The complete mathematical formulation of the energy system is explained in Mbenoun et al., 2024. Here are the main principles of the methodology defined to model the complete energy system.

Topology

The optimization problem is described as a hierarchical hypergraph composed of nodes connected by hyperedges. Each node can be seen as an optimization sub-problem with its own sets of parameters, variables, constraints, local objectives and its own sub-hypergraph. Constraints composed of variables from different nodes can then be defined in hyperedges connecting different nodes.

Nodes typically represent a technology or a process. 5 generic nodes are defined to model 5 types of technologies or processes:

• Conversion nodes, converting a set of commodities into another set via a technology or process, taking into account conversion factors between commodities, capacity constraints, maximum deployable capacity, ramp-up and ramp-down constraints, e.g. CCGTs and electrolysers;
• Flexibility nodes, maintaining equilibrium between production and demand, taking account of round-trip efficiency, self-discharge rate, injection and withdrawal constraints, storage capacity constraints, storage level constraints (same level at beginning and end of simulation period), e.g. batteries, storage tanks, underground storage and demand-side response (load shedding and load shifting);
• Import/export nodes, importing/exporting commodity from/to neighbouring countries, taking account of capacity constraints, maximum yearly import/export of commodity;
• Transmission nodes, transporting energy via electrical lines or pipelines, taking account of capacity constraints (in forward and/or reverse flow), maximum deployable capacity;
• Demand nodes, consuming commodity according to yearly quantities defined in a 2050 demand scenario, with hourly consumption profiles; if demand cannot be supplied, a high “Energy Not Served” cost is added to the total system cost.

A sixth node type, referred to as “cluster”, connects nodes producing/importing or consuming/exporting the same commodity and ensure the balance of flows for that commodity. A cluster can itself connect other clusters.

Simulations are carried out on a one-year calendar period, with hourly resolution.

Main assumptions

The model is based on several key assumptions:

• Central planning and operation. A single entity “system operator” makes investment decisions and manages the system with the aim of minimizing the total system cost.
• Perfect foresight and knowledge. The system operator has complete knowledge and foresight: it knows all technical and economic parameters as well as weather events and demand patterns.
• Optimal investment and operational decisions. Investment decisions are made at the start of the time horizon and assets are immediately available. Hourly time steps are used to make operational decisions. Both operational and investment decisions are resolved at the same time by the same optimization problem.
• Models for technologies and process. Input-output relations express mass and energy balances in order to size and operate each technology. Efficiencies, capacity constraints and ramp-up / ramp-down constraints are simulated. Storage systems assume that the filling level is the same at the beginning and at the end of the year, and take round-trip efficiency into account.

GBOML

In the framework of the INTEGRATION project, the GBOML language – Graph-Based Optimization Modeling Language – has been developed to describe the topology and parameters of energy system optimisation problems. A compiler processes GBOML files, feeds a linear optimizer and gets results that can be analysed. The results are the optimal capacity to build for each technology (in transport and distribution networks, production equipements like solar panels, on-and-offshore windmills, power plants or electrolyzers, etc), the optimal use of each technology hour by hour (production, transported flow, converted flow, storage filling level), the total cost of the energy system and each technology, a kind of “market price” of energy commodities hour by hour (the model calculates the impact of the infrastructure on the costs, not the behaviour of “commercial” actors); the CO₂ abatement cost; the “Energy Not Served” quantity for each commodity, and the “Curtailment” of variable renewable electricity production.

The GBOML grammar and the compiler are open-source. All information related to GBOML is available at https://orbi.uliege.be/handle/2268/289210.

This demonstrator uses the GBOML language to process the Belgian energy system in 2050 using ENTSOG-ENTSO-E’s 2022 scenarios. Results are presented and illustrated with graphs in the Base Case, Sensitivities and Interactive Results section.

System description

The methodology is applied on Belgium’s energy system in 2050. It aims at a net-zero energy system composed of electricity, methane and hydrogen (including derivatives like ammonia or methanol). The topology and main parameters are described in the System section.

Base Case, Sensitivities and Interactive Results

The main results of Belgium’s energy system in 2050 are presented in the Base Case section with PowerBI graphs that help to analyse the detailed results of the optimal energy system with the parameters of the Base Case.

Some parameters of the Base Case have been modified to analyse how they influence results. The results are presented in the Sensitivities section with PowerBI graphs highlighting the changes:

• Sensitivity 1 “High Renewable”: the potential of solar PV, onshore and offshore wind is increased in order to test how much variable Renewable Energy Sources (RES) can be integrated into the Belgian energy system;
• Sensitivity 2: “Farther Offshore Wind”: the distance of offshore wind is increased to identify when it is more interesting to produce hydrogen offshore rather than transporting it as electricity, and when offshore hydrogen becomes more expensive than importing it;
• Sensitivity 3: “CO₂ Budget”: if some CO₂ emissions are allowed in Belgium in 2050 (within a net-zero EU energy system), the optimal energy system in Belgium is cheaper as some high-cost CO₂ abatement solutions are not deployed;
• Sensitivity 4: “H₂ Import Cost”: the cost of importing hydrogen is increased to showcase the trade-off between imports and domestic hydrogen production, possibly impacting renewable electricity deployment in Belgium;
• Sensitivity 5: “CO₂ Export Capacity”: the capacity to export CO₂ by pipeline is decreased to analyse how it impacts the deployment and import of renewable electricity and the electricity system as a whole.

The Interactive Results section provides all data of the Base Case and Sensitivities with the same level of detail as for the Base Case.

Notes

References

• Mathias Berger, David-Constantin Radu, Raphaël Fonteneau, Thierry Deschuyteneer, Ghislain -Detienne, and Damien Ernst, “The Role of Power-to-Gas and Carbon Capture Technologies in Cross-Sector Decarbonisation Strategies”, in Electric Power Systems Research, 180, 2020, https://orbi.uliege.be/handle/2268/235110.
• Mathias Berger, David-Constantin Radu, Ghislain Detienne, Thierry Deschuyteneer, Aurore Richel, and Damien Ernst, “Remote Renewable Hubs for Carbon-Neutral Synthetic Fuel Production”, in Frontiers in Energy Research, 2021, https://orbi.uliege.be/handle/2268/250796.
• Bardhyl Miftari, Mathias Berger, Hatim Djelassi, and Damien Ernst , “GBOML: Graph-Based Optimization Modeling Language”, in Journal of Open Source Software, 2022, https://orbi.uliege.be/handle/2268/289210.
• Bardhyl Miftari, Mathias Berger, Hatim Djelassi, and Damien Ernst , “Graph-based optimization modeling language documentation”, online documentation, 2022, https://gboml.readthedocs.io/en/latest/.
• Bardhyl Miftari, Mathias Berger, Guillaume Derval, Quentin Louveaux, and Damien Ernst , “GBOML: A Structure-exploiting Optimization Modelling Language in Python”, published in Optimization Methods and Software, 2023, https://orbi.uliege.be/handle/2268/296930.
• Jocelyn Mbenoun, Amina Benzerga, Bardhyl Miftari, Ghislain Detienne, Thierry Deschuyteneer, Juan Vazquez, Guillaume Derval, and Damien Ernst , “Integration of offshore energy into national energy system: a case study on Belgium”, 2024, https://orbi.uliege.be/handle/2268/314586.