With the increasing integration of single-phase resources, for example, PV, batteries and solid-state power substations (SSPSs), in residential distribution networks, voltage regulation and phase balancing of distribution feeders are facing growing challenges. To solve these challenges, a linearised three-phase optimal power flow (OPF) model is proposed to coordinate the operation of residential solid-state power substations for voltage regulation and phase balancing of distribution feeders. The proposed three-phase OPF model schedules both real and reactive power of each components in the SSPSs with the purpose of minimising the total operating cost as well as improving the grid performance, for example, voltage regulation and phase balancing. Results of case studies validate the accuracy of the proposed three-phase OPF model. In addition, the effectiveness of coordinating multiple SSPSs for voltage regulation and phase balancing has been demonstrated. article for publication, acknowledges that the US government retains a non-exclusive, paid-up, irrevocable, worldwide licence to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).How to cite this article: Liu G., et al.: Linearised threephase optimal power flow for coordinated optimisation of residential solid-state power substations. IET Energy Syst. Integr. 1-11 (2021).