bv_cvxbook_extra_exercises

E for each t there is at least one i with ai t and di

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Unformatted text preview: er output of generator i from ut to ut+1 incurs an additional cost ψi (ut+1 − ut ), where ψi is a convex function. (This cost can be a real one, due to increased fuel use during a change of power, or a fictitious one that accounts for the increased maintenance cost or decreased lifetime caused by frequent or large changes in power output.) We will use the power change cost functions ψi (v ) = γi |v |, where γi are positive. Power plants with large capacity (i.e., Pimax ) are typically more efficient (i.e., have smaller αi , βi ), but have smaller ramp-rate limits, and higher costs associated with changing power levels. Small gas-turbine plants (‘peakers’) are less efficient, have less capacity, but their power levels can be rapidly changed. The total cost of operating the generators is n n T −1 T φi (pi,t ) + C= i=1 t=1 i=1 t=1 136 ψi (pi,t+1 − pi,t ). Choosing the generator output schedules to minimize C , while respecting the constraints described above, is a convex optimiz...
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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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