Topology-Dependent Hosting Capacity Impacts of Grid-Forming Inverters in Unbalanced Distribution Networks: Cross-Feeder Optimisation Using Metaheuristic Droop Coordination

Grid-forming (GFM) inverters are increasingly being deployed in distribution networks to improve system strength and provide synthetic inertia. However, their steady-state influence on hosting capacity (HC) is not yet fully understood, particularly across different distribution network topologies. This study shows that the relationship between GFM droop control and HC is strongly topology-dependent. In overvoltage-limited feeders, non-optimised GFM reactive power absorption reduces HC, whereas in undervoltage-limited feeders, the same reactive support mechanism significantly enhances HC. To analyse and optimise this behaviour, this study proposes the Coordinated Hosting-Capacity and Stability Algorithm (CHSA), which determines the optimal site-specific GFM droop parameters (mp,nq,ωc) using a steady-state multi-constraint metaheuristic co-simulation framework. In this context, stability refers exclusively to steady-state voltage feasibility, that is, the maintenance of nodal voltages within statutory limits under varying DER injection levels. For the overvoltage-limited Australian-adapted IEEE 123-bus unbalanced multi-phase feeder, mid-range GFM settings introduce a GFM Hosting-Capacity Penalty (CPGFM) of 95.19 kW, reducing HC from the 950.00 kW grid-following (GFL) reference ceiling to 854.81 kW. By coordinating the reactive droop parameters, the proposed CHSA recovers 92.65 kW (97.3% of CPGFM), increasing HC to 947.46 kW while eliminating voltage violations, with all inverters operating at 33.3% of their rated apparent power capacity. For the undervoltage-limited IEEE 34-bus feeder, the same GFM reactive support mechanism increases HC from 19.90 kW under GFL operation to 237.41 kW with the optimised GFM configuration, representing a nearly twelve-fold improvement. Independent verification using Particle Swarm Optimisation confirms that both algorithms converge to the same operating point: on the representative run (seed 42), HC values differ by only 1.23 kW, while mean HC across 20 independent seeds differs by 0.99 kW (HBO: 947.70±0.72 kW; PSO: 948.69±0.00 kW), indicating that the results are governed by network characteristics rather than the choice of optimisation algorithm. These findings demonstrate that the HC limitations often associated with GFM technology arise mainly from suboptimal control coordination rather than inherent architectural constraints. Furthermore, the proposed CHSA provides a general framework for voltage-constraint-aware droop coordination across distribution networks with contrasting topological characteristics.