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Optimal scheduling of combined heat and power plants using mixed-integer nonlinear programming

ENERGY 2014年 77卷 675-690页

作者： Kim, Jong Suk Edgar, Thomas F. Univ Texas Austin McKetta Dept Chem Engn Austin TX 78712 USA Univ Texas Austin Energy Inst Austin TX 78712 USA

This paper presents the application of MINLP (mixed-integer nonlinear programming) approach for scheduling of a CHP (combined heat and power) plant in the day-ahead wholesale energy markets. This work employs first principles models to describe the nonlinear dynamics of a CHP plant and its individual components. The MINLP framework includes practical constraints such as minimum/maximum power output and steam flow restrictions, minimum up/down times, start-up and shut-down procedures, and fuel limits. Special care is given to the explicit modeling of the unit start-up types (hot, warm, and cold), which depend on the component's prior reservation time, resulting in the differences in the time-dependent start-up costs of generating units. The model also accounts for the different operating modes (synchronization, soak, dispatch, and desynchronization) during start-up and shut-down of each unit. We provide case studies involving the Hal C. Weaver power plant complex at the University of Texas at Austin to demonstrate the effectiveness of the proposed methodology. The results show that the optimized operating strategies can yield substantial net incomes from electricity sales. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Scheduling Unit commitment Economic dispatch Combined heat and power Day-ahead wholesale energy market mixed-integer nonlinear programming

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Logically constrained optimal power flow: Solver-based mixed-integer nonlinear programming model

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2018年 97卷 240-249页

作者： Pourakbari-Kasmaei, Mandi Sanches Mantovani, Jose Roberto State Univ Sao Paulo Dept Elect Engn Ilha Solteira Brazil

There is increasing evidence of the shortage of solver-based models for solving logically-constrained AC optimal power flow problem (LCOPF). Although in the literature the heuristic-based models have been widely used to handle the LCOPF problems with logical terms such as conditional statements, logical-and, logical-or, etc., their requirement of several trials and adjustments plagues finding a trustworthy solution. On the other hand, a well-defined solver-based model is of much interest in practice, due to rapidity and precision in finding an optimal solution. To remedy this shortcoming, in this paper we provide a solver-friendly procedure to recast the logical constraints to solver-based mixed-integer nonlinear programming (MINLP) terms. We specifically investigate the recasting of logical constraints into the terms of the objective function, so it facilitates the pre-solving and probing techniques of commercial solvers and consequently results in a higher computational efficiency. By applying this recast method to the problem, two sub-power- and sub-function-based MINLP models, namely SP-MINLP and SF-MINLP, respectively, are proposed. Results not only show the superiority of the proposed models in finding a better optimal solution, compared to the existing approaches in the literature, but also the effectiveness and computational tractability in solving large-scale power systems under different configurations.

关键词： FACTS devices Logical constraint mixed-integer nonlinear programming Optimal power flow Solver-based model Non-smooth terms

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Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

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ENGINEERING OPTIMIZATION 2016年第10期48卷 1693-1706页

作者： Uilhoorn, F. E. Warsaw Univ Technol Dept Environm Engn Warsaw Poland

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

关键词： mesh adaptive direct search genetic algorithm ARMA Kalman filter mixed-integer nonlinear programming

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CONCRETE STRUCTURE DESIGN USING mixed-integer nonlinear programming WITH COMPLEMENTARITY CONSTRAINTS

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SIAM JOURNAL ON OPTIMIZATION 2011年第3期21卷 833-863页

作者： Guerra, A. Newman, A. M. Leyffer, S. Colorado Sch Mines Div Engn Golden CO 80401 USA Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Argonne Natl Lab Div Math & Comp Sci Argonne IL 60439 USA

We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative sizes of cross-section dimensions of elements within the structure. Other restrictions define a stiffness and displacement correlation among all structural elements via finite element analysis. The design of minimum cost RC structures introduces a new class of optimization problems, namely, mixed-integer nonlinear programs with complementarity constraints. The complementarity constraints are used to model RC element strength and American Concrete Institute code-required safety factors. We reformulate the complementarity constraints as nonlinear equations and show that the resulting ill-conditioned MINLPs can be solved by using an off-the-shelf MINLP solver. Our work provides discrete-valued design solutions for an explicit representation of a process most often performed implicitly with iterative calculations. We demonstrate the capabilities of a mixed-integer nonlinear algorithm, MINLPBB, to find optimal sizing and reinforcing for cast-in-place beam and column elements in multistory RC structures. Problem instances contain up to 678 variables, of which 214 are integer, and 844 constraints, of which 582 are nonlinear. We solve problems to local optimality within a reasonable amount of computational time, and we find an average cost savings over typical-practice design solutions of 13 percent.

