## 2 Computational Simulation Models  
In order to attain the main goals proposed in this paper, a test network was modeled and studied in a computational simulation environment. The overall structure of the test network comprises a hybrid AC/DC distribution grid supplied by an ST that is connected to an upstream MV distribution grid, as depicted in Figure 1. The modeled ST is described in Section 2.1. The modeled hybrid AC/DC distribution network emerging from the ST comprises MV and LV DC networks (described in Section 2.2) and an LV AC network (described in Section 2.3). The controllable Distributed Energy Resources (DER) incorporated in the hybrid distribution network were modeled according to the description presented in Section 2.4. The MV AC network representing the main power system to which the ST is connected is modeled through a simplified equivalent generator and an equivalent load, as described in Section 2.5.  
The computational simulation models were developed in a MATLAB(r)/Simulink(r) environment in accordance with some underling principles. The development of simulation models for electric power systems incorporating a large number of power-converter-based systems is usually based on the use of phase simulation models, as is evidenced in [25; 32; 33]. The phasor modeling approach has been demonstrated to have adequate representativeness regarding the main dynamics of the system, while demanding a low computational burden. This is achieved by neglecting the switching nature of electronic switches in power converters, as well as harmonics. More recently, and within the scope of developing simulation models for ST, a Dynamic Average Modeling (DAM) technique is proposed in [34]. DAM approximates the behavior of power electronic converters by applying the moving average operator at the switching frequency to the detailed switching model. Using this technique, the switching effects are removed from the model, but preserving the dynamic behavior of the electronic power converters [34]. As a result, a DAM can reproduce with a high accuracy the transient behavior of the original detailed switching model but using a larger time step size, thus allowing a faster simulation of systems containing several power electronic converters [34]. Therefore, the DAM modeling approach is used in this work given its superior performance in the representation of the converter operation with larger simulation steps.  
Figure 1: Overall structure of the complete computational model.  
Based on the aforementioned considerations, the developed models were structured in two layers at the simulation level aggregating, respectively, the electric grid components and the control structures of the ST itself, each one running at different time steps, as follows:  
* The simulation layer encompassing the electrical grid components (cables, loads--impedance types--filter of the power converters, etc.) was defined to operate with a time step of 10 \(\upmu\)s (100 kHz). The chosen time step was chosen as a compromise between simulation accuracy and simulation speed, following the value adopted in [34];
* The simulation layer encompassing the control structures and electronic power components of the ST itself was modeled according to the aforementioned DAM approach, but considering a switching frequency of 20 kHz for the power converters, which results in a simulation time step of 50 \(\upmu\)s. The switching elements are replaced by controlled voltage and current sources, where the respective controlling signals are discretized according the switching frequency chosen to the replaced switching elements. The motive for this distinction is because a switching frequency of 20 kHz is more realistic (comparatively to 100 kHz) when considering high power electronic converters [22; 35; 36]. Thus, this approach allows further improvements in the computational performance of the developed models.