Network-Constrained AC Unit Commitment Under Uncertainty: A Benders’ Decomposition Approach

Abstract

Abstract-This paper proposes an efficient solution approach based on Benders' decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders' approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach.

Strategic Sizing of Energy Storage Facilities in Electricity Markets

“…The well-functioning of Benders' decomposition in non-convex problems, e.g., a bi-level problem, is generally not guaranteed. However, there are several studies in the literature, e.g., [24]- [26], that efficiently applied this technique into "stochastic" non-convex problems providing that a sufficient number of scenarios is considered. The reason for this is that the objective function of the non-decomposed model convexifies with respect to the complicating variables as the number of scenarios and their diversity increases.…”

Optimized Sizing and Scheduling of Hybrid Energy Storage Systems for High-Speed Railway Traction Substations

“…Significant computational resources and time cost are required when all the scenarios are included in the stochastic bi-level model, thus a tradeoff between the solution accuracy and computation speed should be achieved [35][36][37]. Aiming at dealing with the contradiction of computational complexity and time limitation, scenario reduction method is developed in previous studies [34,38,39].…”

“…Equations (32)- (35) set up the limitation of discharging and charging power, which means that both the power rating and available energy variation at time interval can decide the upper bound of power. Equations (36) and (37) state that stored energy at initial stage equals that at final stage for the convenience of scheduling in the next day, as the diurnal operation of HESS is regarded as repeated within the project service period. Equations (38)- (43) demonstrate the fact that charging status cannot coexist with discharging status simultaneously.…”

Two-Stage Stochastic Model Using Benders’ Decomposition for Large-Scale Energy Resource Management in Smart Grids

“…Including all the generated scenarios in the optimization problem results in a large-scale optimization problem [26]. Generally, there should be a tradeoff between model accuracy and computation speed [25], [29]. In order to handle the computational tractability of the problem, the standard scenario reduction techniques developed in [30] is used.…”