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An essential challenge in generation scheduling (GS) problems of hydrothermal power systems is the inclusion of adequate modeling of the hydroelectric production function (HPF). The HPF is a nonlinear and nonconvex function that depends on the head and turbined outflow. Although the hydropower plants have multiple generating units (GUs), due to a series of complexities, the most attractive modeling practice is to represent one HPF per plant, i.e., a single function is built for representing the plant generation instead of the generation of each GU. Furthermore, due to the computation time constraints and representation of nonlinearities, the HPF must be given by a piecewise linear (PWL) model. This paper presented some continuous PWL models to include the HPF per plant in GS problems of hydrothermal systems. Depending on the type of application, the framework allows a choice between the concave PWL for HPF modeled with one or two variables and the nonconvex (more accurate) PWL for HPF dependent only on the turbined outflow. Basically, in both PWL models, offline, mixed-integer linear (or quadratic) programming techniques are used with an optimized pre-selection of the original HPF dataset obtained through the Ramer-Douglas-Peucker algorithm. As a highlight, the framework allows the control of the number of hyperplanes and, consequently, the number of variables and constraints of the PWL model. To this end, we offer two possibilities: (i) minimizing the error for a fixed number of hyperplanes, or (ii) minimizing the number of hyperplanes for a given error. We assessed the performance of the proposed framework using data from two large hydropower plants of the Brazilian system. The first has 3568 MW distributed in 50 Bulb-type GUs and operates as a run-of-river hydro plant. In turn, the second, which can vary the reservoir volume by up to 1000 hm3, possesses 1140 MW distributed in three Francis-type units. The results showed a variation from 0.040% to 1.583% in terms of mean absolute error and 0.306% to 6.356% regarding the maximum absolute error even with few approximations.

To achieve maximum profit by dispatching a battery storage system in an arbitrage operation, multiple factors must be considered. While revenue from the application is determined by the time variability of the electricity cost, the profit will be lowered by costs resulting from energy efficiency losses, as well as by battery degradation. In this paper, an optimal dispatch strategy is proposed for storage systems trading on energy arbitrage markets. The dispatch is based on a computationally-efficient implementation of a mixed-integer linear programming method, with a cost function that includes variable-energy conversion losses and a cycle-induced battery capacity fade. The parametrisation of these non-linear functions is backed by in-house laboratory tests. A detailed analysis of the proposed methods is given through case studies of different cost-inclusion scenarios, as well as battery investment-cost scenarios. An evaluation with a sample intraday market data set, collected throughout 2017 in Germany, offers a potential monthly revenue of up to 8762 EUR/MWh cap installed capacity, without accounting for the costs attributed to energy losses and battery degradation. While this is slightly above the revenue attainable in a reference application—namely, primary frequency regulation for the same sample month (7716 EUR/MWh cap installed capacity)—the situation changes if costs are considered: The optimisation reveals that losses in battery ageing and efficiency reduce the attainable profit by up to 36% for the most profitable arbitrage use case considered herein. The findings underline the significance of considering both ageing and efficiency in battery system dispatch optimisation.

We consider the problem of designing lightweight load-bearing frame structures with additive manufacturability constraints. Specifically, we focus on mathematical programming approaches to finding exact globally optimal solutions, given a pre-specified discrete ground structure and continuous design element dimensions. We take advantage of stiffness matrix decomposition techniques and expand on some of the existing modeling approaches, including exact mixed-integer nonlinear programming and its mixed-integer linear programming restrictions. We propose a (non-convex) quadratic formulation using semi-continuous variables, motivated by recent progress in state-of-the-art quadratic solvers, and demonstrate how some additive-specific restrictions can be incorporated into mathematical optimization. While we show with numerical experiments that the proposed methods significantly reduce the required solution time for finding global optima compared to other formulations, we also observe that even with these new techniques and advanced computational resources, discrete modeling of frame structures remains a tremendously challenging problem.

