Time-series aggregation for synthesis problems by bounding error in the objective function

The complexity of synthesis problems for energy systems is commonly reduced by time-series aggregation. The accuracy of time-series aggregation is commonly measured by the capability of the aggregated time series to represent the full time series. However, this accuracy measure is not linked to the goal of the synthesis problem: to make the right investment decisions. In this work, we propose a method to bound the error of time-series aggregation by measuring the accuracy of the aggregation in the domain of the objective function: For each design, the error is calculated between the cost considering the aggregated time series and the full time series. An adaptive procedure determines the aggregated time series required to accurately represent the costs of the full time series. Feasibility time steps are also identified to ensure security of supply. Results of a case study on the synthesis of an energy supply system show that aggregation to less than 10 time steps is sufficient to represent the full time series with excellent accuracy.

[1]  Lion Hirth,et al.  Carpe diem: A novel approach to select representative days for long-term power system modeling , 2016 .

[2]  André Bardow,et al.  Time-series aggregation for synthesis of distributed energy supply systems by bounding error in operational expenditure , 2016 .

[3]  Z. Kravanja,et al.  Selection of the Economic Objective Function for the Optimization of Process Flow Sheets , 2006 .

[4]  Christodoulos A. Floudas,et al.  Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: II. Sequential reduction , 2016, Comput. Chem. Eng..

[5]  Peter J. Rousseeuw,et al.  Clustering by means of medoids , 1987 .

[6]  André Bardow,et al.  SPREAD - Exploring the decision space in energy systems synthesis , 2017, Comput. Chem. Eng..

[7]  Desta Z. Fitiwi,et al.  A new approach of clustering operational states for power network expansion planning problems dealing with RES (renewable energy source) generation operational variability and uncertainty , 2015 .

[8]  George Mavrotas,et al.  A mathematical programming framework for energy planning in services' sector buildings under uncertainty in load demand: The case of a hospital in Athens , 2008 .

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

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

[11]  Robin Smith,et al.  A multi-period Mixed Integer Linear Program for design of residential distributed energy centres with thermal demand data discretisation , 2016 .

[12]  Nilay Shah,et al.  Optimisation based design of a district energy system for an eco-town in the United Kingdom , 2011 .

[13]  F. Phillipson,et al.  Data granularity and the optimal planning of distributed generation , 2016 .

[14]  Vijay Chandru,et al.  Modelling electricity demand with representative load curves , 1999 .

[15]  François Maréchal,et al.  Multi-objectives, multi-period optimization of district energy systems: I. Selection of typical operating periods , 2014, Comput. Chem. Eng..

[16]  Iain Staffell,et al.  Divide and Conquer? ${k}$-Means Clustering of Demand Data Allows Rapid and Accurate Simulations of the British Electricity System , 2014, IEEE Transactions on Engineering Management.

[17]  P. Ineichen,et al.  A new simplified version of the perez diffuse irradiance model for tilted surfaces , 1987 .

[18]  Diane Hildebrandt,et al.  Process Synthesis Targets: A New Approach to Teaching Design , 2009 .

[19]  E. Skoplaki,et al.  ON THE TEMPERATURE DEPENDENCE OF PHOTOVOLTAIC MODULE ELECTRICAL PERFORMANCE: A REVIEW OF EFFICIENCY/ POWER CORRELATIONS , 2009 .

[20]  Jose Manuel Cejudo-Lopez,et al.  Selection of typical demand days for CHP optimization , 2011 .

[21]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[22]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[23]  André Bardow,et al.  The optimum is not enough: A near-optimal solution paradigm for energy systems synthesis , 2015 .

[24]  Fredrik Haglind,et al.  A method for aggregating external operating conditions in multi-generation system optimization models , 2016 .

[25]  Ignacio E. Grossmann,et al.  Systematic Methods of Chemical Process Design , 1997 .

[26]  Ali Elkamel,et al.  An order-specific clustering algorithm for the determination of representative demand curves , 2008, Comput. Chem. Eng..

[27]  François Maréchal,et al.  Multi-period analysis of heat integration measures in industrial clusters , 2015 .

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

[29]  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 .

[30]  Werner Römisch,et al.  Scenario Reduction Algorithms in Stochastic Programming , 2003, Comput. Optim. Appl..

[31]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[32]  Andreas Rieder,et al.  Multi criteria dynamic design optimization of a small scale distributed energy system , 2014 .

[33]  R. M. Moharil,et al.  K-Means clustering technique applied to availability of micro hydro power , 2014 .

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

[35]  Zukui Li,et al.  Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: I. Single reduction via mixed integer linear optimization , 2014, Comput. Chem. Eng..

[36]  Consolación Gil,et al.  Optimization methods applied to renewable and sustainable energy: A review , 2011 .

[37]  Pierluigi Mancarella,et al.  Multi-energy systems : An overview of concepts and evaluation models , 2015 .

[38]  Sergei Vassilvitskii,et al.  k-means++: the advantages of careful seeding , 2007, SODA '07.

[39]  Fu Lin,et al.  A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings , 2016, Comput. Optim. Appl..

[40]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

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

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

[43]  Anil K. Jain.  Data clustering: 50 years beyond K-means , 2010, Pattern Recognit. Lett..

[44]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[45]  Charles A. Kang,et al.  Optimization of carbon-capture-enabled coal-gas-solar power generation , 2015 .

[46]  J. C. Bruno,et al.  Selection of typical days for the characterisation of energy demand in cogeneration and trigeneration optimisation models for buildings , 2011 .