Designing the future energy supply in accordance with ambitious climate change mitigation goals is a challenging issue. Common tools for planning and calculating future investments in renewable and sustainable technologies are often linear energy system models based on cost optimisation. However, input data and the underlying assumptions of future developments are subject to uncertainties that negatively affect the robustness of results. This paper introduces a quadratic programming approach to modifying linear, bottom-up energy system optimisation models in order to take cost uncertainties into account. This is accomplished by implementing specific investment costs as a function of the installed capacity of each technology. In contrast to established approaches like stochastic programming or Monte Carlo Simulation, the computation time of the quadratic programming approach is only slightly higher than that of linear programming. The model’s outcomes were found to show a wider range as well as a more robust allocation of the considered technologies than the linear model equivalent.