Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Dr. Taufiquar Khan

Committee Member

Dr. Warren Adams

Committee Member

Dr. Yuyuan Ouyang

Committee Member

Dr. Tongxin Zheng


Renewable energy sources are indispensable components of sustainable electrical systems that reduce human dependence on fossil fuels. However, due to their intermittent nature, there are issues that need to be addressed to ensure the security and resiliency of these power systems. This dissertation formulates several practical problems, from an optimization perspective, stemming from the increasing penetration of intermittent renewable energy to power systems. A number of Optimal Power Flow (OPF) formulations are investigated and new formulations are proposed to control both operations and planning risks by utilizing the Conditional Value–at–Risk (CVaR) measure. Our formulations provide system operators and investors analysis tools to minimize their expected cost while hedging against risk from various sources of uncertainty.

A security–constrained OPF formulation with a CVaR constraint to limit the risk of system line overloading in the case of contingencies is proposed. A novel inverse problem formulation of OPF for uncertainty quantification where we approximate the distribution of wind power forecast errors with a probability mass function (PMF) given the generator outputs is also proposed. This PMF facilitates the application of CVaR constraints in controlling the operations risks of line overloading and load shedding due to the uncertainty of wind power forecast error. A stochastic multi–period investment and planning model with economic risk constraints facing an uncertain environment around distributed energy resources technology costs and regulatory policies is also investigated. The efficacy of the proposed formulations is demonstrated using a wide range of case studies representing practical scenarios.



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