I. Introduction
The energy transition requires renewable generation to incrementally supplant conventional generation, enabling clean energy provision and conservation of fossil fuels. Thermal power plants enable flexible provision of active and reactive power supply in the grid for a secure and reliable supply of energy. Ancillary services like frequency control and operational management e.g. steady state voltage control and congestion management require continuous adaptation of active and reactive power flexibilities (PQ-flexibility). Increased decommissioning of thermal power plants requires a gradual transformation of distribution grids. Distributed energy resources (DERs) predominate the distribution grid and therefore, can potentially contribute significantly towards ancillary services provision. An aggregation of the DER based PQ-flexibilities from the distribution grid level is required for assessing the flexibility potential at the vertical transformer interconnection between the grid levels. In current literature, such a PQ-flexibility map is known as a Feasible Operating Region (FOR), subject to technical grid constraints and DER PQ-capabilities. Methods to determine an FOR is prevalent in literature. A wide variety of approaches ranging from random sampling techniques to heuristic and mathematical optimization are presented [1]–[8]. The FOR determination techniques are primarily demonstrated at the high voltage to medium voltage (HV/MV) grid interconnection, tested across radial distribution grids. A present challenge in FOR determination is addressing the volatility of the renewables as accurate estimation of renewable power injection is prone to errors. Uncertainty in renewable power injections result in uncertain power flows in the grid affecting accurate determination of the FOR at the vertical interconnection. State of the art researches have addressed this issue by adapting different approaches. A scenario-based robust optimization method is proposed in [9], [10], using worst case analysis. A distributionally robust chance constrained (DRCC) formulation is proposed in [11] where dispatch plans of active and reactive power are ensured within parameterised confidence levels. A similar flexibility aggregation method utilizing DRCC quantifies forecast errors of bus power injections as risk parameters [12]. Further uncertainties, considering different day types, probabilistic risk parameterised adherence to bus voltage and branch current constraints are addressed. A data driven optimal flexibility aggregation is proposed in [13] considering time coupled, uncertain and non-convex nature of loads. In [14], the robust optimization uses bus grid voltages and currents as affine functions of uncertainty deviations. FORs are determined using the confidence intervals in deterministic chance constrained optimization. The robust optimization methods present efficient means of quantifying PQ-flexibility aggregation under uncertainties. However, a statistical analysis of the confidence intervals is important to establish critical reliability parameters for flexibility aggregation.