Optimal Operation of Unbalanced Three-Phase Islanded Droop-Based Microgrids

Reformulation, linearization, and a hybrid iterated local search algorithm for economic lot-sizing and sequencing in hybrid flow shop problems

This study deals with an aircraft-to-target assignment (ATA) problem considering the modern air operation environment, such as the strike package concept, multiple targets for a sortie, and the strike packages’ survivability. For the ATA problem, this study introduces a novel mathematical model in which a heterogeneous vehicle routing problem (HVRP) and a weapon-to-target assignment (WTA) problem are conceptually integrated. The HVRP generates the flight routes for strike packages because this study confirms that the survivability of a strike package depends on the path, and the WTA problem evaluates the likelihood of successful target destruction of assigned weapons. Although the first version of the model is developed as a mixed-integer nonlinear programming (MINLP) model, this study attempts to convert it to a mixed-integer linear programming (MILP) model using the logarithmic transformation and piecewise linear approximation methods. For an ATA problem, this activity could provide an opportunity to use the excellent existing algorithms for searching the optimal solution of LP models. To maximize the operational effectiveness, the MILP model simultaneously determines the following for each strike package: (a) composition type, (b) targets, (c) flight route, (d) types, and (e) quantity of weapons for each target.

Optimal Antibody Purification Strategies Using Data-Driven Models

Microgrids have become valuable assets because they improve the reliability of consumers while integrating renewables via distributed energy resources (DERs). Thus, making them cost-efficient is essential to secure their proliferation. This paper proposes a new method for the optimal design of microgrids. The proposed two-stage method optimizes the size and the location of the DERs, i.e., the renewable energy sources (RESs), distributed generation (DG) units, and battery energy storage systems (BESSs). Furthermore, the overall operation of the microgrid is optimized using a stochastic scenario-based approach, considering grid-connected and unintentional islanded modes. The proposed method also considers internal network reinforcements. Thus, the first stage is an energy-based approach, formulated as a mixed-integer linear programming (MILP) problem, and it is used to size the DERs, whereas the second stage uses an optimal AC power flow (AC-OPF) to formulate a mixed-integer nonlinear programming (MINLP) model that allocates the DERs and selects the best conductor for each circuit. The multi-objective nature of the problem is addressed via Pareto optimization to analyze the trade-off between operational and capital costs. The MINLP model is linearized through piece-wise approximations and solved using commercial solvers. Furthermore, the impact of battery degradation is analyzed through a simple adaptation of the Stage 1 model. Results were obtained with data from the real university campus microgrid CampusGrid, located at the State University of Campinas (UNICAMP), in São Paulo, Brazil.

Energy transmission in cooling/heating and gas pipelines has time-delay, which impacts the power balance between various sources and loads in the optimal dispatch of an integrated energy campus microgrid (IECM). This article proposed an optimal dispatch model for IECMs, which considered the time-delay of energy transmission in cooling/heating and gas pipelines. In this model, the electricity and natural gas purchase cost of the IECM was made into an objective function. Partial differential equations (PDEs) were used to describe the time-delay in pipelines, and the discrete variables that described the switching number of absorption chillers and heat exchange units were included in the constraints. The proposed model was essentially a mixed-integer nonlinear programming (MINLP) model with PDE constraints. Orthogonal collocation on finite elements (OCFE) in the two-dimensional domain was used to transform PDEs into algebraic equations (AEs). Several linearization methods, including piecewise linearization and the big M method, were used to transform the initial MINLP model into a mixed-integer linear programming (MILP) model to reduce computational complexity. OCFE was compared with the first-order finite difference method, and simulation results were used to demonstrate the accuracy and efficiency of the proposed algorithm. The impact of the time-delay of pipelines on IECM was analyzed through comparison with a steady-state model.

