A power company is developing an upgrade to an existing power plant and needs to make a requirements decision with respect to the maximum power output capacity for the upgrade. This power plant is part of a system of other power plants and transmission lines. Your analysis organization has been asked to develop a simulation and perform a study to determine the requirement for the upgraded power plant's maximum power output.

The system will consist of three power plants (A, B, C) each in a different city (C1, C2, C3). Power plant A is the plant that will undergo an upgrade. Power plan A is near C1, B is near C2, C is near C3. The cities are spread over a 100 km x 100 km area. C1 is at location (45,10), C2 is at (10, 90), and C3 is at (90, 90). Each city may be modeled as a circle of diameter 5 km. The power plants may be modeled as 1 km x 1 km squares located 6 km north of the center of each city. The power plants are connected by transmission lines to one another and to the nearest city.

C1, C2, and C3 each consume energy at an average daily rate of Pa = 9 TW. However usage varies with time of day and there is also a random component. The usage for each city (Ci) may be modeled as:

Pui = Pa + Pdv sin(π Tod/12 hr) + Prv,

where Pdv = 1 TW (the diurnal variance) is the degree to which power consumption varies over the course of the day, Tod is the time of day (0-23 hr), and Prv = (rand-0.5) * 1 TW is the random variance in power consumption.

Power Plants A, B, and C are each currently able to supply sustained peak powers of 10 TW (hence the need for an upgrade). If one power plant is not able to supply all the power to its city, one of other power plants may fill that demand using any excess capacity on its part. Note: for the purposes of this study, we will assume that ONLY the upgraded plant A will provide all excess power.