Circle diagram of a three-phase Induction motor.

Experiment No. 14

Aim of the Experiment: –

Circle diagram of a three-phase Induction motor.

Apparatus Required: –

Sl. No.NameSpecificationQuantity
1Three-Phase Auto-Transformer(0-600) V, 10 KVA1 no.
2Three-Phase IM400V, 6.9A, 1440 rpm, 50Hz1 no.
3Ammeter(0-10) A, MI1 no.
4Voltmeter(0-500) V, MI 1 no.
5Wattmeter(0-1500) W2 nos.
6TachometerDigital Type1 no.
7Connecting WirePVC Insulated CopperAs per required
Table: 14.1

Circuit Diagram: –

Fig. No. 3.1: Circuit diagram for No-load and block rotor test of three phase Induction Motor (for circle diagram) .

Theory : –

Fig. 14.2. Equivalent Circuit of an Induction Motor

It is also known as series circuit consisting of constant reactance but variable resistance, the locus of the current is a circle of diameter V/X.

In the above figure (Fig. 14.2) the current I0 to the shunt circuit is constant, in the circuit to the right X01 = X1 + X2/K2 , the equivalent reactance referred to primary (stator) is constant, R01 = R1 + R2/K2 , the equivalent resistance referred to primary is also constant but load resistance RL‘ varies with the load on the motor,

So, the locus of I1‘ is a circle of diameter V/X01 and having coordinates (V/2X01 , O) with respect to O’ .

Since the total current I1 drawn by the motor from the supply main is phasor sum of constant current I0 and variable I1‘ , the locus of I1 is also a circle. The same circular are O’PAB acts as locus of I1 referred to point O, which acts as locus of I1‘ referred to point O’ .

Hence, operating characteristics of an induction motor can be determined by using of a circle diagram easily and conveniently.

fig. 14.3 : Circle Diagram for an Induction Motor.

Precautions: –

  1. Ensure the motor is unloaded to minimize mechanical losses.
  2. Supply rated voltage to avoid saturation of the core.
  3. Ensure proper locking of the rotor to avoid accidents.
  4. Use reduced voltage to prevent damage from high currents.
  5. Maintain safety measures as high currents can cause overheating.

Procedures: –

For No-Load test:

  1. Connect the circuit as per circuit diagram.
  1. Keep the variac to be at zero output.
  2. First switch on the 3ф supply.
  3. Gradually increase the voltage applied to the machine to the rated voltage. Motor runs at a speed quite close to its synchronous speed.
  4. Take the reading of voltmeter, ammeter ,wattmeter & speed on rated voltage.

For Block Rotor test:

  1. Connect the circuit as per circuit diagram.
  1. Keep the variac to be at zero output.
  2. First switch on the 3ф supply.
  3. Now, keeping the rotor still (block the rotor from running), slowly increase the autotransformer output until rated current flows (Typically, this happens at 25% of the rated voltage).
  4. Take the reading of voltmeter, ammeter ,wattmeter on rated current.

Observation Table: for No-Load test-

Sl. No.V0 ( in volts.)I0 (in Amps.)W1 (in watts.)W2 (in watts.)P0= W1+W2 (in watts.)
01
Table No: 3.2

Calculation: –

From No-load test data:

\[\color\green{No-load\;\;power\;=}\] \[\color\red{Windage \;and \;friction \;losses\;+\;core \;losses}\] \[\color\green{P_0}\;=\;\color\red{P_{wf}\;+\;P_i}\]
\[\color\green{windage \;and \;friction \;losses\; is \;small.}\] \[\color\magenta{No-load \;power \;factor\;=}\] \[\color\green{\cos\phi_0\;=}\color\red{\dfrac{P_0}{\sqrt{3}*V_0*I_0}}\] \[\color\magenta{No-load \;energy \;component\;current\;=}\] \[\color\green{I_e\;=}\color\red{I_0*cos\phi_0\;=I_0*\dfrac{P_0}{\sqrt{3}*V_0*I_0}\;=\;\dfrac{P_0}{\sqrt{3}*V_0}}\] \[\color\magenta{No-load \;magnetising \;component\;current\;=}\] \[\color\green{I_m\;=}\color\red{\sqrt{I_0^2-I_e^2}}\] \[\color\magenta{No-load \;Impedance\;=}\] \[\color\green{Z_0\;=}\color\red{\dfrac{\dfrac{V_0}{\sqrt{3}}}{I_0}}\] \[\color\magenta{No-load \;Resistance\;=}\] \[\color\green{R_0\;=}\color\red{\dfrac{\dfrac{V_0}{\sqrt{3}}}{I_e}\;=\;\dfrac{\dfrac{V_0}{\sqrt{3}}}{\dfrac{P_i}{\sqrt{3}*V_0}}\;=\;\dfrac{V_0^2}{P_i}}\] \[\color\magenta{No-load\;Reactance\;=}\] \[\color\green{X_0\;=}\;\color\red{\sqrt{Z_0^2-R_0^2}}\]

