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Scheduling of Power Units via Relaxation and Decomposition

Constante Flores, Gonzalo Esteban
http://orcid.org/0000-0002-9668-5889
http://rave.ohiolink.edu/etdc/view?acc_num=osu1669958189437929

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
This dissertation focuses on the scheduling of generating units in electric power systems. Our work is motivated by the growing integration of weather-dependent generation and natural-gas-fired power plants, which have arisen important challenges in the operation of power grids in recent years. We propose models and algorithms for realistic power systems to address the generation scheduling problem with different features, namely, alternating current network constraints, uncertain weather-dependent generation, coordinated operation with natural-gas systems, and inclusion of network security constraints. Each one of these characteristics is carefully and independently analyzed in each chapter of this dissertation. The proposed models, which are generally large-scale and intractable for state-of-the-art optimization solvers, show a decomposable structure that we exploit to develop computationally efficient solution algorithms. In particular, the proposed models pertain to the class of mathematical problems with complicating variables. Therefore, a Benders decomposition framework is the corner stone of the algorithms that we propose. Our algorithms aim at mitigating the pernicious interaction between binary variables (modeling the commitment status of the generating units), nonlinear constraints (enforcing the power flow equations and transmission capacity limits), and the size of the problem. Accurate relaxation techniques are also an integral part of the models proposed. The first characteristic we studied corresponds to considering more accurate models of the nonconvex power flow equations. To address this problem, we relax the problem by replacing the power flow equations with a second-order conic relaxation. We propose two solution strategies for the resulting relaxed problem for small- to large-scale power systems. Additionally, we provide a technique to check the feasibility of the commitment of the units with respect to the original power flow equations based on the solution of a sequence of convex problems. The second characteristic we studied pertains to incorporating stochastic models of uncertain weather-dependent generation. We model this problem as a two-stage stochastic programming problem. We examined two versions of this problem: (i) a daily scheduling with network constraints, and (ii) a risk-constrained daily scheduling with weekly dispatched energy storage. To tackle this problem, we propose a hybrid decomposition technique that blends ideas from Benders decomposition and the column-and-constraint generation algorithm. The third characteristic we studied pertains to coordinating the operation of natural-gas systems and power systems. We model this problem as a bilevel optimization problem where the gas prices of the natural-gas-fired units are given by the dual variables of the natural-gas market clearing problem. We propose a single-level mixed-integer nonconvex reformulation and a mixed-integer second-order conic relaxation. To solve this problem, we propose a solution technique that uses concepts from Benders decomposition and the outer approximation algorithm. The last characteristic we studied corresponds to tackling the challenges of including network security constraints. We consider the corrective version of the generation scheduling problem that allows recourse actions by the generators to mitigate the impact of a contingency. To address this problem, we propose a solution method that uses a network reduction technique, which significantly improves the solution time, within a Benders decomposition framework.
Antonio Conejo (Advisor)
Andrea Serrani (Committee Member)
Parinaz Naghizadeh (Committee Member)
Kirk Mykytyn (Committee Member)
399 p.
Electrical Engineering
scheduling; unit commitment; Benders decomposition; decomposition techniques

Recommended Citations

Citations

  • Constante Flores, G. E. (2022). Scheduling of Power Units via Relaxation and Decomposition [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1669958189437929

    APA Style (7th edition)

  • Constante Flores, Gonzalo. Scheduling of Power Units via Relaxation and Decomposition. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1669958189437929.

    MLA Style (8th edition)

  • Constante Flores, Gonzalo. "Scheduling of Power Units via Relaxation and Decomposition." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1669958189437929

    Chicago Manual of Style (17th edition)

osu1669958189437929
184
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This open access ETD is published by The Ohio State University and OhioLINK.