The recent geopolitical conflicts in Europe highlighted the sensibility of the current energy system to the volatility of energy carrier prices. In the prospect of defining robust energy system configurations to ensure energy supply stability, it is necessary to understand which parameters modulate the system configuration. This paper presents a framework that identifies a panel of technological solutions at the district level. First, a global sensitivity analysis is performed on a mixed integer linear programming model which optimally size and operate the system. The sensitivity analysis determines the most influential parameters of the model and provides a representative sampling of the solution space. The latter is then clustered using a density-based algorithm to identify typical solutions. Finally, the framework is applied to a suburban and residential Swiss neighborhood. The main outcome of the research is the high sensitivity of the model to energy carrier prices. As a result, the sampling space separates itself into two system types. The ones based on a natural gas boiler, and the ones relying on a combination of electrical heater and heat pump. For both types, the electricity demand is either fulfilled by PV panels or by electricity imports.