課程名稱︰電力工程導論
課程性質︰電機工程學系元件與電路整合系統類複選必修
課程教師︰劉志文
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰2020/6/16
考試時限（分鐘）：14:20-16:20
試題 :
1,2題各15分, 3-5題各10分, 6,7題各20分.
1. A generator delivers PG = 1.0 at 0.8PF lagging to a bus with voltage｜VA｜=1
Sketch a phasor diagram and calculate ｜Ea｜ for
(a) A round rotor : Xs = 2, r = 0
(b) A salient-pole rotor : Xd = 1, Xq = 0.8, r = 0
2. A generator with resistances Xd = 2 and Xq = 1 delivers SG = 1∠45° to a
bus with voltage Va = 1∠0°. Find Ia, Iad, Iaq, Ea, and the rotor angle Θ0
(i.e., the rotor angle Θ at t = 0).
3. A round-rotor generator (Xs = 1, r = 0.1) is synchronized to a bus whose
voltage is 1∠0°. At synchronization iF = 500A (actual). The generator is
then adjusted until SG = 0.6 + j0.8. (SG = power supplied to the generator
bus.)
(a) Find iF and the generator efficiency (assuming no generator losses
expect I^2*R losses).
(b) With the same iF, what is the ultimate (maximum) active power the
generator can deliver?
4. Given a turbine-generator unit rated 100 MVA with a per unit inertia const-
ant, H = 6sec.
(a) Calculate the kinetic energy stored at synchronous speed (3600rpm).
(b) Compare this figure with the kinetic energy of a 10-ton truck going at
70 mph.
(c) Suppose that the generator is delivering 100MW and then, at t = 0, the
line circuit breakers open. Calculate the shaft acceleration in
rad/sec^2.
(d) At this rate, how long does it take for δ to increase from δ0 to
δ0 + 2π radians?
5. In the model used to study the stability of the single generator connected
to an infinite bus, we assumed that PM = P0M was constant. Consider steam
governor action such that the mechanical power input to the generator is
given by Fig.1
0
P = P - k(w-w0)
M M
where k is positive and w is the angular velocity of the (two-pole) turbo-
generator shaft. Show how this feedback, in effect, changes the mechanical
friction constant D. Is this a stabilizing factor? What happens if the const
k is negative?
https://imgur.com/yD3fSko
6. Consider a round-rotor generator delivering a steady-state power PG = 0.5 to
an infinite bus through a transmission line with reactance XL = 0.5. Assume
that ｜Ea｜ = 1.5, V_infinity = 1∠0°, H = 5 sec, and Xd = Xq = 1. Neglect
resistance.
(a) Find the two possible steady-state (equilibrium) values of power angle
δ = ∠Ea - ∠V_infinity that lie in the interval [0, 2π].
(b) Which of these two equilibrium values are we likely to observe in pract-
ice? Hint: Linearize around the equilibrium value and consider the natu-
ral frequencies found from the linear differential equation in △δ.
7. A round-rotor generator is delivering a steady-state power PG = 0.4 to a
transmission line with reactance XL = 0.3. Assume that｜Ea｜ = 2, V_infinity
= 1∠0°, H = 0.4sec, and Xd = Xq = 1.2. At t = 0 the circuit breakers open
and reclose T seconds later.
(a) Find the critical clearing angle δTC.
(b) Find the corresponding critical clearing time T_critical.
(c) Using T = 0.9T_critical, find δmax and δmin.