A Linear Programming Formulation of the Unit Commitment Problem

I show how the unit commitment problem may be recast to a jobscheduling problem amenable to a linear programming solution. While this will require a much larger memory footprint than an equivalent mixed integer programming model, I hope to show that the LP approach lead to both faster time-to-solution and greater numerical stability. 1 The Unit Commitment Problem At its most basic, the unit commitment problem creates the lowest-cost schedule for a group of producers to meet the demands of a group of consumers, with the additional constraint that each producer must be “on” or “off”. The most common application is in electrical power dispatch scheduling where there are additional constraints such as minimum ramp-up and ramp-down times and maximum up-times. A naive solution is straightforward: the scheduled time is divided up into timeslices with each timeslice having a particular demand value. For each timeslice, each generator is assigned an “on” or “off” value consistent with the other constraints in the system. Different generators have different associated costs and demand is usually nonlinear. Dozens of approaches have been formulated since the unit commitment problem was first formalized [13]. There are two major reviews of this literature [25,37]; what follows in table 1 is only samples the literature containing novel approaches and combinations of approaches. We propose yet another approach: linear programming.