Mathematical programming approaches for two problems in energy systems

Official URL: https://risc01.sabanciuniv.edu/record=b2766795_(Table of contents)

A wide variety of problems in energy systems can be formulated as mathematical programs. In the first part of this thesis, we focus on the integrated maintenance and operations planning problem in power systems, which is formulated as a mixedinteger joint-chance constrained stochastic program. Due to the intractability of the joint chance-constraint, we propose a cutting-plane method to obtain its exact reformulation and derive its second-order cone programming based safe approximation. To solve this program, we propose a decomposition algorithm by exploiting the features of the integer L-shaped method and introduce various algorithmic enhancements. We design an extensive computational study and demonstrate the performance of the proposed approach with reliable and cost-effective maintenance and operational schedules. In the second part of this thesis, we focus on the multi-period natural gas storage optimization problem by considering the important aspects of gas physics and switching status of active elements. Under steady-state conditions, we formulate this problem as a nonconvex mixed-integer nonlinear program. We propose mixed-integer linear and second-order cone programming relaxations of this complex problem to obtain tight dual bounds. We design a computational study to compare these formulations on different instances from the literature. Our results demonstrate the computational efficiency of our approach and its ability to obtain (near) globally optimal solutions in comparison with a global optimization solver