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Unformatted text preview: ation problem. The problem data are dt (the demands), the generator
power limits Pimin and Pimax , the ramprate limits Ri , and the cost function parameters αi , βi , and
γi . We will assume that problem is feasible, and that p⋆ are the (unique) optimal output powers.
i,t
(a) Price decomposition. Show that there are power prices Q1 , . . . , QT for which the following
holds: For each i, p⋆ solves the optimization problem
i,t
T −1
T
minimize
t=1 (φi (pi,t ) − Qt pi,t ) +
t=1 ψi (pi,t+1 − pi,t )
min ≤ p ≤ P max ,
subject to Pi
t = 1, . . . , T
i,t
i
pi,t+1 − pi,t  ≤ Ri , t = 1, . . . , T − 1. The objective here is the portion of the objective for generator i, minus the revenue generated
by the sale of power at the prices Qt . Note that this problem involves only generator i; it can
be solved independently of the other generators (once the prices are known). How would you
ﬁnd the prices Qt ?
You do not have to give a full formal proof; but you must explain your argument fully. You
are welcome to use results from the...
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 Fall '13
 F.Borrelli
 The Aeneid

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