Data-Driven Optimization under Uncertainty for Renewable Energy Integration and Management
Distributionally Robust Optimization
Optimization under Uncertainty
Power Systems Planning
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PublisherThe University of Arizona.
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AbstractHigh levels of clean renewable energy are being integrated into the power systems as a result of recent government incentives and technological advancements. The electricity generated from renewable resources such as wind and solar are highly intermittent and uncertain, significantly threatening the stability, reliability, and efficiency of the power grid. In particular, the electrical power system is known to be notoriously complex and small violations of the system limits can lead to systemwide catastrophic events. Therefore, the increasing level of uncertainty introduced into the network through renewable distributed generation units is further complicating the planning and operation of the network at various stages; from long-term planning decisions to the real-time operation decisions.As a result of recent computational advances alongside large-scale availability of data, data-driven distributionally robust and stochastic optimization methodologies have been extensively developed to find low cost and highly reliable solutions to large-scale complex problems under uncertainty. In this dissertation, we develop novel data-driven distributionally robust and stochastic optimization methodologies for addressing (i) long-term planning, (ii) short-term planning and (iii) real-time operational decisions of a power system under high penetration of uncertain renewable energy. First and to address the long-term planning of renewables, we propose a distributionally robust model for the optimal sizing of new renewable sites in an existing distribution system. In particular, we first propose a two-stage data-driven distributionally robust optimization model (O-DDSP) for the optimal planning of renewable distributed generation units (RDGs). The objective is to minimize the total cost of RDG installation plus the total operational cost on a planning horizon. Next, we introduce a tight approximation of O-DDSP based on principal component analysis (leading to a model denoted by P-DDSP), which reduces the original problem’s size by projecting the ambiguity set to lower dimensions. Finally, extensive numerical experiments demonstrate that our solution methodology significantly out-performs the state-of-art. Our optimal RDGs planning decisions lead to significant savings as well as increasing penetration of intermittent renewable energy in the distribution network. Next and to tackle the short-term challenges that are caused by high penetration of renewables in the power systems, we propose a mixed-integer stochastic optimization methodology for integrated transmission and distribution systems planning. In particular, through a careful and systematic analysis of the power system planning problems, we underline the necessity of developing methods that can tackle the planning of both the power transmission system (TS) and distribution system (DS) and realize the potential benefits of considering their planning in a coordinated mode. To that end, we introduce an integrated transmission and distribution system (InTDS) problem which minimizes both the unit commitment costs of the TS and the distributed energy resource (DER) management costs of the DSs, respectively, while respecting the technical constraints of both systems. We show that our integrated model achieves significant lower costs as compared to solving these problems separately. At last and to address the real-time operation of power system under high penetration of renewables, we propose a chance-constrained stochastic optimization methodology for the optimal power flow (OPF) problem. The increasing penetration of renewable energy in power systems calls for secure and reliable system operations under significant uncertainty. To that end, we introduce a fully two-sided chance-constrained ACOPF problem (TCC-ACOPF), in which the active and reactive generation, voltage, and power flow all remain within their upper and lower bounds simultaneously with a predefined probability. Instead of applying Bonferroni approximation or scenario-based approaches, we present an efficient second order conic (SOC) approximation of the TCCs under Gaussian Mixture (GM) distribution via a piecewise linear (PWL) approximation. We show that our SOCP provides consistently more robust solutions (about 60% reduction in constraint violation) without significant additional computational costs, as compared to other state-of-art ACOPF formulations.
Degree ProgramGraduate College
Systems & Industrial Engineering