Optimal economic dispatch for power generation under the lagrange method

The goal of this research to optimize economic dispatch for power generation on the electrical system. In this research there are two kinds of power generation installed on the electrical power system: $2\times 50\ \text{MW}$. The total load and cost for generators-1 and 2 are: 41.63 MW (23,489,069.25 IDR/h) and 41.73 MW (21,291,609.38 IDR/h), respectively. To define optimum cost for both generations, the Lagrange method was applied to compute total cost for every generator considering the electricity demand. Based on the results of research illustrated, the total load and cost for generation-1 and 2 can be optimized to be 43.41 MW (24,540,714 IDR/h) and 39.95 MW (20,221,493), respectively. This indicates that the Lagrange method is an effective way to reduce the total cost of generation. The total cost reduction can be achieved to be 31,205 IDR/h.