110年 - 110 國立臺灣大學_碩士班招生考試_電機工程研究所乙組:電力工程(含電力系統、電機機械、電力電子)#101255

1. A 380 V, 20HP, 60 Hz four-pole Y-connected three phase induction motor has the following impedances in ohms per phase referred to the stator circuit: R₁=0.6 ohm, X_l= 1 ohm, R₂=0.3 ohm, X₂ =0.45 ohm, (magnetizing reactance) =25 ohm.
The total rotational losses are 1000W and are assumed to be constant. The core loss is neglected. For a rotor slip of 2 percent at the rated voltage and rated frequency, find the motor's stator current. (10%)

2. The synchronous reactance for a round rotor synchronous generator is 1.0 and the armature resistance is negligible. Find the real power delivered by the generator when the terminal voltage is and the open-circuit voltage is(10%)

(a) Compute the per unit values for the resistances and leakage reactance for the two windings. (10%)

(b) When the low voltage winding delivers power to a load of 20KW, 0.9 power factor lagging at 200V, find the per unit voltage at the high voltage side. (6%)

4. Given the 60 Hz, balanced three-phase system shown below, find when(10%)

5. Assume tha . Find the maximum value for (10%)

6. The radius of each sub-conductor is 1 cm for the following 345 KV, 60 Hz, completely transposed balanced three phase lines. Find the per phase inductance In H/m and per phase capacitance to neutral in F/m. (10%)

(a) How many modes if the converter operates in continuous conduction mode (CCM)? Draw the equivalent cireuit of each mode. (4%)

(b) Determine the inductance of L if the co nverter is operating at the boundary conduction mode (BCM), where inductor current touches zero right before switch turn-on. (4%)

(c) Follow qucestion (b). Draw the time waveforms of below variables for two switching periods. Mark the peak and valley values. Define the variable polarity in the circuit. Calculation procedure is required. Duty cycle, current through L, current through Co, voltage across L. (8%)

(a) What is the de voltage across C_lwhen the converter below is in steady-state operation? (5%)

(b) Find the RMS value of a sine wave signal with peak value of 10 V. (3%)

(c) Why the diode D_lin the buck converter below will turn-on after Q_l tumn-of!? (3%)

(d) Why the integration of inductor r voltage across a switching period is zero for a buck converter at steady-state? (3%)

(e) Follow (c). Assume there is a small inductor in series with R_L. Draw the voltage waveform of this inductor voltage for two switching periods. (4%)

110年 - 110 國立臺灣大學_碩士班招生考試_電機工程研究所乙組:電力工程(含電力系統、電機機械、電力電子)#101255

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