Capacity Planning for an Electric Utility (Two-Stage Stochastic Optimization with Recourse)
In this era of deregulation, power companies have many complex decisions to make. For example, should a power company sell some of their power plants and buy power from other producers? The problem with this is that on hot days when power usage is high it can be very expensive to purchase power. If we choose to never purchase power from other producers, however, we incur high daily fixed costs for operating our plants. Consider the following example.
Power Company PSI currently operates four power plants. Figure 1 gives daily capacity (in 000’s of kWh) and cost information for each plant.
Plants 1 2 3 4
Fixed cost/day 110 220 280 320
Variable cost/kwh(000) 4.3 4.2 4.5 4
Capacity 60 70 50 80
Figure 1
For example, plant 1 can produce 60,000 kWh per day. It costs $4.3 to produce 1000 KWh at Plant 1. Also, the fixed cost per day of operating Plant 1 is $110.
Daily demand for power is highly uncertain. There are three types of days: high demand, medium demand and low demand. The probability of each type of day occurring and the mean and standard deviation of demand (in 000’s of kWh) for each type of day are given below.
Type of Day Probability Mean Sigma Cost/kwh(000)
High 0.2 200 40 15
Medium 0.6 100 20 10
Low 0.2 50 10 5
For example, there is a 20% chance of high demand day, a 60% chance of a medium demand day, and a 20% chance of a low demand day. On a high demand day, the demand distribution is normal with mean of 200,000 kWh and standard deviation of 40,000 kWh. The cost of buying 1000 kWh on each type of day is also given.
Which plants should PSI keep open?
