bv_cvxbook_extra_exercises

E the optimal value of the problem minimize tr c t s

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: re given s, and want to find p and φ that satisfy these equations. We are interested in solutions with voltage phase angle differences that are smaller than ±90◦ . (Under normal conditions, real power lines are never operated with voltage phase angle differences more than ±20◦ or so.) 141 You will show that the DC power flow equations can be solved by solving the convex optimization problem m minimize i= j ψ j ( pj ) subject to Ap = s, with variable p, where u ψ j (u) = 0 sin−1 (v/κj ) dv = u sin−1 (u/κj ) + κj ( 1 − (u/κj )2 − 1), with domain dom ψj = (−κj , κj ). (The second expression will be useless in this problem.) (a) Show that the problem above is convex. (b) Suppose the problem above has solution p⋆ , with optimal dual variable ν ⋆ associated with the equality constraint Ap = s. Show that p⋆ , φ = ν ⋆ solves the DC power flow equation. Hint. Write out the optimality conditions for the problem above. 16.7 Power transmission with losses. A power transmission grid is modele...
View Full Document

Ask a homework question - tutors are online