Dynamic Equivalent of PV-Integrated Active Distribution System Using Neural Networks

As the distribution systems (DSs) are transitioning into active distribution networks (ADNs) with increasing photovoltaic (PV) penetration, computationally tractable dynamic models become necessary for real-time analysis and control. This article presents a two-stage data-driven modeling framework based on NARX type recurrent neural networks (RNNs) to develop dynamic equivalent models (DEMs) for smart PV systems and PV-integrated ADNs. Initially, DEMs are developed to capture the nonlinear power dynamics of residential PV systems with ancillary voltage support. The framework is further extended to autonomously capture substation-level ADN power exchange across varying PV penetration levels. The practical implementation of the DEMs is supported by integration strategy that allows seamless coupling of the data-driven models with conventional modeling counterparts. The proposed approach is validated on modified IEEE 123-node and 8500-node test feeders under unbalanced loading and dynamic environmental profiles. Case studies on 123-node feeder show that the RNN-based DEM of ADN achieves average MSEs of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.12\times 10^{-4}$</tex-math></inline-formula> p.u. for active power and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$7.04\times 10^{-4}$</tex-math></inline-formula> p.u. for reactive power, while maintaining robustness across PV penetration levels up to 60%. Importantly, the proposed DEM provides over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1000\times$</tex-math></inline-formula> simulation time speed-up compared to detailed model-based PV-integrated ADNs for the larger test feeder, offering a scalable solution for both DSOs and TSOs in dynamic power flow studies.