Smooth Mathematical Representation of the DER_A Aggregated Model

System dynamic models for hundreds of inverter-based generators are necessary to represent the whole behavior and to perform stability analysis at the transmission and distribution level in the electric power system. Aggregated models such as DER_A and PVD1 have been proposed, however, they have many parameters and there is currently no methodology to parameterize them. Many of the parameterization methods for this type of model require only smooth functions. Because these models have non-linear blocks, such as saturation and dead-band functions, this paper proposes a smooth mathematical representation of the DER_A aggregated model. The proposed smooth mathematical representation uses a novel smooth function proposed to represent the saturation function and further uses a proposed method to obtain a smooth dead-band function from the proposed smooth saturation function. Finally, the impact of the use of smooth functions on the dynamics of the DER_A model states is experimentally presented and it is also demonstrated by means of electrical signals that the proposed smooth mathematical representation can represent the dynamics of the aggregated DER_A model, paving a way for future research on parameter identification and stability assessment of the aggregated inverter-based generation models.