Abstract The single-unit commitment problem (1UC) is the problem of finding a cost optimal schedule for a single generator given a time series of electricity prices subject to generation limits, minimum up- and downtime and ramping limits. In this paper we present two efficient dynamic programming algorithms. For each time step we keep track of a set of functions that represent the cost of optimal schedules until that time step. We show that we can combine a subset of these functions by only considering their minimum. We can construct this minimum either implicitly or explicitly. Experiments show both methods scale linear in the amount of time steps and result in a significant speedup compared to the state-of-the-art for piece-wise linear as well as quadratic generation cost. Therefore using these methods could lead to significant improvements for solving large scale unit commitment problems with Lagrangian relaxation or related methods that use 1UC as subproblem.

中文翻译：

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具有斜坡限制的单机承诺的改进算法

摘要 单机组承诺问题 (1UC) 是在给定受发电限制、最小起停时间和斜坡限制的电价时间序列的情况下为单个发电机找到成本最优计划的问题。在本文中，我们提出了两种有效的动态规划算法。对于每个时间步，我们都会跟踪一组函数，这些函数代表了该时间步之前最优计划的成本。我们表明我们可以通过只考虑它们的最小值来组合这些函数的一个子集。我们可以隐式地或显式地构造这个最小值。实验表明，与分段线性和二次生成成本的最新技术相比，这两种方法在时间步长的数量上都是线性的，并导致显着的加速。