1. Consider a three-phase power system with one-line diagram shown in Figure 1. The three-phase trans- former between CBs 1 and 2 (CB: circuit breaker) nameplate ratings are listed: 5MVA, 13.8A-138.0YkV, the transformer reactance X₁1 = 3.80 (viewed from low voltage side 13.8kV, resistance is negligible). The impedance of the transmission line between CBs 3 and 4 is ZL1 = (10+j100). -(50 pts) (a) Pick up SB = 100MVA for the entire three-phase system, and rated voltage VB = 138.0kV, calculate the per-unit line L1 and transformer impedance values. (b) If an SLG fault occurs at the midpoint of the line (L2) between CBs 5 and 6, which breaker(s) should operate? If the CB 5 or CB 6 does not operate, which breaker(s) will provide the backup protection? (c) List the operating CB(s) for different zones, which are listed in Figure 2. (d) If the second generator is connected at bus 3, the system (generators, buses, and transmission lines) is protected by overcurrent relays R1 to R12. Assuming the directional overcurrent relays are used for three transmission lines, what is the remote backup relay(s) for R7? And why? G Generator mm www Transformer - GSU Bus 1 depending on which breakfas Bus 3 Transmission line L1 Shunt Reactor L3 Shunt Capacitor Figure 1: A three-phase power system. Bus 2 Distribution Transformer Feeder

The switch in the circuit has been closed for a long time, and it is opened at t=0. Find v(t) for t>= 0. Calculate the initial energy stored in the capacitor. (a). When the switch is closed, calculate the value of Vc. (b). When the switch is opened, find the time constant. (c). Find v(t) for t>= 0. (d). Find p(t) for t>= 0. (e). Calculate the initial energy stored in the capacitor.

Design a buck converter to produce an output voltage of 18 V across a 10-N load resistor.The output voltage ripple must not exceed 0.5 percent. The de supply is 48 V. Design for continuous inductor current. Specify the duty ratio, the switching frequency, the values of the inductor and capacitor, the peak voltage rating of each device, and the rms current in the inductor and capacitor. Assume ideal components.

2.3 If, for a particular junction, the acceptor concentration is 10 17//cm 3' and the donor concentration is 10 16 cm², a) find the junction built-in voltage. b) Assume n; = 1.5×10 10. Also, find the width of the depletion region (W) and its extent in each of the p and n regions when the junction terminals are left open. c) Calculate the magnitude of the charge stored on either side of the junction. Assume that the junction area is 100 µm².

(2) A variable dielectric capacitive displacement sensor consists of two square metal plates of side l =5 cm, separated by a gap of d = 1 mm. A sheet of dielectric material 1 mm thick and of the same area as the plates can be slid between them as shown in below. Given that the dielectric constant (ɛ)of air is 1 and that of the dielectric material is 4: (a) Calculate the capacitance, C, of the sensor when the input displacement x = 0.0, 2.5 and 5.0 cm. (b) The sensor is placed into a bridge as shown below. Given V; = cos(400 n t) V , R3/R2 = 1, and the bridge is balanced when C = C min, find the output voltage, Eth , when the input displacement x = 2.5 and 5.0 cm.

17 Assuming that the switch in Fig. 7.87 has been in position A for a long time and is moved to position Bat t = 0, Then at t = 1 second, the switch moves from B to C. Find Vc(1) for t>= 0.

Two electric circuits, represented by boxes A and B,are connected as shown in Fig. P1.14. The reference direction for the current i in the interconnection and the reference polarity for the voltage v across the interconnection are as shown in the figure. For each of the following sets of numerical values, calculate the power in the interconnection and state whether the power is flowing from A to B or vice versa. a) i 6 A,v= 30 V b) i -8 A,v = -20 V c) i 4 A,v = -60 V d) i = -9 A,v = 40 V

5.2 A 200-km, 230-kV, 60-Hz, three-phase line has a positive-sequence series impedance z = 0.08 + j 0.48 Q/km and a positive-sequence shunt admittance y = j 3.33 × 10-6 S/km. At full load, the line delivers 250 MW at 0.99 p.f. lagging and at 220 kV. Using the nominal TT circuit, calculate: (a) the ABCD parameters, (b) the sending-end voltage and current, and (c) the percent voltage regulation.

5.14 A 500-km, 500-kV, 60-Hz, uncompensated three-phase line has a positive-sequence series impedance z = 0.03 +j 0.35 Q/km and a positive-sequence shunt admittance y = j 4.4 × 10¬6 S/km. Calculate: (a) Z,(b) (yl), and (c) the exact ABCD parameters for this line.

Problem 5.23 Find the magnetic vector potential of a finite segment of straight wire carrying a current I. [Put the wire on the z axis, from z1 to z2, and use Eq. 5.66.]Check that your answer is consistent with Eq. 5.37.