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The hybrid distribution transformer (HDT) is one of the essential pieces of equipment for future smart distribution networks. This paper proposes a control scheme based on the Lyapunov energy function (LEF) with output voltage feedback loops for the HDT series converter to overcome the limitations of the existing HDT control schemes, including steady-state error (SSE), and improve the transient response of the distribution network. Accordingly, an energy function is defined based on the energy of the series converter. The switching functions resulting from the control scheme based on the single-loop direct Lyapunov method (DLM) cause a significant SSE in the output voltage and distort the output voltage waveforms. The output voltage feedback loops of the LV network were added to the switching variables resulting from the LEF to fix SSE, achieve fast-tracking of the reference voltage, and compensate for the sag or swell of the of the grid. Simulation and experimental results on an HDT experiment prototype confirmed the proposed control method's steady state and dynamic performance. As a result of combining the output voltage feedback loops in the control variables, the proposed method has stable and dynamic performance in fast-tracking the reference voltage and robustness to parametric uncertainty in the proposed HDT series converter. Simple implementation and understanding are other advantages of the proposed control scheme.

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