Data-Efficient Physics-Informed Learning to Model Synchro-Waveform Dynamics of Grid-Integrated Inverter-Based Resources

Technical Summary: Data-Efficient Physics-Informed Learning to Model Synchro-Waveform Dynamics of Grid-Integrated Inverter-Based Resources

Problem Statement
The increasing penetration of Inverter-Based Resources (IBRs) is transforming power systems from synchronous to power-electronics-based generation. Unlike traditional generators, IBRs exhibit fast, control-driven transient dynamics during network disturbances, often including significant sub-cycle transients. These dynamics are difficult to capture using traditional phasor and SCADA measurements. While Waveform Measurement Units (WMUs) provide high-resolution, time-synchronized raw voltage and current samples, learning accurate transient models from this data remains challenging. Physics-only models can be computationally burdensome at sub-cycle time scales, while purely data-driven models require large volumes of labeled disturbance data, which are scarce due to the infrequency of network disturbances.

Methodology
The authors propose a Physics-Informed Machine Learning (PIML) framework to estimate IBR terminal current responses using a limited number of disturbance signatures. The approach leverages time-synchronized waveform measurements from two locations: the IBR terminal (measuring voltage $v_1(t)$ and current $i_1(t)$) and the grid-side of the connecting line (measuring voltage $v_2(t)$).

Instead of modeling raw waveforms, the method operates on first-order differential waveforms ($\Delta x(t)$), which isolate transient disturbance signatures from pre-disturbance steady states. The core of the methodology involves learning an unknown nonlinear function $f(\cdot)$ that maps the differential terminal voltage to the differential terminal current ($\Delta i_1 = f(\Delta v_1)$).

The framework incorporates physical laws by enforcing the grid-side circuit relationship:
$$\Delta v_2(t) = \Delta v_1(t) - R \Delta i_1(t) - L \frac{d\Delta i_1}{dt}$$
where $R$ and $L$ represent the line resistance and inductance. The learning process is formulated as a minimization of a loss function that combines:

1. Data-driven loss: The mean-squared error (MSE) between predicted and observed differential currents.
2. Physics-informed loss: A regularization term that penalizes deviations from the circuit equation (2).

The paper addresses two specific scenarios:

• Known Parameters: $R$ and $L$ are assumed known. The model uses two neural networks: one to predict the current response and a second to enforce the circuit equation constraint.
• Unknown Parameters: $R$ and $L$ are treated as learnable scalars (constrained to be non-negative via softplus activation). The framework jointly learns the transient dynamics map $f(\cdot)$ and the circuit parameters $R$ and $L$ via gradient-based optimization.

Key Contributions

1. Novel PIML Framework: The paper introduces the first application of PIML to synchro-waveform analytics for IBRs. It integrates grid-side waveform measurements and circuit equations to constrain the learning process.
2. Data Efficiency: The proposed method significantly reduces the amount of labeled disturbance data required to achieve accurate models compared to purely data-driven baselines.
3. Joint Parameter Estimation: The framework enables the simultaneous estimation of unknown line parameters ($R, L$) alongside the IBR transient dynamics, addressing a practical limitation where line parameters may be uncertain.
4. Robustness Across Sampling Rates: The method is validated across multiple sampling rates (32, 64, and 128 samples per 60 Hz cycle), demonstrating consistent performance even at lower resolutions.

Experimental Results
The authors evaluated the approach using a dataset of 80 disturbance events, varying the number of training events from 3 to 50.

• Performance with Known Parameters: Across all sampling rates, the PIML model achieved consistently lower testing MSE than the data-only baseline. For instance, at a sampling rate of 128 samples/cycle with only 3 training events, the PIML model reduced the error by approximately 58% compared to the data-only model.
• Data Efficiency Gains: To achieve comparable error levels, the physics-informed approach required approximately 7 to 9 times fewer training events than the data-only model when parameters were known. When parameters were unknown, the efficiency gain was lower (approx. 2.3x to 5.7x) but still significant.
• Parameter Identification: In the unknown parameter case, the model successfully converged to the true values of $R$ (10 $\Omega$) and $L$ (0.2 mH) during training, as illustrated by the convergence plots.
• Low Sampling Rates: The PIML model maintained robust performance and lower error rates even at the lowest tested sampling rate (32 samples/cycle), where the data-only baseline struggled.

Significance and Claims
The paper claims that this work bridges the gap between physics-based and data-driven modeling for IBRs. By leveraging existing but underutilized grid-side waveform measurements, the proposed PIML framework allows for accurate modeling of fast sub-cycle IBR dynamics with substantially fewer disturbance events. This is particularly significant for practical applications where collecting large labeled datasets is infeasible. The ability to jointly identify circuit parameters further enhances the utility of the framework in real-world settings where line parameters are uncertain. The authors conclude that this approach offers a data-efficient path to modeling synchro-waveform dynamics, with future work planned to address more complex network topologies, noise, and unbalanced conditions.