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 --- # Inductor Design -- ## Can be used in power electronics <img src="http://www.coilws.com/images/Inductors%20Group.jpg" alt="Drawing" style="width: 600px;"> --- # Inductor Design -- ## Can be used in line-current filtering <img src="https://kebamerica.com/wp-content/uploads/2020/02/Elevator-Harmonics-Filter-1024x607.png" alt="Drawing" style="width: 700px;"> --- # Inductor Design -- ## Can be used in grid level: Reactors <img src="http://westimqpower.com/wp-content/uploads/2016/03/69kV-Shunt-Reactors_SDGE_korrigiert-1500x630.jpg" alt="Drawing" style="width: 700px;"> --- ## [Shunt Reactors](http://electrical-engineering-portal.com/differences-between-shunt-reactor-and-power-transformer) ### [Gapped Core](http://hobbydocbox.com/Radio/69008077-Shunt-reactor-cores-up-to-765-kv-mvar.html) <img src="https://www.enpay.com/Files/Products/shunt2.jpg" alt="Drawing" style="width:800px;"> --- ## [Same Idea](http://hobbydocbox.com/Radio/69008077-Shunt-reactor-cores-up-to-765-kv-mvar.html) with a Gapped E-Core <img src="https://meettechniek.info/compendium/magn-images/air-gap.jpg" alt="Drawing" style="width:500px;"> --- # Real Inductors/Transformers Have: -- - ## Losses -- (Copper and Core) -- - ## Leakage flux -- - ## Magnetizing current -- - ## Hysteresis --- # Realistic Equivalent Circuit of a Transformer ## = Ideal Transformer + External Impedances --  --- # Winding Resistances: (\\(R_1, R_2\\)) or (\\(R_p, R_s\\)) - ## Resistance of the copper [Winding machine](http://www.youtube.com/watch?v=I_kJCLWwI2Y), [Winding for large transformers](http://youtu.be/yYFm3vxOVgw?t=24s), [Toroidal winding](https://www.youtube.com/watch?v=E-FpeRf3RvQ) -- - ### Question: In a step-down transformer which one is larger? ### \\(R_1\\) or \\(R_2\\)? -- - ## Copper Losses: \\(I^2 R \\) -- [Overloaded Transformer](https://www.youtube.com/watch?v=yldWvMXsD00), [Transformer Fails](https://www.youtube.com/watch?v=D8EQPx-ptKk) --- # Leakage Flux -- ## Leakage Reactance: \\( X_{leakage} \\)  - ## Leakage through Air (Linear B-H, no hysteresis) --- # How to minimize leakage flux? -- <img src="http://www.ikes.16mb.com/pict/transformer/x_sect_s.jpg" alt="Drawing" style="width: 500px;"/> - ## Where is the secondary winding? --- # How to minimize leakage flux? <img src="http://sub.allaboutcircuits.com/images/52012.jpg" alt="Drawing" style="width: 400px;"/> --- # Magnetizing Flux -- ## A term represents the necessary flux in the core. ##Magnetizing Reactance: \\( X_{m} \\)  --- # Core Losses - ## Eddy Current Loss (\\(\propto\\) Frequency\\(^2\\)) - ## Hysteresis Loss (\\(\propto\\) Frequency) <img src="http://info.ee.surrey.ac.uk/Workshop/advice/coils/loop_area.png" alt="Drawing" style="width: 600px;"/> --- #Excitation Current ## $$I_e(t) = I_c(t) + I_m(t)$$ ### Excitation Current = Core Loss Component + Magnetizing Component --- # Realistic Equivalent Circuit of a Transformer  ### \\(V_p , V_s, I_p, I_s \\): Primary, secondary voltages and currents -- ### \\(R_p , R_s\\): Primary, secondary coil resistances -- ### \\(X_p , X_s\\): Leakage Reactances --- # Realistic Equivalent Circuit of a Transformer  ### \\(R_c \\): Core Loss Resistance (to model hystresis/eddy current losses) -- ### \\(X_m\\): Magnetizing Reactance (due to non-zero \\(\int H dl\\) in the core) -- ### \\(E_p , E_s\\): Induced voltages in the ideal