Short-Term Scheduling of Combined Cycle Units Using Mixed Integer Linear Programming Solution

Combined cycle plants (CCs) are broadly used all over the world. The inclusion of CCs into the optimal resource scheduling causes difficulties because they can be operated in different operating configuration modes based on the number of combustion and steam turbines. In this paper a model CCs based on a mixed integer linear programming approach to be included into an optimal short term resource optimization problem is presented. The proposed method allows modeling of CCs in different modes of operation taking into account the non convex operating costs for the different combined cycle mode of operation.

The Linear Formulation of Thermal Unit Commitment Problem with Uncertainties through a Computational Mixed Integer

The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with security due to the new challenges in power system supply. In solar and wind renewable energy, the only partially predictable is the output with very low controllability which creates unit commitment problems in thermal units. In this research paper, a different linear formulation via mixed integer is presented that only requires “binary variables” and restraints concerning earlier stated models. The framework of this model allows precisely the costs of time-dependent startup & intertemporal limitations, for example, minimum up & down times and a ramping limit. To solve the unit commitment problem efficiently, a commercially available linear programming of mixed-integer is applied for sizeable practical scale. The results of the simulation are shown in conclusions.

A mixed integer linear programming approach for municipal solid waste management

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Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

Detection of gross errors using mixed integer optimization approach in process industry

A novel mixed integer linear programming (NMILP) model for detection of gross errors is presented in this paper. Yamamura et al.(1988) designed a model for detection of gross errors and data reconciliation based on Akaike information cri- terion (AIC). But much computational cost is needed due to its combinational nature. A mixed integer linear programming (MILP) approach was performed to reduce the computational cost and enhance the robustness. But it loses the super performance of maximum likelihood estimation. To reduce the computational cost and have the merit of maximum likelihood estimation, the simultaneous data reconciliation method in an MILP framework is decomposed and replaced by an NMILP subproblem and a quadratic programming (QP) or a least squares estimation (LSE) subproblem. Simulation result of an industrial case shows the high efficiency of the method.

Integer Programming Formulations for Maximum Lifetime Broadcasting Problems in Wireless Sensor Networks

Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.

电力系统混合整数线性规划问题的运筹决策关键技术综述与展望

机组组合、检修计划、拓扑运行优化、电力系统规划等电力系统混合整数线性规划(MILP)问题旨在实现电力资源的最佳配置,应用广泛,其精准性与高效性直接影响了电力系统的安全性与经济性。随着“双碳”目标的提出,新型电力系统MILP问题模型复杂度更高、计算效率要求更严格,对当前运筹决策技术提出了更严峻的挑战。然而,现有依赖于国外进口求解器的电力系统运筹决策技术面临“组合爆炸”,且求解器依赖进口面临“卡脖子”困境,亟须实现技术突破。为此,该文系统地梳理了电力系统MILP问题的运筹决策技术,以及近年来通用MILP问题的最新进展,并展望了电力系统MILP问题运筹决策关键技术未来的研究方向,旨在为我国相关研究工作提供参考和思路。

考虑节点度紧致化的最优主动解列模型

为解决主动解列模型的连通性和解列模型趋于复杂化导致计算效率下降的问题,本文提出了考虑节点度紧致化的主动解列模型。首先基于单商品流的思想,提出保证孤岛连通性的解析约束;再结合主动解列自身特点和复杂网络中度的概念,提出一种模型紧致化方法以压缩混合整数规划模型的可行域;最后以切负荷与最小潮流中断之和最小为目标求取最优的解列断面。所提模型能保证孤岛内的连通性并且能够较快地求解大型系统的解列问题。3个测试系统的仿真实验表明了该模型的有效性和快速性。

分支定界搜索信息深度引导的电-气互联系统调度决策加速求解方法

电-气互联系统调度决策问题旨在实现天然气系统和电力系统中可调节资源的最佳配置,其精准性与高效性直接影响电-气互联系统运行的安全性与经济性。为描述可调节资源离散状态、非线性运行特性等物理性质,电-气互联系统调度决策问题中含有规模庞大的离散决策变量,模型复杂度高,使得现有依赖于商业混合整数线性规划(MILP)求解器的电力系统运筹优化技术面临“组合爆炸”的计算负担。为此,该文提出一种分支定界搜索信息深度引导的电-气互联系统调度决策加速求解方法。所提方法利用分支定界初始搜索阶段的信息构建小规模辅助MILP模型,并内嵌于分支定界搜索过程,引导剪除更多冗余搜索空间,在不损失最优性的前提下加速收敛。基于RTS-GMLC电力系统和天然气系统不同负荷水平及线性分段数下的30个算例仿真结果说明,相比于直接使用商业MILP求解器,所提方法在不损失最优性的前提下可实现平均4.20倍的加速,验证了所提方法的有效性。

