Fast unit commitment based on optimal linear approximation to nonlinear fuel cost: Error analysis and applications

Mixed-integer linear programming (MILP) based techniques are among the most widely applied methods for unit commitment (UC) problems. The fuel cost functions are often replaced by their piecewise linear approximations whereas it is more or less disturbing to use piecewise linear approximations without knowing the exact effect on solution deviation from the optima. Therefore, error analysis is important since the optimal solutions are different when different objective functions are adopted. Another important problem is balancing between solution quality and computation efficiency since better solution quality relies on finer discretization with exponentially increased computational efforts. A detailed error analysis is presented in this paper. It is found that the approximation error is inverse proportional to the square of the number of piecewise segments. Lower bounds on the minimum necessary number of discretization segments are also derived. A 2-Stage Procedure is then established to achieve a better balance between solution quality and computation efficiency. Numerical testing to 2 groups of UC problems is exciting. It is found that the operating cost increases no more than 0.6% in all cases while the CPU time is greatly reduced regarding other MILP approaches. The results are still valid in electric power market clearing computation.