EE568-Selected Topics in Electrical Machines

class: center, middle

# EE568-Selected Topics in Electrical Machines

## Ozan Keysan

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

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

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# Windings of Electrical Machines
--

### [Bobinaj](https://www.youtube.com/watch?v=qnU_AFy3ML0), [Pakistan Machine Winding Shop](https://www.youtube.com/watch?v=5YTbkETpZN8)
---

# Roles of Windings in Electrical Machines
---

# Armature Winding:

## Power-producing winding of an electrical machine
--

## Can be on
--
 the rotor (DC machines),
--
 or on the stator (synchronous machines)

---
# Field (Magnetizing) Winding:
--

## Creates the magnetic field required for energy conversion.
--

## Not all machines have a field winding (i.e. PM machines, reluctance machines)

---
# Field (Magnetizing) Winding:

## Can be on the stator: Field winding of a DC machine

<img src="http://www.gef.com.my/images/DC_Field_Coil_Winding_After_Service_Re-varnish.jpg" alt="Drawing" style="width: 500px;">
---
# Field (Magnetizing) Winding:

## Can be on the rotor: Synchronous Machine
--

## Salient Pole Rotor

<img src="http://www.kencoil.com/wp-content/uploads/2017/03/39b.jpg" alt="Drawing" style="width: 600px;">
---
# Field (Magnetizing) Winding:

## Can be on the rotor: Synchronous Machine
--

## Cylindrical Rotor

<img src="https://3.bp.blogspot.com/-yB8dCzX2duw/V4t-BfncMFI/AAAAAAAABiY/cS_7dqlDz7kVDXQtMojGfpnhFeUQ5Y4AwCK4B/s400/rotor%2Bof%2Ban%2Balternator.jpg" alt="Drawing" style="width: 800px;">
---
# Rotating Field Windings
--

### In Induction (asynchronous) machines, windings both creates field and performs energy conversion, so it is slightly differs from armature windings by definition
--

---
# Rotating Field Windings

## Induction Motor Rotor Side:
--

## Squirrel-Cage Rotor

---

## Squirrel-Cage Rotor

### Can be made from copper or aluminium. Coil ends are short-circuited.
---
# Rotating Field Windings

##  Wound Rotor Induction Machine
--

<img src="https://www.industrial-electronics.com/images/imc7e_44-1.jpg" alt="Drawing" style="width: 600px;">
---
# Damper Winding
--

## [What is it used for](https://instrumentationtools.com/damper-windings-used-synchronous-motors/)?
---

# Damper Winding

### Helps to self-start of a synchronous machine and Reduces oscillations in transient conditions.

### [61MVA Stator & Rotor Rewinding](https://www.youtube.com/watch?v=ov8KAjxMxlU), [coil manufacturing](https://www.youtube.com/watch?v=Y7T6I1wg7tQ)
---
# Other Windings

## Helps to reduce armature reaction

- ## [Commutating Windings](http://www.studyelectrical.com/2015/01/compensating-windings-interpoles-dc-generator-motor.html)

- ## [Compensating Windings](https://www.quora.com/Electrical-Machines-What-do-interpoles-do-in-DC-motors) (Interpoles)

---
# Winding Types

---
# Exercise
--

## Field Winding of a Salient Pole Synchronous Machnie

#### Calculate the required field winding current to get Bmax=0.82T, if there are 95 turns per pole. Assume sinusoidal flux density distribution and the minimum airgap distance is 3.5mm

---
# Exercise

<img src="./images/ee564/field_exercise.png" alt="Drawing" style="width: 800px;">
---
# Slot Windings
--

### Current Linkage distribution in a two-pole cylindrical winding.

#### \\(z_Q\\) conductors in each slot with current \\(I_f\\)
---
### Some Definitions
--

## Pole Pitch: 
--

## \\(\tau_p = \dfrac{\pi D}{2p} \\) 
###\\(p\\): pole pairs, \\(D\\): air-gap diameter
---

### Some Definitions

## Slot Pitch:
--

## \\(\tau_u = \dfrac{\pi D}{Q} \\)

###\\(Q\\): number of slots
--

## Slot Angle (electrical):
--

### \\(\alpha_u = \dfrac{2\pi}{(Q/p)} \\)

---
### Some Definitions

## Slots per-pole per-phase (q):
--

## \\(q = \dfrac{Q}{2pm} \\)

###\\(m\\): number of phases

---
### Some Definitions

## Slots per-pole per-phase (q):

## If \\(q\\) is integer:
--
 Integral Slot Winding
--

## If \\(q\\) is fractional:
--
 Fractional Slot Winding
---
# 3-Phase Integral Slot Stator Winding
--

## Simplest case for rotating MMF

- ## m = 3
- ## p = 1
- ## q = 1
--

- ## Q = 6
---
## Simplest case:

