How to Improve Linear Fuel-Cost Function to Compete with Quadratic and Cubic Functions

To model the operating cost of thermal generating units, it is common to use polynomial relations between their power output and fuel input. These mathematical relations are known as fuel-cost functions, which are the heart of optimization algorithms. These functions could be modeled as first, second, or third order polynomial equations. The first order or linear equation is weak to explain the variability of units' operating cost. Also, the third order or cubic polynomial equation is rarely used in the literature, because its third element does not have any significant contribution to add. Thus, the second order or quadratic polynomial equation becomes the most popular fuel-cost function. Sometimes, different linear equations grouped as a piecewise function are used to accelerate the computational speed and linear programming algorithms can be directly involved. This study tries to achieve the goal of the last approach without using any piecewise function. That is, improving the preceding single linear equation to be a competitive fuel-cost function.