# Performance and Control Strategy of Real-Time Simulation of a Three-Phase Solid-State Transformer
## 1 Introduction  
Real-Time Digital Simulation (RTS, abbreviation recommended by IEEE) has been widely used for the studies on electrical power systems with a cornerstone role on the development and planning of the electrical power system. In recent years, the increase in the computational capacity and the appearance of high-speed platforms have provided a powerful tool for the study of power electronic converters, especially in the areas of rapid prototyping, control tests, phenomena investigation, fault and protection studies, among others. Typical offline simulations are performed to obtain a valid result regardless time, holding any subprocess in order to achieve the output calculation. Conversely RTS incorporate high-speed dedicated processing hardware to solve the system model variables, with a fixed time-step within the same time in the reality [1], also the simulation algorithm operates as the physical system would. Because of this RTS allow a reduction in simulation times of complex systems; offline simulations can take hours to deliver a few seconds of the system dynamics, while in real-time simulators one simulation second corresponds to an operating second of the physical system. RTS operates at a predetermined simulation time-step intervals (\(T_{s}\)), in which, the algorithm gets the inputs and proceeds to perform all the necessary calculations (control algorithms, model calculations) in order to write all the outputs. For industrial applications a 50 \(\upmu\)s time-step is an accepted target to achieve an accurate representation for a physical system over a frequency range up to 3 kHz [2]. Due to the discrete computing time, two scenarios based on the fixed time \(T_{s}\) and the complexity of the model may occur [3]. The first one is when the real-time algorithm can find a solution in \(T_{s}\) meaning that the selected time-step is enough for the real-time execution mode. A second scenario happens when the given \(T_{s}\) is smaller than the necessary time to obtain a valid response, with the need to extend the solving time algorithm to the next time-step generating an overrun, loosing real-time synchronization with an offline simulation. All this gives RTS the capability to recreate power electronic converter voltages and currents signals with a high-accuracy level within frequency range [2]. Making posible to do further advanced studies without the need to have a physical prototype. Adding also a security margin in the case of control strategies and fault protection schemes that will be implemented physically, bringing the possibility of having a look of critical operating points of the electronic converters without involving any risk. One of the power electronics topologies that has received attention in many research fields for its capabilities is the solid-state transformer (SST), whose characteristics make it feasible to be applied in the modern power electric due to its capability to integrate distributed energy resources (DER), can also operate as a power management system in smart grid applications [4; 5; 6], interconnecting wind and solar PV [7; 8; 9], for locomotive traction [10; 11] and as a scheme that can provides ancillary services to the distribution network like power factor correction, reactive power compensation, harmonic mitigation, among others [12; 13]. SST are power electronics converters which can interface two AC voltage sources providing galvanic isolation through a high frequency DC-DC link, achieving a notorious reduction in the volume and weight of the coupling transformer. Because of this, the real-time simulation of SST requires a very small \(T_{s}\) for the fixed-step solvers, which in most cases is not feasible for RTS. To overcome this issue, strategies have been reported like the use of Dynamic Average Models (DAM) [14; 15], in which the fundamental system dynamic is represented through ideal voltage and current sources, neglecting all the other components.