融合原子交换特征信息的代谢路径预测

为获取从任意起始代谢物到目标代谢物的生化相关性较好的代谢路径,提出一种融合原子交换特征信息的基于约束的代谢路径预测算法PVA。结合代谢网络中具有的原子交换特征信息,建立一种基于约束的混合整数线性规划(MILP)代谢路径预测模型,以搜索从任意起始代谢物到目标代谢物并包含特定原子交换信息的代谢路径。实验结果表明,与同类方法相比,PVA能够有效地发现生化相关性更好的代谢路径。

考虑梯级水电融合抽蓄改造的风光资源多目标容量配置

为实现梯级水风光蓄联合发电系统高效多能互补,研究考虑梯级水电融合抽蓄改造的风光发电多目标容量优化配置方法。以联合发电系统外送通道利用率最大和受端电网剩余负荷峰谷差最小为目标,优化联合发电系统风电和光伏发电的配置容量;考虑风电和光伏发电季节性波动,基于K-means聚类构建风电和光伏发电出力的典型场景,提出了梯级水风光蓄全场景互补运行模型,并发展了便于快速求解的混合整数线性化模型。以小金川梯级小水电周边的风电场与光伏电站为例,对所提方法的有效性进行了验证,分析了梯级水风光蓄联合系统的互补性,对比说明了混合式抽蓄在联合发电系统中的作用。

基于混合整数规划的数据中心冷却能耗优化

以广州某数据中心水蓄冷冷却系统为研究对象,提出了一种基于混合整数线性规划的模型预测控制方法.该方法以数据中心冷却系统的能耗最低为优化目标,通过对冷却系统和环境条件进行建模,并结合能源成本和冷却系统效率,确定最佳的冷水机组运行策略和水蓄冷冷却系统的时序控制.在优化过程中,考虑了冷水机组的最小连续运行时间对冷却系统能耗的影响,并确定了最佳取值,提高了机组的稳定性,减少了因冷机频繁启停带来的能耗浪费.通过全年能耗模拟,相较于传统控制方法,该方法将总能耗降低了6.52%,总运行费用降低了6.93%.

Optimal configuration of distributed power flow controller to enhance system loadability via mixed integer linear programming

The increase of energy consumption has caused power systems to operate close to the limit of their capacity.The distributed power flow controller(DPFC),as a new member of distributed flexible AC transmission systems,is introduced to remove this barrier.This paper proposes an optimal DPFC configuration method to enhance system loadability considering economic performance based on mixed integer linear programming.The conflicting behavior of system loadability and DPFC investment is analyzed and optimal solutions are calculated.Thereafter,the fuzzy decision-making method is implemented for determining the most preferred solution.In the most preferred solution obtained,the investment of DPFCs is minimized to find the optimal number,locations and set points.Simulation results on the IEEERTS79 system demonstrate that the proposed method is effective and reasonable.

A Green Mixed Integer Linear Programming Model for Optimization of Byproduct Gases in Iron and Steel Industry

Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to construct an integrated optimized system, taking economics, energy consumption and environment into consideration. Therefore, the environmental cost caused by pollutants discharge should be factored in total cost when optimizing byproduct gas distribution. A green mixed integer linear programming （MILP） model for the optimization of byproduct gases was established to reduce total cost, including both operation cost and environmental cost. The operation cost included penalty for gas deviation, costs of fuel and water consumption, holder booster trip penalty, and so forth; while the environmental cost consisted of penalties for both direct and indirect pollutants discharge. Case study showed that the proposed model brought an optimum solution and 2.2% of the total cost could be reduced compared with previous one.

Multi-objective optimization for electric water heater using mixed integer linear programming

Due to the capacity of thermal storage,electric water heater(EWH)is one of the best candidates for demand response programs.However,few attentions are given to the modeling and optimization of EWHs with thermostatically-controlled automatic water mixer(TCAWM).In this paper,differential thermodynamic model is established for EWHs with TCAWM and a piecewise linear approximation method is performed for the nonlinear thermodynamic model.The multi-objective optimization model is established by introducing an index reflecting the comfort degree of users,so that the optimal energy usage of the EWH can be obtained by mixed integer linear programming.Testing examples verify the effectiveness of the proposed method.

