On the applicability of the alternating projections method for privacy-preserving scheduling in local energy communities

Local energy communities enable proper infrastructure and management mechanisms to empower final users to partake actively in the operation of electrical systems while sharing resources to pursue common objectives. As an aggregated structure, suitable energy management and scheduling tools need to be developed and tested to ensure that local resources are properly operated to maximize the economy and efficiency of energy communities. However, final electricity users may be reluctant to share confidential information, which needs to be taken into account when developing novel computational tools for energy communities. This paper applies the well-known Alternating Projection Method (APM) and differential privacy (DP) to the day-ahead scheduling problem in energy communities. As a result, two novel iterative methodologies are proposed enabling decentralized privacy-aware resolution in energy communities. Different numerical results are discussed on 100 different community instances, analyzing both economic and energetic indicators. Specifically, with no added noise (σ=0) APM is numerically identical to the centralized benchmark across all cases . Additionally, for 0<σ≤1, the mean absolute percentage error in imported energy remains less than 20 %. Results reveal that the application of the APM is capable of reproducing exactly the results of the centralized approach, while the application of differential privacy may lead to large errors, especially regarding economic results when exportable capacity is large. Moreover, results reveal that the computational burden of the new methodologies is reasonable and therefore does not pose a barrier to their implementation. Indeed, as all steps in our implementation rely on Linear Programming (LP) and as there are many stable LP solvers (both open-source and commercial) it is easy for practitioners to deploy our approach for real-life scenarios. Our numerical experiments show that the considered privacy-aware techniques were quite efficient, achieving the solution in less than a minute in all cases. Moreover, the considered privacy-aware APM presents a highly parallelizable structure which allows the results to be even further improved.