< 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) ---