bv_cvxbook_extra_exercises

executing this le will also give a plot showing the

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Unformatted text preview: ation problem. The problem data are dt (the demands), the generator power limits Pimin and Pimax , the ramp-rate 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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