Lecture (20) DC Machine Examples Start of Synchronous Machines
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1 Lecture (20) DC Machine Examples Start of Synchronous Machines Energy Systems Research Laboratory, FIU All rights reserved. 20-1
2 Energy Systems Research Laboratory, FIU All rights reserved. 20-2
3 Ra R f + I m V t T e, ω m Series DC Motor - Ra + I m V t Series DC Generator - Energy Systems Research Laboratory, FIU All rights reserved. 20-3
4 Ra + I a I a R f I t V t T e, ω m Shunt DC Motor Ra + I a I a R f I t V t Shunt Generator Energy Systems Research Laboratory, FIU All rights reserved. 20-4
5 + S 2 I t R S S 1 F 1 I a Ra V t - R f A 1 F 2 A 2 Short Shunt Compound DC Motor + S 2 I t R S S 1 F 1 I a Ra V t - R f A 1 F 2 A 2 Short Shunt Compound DC Generator Energy Systems Research Laboratory, FIU All rights reserved. 20-5
6 + S 2 R S S 1 I t I f F 2 I a Ra V t R f A 1 _ F 1 A 2 Long Shunt Compound DC Motor + S 2 R S S 1 I t I f F 2 I a Ra V t R f A 1 _ F 1 A 2 Long Shunt Compound DC Generator Energy Systems Research Laboratory, FIU All rights reserved. 20-6
7 Example Shunt DC Machine V t = 440 volts R f = 110 Ω R a = 0.15 Ω Connected to 22 kw load Calculate the developed power as a motor and as a generator Energy Systems Research Laboratory, FIU All rights reserved. 20-7
8 Motor P Generator Ra = 0.15 I a I f R I t f V t R f =110 Ω L o a d 22 kw T e, ω m Energy Systems Research Laboratory, FIU All rights reserved. 20-8
9 Motor P develop = I a I a = I t - I f = Load V t V R t f I a = 22, = 46 A = V t - I a R a = 440 (46) (0.15) = V. P develop = = 19,922.6 W Energy Systems Research Laboratory, FIU All rights reserved. 20-9
10 For a Generator Ra = 0.15 Load I a I f R f I t V t 22 kw = V t + I a R a I t = 22kW = 50 A 440 Energy Systems Research Laboratory, FIU All rights reserved
11 440 I f = = 4 A 110 I a = = 54 A = ( ) = V. P developed = = kw Energy Systems Research Laboratory, FIU All rights reserved
12 Problem #2. 5 hp, shunt DC machine, 1800 rpm I t = 36 A, R a = 0.3 Ω, R f = 120 Ω. Ra I a I f R f I t = 36 A s o V t u r c e Energy Systems Research Laboratory, FIU All rights reserved
13 Find the rotational losses. Find η =?, Assume V t = 120 V. P out = 5 ( 746 ) = 3730W P in = 120 ( 36 ) = 4320W 3730 η = 100 % = % 4320 Energy Systems Research Laboratory, FIU All rights reserved
14 P losses = P in - P out = = 590 W. 120 I f = = 1 A 120 I a = 36-1 = 35 A Energy Systems Research Laboratory, FIU All rights reserved
15 P copper loss = P f loss + P a loss = I f 2 R f + I a 2 R a = (1) 2 (120) + (35) 2 (0.3) = W P rotational = = W Energy Systems Research Laboratory, FIU All rights reserved
16 Problem #3. Series Motor, R a + S = 0.2 Ω, I a rated = 50 A, V t = 240 V. Find the Starting Current. Ra + R s = 0.2 Ω + I a - Energy Systems Research Laboratory, FIU All rights reserved
17 I a starting = V t E R t a = = 1200 A = % = 2400% 50 Energy Systems Research Laboratory, FIU All rights reserved
18 Calculate the Resistance Now limit the starting current to 150% (of full load rated current) by inserting an external resistance = R ext. 75 ( R ext. ) = 240 R ext. = 3 Ω Energy Systems Research Laboratory, FIU All rights reserved
19 Example in class A DC Motor Connected to, 600-V, 18 kw Source. A. Calculate the Starting Current drawn from the source B. Limit the Starting Current to equal the rated current obtained by 18 kw, 600 Voltage source. (Hint: a Starting resistance is added to the armature) Ra=0.1 I a V t V t =600V I f R f =150 Energy Systems Research Laboratory, FIU All rights reserved
20 Synchronous Machines e = d λ = dt N d φ dt E = 4.44 f N ph φ p k w k w = k d k p k s Distribution pitch skewing Factor factor factor n s = 120 f 1 n s α, n s α f P P Energy Systems Research Laboratory, FIU All rights reserved
21 Example P = 6, f = 60 Hz, find n s at 50 Hz operation. n s = 120 f P ( ) n s (60HZ) = 6 = 1200 rpm Energy Systems Research Laboratory, FIU All rights reserved
22 ( 120 n s (50HZ) = 6 50) = 1000 rpm E c = E b = E b E c = 120 Energy Systems Research Laboratory, FIU All rights reserved
23 Example 600 V, n s = 375 rpm, P = 16 poles n s = 120 f P E = 4.44 f φ p N ph k w 375 = 120 f 16 Variables constant f = 50 Hz Energy Systems Research Laboratory, FIU All rights reserved
24 Example 3-φ, synchronous generator, has = 620 V. at 60 Hz. If we 1. Reduce φ p by 15%, and 2. Increase n s by 10%, then 3. Find nd f E E = 2 E Energy Systems Research Laboratory, FIU All rights reserved
25 ( )( φ ) E f = f φ p N 3 ph p K N w ph K w E = 3 1 ( ) ( ) = V Energy Systems Research Laboratory, FIU All rights reserved
26 1. 1 n n s n s = s = 120 f P 120 P 120 P f new f 1.1 = f new f f new = Hz = 66 Hz Energy Systems Research Laboratory, FIU All rights reserved
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