III. Electromechanical Energy Conversion
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1 . Electoancal Enegy Coneson Schematc epesentaton o an toancal enegy coneson ece coppe losses coe losses (el losses) ancal losses Deental enegy nput om tcal souce: W V t Rt e t t W net ancal enegy output Deental enegy balance eqn.: W W W el losses Fo a lossless magnetc enegy stoage system: W W W ancal losses
2 . Enegy n Magnetc Fel W W e t N t t W N W F W W F F F Coenegy wth = an F = F W F W W F
3 Fo a lnea magnetc ccut: W W F R F whee R an ae the eluctance an pemeance o the magnetc ccut espectely. Enegy & Foce n Sngly-Excte E.M.C ece Electoancal elay Assume moble amatue s ntally at open poston When the col s excte by (t), (t) s pouce n M.C. an an tomagnetc oce s exete on moble amatue tenng to algn t wth the ensest pat o M.F. When the amatue moes 3
4 Amatue Moement Slow moton case Fast moton case ( s gaually ncease ung moton) ( s constant ung moton) Nomal moton case () Slow moton W W W W W F A A 3 A A A F F A 4 F s constant ung moton W W W A 3 A 4 Shae aea ges W 4
5 () Fast moton s constant ung moton W W W W W W F A W F W F A A A A A A 3 A Shae aea ges W () Nomal moton W W W Shae aea ges W 5
6 W x W > then tcal system oes wok on the amatue W then ancal system oes wok on the amatue (a) Mechancal oce n ast moton W W W F W x W F x Note that W, x W, x W, x x x So W, x F s nepenent o x an W, x x 6
7 (a) Mechancal oce n slow moton W W W F, x F W x F, F, x F W x F, W F, x F F F x F, x F x Note that So W W F, x F W F F, x F, x W F, x x F x F s nepenent o x an W x F, x Fo a lnea magnetc ccut. When s constant ung moton W W F R F whee R an ae the eluctance an pemeance o the magnetc ccut espectely R x. When F s constant ung moton F x x 7
8 Ex-: Dee an expesson o the tomagnetc oce pouce by the E.M.D. shown n the gue an then plot aganst x. Note: ntal gap length s c an s constant ung moton Ex-: Fo the tomagnet shown below: (a) Fo V = Vc, etemne the enegy stoe n magnetc el an the ltng oce pouce (b) Fo V = Vac at 6 Hz, etemne the aeage ltng oce pouce Note: ntal gap length s 5 mm, ntenal esstance o the wnng = 6, N = 3, A c = A g = 6 x 6 = 36 cm. 8
9 3. Rotatng Machnes nea Moton nea Dsplacement x, m nea Spee, m/s Mass m, kg Foce, N Rotatonal Moton Angula Dsplacement, a Angula Spee, a/s neta J, kg m Toque T e, Nm ast moton slow moton W, x x W x F, x Fo lux nepenent o ung moton: W, Te Fo mm nepenent o ung moton: W Te F, (a) Sngly-excte ece t Fo a lnea M.C. T e T e t t 9
10 Ex: The sel nuctance n the gue as a uncton o oto poston s gen by = + cos( ) whee the stato cuent s (t) = m sn(t) () Obtan an expesson o tomagnetc toque pouce (nstantaneous toque) () et = t +, n necessay conton o non-zeo aeage toque (b) Doubly-excte ece M M t t t t M M t e t e M e M t t t t M e M e t t t t Temnal oltage equaton (n matx om): e t M M t M M ω
11 Total powe T T T T t R V cu M t M t t M t Total tcal powe nput: Coppe loss Rate o ncease n stoe enegy n MF + Elect.powe conete to. en. (n matx om) ω M M t M M Magnetc stoe enegy W M M t M t t M t t W cu M M t M t t M t T e M T e T T e n matx om:
12 Ex: T e? Ex: T e?
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