A functional optimization based dynamic economic load dispatch considering ramping rate of thermal units output

Economic load dispatch among thermal units is one of the most important problems in power systems operation. Usually so called equal marginal cost criterion is adopted to this calculation. Recently global trend of utilizing more and more renewable energy makes this problem more important than ever. In case of large penetration of fluctuating power sources such as PV or wind, thermal units might be more often required a severe operation pattern because the outputs from PV and wind power generators are affected by uncertain change of weather condition. In a sense the large scale utilization of natural energy depends on the flexible and adaptive operation of thermal units. In such a situation it is easily imagined that thermal units would be required to change their output faster than before sometimes almost violating the limitation due to the physical constraints of the plant. We will need a load dispatch calculation method which maximally utilizes their output change capability within the upper limits of the ramp rate. Dynamic economic load dispatch has been studied for a long time to give appropriate load dispatch among generators considering the above stated constraints. However the existing methods are not enough in case of the scenario of very steep demand change. Some more sophisticated calculation scheme is highly needed today which gives us feasible solution in severer situations. This paper proposes a new calculation scheme for the above stated dynamic economic load dispatch problem based on functional optimization which numerically solves Euler's differential equation in the field of calculus of variations. The constraints related to unit output and output ramp rate are readily considered by the logarithmic penalty function terms in the objective function together with the equality constraint regarding the total demand/supply balance. Numerical examples show that the proposed method can solve the above stated severe situation which has been difficult to treat by the existing methods. Convergence performance is also discussed.