Path Optimization in Free Energy Calculations

Free energy calculations are a computational method for determining thermodynamic quantities, such as free energies of binding, via simulation.

Currently, due to computational and algorithmic limitations, free energy calculations are limited in scope.

In this work, we propose two methods for improving the efficiency of free energy calculations.

First, we expand the state space of alchemical intermediates, and show that this expansion enables us to calculate free energies along lower variance paths.

We use Q-learning, a reinforcement learning technique, to discover and optimize paths at low computational cost.

Second, we reduce the cost of sampling along a given path by using sequential Monte Carlo samplers.

We develop a new free energy estimator, pCrooks (pairwise Crooks), a variant on the Crooks fluctuation theorem (CFT), which enables decomposition of the variance of the free energy estimate for discrete paths, while retaining beneficial characteristics of CFT.

Combining these two advancements, we show that for some test models, optimal expanded-space paths have a nearly 80% reduction in variance relative to the standard path.

Additionally, our free energy estimator converges at a more consistent rate and on average 1.8 times faster when we enable path searching, even when the cost of path discovery and refinement is considered.

Capacity Investment in Renewable and Conventional Energy Sources

This dissertation studies capacity investments in energy sources, with a focus on renewable technologies, such as solar and wind energy. We develop analytical models to provide insights for policymakers and use real data from the state of Texas to corroborate our findings.

We first take a strategic perspective and focus on electricity pricing policies. Specifically, we investigate the capacity investments of a utility firm in renewable and conventional energy sources under flat and peak pricing policies. We consider generation patterns and intermittency of solar and wind energy in relation to the electricity demand throughout a day. We find that flat pricing leads to a higher investment level for solar energy and it can still lead to more investments in wind energy if considerable amount of wind energy is generated throughout the day.

In the second essay, we complement the first one by focusing on the problem of matching supply with demand in every operating period (e.g., every five minutes) from the perspective of a utility firm. We study the interaction between renewable and conventional sources with different levels of operational flexibility, i.e., the possibility

of quickly ramping energy output up or down. We show that operational flexibility determines these interactions: renewable and inflexible sources (e.g., nuclear energy) are substitutes, whereas renewable and flexible sources (e.g., natural gas) are complements.

In the final essay, rather than the capacity investments of the utility firms, we focus on the capacity investments of households in rooftop solar panels. We investigate whether or not these investments may cause a utility death spiral effect, which is a vicious circle of increased solar adoption and higher electricity prices. We observe that the current rate-of-return regulation may lead to a death spiral for utility firms. We show that one way to reverse the spiral effect is to allow the utility firms to maximize their profits by determining electricity prices.