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. -- https://imgur.com/yEoiJJx 你們或許從肉身的枷鎖中解放了出來，但難道不是又進了另一個更為痛苦的牢籠嗎？ 在人們造出的名為「社會」的牢籠中，被別人決定自身價值、被別人裁決的生活。我不想 為了在樂園生活而願意淪為一名奴隸。—丁格 ———《樂園追放—Expelled from Paradise》 --

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