The energy management strategy of a hybrid-electric aircraft is coupled with the design of the propulsion system itself. A new design space exploration methodology based on Set-Based Design is introduced to analyse the effects of different strategies on the fuel consumption, NOx and take-off mass. Probabilities are used to evaluate and discard areas of the design space not capable of satisfying the constraints and requirements, saving computational time corresponding to an average of 75%. The study is carried on a 50-seater regional turboprop with a parallel hybrid-electric architecture. The strategies are modelled as piecewise linear functions of the degree of hybridisation and are applied to different mission phases to explore how the strategy complexity and the number of hybridised segments can influence the behaviour of the system. The results indicate that the complexity of the parametrisation does not affect the trade-off between fuel consumption and NOx emissions. On the contrary, a significant trade-off is identified on which phases are hybridised. That is, the least fuel consumption is obtained only by hybridising the longest mission phase, while less NOx emissions are generated if more phases are hybridised. Finally, the maximum take-off mass was investigated as a parameter, and the impact to the trade-off between the objectives was analysed. Three energy management strategies were suggested from these findings, which achieved a reduction to the fuel consumption of up to 10% and a reduction to NOx emissions of up to 15%.