Enhanced Optimization-Based PV Hosting Capacity Method for Improved Planning of Real Distribution Networks

This paper presents an optimization-based method to support distribution system operators (DSOs) in planning large-scale photovoltaic (PV) integration at the medium-voltage (MV) level. The PV hosting capacity (PV-HC) problem is formulated as a mixed-integer quadratically constrained program (MIQCP) without linearizing approximations to determine PV sizes and locations while enforcing operating limits and planning constraints, including candidate PV locations, per-unit PV capacity limits, active power exchange with the upstream grid, and PV power factor. Our method defines two HC solution classes: (i) sparse solutions, which allocate the PV capacity to a limited subset of candidate nodes, and (ii) non-sparse solutions, which are derived from locational hosting capacity (LHC) computations at all candidate nodes, and are then aggregated into conservative zonal HC values. The approach is implemented in a Hosting Capacity–Distribution Planning Tool (HC-DPT) composed of a Python–AMPL optimization environment and a Python–OpenDSS probabilistic evaluation environment. The worst-case operating conditions are obtained from probabilistic models of demand and solar irradiance, and Monte Carlo simulations quantify the performance under uncertainty over a representative daily window. To support integrated assessment, the index Gexp is introduced to jointly evaluate exported energy and changes in local distribution losses, enabling a system-level interpretation beyond loss variations alone. A strategy was also proposed to derive worst-case scenarios from zonal HC solutions to bound performance metrics across multiple PV integration schemes. Results from a real MV case study show that PV location policies, export constraints, and zonal HC definitions drive differences in losses, exported energy, and solution quality while maintaining computation times compatible with DSO planning workflows.