Multi-objectives, multi-period optimization of district energy systems: I. Selection of typical operating periods

Abstract

The long term optimization of a district energy system is a computationally demanding task due to the large number of data points representing the energy demand profiles.In order to reduce the number of data points and therefore the computational load of the optimization model, this paper presents a systematic procedure to reduce a complete data set of the energy demand profiles into a limited number of typical periods, which adequately preserve significant characteristics of the yearly profiles. The proposed method is based on the use of a k-means clustering algorithm assisted by an ✏-constraints optimization technique. The proposed typical periods allow us to achieve the accurate representation of the yearly consumption profiles, while significantly reducing the number of data points.The work goes one step further by breaking up each representative period into a smaller number of segments. This has the advantage of further reducing the complexity of the problem while respecting peak demands in order to properly size the system. Two case studies are discussed to demonstrate the proposed method. The results illustrate that a limited number of typical periods is su cient to accurately represent an entire equipments' lifetime.Keywords: Typical periods, District energy systems, Mixed Integer Linear Programming, Evolutionary algorithm, Multi-objective optimization, Cluster analysis, k means algorithm IntroductionMulti period mixed integer linear programming (MILP) is an e↵ective method for designing distributed energy systems [1,2]. It provides guidance for choosing optimal system configurations for minimizing costs and environmental impacts. The evaluation of the district energy system performance requires the estimation of the investment and of the corresponding operating costs. The calculation of the operating costs should consider the hourly, daily and seasonal variations of energy demand and the contribution of each production unit. It is therefore necessary to extend the optimization to the multi-period model. Due to the high number of variables, such a detailed description of the system requires excessive computational resources for solving the MILP optimization model.Using the typical periods provides an e cient alternative for reducing the number of variables. The notion of the limited typical periods relies upon the assumption that a year can be accurately represented by a limited set of periods. The term period describes a portion of time of a certain duration. It can be a set of days, weeks, working days or weekends, defined by a sequence of time steps, over the life time of the equipment.The problem of selecting typical operating periods based on the energy demand variations has been approached in di↵erent ways. Maréchal et al. [3] proposed an evolutionary algorithm optimization approach to select typical production scenarios for an industrial cluster. Ortiga et al.[4] developed a graphical method to select a reduced number of periods that reproduce the heating and cooling load duration curves...

Multi-objective, multi-period optimization of district energy systems: Networks design

“…The demand profile is characterized by power requirement and corresponding temperatures for different typical days. The typical days selection method is presented in Fazlollahi et al [2012].…”

“…The hourly heat demand profile of each node is estimated by using meteorological data and the heating signature (Girardin et al [2010]). In order to reduce the optimization size the hourly profile, with 8760 time steps, is compressed to 7 typical days with 5 segments (Fazlollahi et al [2012]). It is shown for node C1 in Fig.2.…”

Multi-objectives, multi-period optimization of district energy systems: III. Distribution networks

“…One way to reduce the size of the optimization model is to represent the yearly profile using a limited set of typical operating periods. A clustering method is developed [23] to select the typical periods. 7' 8'…”

“…These 13 integrated zones are optimized by applying the aggregation approach [34]. Figure 5 refers to the hourly energy demand profiles of 450,000 inhabitants, solar irradiation and electricity price (eex.com 2011) of a typical year and 8 representative typical operating periods [23].…”

Multi-Objective Combinatorial Optimization of Trigeneration Plants Based on Metaheuristics

“…Typical weeks might be used, as well [6]. In [7,8], the methodologies for choosing typical days i.e., periods, are suggested. In contrast, in [9], a full year is analyzed, although with a somewhat longer time step of 4 h. In [10], the consideration of a whole observed period is suggested based on moving-horizon short-term operation optimization.…”