A MILP model for energy system infrastructure planning under scenario-based uncertainty

Pedro Magalhães, Peder Bacher, Henrik Madsen

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This document describes a mathematical model for energy system infrastructure planning problems. Its aim is to identify the most socioeconomically desirable energy system configuration for a given problem described within a MILP optimisation framework. The best configuration is identified in a way consistent with net present value calculations for a set of investments and operational needs. The energy system is complemented or created from scratch by the investments, enabling or providing alternative ways for the operational needs to be met. These are expressed as flow requirements in a set of networks that partly describe the energy system. Meeting them may require flows in and out of the system, potentially resulting in expenditures and revenue, in accordance with the respective tariffs. Internal flow distribution proceeds along pre-existing paths or those created through new investments, and is otherwise free, though not necessarily lossless. Losses are path segment-specific, depend on the solution deployed to allow flow along it, and can have static and flow-proportional components. Flows within the system have to be in equilibrium with another and compensate for losses and operational needs. The latter can also be dynamic if specified through modular sets of difference equations and constraints that can also be used to model interactions between networks. These structures are here termed flow converters and can also be introduced through investments. The formulation proposed also includes novelties, namely the structures necessary to use special ordered sets for selecting investments in paths, an alternative way to model static losses without intermediate nodes, and the possibility to define investments in groups of arcs rather than only on individual ones. Other key assumptions include the inexistence of flow delays and the precedence of investments relative to the planning period. Beyond these assumptions, the model design prioritised versatility and organisation over more streamlined approaches, as the model was primarily developed for scientific applications.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages88
ISBN (Electronic)978-87-643-0118-2
Publication statusPublished - 2023


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