Juliette Franzman | Searcharxiv

arXiv2026

High-Fidelity Capacity Expansion Planning for Puerto Rico's Electric Power System

This study presents a mathematical optimization framework and analysis to inform practical long-term investment planning in Puerto Rico's electric power system. We utilize a high-resolution capacity expansion planning model to identify least-cost generation and storage investments that improve reliability. The model co-optimizes new investments with thermal retirements and includes detailed dispatch, unit commitment, fuel selection, storage operation, engineering limits, system constraints, fuel supply limits, and load balance. Key advances over prior studies on Puerto Rico's system include: (i) Nodal transmission representation at 38 kV and above; (ii) hourly chronological simulation for representative days; (iii) explicit unit commitment for existing and new thermal units with realistic ramping, minimum up and down times, and startup costs; (iv) system-wide fuel supply constraints; and (v) operational scenarios reflecting load variability, renewable availability, and high forced outage rates in legacy units. Using data from LUMA, the Puerto Rico Electric Power Authority (PREPA), U.S. Department of Energy, and public sources, the study builds representative Puerto Rico systems for 2024 and 2030, with the latter including planned generation and storage projects. It tests scenarios with different future load levels, fuel supply assumptions, planned additions, and allowed technologies. Under the study assumptions, least-cost portfolios that meet reliability targets require about 1.5 GW or more of new H-class combined cycle capacity, in addition to planned projects. These additions mainly replace unreliable legacy thermal units rather than serve new load. The new CC investments eliminate modeled load shedding in the bulk system and restore a robust reserve margin, even under stressed load and outage conditions.

math.OC↗

arXiv2023

Data Mining for Faster, Interpretable Solutions to Inverse Problems: A Case Study Using Additive Manufacturing

Solving inverse problems, where we find the input values that result in desired values of outputs, can be challenging. The solution process is often computationally expensive and it can be difficult to interpret the solution in high-dimensional input spaces. In this paper, we use a problem from additive manufacturing to address these two issues with the intent of making it easier to solve inverse problems and exploit their results. First, focusing on Gaussian process surrogates that are used to solve inverse problems, we describe how a simple modification to the idea of tapering can substantially speed up the surrogate without losing accuracy in prediction. Second, we demonstrate that Kohonen self-organizing maps can be used to visualize and interpret the solution to the inverse problem in the high-dimensional input space. For our data set, as not all input dimensions are equally important, we show that using weighted distances results in a better organized map that makes the relationships among the inputs obvious.

cs.LG↗