A trend is emerging towards the activation of distribution networks, which have only been passive until now. The main purpose is to use the existing infrastructure more efficiently. Due to the vast number of low and medium voltage networks this can only be achieved with autonomous decentralized grid monitoring and usage management systems. The most sophisticated task is the autonomous determination of remaining transfer capability. The authors wish to contribute a novel approach for solving this problem based on the online approximation of operational constraints in the domain of complex nodal power.Index Terms-Power system, loadability limit, loadability surface, operational constraints, thermal limit I. NOMENCLATURE Number of nodes, Number of lines, , Actual and base-case real-valued active power flow on line between node and Real-valued rated active power flow on line between node and node , , Actual, base-case and increment complexvalued line current on line between node and Real-valued rated current of line between node and , , Actual, base-case and increment complexvalued vector of nodal power , , Normal vectors of limiting hyperplanes in different domains Orthogonal vector of limiting hyperplane in the domain of complex nodal power O. , , , Relative distances of limiting hyperplanes to the origin in different domains , , Nodal admittance matrix, its elements and line admittance matrix , Complex-valued nodal voltage and power , , Vectors of nodal voltages and their increments , , Vector of line currents and their increments , , Result matrices of Singular Value Decomposition Jacobian matrix at expansion point , Real and imaginary part of , Real and imaginary part of Pseudo inverse of , Number of sampling points and its index variable , Start and end node of a given line II. INTRODUCTIONHE ongoing trend towards higher mean distances between load an generation centers, as well as the wish to exploit the transfer capabilities of the existing infrastructure more efficiently, lead to both transmission networks and distribution networks being operated closer to their operational limits. On transmission network level the use of market-based allocation mechanisms in power plant dispatching introduce the need for a more precise representation of the network constraints usable within market mechanisms. Although the actual relationships are of a non-linear nature, the market mechanisms usually require the constraints to be formulated in a linear fashion. This has been addressed with several approaches, of which the ATC calculation and use PTDFs with linear restrictions are the most frequently used [4]-[9]. More sophisticated approaches are based on the localization of feasibility boundaries, but suffer from a highly increased computational complexity [1], impeding the ex-ante application to determine the whole set of allowable grid usage patterns.