# WP5 Advanced mathematical modelling

In WP5 complex mathematical problems connected to modelling of large integrated systems will be analysed and the work will act as a support function to WP4 by developing solutions to handle the large numbers of variables and equations imposed in large energy system models. The WP will handle four tasks:

- 5.1: Dynamic aggregation of variables or constraints. Since many energy models become very large, it is often necessary to aggregate variables in the time and geography domains or to merge different energy modes. However, this leads to loss of precision, and it has not been studied in depth what is the best compromise in aggregations methods so that solution quality is balanced against solution times. Basic aggregation techniques [37] as well as dynamic methods [38] will be applied.
- 5.2: Tuning of solution times. Balmorel and Sifre are linear programming models, and several algorithms can be used to solve this problem, including primal, dual and interior point methods. Due to the size of the models, it is not trivial to solve the model, so an analysis of which algorithms are most suitable will be performed. Many solvers also provide a number of parameters that can be used to tune the algorithm. These parameters will be tuned, either manually or using automatic algorithm configuration tools [39].
- 5.3: Binary decision variables. In order to properly model several gas decisions, it is necessary to apply binary decision variables in e.g. Balmorel. Although several solvers are able to handle binary variables, the complexity of solving the model grows exponentially and hence careful modelling and solution methods must be applied. It will be investigated which model formulations are suited for decomposition (Dantzig-Wolfe decomposition, Benders decomposition) and prototype tests are carried out.
- 5.4: Handling uncertainties in gas models. Stochastic programming is frequently used to model uncertainty in energy models. However these models quickly become very large and difficult to solve due to the large number of scenarios. It will be investigated whether a combination of stochastic programming and optimal control approaches can be used to ensure both precision and reasonable solution times.

## Participating partners:

- Prof. D.Pisinger
- DTU Management Engineering
- Danish Energy Association
- RAM-løse EDB
- EA Energy Analyses
- Energinet.dk