Unit commitment problem: A new formulation and solution method

• The combinatorial complexity of unit commitment problem was greatly reduced.
• Time dependent costs and constraints of thermal generators are not linearized.
• Achieved near optimal unit commitment schedule which is better than MILP solution.

In this paper, we present a new formulation and solution method for the well known unit commitment problem (UCP) for scheduling the thermal generators in a day-ahead electricity market. Compared to the traditional approach, our approach has several advantages such as: (a) reducing the combinatorial complexity (i.e., the size of the binary state space) significantly, (b) eliminating the need for linearizing the constraints associated with the minimum ON time and minimum OFF time for any thermal generator, (c) eliminating the need for defining new binary decision variables to represent the startup and shutdown decisions for any thermal generator in each hour and (d) eliminating the need to linearize the non-linear cost functions associated with any thermal generator (e.g., time dependent exponential startup cost function). According to our formulation, the UCP can be stated as finding a feasible path of ON–OFF states for each generator (i.e., a sequence of unit commitment states that satisfy the corresponding minimum ON time and minimum OFF time constraints over the scheduling horizon) such that the total generation cost is minimized while meeting the demand and reserve requirement in each hour for the next day. We show how a near optimal solution for the UCP can be constructed using our solution method which is based on the Lagrangian relaxation (LR) method. Although only a near optimal solution is found, we show that our solution is comparable to that obtained when the UCP is modeled as a mixed integer linear program (MILP).