In the summer, peak electricity loads can force the startup of temporary power plants called peaker plants. Peaker Plants are used to augment the power supplied by the normal full time plants, called baseline plants. Suppose New Jersey Electric Power (NJEP) has baseline plants that can produce up to 18,000 MW (megawatts) as well as three peaker plants that can each add 500 MW of additional power.

In an emergency, NJEP can further reduce overall power consumption by up to 4% by dropping the transmission voltage (essentially, give everyone 4% less electric power than they want). This causes an intentional brownout. If power demand still exceeds what NJEP can handle using brownout conditions, they would be forced to implement rolling blackouts, which involves temporarily cutting power to a rolling subset of customers.

An epic 5-day heat-wave is forecast to hit New Jersey beginning in 24 hours. Based on the weather forecast, it is estimated that NJEP's peak load demand over each day of the 5 day heat-wave will be normally distributed with the following parameters:

Forecasted Peak MW Consumption

Day 1 Day 2 Day 3 Day 4 Day 5

m 15000 16000 16500 17000 16500

s 1500 1600 1650 1700 1650

NJEP wants to decide how many peaker plants to fire up to reduce the probability of brownouts and/or rolling blackouts. The decision must be made soon to allow sufficient ramp up time.

Q. Assume NJEP fires up 2 peaker plants in advance of the heat wave.

• What is the probability NJEP exceeds their total capacity for at least one day of the heat wave?
• What is the probability they must resort to brownouts at peak load for at least one day during the heat wave?
• What is the probability they must resort to rolling blackouts at peak load for at least one day during the heat wave?

Q. Assume NJEP fires up all 3 peaker plants in advance of the heat wave.

• What is the probability NJEP exceeds their total capacity for at least one day during the heat wave?
• What is the probability they must resort to brownouts at peak load for at least one day during the heat wave?
• What is the probability they must resort to rolling blackouts at peak load for at least one day during the heat wave?