Power systems optimal load flow studies are performed for standard test cases using several methods of minimization. Comparisons of the solutions are made based on digital computer results. A general discussion is made of optimization and the necessary conditions for solution. Cost functions are written for the minimum costs and losses problem and then augmented to satisfy variable constraints. Through the use of common routines and format, sufficient basis for comparison of the several methods was established. Among the methods, steepest descent was chosen as most attractive and a further study was performed. Results of this are presented and conclusions drawn to improve the economical operation of our power system utilities.