含循环换电负荷及充电站的微电网多目标优化调度

电动换电重卡由于具有充电功率高、周期性强的循环换电负荷特性,一旦短时大量接入微电网中,将带来经济性和安全性的挑战。首先讨论电动汽车充电、循环换电负荷的不同特性,建立含循环换电负荷及充电站的微电网模型;提出一种综合考虑微电网经济性及联络线功率波动性的多目标调度优化方法;采用线性加权方法将多目标问题转化为单目标问题;最后利用CPLEX工具对仿真算例进行求解,仿真算例表明,所提优化方案可有效求解综合考虑不同权重下微电网净利润、联络线交换功率及换电站内电池最优调度问题,能在尽可能减小微电网与上级电网交换功率波动性的同时,使得微电网获得最大净利润。

基于CSA-AFSA算法的集装箱港口连续型泊位分配优化

为提升集装箱港口运营效率,笔者研究了考虑潮汐因素与泊位偏好的连续型泊位分配问题。引入了船舶时空矩形不可重叠约束和潮汐时间窗约束,构建以最小化船舶等待、延迟离港、泊位偏离以及在港期间油耗费用和最小为目标的混合整数线性规划模型;根据模型特征,采用CPLEX求解软件、鱼群算法、布谷鸟搜索算法和布谷鸟鱼群混合算法进行求解,以计划周期为36 h的20个不同规模的船舶到港数据为研究算例,通过算例求解得到符和潮汐时间窗、泊位偏好等要求的泊位分配方案。算例求解表明:算例规模较小时,CPLEX可以在较短时间内求出最优泊位分配方案;算例规模较大时,CPLEX求解时间较长,布谷鸟鱼群混合算法可以在平均3 min内求出与CPLEX差距为0.39%~4.20%的次优解;不同算法间的对比表明,布谷鸟鱼群混合算法求解能力更优,混合算法所得泊位分配方案中,乘潮船舶的进出港时刻均在潮汐高水位时段,且85%以上的船舶在偏好泊靠点200 m内接受装卸服务。

考虑需求响应和风电不确定性的电网调度

风电不确定性对电力系统的影响日益增加,文中提出一种考虑需求响应的电网源荷网经济调度方法。根据需求价格弹性理论和消费者心理学原理构建价格型需求响应模型,基于灵活补偿激励型需求响应充分考虑两类需求响应互补特性,增加两类需求响应对系统的备用约束。引入通用概率分布描述风电出力特性,以期望成本量化风电不确定性惩罚成本,并将目标函数中的非线性变量线性化处理,采用混合整数线性规划问题对模型进行求解。仿真结果表明,所提模型能够有效降低负荷的峰谷差,提高风电的消纳能力。

含分布式新能源和需求响应负荷的虚拟电厂定价机制及优化调度

面对电网中分布式风电、光伏发电以及柔性负荷的广泛接入,将这些资源通过虚拟电厂(VPP)进行聚合,采用合理的电价机制来引导用户参与需求响应,可以有效提升新能源的消纳能力并降低整体运营成本。传统的分时电价机制往往难以实现需求响应负荷与新能源出力的良好匹配,可能会导致需求响应的不合理或过度反应。为此,针对包括分布式风电、分布式光伏发电和柔性负荷的VPP,提出了一种基于新能源出力的VPP内部定价机制,并设置电力交易优先级来引导VPP内部各资源优化运行,以VPP的整体运营成本最小化为目标,构建了一个VPP优化调度的混合整数线性规划模型。基于内蒙古某地区的实际数据进行仿真计算,结果表明,与基于传统分时电价的优化结果相比,该方法能显著提高新能源的利用率并降低VPP的运行费用。

A mixed-integer linear programming approach for robust state estimation

In this paper,a mixed integer linear programming(MILP)formulation for robust state estimation(RSE)is proposed.By using the exactly linearized measurement equations instead of the original nonlinear ones,the existingmixed integer nonlinear programming formulation for RSE is converted to a MILP problem.The proposed approach not only guarantees to find the global optimum,but also does not have convergence problems.Simulation results on a rudimentary 3-bus system and several IEEE standard test systems fully illustrate that the proposed methodology is effective with high efficiency.