<img src="./images/ee564/slot_q6.png" alt="Drawing" style="width: 500px;">
---
## MMF from a single phase
--

<img src="./images/ee564/single_slot_mmf.png" alt="Drawing" style="width: 700px;">
--

## Peak MMF: \\(\dfrac{4}{\pi}\dfrac{i_U z_Q}{2}\\)
---
## MMF from three phase

<img src="./images/ee564/3ph_mmf1.png" alt="Drawing" style="width: 700px;">
---

## MMF from three phase

---
# Three Phase AC: Rotating MMF

<img src="http://www.ece.umn.edu/users/riaz/animations/sinwaves0.gif" alt="Drawing" style="width: 750px;"/>
---
# Three Phase AC: Rotating MMF

<img src="http://www.ece.umn.edu/users/riaz/animations/vecmovieslow.gif" alt="Drawing" style="width: 500px;"/>
---
# Three Phase AC: Rotating MMF

### Derivation left as an exercise!
---
## Manufacturing of Coils

### Chevy Spark EV [Motor Manufacturing](https://www.caranddriver.com/news/a18744950/we-build-the-chevy-spark-evs-ac-permanent-magnet-motor/)

### [Disributed winding schematic](https://www.researchgate.net/profile/Jakob_Igelspacher/publication/241174581/figure/fig3/AS:340780838342662@1458259891354/Fig-4-Schematic-example-of-a-distributed-winding-of-an-axial-flux-induction-machine.jpg)

### [Preformed coils](https://www.heinrich-schuemann.de/ankerformspulen-200.html), [Preformed coils-2](https://www.heinrich-schuemann.de/files/uploads/Produkte/Elektromaschinenbau/ankerformspulen/anker-w1p.jpg)

### [Coils in the stator](https://empoweringpumps.com/sulzer-hydro-generator-refurbishment-increases-output-by-15/), [Coils in the stator-2](https://4.imimg.com/data4/YY/YY/GLADMIN-/wp-content-uploads-2015-11-diamond_coils_03-500x500.jpg)

---
# Distributed Winding

### Many coils are connected in series and distributed over many slot to achine a more sinusoidal MMF distribution

--
<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/distributed_coil.png" alt="Drawing" style="width: 400px;"/>
---
# Distributed Winding MMF

### Let's calculate the MMF with the distributed coil:
--

---
# Distributed Winding Manufacturing

###Videos

- [Production of electric machines](https://www.youtube.com/watch?v=5Mu42TzHy8M) (T=6:00)

- [Rewinding a Large Motor](https://www.youtube.com/watch?v=_65mXQ-GNVM) (T=0:20)

- [BMW Electric Motor - Drive](https://www.youtube.com/watch?v=Qktx5yx1Bjw)

- [Induction Motors: Overhauling a Motor](https://www.youtube.com/watch?v=yPvYd03cKJU)

---
## Full-Pitch Coil ?
--

---
## Full-Pitch Coil ?

### (a)Full-pitched coil,  (b) Short-pitched coil

---
# Winding Factors

### Constants related to estimate characteristics of MMF and voltage of windings.

### An easier method for analytical calculations
--

- ## Distribution Factor (\\(k_d\\))
--

- ## Pitch Factor (\\(k_p\\))

---
# Distribution Factor

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/distributed_coil.png" alt="Drawing" style="width: 500px;"/>
 
---
# Distribution Factor

## Vector sum of voltages in a distributed coil is less than the algebraic sum of the voltage in each coil.
--

## \\(k_d = \dfrac{\mathrm{Vector\,Sum\,of\,Voltages}}{\mathrm{Algebraic\,Sum\,of\,Voltages}}\\)

---
# Distribution Factor

### Q1: What is the distribution factor of a concentrated coil?
--

### Q2: What is the distribution factor of two coils seperated by \\(\pi/3\\)?
--

### Q3: What is the distribution factor of three coils seperated by \\(\pi/6\\)?
--

### Generalized equation

---
# Distribution Factor

## \\(k_d = \dfrac{sin(q \dfrac{\alpha}{2})}{q sin(\dfrac{\alpha}{2})}\\)

## \\(q\\): Number of coils
## \\(\alpha\\): Angle between each coil

---
# Pitch-Factor
--

## Review of Definitions:

- # Full-pitched (= \\(\pi\\) electrical)
--

- # Under-pitched (< \\(\pi\\) electrical)
--

- # Over-pitched (> \\(\pi\\) electrical)
---

## A 2-pole machine with sinusoidal \\(B_{gap}\\)

---
## A 2-pole machine with sinusoidal \\(B_{gap}\\)

