Optimizing Power Systems with Representative Week Selection
摘要
Planning strategies for electrical grids involve the use of mathematical models that consider the deployment of both generation and storage infrastructure. These models seek to optimize reliability and adaptability in meeting future electricity requirements while reducing environmental burdens. Nonetheless, solving these problems over long-term horizons can be computationally challenging. In this chapter, we assess three distinct approaches to select representative weeks, evaluating their precision in capturing the net load duration curve (NLDC) for five regions of the Mexican peninsular power system and within the model’s objective function scope. The examined selection techniques included: K-means clustering with the Euclidean distance, K-means clustering using the dynamic time warping (DTW) measure and a combinatorial algorithm. The combinatorial approach yielded a RMSE of 2.80. In contrast, the DTW-based k-means produced an RMSE of 3.21, while the Euclidean-based k-means reached 5.49. The DTW k-means required 17 to 70 times more processing time than the combinatorial and Euclidean-based methods, largely because of the lack of restrictions on deformation tolerance. From a cost standpoint, the combinatorial strategy led to total system expenditures of $4.4274 × 1010, whereas DTW and Euclidean k-means yielded costs 0.1% and 0.2% lower, respectively. However, this apparent cost reduction stems from an underestimation of actual system expenses, as the methods do not fully capture real-world operating conditions and tend to generate overly optimistic scenarios.