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Progressive hedging for stochastic energy management systems The mixed-integer linear case

ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2021年第1期12卷 1-29页

作者： Kaisermayer, Valentin Muschick, Daniel Horn, Martin Goelles, Markus BEST Bioenergy & Sustainable Technol GmbH Inffeldgasse 21-B A-8010 Graz Austria Graz Univ Technol Inst Automat & Control Inffeldgasse 21-B A-8010 Graz Austria

Energy systems have increased in complexity in the past years due to the ever-increasing integration of intermittent renewable energy sources such as solar thermal or wind power. Modern energy systems comprise different energy domains such as electrical power, heating and cooling which renders their control even more challenging. Employing supervisory controllers, so-called energy management systems (EMSs), can help to handle this complexity and to ensure the energy-efficient and cost-efficient operation of the energy system. One promising approach are optimization-based EMS, which can for example be modelled as stochastic mixed-integer linear programmes (SMILP). Depending on the problem size and control horizon, obtaining solutions for these in real-time is a difficult task. The progressive hedging (PH) algorithm is a practical way for splitting a large problem into smaller sub problems and solving them iteratively, thus possibly reducing the solving time considerably. The idea of the PH algorithm is to aggregate the solutions of subproblems, where artificial costs have been added. These added costs enforce that the aggregated solutions become non-anticipative and are updated in every iteration of the algorithm. The algorithm is relatively simple to implement in practice, re-using almost all of a possibly existing deterministic implementations and can be easily parallelized. Although it has no convergence guarantees in the mixed-integer linear case, it can nevertheless be used as a good heuristic for SMILPs. Recent theoretical results shown that for applying augmented Lagrangian functions in the context of mixed-integer programmes, any norm proofs to be a valid penalty function. This is not true for squared norms, like the squared L-2-norm that is used in the classical progressive hedging algorithm. Building on these theoretical results, the use of the L-1 and L-infinity-norm in the PH algorithm is investigated in this paper. In order to incorporate these into the

关键词： Energy management system Stochastic programming Progressive hedging mixed-integer linear programming

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Stochastic programming approach for optimal day-ahead market bidding curves of a microgrid

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APPLIED ENERGY 2023年 336卷

作者： Herding, Robert Ross, Emma Jones, Wayne R. Charitopoulos, Vassilis M. Papageorgiou, Lazaros G. UCL Univ Coll London Sargent Ctr Proc Syst Engn Dept Chem Engn Torrington Pl London WC1E 7JE England Global Solut Int BV NL-1031 HW Amsterdam Netherlands Shell plc Shell Ctr London SE1 7NA England

The deregulation of electricity markets has driven the need to optimise market bidding strategies, e.g. when and how much electricity to buy or sell, in order to gain an economic advantage in a competitive market environment. The present work aims to determine optimal day-ahead market bidding curves for a microgrid comprised of a battery, power generator, photovoltaic (PV) system and an electricity load from a commercial building. Existing day-ahead market bidding models heuristically fix price values for each allowed bidding curve point prior to the optimisation problem or relax limitations set by market rules on the number of price-quantity points per curve. In contrast, this work integrates the optimal selection of prices for the construction of day-ahead market bidding curves into the optimisation of the energy system schedule;aiming to further enhance the bidding curve accuracy while remaining feasible under present market rules. The examined optimisation problem is formulated as a mixed integer linear programming (MILP) model, embedded in a two-stage stochastic programming approach. Uncertainty is considered in the electricity price and the PV power. First stage decisions are day-ahead market bidding curves, while the overall objective is to minimise the expected operational cost of the microgrid. The bidding strategy derived is then examined through Monte Carlo simulations by comparing it against a deterministic approach and two alternative stochastic bidding approaches from literature.

