bv_cvxbook_extra_exercises

165 minimum energy processor speed scheduling a

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Unformatted text preview: label the generators i = 1, . . . , n, and the time periods t = 1, . . . , T . We let pi,t denote the (nonnegative) power output of generator i at time interval t. The (positive) electrical demand in period t is dt . The total generated power in each period must equal the demand: n pi,t = dt , t = 1, . . . , T. i=1 Each generator has a minimum and maximum allowed output power: Pimin ≤ pi,t ≤ Pimax , i = 1, . . . , n, t = 1, . . . , T. The cost of operating generator i at power output u is φi (u), where φi is an increasing strictly convex function. (Assuming the cost is mostly fuel cost, convexity of φi says that the thermal eﬃciency of the generator decreases as its output power increases.) We will assume these cost functions are quadratic: φi (u) = αi u + βi u2 , with αi and βi positive. Each generator has a maximum ramp-rate, which limits the amount its power output can change over one time period: |pi,t+1 − pi,t | ≤ Ri , i = 1, . . . , n, t = 1, . . . , T − 1. In addition, changing the pow...
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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.

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