Brent method for Dynamic Economic Dispatch with transmission losses

This paper presents application of Brent method to solve dynamic economic dispatch (DED) problem with transmission losses. The algorithm involves the selection of incremental fuel costs (lambda values) and then the optimal lambda is evaluated from the power balance equation by Brent method at predicted power demand. In real time operation, thermal gradients inside the turbine should be kept within safe limits to avoid shortening the life of generating units. This mechanical constraint is translated into a limit on the rate of increase and decreases of the output power during the variation in the power demand and is known as ramp rate limits. The constraint of ramp rate limits distinguishes the DED problem from the traditional static economic dispatch (ED) problem. Due to ramp rate limits, DED problem cannot be solved for a single value of the power demand. The main objective is to determine the optimal schedule of output powers of online generating units with predicted power demands over a certain period of time to meet power demands at minimum operating cost. The proposed method has been tested on a power system having 6 and 15 generating units. The results of the proposed algorithm are compared with the conventional lambda iterative method in terms of solution quality and computational time. It is observed from the case studies that the Brent method provides qualitative solution with less computational time compare to lambda iterative method.