Accuracy study of linearization methods for quadratic cost curves of thermal units in unit commitment problems

To solve the unit commitment (UC) problems with efficient mixed-integer linear programming solvers, the quadratic cost functions (QCFs) of thermal units are always approximated to piecewise linear (PWL) functions. This study examines the accuracies of different approximation methods for piecewise linearizing the QCFs of units in UC problems. We use five piecewise linearization methods-evenly spaced PWL interpolation, evenly spaced PWL tangent, evenly spaced PWL-e(max)/2 shifted interpolation, tighter PWL interpolation, and evenly spaced PWL least-squares fit-to approximate the QCFs of units. The authors first perform a series of reproductivity studies to verify the program. Then, numerical tests are conducted using different methods on the systems with 10, 100, and 800 units. The results show that different approximation methods lead to considerable differences in operating costs and the tighter PWL interpolation, compared with the other methods, is preferred in terms of approximation accuracy.