# Homework 5 introduction to Machinery Principles

Question # 40780 | 3 weeks ago |
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$20 |
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**Homework5**

** **

**Introduction to Machinery Principles
**

**Name:**
__________________________________________**ID:**__________

**Posted**: Sat, Nov 10

**Due**: Tue, Nov20, beginning of class.

You can use this document to
insert your answers or submit handwritten documents. Only hardcopies will be
accepted, no emails. The score for late HWs will be reduced by 20% if submitted
by the beginning of the next class day after the due date. After that, the
score will be zero.

The HWs can be typed or handwritten, but for maximum credit, they must be
neatly written, organized, and complete. Write down important formulas that you
are using. Show your calculations and carry at least five significant digits in
your calculations, and record four s.d. in your answers. You may need to
consult the text, the PowerPoints, or both.

___________________________

A B C D E F G

2 6 9 9 1 4 7

Note that *AB* = 26, not 2´6. Also, *A.B* = 2.6, not 2´6.

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**Read Chapter 4
**

1. (8
pts) (Chapman 4.2) A Y-connected, four pole, synchronous generator is rated at(1*D*.*E*)
kV, 50 MVA, (0.8*F*) powerfactorlagging,
60-Hz and has a synchronous reactance *XS*of
(2.*G*)Ω and an armature resistance *RA*of (0.*C*)Ω.

- At 60 Hz, its friction and windage losses are 1.2 MW and its core losses are
1.6 MW.

- The field circuit has a DC voltage of 120 V, and the maximum field *IF* is 10 A.

- The current of the field circuit is adjustable over the range from 0 to 10A.
The open-circuit characteristic of this generator is shown in figure below.

**See Example 4-2**

a) Approximately
how much field current is required to make the terminal voltage*VT* (or the line voltage*VL*) equal to (1*D*.*E*) kV when the generator is running **at no load**(open circuit).

b) Calculate the phase voltage **V***j* of this generator **at rated conditions**. (Assume the phase voltage is the reference
voltage and has an angle of zero.)

c) What is the impedance angle
at **rated
conditions**? What is the current angle
of the current **I***A* ?

d) Calculate **I***A*
at rated conditions. (See Eq. 4-36).

e) What is the internal generated voltage **E***A*of
this machine at rated conditions? Sketch the phasor diagram including the
values you have calculated and assuming the internal resistance is negligible.

f) How much field current is required to make the line
voltage *VL* equal to (1*D.E*)kV when the generator is runnng at **rated conditions**?

g) Suppose that this generator is running at **rated conditions**, and then the load is
removed without changing the field current. What would the terminal voltage of
the generator be?

h) How much steady-state power and torque must the generator’s
prime mover be capable of supplying to handle the **rated conditions**?

Figure 1: Generator Stator Terminal Voltage vs Rotor Field Current (Figure P4-1)

**Ans**.

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2. (4
pts) (Chapman 4-4) Assume that the field current of the generator in Problem
4-2 is adjusted to achieve **rated voltage**at full load
conditions in each of the questions below (using your ID values).

a) What is the efficiency of the generator at rated load?

b) What is the voltage regulation of the generator if it is loaded to rated VA
with a

PF = 0.9 lagging load?

c) What is the voltage regulation of the generator if it is loaded to rated VA
with a

PF = 0.9 leading load?

d) What is the voltage regulation of the generator if it is loaded to rated V
with a unitypower factor load?

**Ans.**

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3. (3
pts) (Chapman 4-5) Assume that the field current of the generator in 4-2(using
your ID values)has been adjusted so that it supplies the rated voltage when
loaded with rated current at unity power factor.

a) What is the torque angle *δ *of the generator when supplying rated
current at unity power factor?

b) What is the maximum power that
this generator can deliver to a unity power factor load when the field current
is held at the same value as in Part (a)? Assume the resistance *RA* can be ignored.

c) When this generator is running
at full load with unity power factor, how close is it to the static stability
limit of the machine?

**Ans**.

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4. (4 pts) (Chapman 4-6) The internal generated voltage of a 2-pole,
∆-connected, 60 Hz**,**three phase
synchronous generator is 14.4 kV, and the terminal voltage is 12.8 kV. The
synchronous reactance of this machine is (*C*.2)
Ω, and the armature resistance can be ignored.

*
*a) If the torque angle of
the generator

*δ*= (1

*E*)°, how much power is being supplied by this generator at the current time? (Note that in this case,

*Pconv = Pout*. See Eq 4-20)

b) What are the impedance angle and the power factor of the generator under these conditions?

c) Sketch the phasor diagram under these circumstances.

d) Ignoring all losses in this generator, what torque must be applied to its shaft by the prime mover at these conditions? (With no losses,

*tapp*=

*tind*. See Eq. 4-14)

**Ans.**

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