Accurate Frequency Response Modeling in Integrated T&D Co-Simulation via EWMA-RTTA-Based Quadratic Extrapolation

The large-scale integration of inverter-based resources (IBRs), particularly distributed photovoltaics (DPVs), into distribution networks increases the need for integrated transmission and distribution (T&D) co-simulation. A key challenge in such co-simulation lies in accurately modeling system frequency across two asynchronous simulation environments. For example, the transmission system, simulated in the phasor domain, can operate with a simulation timestep of 10 ms, while the distribution system, simulated in the electromagnetic transient domain (EMT) to include IBR models, uses a much finer timestep of 100 microseconds. To ensure accurate PLL-based frequency estimation in distribution systems, it is essential to predict voltage magnitude and phase angle variations within the 10 ms transmission intervals, rather than using constant values that cause inaccurate frequency calculations. This issue becomes particularly critical when modeling primary and secondary frequency response services provided by IBRs. To address this challenge, we propose an automated Exponentially Weighted Moving Average Real-Time Threshold Adaptation (EWMA-RTTA) method, which utilizes Quadratic Extrapolation to predict voltage magnitude and phase angle trends more precisely. The proposed method is validated using two Opal-RT simulators: one simulating an IEEE 118-bus transmission system and the other simulating an IEEE 123-bus distribution network. Simulation results demonstrate that our approach improves the normalized mean absolute error (nMAE) by a factor of 25.7 compared to methods that do not account for time mismatches, offering a scalable and accurate solution for modeling IBR-based frequency response in modern power systems.