4. Consider the following 2-CNF formula. F=(a \vee d) \wedge(a \vee \neg d) \wedge(\neg b \vee e) \wedge(\neg e \vee \neg d) \wedge(d \vee b) \wedge(b \vee c) (a) Draw the digraph corresponding to F. (b) Use the digraph to list all satisfying assignments to F.

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

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.

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.

2.16. A balanced A-connected load consisting of a pure resistances of 18 N per phase is in parallel with a purely resistive balanced Y-connected load of 12 Q per phase as shown in Figure 2.26. The combination is connected to a three-phase balanced supply of 346.41-V ms (line-to-line) via a three-phase line having an inductive reactance of j3 Q per phase. Taking the phase voltage Van as reference, determine (a) The current, real power, and reactive power drawn from the supply. (b) The line-to-neutral and the line-to-line voltage of phase a at the combined load terminals.

5-25 A wind turbine with a blade diameter of 25 m is to be installed in a location where average wind velocity is 6 m/s. If the overall efficiency of the turbine is 34 percent, determine (a) the average electric power output, (b) the amount of electricity produced from this turbine for an annual operating hours of 8000 h, and (c) the revenue generated if the electricity is sold at a price of $0.09/kWh.Take the density of air to be 1.3 kg/m'.

Determine the current drawn from a three-phase 440-Vline by a three-phase 15-hp motor operating at full load,90% efficiency, and 80% power-factor lagging. Find the values of P and Q drawn from the line.

The portion of a power system shown by the one-line diagram of Fig. 5, with generating sources back of all three ends, has conventional primary and back-up relaying. In each of the listed cases, a short circuit has occurred and certain circuit breakers have tripped as stated. Assume that the tripping of these breakers was correct under the circumstances. Where was the short circuit? Was there any failure of the protective relaying, including breakers, and if so, what failed? Assume only one failure at a time.Draw a sketch showing the overlapping of primary protective zones and the exact locations of the various faults. Note: This problem was taken from the book “The Art and Science of Protective Relaying, " by C. Mason, recommended in class. Note: Assume that the system has remote back-up only. It does not have local back-up.

Question 5. Solve your model to derive an expression for the converter efficiency,and enter your expression in the field below. Your expression should be a function of Vg, D, n, Vd, the loss resistors Rp, Rs, and Ron, and the load resistance R.

5.1. A three-phase transmission line has flat horizontal spacing with 2 m between adjacent conductors. At a certáin instant the charge on one of the outside conductors is 60 µC/km, and the charge on the center conductor and on the other outside conductor is - 30 µC/km. Thc radius of each conductor is 0.8 cm. Neglect the effect of the ground and find the voltage drop between the two identically charged conductors at the instant specificied.