**Optimal design and operation of integrated energy systems under uncertainty**

When conceptualizing a new or expanding an existing energy system, the integration of heat and power sectors and the incorporation of renewable energy sources offer potential benefits in the form of reduced greenhouse gas emissions and increased overall techno-economic efficiencies. However, availability of renewable energies such as wind and solar radiation is inherently difficult to predict with high spatial and temporal resolution, especially if a long prediction horizon is required. Likewise, the future costs of fossil fuels and grid electricity as well as energy demands themselves are, to some extent, uncertain.

This uncertainty complicates the optimal selection of technologies (e.g., photovoltaic modules, batteries, fuel cells, etc.), their dimensions and the system connectivity. In this situation, a reasonable strategy is to find a design that is optimal in the sense that it minimizes the expected total annualized costs (TAC) over a series of different scenarios, while guaranteeing feasible operation in all considered future scenarios. Here, TAC is the sum of annualized design costs and the expected value of costs for optimal system operation. For each scenario, the costs for optimal operation depend on both the chosen design and the realization of the random parameters.

Due to the stochastic nature of the underlying data, finding the optimal system design requires solving a stochastic optimization problem. A high temporal resolution and a reasonably large number of scenarios are required to represent the dynamics of system operation and the parametric uncertainties, respectively. The presence of discrete decision variables as well as nonlinear and nonconvex model components further complicates the problem, resulting in a large-scale nonconvex mixed-integer nonlinear program (MINLP). Standard nonlinear programming (NLP) solvers cannot reliably solve these problems to global optimality. Moreover, due to their large-scale nature, these problems are often intractable without special algorithmic treatment. Therefore, additional problem manipulations such as decomposition into smaller subproblems, convex relaxation and spatial branch and bound algorithms have to be employed.

At IEK-10 we are pursuing several goals:

- establishing energy system modeling practices that allow for an easy integration of uncertainty information
- generating stochastic optimization problems from energy system models and data
- implementing preprocessing routines for data management and scenario generation
- developing optimization algorithms for nonconvex stochastic MINLPs

Contact person: Marco Langiu