Comparative framework of representative weeks selection methods for the optimization of power systems

Abstract

Considering the reliability and flexibility to supply future energy demand, power grid planning models are composed of mathematical formulations that represent investments in the installation and operation of generation and storage systems to reduce costs and environmental impacts. However, these can be computationally intractable to solve for many periods. Hence, in this paper, three methods are compared to obtain representative weeks in terms of their accuracy in representing the net load duration curve (NLDC) of the 5 regions that compose the Mexican peninsular electric system and in the objective function domain of a proposed model. The selection methods used for representative weeks were k-means with Euclidean metric, k-means with dynamic time warping (DTW) metric and a combinatorial method. It was observed that the combinatorial method obtained a root mean square error (RMSE) in the representation of 2.80, followed by k-means with DTW metric with 3.21 and finally k-means with Euclidean metric with 5.49. K-means with DTW metric requires about 17 and 70 times more computational time than the combinatorial method and k-means with Euclidean metric, because it had no restrictions on the amount of deformation allowed. In terms of the objective function, the combinatorial method had higher total system costs with $ 4.4274 × 10¹⁰, while they were 0.1 % and 0.2 % lower in k-means with DTW and k-means with Euclidean metric, respectively. These lower costs are due to underestimation of the system cost, as the methods do not adequately reflect operational situations and generate less expensive scenarios than are actually the case.