关键词： mixed-integer linear programming Stochastic programming Optimisation under uncertainty Microgrid Bidding curve Day-ahead market

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Unsupervised parallel machines scheduling with tool switches

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COMPUTERS & OPERATIONS RESEARCH 2023年第1期160卷

作者： Dang, Quang-Vinh Herps, Koen Martagan, Tugce Adan, Ivo Heinrich, Jasper Eindhoven Univ Technol Dept Ind Engn & Innovat Sci POB 513 NL-5600 MB Eindhoven Netherlands KMWE Precis BIC 1POB 7930 NL-5605 SH Eindhoven Netherlands

This paper addresses the problem of scheduling jobs on identical parallel machines with tool switches in a high-mix, low-volume manufacturing environment. Inspired by the initiatives on "lights-out factory"at our industry partner, our problem setting involves several complex features. For example, we consider unsupervised production hours (e.g., night shifts where operators are not available) in which tool switches cannot occur. Moreover, motivated by current practice, tool switches in our problem setting cause costs instead of delays. Also, a subset of jobs is prioritized to be completed within a scheduling horizon, and a job may consist of ordered operations due to reentry to machines. The objective is to maximize the profit generated by the manufacturing system, which is composed of revenue generated by the finished operations minus tool switching costs and penalty costs of unfinished priority jobs. The decisions involve assigning operations to machines, sequencing these operations, and determining a tool-switching plan. A mix-integer linear programming model is first formulated. We then propose a genetic algorithm to solve industry-size problem instances, in which tailored crossover and mutation mechanisms are introduced. We illustrate the performance of the proposed GA with industry case studies using real-world data. We also make the anonymized data set publicly available. Computational experiments reveal that approximately 26% profit improvement can be achieved by using the proposed GA instead of the current way of scheduling at our industry partner. Moreover, we find that the proposed GA brings higher benefits when the duration of the unsupervised shifts gets longer, and there is high pressure on prioritizing jobs in the schedule.

关键词： Scheduling Tool switches Unsupervised production Genetic algorithm mixed-integer linear programming

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Comparative Analysis and Optimal Operation of an On-Grid and Off-Grid Solar Photovoltaic-Based Electric Vehicle Charging Station

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ENERGIES 2023年第24期16卷 8086页

作者： Dukpa, Andu Butrylo, Boguslaw Venkatesh, Bala Univ New Brunswick Fac Engn 15 Dineen Dr Fredericton NB E3B 5A3 Canada Bialystok Tech Univ Fac Elect Engn Ul Wiejska 45D PL-15351 Bialystok Poland Toronto Metropolitan Univ Dept Elect Comp & Biomed Engn 350 Victoria St Toronto ON M5B 2K3 Canada

One of the key strategies for decarbonization and green transportation is using electric vehicles (EVs). However, challenges like limited charging infrastructure, EV battery characteristics, and grid integration complexities persist. This study proposes a mixed-integer linear programming (MILP) approach to optimize a grid-connected solar PV-based commercial EV charging station (SPEVCS) with a battery energy storage system (BESS) for profit maximization. The MILP model efficiently manages SPEVCS operations, considering solar power fluctuations, EV charging patterns, and BESS usage. By coordinating charging schedules, grid stability is reinforced, and excess solar power can be lucratively managed. Comparing grid-connected and off-grid SPEVCS scenarios highlights grid integration benefits. Solar power mismatches with optimal charging periods pose a challenge, addressed here by BESS utilization and import/export of deficit/surplus power from/to the grid. The proposed framework incorporates solar power forecasts and probabilistic EV arrival predictions, enhancing decision accuracy. This approach fosters viable commercial EV charging, promotes green transportation, and reinforces grid resilience.

关键词： solar photovoltaic electric vehicles grid profit maximization mixed-integer linear programming

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COMPUTERS & OPERATIONS RESEARCH 2023年 149卷

作者： Wang, Jianjiang Song, Guopeng Liang, Zhe Demeulemeester, Erik Hu, Xuejun Liu, Jin Natl Univ Def Technol Coll Syst Engn Changsha Peoples R China Tongji Univ Sch Econ & Management Shanghai Peoples R China Katholieke Univ Leuven Fac Econ & Business Res Ctr Operat Management Dept Decis Sci & Informat Management Leuven Belgium Hunan Univ Business Sch Changsha Peoples R China

