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We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and physics-inspired solution methods whose standard optimization form is equivalent to the QUBO. These methods include quantum annealing, quantum gate-circuit optimization algorithms (Quantum Optimization Alternating Ansatz, Variational Quantum Eigensolver), other hardware-accelerated platforms, such as Coherent Ising Machines and Simulated Bifurcation Machines, and more traditional methods such as simulated annealing. Besides working with reformulations, QUBO.jl allows its users to interface with the aforementioned hardware, sending QUBO models in various file formats and retrieving results for subsequent analysis. QUBO.jl was written as a JuMP / MathOptInterface (MOI) layer that automatically maps between the input and output frames, thus providing a smooth modeling experience.

This paper exploits the decomposition structure of the large-scale hydrothermal generation expansion planning problem with an integrated modified Benders Decomposition and Progressive Hedging approach. We consider detailed and realistic data from the Brazilian power system to represent hourly chronological constraints based on typical days per month and year. Also, we represent the multistage stochastic nature of the optimal hydrothermal operational policy through co-optimized linear decision rules for individual reservoirs. Therefore, we ensure investment decisions compatible with a nonanticipative (implementable) operational policy. To solve the large-scale optimization problem, we propose an improved Benders Decomposition method with multiple instances of the master problem, each of which strengthened by primal cuts and new Benders cuts generated by each master's trial solution. Additionally, our new approach allows using Progressive Hedging penalization terms for accelerating the convergence of the method. We show that our method is 60\% faster than the benchmark. Finally, the consideration of a nonanticipative operational policy can save 7.64\% of the total cost (16.18\% of the investment costs) and significantly improve spot price profiles.

Energy storage systems - in particular, Pumped Hydropower Storage (PHS) - will be increasingly important to support the transition of power systems toward zero emissions. The reason is that PHS can mitigate the variability and uncertainty of renewable energy production from solar and wind power to balance electricity demand with supply. In this paper, we propose an integer programming problem for PHS siting that uses a Digital Elevation Model (DEM) to meet an energy storage requirement. It assumes the existence of a reservoir, lake, or river, and decides where to build a reservoir that will constitute the PHS with the existing body of water. This model finds minimum-cost project candidates given parameters such as desired head, power, and operation time. The paper discusses different solution methods to assure reservoir closure and avoid its fragmentation. A heuristic explores the representations of the DEM, from more aggregate to more precise, to sequentially refine the solution based on the last selected site, which reduces computational effort. The formulation is general and the objective function includes both construction and equipment costs. Constraints are related to the energy storage target and reservoir closure based on the DEM. We illustrate the methodology by selecting multiple PHS projects next to the reservoir of the Sobradinho hydropower plant in Brazil. The result of this model can be seen as a bottom-up step that prepares PHS candidate projects to be considered by an integrated resource planning model in a top-down step, that would select from these shortlisted projects., Comment: 15 pages, 4 figures, 5 tables

This paper describes the application of a Progressive Hedging (PH) algorithm to the least-cost var planning under uncertainty. The method PH is a scenario-based decomposition technique for solving stochastic programs, i.e., it decomposes a large scale stochastic problem into s deterministic subproblems and couples the decision from the s subproblems to form a solution for the original stochastic problem. The effectiveness and computational performance of the proposed methodology will be illustrated with var planning studies for the IEEE 24-bus system (5 operating scenarios), the 200-bus Bolivian system (1,152 operating scenarios) and the 1,600-bus Colombian system (180 scenarios).

This paper describes an area decomposition and a robust optimization strategy for the planning of large-scale transmission networks considering uncertainty in variable renewable energy (VRE) and hydropower generation. The strategy is illustrated with a study of Brazil's power grid expansion from 2027 to 2036. The country's network has over 10 thousand buses and 14 thousand circuits and covers an area equivalent to the USA. A clustering scheme based on bus marginal costs is used to decompose the grid into seven regions. Each regional planning is then solved by a heuristic and Benders decomposition methods to produce a robust least-cost plan for 3,000 dispatch scenarios., Comment: 12 pages, 7 figures