bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

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Unformatted text preview: acterized by strong fluctations in availability with ai = 1 meaning a strong wind 137 is blowing, and ai = 0 meaning no wind is blowing. A solar farm has ai = 1 only during peak sun hours, with no cloud cover; at other times (such as night) we have ai = 0. Energy demand d ∈ R+ is also modeled as a random variable. The components of a (the availabilities) and d (the demand) are not independent. Whenever the total power available falls short of the demand, the additional needed power is generated by (expensive) peaking power plants at a fixed positive price p. The average cost of energy produced by the peakers is E p( d − c T a ) + , where x+ = max{0, x}. This average cost has the same units as the cost bT c to build and operate the plants. The objective is to choose c to minimize the overall cost C = bT c + E p ( d − c T a ) + . Sample average approximation. on a sample average of peaker cost, To solve this problem, we will minimize a cost function based C sa = bT c + 1 N N j =1 p( d (j ) − c T a (j ) ) + where (a(j ) , d(j ) ), j = 1, . . . , N , are (given) samples from the joint distribution of a and d. (These might be obtained from historical data, weath...
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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 University of California, Berkeley.

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