Observation Table: for Block rotor test-

Sl. No.Vs ( in volts.)Is (in Amps.)W1 (in watts.)W2 (in watts.)Ps= W1+W2 (in watts.)
01
Table No: 3.3

Calculation: –

From Blocked rotor test data:

\[\color\green{Short \;circuit \;power \;factor\;=}\] \[\color\magenta{cos\;\phi_s\;=}\color\red{\;\dfrac{P_s}{\sqrt{3}*V_s*I_s}}\] \[\color\green{Short \;circuit \;power\;=}\] \[\color\magenta{P_s\;=}\color\red{3*I_s^2*R_{01}}\] \[\color\green{Motor \;equivalent\; resistance\; per\; phase,\; as\; referred\; to\; stator,}\] \[\color\magenta{R_{01}\;=}\color\red{\dfrac{P_s}{3*I_s^2}}\] \[\color\green{Motor \;equivalent\; impedance\; per\; phase,\; as\; referred\; to\; stator,}\] \[\color\magenta{Z_{01}\;=}\color\red{\dfrac{\dfrac{V_s}{\sqrt{3}}}{I_s}}\] \[\color\green{Motor \;equivalent\; reactance\; per\; phase,\; as\; referred\; to\; stator,}\] \[\color\magenta{X_{01}\;=}\color\red{\sqrt{Z_{01}^2-R_{01}^2}}\]

For Draw of Circle Diagram:

  1. Draw horizontal axis OX and vertical axis OY. Here the vertical axis represents the voltage reference.
  2. With suitable scale, draw phasor OO’ with length corresponding to I0 at an angle Φ0 from the vertical axis. Draw a horizontal line O’B.
  3. Draw OA equal to ISN at an angle ΦSC and join O’A.
  4. Draw the perpendicular bisector to O’A to meet the horizontal line O’B at C.
  5. With C as center, draw a semi circle passing through O’ and A. This forms the circle diagram which is the locus of the input current.
  6. From point A, draw a vertical line AF to meet the line O’B.
  7. Fix the point E as below.
    For wound rotor machines where equivalent rotor resistance R2′ can be found out:
    Divide AF at point E so that AE: EF = equivalent rotor resistance : stator resistance.
    For squirrel cage rotor machines:
    Find Stator copper loss using ISN and stator winding resistance R1.
    Rotor copper loss = total copper loss – stator copper loss.
    Divide AF at point E so that AE : EF = rotor copper loss : stator copper loss
    • Note: If data for separating stator copper loss and rotor copper loss is not available then assume
  8. For a given operating point P, draw a vertical line PQRST as shown.
    Then, PT = input power, PQ = output power, QR = rotor copper loss, RS = stator copper loss, ST = constant loss (iron loss + mechanical loss)
  9. Efficiency of the machine at the operating point P, η = PT/PQ.
  10. Power factor of the machine at operating point P = cosΦ1
  11. Slip of the machine at the operating point P, s = QR/PR.
  12. Starting torque at rated voltage (in syn. watts) = AE.
  13. To find the operating points corresponding to maximum power and maximum torque, draw tangents to the circle diagram parallel to the output line and torque line respectively. The points at which these tangents touch the circle are respectively the maximum power point (Tmax) and maximum torque point (Pmax).

Conclusion: –

To be written by student.

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