In this study, the negative-sequence voltage unbalance is calculated for increasing numbers of single-phase photovoltaic inverters (PVIs) connected to low-voltage distribution networks. The transfer impedance matrix is used to calculate the negative-sequence voltage for each of the possible locations in the networks and a stochastic method is applied to estimate the voltage unbalance. The method has been applied to six- and 28-customer networks for the connection of 6 kW single-phase PVIs. Furthermore, the hosting capacity for each network has also been estimated. From the results, it was observed that it is likely that the contribution from single-phase PVIs to the voltage unbalance exceeds 1%, but unlikely that it will reach 2%.