A Benders Decomposition Method on OPF Considering Bilateral Correction

Hybrid Energy Storage Systems (HESS) has the ability of providing fast and accurate response to second-to-second changes of the grids for keeping the power system uninterrupted and stable. This paper presents an enhanced Corrective Security Constrained Optimal Power Flow (CSCOPF) model by combining the technical merits of different Energy Storage technologies. The proposed HESS can be employed to take part in not only the traditional long-term rescheduling corrective control actions, but also the short-term post-contingency fast corrective control, which takes into account the current state of charge (SOC) and the energy capacity model of the HESS. An improved Benders decomposition (BD) method is developed to solve the enhanced CSCOPF problem and the effectiveness of the proposed method is evaluated and demonstrated in the paper by standard power systems.

The robust Mixed-Integer Linear Programming (MILP) model is an approach to address uncertainty in linear optimization involving integer and continuous variables, which can be solved using the Benders Decomposition method. One of its applications is facility location problems, which often face demand, costs, and capacity uncertainties. This article presents a systematic literature review (SLR) on solving robust MILP models using the Benders Decomposition method and its application to facility location problems. The objectives are to explore the state-of-the-art and research trends, identify issues modeled as robust MILP and solved using Benders Decomposition, and determine the most frequently used uncertainty sets. SLR was conducted using the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) method on the Scopus, Science Direct, and Dimensions databases for the last five years of publication, with bibliometric analysis using VOSviewer and RStudio. The results show that there are limited articles that discuss the solution of the robust MILP model on the problem of facility location with the ellipsoidal uncertainty set. In addition, the Benders Decomposition method is widely used to solve robust MILP problems in energy, logistics, supply chains, and scheduling, with interval uncertainty sets being the most common. This topic is an influential theme and has the potential to be explored further.

Preface. Part I: Motivation. 1. Linear and Integer Linear Optimization. Part II: Theory. 2. Linear Systems and Projection. 3. Linear Systems and Inverse Projection. 4. Integer Linear Systems: Projection and Inverse Projection. Part III: Algorithms. 5. The Simplex Algorithm. 6. More on Simplex. 7. Interior Point Algorithms: Polyhedral Transformations. 8. Interior Point Algorithms: Barrier Methods. 9. Integer Programming. Part IV: Solving Large Scale Problems: Decomposition Methods. 10. Projection: Benders's Decomposition Methods. 11. Inverse Projection: Dantzig-Wolfe Decomposition. 12. Lagrangian Methods. Part V: Solving Large Scale Problems: Using Special Structure. 13. Sparse Methods. 14. Network Flow Linear Programs. 15. Large Integer Programs: Preprocessing and Cutting Planes. 16. Large Integer Programs: Projection and Inverse Projection. Part VI: Appendix. A. Polyhedral Theory. B. Complexity Theory. C. Basic Graph Theory. D. Software and Test Problems. E. Notation. Bibliography. References. Author Index. Topic Index.

The BusPlus project aims at improving the off-peak hours public transit service in Canberra, Australia. To address the difficulty of covering a large geographic area, proposes a hub and shuttle model consisting of a combination of a few high-frequency bus routes between key hubs and a large number of shuttles that bring passengers from their origin to the closest hub and take them from their last bus stop to their destination. This paper focuses on the design of the bus network and proposes an efficient solving method to this multimodal network design problem based on the Benders decomposition method. Starting from a mixed-integer programming (MIP) formulation of the problem, the paper presents a Benders decomposition approach using dedicated solution techniques for solving independent subproblems, Pareto-optimal cuts, cut bundling, and core point update. Computational results on real-world data from Canberra’s public transit system justify the design choices and show that the approach outperforms the MIP formulation by two orders of magnitude. Moreover, the results show that the hub and shuttle model may decrease transit time by a factor of two, while staying within the costs of the existing transit system.

In midterm planning, the objective of an electricity retailer is to manage a portfolio of different contracts and determine the selling price offered to its clients. Assuming that, within an electricity market framework, rival retailers compete for prices in order to achieve the largest possible number of clients. In addition, the reasonable criterion for the retailer is to select a solution that attains the minimum selling prices while satisfying the constraints. The proposed framework in this paper is modeled in the form of a multiobjective framework to simultaneously maximize retailers' profit and minimize selling prices to clients. The normal boundary intersection method is implemented to generate Pareto-optimal solutions. The best compromise solution is adopted using a fuzzy decision maker. Roulette wheel mechanism and lattice Monte Carlo simulation are employed for random scenario generation wherein the stochastic optimization problem is converted into its respective deterministic equivalents. Benders decomposition has been employed as a robust algorithm to reach the optimal solution. The efficiency of the presented method is verified by making a comparison of its performance with another multiobjective optimization method through a real case study to show its superiority.

