Educational and Applied Contributions in Energy System Optimization Using a YALMIP-Based MILP Framework

As the energy sector undergoes rapid decarbonization, the design and operation of Integrated Energy Systems (IES) that combine various energy vectors including electricity, natural gas, hydrogen, heating, and cooling systems are becoming essential components of modern infrastructure. Within such systems, Power-to-Gas (PtG) acts as a key coupling technology that enables flexible sector integration by converting surplus renewable electricity into hydrogen or synthetic methane. Modelling and optimizing such systems often require advanced mathematical formulations that, while rigorous, can be challenging for students to grasp, particularly when expressed in traditional matrix notation. This paper proposes the use of Yet Another Linear Matrix Inequality Parser (YALMIP)-based teaching framework, a Matrix Laboratory (MATLAB)-based optimization modelling toolbox, as an intuitive and pedagogically effective platform for introducing optimization in IES. Compared to traditional approaches that require matrix-based formulation (e.g., specifying cost vectors and constraint matrices), YALMIP allows students to directly express constraints and objectives in natural, equation-based form, which aligns closely with how such problems are conceptually taught and understood. Using a dynamic mixed- integer linear programming (MILP) model of an IES that incorporates PtG as a coupling component and that includes renewable energy prioritization, grid emission factors, and CO₂ cost penalties, reflecting current energy transition policies and constraints, this paper presents a custom-formulated optimization framework for an IES, and it illustrates how students can explore real-world operational trade-offs. While this material has not yet been implemented in classroom instruction, it is presented as a proof of concept for teaching with the potential to support future course integration or serve as a basis for applied student assignments.