Question 1: The single-line diagram of a simple radial system is shown below. Assume the C08 relay for CB 1 has a current tap setting of 3 A, a time dial setting of 1, and a CT ratio of 100/5. The C08 relay for CB2 has a current tap setting of 2 A, a time dial setting of 2, and a CT ratio of 150/5.

(a) A 3-phase fault occurs at bus #1 equal to 360 A per phase. Assuming that CB1 is a 5-cycle breaker and the CT has no error, what is the total time in milliseconds required for CB 1 to clear the fault?

(b) If CB 1 fails to open for the fault described in part (a), how long does it take in milliseconds for CB2 to clear the fault assuming a 3-cycle breaker and no CT error?

(c) Instead of a fault at bus 41, assume a 3-phase fault occurs at bus #2 equal to 1200 A per phase. How long does it take CB2 to clear the fault in milliseconds assuming a 3-cycle breaker and no CT error?

(d) How many milliseconds does it take CB2 to clear the fault described in part (c) assuming the CT error is 50% rather than 0%?

(e) Estimate the value of ZB in ohms to two significant figures in part (d) using the CT information in Figure 10.8 on page 531 in your textbook.

Question 2: A synchronous generator having a terminal voltage of 1.02 pu is supplying 0.90 pu average power to the infinite bus in the simple system shown below. The voltage of the infinite bus is 1.00 pu at zero degrees. Assuming pu values of 0.20, 0.12, and 0.50 for the transient reactance of the generator, the reactance of the transformer, and the series reactance of the transmission line, respectively, determine the power-angle equation for the generator.

Question 3. A synchronous generator is tied to an infinite bus through a transmission line having negligible series resistance and shunt capacitance. The pu power-angle equation for the generator is

P_e = 1.25 sin(δ)

during normal system operation.

(a) Assume that δ = 20 degrees when suddenly a 3-phase fault occurs at the terminals of the generator. If the power angle increases to 75 degrees during the time needed for the circuit breaker to clear the fault (i.e., during the time that P_e is zero), draw a sketch using the equal-area criterion which demonstrates that the generator remains synchronized with the infinite bus.

(b) For the situation described in part (a), determine the maximum numerical value in degrees (to the nearest whole number) that δ "swings" to after the fault is cleared. (Hint: the answer is between 90 and 125 degrees.)

Question 4. A power plant has three generators with the incremental costs
dC₁/dP₁ = 0.0121P₁+ 8.0 $/(MW-hour)
dC₂/dP₂ = 0.014P₂ + 7.0 $/(MW-hour)
dC₃/dP₃ = 0.017P₃ + 6.0 $/(MW-hour)

where P₁, P₂, and P₃ are in MW.

(a) Determine the plant λ for economic dispatching and the power settings for each of the generators if the total plant power is 1200 MW.

(b) Assuming that P₃ = 0 (because the third generator is off line for repairs), determine the optimum values of P1 and P2 if the total plant power is 1200 MW.

(c) Calculate the increase in fuel cost per hour if the situation in part (b) is employed rather than the situation in part (a).