In this paper, we investigate a variant of the unrelated parallel machine scheduling problem with multiple time windows that is widely employed in the scheduling of earth observation satellites. Two mixed-integer linear programming formulations are proposed based on the concept of non-immediate precedence and the deep analysis of the relationship of time windows. To facilitate the problem solving, we develop a bidirectional rolling horizon preprocessing algorithm to reduce the problem size. Based on detailed overlapping analysis, more inequalities are obtained to tighten the formulations. Furthermore, the dominance among derived inequalities is analyzed, and only nondominated inequalities are appended to limit the size of the problem. The proposed formulation and algorithm can optimally solve instances of up to 800 jobs and 20 machines within 20 min. Moreover, to verify the practicality of our method, we also conducted numerous experiments on realistic instances of satellite scheduling. The experimental results prove that our algorithm is effective for obtaining optimal solutions and can be applied in practice.

关键词： Scheduling Unrelated parallel machines Earth observation satellites mixed-integer linear programming Preprocessing Tightening strategies

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An Optimization-Based Model for A Hybrid Photovoltaic-Hydrogen Storage System for Agricultural Operations in Saudi Arabia

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PROCESSES 2023年第5期11卷 1371页

作者： Mohammed, Awsan King Fahd Univ Petr & Minerals Construction Engn & Management Dhahran 31262 Saudi Arabia King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Smart Mobil & Logist Dhahran 31261 Saudi Arabia

Renewable energy technologies and resources, particularly solar photovoltaic systems, provide cost-effective and environmentally friendly solutions for meeting the demand for electricity. The design of such systems is a critical task, as it has a significant impact on the overall cost of the system. In this paper, a mixed-integer linear programming-based model is proposed for designing an integrated photovoltaic-hydrogen renewable energy system to minimize total life costs for one of Saudi Arabia's most important fields, a greenhouse farm. The aim of the proposed system is to determine the number of photovoltaic (PV) modules, the amount of hydrogen accumulated over time, and the number of hydrogen tanks. In addition, binary decision variables are used to describe either-or decisions on hydrogen tank charging and discharging. To solve the developed model, an exact approach embedded in the general algebraic modeling System (GAMS) software was utilized. The model was validated using a farm consisting of 20 greenhouses, a worker-housing area, and a water desalination station with hourly energy demand. The findings revealed that 1094 PV panels and 1554 hydrogen storage tanks are required to meet the farm's load demand. In addition, the results indicated that the annual energy cost is $228,234, with a levelized cost of energy (LCOE) of 0.12 $/kWh. On the other hand, the proposed model reduced the carbon dioxide emissions to 882 tons per year. These findings demonstrated the viability of integrating an electrolyzer, fuel cell, and hydrogen tank storage with a renewable energy system;nevertheless, the cost of energy produced remains high due to the high capital cost. Moreover, the findings indicated that hydrogen technology can be used as an energy storage solution when the production of renewable energy systems is variable, as well as in other applications, such as the industrial, residential, and transportation sectors. Furthermore, the results revealed the feasibility of

关键词： mixed-integer linear programming optimization photovoltaic system hydrogen storage

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New Bilevel Model to Enhance Optimal Interaction between Retailer and Customers Based on the Multiobjective Robust Approach in the Energy Market

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2023年第1期2023卷

作者： Apornak, Kourosh Soleymani, Soodabeh Faghihi, Faramarz Mozafari, Babak Islamic Azad Univ Dept Elect Engn Sci & Res Branch Tehran Iran

In electricity markets, the optimal management of buying and selling energy is achieved based on the correct interaction of players. This study proposes a multiobjective bilevel model for optimal decision making of retailer based on interactions with selected customers and wholesalers with appropriate environmental performance in electricity market contracts. In this regard, at the upper level, the retailer's first objective which is profit maximization is realized, while at the lower level, the objective of minimizing customer costs is achieved. Also, the second goal of the retailer is to buy more energy from wholesalers with better environmental performance. For the presented model, in order to properly model the uncertainty of the generation capacity of wholesalers, the robust optimization approach (ROA) has been used. Finally, the mixed integer linear programming (MILP) based on McCormick's linearization method and Karush-Kuhn-Tucker conditions will be solved by CPLEX solver in GAMS software. The final results show the optimal decision of the retailer in choosing customers with the aim of maximizing profit so that the selected customers also pay the minimum cost for the purchased energy.