Unrelated parallel machine scheduling problem with special controllable processing times and setups

An efficient yet accurate optimization algorithm for thermal systems integrating heat current method and generalized Benders decomposition

Cost minimization in allocation of reactive power sources

Loading margin calculation with line switching: A decomposition method

Two most important challenges for Independent System Operator (ISO) are system security and reliability in deregulated power system. Grid integrated Battery-Based Energy Storage Transportation (BEST) can be utilized by ISO to compensate these issues. BEST can act as load as well as source and needs to be modeled adequately in Security Constrained Unit Commitment (SCUC) formulation with adequate reserve constraint to gain the reliable performance. In this regard this paper proposes a SCUC scheduling with BEST considering N-1 contingency is performed in DC network security assessment. Due to consideration of network security constraints the proposed model is computational demanding and necessitates computational fast approach to optimize generation and vehicle routing problem (VRP) schedule. Therefore, proposed model is solved by Benders Decomposition (BD) method which reduces computational time. Modified IEEE 30-bus system is considered as numerical case study. In addition comparative analysis explores the impact of overall operational costs; transportation costs; and locational marginal price.

The future microgrids (MGs) hosting a great deal of uncertain and intermittent local renewable generations are envisioned to need for fast and flexible units in the generation side. Demand response, however, as a load shaping tool can alleviate the needs. This paper proposes a model to consider demand response potentials activated by time-varying prices in MG design studies. The model aims at maximizing MG owner’s profit while technical limits and constraints are adhered. The model also ensures that the designed MG is resilient against islanding events. To handle complexity of the model, Benders decomposition is used to decompose the model into a master problem and two types of sub-problems. The master problem optimizes binary variables indicating installing status of generating units and batteries. The first type of sub-problems optimizes continuous variables, and the second ensures the resilient operation of the MG against islanding events. In the model, the uncertainties associated with load and intermittent generation resources are captured via a scenario-based stochastic approach. The demand behavior in response to time-varying prices is modeled via price elasticity coefficients. The effectiveness of the proposed model is demonstrated through extensive numerical studies and sensitivity analyses.

Global optimization of an industrial natural gas production network

With the increasing proportion of wind power connected to grid, power system dispatching is facing more and more challenges from uncertainty. To cope with this uncertainty, robust optimization has been applied in unit commitment (UC) problem. In this paper, a multi‐band uncertainty set considering the temporal correlation (MBUSCTC) of wind/load prediction error is proposed firstly, which has two characteristics: (1) The MBUSCTC rigorously and realistically reflect the distribution characteristics of uncertainties in uncertainty intervals, thereby effectively reducing the conservatism of the traditional singe‐band uncertainty set; (2) the temporal correlation constraints of wind power/load prediction errors in MBUSCTC could limit the realization of uncertainties fluctuating frequently in uncertain intervals, thereby eliminating scenarios with lower probability in uncertainty sets. Then the proposed MBUSCTC is applied to UC problem, leading a robust UC model based on MBUSCTC, which is solved by Benders decomposition method and C&CG method. Finally, case studies based on the modified IEEE‐118 bus system and an actual power system of China demonstrate that the proposed method can effectively reduce the conservativeness of the robust UC model and ensure the robustness of the unit commitment solution.

Disruption management is a common and unavoidable problem in airline operations. As an effective recovery option, cruise speed control has been widely used in airline disruption management. However, when controlling cruise speeds in airline recovery problems, few studies explicitly consider slot capacity restriction, although it is quite critical in airline operations. To fill the research gap and capture the interdependence between aircraft rerouting and crew recovery, we develop a mathematical model to describe the integrated aircraft and crew recovery (IACR) with cruise speed control under slot capacity restriction. To evaluate the impact of the recovery plan on passenger itineraries, we also consider the cost related to disrupted passengers in the IACR. In order to reduce the solution difficulty caused by the nonlinear fuel burn function, nonlinear constraints, and logical constraints, we reformulate the proposed model as a conic quadratic mixed integer programming (CQMIP) problem. Based on the multi-stage characteristic of the CQMIP problem, we propose a Benders decomposition method to obtain high-quality solutions within reasonable runtime, whose effectiveness is validated by comparing the associated result with that by CPLEX. Furthermore, computational experiments show the necessity of considering slot capacity restriction and the benefit of controlling cruise speeds.

Robust optimisation has been applied to the dispatching problem considering fault outage of power systems. The traditional fault outage uncertainty set are too conservative. To solve this problem, a robust contingency constrained unit commitment (CCUC) model considering the outage probability of units and transmission lines is proposed. The proposed model has the following characteristics: (i) the outage probability of units is determined by normal operation time and fault repair time, whereas the outage probability of transmission lines is determined by length and load rate; (ii) based on the probability criterion of unit outage contingencies, the outage probabilities of units and transmission lines are both incorporated into the modelling of uncertainty sets; (iii) the robust CCUC model obtains UC decision of base case and the UC decision under uncertainty scenarios can adjust the output of units by spinning reserve capacity to cope with stochastic fault outage scenarios. The proposed robust CCUC model is solved with Benders‐column and constraint generation (C&CG) method combined with Benders decomposition method and C&CG method. Simulations on the modified IEEE‐RTS‐79 system and IEEE‐RTS‐96 system demonstrate the effectiveness and reliability of the proposed robust CCUC model.