class: center, middle # EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113
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Tel: 210 7586 --- # Group Exercise: [Solution](./files/ee362_solved_problem1.pdf) -- ### 10-pole 50 Hz Y connected 3-phase alternator has: -- ### 210 slots, double layer winding with 4 turns/coil side -- ### Coil pitch:18 slots, coil spread (\\(q \alpha\\)): 60 degrees -- ---- ### a) Find the synchronous speed (in rpm) -- ### b) Find the slots per pole per phase -- ### c) Find the number of series turns/phase (poles are connected in series) --- # Group Exercise: [Solution](./files/ee362_solved_problem1.pdf) ### 10-pole 50 Hz Y connected 3-phase alternator has: ### 210 slots, double layer winding with 4 turns/coil ### Coil pitch:18 slots, coil spread: 60 degrees ---- -- ### d) Calculate coil pitch in electrical degrees -- ### e) Calculate the pitch factor, distribution factor and the winding factor --- # Group Exercise: [Solution](./files/ee362_solved_problem1.pdf) #### If the machine has an [airgap flux density](https://www.google.com/search?q=plot+x&ie=utf-8&oe=utf-8#q=plot+sin%28x%29+%2B+0.25*sin%283*x%29+%2B+0.15*sin%285*x%29) of: ### \\(B(\theta)=sin(\theta)+0.25 sin(3\theta)+0.15sin(5\theta)\\) -- ### Airgap Diameter: 1.5m, Core length: 0.5 m -- ### Find the flux per pole (\\(\Phi_p\\)) for each component -- ### Hint: Calculate the fundamental first, and the other harmonics afterwards. ### \\(\Phi\_{1} = B\_{average} . A\_{pole}\\) --- ## 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: [Solution](./files/ee362_solved_problem1.pdf) ## V1=8642 V ## V3=1119 V ## V5=119 V ## Waveform of the [total phase voltage](https://www.google.com.tr/search?q=plot+x&ie=utf-8&oe=utf-8&gws_rd=cr&ei=JrLxVtM3wpawAZ_KlbAM#q=plot+8642*sqrt%282%29*sin%28x%29+-+1119*sqrt%282%29*sin%283*x%29+%2B+119*sqrt%282%29*sin%285*x%29) --- # 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?q=plot+x&ie=utf-8&oe=utf-8&gws_rd=cr&ei=JrLxVtM3wpawAZ_KlbAM#q=plot+%288642*sqrt%282%29*sin%28x%29+-+1119*sqrt%282%29*sin%283*x%29+%2B+119*sqrt%282%29*sin%285*x%29%29-%288642*sqrt%282%29*sin%28x-2*pi%2F3%29+-+1119*sqrt%282%29*sin%283*%28x-2*pi%2F3%29%29+%2B+119*sqrt%282%29*sin%285*%28x-2*pi%2F3%29%29) --- ## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362) --- # Exercise #2 #### Consider a cylindrical AC machine. The stator has 2-pole 3-phase double-layer 8/9 pithced distributed winding spread over 18 stator slots. Each coil side contains 5 conductors. The stator winding is excited by 3-phase 50 Hz alternating currents: #### \\(I_a = 11.5 cos (\omega t)\\), \\(\; I_b = 11.5 cos (\omega t - 120^o)\\), \\(\; I_c = 11.5 cos (\omega t -240^o)\\) A -- ### Air-gap diameter is 20 cm, air-gap distance is 0.5 mm, axial length is 30 cm. -- ### a) Calculate the stator-winding factor -- ### b) Calculate the first-harmonic magnitude of the flux per pole. Source: Y. Üçtuğ Solved Problems, CH-1, Q-1 --> >