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Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints

Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
Istituto di Analisi dei Sistemi ed Informatica "Antonio Ruberti," C.N.R., Viale Manzoni 30, 00185 Rome, Italy
frangio{at}di.unipi.it
gentile{at}iasi.cnr.it

We present a dynamic programming algorithm for solving the single-unit commitment (1UC) problem with ramping constraints and arbitrary convex cost functions. The algorithm is based on a new approach for efficiently solving the single-unit economic dispatch (ED) problem with ramping constraints and arbitrary convex cost functions, improving on previously known ones that were limited to piecewise-linear functions. For simple convex functions, such as the quadratic ones typically used in applications, the solution cost of all the involved (ED) problems, consisting of finding an optimal primal and dual solution, is O(n³). Coupled with a special visit of the state-space graph in the dynamic programming algorithm, this approach enables one to solve (1UC) with simple convex functions in O(n³) overall.

Subject classifications: dynamic programming; unit commitment problem; ramping constraints.
History: Received July 2004; revision received March 2005; accepted May 2005.