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Optimization for the minimum fuel consumption problem of a hybrid electric vehicle using mixed-integer linear programming

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ENGINEERING OPTIMIZATION 2023年第9期55卷 1516-1534页

作者： Yamanaka, Gentaro Kuroishi, Masakatsu Matsumori, Tadayoshi Toyota Cent Res & Dev Labs Inc Nagakute Aichi Japan

In this study, a mixed-integer linear programming (MILP) formulation for obtaining the operating points of hybrid electric vehicle (HEV) powertrains is proposed. This study focuses on linearizing the nonlinear terms, such as an engine fuel consumption map, or bilinear terms represented by the energy of the motor. To address this problem, a conventional piecewise linear (PWL) method and a multi-layer perceptron (MLP) regression approach are adopted. Although the optimal solution cannot be determined using a PWL approximation for the fuel consumption map, it can be obtained using an MLP regression. Furthermore, the PWL method achieves better results than the MLP approach in terms of the accuracy of its bilinear approximation. Obtaining the optimal solution using MILP helps in acquiring a Lagrange multiplication of the design variables by solving the dual problem, which allows an efficient design revision strategy to be obtained.

关键词： HEV hybrid electric vehicle powertrains mixed-integer linear programming operating point optimization

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Evaluating the effectiveness of mixed-integer linear programming for day-ahead hydro-thermal self-scheduling considering price uncertainty and forced outage rate

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ENERGY 2017年 122卷 182-193页

作者： Esmaeily, Ali Ahmadi, Abdollah Raeisi, Fatima Ahmadi, Mohammad Reza Nezhad, Ali Esmaeel Janghorbani, Mohammadreza Islamic Azad Univ Dept Elect Engn Karaj Branch Karaj Iran Islamic Azad Univ Dept Elect Engn Marvdasht Branch Marvdasht Iran Hormozgan Univ Dept Management Bandarabbas Iran Islamic Azad Univ Young Researchers & Elite Club Shiraz Branch Shiraz Iran Islamic Azad Univ Dept Elect Engn Cent Tehran Branch Tehran Iran

A new optimization framework based on MILP model is introduced in the paper for the problem of stochastic self-scheduling of hydrothermal units known as HISS Problem implemented in a joint energy and reserve electricity market with day-ahead mechanism. The proposed MILP framework includes some practical constraints such as the cost due to valve-loading effect, the limit due to DRR and also multi-POZs, which have been less investigated in electricity market models. For the sake of more accuracy, for hydro generating units' model, multi performance curves are also used. The problem proposed in this paper is formulated using a model on the basis of a stochastic optimization technique while the objective function is maximizing the expected profit utilizing MILP technique. The suggested stochastic self scheduling model employs the price forecast error in order to take into account the uncertainty due to price. Besides, LMCS is combined with roulette wheel mechanism so that the scenarios corresponding to the non-spinning reserve price and spinning reserve price as well as the energy price at each hour of the scheduling are generated. Finally, the IEEE 118-bus power system is used to indicate the performance and the efficiency of the suggested technique. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： mixed-integer linear programming Uncertainty Modeling Electricity market Self-scheduling

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Consumer payment minimization under uniform pricing: A mixed-integer linear programming approach

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APPLIED ENERGY 2014年 114卷 676-686页

作者： Fernandez-Blanco, Ricardo Arroyo, Jose M. Alguacil, Natalia Univ Castilla La Mancha ETSI Ind Dept Ingn Elect Elect Automat & Comunicac E-13071 Ciudad Real Spain

This paper presents a multi-period auction for a day-ahead pool-based electricity market in which consumer payment for energy is minimized under uniform pricing. This optimization problem has been recently characterized as a non-separable, non-linear, mixed-integer, and combinatorial problem for which exact solution techniques are unavailable. We present a novel approach suitable for existing mixed-integer linear solvers. A major contribution of this paper is the explicit characterization of uniform market-clearing prices as primal decision variables. The proposed methodology allows considering both quadratic and piecewise linear supply offers. In addition, the market-clearing procedure also takes into account inter-temporal operational constraints such as start-ups, ramp rates, and minimum up and down times, which may be part of generation offers. This approach provides the system operator and market agents with a valuable tool to assess consumer payment minimization versus currently used declared social welfare maximization. This conclusion is backed by simulation results obtained with off-the-shelf software. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Consumer payment minimization Declared social welfare maximization Inter-temporal constraints Market-clearing procedure mixed-integer linear programming Uniform pricing

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OPTIMAL PLANNING OF GAS-TURBINE COGENERATION PLANTS BASED ON mixed-integer linear-programming

