ALGORITHMS FOR OPERATION OF POWER SYSTEMS: RISK, UNCERTAINTY, DISCRETENESS, AND NONCONVEXITY
Open Access
- Author:
- Wan, Wendian
- Graduate Program:
- Industrial Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 13, 2019
- Committee Members:
- Vinayak V Shanbhag, Dissertation Advisor/Co-Advisor
Vinayak V Shanbhag, Committee Chair/Co-Chair
Vittaldas V Prabhu, Committee Member
Guodong Pang, Committee Member
Mort D Webster, Outside Member
Robert Carl Voigt, Program Head/Chair
Mort D Webster, Committee Chair/Co-Chair - Keywords:
- stochastic programming
economic dispatch
power system optimization
nonconvex optimization - Abstract:
- This dissertation considers the development of computational schemes for a class of operational problems in power systems, complicated by uncertainty, discreteness, and nonconvexity. In Chapter 2, we consider a class of risk-based two-stage economic dispatch problems, a class of problems that can be captured by stochastic convex programs where the integrands are nonsmooth convex functions and each function evaluation requires solving a convex optimization problem. We proceed to show that the risk of the second-stage cost satisfies smoothability requirements under suitable assumptions. This allows for adapting a variable sample-size accelerated proximal scheme (VS-APM) for such problems. Notably, this scheme is a stochastic approximation scheme that combines smoothing, acceleration, and variance reduction. The resulting expected sub-optimality diminishes to zero at the rate of O(1/k). We observe that the scheme performs well in comparison with standard stochastic gradient as well as stochastic cutting-plane schemes on a range of IEEE test problem sets. In Chapter 3, we consider a class of stochastic integer programs that arise from a two-stage stochastic unit commitment problem. We present a computational framework for addressing such a problem by combining the VS-APM scheme with a branching scheme. Such a framework is fairly adaptable and can allow for a broad range of risk-based convex models. Preliminary testing suggests that the scheme competes well with CPLEX when the problem has first-stage integers and the number of second-stage scenarios grows to be large. In more general problems with second-stage problems, the scheme can obtain global solutions for modest sized problems. Finally in Chapter 4, we consider the optimal power flow problem with AC power flow constraints. The resulting problem is known to be a highly nonconvex problem and the solution of such problems is generally challenging. We consider an avenue for resolving such problems that relies on an alternating direction method of multipliers (ADMM) scheme. This scheme can be implemented in a networked setting and its performance is seen to scale with the number of scenarios when stochastic variants are considered.