Electricity Price Models

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Electricity Price Models in the Context of Increasing Renewable Energy Generation Felipe dos Santos Couto, f.couto@columbia.edu SEAS ’22, Mechanical Engineering, Columbia University Supervising Faculty, Sponsor, and Location of Research Dr. Bolun Xu, Undergraduate Research Involvement Program, The Earth Institute, Columbia University Abstract Renewable energy is no longer an interesting possibility for the future but rather an urgent demand in the present to fight the climate crisis. Nevertheless, academia, industry, and public entities still face many challenges to increase penetration of renewable sources on the world energy mix. In this context, storing energy has risen as a key alternative and numerous storage solutions have been developed. The purpose of this study is to better understand how large-scale energy storage systems (ESS) impact electricity prices. We developed interpretable machine learning models and analyzed how supply and demand attributes correlate with price fluctuations – especially, price spikes, which are a major sign of market inefficiency. Optimal Regression Trees and Multiple Linear Regressions were applied to the Southwest Power Pool market data, shedding some light upon the attributes’ sensitivities. We then utilized the sensitivities to estimate price reductions due to energy storage. Results showed a potential reduction, on average, of 19.0% on price spikes. Further studies shall continue to investigate the effects grid-scale ESS on prices. By doing so, we hope to corroborate with the expansion of renewable energy generation and ESS on the grid. Keywords renewable energy, energy storage, interpretable machine learning, electricity price models 6
A Parametric, Ultrasound-Based Model of the Uterus in Late Gestation Divya Rajasekharan & Arielle Feder, dr2940@columbia.edu & adf2153@columbia.edu SEAS ’21 & ’22, Mechanical Engineering, Columbia University Supervising Faculty, Sponsor, and Location of Research Dr. Kristin Myers, Summer@SEAS, Myers Soft Tissue Lab, Columbia University Abstract Pregnancy poses an interesting mechanical problem, as the female body must evolve to accommodate a growing fetus. Since direct research into the mechanical environment of pregnancy is precluded for clear ethical reasons, 3D models provide a unique opportunity to study the mechanical properties of the uterus via simulation. In late pregnancy (LP), the geometry of the uterus changes distinctly: the elliptical shape of early pregnancy grows more tapered towards the cervix end, terminating in a V-like profile in the coronal plane. This shift raises the question of whether geometric changes are necessary to mediate important developments in the load-bearing properties of the uterus. To investigate this possibility, we built two uterus models to accommodate the late-gestation coronal shape with varying degrees of accuracy. The first is based on a limited number of ultrasound measurements, with overall shape informed by patient-averaged characteristics derived from MRI. The second is a highly parameterized model, driven by MRI measurements. Two additional models—a ground truth model segmented directly from MRI and the lab’s current, elliptical parametric model—were used as points of reference. By comparing these models’ behavior in a simple static load analysis for 5 LP patients, we evaluated the mechanical significance of the change in LP coronal shape. We found that the stress distribution was highly dependent on local fluctuations in uterine wall thickness. Models based on limited ultrasound measurements were not always sensitive enough to capture this variation. In the LP models, we observed that the tapering of the uterus had the effect of drawing pressure loads away from the cervical os and into the lower side walls, while the blunter coronal profile of early-gestation allowed stress to concentrate at the os. Finally, the first and second principal strain directions— oriented circumferentially and longitudinally, respectively—were consistent across all four models. In conclusion, the late pregnancy uterus exhibits load bearing properties distinct from earlier pregnancy, mediated by a change in coronal shape. Furthermore, a parametric modeling framework, which accounts for the coronal shape on a patientaveraged basis, may be a viable option to efficiently represent the load-bearing characteristics of the LP uterus when compared to higher resolution, but computationally intensive, MRI-driven models. Keywords pregnancy, biomechanics, 3D modeling, simulation, finite element analysis (FEA), ultrasound, magnetic resonance imaging (MRI) 7
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