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 1987年第4期11卷 507-518页

作者： HORII, S ITO, K PAK, PS SUZUKI, Y OSAKA UNIV FAC ENGNOSAKAJAPAN

An optimal planning problem of a co-generation plant is studied which is constructed by combining gas turbine generators, waste heat boilers, auxiliary boilers, etc. The planning problem proposed is to determine the optimal configuration of the plant equipment taking into account the optimal operational policy of the plant for the annual energy demands of electric power and heat given a priori . Based on the annual cost method, the long-term economics of the plant is evaluated by the annual total cost, which is the objective function to be minimized. This optimal planning problem is formulated as a mixed-integer linear programming problem, and the optimal solution is derived by adopting the branch and bound method. As a result, both the configuration of the plant equipment and the operational policy are optimally determined reflecting the difference in economics and efficiency of the scale of each equipment. In addition, both the power to be purchased and the value of maximum contract demand of the purchased power is optimally determined. Using a numerical example, the validity and effectiveness of the optimal planning method proposed here is ascertained.

关键词： Co-generation plant Gas turbine Optimization mixed-integer linear programming

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Predictive route control for automated baggage handling systems using mixed-integer linear programming

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2011年第3期19卷 424-439页

作者： Tarau, A. N. De Schutter, B. Hellendoorn, J. Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed-integer optimization problem, usually very expensive in terms of computational effort. Therefore, we present an alternative approach for reducing the complexity of the computations by simplifying and approximating the nonlinear optimization problem by a mixed-integer linear programming (MILP) problem. The advantage is that for MILP problems solvers are available that allow us to efficiently compute the global optimal solution. The solution of the MILP problem can then be used as a good initial starting point for the original nonlinear optimization problem. We use model predictive control (MPC) for solving the route choice problem. To assess the performance of the proposed (nonlinear and MILP) formulations of the MPC optimization problem, we consider a benchmark case study, the results being compared for several scenarios. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Baggage handling systems Route choice control mixed-integer linear programming

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Determination of optimal breakpoint set of overcurrent relays using modified depth-first search and mixed-integer linear programming

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第23期14卷 5607-5616页

作者： Ghotbi-Maleki, Mahdi Chabanloo, Reza Mohammadi Ebadi, Mohammad Amin Savaghebi, Mehdi Shahid Beheshti Univ Dept Elect Engn AC Tehran Iran Univ Southern Denmark Dept Mech & Elect Engn Elect Engn Sect DK-5230 Odense Denmark

In the process of determination of breakpoints for overcurrent relays (OCR), different sets with equal number of OCRs can be selected as minimum breakpoint set (MBPS). Therefore, determination of the most appropriate MBPS is an issue which must be considered. This paper proposes a prioritization between different MBPSs based on the sum of operating times of OCRs. In this case, a set which results the minimum sum of operating times is selected as the appropriate MBPS. For this purpose, the proposed method combines two problems: determination of MBPS and coordination of OCRs, and is expressed in mixed-integer linear programming (MILP) form. Also, a modified depth-first search (DFS) algorithm is applied to determine the OCRs contained loops of studied networks. It is shown that the proposed method has the capability to be combined with previous defined expert rules in this field in order to consider the network conditions in the process of determination of optimal breakpoint set (OBPS). The proposed method has been implemented on various size networks, and the results show the effectiveness of proposed method in determining breakpoint set with the least number in first priority and minimum operating times of relays in second priority.

关键词： relay protection overcurrent protection integer programming linear programming search problems minimum breakpoint set mixed-integer linear programming optimal breakpoint set 14-bus 30-bus 118-bus 3120-bus overcurrent relays power delivery systems modified depth-first search network conditions expert rule

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mixed-integer linear programming Model to Assess Lithium-Ion Battery Degradation Cost

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ENERGIES 2022年第9期15卷 3060-3060页

作者： Oliveira, Debora B. S. Gloria, Luna L. Kraemer, Rodrigo A. S. Silva, Alisson C. Dias, Douglas P. Oliveira, Alice C. Martins, Marcos A. I. Ludwig, Mathias A. Gruner, Victor F. Schmitz, Lenon Coelho, Roberto F. CERTI Fdn Ctr Sustainable Energy BR-88040900 Florianopolis SC Brazil AES Brazil R&D & Innovat BR-04578000 Sao Paulo Brazil Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

This work proposes a mixed-integer linear programming model for the operational cost function of lithium-ion batteries that should be applied in a microgrid centralized controller. Such a controller aims to supply loads while optimizing the leveled cost of energy, and for that, the cost function of the battery must compete with the cost functions of other energy resources, such as distribution network, dispatchable generators, and renewable sources. In this paper, in order to consider the battery lifetime degradation, the proposed operational cost model is based on the variation in its state of health (SOH). This variation is determined by experimental data that relate the number of charge and discharge cycles to some of the most important factors that degrade the lifespan of lithium-ion batteries, resulting in a simple empirical model that depends on the battery dispatch power and the current state of charge (SOC). As proof-of-concept, hardware-in-the-loop (HIL) simulations of a real microgrid are performed considering a centralized controller with the proposed battery degradation cost function model. The obtained results demonstrate that the proposed cost model properly maintains the charging/discharging rates and the SOC at adequate levels, avoiding accelerating the battery degradation with use. For the different scenarios analyzed, the battery is only dispatched to avoid excess demand charges and to absorb extra power produced by the non-dispatchable resources, while the daily average SOC ranges from 48.86% to 65.87% and the final SOC converges to a value close to 50%, regardless of the initial SOC considered.

