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Urban areas have been responsible for the majority of the European Union (EU)-wide primary energy demand and CO2 emissions. To address this issue, the European Union introduced the concept of Positive Energy Districts (PEDs). PEDs are required to have an annual positive primary energy balance. However, if directly addressed in the literature, this energy balance only includes annually fixed primary energy factors and often neglects grid impacts. To bridge this gap, this work proposes a mathematical optimisation approach for PEDs, working towards an open-source model. The model’s main novelty is an hourly primary energy balance constraint. The performed case study on the island La Palma for both an urban and a rural neighbourhood show that the PED concept has a higher net present value (NPV) than solely buying electricity from the grid in all feasible cases. Depending on the space available for PV installations, the NPV increases between 29 and 31% and 25–27% for the rural and urban PED scenarios, respectively. However, in the scenarios with reduced grid impact, the NPV decreases due to the expensive battery installations. Comparing the significantly fossil-based electricity grid mix of La Palma with the renewable-based one of El Hierro shows that the primary energy-based optimisation has more room for flexibility in the high renewable mix. While the dynamic primary energy balance constraint appears promising for operational optimisation, the allocation of correct primary energy factors is crucial.

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