transformer --- # Transformer Design -- ### A few handouts available in ODTUClass --- # Core Design -- ## [Core Manufacturing](https://www.youtube.com/watch?v=FXcBKxAc4_k) <img src="http://www.teuklaminations.com/wp-content/uploads/2016/06/TEUK-Unicore.jpg" alt="Drawing" style="width: 500px;"/> --- # Core Design ## Shell Type -- <img src="./images/ee564/shell_type.png" alt="Drawing" style="width: 600px;"/> --- # Core Design -- ## Core Type -- <img src="./images/ee564/core_type.png" alt="Drawing" style="width: 600px;"/> --- # Core Design ## 3P-Core Type -- <img src="./images/ee564/3p_core_type.png" alt="Drawing" style="width: 600px;"/> --- # Core Design ## 5P-Core Type -- <img src="./images/ee564/3p_core_type.png" alt="Drawing" style="width: 600px;"/> --- # Transformer Winding <img src="./images/ee564/transformer_winding.png" alt="Drawing" style="width: 400px;"/> ### [Transformer Winding Process](https://www.youtube.com/watch?v=yYFm3vxOVgw) --- # Temperature Effect ### How does the resistance change with time? -- ## Temperature Coefficient ## $$R(T) = R(T_0)(1 + \alpha\Delta T)$$ -- ### For copper (at 20 C): \\( \alpha = 0.003862\;K^{-1} \\) [Ref1](http://hyperphysics.phy-astr.gsu.edu/hbase/tables/rstiv.html), [Ref2](http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity) -- ## Resistivity of copper increases by 30% from 20C to 100C. --- # Conductor Standard Sizes -- ## - American Wire Gauge (AWG) -- ## - National Electrical Manufacturers Association (NEMA) -- ## - International Electrotechnical Commission (IEC) --- # Conductor Standard Sizes -- ## A few References - ### [AWG](http://en.wikipedia.org/wiki/American_wire_gauge) - ### [AWG Sizes](http://www.engineersedge.com/copper_wire.htm) - ### [Magnet Wire Types](http://mwswire.com/magnet-wire/) - ### [MWS Wire Technical Data Book](http://mwswire.com/document-resource-center/) - ### [Bemka (tr) Wire Sizes](http://www.bemkawire.com.tr/en/home/content/251) - ### [NEMA Wire Catalogue](http://www.mwswire.com/pdf_files/mws_tech_book/TechBook040114.pdf) - ### [Current Ratings](http://www.batt.co.uk/upload/files/table4d1abs6004bs6231bs6346_1220253954.pdf) --- # Transformer Design Exercise -- - ## Design a Transformer with the following specifications: -- - ## 1 MVA, Single Phase -- - ## 34.5 kV, 400V Single Phase -- - ## 50 Hz -- - ## Ambient Temp: -30, 50 C. Cooling: ONAN --- # Design Steps -- - ### Choose Core Material -- - ### Choose Operating Flux Density -- - ### Determine Core Dimensions & Number of Turns -- - ### Determine Core Losses, Copper Losses and Equivalent Circuit Parameters -- - ### Determine operating temp. -- - ### Determine mass, cost etc. --- # Useful Links - [Basic Dimensions-Magnetic Circuits](http://ecee.colorado.edu/copec/book/slides/Ch13slides.pdf) - [Transformer Design](http://ecee.colorado.edu/~ecen5797/course_material/Ch15slides.pdf) - [Power Transformer Design](http://www.cs.toronto.edu/~relu/audio/docs/pwrtransformerdesign.pdf) - [Design of Transformers](http://www.freebookezz.com/pdf/17958618263/) - [Conventional Transformer Design](http://link.springer.com/chapter/10.1007/978-1-84882-667-0_2) - Material Selection: See previous lecture notes - [Lekage Flux Calculation](https://www.pes.ee.ethz.ch/uploads/tx_ethpublications/06_Integration_Leakage_CIPS2012.pdf), page 4 --- ## You can download this presentation from: [keysan.me/ee564](http://keysan.me/ee564)