EE362-Electromechanical Energy Conversion-II

class: center, middle

# EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II

# Salient Pole Synchronous Machines

## Ozan Keysan

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

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

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# Cylindrical Machine vs. Salient Pole

### Salient Pole: Position dependent air-gap reluctance(and hence inductance; \\(L=N^2/R\\))

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# Torque in Cylindrical Rotor, Cylindrical Stator

### \\(T=i\_1 i\_2 \dfrac{\partial M}{\partial \theta}\\) 
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# Torque in Salient Rotor, Cylindrical Stator

### \\(T= i\_1 i\_2 \dfrac{\partial M}{\partial \theta} + \dfrac{1}{2}i\_1^2 \dfrac{\partial L\_{11}}{\partial \theta} \\)

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## Cylindrical Rotor Synchronous Machine

### No saliency in the rotor: no reluctance torque

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## SMPM: Surface Mount Permanent Magnet Motor

### No saliency in the rotor: no reluctance torque

<img src="./images/ee362/spm.png" alt="Drawing" style="width: 400px;"/>
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# Salient Pole Rotor Synchronous Machines

### Airgap is not uniform.

### There are both reluctance and synchronous torque components

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## Motors With Saliency (has reluctance torque)

## IPM: Interior Permanent Magnet Motor

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## Motors With Saliency (has reluctance torque)

### SRM: [Synchronous Reluctance Motor](https://www.youtube.com/watch?v=vvw6k4ppUZU) 
####(with or without PMs)

### [ABB Synchronous Reluctance Motors](https://www.youtube.com/watch?v=b3uprygbBWQ)
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## Motors With Saliency (has reluctance torque)

## Most electric car motors have reluctance torque

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## Motors With Saliency (has reluctance torque)

### [Tesla Model 3 Motor](https://www.youtube.com/watch?v=wFZZ5PICQeo), [Types of EV Motors](https://www.youtube.com/watch?v=6H5vtu5_SF4)

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## Salient Pole Synchronous Motor

## Renault Zoe, 80kW motor

<img src="./images/ee362/salient_zoe.jpg" alt="Drawing" style="width: 600px;"/>
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# D-Q Axis

<img src="http://lh4.ggpht.com/-hHkxzXhl9E4/TgegixkBCfI/AAAAAAAABoU/88gA-WY2rfc/2_thumb1.jpg?imgmax=800" alt="Drawing" style="width: 500px;"/>
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# D-Q Axis

## Direct Axis: d-axis

## Quadrature Axis: q-axis
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# D-Q Axis

### Remember [reluctance torque](https://www.youtube.com/watch?v=hDJnLt7cBTY)

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# D-Q Axis

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# D-Q Axis

## Salient Pole Machine: \\(L_d > L_q \rightarrow X_d > X_q\\)

### (Usually \\(X_q = 0.6 - 0.7 \; X_d\\))

## Cylindrical Machine: \\(X_d = X_q = X\_s\\)
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# Phasor Diagram in a Salient Pole Machine

## Separate \\(I_a\\) in to two components:

## \\(\vec{I_a} = \vec{I_d} + \vec{I_q}\\)

- ## Direct-axis current \\(I_d\\): In phase with \\(\phi_f\\)

- ## Quadrature-axis current \\(I_q\\): Perpendicular to \\(\phi_f\\), and therefore in-phase with \\(E_f\\) (due to derivative relation (jw) between flux and voltage)

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## Phasor Diagram in a Salient Pole Machine (Generating)

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## Phasor Diagram in a Salient Pole Machine (Motoring)

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# Phasor Diagram in a Salient Pole Machine

## Some key points:

## \\(|E_f| = V_t cos(\delta) + X_d I_d \\)

## \\(I_d \\) has more effect on \\(E_f\\) (creates field flux)
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# Phasor Diagram in a Salient Pole Machine

## Some key points:

## \\( V_t sin(\delta) = X_q I_q \\)

## \\( I_q \\) has more effect on load angle \\(\delta\\) (creates torque)

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# Phasor Diagram in a Salient Pole Machine

## including \\(R_a\\) (in generator mode)

<img src="./images/salient_phasor.png" alt="Drawing" style="width: 800px;"/>
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# Phasor Diagram in a Salient Pole Machine

## including \\(R_a\\)

## \\(|E_f| = V_t cos(\delta) + X_d I_d + R_a I_q \\)

## \\( V_t sin(\delta) + R_a I_d = X_q I_q \\)
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# Power in Salient Pole Machines

## Again the similar geometry tricks:

## Start with: \\(P = 3 V\_t  I\_a cos (\theta) \\)
--

## \\( I\_a cos (\theta) =\\)\\( I\_d sin (\delta) + I\_q cos (\delta) \\)
--

## \\(P = 3 V\_t (I\_d sin (\delta) + I\_q cos (\delta) ) \\)
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# Power in Salient Pole Machines

## \\( V_t sin(\delta) = X_q I_q \\)
--
 \\( \rightarrow I_q =\dfrac{V_t sin(\delta)}{Xq} \\)
--

## \\( V_t cos(\delta) = E_f - X_d I_d \\)
--
 \\( \rightarrow I_d =\dfrac{E_f - V_t cos (\delta)}{X_d} \\)
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# Power in Salient Pole Machines

### Total Power:

### \\(P = 3 \left[ \dfrac{V_t E_f}{X_d}sin(\delta)+ \dfrac{V_t^2(X_d - X_q)}{2 X_d X_q}sin(2\delta) \right]\\)
--

- ## First Term: Same with Cylindrical Machines
--

- ## Second Term: Reluctance Power (Independent of  \\(E_f\\), even exists if \\(I_f=0\\))

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# Power in Salient Pole Machines

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# Example:

### A 3-phase star connected salient pole generator has a direct-axis impedance of \\(10 \Omega\\), and quadrature axis impedance of \\(6.5 \Omega\\).
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### If the generator is supplying 10 A, with a phase angle of 20 degrees lagging. Calculate:
--

### a) Load Angle
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### b) D-Q components of the armature current
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### c) Magnitude of Ef

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## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)