关键词： complementarity problems applications in optimization mixed-integer nonlinear programming

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Optimal scheduling of buildings with energy generation and thermal energy storage under dynamic electricity pricing using mixed-integer nonlinear programming

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APPLIED ENERGY 2015年 147卷 49-58页

作者： Lu, Yuehong Wang, Shengwei Sun, Yongjun Yan, Chengchu Hong Kong Polytech Univ Dept Bldg Serv Engn Kowloon Hong Kong Peoples R China City Univ Hong Kong Div Bldg Sci & Technol Kowloon Hong Kong Peoples R China

The increasing complexity of building energy systems integrated with renewable energy systems requires essentially more intelligent scheduling strategy. The energy systems often have strong nonlinear characteristics and have discrete working ranges. The mixed-integer nonlinear programming approach is used to solve their optimal scheduling problems of energy systems in building integrated with energy generation and thermal energy storage in this study. The optimal scheduling strategy minimizes the overall operation cost day-ahead, including operation energy cost and cost concerning the plant on/off penalty. A case study is conducted to validate the proposed strategy based on the Hong Kong Zero Carbon Building. Four scenarios are investigated and compared to exam the performance of the optimal scheduling. Results show that the strategy can reduce operation energy cost greatly (about 25%) compared with a rule-based strategy and the reduction is even increased to about 47% when a thermal energy storage system is used. The strategy can also reduce the on/off frequency of chillers significantly. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Optimal scheduling mixed-integer nonlinear programming Zero energy building Renewable energy systems Thermal energy storage

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A mixed-integer nonlinear programming approach to the optimal design of heat network in a polygeneration energy system

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APPLIED ENERGY 2014年 114卷 146-154页

作者： Zhang, Jianyun Liu, Pei Zhou, Zhe Ma, Linwei Li, Zheng Ni, Weidou Tsinghua Univ Dept Thermal Engn Tsinghua BP Clean Energy Res & Educ Ctr State Key Lab Power Syst Beijing 100084 Peoples R China

A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant;however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Heat recovery steam generator Polygeneration mixed-integer nonlinear programming Design optimization

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On the solution of mixed-integer nonlinear programming models for computer aided molecular design

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COMPUTERS & CHEMISTRY 2002年第6期26卷 645-660页

作者： Ostrovsky, GM Achenie, LEK Sinha, M Univ Connecticut Dept Chem Engn Storrs CT 06269 USA

This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branching functions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： global optimization linear underestimators computer aided molecular design branch-and-bound procedure mixed-integer nonlinear programming

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Model updating based on mixed-integer nonlinear programming under model-form uncertainty in finite element model

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ENGINEERING WITH COMPUTERS 2021年第4期37卷 3699-3725页

作者： Jin, Seung-Seop Park, Young-Soo Kim, SungTae Park, Young-Hwan KICT Sustainable Infrastruct Res Ctr Goyang South Korea KICT Dept Infrastruct Safety Res Goyang South Korea

In this paper, a new finite element model updating (FEMU) method is proposed based on mixed-integer nonlinear programming (MINLP) to deal with model-form uncertainty in FE models. Depending on modelers' preference and experience, various FE models can be constructed for a specific structure in practice. However, no one can guarantee that a specific model representation is always best (Model-form uncertainty). Conventional method should perform model updating for each FE model independently and select a best one among them, so that it becomes computationally intensive with many candidate FE models. To handle model-form uncertainty, this study formulates FEMU as the MINLP problem. The proposed method assigns an integer variable for model choice, while continuous real variables are used for the updating parameters. With this formulation, the optimization algorithm can explore both model and parameter space simultaneously to deal with the model-form uncertainty in FE models. Firstly, three numerical experiments were explored to evaluate the performance of the proposed method by considering possible situations in reality as follows: (1) a true FE model exists in model space with an admissible FE model;(2) only admissible FE model exists in model space;and (3) no true and admissible FE models exist in model space. Then, the proposed method was experimentally validated through a real bridge. The results show that the proposed method can find a best FE model with optimal estimates of the updating parameters with much less computational efforts against the conventional FEMU.

关键词： Finite element model updating Model-form uncertainty mixed-integer nonlinear programming Genetic algorithm

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A trust region SQP algorithm for mixed-integer nonlinear programming

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OPTIMIZATION LETTERS 2007年第3期1卷 269-280页

作者： Exler, Oliver Schittkowski, Klaus Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany CSIC IIM Spanish Council Sci Res Proc Engn Grp Vigo 36208 Spain

We propose a modified sequential quadratic programming method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when in-or decrementing an integer value, successive quadratic approximations are applied. The algorithm is stabilized by a trust region method with Yuan's second order corrections. It is not assumed that the mixed-integer program is relaxable or, in other words, function values are evaluated only at integer points. The Hessian of the Lagrangian function is approximated by a quasi-Newton update formula subject to the continuous and integer variables. Numerical results are presented for a set of 80 mixed-integer test problems taken from the literature. The surprising result is that the number of function evaluations, the most important performance criterion in practice, is less than the number of function calls needed for solving the corresponding relaxed problem without integer variables.

关键词： mixed-integer nonlinear programming Sequential quadratic programming SQP Trust region methods

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Approximating electrical distribution networks via mixed-integer nonlinear programming

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2011年第2期33卷 245-257页

作者： Lakhera, Sanyogita Shanbhag, Uday V. McInerney, Michael K. Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA Citibank NA New York NY USA

Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an approximate electrical load distribution over a network of a prespecificed discretization. Together with partial information about existing substations, we determine the optimal placement of electrical substations to sustain such a load that minimizes the cost of capital and losses. This requires solving large-scale quadratic programs with discrete variables for which we present a novel penalization-smoothing scheme. The choice of locations allows one to determine the optimal flows in this network, as required by physical requirements which provide us with an approximation of the distribution network. Furthermore, the scheme allows for approximating systems in the presence of no-go areas, such as lakes and fields. We examine the performance of our algorithm on the solution of a set of location problems and observe that the scheme is capable of solving large-scale instances, well beyond the realm of existing mixed-integer nonlinear programming solvers. We conclude with a case study in which a stage-wise extension of this scheme is developed to reflect the temporal evolution of load. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Optimization nonlinear programming mixed-integer nonlinear programming Distribution system design GIS

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