The Future Energy Market Model (FEM): A Mathematical Description

This document provides a comprehensive mathematical formulation of the Future Energy Market (FEM) model, a multi-period, multi-scenario energy system optimization model for coupled electricity and district heating systems. The model is formulated as a linear program that minimizes total system costs including investment and operational expenditures, while ensuring energy balance, technical constraints, fuel limitations, etc. The model incorporates detailed representations of generation technologies including renewables, conventional thermal plants, and combined heat and power; storage systems such as batteries, pumped hydro, heat storages, fossil methane and hydrogen; demand-side flexibility from electric vehicles, heat pumps, and demand-side response; as well as transmission networks. This documentation focuses on the essential mathematical structure and is designed to be accessible to energy system modelers and researchers.