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.

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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(1D.E) kV, 50 MVA, (0.8F) powerfactorlagging, 60-Hz and has a synchronous reactance XSof (2.G)Ω and an armature resistance RAof (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 voltageVT (or the line voltageVL) equal to (1D.E) kV when the generator is running at no load(open circuit).

b)     Calculate the phase voltage Vj 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 IA ?

d)     Calculate IA at rated conditions. (See Eq. 4-36).

e)     What is the internal generated voltage EAof 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 (1D.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)

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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 voltageat 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?

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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?

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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= (1E )°, 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)



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