Page 25 - Solutions Manual to accompany Electric Machinery Fundamentals

 R  R  R  R R
TOT stator air gap 1 rotor air gap 2
At a flux density of 1.2 T, the relative permeability  of the stator is about 3800, so the stator reluctance
r
is

l 0.60 m

R stator  stator   50.3 kA t/Wb



 stator A  stator 3800 4  10  7   H/m 0.05 m 0.05 m 
At a flux density of 1.2 T, the relative permeability  of the rotor is 3800, so the rotor reluctance is
r
l 0.05 m

R rotor  rotor   4.2 kA t/Wb



 stator A  rotor 3800 4  10  7   H/m 0.05 m 0.05 m 
The reluctance of both air gap 1 and air gap 2 is
l 0.0005 m

 R  R air gap   221 kA t/Wb

air gap 1 air gap 2  A air gap  air gap 10 H/m 0.0018 m 2 

 4 
7
Therefore, the total reluctance of the core is
 R  R  R  R R
TOT stator air gap 1 rotor air gap 2





 R 50.3 221 4.2 221 496 kA t/Wb
TOT
The required MMF is

 F R  0.003 Wb 496 kA t/Wb  1488 A t 
TOT TOT
Since F  Ni , and the current is limited to 1 A, one possible choice for the number of turns is N = 2000.
This would allow the desired flux density to be achieved with a current of about 0.74 A.

1-18. Assume that the voltage applied to a load is V  208 30 V and the current flowing through the load
2 20
is I  A .
(a) Calculate the complex power S consumed by this load.
(b) Is this load inductive or capacitive?
(c) Calculate the power factor of this load?
(d) Calculate the reactive power consumed or supplied by this load. Does the load consume reactive
power from the source or supply it to the source?
SOLUTION

(a) The complex power S consumed by this load is

208

S  VI *   30 208    V 2 20 A *    30 V 2 20 A 

 S 416   50 VA
(b) This is a capacitive load.
(c) The power factor of this load is
PF   cos   50  0.643 leading

(d) This load supplies reactive power to the source. The reactive power of the load is



QVI  sin  208 V 2 A sin  50     319 var
1-19. Figure P1-14 shows a simple single-phase ac power system with three loads. The voltage source is


 V 240 0 V , impedances of these three loads are





Z 10 30  Z  10 45  Z  10 90 
1 2 3
19