A new optimal solution space based method for increased resolution in energy system optimisation Johan Sandberg a,⇑ , Mikael Larsson b , Chuan Wang b , Jan Dahl a , Joakim Lundgren a a Division of Energy Science, Luleå University of Technology, SE-971 87 Luleå, Sweden b Centre for Process Integration in Steelmaking, Swerea MEFOS AB, SE-971 25 Luleå, Sweden article info Article history: Received 22 March 2011 Received in revised form 17 October 2011 Accepted 24 November 2011 Available online 24 December 2011 Keywords: Process integration Industrial heating system Optimisation MILP Waste heat abstract In this paper a new method for increased time resolution in multi-period Mixed Integer Linear Program- ming (MILP) optimisation is presented and applied to a district heating system. The proposed method facilitates the analysis of many time periods in multi period MILP optimisation projects. In the paper, a 365 time period model spanning 1 year developed with the novel method is compared to a 12 time period model developed with a more conventional methodology. The new method offers a significant decrease in the amount of input data for multi period models and facilitates changes to the analysed time span or resolution in time. In the application of the new method oil savings of 7% compared to the current operational strategy of the district heating system are revealed. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Mixed Integer Linear Programming (MILP) is a widely applied process integration method for optimisation studies in many dif- ferent industrial systems, for example in the pulp and paper indus- try [1,2], the petrochemical industry [3,4], the steel industry [5,6] and in district heating systems [7,8]. Central to any MILP modelling project is the choice of whether and how to model the systems’ variations over time. The simplest method may be to choose static modelling without any time dependence. If the dynamics is of significance, there are a few com- mon different strategies to choose from. One is to create a steady state model and complete it with a sensitivity analysis [5]. Another common way is to divide the time span into a number of time peri- ods with equal or varying lengths [3]. Yet another approach is to use duration curves, where the studied time span is divided into a number of periods, each representing a specific state of the system rather than a specific chronological period [9]. When choosing time resolution, the frequency of variation in the system must be taken into account. The ideal situation would be to select a time resolution that allows the model to reflect the smallest fluctuations in the system. However, an increased time resolution typically increases the amount of input data linearly. An increased amount of input data increases the work effort and complexity of the model and in some cases also the requirements of the MILP optimisation solver software or hardware. In practice, the choice of time resolution often becomes a trade off between preserving the real life behaviour of the system and the computational time and resources available. While factors that influence the system might fluctuate with a frequency of days, hours or even minutes – the time period being studied often spans a period many times longer. A system might need a time resolution in the scale of minutes to be properly modelled while the time period being studied might span a full year or even more thus requiring many thousand time periods to be calculated, formulated mathematically and solved [8,10]. Multi period optimisation models with a time resolution of sub hour, hours or days are not rare in the literature [11,12]. However, studies of high resolution in time over long periods rare. When applying a high resolution in time the studied time span tend to shorten in order to keep the number of time periods in the optimi- sation model to a reasonable amount. Exceptions to this rule are however to be found [10]. Different decomposition methods to meet the increased complexity of followed by many time periods have been presented in the past [13,14]. The main objective of this paper is to describe and illustrate the use of a new method for MILP optimisation of industrial systems. The method is titled Optimal Solution Space Method (OSSM) and makes use of the linearity of MILP models. The new method decou- ples the relation between increased time resolution and increased amounts of input data and solving complexity. It also simplifies 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.11.062 ⇑ Corresponding author. Tel.: +46 702198084. E-mail addresses: Johan.Sandberg@ltu.se (J. Sandberg), Mikael.Larsson@swerea.se (M. Larsson), Chuan.Wang@swerea.se (C. Wang), Jan.Dahl@ltu.se (J. Dahl), Joakim. Lundgren@ltu.se (J. Lundgren). Applied Energy 92 (2012) 583–592 Contents lists available at SciVerse ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy