... 36.87° A )( 0 .20 Ω + j 0.750 Ω ) = 106 .2 2. 6° V The excitation current of this transformer is 106 .2 2. 6° V 106 .2 2. 6° V + = 0.354 2. 6° + 1. 328 ∠ − 87.4° j80 Ω 300 Ω = 1.37∠ − 72. 5° A I EX = IC ... first column being mmf and % the second column being flux load p 22_ mag.dat; mmf_data = p 22( :,1); flux_data = p 22( : ,2) ; % Initialize values S = 1000; Vrms = 120 ; VM = Vrms * sqrt (2) ; NP = 500; % % ... first column being mmf and % the second column being flux load p 22_ mag.dat; mmf_data = p 22( :,1); flux_data = p 22( : ,2) ; % Initialize values S = 1000; Vrms = 24 0; VM = Vrms * sqrt (2) ; NP = 1000; % %...
... V A = 24 0 V, then E A = 24 0 V, and n= 9-9 120 V 27 1 V If V A = 180 V, then E A = 180 V, and n= (a) no If V A = 120 V, then E A = 120 V, and n= (a) EA E Ao 24 0 V 27 1 V ( 120 0 r/min ) = 1063 r/min ... know that % % Ea2 K' phi2 n2 Eao2 n2 % - = = -% Ea1 K' phi1 n1 Eao1 n1 % % Ea2 Eao1 % ==> n2 = - n1 % Ea1 Eao2 % % where Ea0 is the internal generated voltage at 120 0 r/min % for ... generated voltage E A = V A = 120 V Therefore, the speed n with a voltage of 120 V would be 22 0 EA n = E Ao no n= 9-10 EA E Ao no = 120 V ( 120 0 r/min ) = 5 02 r/min 28 7 V If the motor is connected...
... 0.75 A = 99 .25 A , and E A = VT − I A R A = 24 0 V − (99 .25 A )( 0.14 Ω ) = 22 6.1 V Therefore, the speed at full load will be n= (c) EA 22 6.1 V no = ( 120 0 r/min ) = 1060 r/min E Ao 25 6 V If Radj ... 0.75 A = 99 .25 A , and E A = VT − I A ( RA + RS ) = 24 0 V − (99 .25 A )(0.14 Ω + 0.05 Ω ) = 22 1.1 V The actual field current will be IF = VT 24 0 V = = 0.75 A RF + Radj 20 0 Ω + 120 Ω and the effective ... when E A rises to E A = 24 0 V − ( 0 .28 4 Ω )(54 A ) = 22 4.7 V If the resistance is cut out when E A reaches 22 8,6 V, the resulting current is IA = 24 0 V − 22 4.7 V = 1 02 A < 135 A , 0.15 Ω so there...
... 120 ∠ - 120 ° V = 20 8∠30° V Vbc = Vbn − Vcn = 120 ∠ − 120 ° V - 120 ∠ - 24 0° V = 20 8∠ - 90° V Vca = Vcn − Van = 120 ∠ − 24 0° V - 120 ∠0° V = 20 8∠150° V 28 5 I ab = Vab 20 8∠30° V = = 20 .8∠10° A 10 20 ° Ω ... real and reactive power of each load is P1 = Vφ Q1 = P2 = Z Vφ Z Vφ Q2 = (d) Z Vφ Z cosθ = (25 3 .2 V )2 cos 36.87° = 61.6 kW 2. 5 Ω (25 3 .2 V )2 sin 36.87° = 46 .2 kvar sin θ = 2. 5 Ω cosθ = ( 25 3 .2 V ... cos 27 ° = 25 48 W (d) The air-gap power is PAG,F = I 12 ( 0.5RF ) = (13.0 A ) (13 .29 Ω ) = 22 46 W PAG,B = I 12 ( 0.5 RB ) = (13.0 A ) (0.370 Ω ) = 62. 5 W PAG = PAG,F − PAG,B = 22 46 W − 62. 5 W = 21 84...
