An adaptive discretization MINLP algorithm for optimal synthesis of decentralized energy supply systems

Abstract Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and part-load performances are nonlinear. Thus, this optimization problem can be modeled as a nonconvex mixed-integer nonlinear programming (MINLP) problem. We present an adaptive discretization algorithm to solve such synthesis problems containing an iterative interaction between mixed-integer linear programs (MIPs) and nonlinear programs (NLPs). The proposed algorithm outperforms state-of-the-art MINLP solvers as well as linearization approaches with regard to solution quality and computation times on a test set obtained from real industrial data, which we made available online.

[1]  Poul Alberg Østergaard,et al.  Reviewing optimisation criteria for energy systems analyses of renewable energy integration , 2009 .

[2]  Robin Smith,et al.  Synthesis of industrial utility systems: cost-effective de-carbonisation , 2005 .

[3]  André Bardow,et al.  Superstructure-free synthesis and optimization of distributed industrial energy supply systems , 2012 .

[4]  Nikolaos V. Sahinidis,et al.  A polyhedral branch-and-cut approach to global optimization , 2005, Math. Program..

[5]  James E. Campbell,et al.  An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment , 1981 .

[6]  I. Grossmann,et al.  Global optimization of bilinear engineering design models , 1994 .

[7]  François Maréchal,et al.  Targeting the integration of multi-period utility systems for site scale process integration , 2003 .

[8]  Endre Rev,et al.  Process flowsheet superstructures: Structural multiplicity and redundancy: Part II: Ideal and binarily minimal MINLP representations , 2005, Comput. Chem. Eng..

[9]  Ignacio E. Grossmann,et al.  A structural optimization approach in process synthesis—I: Utility systems , 1983 .

[10]  Richard Flavell,et al.  An Approach to Sensitivity Analysis , 1975 .

[11]  Myun-Seok Cheon,et al.  Solving Mixed Integer Bilinear Problems Using MILP Formulations , 2013, SIAM J. Optim..

[12]  André Bardow,et al.  How to Explore and Analyze the Decision Space in the Synthesis of Energy Supply Systems , 2016 .

[13]  Urmila M. Diwekar,et al.  A Mixed-Integer Programming Model for Pollution Trading , 2011 .

[14]  E. Fabrizio.  Modelling of multi-energy systems in buildings , 2008 .

[15]  André Bardow,et al.  Automated superstructure-based synthesis and optimization of distributed energy supply systems , 2013 .

[16]  Endre Rev,et al.  Process flowsheet superstructures: Structural multiplicity and redundancy: Part I: Basic GDP and MINLP representations , 2005, Comput. Chem. Eng..

[17]  Robin Smith,et al.  Modelling and Optimization of Utility Systems , 2004 .

[18]  François Maréchal,et al.  Multiobjective Design and Optimization of Urban Energy Systems , 2008 .

[19]  A. Jupke,et al.  STRUCTese® – Energy efficiency management for the process industry , 2013 .

[20]  Sven Leyffer,et al.  Branch-and-Refine for Mixed-Integer Nonconvex Global Optimization , 2008 .

[21]  Luis M. Serra,et al.  Structure optimization of energy supply systems in tertiary sector buildings , 2009 .

[22]  Enrico Sciubba,et al.  A Brief Review of Methods for the Design and Synthesis Optimization of Energy Systems , 2002 .

[23]  André Bardow,et al.  Exploring the Near-Optimal Solution Space for the Synthesis of Distributed Energy Supply Systems , 2013 .

[24]  André Bardow,et al.  DESSLib - Benchmark Instances for Optimization of Decentralized Energy Supply Systems , 2016 .

[25]  Nilay Shah,et al.  Modelling and optimization of retrofitting residential energy systems at the urban scale , 2014 .

[26]  Efstratios N. Pistikopoulos,et al.  Modelling and optimization aspects in energy management and plant operation with variable energy demands-application to industrial problems , 1998 .

[27]  Björn Geißler,et al.  Using Piecewise Linear Functions for Solving MINLP s , 2012 .

[28]  Cheng-Liang Chen,et al.  A flexible structural and operational design of steam systems , 2010 .

[29]  Zacharias B. Maroulis,et al.  Real-time management and optimisation of industrial utilities systems , 1996 .

[30]  Gaetano Florio,et al.  A mixed integer programming model for optimal design of trigeneration in a hospital complex , 2007 .

[31]  Steven Clark,et al.  General Algebraic Modeling System , 2014 .

[32]  Pedro M. Castro,et al.  Global optimization of bilinear programs with a multiparametric disaggregation technique , 2013, Journal of Global Optimization.

[33]  Tobias Achterberg,et al.  Constraint integer programming , 2007 .

[34]  Christos A. Frangopoulos,et al.  Optimization of energy systems based on Evolutionary and Social metaphors , 2008 .

[35]  Yiping Feng,et al.  Effective Solution Approach for Integrated Optimization Models of Refinery Production and Utility System , 2015 .

[36]  Tetsuya Wakui,et al.  Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation , 2015 .

[37]  Mirko M. Stojiljković,et al.  Multi-Objective Combinatorial Optimization of Trigeneration Plants Based on Metaheuristics , 2014 .

[38]  Michael R. Bussieck,et al.  General Algebraic Modeling System (GAMS) , 2004 .

[39]  Ignacio E. Grossmann,et al.  A Rigorous MINLP Model for the Optimal Synthesis and Operation of Utility Plants , 1998 .

[40]  M. El‐Halwagi,et al.  Convex Hull Discretization Approach to the Global Optimization of Pooling Problems , 2009 .

[41]  N. El‐Farra,et al.  Energy demand management for process systems through production scheduling and control , 2015 .