This research presents the modelling and design of a solid-state transformer (SST) for smart energy, by scrutinizing and analyzing the problems associated with Low-Frequency Transformers (LFT) and presenting the SST as a model and solution in the smart energy system.The behaviour of the SST in dynamic conditions that is suitable to a smart energy system was carried out, through the analysis of the SST vital components (converters) and their parameters which should be designed first. This is done by an erudite mathematical analysis, culminating in various equations representing their behaviour, function, and their ratings. The required voltage, current and power rating of each component is represented by corresponding equations that unveils the impedance matching requirement, ensures that maximum power is transferred between connecting components of the SST in the smart energy system. The components of the SST analyzed include the Cascaded Hybrid Bridge (CHB) converter which converts AC to DC and connects to the Dual Active Bridge (DAB) through a DC link capacitor. The DAB is another converter that uses a high frequency transformer situated in between the DC - DC and transforms DC/AC to AC/DC, while ensuring galvanic isolation in the SST high voltage side and low voltage side, and it links to the Three Phase Four Leg (3P4L) converter through a DC link capacitor. The 3P4L DC/AC converter links the SST to the load or grid. The equations, mathematical functions, and algorithms developed in this study will help in the design of converters DC links, and the combinations of these components culminating in the design of the SST.To assist in retrieving the converters filter parameters, the algorithms are written in simple but engineering and mathematical problem-solving centered methodology, for easy implementation in the various programming language. The efficiency analyses of the SST are performed using the POET framework. The verification, modelling and design are done using MATLAB Simulink. Hence, the potential use or applications of SST as a component of a power grid, modern house, and smart energy is unveiled.The research ethical reference number: 2021FEBEREC-STD-109