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/2pole_voltage.jpg" alt="Drawing" style="width: 800px;"/>
---
# Full-pitched vs Fractional-pitched Coil

- ## Full-pitch = 180 degrees (\\(\pi\\))
--

- ## Under pitch < 180 degrees (\\(\pi\\))
--

- ## \\(V\_{full-pitch} > V\_{under-pitch}\\)
--

- # If so, what is the point?

---
# A big Parenthesis

## Fourier Series
--

> ## All waveforms, no matter what you scribble or observe in the universe, are actually just the sum of simple sinusoids of different frequencies.

---
# Fourier Series

![](http://media.giphy.com/media/Km4XeiMqFNCDK/giphy.gif)

[Fourier Series using Circles](https://www.youtube.com/watch?v=LznjC4Lo7lE), [Complex Orbits](https://www.youtube.com/watch?v=QVuU2YCwHjw), [Useful applets](http://www.falstad.com/fourier), [Fourier examples](http://ptolemy.eecs.berkeley.edu/eecs20/week8/examples.html)

[More Useful Links on Fourier Series](http://keysan.me/explained/)
---
# Fourier Series

<a href="https://www.google.com/search?q=plot+(sin(x)%2B0.25*sin(3*x)%2B0.1*sin(5*x))">Google Plot</a>

--
- ## Let's see what happens with a 2/3 under pitched coil?
--

- ## Under-Pitched coils are very useful for the elimination of harmonics
---

#Pitch Factor

## Voltage in a short-pitched coil is less than a full-pitched coil

## \\(k_p = \dfrac{\mathrm{Short-Pitched\;Coil\;Flux}}{\mathrm{Full-Pitched\;Coil\;Flux}}\\)
---
#Pitch Factor

# \\(k_p = sin(\dfrac{\lambda}{2})\\)

# \\(\lambda\\): Coil-pitch in electrical degrees
---
# Pitch and Distribution Factor for Harmonics
## For harmonic number n:

## \\(k_p(n) = sin(\dfrac{n\lambda}{2})\\)
--

## \\(k_d(n) = \dfrac{sin(q n \dfrac{\alpha}{2})}{q sin(\dfrac{n\alpha}{2})}\\)
---
# Winding Factor:
## is the combination of distribution and pitch factor 
--

#\\(k_w = k_d \times k_p\\)
--

## gives an idea about the magnitude of the coil voltage (or MMF) compared to concentrated and full-pitched winding.

---
# Group Exercise
--

### A rotating magnetic flux created by a 3-ph 50 Hz, 600 rpm alternator has a distribution of magnetic flux density:
--

### \\(B(\theta)=\hat{B}_1 sin(\theta)+\hat{B}_3 sin(3\theta)+\hat{B}_5sin(5\theta)\\)
--

### \\(B(\theta)=0.9sin(\theta)+0.25 sin(3\theta)+0.18sin(5\theta)\\)

---

# Group Exercise

## The machine has:

- ### 180 slots, double-layer winding, Y-connected
--

- ### Each coil has 3 turns with a span of 15 slots
--

- ### Armature diameter = 135 cm
--

- ### Effective axial length = 0.5 m

---
# Group Exercise
--

## Draw the winding diagram
--

## Calculate the MMF for:
--

- ### ia=1 A, ib=-0.5 A, ic=-0.5A
--

- ### ia= -0.5A, ib=1 A, ic=-0.5A
---

# Group Exercise

## Calculate:
--

- ## Number of poles, pole area
--

- ## Fundamental flux per-pole
--

- ## Winding and distribution factors for each winding
--

- ## Induced voltage rms per phase and line-to-line

---

## Now find the RMS of phase voltage and line voltages.
--

### \\(V\_{rms(i)} = \dfrac{1}{\sqrt{2}} 2\pi f\_i k\_{w(i)}  N\_{ph} \Phi\_{(i)} \\) which is equal to:
--
 
### \\(V\_{rms(i)} = 4.44 f\_i k\_{w(i)}  N\_{ph} \Phi\_{(i)} \\)

### \\(i\\): harmonic order, \\(\quad f\\): frequency
### \\(k_w\\): winding factor
### \\(N_{ph}\\): number of coils per phase
### \\(\Phi\\): flux per pole.

