There are two power-generating stations that are connected by a double circuit transmission line as shown below.

The "up" time of each component of the power system is uniformly distributed, independent, and shown in the following table:

The load draws as many MWs as the power stations and transmission lines can deliver, otherwise it is lowered to balance with the generation and available transmission capacity. The power stations and transmission lines can deliver the following MW amounts to the Load: 200, 150, 100, 50, and 0.

Assume that both power stations have a capacity of 100 MW. Power station 2 operates only at 100 MW or 0 MW (if it is out). Power station 1 can operate at 100 MW or 50 MW or 0 MW (if it is out). The power stations are always operated so as to deliver the most MW possible when they are operating.

Assume that each transmission line can carry only 50 MW and that if one line is out and Power station 1 is operating then Power station 1 output is dropped to 50 MW. If both lines are out then Power station 1 is forced off line and delivers nothing.

(a) Determine how many hours over an average year the load provided is 200MW, 150MW, 50MW, and 0MW.

(b) How does this answer change if the "up" times are all 99%?

The two power stations have been retrofitted with new generation technology. Rather than simply being able to operate at 100MW, 50MW, or 0MW and 100MW or 0MW, respectively, they can now produce power at any number of MWs between 100MW and 0MW. The hourly production of Power Station 1 normally distributed with a mean of 75MW and a standard deviation of 5MW. The hourly production of Power Station 2 is normally distributed with a mean of 65MW and a standard deviation of 10MW. Line A and Line B have uniformly distributed, independent up times of 87% and 78%, respectively.

(c) What is the expected number of MW-hours that will be delivered to the load over a standard year?

(d) There are, on average, 660g CO2 from fossil sources emitted for every kWh of electrical energy produced in the United States. Assuming that this number is normally distributed with a Coefficient of Variation of 5%, what is the expected CO2 emission from fossil sources for the year from the two power stations in the problem?