... 3Vφ E A Xd 3V 2 X d − X q sin 2 sin δ + Xd Xq 29 7 3(7 621 )(9890) 3(7 621 ) 0. 62 − 0.40 P= sin δ + (0. 62 )(0.40 ) sin 2 0. 62 P = 364.7 sin δ + 77.3 sin 2 MW A plot ... Physics, 2nd ed., McGraw- Hill, New York, 1991 Sears, Francis W., Mark W Zemansky, and Hugh D Young: University Physics, Addison-Wesley, Reading, Mass., 19 82 cha6 523 9_ch 02. qxd 10/16 /20 03 12: 20 PM ... angle is about 2. 2° different (c) The power supplied by this machine is given by the equation P= 3Vφ E A Xd sin δ + 3V 2 X d − X q sin 2 Xd Xq 3 (27 7 )( 322 ) 3 (27 7) 0 .25 − 0.18 ...
... three-phase and four-phase stepper motors REFERENCES Fitzgerald, A E., and C Kingsley, Jr Electric Machinery New York: McGraw- Hill, 19 52 National Electrical Manufacturers Association Motors and Generators, ... NEMA, 1993 Veinott, G C Fractional and Subfractional Horsepower Electric Motors New York: McGrawHill, 1970 Werninck, E H (ed.) Electric Motor Handbook London: McGraw- Hill, 1978 ... power system supplying a constant 24 0 V, and the ac machine is connected to a 480-V, 60-Hz infinite bus The dc machine has four poles and is rated at 50 kW and 24 0 V It has a per-unit armature...
... 13 .2 kV/ 13 .2 N C + 13 .2 N SE = 13.8 N C 13 .2 N SE = 0.6 N C Therefore, N C / N SE = 22 (b) The power advantage of this autotransformer is S IO N C + N SE N C + 22 N C = = = 23 SW NC NC so 1 /22 ... is Z base,P = (VP )2 = (20 ,000 V )2 = 20 kΩ 20 kVA S The base impedance of this transformer referred to the secondary side is Z base,S = (VS )2 = (480 V )2 S 20 kVA = 11. 52 Ω The open circuit ... are balanced, and the total load is found as: P1 = 120 kW 45 Load Load Q1 = P tan θ = ( 120 kW ) tan cos-1 (0.8) = 90 kvar P2 = 50 kW Q2 = P2 tan θ = (50 kW ) tan cos-1 (0.9 ) = 24 .2 kvar PTOT =...
... = − M cos ω t 22 5π π 5π / π /6 VM sin ω t d (ω t ) =− 3VM 3 3 − − = VM = 0. 827 0 VM 22 2π The rms voltage is Vrms = Vrms = T v (t ) dt = 2 5π / π /6 3VM 1 ω t − sin 2 t 2 VM sin ω t d ... , Z ) pu on base (Vbase )2 ( Sbase ) (8314 V )2 (1000 kVA) = 0.040 (8314 V )2 (500 kVA) (8314 V )2 (1000 kVA ) = 0.170 X 2, pu = 0.085 (8314 V )2 (500 kVA ) R2,pu = 0. 020 60 The per-unit impedance ... − sin 2 6 3 Vrms = 3VM π 5π π − sin − sin 2 3 Vrms = 3VM π 3 − − − 22 = = 3VM π 3 − − − 22 3VM π + = 0.8407 VM 2 The resulting ripple factor is r= Vrms VDC − × 100% = 0.8407 VM 0. 827 0 VM...
... and the firing angle is in degrees relative to time zero Start Time (ω t) Stop Time (ω t) Positive Phase Negative Phase − T / 12 T / 12 3T / 12 5T / 12 7T / 12 9T / 12 11T / 12 T / 12 3T / 12 ... ω R 2C V B1 = M RC RC Finally, 85 B1 = VM and + ω R 2C B2 = −ω RC VM + ω R 2C Therefore, the forced solution to the equation is vC , f ( t ) = VM ω RC VM sin ωt − cos ωt + ω R 2C + ω R 2C and ... D3, and capacitor C2 will charge to V volts through diode D2 (a) (2) Now, assume that SCR2 and SCR3 are triggered At the instant they are triggered, the voltage across capacitors C1 and C2 will...