关键词： mixed-integer linear programming

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Bad data identification method considering the on-load tap changer model

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Frontiers in Energy Research 2024年 12卷

作者： Hu, Shiyao Rong, Chunyan Zhang, Mengnan Chai, Linjie Ma, Yuxuan Zhang, Tianlei Economic and Technology Research Institute of State Grid Hebei Electric Power Co. Ltd. Hebei Shijiazhuang China School of Electrical and Control Engineering North China University of Technology Beijing China

With the connection and integration of renewable energy, the on-load tap-changer (OLTC) has become an important device for regulating voltage in distribution networks. However, due to non-smooth and non-linear characteristics of OLTC, traditional bad data identification and state estimation methods for transmission network are limited when applied to the distribution network. Therefore, the nonlinearity and droop control constraints of the OLTC model are considered in this paper. At the same time, the quadratic penalty function is introduced to realize the fast normalization of the tap position. It proposes a two-stage bad data identification method based on mixed-integer linear programming. In the first stage, suspicious measurements are identified using projection statistics and maximum normalized residual methods for preprocessing the measurement data. In the second stage, a linearization approach utilizing hyhrid data-physical driven is applied to handle nonlinear constraints, leading to the development of a bad data identification model based on mixed-integer linear programming. Finally, the proposed methodology is validated using a modified IEEE-33 node test feeder example, demonstrating the accuracy and efficiency of bad data identification. Copyright © 2024 Hu, Rong, Zhang, Chai, Ma and Zhang.

关键词： mixed-integer linear programming

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General models for topology layout of oil and gas star-tree pipeline network

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第6期41卷 5865-5886页

作者： Zhou, Jun Zhang, Daixin Zhou, Liuling Liang, Guangchuan Zhou, Xuan Li, Zelong Southwest Petr Univ Petr Engn Sch Chengdu Peoples R China PetroChina Southwest Oil & Gasfield Co Chengdu Peoples R China Logist Engn Univ Chongqing Peoples R China

Oil&gas gathering pipeline network structure is a significant part of oil&gas field construction, and the rational construction of pipeline network is directly related to the efficiency and benefits of oil&gas field production. Therefore, optimizing the gathering and transportation system of oil and gas fields is the key to reducing development costs. The startree type pipe network is widely used in the gathering and transportation system. In order to optimize the star-tree pipe networks (STPNs) that has restrictions on the processing capacity and gathering radius of the station as a whole, this paper establishes four models of pipe network layout with specific constraints. They are mixed-integer linear programming Models with a large number of discrete variables. We take two virtual fields as examples, use CPLEX solver to solve the above four models as a whole, to obtain the optimal scheme, and also figure out the investment of the pipeline network. We further optimize the hierarchical optimization of the pipeline network with special constraints, then compare and analyze results obtained by the overall optimization. Finally, models are applied to an actual oil field and an actual gas field as examples to optimize the layout, which verifies the validity and feasibility of the models.

关键词： Star-tree pipeline network layout mixed-integer linear programming optimization

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Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

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IEEE TRANSACTIONS ON SMART GRID 2021年第1期12卷 383-397页

作者： Venzke, Andreas Chatzivasileiadis, Spyros Tech Univ Denmark Dept Elect Engn DK-2800 Lyngby Denmark

This paper presents for the first time, to our knowledge, a framework for verifying neural network behavior in power system applications. Up to this moment, neural networks have been applied in power systems as a black box;this has presented a major barrier for their adoption in practice. Developing a rigorous framework based on mixed-integer linear programming, our methods can determine the range of inputs that neural networks classify as safe or unsafe, and are able to systematically identify adversarial examples. Such methods have the potential to build the missing trust of power system operators on neural networks, and unlock a series of new applications in power systems. This paper presents the framework, methods to assess and improve neural network robustness in power systems, and addresses concerns related to scalability and accuracy. We demonstrate our methods on the IEEE 9-bus, 14-bus, and 162-bus systems, treating both N-1 security and small-signal stability.

关键词： Power system stability Biological neural networks Training Robustness Security Machine learning Neural networks mixed-integer linear programming security assessment small-signal stability

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