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...

The design and operations of energy systems are key issues for matching energy supply and consumption. Several optimization methods based on the mixed integer linear programming (MILP) have been developed for this purpose. However, due to uncertainty of some parameters like market conditions and resource availability, analyzing only one optimal solution with mono objective function is not su cient for sizing the energy system. In this study, a multi-period energy system optimization (ESO) model with a mono objective function is first explained. The model is then developed in a multi-objective optimization perspective to systematically generate a good set of solutions by using integer cut constraints (ICC) algorithm and ✏ constraint. These two methods are discussed and compared. In the next step, the ESO model is reformulated as a multi-objective optimization model with an evolutionary algorithm (EMOO). In this step the model is decomposed into master and slave optimization. Finally developed models are demonstrated by means of a case study comprising six types of conversion technologies, namely, a heat pump, boiler, photovoltaics, as well as a gas turbine, fuel cell and gas engine. Results show that, EMOO is particularly suited for multi-objective optimizations, working with a population of potential solutions, each presenting a di↵erent trade-o↵ between objectives. However, MILP with ICC and ✏ constraint is more suited for generating a small set of ordered solutions with shorter resolution time.

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A systematic procedure including process design and integration techniques for designing and operating energy distribution networks, and for transportation of resources is presented in this paper. In the developed model a simultaneous multi-objectives and multi-period optimization is principally investigated. In addition to optimize the transportation of resources/products, the proposed method helps decision makers to decide; which type and size of poly-generation technologies, centralized or decentralized, are best suited for the district, where in the district shall the equipment be located (geographically), how the services should be distributed, and what are the optimal flow, supply and return temperatures of the distribution networks. The design and the extension of distribution networks and transportation of resources, based on the geographical information system (GIS), are the novelties of the pressnt work.