Practical sensitivity-based optimization technique to solve the hosting capacity problem in unbalanced low voltage networks

This work addresses the problem of computing the hosting capacity of distributed energy resources, both generation and demand, in a three-phase four-wire low voltage network. A new methodology, based on the use of voltage and current sensitivities coefficients to model the system, allow to define a second-order cone programming formulation that granted the convexity of the problem. This approach results in a very practical and accurate tool capable of solving the hosting capacity problem, for generation and demand hosting capacity, in large unbalanced distribution networks, regardless of the initial operating conditions or its radial or meshed topology, and considering the limiting constraints on voltages, currents, reverse power flows and voltage unbalances. Tests on numerous different real low-voltage networks demonstrate the practical usefulness of the tool, highlighting the accuracy of the results obtained. For the largest tested distribution network, a comparison has been included between the results obtained with the proposed methodology and those derived from using a Monte-Carlo-based probabilistic approach, demonstrating the computational advantage of the new method and the good accuracy of the optimum obtained. With the new hosting capacity computation tool, it has been possible to identify technically safe scenarios that allow for the accurate quantification and localization of the nodes and phases to which the new generation/demand must be connected, reaching penetration levels of up to 32%/21% with respect to the transformer’s rated power.