Power system operators require advanced applications in the control centers to tackle increasingly variable power transfers effectively. One urgently needed application concerns estimating the feasible available aggregated flexibility from a power system network, which can be effectively deployed to mitigate issues in interconnected networks. This paper proposes the TensorConvolution+ algorithm to address the above application. Unlike related literature approaches, TensorConvolution+ estimates the density of feasible flexibility combinations to reach a new operating point within the p-q flexibility area. This density can improve the decision-making of system operators for efficient and safe flexibility deployment. The proposed algorithm applies to radial and meshed networks, is adaptable to new operational conditions, and can consider scenarios with disconnected flexibility areas. Using convolutions and tensors, the algorithm efficiently aggregates the combinations of flexibility providers' adjustable power output that can occur for each flexibility area set point. Simulations on the meshed Oberrhein and radial CIGRE test networks illustrate the effectiveness of TensorConvolution+ for flexibility estimation with high numerical confidence and a minor computing effort. Additional simulations highlight how system operators can interpret the estimated density of feasible flexibility combinations for decision-making purposes, the algorithm's capability to estimate disconnected flexibility areas, and adapt to new operating conditions.

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Power electronic interfaced devices progressively enable the increasing provision of flexible operational actions in distribution networks. The feasible flexibility these devices can effectively provide requires estimation and quantification so the network operators can plan operations close to real- time. Existing approaches estimating the distribution network flexibility require the full observability of the system, meaning topological and state knowledge. However, the assumption of full observability is unrealistic and represents a barrier to system operators' adaptation. This paper proposes a definition of the distribution network flexibility problem that considers the limited observability in real-time operation. A critical review and assessment of the most prominent approaches are done, based on the proposed definition. This assessment showcases the limitations and benefits of existing approaches for estimating flexibility with low observability. A case study on the CIGRE MV distribution system highlights the drawbacks brought by low observability.@en