---
# True RMS

### RMS values of all harmonics

# \\(\sqrt{\sum{V_{rms-i}^2}}\\)

### For fundamental, 3rd and 5th harmonics

# True RMS = \\(\sqrt{V\_{1}^2+V\_{3}^2+V\_{5}^2}\\)

---
# Induced Voltages

## V1=4482 V
## V3=613 V
## V5=49.5 V

## Waveform of the [total phase voltage](https://www.google.com.tr/search?ei=67W3WqSJDMOv6ATzqZ_QDQ&q=plot+4482*sqrt%282%29*sin%28x%29+-+613*sqrt%282%29*sin%283*x%29+%2B+49.5*sqrt%282%29*sin%285*x%29&oq=plot+4482*sqrt%282%29*sin%28x%29+-+613*sqrt%282%29*sin%283*x%29+%2B+49.5*sqrt%282%29*sin%285*x%29&gs_l=psy-ab.3...10186.25518.0.26977.18.18.0.0.0.0.317.2643.0j12j3j1.16.0....0...1c.1.64.psy-ab..2.0.0....0.DBXGbFsm7D8)

---
# Line Voltage

## \\(V\_{BA}=V\_{Bn}-V\_{An}\\)
## No 3rd Voltage Harmonics in Y-connected line-to-line voltages

## Waveform of the [line voltage](https://www.google.com.tr/search?ei=R7a3WoqpNszO6AS415iIDg&q=plot+4482*sqrt%286%29*sin%28x%29+%2B+49.5*sqrt%286%29*sin%285*x%29&oq=plot+4482*sqrt%286%29*sin%28x%29+%2B+49.5*sqrt%286%29*sin%285*x%29&gs_l=psy-ab.3...4540.15170.0.25670.9.9.0.0.0.0.179.1246.0j9.9.0....0...1c.1.64.psy-ab..0.0.0....0.8eSFbs9SpcI)

---
# Fractional Slot Windings
--

### Slots-per-pole-per-phase (q) is fractional
--

- ### Gives more choice in winding design
--

- ### Voltage waveform can be improved by eliminating certain harmonics
--

- ### Vast possibilities, but not every possibility produces a symmetrical rotating MMF

---

## Fractional Slot Example
--

## Consider a 10-pole machine
--

## What can be the number of slots?
--

- ## 30 slots? q=
--
1

- ## 60 slots? q=
--
2

- ## How about 42 slots?
--

## q = 42/(10*3) = 7/5
 
---
## 42 slot, 10 pole

---
## 42 slot, 10 pole

## Phase shift between coils?
--

### \\(360*(10/2)/42=42.85^o\\)
--

### Let's choose a coil span of 4 slots. Coil pitch?
--

### \\(42.85*4 = 171.5^o\\), Pitch factor?
--

### \\(sin(171.5/2) = 0.997\\)
---

# Why Fractional Winding?

## Integer Slot: 4 pole, 12 slot

<img src="./images/ee564/4pole_12slot.png" alt="Drawing" style="width: 500px;">
---

# Why Fractional Winding?

## Can you guess the magnitude of cogging torque?

---

# Why Fractional Winding?

## Can you guess the magnitude of cogging torque?

<img src="./images/ee564/4pole_12slot_flux.png" alt="Drawing" style="width: 500px;">
---

# How can you reduce cogging torque?

## Skewing is an option, but increases phase resistance

---

# Why Fractional Winding?

## Repeat the same thing with 4 pole, 15 slot?

---

# Why Fractional Winding?

## Even more poles: 10 pole, 12 slot?

---
## Conditions for Symmetrical Rotating MMF
--

### 1- Number of coils per phase winding should be an integer
--

### Single-layer windings:

### \\(\dfrac{Q}{2m} = pq \in N\\)
--

### Double-layer windings:

### \\(\dfrac{Q}{m} = 2pq \in N\\)

### Easier to achieve symmetrical MMF with double-layer windings

---
## Conditions for Symmetrical Rotating MMF
--

### 2- The angle between phase windings (\\(\alpha\_{ph}\\)) should be an integer multiple of slot angle \\(\alpha_z\\)
--

### Normal Systems:

### \\(\dfrac{\alpha\_{ph}}{\alpha\_{z}}=\dfrac{Q}{mt} \in N\\)

### t: largest common divider of Q and p

### Reading Assignment Pyrhonen Sections 2-9:2-12

---
# Winding Voltage Phasor Diagrams

---
# Voltage induced in a straight wire?