... equation nm = 120 f e P To make a 50 Hz and a 60 Hz machine have the same mechanical speed so that they can be coupled together, we see that nsync = 120 (50 Hz ) 120 (60 Hz ) = P P2 P2 12 = = P 10 ... Baa = sin(w*t) * (cos(0) + j*sin(0)); Bbb = sin(w*t +2* pi/3) * (cos (2* pi/3) + j*sin (2* pi/3)); Bcc = sin(w*t -2* pi/3) * (cos( -2* pi/3) + j*sin( -2* pi/3)); % Calculate Bnet Bnet = Baa + Bbb + Bcc; % ... number of poles and electrical frequency is nm = 120 f e P The resulting table is Number of Poles f e = 25 Hz 10 12 14 1500 r/min 750 r/min 500 r/min 375 r/min 300 r/min 25 0 r/min 21 4.3 r/min The...
... (1800 r/min )( ) = = 60.00 Hz 120 120 f nl2 = The full-load frequency of generator corresponds to a frequency of f fl2 = (a) nm P (1785 r/min )( ) = = 59.50 Hz 120 120 The speed droop of generator ... column being field % current and the second column being line current % (= armature current) load p 52. scc; if_scc = p 52( :,1); ia_scc = p 52( : ,2) ; % Calculate Xs if = 0.001:0. 02: 1; vt = interp1(if_occ,vt_occ,If); ... P (3630 r/min )( ) = = 60.5 Hz 120 120 The full-load frequency of generator corresponds to a frequency of 121 f fl1 = nm P ( 3570 r/min )( ) = = 59.5 Hz 120 120 The no-load frequency of generator...
... A2 sin δ With a 5% decrease, E A2 = 12, 570 V , and δ = sin −1 E A1 13 ,23 0 V sin δ = sin −1 sin 27 .9° = 29 .5° E A2 12, 570 V Therefore, the new armature current is IA = (e) E A2 − Vφ jX S = 12, 570 29 .5° ... + (34) ( 62. 21 − f ) + (34) ( 62. 21 − f ) + (34) (61.03 − f ) PLOAD = sP1 f nl1 − fsys + sP f nl2 − f sys + sP f nl3 − fsys + sP f nl4 − f sys ( 29 0 MW = ( 34 ) 62. 21 − fsys sys 8. 529 = 24 7.66 − ... is IA = E A2 − Vφ jX S = 11,907∠31.3° − 7044∠0° = 848∠ − 26 .8° A j8.18 With a 15% decrease, E A2 = 11 ,24 6 V , and δ = sin −1 E A1 13 ,23 0 V sin δ = sin −1 sin 27 .9° = 33.4° E A2 11 ,24 6 V Therefore,...
... English units is τ load = POUT ωm = ( 21 000 hp)(746 W/hp) ( 120 0 r/min ) 2 rad 60 s τ load = 6-13 = 124 ,700 N ⋅ m 1r 525 2 P 525 2 ( 21 000 hp ) = = 91,910 lb ⋅ ft nm ( 120 0 r/min ) A 440-V three-phase ... 1∠0° − 1.33∠ − 24 .9° = 0.663 20 .2 pu j0.90 In actual amps, this current is I A = (1404 A )( 0.663 20 .2 ) = 931 20 .2 A The reactive power supplied at the conditions of maximum E A and 10 MW power ... 159 I A2 = 50∠36.87° A The internal generated voltage required to produce this current would be E A2 = Vφ − R AI A2 − jX S I A2 E A2 = 120 ∠0° V − j (0.8 Ω )(50∠36.87° A ) E A2 = 147.5∠ − 12. 5°...
... = cos−1 S LR = 14 .2 V = 0 .22 02 Ω 64.5 A 22 00 W = 36. 82 ( 24 .6 V )(64.5 A ) Therefore, RLR = Z LR cos θ LR = ( 0 .22 02 Ω ) cos ( 36. 82 ) = 0.176 Ω ′ ⇒ ⇒ R1 + R2 = 0.176 Ω R2 = 0.071 Ω X LR = ... induction motor at 50 Hz is shown below: IA R1 + Vφ jX1 0 .20 Ω j0.3 42 Ω j 12. 5 Ω jX2 j0.3 42 Ω 0. 120 Ω jXM 1− s R2 s 2. 28 Ω - (a) R2 The easiest way to find the line current (or armature ... (N-m) 500 300 20 0 100 27 00 27 50 28 00 n m 190 28 50 (r/min) 29 00 29 50 3000 This machine is rated at 75 kW It produces an output power of 75 kW at 3.1% slip, or a speed of 29 07 r/min 7-18 A 20 8-V, 60...