Smart city power distributions have become promising technologies to meet the demand for energy in developed countries. However, increase in smart grids causes several power quality problems on the smart grid, in particular, current and voltage harmonic distortions, sudden voltage sag and swells, fault current, and isolation deterioration. Smart transformers are potential solutions to improve the power quality on the electric grid. They present energy efficiency, ensure grid reliability and power flow control, voltage regulation, bidirectional power flow, fault current limiting, harmonic blocking, and galvanic isolation. Therefore, this paper offers an optimal selection of a three-stage (AC-DC-DC-AC) smart transformer model and power control strategy for solar PV power plant integrated smart grids. The topology of the rectifier, isolated bidirectional converter, and inverter has soft-switching features. This enables low conduction loss, low electromagnetic interference (EMI), high efficiency, achievable zero-voltage switching for converters, and zero-current switching for electrical auxiliary systems. Operation strategies of the proposed ST, PWM control, voltage, and current control between converters, including a medium-voltage (MV) high-frequency transformer to realize a 10 kVA, 450 Vdc to 220 Vdc, or 220 Vac ST, are presented. Significantly, the ST prototype achieves 96.7% conversion efficiency thanks to its control strategy, even under unstable power generation conditions from the solar PV plant. Experimental results obtained on the 344 Vac 10.4 A load current validates the dv/dt rate 6.8 kV/us. The dynamic and experimental results of the proposed bidirectional smart transformer demonstrate the success in preventing power quality problems for photovoltaic integrated smart city power distribution.