Robust Capacity Expansion Modelling for Renewable Energy Systems

TL;DR

This work tackles capacity expansion under weather-driven uncertainty for renewable-dominated energy systems by casting the problem as adaptive robust optimization with limited recourse. An iterative approach solves a base CAPEX problem for a reference year and validates it across multiple weather years using unit-commitment evaluations, triggering three candidate modifications to enforce robustness when supply gaps arise; the resulting CAPEX$^*$ problems are re-solved until feasibility is achieved for all years. On a German system model (ETHOS.FINE) with 40 weather years, the iterative modifications yield robust solutions with total annual costs increasing by about $1.6$–$2.9\%$ above a dual lower bound, underscoring the cost of robustness while confirming practical feasibility. The study also emphasizes the importance of using atypical time-series (e.g., dark lulls and cold spells) to stress-test designs, and it provides publicly available data and code to support replication and further research in robust energy-system design.

Abstract

Future greenhouse gas neutral energy systems will be dominated by renewable energy technologies whose energy output and utilisation is subject to uncertain weather conditions. This work proposes an algorithm for capacity expansion planning if only uncertain data is available for a year's operative parameters. When faced with multiple possible operating years, the quality of a solution derived on a single operating year's data is evaluated for all years, and the optimisation problem is iteratively modified whenever supply gaps are detected. These modifications lead to solutions with sufficient back-up capacity to overcome periods of cold dark lulls, and sufficient total annual energy supply across all years. A computational study on an energy system model of Germany for 40 different operating years shows that the iterative algorithm finds solutions that guarantee security of supply for all considered years increasing the total annual cost by 1.6-2.9% compared to a lower bound. Results also underline the importance of assessing the feasibility of energy system models using atypical time-series, combining dark lull and cold period effects.

Figures (13)

• Figure 1: Flowchart depicting the proposed methodology for determining robust energy systems. In each main loop iteration, $n-1$ unit commitment problems (UC) and one modified capacity expansion problem (CAPEX$^*$) are solved until loss of load is sufficiently small.
• Figure 2: Total annual cost comparison by technology for energy system models optimised from 1980--2019 aggregated for a $38$ node Germany model set up in ETHOS.FINE.
• Figure 3: Total annual cost comparison by technology for energy system models optimised from $1980-2019$ on a single node Germany model set up using gurobipy.
• Figure 4: $6$ time periods from the $40$ years of weather and $1$ year of future electricity demand data for Germany. The electricity demand is normalised to prevent overweighing; the weather data is aggregated. The upper three diagrams represent non--critical time periods, the lower three critical ones. Subfigure a) is a typical summer period with high PV availability and low electricity demand due to low heating requirements. In b) and c), typical autumn and winter period are shown. They are characterised by low availability of PV, but ample wind power to supply sufficient electricity. Note the increased electricity demand due to increased heating required. In d), a typical dark lull is characterised by low availability of PV and negligible amounts of wind, which coincides with high electricity demand due to increased heating. Subfigure e) shows an elongated dark lull period. Low availability of both PV and wind combined with increased electricity demand lead to overall difficult period requiring large amounts of hydrogen to be burned in the energy system. The last graphic f) shows the most critical period in the 40 years of weather data. Negligible wind combined with low availability of PV coincide with the highest electricity demand in the data due to high heating demand during an extreme cold spell in all of Germany.
• Figure 5: Total annual cost comparison from $1980-2019$ for robust solutions using modification smoothed \ref{['mod:1_demand']} for the single node model in gurobipy, no temporal aggregation.

Theorems & Definitions (1)

• Definition 1: Robust energy systems