Document Type


Date of Degree

Fall 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Industrial Engineering

First Advisor

Pavlo Krokhmal

Second Advisor

Yong Chen


The need for effective energy harvesting from renewable resources becomes increasingly important, especially in the light of the inevitable depletion of the fossil fuel energy sources. Among renewable energy sources, wind energy represents one of the most attractive alternatives. In this thesis, we construct several stochastic optimization models, including the traditional risk-neutral expectation based model, and risk-averse models based on linear and nonlinear coherent measures of risk, to study the strategic planning and operation of futuristic power grids where the loads are served from renewable energy sources (wind farms) through High Voltage Direct Current lines. Exact solutions algorithms that employ Benders decomposition and polyhedral approximations of nonlinear constraints have been proposed for the formulated linear and nonlinear mixed-integer optimization problems. The conducted numerical experiments illustrate the efficiency of the developed algorithms, as well as effectiveness of risk-averse models in reducing the power grid's exposure to power shortage risks when the energy is produced from renewable sources. We further extend the risk-averse models to demonstrate how energy storage devices may impact the risk profile of power shortages in the renewable energy power grid. Additionally, we consider convex relaxations of optimal power flow problem over radial networks, that allow for solving mixed-integer optimization problems in traditional alternating current distribution networks. Exactness of a specific second-order cone programming relaxation has been discussed. We finally propose an “ extended” optimal power flow problem and prove its second-order cone programming relaxation to be exact theoretically and empirically.

Public Abstract

As renewable energy resources increasingly contribute to the global energy consumption and gradually replace traditional fossil fuels, how to harvest and utilize renewables in an effective and efficient way becomes crucial. The advantages of renewable energy as a clean, plentiful and commonly available source of energy usually come at a cost of uncertainty or intermittency, which would impact on the stability of power grids and even cause mismatch between the power supply and load (considered as power shortage risk) in some scenarios when using or integrating renewable energy into transmission and distribution networks. Therefore, how to mitigate the negative impact from the intermittency of renewable energy and hedge the power shortage risk, is the main purpose of this study.

In this thesis, we focus on wind energy and consider the wind farm location problem. Several stochastic optimization models are proposed in terms of various criteria including risk-neutral expectation, linear and nonlinear coherent measures of risk, which aim to demonstrate the importance of strategic planning of wind farms and in which way power shortage risk can be reduced. Furthermore, we also investigate the impact of energy storage devices on the risk profile of power shortage by extending the risk-averse models. Lastly, the convexification of optimal power flow problem over radial networks is studied, which is conducive to solving mixed-integer optimization problems in traditional alternating current distribution networks.




xii, 126 pages


Includes bibliographical references (pages 115-126).


Copyright 2015 Bo Sun