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The increasing penetration of renewable generation and large implementation of the DC loads are challenges that stress the current distribution systems by causing uncertain voltage variations. The AC−DC hybrid distribution network is seen as an innovative solution to address the problem of accommodating highly dispersed sustainable energy. Specifically, the solid-state transformer (SST), which is capable of enhancing power-quality performance and controllability of the power distribution, has attracted increasing focus in this decade as a promising advanced converter. It is of great interest to investigate how to operate the multiple SSTs with different modes in a coordinated manner to optimise the distribution network performance. This paper formulates the coordinated operation model for multiple SSTs to enable fast voltage regulation for the hybrid active distribution network equipped with large-scale penetration of invertor-based solar power and DC load. A hybrid optimal power flow describing the controlling modes of SSTs and operating interaction between AC−DC subsystems is proposed in this paper. The case studies on a modified IEEE 33-AC−DC hybrid power distribution system show that the voltage profile can be optimised by using the flexible controlling resource of SSTs, facilitating the timely performance adjustment in the presence of fast fluctuating distributed generator's output.