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<<!DOCTYPE html>
<html>
<head>
<title>EE568-Selected Topics in Electrical Machines</title>
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class: center, middle
# EE-568 Selected Topics in Electrical Machines
## Ozan Keysan
[keysan.me](http://keysan.me)
Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
# Permanent Magnets Machines
<img src="https://windings.com/wp-content/uploads/magnet.jpg" alt="Drawing" style="width: 500px;"/>
### Becoming more and more popular with high efficiency and high torque density
---
#Applications
<img src="https://www.tcd.ie/Physics/research/groups/magnetism/img/per_mag_2.jpg" alt="Drawing" style="width: 800px;"/>
---
# History
<img src="http://www.magnetnrg.com/uploads/2/0/0/5/20054943/2633149.jpg" alt="Drawing" style="width: 750px;"/>
---
# Neodymium Magnets (NdFeB)
### Strongest and most common (60% market share)
### Neodmymium is mostly exported by China
### Expensive (600 TL/kg, $85/kg) (2020)
<img src="./images/ee564/nd_cost.png" alt="Drawing" style="width: 350px;"/>
---
# Magnetization Directions
<img src="http://www.flaig-te.de/images/Rohmagnete/roh_englisch_1.jpg" alt="Drawing" style="width: 800px;"/>
---
#B-H Curve of a Magnet
--
### Desired Properties:
--
### Large Remanence flux density (retentivity, point that crosses B axis)
--
### Large [coercivity](http://hyperphysics.phy-astr.gsu.edu/hbase/solids/imgsol/coercivity.gif) (point that crosses H axis)
--
---
# Magnet Strength Comparison
<img src="http://www.kjmagnetics.com/images/blog/demag.curves2d.gif" alt="Drawing" style="width: 600px;"/>
---
## Intrinsic vs Normal B-H Charateristics
<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/intrinsic.jpg" alt="Drawing" style="width: 360px;"/>
### We can only measure normal curve
[More info about magnets](http://what-when-how.com/electric-motors/hard-magnetic-materials-permanent-magnets-electric-motors/), [Magnet Guide](http://www.allianceorg.com/pdfs/Magnet_Tutorial_v85_1.pdf), [Demagnetization](http://www.shinetsu-rare-earth-magnet.jp/e/design/)
---
# Demagnetization of PMs
<img src="https://www.kjmagnetics.com/images/blog/BHexplained.png" alt="Drawing" style="width: 600px;"/>
### If external magnetic fields get below the knee point, PM will lose strength
---
# Demagnetization of PMs
## Recoil Line
### Magnets will loose strength if the reverse magnetic field goes beyond the knee point.
<img src="http://www.eeeguide.com/wp-content/uploads/2015/11/Application-of-Permanent-Magnet-Materials3.png" alt="Drawing" style="width: 600px;"/>
---
# Magnets with Temperature
### Real Datasheet of Sm-Co (Samarium-Cobalt Magnet)
<img src="https://www.mpimagnets.com/wp-content/uploads//2018/09/06.jpg" alt="Drawing" style="width: 600px;"/>
