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A high frequency solid-state transformer (SST) proposed by FREEDM centre is an interesting alternative to conventional distribution transformer in microgrids as it supports additional functionalities such as active-reactive power flow control, fault current limitation and voltage regulation. This paper proposes a dynamic phasor based robust control of SST through the modular control of each stage. The control problem is formulated in frequency domain by representing the system states with time varying Fourier coefficients or dynamic phasors (DP). This formulation transforms the oscillating waveforms of ac circuits to constant or slowly varying variables, hence allow the use of PI controller to track the sinusoidal references. For rectifier and inverter stages of SST, dq transformation is applied on DP which facilitates the design of PI controller to smoothen out the ripples in the output voltage waveform. The controller gains are tuned to reject input and load disturbances and attenuate measurement noise using loop shaping and pole assignment technique. The robustness of the controller is assured analytically against parametric uncertainties using small gain theorem. Simulation results are provided to support the proposed control scheme. Hardwarein- Loop (HIL) simulation is carried out on critical stages using Opal-RT and dSPACE simulators to confirm the effectiveness of the proposed scheme.