Incorporating microgrids coupling with utilization of flexible switching to enhance self-healing ability of electric distribution systems

Electric distribution networks have to deal with issues caused by natural disasters. These problems possess unique characteristics, and their severity can make load restoration methods impotent. One solution that can help in alleviating the aftermath is the use of microgrids (MGs). Employing the cumulative capacity of the generation resources through MG coupling facilitates the self-healing capability and leads to better-coordinated energy management during the restoration period, while the switching capability of the system should also be considered. In this paper, to form and schedule dynamic MGs in distribution systems, a novel model based on mixed-integer linear programming (MILP) is proposed. This approach employs graph-related theories to formulate the optimal formation of the networked MGs and management of their proper participation in the load recovery process. In addition, the Benders decomposition technique is applied to alleviate computability issues of the optimization problem. The validity and applicability of the proposed model are evaluated by several simulation studies.     

The constrained two-dimensional guillotine cutting problem with defects: an ILP formulation,a Benders decomposition and a CP-based algorithm

This paper addresses a variant of two-dimensional cutting problems in which rectangular small pieces are obtained by cutting a rectangular object through guillotine cuts. The characteristics of this variant are (i) the object contains some defects, and the items cut must be defective-free; (ii) there is an upper bound on the number of times an item type may appear in the cutting pattern; (iii) the number of guillotine stages is not restricted. This problem commonly arises in industrial settings that deal with defective materials, e.g. either by intrinsic characteristics of the object as in the cutting of wooden boards with knotholes in the wood industry, or by the manufacturing process as in the production of flat glass in the glass industry. We propose a compact integer linear programming (ILP) model for this problem based on the discretisation of the defective object. As solution methods for the problem, we develop a Benders decomposition algorithm and a constraint-programming (CP) based algorithm. We evaluate these approaches through computational experiments, using benchmark instances from the literature. The results show that the methods are effective on different types of instances and can find optimal solutions even for instances with dimensions close to real-size.     

Optimization of a multiperiod refinery planning problem under uncertainty

Uncertainty in refinery planning presents a significant challenge in determining the day-to-day operations of an oil refinery. Deterministic modeling techniques often fail to account for this uncertainty, potentially resulting in reduced profit. The stochastic programming framework explicitly incorporates parameter uncertainty in the problem formulation, thus giving preference to robust solutions. In this work, a nonlinear, multiperiod, industrial refinery problem is extended to a two-stage stochastic problem, formulated as a mixed-integer nonlinear program. A crude-oil sequencing case study is developed with binary scheduling decisions in both stages of the stochastic programming problem. Solution via a decomposition strategy based on the generalized Benders decomposition (GBD) algorithm is proposed. The binary decisions are designated as complicating variables that, when fixed, reduce the full-space problem to a series of independent scenario subproblems. Through the application of the GBD algorithm, a feasible mixed-integer solution is obtained that is more robust to uncertainty than its deterministic counterpart.     

考虑动态频率约束的含高渗透率光伏电源的孤立电网机组组合

孤立电网具有低惯性及一次调频能力弱的特点,高渗透光伏接入孤立电网后会进一步降低孤立电网惯性及其调频能力。为了保障系统有充足的频率响应能力,本文在UC中考虑动态频率约束,并且通过光伏电源减出力参与调频来增强系统的调频能力。推导考虑光伏电源调频情况下,系统发生故障时最大频降、最大频降出现时间的表达式。基于此,推导了光伏的最小调频容量表达式,用以限制UC在优化过程留有充足但不过量的光伏电源调频容量。根据以上推导建立考虑动态频率约束的含高渗透率光伏电源的孤立电网UC优化模型。针对所提的混合整数非线性优化模型,采用产生Benders割以及优化割的方法来降低问题的求解复杂度。最后采用含高渗透率光伏电源的孤立电网算例进行测试,结果表明所提模型能够兼具安全性和经济性,测试过程也表明了所提求解方法的有效性及优越性。     

