Optimal Photovoltaic Siting and Sizing for Maximum Hosting Capacity under Thermal and Voltage Limits

— Growing interest in integrating solar energy into electrical grids has significantly increased photovoltaic (PV) penetration. Beyond certain operational thresholds, however, high PV penetration can cause technical grid constraints, including overvoltages and equipment thermal overloads. This threshold, known as Hosting Capacity (HC), defines the maximum PV capacity a network can accommodate while keeping line and equipment loading and bus voltages within allowable operational limits. This study develops an optimisation framework that provides a coordinated approach to obtain maximum hosting capacity and minimum total active power losses when installing a PV system at each PQ bus, while examining the relationship between hosting capacity and distinct network voltage levels. The benchmark IEEE 14-bus test system was evaluated using three optimisation approaches: Incremental PV Penetration (IPVP), the Interior-Point Method (IPM), and Particle Swarm Optimisation (PSO). IPVP and IPM were implemented in DIgSILENT PowerFactory, while PSO was executed in MATLAB via MATPOWER. The three methods produced highly consistent results, validating the framework. Optimal PV sizes and locations were determined for each PQ bus, and HC was evaluated considering line, equipment, and bus-voltage limits. Comparative analysis revealed a close relationship between optimal PV placement and hosting capacity, showing that while optimal placement significantly enhances network HC, loss minimisation and hosting capacity bounds serve complementary roles that must be optimised jointly to ensure safe and efficient renewable integration.