A new, R-graph based, superstructure and corresponding MINLP model for designing conventional distillation columns are presented. A GDP representation (GR) of the superstructure is first constructed, then it is transformed to MINLP representation to which, in turn, additional trivial improvements are added. The new model has been tested on binary mixture examples, and the obtained results are compared to the results of an MINLP model which developed according to the GDP model of Yeomans and Grossmann. 9 The new model yields shorter computation time and provides better local optima. Additionally, the new model has been used for optimizing a complex multicomponent separation system consisting of several distillation columns. In order to handle such a complex system with a huge number of nonlinear equations, the outer approximation algorithm is modified to provide good initial values for the NLP subproblems. Distillation is one of the most widespread processes applied for separating multicomponent liquid mixtures. It is used for working up large volume or stream, and it requires high investment and operation outlays. The significance of the design of economically optimal distillation processes is of no question. Enormous interest has also been addressed to the area of designing optimal heat integrated distillation columns and distillation sequences. Minimizing the cost of a distillation process implies finding the optimal configuration of each individual column, as well. In the present article we consider staged column models only. The number of stages, and the stage numbers of the feed and side-stream points, are discrete decision variables. The total cost of a column may be modeled as the sum of the fix (capital) cost, depending on the number of stages and on the column diameter, and the variable (operation) cost related to the utility consumption. The objective of the design procedure is to find the optimal configuration of the column, which has the minimum total (annualized) cost. In order to model these processes, discrete decisions are required for calculating the number of stages. Optimizing single columns is a well-known procedure; all the basic textbooks outline how to do it in an easy manner. 1 After approximately determining the minimum and the estimated optimal number of theoretical stages, optimizing over the continuous variables is performed at varied values of the discrete variables. This is a 2-dimension discrete array of continuous optimization tasks in the case of a single-feed, two-product column, because there are merely two column sections in this case. This task becomes much more difficult if several feeds and side-products are to be taken into account. The real problem, however, is synthesizing a distillation sequence, or a system of advanced distillation columns, or a complex flowsheet containing distillation units when the number of distillation columns and their connections are not known in advance. In order to solve the complex synthesis problem outlined above, a proper superstructure for a single column, together with a proper generalized disjunctive programming (GDP) model or a proper mixed-integer nonlinear programming (MINLP) model, is a minimum requirement. Once such a model works well for a single column, the problem of more complex flowsheets may also be addressed. Mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) are the two exact methodologies commonly applied for solving process engineering problems with discrete decisions. The former includes algebraic equations describing the process, and binary variables related to discrete decisions. The latter method uses logic variables and expressions to represent the problem. 2 Both formulations have been successfully applied to rigorous models of distillation columns. Both methods apply a fixed maximum number of stages, and the actually used stages are selected from this set. Mathematical formulations that represent rigorous models of distillation column configurations fall into two categories: (i) one task-one equipment (OTOE) representations and (ii) variable task-equipment (VTE) representations. 3

An optimal stochastic energy management system for resilient microgrids

Optimal controlled-islanding with AC power flow constraints: A benders-decomposition approach

New approach for scheduling crude oil operations

A Combined Central and Local Voltage Control Strategy of Soft Open Points in Active Distribution Networks

Integration of sale and leaseback in the optimal design of supply chain networks

A master–slave solving method with adaptive model reformulation technique for water network synthesis using MINLP

Disasters pose a serious threat to people’ lives and urban environment, affecting the sustainable development of society. Then it's crucial to quickly develop an efficient rescue plan for the disaster area. However, disaster rescue is rather difficult due to the requirement to develop the optimal rescue plan as quickly as possible according to the information of trapped people and rescue teams, and the amount of information will continue to increase as the rescue proceeds. At present, most of the rescue plans are manually made based on previous rescue experience. But obviously these plans might be the not optimal one. Considering the real-time location data of trapped people, this paper develops a Mixed Integer Non-linear Programming (MINLP) model to find the highest efficient rescue plan To solve the model accurately and efficiently, a bi-level decomposition (BLD) algorithm is presented to iteratively solve a discretized Mixed Integer Linear Programming (MILP) model and its nonconvex Non-linear Programming (NLP) model until a converged solution is obtained. In addition, since more trapped people could be found over time, the built rescue units should also be considered when making a rescue plan for a new stage. To further improve the solving efficiency, an accelerated bi-level decomposition (ABLD) algorithm is also proposed. Finally, a real-world disaster rescue is given to validate the superiority of the proposed ABLD algorithm relative to particle swarm optimization (PSO) algorithm and BLD algorithm.

The Design and Synthesis of Batch/Semicontinuous Processes

In this paper, we develop a mathematical model of a technician routeing and scheduling problem with time windows (TRSPTW) and overnight shifts, which we title the ‘overnight TRSPTW’. This problem is motivated by a real application in the telecommunications industry in Saskatchewan, Canada. A mixed-integer nonlinear programming (MINLP) model is employed to achieve two key objectives: (1) minimising the total costs associated with technicians and subcontractors, including travel costs, accommodation costs and penalty costs caused by late starts and (2) minimising imbalanced workloads. Furthermore, the present work aims to determine the daily assignment of technicians to communities, depots and routes; find a high-quality schedule for technicians’ start times in communities and lunch breaks and determine the daily assignment of tasks to the subcontractor. The bi-objective MINLP model used to solve the overnight TRSPTW is a typical NP-hard problem in combinatorial optimisation. As such, we introduce a new hybrid category of TRSPTW that combines centroid-based clustering, which is an unsupervised machine learning (ML) approach, with a bi-objective zebra optimisation algorithm (BOZOA). The resultant algorithm blends the advantages of the ZOA and ML to strike a balance between the exploration and exploitation of the solution region. Finally, we compare our results with those obtained using an exact solver for small-, medium-, and large-sized instances. The performance evaluation and validation results revealed that the proposed ML-based BOZOA provides very good performance in solving TRSPTWs at a variety of scales with respect to the optimality criteria, including, number of taken iterations, infeasibility, optimality error and complementarity compared with both an exact solver and two inspired algorithms from ZOA. Highlights An ML-based bi-objective zebra optimisation algorithm to treat large-scale TRSPs Centroid-based clustering on the population of zebras to avoid bias towards a specific search space Making a trade-off between exploration and exploitation of the feasible region in the developed algorithm A new MINLP model of a weighted bi-objective TRSP with limited capacity depots Workload function, penalty function for lateness, subcontracts, time windows for tasks and breaks Experiments using real data to show the performance of the model and solution method