The challenges of the unit commitment problem for real-life small-scale power systems

• MIP formulation for variable cold and hot start-up costs.
• 10-min spinning, non-synchronized, operational, and distributed reserves.
• Spinning and regulation reserves.
• Better linearization of generators’ quadratic cost function.
• Use of IBM-CPLEX 12.6 to solve the mathematical model.

Small-scale power systems mainly present two particular problems when it comes to their modeling and solution. Due to their size, it is important to consider and meet various types of reserve requirements in order to have a reliable operation of the power system. It is also important to consider variable start-up costs in order to obtain a more accurate unit commitment. In this paper six different types of reserve requirements are considered for the unit commitment problem: spinning reserve, regulation reserve (AGC per unit), ten-minute reserve, ten-minute non-synchronized reserve, ten-minute operational reserve, and ten-minute distributed reserve. Additionally, a Mixed Integer Programming formulation is introduced to represent variable start-up costs. The model introduced here is currently in use by the Baja California (México) power system operator.