The growing demand for electricity and the reconstruction of poor areas in Africa require an effective and reliable energy supply system. The construction of reliable, clean, and inexpensive microgrids, whether isolated or connected to the main grid, has great importance in solving energy supply problems in remote desert areas. It is a complex interaction between the level of reliability, economical operation, and reduced emissions. This paper investigates the establishment of an efficient and cost-effective microgrid in a remote area located in the Djado Plateau, which lies in the Sahara Ténéré desert in northeastern Niger. Three cases are presented and compared to find the best one in terms of low costs. In case 1, the residential area is supplied by PVs and a battery energy storage system (BESS), while in the second case, PVs, a BESS, and a diesel generator (DG) are utilized to supply the load. In the third case, the grid will take on load-feeding responsibilities alongside PVs, a BESS, and a DG (used only in scenario 1 during the 2 h grid outage). The central objective is to lower the cost of the proposed microgrid. Among the three cases, case 3, scenario 2 has the lowest LCC, but implementing it is difficult because of the nature of the site. The results show that case 2 is the best in terms of total life cycle cost (LCC) and no grid dependency, as the annual total LCC reaches about $2,362,997. In this second case, the LCC is 11.19% lower compared to the first case and 5.664% lower compared to the third case, scenario 1.

Habitat fragmentation is a critical threat to biodiversity, as it creates isolated patches of habitat and hinders species movement and survival. Systematic conservation planning (SCP) has advanced to include landscape connectivity, often using graph‐based models to assess and enhance habitat networks. We introduce GECOT, an open‐source command line tool for solving budget‐constrained multispecies landscape connectivity optimization problems when measuring landscape connectivity with the probability of connectivity (PC) indicator. GECOT builds on a theoretical framework to model conservation and restoration planning as a connectivity optimization problem where options impact the quantity or quality of available habitat and the permeability of habitat and landscape matrix. For a given case study, GECOT can be used to find the optimal solution using a mixed‐integer linear solver or heuristic solutions with different sub‐optimal algorithms when the optimal solution is too expensive in computation time.

Purpose: Electronic devices consumption, especially smartphones for communication, have increased significantly, causing the potential for electronic waste to increase too. However, the high potential of this flow has not been matched by good waste management. This study aims to develop a management network for e-waste that collaborates formal and informal channels to provide optimal supply chain benefits in terms of economic and environmental aspectsDesign/methodology/approach: This research designs an e-waste management network followed by building a single-objective mathematical model that considers economic and environmental aspects. This model was solved using Mixed Integer Linear Programming.Findings: The supply chain will benefit from the proposed management network by collaborating formal and informal channels. With an incentive of 10,000 IDR, it is hoped that it will be able to invite consumers and informal collectors to collect waste informal channels. The total profit from managing electronic waste supply every month from Yogyakarta Province is 5.529 x 1010 IDR with the composition, consumers 81.2%, informal 13.3% channel obtained from informal collectors and repairing centers and 2.1% for formal channels, and there is an intangible profit of 3.4%. The formal channel provides more significant benefits than the informal, but requires a significant investment. This formal channel feasible if at least 33% of the total supply goes to this channel.Research limitations/implications: The model designed is deterministic. Therefore, it can be developed into a probabilistic model for further research to represent more real cases in the field.Practical implications: Regulation is the factor that most influences consumers' intentions and behavior to participate in e-waste management programs. It will be able to change consumer behavior by forcing consumers to participate in e-waste collection programs. Therefore, a government regulation is needed that organizes and supervises the implementation of the proposed management model.Social implications: Currently, the practice developing in the community is that the informal sector carries out smartphone waste management, therefore in the designs made, informal actors are still given space in waste management for the repair process and the secondhand market. Meanwhile, further processing, such as recycling, must be carried out through formal channels taking into account the environmental impact.Originality/value: Few studies have developed an electronic waste management model by collaborating informal and formal channels that consider economic and environmental aspects, and its implementation is organized and supervised by government regulations.

