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Unformatted text preview: y sources, such as coal-ﬁred
plants, several wind farms, and solar farms. Our job is to size each of these, i.e., to choose its
capacity. We will denote by ci the capacity of plant i; these must satisfy cmin ≤ ci ≤ cmax , where
cmin and cmax are given minimum and maximum values.
Each generation source has a cost to build and operate (including fuel, maintenance, government
subsidies and taxes) over some time period. We lump these costs together, and assume that the
cost is proportional to ci , with (given) coeﬃcient bi . Thus, the total cost to build and operate the
energy sources is bT c (in, say, $/hour).
Each generation source is characterized by an availability ai , which is a random variable with values
in [0, 1]. If source i has capacity ci , then the power available from the plant is ci ai ; the total power
available from the portfolio of energy sources is cT a, which is a random variable. A coal ﬁred plant
has ai = 1 almost always, with ai < 1 when one of its units is down for maintenance. A wind farm,
in contrast, is char...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
- Fall '13
- The Aeneid