<img src="http://www.solitaryroad.com/c1048/ole3.gif" alt="Drawing" style="width: 450px;">
---
# Voltage induced in a straight wire?

# \\(e = Blv\\)

## v: linear velocity
---
# Winding Voltage Phasor Diagrams

## 2 pole, 3phase, 12 slot machine
--

---
# Winding Voltage Phasor Diagrams

## Induced Phase Voltages
--

---
## Two possible ways to put the coils
--

## Lap winding
--

### Most common type

---

## Concentric winding
--

### They have exactly the same voltage waveforms

---

## Fractional Slot Example:
--

## 12 slot, 10 pole, single layer
--

---

## Fractional Slot Example:
--

### \\(\alpha_u=\\)
--
\\(360*5/12=150^o\\)
--

---

## Fractional Slot Example:

### Phase Induced Voltage

---

## Example (2-16)

### Create a voltage phasor diagram of a single layer integral slot winding for which Q=36, p=2, m=3
--

---

## Example (2-16)

### Create a voltage phasor diagram of a single layer integral slot winding for which Q=36, p=2, m=3

---

## Fractional Single Layer vs Double Layer

# Q=6, m=3, p=2, q=1/2
--

---
# Winding Examples
---

<img src="./images/ee564/winding_ex1.png" alt="Drawing" style="width: 500px;">
--

## Q=24, p=2, 
--
q=2, 
--
Single layer, 
--
integral slot, distributed winding

---

<img src="./images/ee564/winding_ex2.png" alt="Drawing" style="width: 500px;">
--

## Q=12, p=2, 
--
q=1, 
--
Single layer, 
--
integral slot, concentrated winding,

---

<img src="./images/ee564/winding_ex3.png" alt="Drawing" style="width: 500px;">
--

## Q=18, p=2, 
--
q=3/2, 
--
Double layer, 
--
fractional slot winding,

---
<img src="./images/ee564/winding_ex4.png" alt="Drawing" style="width: 500px;">
--

## Q=6, p=2, 
--
q=1/2, 
--
Double layer, 
--
fractional slot concentrated winding,

---
<img src="./images/ee564/winding_ex5.png" alt="Drawing" style="width: 500px;">
--

## Q=6, p=2, 
--
q=1/2, 
--
double layer, 
--
fractional slot, concentrated winding, 
---
# Winding Factor Tables

## Single Layer Winding

---
# Winding Factor Tables

## Double Layer Winding

<img src="./images/ee564/winding_table_double.png" alt="Drawing" style="width: 800px;">
---

# Winding Factor Tables

### Online Calculators

- ### [Emetor](https://www.emetor.com/windings/)

- ### [Winding Scheme Drawer](https://www.bavaria-direct.co.za/scheme/calculator/)
---
# Winding Manufacturing

## Slot Layout
--

---
# Random Wound Coils

### [Random wound coil insertion](https://www.youtube.com/watch?v=5P6YVi2mB6Q)
---

# Form Wound Coils

### [Enercon Generator](https://www.youtube.com/watch?v=MgGk2WvK80M), (8:28)
---

# Form Wound Coils

- ### [Preformed Coil Manufacturing](https://youtu.be/qQ2pS_z3dVc?t=215)
- ### [Coil Spreader](https://www.youtube.com/watch?v=TnKKFZAD2uY)
- ### [Hair Pin Winding Manufacturing](https://youtu.be/fT04LbFXR7E?t=65)

---

# Semi-closed vs Open Slot

---

# Fill Factor Comparison
--

## Random Wound Coil

---

# Fill Factor Comparison

## Form Wound Coil

### Up to 65% fill factor (higher possible with lower voltages)
---

# Fill Factor Comparison

<img src="./images/ee564/fill_factor_formed.png" alt="Drawing" style="width: 800px;">
---

## High Slot Fill Examples

---
# Needle Winding
--

### [BLDC winding](https://www.youtube.com/watch?v=p6ezfPZCSKI), [High Speed Needle Winding](https://www.youtube.com/watch?v=BHUujXg1rf0), [Direct drive winding](https://www.youtube.com/watch?v=-Ao6axiOVRw)

---

# Open Pole Winding
--

### [Chained Poles](https://www.youtube.com/watch?v=-_ZkQh8fF5w)
---

## Self Bonding Wire

---
## You can download this presentation from: [keysan.me/ee564](http://keysan.me/ee564)