关键词： battery energy storage system degradation cost model lithium-ion battery microgrid power dispatch mixed-integer linear programming

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Using a general-purpose mixed-integer linear programming solver for the practical solution of real-time train rescheduling

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期263卷 258-264页

作者： Fischetti, Matteo Monaci, Michele Univ Padua DEI Via Gradenigo 6-A I-35131 Padua Italy Univ Bologna DEI Viale Risorgimento 2 I-40136 Bologna Italy

At a planning level, train scheduling consists of optimizing the routing and scheduling for a set of trains on a railway network. In real-time operations, however, the planned schedule constantly needs to be verified and possibly updated due to disruptions/delays that may require train rerouting or cancelation. In practice, an almost immediate reaction is required when unexpected events occur, meaning that trains must be rescheduled in a matter of seconds. This makes the time-consuming optimization tools successfully used in the planning phase completely inadequate, and ad-hoc (heuristic,) algorithms have to be designed. In the present paper we develop a simple approach based on mixed-integer linear programming (MILP) techniques, which uses an ad-hoc heuristic preprocessing on the top of a general-purpose commercial solver applied to a standard event-based MILP formulation. A computational analysis on real cases shows that our approach can be successfully used for practical real-time train rescheduling, as it is able to deliver (almost) optimal solutions within the very tight time limits imposed by the real-time environment. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization Railways optimization Train rescheduling mixed-integer linear programming Real-time optimization

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Task allocation and trajectory planning for multiple agents in the presence of obstacle and connectivity constraints with mixed-integer linear programming

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INTERNATIONAL JOURNAL OF ROBUST AND NONlinear CONTROL 2020年第14期30卷 5464-5491页

作者： Afonso, Rubens J. M. Maximo, Marcos R. O. A. Galvao, Roberto K. H. Tech Univ Munich Inst Flight Syst Dynam Dept Aerosp & Geodesy Bavaria Germany Inst Tecnol Aeronaut Elect Engn Div Sao Paulo Brazil Inst Tecnol Aeronaut Autonomous Computat Syst Lab LAB SCA Div Comp Sci Sao Paulo Brazil

This article addresses the problem of maneuvering multiple agents that must visit a number of target sets, while enforcing connectivity constraints and avoiding obstacle as well as interagent collisions. The tool to cope with the problem is a formulation of model predictive control including binary decision variables. In this regard, two mixed-integer linear programming formulations are presented, considering a trade-off between optimality and scalability between them. Simulation results are also shown to illustrate the main features of the proposed approaches.

关键词： connectivity maintenance cooperative multiple agents mixed-integer linear programming obstacle avoidance

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Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

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IET GENERATION TRANSMISSION & DISTRIBUTION 2015年第3期9卷 256-266页

作者： Goncalves, Rogerio R. Franco, John F. Rider, Marcos J. UNEMAT Univ Estado Mato Grosso Fac Ciencias Exatas & Tecnol BR-78555000 Sinop Mato Grosso Brazil UNESP Univ Estadual Paulista Fac Engn Ilha Solteira Dept Engn Eletr BR-15385000 Sao Paulo Brazil

This study presents a mixed-integer linear programming (MILP) model to solve the short-term expansion planning problem of radial electrical distribution systems. The proposed model defines the construction of new circuits, the reconductoring of existing circuits, the allocation of capacitor banks (as well as the type and the number of units in operation) and the allocation of voltage regulators to minimise the total annualised investment and operation costs. In the proposed formulation, the steady-state operation of the radial distribution system is mathematically modelled through linear expressions. The use of an MILP model guarantees convergence to optimality by using existing classical optimisation tools. The model was implemented in the mathematical modelling language AMPL and solved using the commercial solver CPLEX. A 54-node test system and 201-node real distribution system were used to demonstrate the accuracy of the mathematical model, as well as the efficiency of the proposed solution technique.

关键词： power distribution planning linear programming integer programming power capacitors voltage regulators radial electrical distribution systems mixed-integer linear programming MILP model short-term expansion planning problem capacitor bank allocation voltage regulator allocation total annualised investment minimization operation cost minimization linear expressions classical optimisation tools AMPL mathematical modelling language commercial solver CPLEX 54-node test system 201-node real distribution system mathematical model

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