Economic Evaluation of residential Energy Systems using MILP Design Optimization Combined with a Real Option Approach

Utilizing deterministic MILP models for design optimization of energy systems has gained a huge popularity in research and by practitioners. These models find an optimal solution for defined economic conditions given by parameters such as energy carrier prices or investment costs. In reality, these quantities inhabit a significant amount of uncertainty and change substantially over time. To evaluate investment decisions in energy systems under dynamic changes of the underlying economic conditions, real option analysis arises as a promising approach in current research. It provides insights about potential optimal investment times for a given system. However, it lacks to serve in-depth understanding about what an optimal system design might be for a set of given investment conditions. Therefore, we propose a two-step economic evaluation approach for local energy systems combining both methods. The first step is to use a MILP model to determine the optimal system designs under the economic conditions of today and different years in the future. In the second step we use a least squares Monte Carlo based option pricing model to value the real option to defer an investment. We conduct a case study given by a typical single-family house in Germany. Our case study considers a range of technology options, including photovoltaics, battery storage, electric air-to-water heat pumps, thermal storages and condensing gas boilers. The results show that the systems prioritization regarding their economic value changes by different maximum waiting times for the deferral option. The economic optimal decision is therefore based on the timespan a decision maker is willing to consider waiting to make an investment decision. Furthermore, in the underlying case study, the timing of the investment has a much greater impact on the economic value than the different system designs of the optimal energy systems for the years we considered in our study.