### Magnets become less stable with increasing temperature.
---
# What is Magnetic Force?
### [Why magnets attract each other?](http://www.youtube.com/watch?v=uTcuDprmues) by Richard Feynman
--
### [Magnets and Special Relativity](https://www.youtube.com/watch?v=1TKSfAkWWN0)
Reading Suggestion: [Eminim Şaka Yapıyorsunuz Bay Feynman](http://www.idefix.com/Kitap/Eminim-Saka-Yapiyorsunuz-Bay-Feynman-Merakli-Bir-Sahsiyetin-Maceralari/Richard-P-Feynman/Bilim/Populer-Bilim/urunno=0000000427673)
<img src="https://cdn-images-1.medium.com/max/2000/1*4MnjkvCDAAJt7d0KrvFBOw.png" alt="Drawing" style="width: 600px;"/>
---
# Magnetic Circuits with Magnets, Load Line
<img src="./images/ee564/magnet_load_line.png" alt="Drawing" style="width: 600px;"/>
[More info on load lines](https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-061-introduction-to-electric-power-systems-spring-2011/readings/MIT6_061S11_ch11.pdf),
---
# Magnetic Circuits with Magnets, Load Line
## Be aware of the temperature variation
<img src="./images/ee564/magnet_load_line_temp.png" alt="Drawing" style="width: 600px;"/>
# The magnet can lose some of its strength
---
# Magnet Grades
## A definition for its strength (i.e. max. stored energy)
<img src="http://www.usrareearthmagnets.com/wp-content/uploads/2019/07/n52-magnets.jpg" alt="Drawing" style="width: 400px;"/>
---
# Magnet Grades
<img src="./images/ee564/magnet_grades.jpg" alt="Drawing" style="width: 600px;"/>
---
# Magnet Grades
## Last letter defines the working temperature
- ## No Letter: < 80 C
--
- ## M: Medium, <100 C
--
- ## H: High, <120 C
--
- ## SH: Super High, <150 C
---
# Magnet Coatings
### Beware NdFeB magnets are prone to corrosion and need to be coated
--
<img src="./images/ee564/magnet_coatings.jpg" alt="Drawing" style="width: 800px;"/>
---
# Modelling of Magnets
## Operation range of a magnet
<img src="./images/ee564/magnet_dynamic_bh.png" alt="Drawing" style="width: 500px;"/>
---
# Modelling of Magnets
## Equivalent Circuit (Flux Source)
<img src="./images/ee564/magnet_equivalent_circuit.png" alt="Drawing" style="width: 700px;"/>
---
# Modelling of Magnets
## Thevenin Equivalent Circuit (MMF Source)
<img src="./images/ee564/magnet_equivalent2.png" alt="Drawing" style="width: 700px;"/>
---
# Modelling of Magnets
## If the magnet is operating in linear region
### \\(B_m = B_r + \mu_R \mu_0 H_m \\)
### \\(H_m\\) is negative (third quadrant in BH graph)
--
### \\(\Phi = B_m A_m \\)
--
\\(\ = B_r A_m + \mu_R \mu_0 A_m H_m \\)
--
### \\(\Phi = B_m A_m \\)
--
\\(\ = \Phi_r + \dfrac{F_m}{R_m} \\)
---
# Modelling of Magnets
### \\(\Phi = \Phi_r + \dfrac{F_m}{R_m} \\)
--
### A constant flux source with a reluctance in parallel (i.e Norton circuit)
### \\(R_m = \dfrac{l_m}{ \mu_0 \mu_r A_m} \\)
### \\(P_m = \dfrac{1}{R_m} \\): Permeance
---
## Thevenin Equivalent Circuit (MMF Source)
<img src="./images/ee564/magnet_equivalent2.png" alt="Drawing" style="width: 400px;"/>
### Magnet can be considered as a coil (MMF source) with:
### \\(NI =\\)
--
\\(\Phi_r R_m =\\)
--
\\(B_r A_m \dfrac{l_m}{\mu_o \mu_r A_m} \\)
--
\\(= \dfrac{B_r l_m}{\mu_o \mu_r} \\)
---
# Group Exercise-#1
--
<img src="./images/ee564/magnet_c_core1.png" alt="Drawing" style="width: 500px;"/>
### Calculate the airgap flux density for:
---
# Group Exercise- #2
--
<img src="./images/ee564/coil_magnet.png" alt="Drawing" style="width: 700px;"/>
### Draw the magnetic equivalent circuit (ignore leakage)
---
# Group Exercise- #2
--
<img src="./images/ee564/coil_magnet_circuit.png" alt="Drawing" style="width: 700px;"/>
### Equivalent magnetic circuit
---
# Group Exercise-#3
--
<img src="./images/ee564/magnet_c_core.png" alt="Drawing" style="width: 650px;"/>
### Calculate the airgap flux density for:
---
# Group Exercise- #4
--
<img src="./images/ee564/magnet_leakage_a.png" alt="Drawing" style="width: 230px;"/>
w a
<img src="./images/ee564/magnet_leakage_b.png" alt="Drawing" style="width: 240px;"/>
<img src="./images/ee564/magnet_leakage_c.png" alt="Drawing" style="width: 250px;"/>