考虑柔性交流输电系统设备控制的校正型安全约束最优潮流

为提升安全约束最优潮流调度的经济性与安全性,提出一种基于直流潮流的考虑柔性交流输电系统(FACTS)设备控制的校正型安全约束最优潮流模型。在线路故障发生后,通过FACTS设备校正措施,将线路潮流控制在其容许范围内。由于所提模型为大规模的非凸、非线性优化问题,难以直接求解,因此先采用大M法,将原非线性优化模型转换为混合整数线性规化模型,并采用Benders分解算法将转换后的模型分解为基态最优潮流主问题与N-1故障校验子问题。通过固定整数变量的方法,将非凸的混合整数优化子问题转换为线性规划子问题,从而能向主问题返回对应的Benders割。6节点系统与IEEE RTS-79节点系统算例验证了所提模型与算法的有效性。结果表明,考虑FACTS设备校正控制的安全约束最优潮流能有效提升调度运行的经济性。     

Computational strategies for improved MINLP algorithms

In order to improve the efficiency for solving MINLP problems, we present in this paper three computational strategies. These include multiple-generation cuts, hybrid methods and partial surrogate cuts for the Outer Approximation and Generalized Benders Decomposition. The properties and convergence of the strategies are analyzed. Based on the proposed strategies, five new MINLP algorithms are developed, and their implementation is discussed. Results of numerical experiments for benchmark MINLP problems are reported to demonstrate the efficiency of the proposed methods.     

Domain reduction for Benders decomposition based global optimization

While domain reduction has been successfully applied in branch-and-bound based global optimization over the last two decades, it has not been systematically studied for decomposition based global optimization, which is usually more efficient for problems with decomposable structures. This paper discusses integration of domain reduction in Benders decomposition based global optimization, specifically, generalized Benders decomposition (GBD) and nonconvex generalized Benders decomposition (NGBD). Revised GBD and NGBD frameworks are proposed to incorporate bound contraction operations or/and range reduction calculations, which can reduce the variable bounds and therefore improve the convergence rate and expedite the solution of nonconvex subproblems. Novel customized bound contraction problems are proposed for GBD and NGBD, and they are easier to solve than the classical bound contraction problems because they are defined on reduced variable spaces. The benefits of the proposed methods are demonstrated through a gas production operation problem and a power distribution system design problem.     

具有安全约束的发电机组组合可行的充分必要条件

在拉格朗日松弛框架下,具有安全约束的发电机组组合问题的求解可以分为 2 个步骤:一是通过求解问题的对偶,以获得原问题近似可行、甚至近优的机组状态,再通过启发式方法或者通过求解一个整数规划问题,调整某些机组的状态,从而获得一个可行的、近优的机组组合状态;二是求解各个调度时段上处于开机状态机组的发电功率,使发电成本最小化.因此,判断某时段机组组合状态是否可行显得尤为重要.为此,利用Benders分解可行性定理,给出并证明了安全约束机组组合可行的充分必要条件以及数值计算方法.结合某电力系统测试算例,验证了相关理论和算法的有效性.     

Multiple allocation hub-and-spoke network design under hub congestion

The multiple allocation hub-and-spoke network design under hub congestion problem is addressed in this paper. A non-linear mixed integer programming formulation is proposed, modeling the congestion as a convex cost function. A generalized Benders decomposition algorithm has been deployed and has successfully solved standard data set instances up to 81 nodes. The proposed algorithm has also outperformed a commercial leading edge non-linear integer programming package. The main contribution of this work is to establish a compromise between the transportation cost savings induced by the economies of scale exploitation and the costs associated with the congestion effects.     

A bi-level probabilistic transmission planning with intermittent generations based on life cycle cost

With the growing development of intermittent renewable energy sources, such as wind and solar, transmission planners are faced with uncertainly varying generations and resultant probabilistic power flow. A bi-level programming model is proposed to coordinate the process of decision making and reliability assessment. Based on the concept of life cycle cost (LCC), its minimization can be defined as the objective function of a transmission planner. This upper level problem needs to be solved jointly with the lower probabilistic optimal power flow problem of minimizing the load shedding in the system. Hence the bi-level problem is transformed into a Mathematical Programming with Equilibrium Constraints (MPEC) with Karush-Kuhn-Tucker conditions. Due to the nonlinearity nature of MPEC, disjunctive inequalities and Generalized Benders Decomposition methods are used to solve this problem. Results of both Garver’s 6-bus test system and a realistic 63-bus system are used to illustrate the rationality and validity of the proposed method.