EE362-Electromechanical Energy Conversion-II

class: center, middle

# EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II

# Induction Motors

## Ozan Keysan

[ozan.keysan.me](http://ozan.keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586

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# Speed of Rotor MMF

## wrt stationary frame
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### Speed of rotor currents + Speed of Rotor
--

### \\(s n_s\\)
--
\\(+ n_r\\)
--
\\(= s n_s + (1-s) n_s\\)
--
\\(= n_s\\)

### Rotor MMF rotates at synchronous speed as seen from the stationary frame.

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# Equivalent Circuit of Induction Motors
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## Assume the rotor is stationary (s=1):

## Then the frequency of rotor currents: \\(f_r =\\)
--
\\(f_s\\)
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## Machine just behaves just like a transformer (secondary short-circuited)

- ### Stator: Primary
- ### Rotor: Secondary

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# Equivalent Circuit, Rotor Stationary (s=1)

### Same as a transformer with secondary side short-circuited

<img src="http://www.eng.uwi.tt/depts/elec/staff/alvin/ee20a/AC_IND7.gif" alt="Drawing" style="width: 700px;"/>
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### Assume now the rotor starts rotating at \\(n_r\\)

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<img src="http://www.eng.uwi.tt/depts/elec/staff/alvin/ee20a/AC_IND9.gif" alt="Drawing" style="width: 600px;"/>

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# Equivalent Circuit with Rotating Rotor
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<img src="http://www.eng.uwi.tt/depts/elec/staff/alvin/ee20a/AC_IND10.gif" alt="Drawing" style="width: 800px;"/>
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## The rotor can be referred to the stator side
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# Equivalent Circuit with Referred Rotor

<img src="http://www.eng.uwi.tt/depts/elec/staff/alvin/ee20a/AC_IND11.gif" alt="Drawing" style="width: 900px;"/>
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## Determination of Equivalent Circuit Parameters

## What was the two tests used for transformers?
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- # Open-circuit Test

- # Short-circuit test
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## Determination of Equivalent Circuit Parameters

## Equivalent tests for induction machines:

- # Open-circuit Test == No-Load Test

- # Short-circuit test == Locked Rotor Test
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# Locked-Rotor Test

## Rotor kept stationary with a mechanical brake
## \\(n_r = 0 \rightarrow s =\\)
--
\\(1\\)
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### Apply a small voltage (10-15% of the rated) to obtain rated current and measure:
--

- ### Input Power
- ### Input Voltage
- ### Current
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# Locked-Rotor Test

### Neglect the parallel branch and s = 1

### The circuit becomes:
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# Locked-Rotor Test

- ### \\(P\_{phase} = \dfrac{P\_{total}}{3} = I_1^2 (r_1 +r'_2) \\)
- ### Measure \\(r\_{1(dc)}\\) using an ohm-meter, assume \\(r\_{1(ac)}=1.1r\_{1(dc)}\\) 
- ### \\(\dfrac{V\_1}{I\_1} = Z\_{eq}= \sqrt{(r_1 +r'_2)^2+(X_1 +X'_2)^2}\\)
- ### Assume \\( X\_{1} = X'\_{2}\\)
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# No-Load Test

## Run the motor at no-load, applying rated voltage
## \\(n_r \simeq n_s \rightarrow s \simeq\\)
--
\\(0\\)
--

### Again measure:

- ### Input Power
- ### Input Voltage
- ### Current
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# No-Load Test

### Rotor-side open-circuited (s=0) and neglect the series branch

- ### \\(P\_{phase} = \dfrac{P\_{total}}{3} = \dfrac{V_1^2}{R_c} \\), find \\(R_c \\)
- ### \\(\dfrac{V\_1}{I\_1} = Z\_{eq}= R_c // X_m \\), find \\(X_m \\)
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## But, how about mechanical ([friction](https://www.youtube.com/watch?v=5JbnDXw-0pM) and windage) losses?
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### Get a few measurements at different voltages to estimate friction.

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# Example:

### Estimate the parameters of a 30 kW, 50 Hz, Delta-connected, 415 V, 3-phase machine, if the test results are as follows:
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### Locked-Rotor Test:
- ### Input Power: 6.4 kW
- ### Line Current: 77 A
- ### Line Voltage: 130 V
- ### Resistance between two lines: 0.293 \\(\Omega\\)

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# Example:

### Estimate the parameters of a 30 kW, 50 Hz, Delta-connected, 415 V, 3-phase machine, if the test results are as follows:
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### No-Load Test:
- ### Input Power: 1.65 kW
- ### Line Current: 22.8 A
- ### Line Voltage: 415 V
- ### Friction and windage losses: 1.15 kW

#### Assume \\(X_1=X_2'\\)
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## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)