to maximum power.
- ƞ1: Efficiency.
- S1: slip.
- PF1: power factor.
- Φ1: PF angle at operating current.
- AB: present rotor power input.

From this information, we finally have the coming diagram.

#### Result obtained from the circle diagram:

From the circle diagram we can obtain:

- Input power.
- Rotational losses.
- Stator copper loss.
- Rotor copper loss.
- Output power.
- Output torque.
- Starting torque.
- Slip.
- Speed.
- Efficiency.
- Also, the power factor.

I think everything will be clear when we see this example;