### Abstract

Energy system models are frequently being influenced by simplifications, assumption errors, uncertainties, incompleteness, and soft constraints which are challenging to model in a good way. In capacity expansion modeling, also the long time horizon and the high shares of renewable energies feed into the uncertainties. Consequently, a single optimal solution might not provide enough information to stand alone. Contrarily, a portfolio of different solutions, all being within an acceptance span of the system costs, would create more valuable decision support tool. This idea is known from the literature where a near optimal solution space typically is explored by introducing integer cuts that iteratively cut off solutions as they are found.

Generalizing this idea, we suggest an approach that explores the near optimal solution space by iteratively finding new solutions which are as different as possible from earlier solutions with respect to investment decisions. Our method deviates from the literature since it maximizes the difference of the found solutions rather than finding k similar solutions. An advantage of this approach is that the resulting portfolio holds high diversity which creates a better basis for good decision making. Moreover, it overcomes a potential struggle of getting symmetric solutions and it strengthens the robustness arguments of the different investment decisions. Furthermore, we suggest to search for alternative solutions in an aggregated solution space whereas the original solution space typically has been used for the search in previous work. We hereby exploit the speed-up achieved through aggregation to find more solutions, and we observe that these solutions might indicate must have investments of the non-aggregated problem.

The suggested approach is tested on a case study for three different limitations on the system costs. Results show that our approach, by far outperforms the approach known from the literature when the neighborhood size exceeds 0.7%. Furthermore, using our approach a portfolio of eight solutions with high diversity is found within the same time as the corresponding non-aggregated optimal solution. By looking into the different solutions, the relative importance of each unit investment is clearly

identified, which potentially could be used to limit the gap between aggregated and non-aggregated solutions. Also, the portfolio in itself compensates for errors introduced by aggregation.

Generalizing this idea, we suggest an approach that explores the near optimal solution space by iteratively finding new solutions which are as different as possible from earlier solutions with respect to investment decisions. Our method deviates from the literature since it maximizes the difference of the found solutions rather than finding k similar solutions. An advantage of this approach is that the resulting portfolio holds high diversity which creates a better basis for good decision making. Moreover, it overcomes a potential struggle of getting symmetric solutions and it strengthens the robustness arguments of the different investment decisions. Furthermore, we suggest to search for alternative solutions in an aggregated solution space whereas the original solution space typically has been used for the search in previous work. We hereby exploit the speed-up achieved through aggregation to find more solutions, and we observe that these solutions might indicate must have investments of the non-aggregated problem.

The suggested approach is tested on a case study for three different limitations on the system costs. Results show that our approach, by far outperforms the approach known from the literature when the neighborhood size exceeds 0.7%. Furthermore, using our approach a portfolio of eight solutions with high diversity is found within the same time as the corresponding non-aggregated optimal solution. By looking into the different solutions, the relative importance of each unit investment is clearly

identified, which potentially could be used to limit the gap between aggregated and non-aggregated solutions. Also, the portfolio in itself compensates for errors introduced by aggregation.

Original language | English |
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Journal | SN Operations Research Forum |

ISSN | 2662-2556 |

Publication status | Accepted/In press - 2020 |