In 1972, a utility owned a nuclear plant that was online 70% of the year, the oil burning plant was only out for unscheduled maintenance 10% of the time, and the gas-fired turbines were online 15% of the time
The nuclear plant is rated at 1000 MW, the oil plant at 940 MW, and the turbine at 200 MW. a. What is the total cost of running these three plants for the utility?
b. How much would the utility have to charge per kWh to make a profit?
A year has 8760 hours (that's why it is the last number on the time axis).
a. If the nuclear plant was online for 70% of 8760 hours, it was available 6132 hours. The
oil-burning plant was available 90% of the time, 7884 hours. The gas turbine was online
1314 hours. Reading from the graph, the nuclear plant cost about $40.40/kW, the oil
burning plant about $33/kW, and the gas turbine, about $25/kW.
The nuclear plant cost 1000 MW x $40.40/kW = $40.4 million to generate 6,132,000
MWh of electricity; the oil-fired plant cost 940 MW x $33/kW = $31.0 million to
generate 7,410,960 MWh, and the gas turbine cost 200 MW x $25/kW = $5.0 million to
generate 282,800 MWh.
b. The total cost is $40.4 million + $31.0 million + $5.0 million = $76.4 million. The total
electricity generated is 6,132,000 MWh + 7,410,960 MWh + 282,800 MWh = 13,805,760
MWh. The cost of generating the electricity was then $76.4 million/13,805,760 MWh =
$76.4/13,805,760 Wh = $76.4/13,806 kWh = $0.0055/kWh. Anything over this amount
makes a profit. At the normal cost, the utility has a profit of over $0.07/kWh.
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