### Which one creates the most flux density (don't ignore leakage flux)?
---
# General PM Machine Structure
--
<img src="./images/ee564/smpm_magnet.png" alt="Drawing" style="width: 500px;"/>
### Surface Mount Permanent Magnet Machine
---
# Magnetic Circuit Model
<img src="./images/ee564/smpm_magnet_circuit.png" alt="Drawing" style="width: 500px;"/>
### SMPM magnetic circuit
---
# Magnetic Circuit Model
<img src="./images/ee564/smpm_magnet_circuit2.png" alt="Drawing" style="width: 400px;"/>
### Series components combined
---
# Magnetic Circuit Model
<img src="./images/ee564/smpm_magnet_circuit3.png" alt="Drawing" style="width: 400px;"/>
### Leakage ignored
---
# Magnetic Circuit Model
<img src="./images/ee564/smpm_magnet_circuit4.png" alt="Drawing" style="width: 500px;"/>
### Magnets combined (it is possible to use half-symmetry too)
---
# Magnetic Circuit Model
<img src="./images/ee564/smpm_magnet_circuit5.png" alt="Drawing" style="width: 500px;"/>
### Steel reluctance ignored (\\(K_r\\) factor added, \\(Kr \gtrapprox 1\\))
---
# Magnetic Circuit Model
## Ideal Airgap Flux Distribution
<img src="./images/ee564/smpm_airgap_flux.png" alt="Drawing" style="width: 500px;"/>
---
### Let's see the induced voltage waveform for a full-pitch coil
--
<img src="./images/ee564/smpm_full_pitch.png" alt="Drawing" style="width: 500px;"/>
---
### Flux and Induced Voltage in the Coil
--
<img src="./images/ee564/smpm_full_pitch_voltage.png" alt="Drawing" style="width: 500px;"/>
---
### How about a fractional-pitch coil ?
--
<img src="./images/ee564/smpm_fractional_pitch.png" alt="Drawing" style="width: 600px;"/>
---
### Flux and Induced Voltage in the Fractional-Pitch Coil
--
<img src="./images/ee564/smpm_fractional_pitch_voltage.png" alt="Drawing" style="width: 600px;"/>
---
## How about fractional pitch magnets?
--
<img src="./images/ee564/fractional_pitch_magnet.png" alt="Drawing" style="width: 500px;"/>
## Reduces the leakage flux between adjacent magnets
---
## Induced voltage in a fractional pitch magnets
<img src="./images/ee564/fractional_magnet_voltage.png" alt="Drawing" style="width: 500px;"/>
---
# Multiple Coils
--
### Nslot= 15, Npoles= 4
<img src="./images/ee564/fractional_slot_15.png" alt="Drawing" style="width: 500px;"/>
---
# Multiple Coils
--
### Nslot= 15, Npoles= 4, 192 degree coil span
<img src="./images/ee564/fractional_slot_15_A.png" alt="Drawing" style="width: 450px;"/>
---
# Multiple Coils
### Flux Linkage in Single Coil
<img src="./images/ee564/fractional_slot_15_flux.png" alt="Drawing" style="width: 500px;"/>
---
# Multiple Coils
### Induced Voltage in Single Coils
<img src="./images/ee564/fractional_slot_15_volages.png" alt="Drawing" style="width: 500px;"/>
---
# Multiple Coils
### Total Induced Voltage
<img src="./images/ee564/fractional_slot_15_combined.png" alt="Drawing" style="width: 500px;"/>
---
# PMSM vs BLDC
--
## Permanent Magnet Synchronous Motor
<img src="https://g-search2.alicdn.com/img/bao/uploaded/i4/i2/2645629644/TB1gSWSXBUSMeJjy1zdXXaR3FXa_!!0-item_pic.jpg" alt="Drawing" style="width: 300px;"/>
---
# PMSM vs BLDC
--
## Brushless DC Motor
<img src="./images/ee564/bldc.jpg" alt="Drawing" style="width: 350px;"/>
### Usually preferred in low cost, small motor
---
# PMSM
--
## Sinusoidal Back-EMF
<img src="./images/ee564/pmsm_emf.png" alt="Drawing" style="width: 600px;"/>
### Sinusoidal back-emf, vector control, precise motion control
---
# BLDC
--
## Trapezoidal Back-EMF
<img src="./images/ee564/bldc_emf.png" alt="Drawing" style="width: 600px;"/>
### Driven by square wave pulses, small power/low cost applications
---
# D-Q Axes Revisited
--
## SM-PMSM
--
(Surface Mount Permanent Magnet Synchronous Machine)
--
<img src="./images/ee564/smpm_Ld_Lq.png" alt="Drawing" style="width: 600px;"/>
--
## Ld = Lq for SMPM machines
---
# D-Q Axes Revisited
--
## IPM
--
(Interior Permanent Magnet Synchronous Machine)
--
<img src="./images/ee564/ipm_Ld_Lq.png" alt="Drawing" style="width: 600px;"/>
--
## Lq > Ld for IPM machines (as \\(\mu_r \approx 1 \\) for PMs)
---
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