Question

B. A regional electric utility currently relies on natural gas for power generation. It has 200 Mw of natural gas capacity that is running on an average of 30 percent efficiency. It is studying options for supplying additional power to its customers. It has all of the following options:

Coal:   A 50 megawatt (Mw) coal plant with a capital cost of $50 million and operating costs of $5 million per year plus the cost of coal. The coal plant would operate at 33 percent efficiency for converting heat for burning coal into electricity, and can expect a 50 percent load factor (capacity factor) and will last for 30 years. Under these assumptions, there are enough local resources (the cheapest source) to supply the power plant with coal for 30 years at a cost of $2.00 per million Btu (MMBtu).

Wind: The region has two potential sites for commercial-scale wind farms. One could support 10 Mw of capacity with a 30 percent load factor. The other could support 20 Mw of capacity, but can only expect a 25 percent load factor. Both wind farms have a capital cost of $1,000 per kilowatt (kw) of installed capacity, and an annual operating and maintenance cost of $50 per year for each kw of installed capacity. The wind mills are expected to last for 20 years before needing to be replaced.

Natural gas: It could build a new 50 Mw plant for additional capacity using modern combined cycle technology that would yield 50 percent efficiency. The capital cost of the new plant would be $10 million, and the operating and maintenance costs of both new and old gas plants is $50 per kw per year, exclusive of the cost of natural gas. Both new and existing gas plants have an expected life of 30 years. The expected load factor for the natural gas plants is 30 percent. The utility has an existing contract for 30 years to purchase up to 6 trillion Btu of natural gas per year at a price of $5.00 per MMbtu. If it wants to use more the 6 trillion Btu in a year, it can purchase as much additional gas as it needs, but has to pay $9.00 per MMbtu.

1. a. Assuming that the utility has to pay an annual rate of 10 percent for investment funds, what is the levelized cost of power for each of the sources, in cents per kwh? Calculate separate costs for the two wind sites and for natural gas using the existing facilities ($0 capital cost), and using a new plant ($10 million capital cost). You may assume that the capital costs are all spent in the first year, and that operating and fuel costs are constant per year for the life of the plant. (Hint: you will need to convert all costs into common units of energy generated per unit of time -- in this case, Mwh -- and apply both the load factor and efficiency percentages to estimate electricity actually generated from total capacity, and scale up fuel costs. Note that there are 8,760 hours in a year, and 1 MMBtu=293 kwh, or 0.293 Mwh. Also, remember to separate gas costs into existing contract gas vs. new purchases.)

b. Now suppose the utility expects to pay a carbon tax of $50 per ton of CO₂ emissions.. You may assume that the coal plant burns coal with an average emissions rate of 95.52 tons per MMBtu, and the average emissions rate of natural gas is 53 tons per MMBtu. How does that change the answers to part a?

2. Extra credit! If the utility minimizes average cost of power, which sources will it use and how much electricity will it generate from each source if it has a demand of:
    a. 400,000 Mwh per year?
    b. 500,000 Mwh per year?

Assume that the utility can build only one of each type of plant, and that there is no carbon tax.

(This problem is more complicated than it might seem, because the utility's power demand does not match up nicely with the capacities of the different generating plants. That means that some plant is left running at less than full capacity, which raises its effective cost per kwh. This is a real problem with electric power planning that electric utilities face all the time.)

Answer 1

regional electric utility currently relies on natural gas for power generation. It has 200 Mw of natural gas capacity that is running on an average of 30 percent efficiency. It is studying options for supplying additional power to its customers. It has all of the following options:

Coal:   A 50 megawatt (Mw) coal plant with a capital cost of $50 million and operating costs of $5 million per year plus the cost of coal. The coal plant would operate at 33 percent efficiency for converting heat for burning coal into electricity, and can expect a 50 percent load factor (capacity factor) and will last for 30 years. Under these assumptions, there are enough local resources (the cheapest source) to supply the power plant with coal for 30 years at a cost of $2.00 per million Btu (MMBtu).