The aggregation of operational active and reactive power flexibilities as the feasible operation region (FOR) is a main component of a hierarchical multi-voltage-level grid control as well as the cooperation of transmission and distribution system operators at vertical system interconnections. This article presents a new optimization-based aggregation approach, based on a modified particle swarm optimization (PSO) and compares it to non-linear and linear programming. The approach is to combine the advantages of stochastic and optimization-based methods to achieve an appropriate aggregation of flexibilities while obtaining additional meta information during the iterative solution process. The general principles for sampling an FOR are introduced in a survey of aggregation methods from the literature and the adaptation of the classic optimal power flow problem. The investigations are based on simulations of the Cigré medium voltage test system and are divided into three parts. The improvement of the classic PSO algorithm regarding the determination of the FOR are presented. The most suitable of four sampling strategies from the literature is identified and selected for the comparison of the optimization methods. The analysis of the results reveals a better performance of the modified PSO in sampling the FOR compared to the other optimization methods.

The research project "SiNED -System Services for secure electricity grids in times of advancing energy transition and digital transformation" acknowledges the support of the Lower Saxony Ministry of Science and Culture through the "Niedersächsisches Vorab" grant program (grant ZN3563) and of the Energy Research Centre of Lower Saxony."ABSTRACT Ancillary services e.g., voltage control, congestion management and frequency control, require to be compensated increasingly from the Distributed Energy Resources (DERs). DERs are predominantly wind and photo-voltaic power plants, the major share of which are installed at the distribution grid level. Therefore, the previously passive distribution grids require transformation towards a more active role. Provision of ancillary services from the distribution grid level, requires assessment of active and reactive power flexibility (PQ-flexibility) potentials. Furthermore, increased renewable penetration correlates to increased responsibility of the Distribution System Operators (DSOs) for assessing the flexibility potentials. An aggregation of distribution grid potentials, subject to technical grid constraints and technological power limitations, is termed as Feasible Operating Region (FOR) of the distribution grid. The FOR effectively serves as an interface between the DSOs and the Transmission System Operators (TSO), for flexibility exchanges and planning of ancillary services provision. The determination of the FOR is established in current research, using different algorithms e.g stochastic methods, meta-heuristic programming and mathematical optimization techniques. In this paper, an FOR determination algorithm using successive linear programming (sLP) is proposed and validated against established optimization approaches on a uniform medium voltage (MV) grid model. Comparisons reveal competitiveness with established methods and an added advantage of fast calculation times, suitable for real time assessments. Further enhancement of the FOR is proposed, by integrating discrete transformer tap-changing operational flexibilities using a successive mixed integer linear programming (sMILP). Results demonstrate an increase in the flexibility potential from the distribution grid.

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