Abstract
In this chapter, we use an interior-point/cutting-plane (IP/CP) method for non-differentiable optimization to solve the dual to a unit commitment (UC) problem. The IP/CP method has two advantages over previous approaches, such as the sub-gradient and bundle methods: first, it has proved to have better convergence characteristics in an actual implementation; and second, it does not suffer from the parameter-tuning drawback. The results of performance tests using systems with up to 104 units confirm the superiority of the IP/CP method over previous approaches to solve the dual UC problem. We discuss issues that have influenced whether or not UC models are used as the clearing mechanism in electricity markets; these issues include duality gap, cost recovery, and the existence of multiple solutions.
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Madrigal, M., Quintana, V.H. (2002). An Interior-Point/Cutting-Plane Algorithm to Solve the Dual Unit Commitment Problem — on Dual Variables, Duality Gap, and Cost Recovery. In: Hobbs, B.F., Rothkopf, M.H., O’Neill, R.P., Chao, Hp. (eds) The Next Generation of Electric Power Unit Commitment Models. International Series in Operations Research & Management Science, vol 36. Springer, Boston, MA. https://doi.org/10.1007/0-306-47663-0_10
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DOI: https://doi.org/10.1007/0-306-47663-0_10
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