Juliette Franzman

Chandrika Kamath, Juliette Franzman, Ravi Ponmalai

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.

Elizabeth Glista, Tomas Valencia Zuluaga, Amelia Musselman et al.

This study presents a mathematical optimization framework and preliminary analysis for long-term investment planning in Puerto Rico's electric power system. We develop a high-resolution capacity expansion model to identify least-cost generation and storage investments that improve system reliability. The model co-optimizes new investments and thermal generator retirements while representing generator dispatch, unit commitment, fuel selection, and storage operations under constraints of equipment engineering limits, fuel supply limitations, and load satisfaction. Key methodological advances relative to prior long-term planning studies for Puerto Rico include: (i) nodal transmission modeling at 38 kV and above, (ii) hourly chronological operations 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) stochastic operating scenarios reflecting load variation, renewable availability, and the high forced outage rates of legacy units. Using data from LUMA, PREPA, DOE, and public sources, we build present-day (2024) and future (2030) test systems, with the latter including planned generation and storage projects. We evaluate planning scenarios that vary future load, fuel supply assumptions, realization of planned expansion, and allowable new technologies. Results show that, given the recent relaxation of interim renewable goals for the near future in Puerto Rico, an optimal portfolio includes at least 1.5 GW of new H-class combined cycle capacity beyond planned projects. These additions are needed mainly to replace unreliable legacy thermal units rather than to serve new load. The new combined cycle units eliminate modeled bulk-system load shedding and restore a strong reserve margin, even under stressed load and outage conditions.