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.
Highlights
The unit commitment (UC) problem revolves around finding the least cost power generation schedule for a set of generators such that the demand is met at each time step subject to technical restrictions [1]
The single-unit commitment problem (1UC) is a special case of the UC problem in which the least cost schedule is searched for only one generator subject to its technical restrictions [2]
The generator is not required to meet a demand, but a time series of elec tricity prices is given that determines how much revenue the generator can make at each time step
Summary
The unit commitment (UC) problem revolves around finding the least cost power generation schedule for a set of generators such that the demand is met at each time step subject to technical restrictions [1]. Xiaohong Guan, and Zhai [4] solved 1UC with piece-wise linear generation cost in O(n3) time by splitting the problem in two parts. Their method of calculating the optimal economic dispatch works for any convex cost function Their algorithm calculates the optimal economic dispatch of all on-periods in O(n3) and finds the shortest path in another O(n3). As a restriction it only works with convex piece-wise linear generation cost and when the ramp up and ramp down limits are equal to each other Stop cost ($) Ramp-down limit (MhW ) Start-up ramp limit (MW) Shut-down ramp limit (MW) Minimum up time (h) Minimum down time (h) track of a finite number of points where the power production could be optimal
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