ECE470 EXAM #3 SOLUTIONS SPRING Work each problem on the exam booklet in the space provided.

Transcription

1 C470 XAM # SOLUTIOS SPRIG 07 Intructon:. Cloed-book, cloed-note, open-mnd exm.. Work ech problem on the exm booklet n the pce provded.. Wrte netly nd clerly or prtl credt. Cro out ny mterl you do not wnt rded. me: Problem : /0 Problem : /0 Problem : /0 Problem 4: /40 Totl: /00 P I,ph Q I,ph I jx o V V 0 V δ K ω I Ueul quton P I,ph P I,ph V X n(δ) P e P m P out P rot Q I,ph Q I,ph V X V X co(δ)

2 Problem (0 Pont) α 4 0 x 4 / π π 4 π π α 0 0 () Wrte our ndependent equton (three Ampere lw nd one Gu lw) n,,, nd ( ) ( ) ( ) ( ) π π π π 0 µ o RL µ o RL µ o RL µ o 4 RL ( 0 4 ) ( ) ( (b) Solve the bove equton or,,, nd 4, nd plot uncton o α n the r p. Alterntvely, ue uperpoton nd plot uncton o α n the r p nd clerly how the -eld o both ull-ptch col ech h / turn (c) Wrte down the undmentl component o the Fourer ere expnon o (α). (You do not need to mply th expreon.) (α) 4 [ ( co α π ) ( co α π )] 4 π π co α )

3 Problem (0 Pont) bx x θ x b b A our-pole, two-phe ynchronou mchne h two ttor wndn (- nd b-b ) nd one rotor eld wndn (- ). () By npecton o the vrou mnetc xe o th mchne, ll n the mn nductnce below: λ λ b λ L l L m 0 M co θ 0 L l L m M n θ b M co θ M n θ L l L m (b) Fnd the mnetc coenery W m W m(, b,, θ). W m W m(, b,, θ) λ λ b b λ (L l L m ) ( b) (L l L m ) M co θ M b n θ (c) Fnd the electromnetc torque T e T e (, b,, θ) developed by th mchne. T e W m ( ) p W m M n θ M b co θ θ m θ

4 Problem (0 Pont) P I,ph Q I,ph I jx o V V 0 V δ K ω I Strtn wth how tht: S I,ph ṼĨ P I,ph V X Q I,ph V X n(δ) V X co(δ) S I,ph ṼĨ ) (Ṽ Ẽ Ṽ jx (Ṽ ) Ṽ Ẽ j jx j j ṼṼ X j V X j ṼẼ X j V e j(0o δ) X j V j V [co(δ) j n(δ)] X X V n(δ) j V V co(δ) X } X {{} X }{{ } P I,ph j Q I,ph 4

5 Problem 4 (40 Pont) A three-phe ynchronou motor wth nelble rmture retnce nd ynchronou rectnce X.44 Ω opertn t the ollown rted condton uppled by the mnucturer nmeplte dt: FRQ VOLTS AMP RATD RPM PF PAS XCITATIO XCITATIO P VOLTS AMP , () Wht the number o pole p per phe? n 0 p p 0 n pole/phe (b) Wht the ht peed ω m n mechncl rd/? ( ( ω m ω π60 40π p) 6) 5.7 mech. rd/ rev π rd or ω m n mn mn rev 60 ec 00 π 60 40π 5.7 mech. rd/ (c) Wht the rted mechncl power output P out (W) o the motor ( hp 746 W)? P out, 000 hp 746 W hp MW (d) Wht the rted mechncl torque output T out (-m) o the motor? T out P out ω m π k-m (e) Wht the three-phe rel power P I,ph (W) nto the motor under rted condton? P I,ph V L I L co ϕ V LL I L co ϕ MW () Wht the ecency η o th motor percent (%)? η P out P I,ph % () Wht re the mechncl power loe P rot (W) o the motor? P I,ph P e P m P out P rot P rot P I,ph P out MW 84 kw (h) Wht the torque nle δ (de) o th motor under rted condton? P I,ph Ṽ Ẽ X Ẽ n δ X P I,ph Ṽ n(δ) / 45.8 V 5

6 Q I,ph Ṽ X Ṽ Ẽ X co(δ) 0 Ẽ co δ Ṽ V tn δ Ẽ n δ Ẽ co δ δ tn o () Wht the per-phe enerted volte Ẽ (V) under rted condton? Ẽ ( Ẽ n δ) ( Ẽ co δ) ( V (j) Wht the bck em contnt K () o th motor? Ẽ K ω I K Ẽ ω I Alternte Soluton: 54 0π Ĩ o Ẽ jx Ĩ Ṽ j j o V Ẽ δ 6