In order to improve the utilisation rate of renewable energy and flexibility of the system, the AC–DC distribution network with multiple park integrated energy subnetwork (PIESN) based on multi-port power electronic transformer (MPPET) is proposed. First, a power-sharing model of interconnected PIESNs based on MPPET is built, in which the port power of MPPET can be controlled. Then the flexibility demand and supply of electricity, heat and cooling are analysed and a flexibility-sharing model among multi-PIESN is established. Multi-energy flexibility conversion mechanism is proposed and the flexibility index is established. Moreover, the optimal operation problem is formulated and solved. The objective function is the comprehensive operation cost, which includes generation cost, energy cost of PIESN, network loss cost, MPPET loss cost, carbon emission cost and electricity storage system operation cost. Finally, simulation on the modified IEEE33 system shows that the proposed model can make the system be in an adequate flexibility, improve the utilisation rate of renewable energy, reduce load shedding and realise the power sharing among multi-PIESNs.