Purpose: Use mathematical models of Mixed Integer Linear Programming oriented to cellular distribution and aggregate production planning in order to obtain the appropriate product family for each manufacturing cell and from this, minimize production and material handling costs through the allocation of production resources.Design/methodology/approach: This article develops two mathematical models in LINGO 18.0 software, performing the computational calculation to obtain the best efficiency in cell formation at minimum production cost.Findings: The mathematical model oriented to the formation of manufacturing cells allows a grouping of products and machines with 82.5% group efficiency. By reallocating machines to each cell and redistributing facilities, the cost of material handling is reduced by 35.1%, and the distance traveled in product manufacturing is reduced by 26.6%. The mathematical model of aggregated planning provides information on production resource requirements such as personnel, machinery, distances traveled, as well as the cost generated by the need to outsource part of the production, inventory maintenance and overtime work.Research limitations/implications: It is necessary to clearly define the capacity variables. The model does not take into account the cost of mobilizing machines and readjusting facilities.Practical implications: The case study company can adequately plan production and efficiently manage its resources.Social implications: The study can be applied to other textile SMEs.Originality/value: The aggregate production planning model requires the assignment of the mathematical model of manufacturing cell formation in order to calculate the resource requirements needed to meet a demand.

Nonlinear characteristics of a battery energy storage system (BESS) may cause errors in the stored energy between the operation plan and the actual operation. These errors may hinder the reliability of the power system especially in environments such as microgrids with limited power generation resources and high uncertainty. This study proposes a method to alleviate the occurrence of such errors in the charging/discharging scheduling process of the BESS by piecewise linearizing its nonlinear characteristics. Specifically, the stored energy in a BESS that changes nonlinearly according to the size of the charging/discharging power was modeled using the special ordered set of the type 2 (SOS2) method. The proposed model and the typical BESS-operation models with constant power conditioning system (PCS) input/output power efficiency were applied to the unit commitment (UC) problem in a microgrid environment, and the results were compared with the actual operation results. The proposed model operated similarly to the actual operation compared to the typical model, reducing the error in charging/discharging energy. Consequently, the proposed model was made cost-effective by reducing the cost of error correction and reduced the risk of deviating from operating range of the BESS. This study demonstrates that the proposed method can efficiently solve the operational problems caused by the nonlinear characteristics of BESS.

This paper presents a novel framework architecture for an online, real-time flexibility assessment and activation platform targeted at unlocking the flexibility potential of commercial buildings and smaller industrial sites, thereby enabling greater levels of renewable grid integration. Renewable integration targets in Europe of up to 40% of power generation from renewable sources by 2030 and over 90% by 2050 aim to decarbonize the electrical grid and increase electrification of transport, industry, and buildings. As renewable integration targets increase, participation in flexibility programs will be required from a much greater range of buildings and sites to balance grids hosting high levels of renewable generation. In this paper, an online implementation of a standardized flexibility assessment methodology, previously developed for offline contract negotiations between stakeholders, is modified to automate the assessment. The automated assessment is then linked to an aggregator-based multi-building or site optimization stage, enabling increased participation of multiple buildings and sites. To implement the assessment, models for individual flexible systems were reviewed, selected, and adapted, including physics-based, data-driven, and grey-box models. A review of optimization for flexibility found mixed-integer linear programming to be the optimal approach for the selection of flexible systems for demand response events.

Purpose: Once a set of suppliers has been determined, according to criteria of quality, price and reliability, among others, there remains the problem of assigning orders to the selected suppliers, in order to cover the needs at the lowest cost. We consider the case in which the needs of a component for a set of plants should be covered by suppliers with linear piecewise concave cost functions, a lower bound on the order size for the non-zero deliveries and a capacity constraint. The purpose is to design procedures for solving this problem. Design/methodology/approach: With the aim of providing practical tools to solve the problem of assigning orders to suppliers with linear piecewise concave costs, two mixed integer linear programs are proposed. Findings: The two MILP models are compared through an extensive computational experiment. This shows that both models, with a slight advantage for one of them, can be solved within a very short time, even when the dimensions of the instance largely exceed those that can occur in real cases. Originality/value: The paper proposes novel models that can be used to solve the problem to optimality in reasonable times and with standard optimization software.