Planning of regional energy systems: An inexact mixed-integer fractional programming model H. Zhu a , W.W. Huang b , G.H. Huang a,c,⇑ a Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan S4S 0A2, Canada b Dept of Civil Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada c S-C Institute for Energy, Environment and Sustainability Research, North China Electric Power University, Beijing 102206, China highlights  An inexact fractional energy system planning (IMIF-EP) model is developed.  IMIF-EP generates useful results for a case of sustainable energy management (SEM).  Issues related to sustainability, uncertainties and dynamics can be reflected.  A comparative case of economical energy management (EEM) is also considered.  Results of two cases show significant differences between SEM and EEM. article info Article history: Received 31 January 2013 Received in revised form 5 May 2013 Accepted 21 July 2013 Available online 23 August 2013 Keywords: Decision making Energy system planning Fractional programming Sustainable management Uncertainty abstract In this study, an inexact mixed-integer fractional energy system planning (IMIF-EP) model is developed for supporting sustainable energy system management under uncertainty. Based on a hybrid of interval- parameter programming (IPP), fractional programming (FP) and mixed integer linear programming (MILP) techniques, IMIF-EP can systematically reflect various complexities in energy management sys- tems. It not only handles imprecise uncertainties and dynamic features associated with power generation expansion planning, but also optimizes the system efficiency represented as output/input ratios. An inter- active transform algorithm is proposed to solve the IMIF-EP model. For demonstrating effectiveness of the developed approach, IMIF-EP is applied to support long-term planning for an energy system. The results indicate that interval solutions obtained from IMIF-EP can provide flexible schemes of resource allocations and facility expansions towards sustainable energy management (SEM) under multiple com- plexities. A comparative economical energy management (EEM) system is also provided. Compared with least-cost models that optimize single criterion, IMIF-EP can better characterize practical energy manage- ment problems by optimizing a ratio between criteria of two magnitudes. In application, IMIF-EP is advantageous in balancing conflicting objectives and reflecting complicated relationships among multi- ple system factors. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Due to increasing concerns of global environmental change, sustainable energy development has caught world-wide attention [1–4]. However, there are many challenges in the processes of environment-friendly energy systems planning [5]. Firstly, energy system planners are facing difficult decisions in terms of identifica- tion for a trade-off between economic development and environ- mental protection. Secondly, the necessary capacity of energy generation should be determined to meet increasing system de- mand, which often means that dynamic features of facility capac- ities need to be reflected and the associated capacity expansion problems should be considered. Thirdly, unforeseen variations ex- ist in system loading, and thus intrinsic uncertainties in some of the key system parameters (e.g. load demands and energy prices) should be properly addressed [6–9]. Therefore, it is desired to de- velop an integrated model that can systematically reflect complex- ities related to issues of system sustainability, uncertainty and dynamics in energy management problems. Previously, many research efforts were made for dealing with the above complexities [10–14]. Among them, optimization methods were widely used to provide sound management schemes under specific system conditions [15–17]. Traditional single- objective programming approaches were normally aimed at 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.07.053 ⇑ Corresponding author at: S-C Institute for Energy, Environment and Sustain- ability Research, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China. Tel.: +1 391 146 8225; fax: +1 306 585 4855. E-mail address: huang@iseis.org (G.H. Huang). Applied Energy 113 (2014) 500–514 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy