Observability and parameter estimation of a generic model for aggregated distributed energy resources

TL;DR

This work tackles the challenge of calibrating an aggregated DER dynamic model (der_a) by first establishing a principled observability framework to determine which of its $48$ parameters are estimable given realistic measurements. It develops a Lie-derivative–based analysis and introduces smoothing techniques for nonlinearities to enable robust Kalman-filter–based parameter estimation, using both EKF and UKF. The authors demonstrate, on a modified IEEE 34-node feeder with inverter-based DERs, that not all parameters are identifiable in general, but a reduced, observable subset can be reliably estimated, yielding parameter trajectories that align with reference dynamics and NERC guidelines. The results provide practical guidance for utilities and researchers to perform online calibration of aggregated DER models and highlight the value of power measurements for observability. MATLAB code is made publicly available to reproduce the results.

Abstract

We propose a novel framework for estimating the parameters of an aggregated distributed energy resources (der_a) model. First, we introduce a rigorous method to determine whether all model parameters are estimable. When they are not, our approach identifies the subset of parameters that can be estimated. The proposed framework offers new insights into the number and specific parameters that can be reliably estimated based on commonly available measurements. It also highlights the limitations of calibrating such models. Second, we introduce a Kalman filtering method to calibrate the der_a model. Since we account for nonlinear effects such as saturation and deadbands, we develop a specific mechanism to handle smoothing functions within the Kalman filter. Specifically, we consider the extended and the unscented Kalman filter. We demonstrate the effectiveness of the proposed framework on a modified IEEE 34-node distribution feeder with inverter-based resources. Our findings align with the North American Electric Reliability Corporation's parameterization guideline and underscore the importance of model calibration in accurately capturing the collective dynamics of distributed energy resources installed on distribution systems.

Figures (10)

• Figure 1: der_a model.
• Figure 2: Parameter weights in the least observable direction for Case 1 (left) and Case 2 (right).
• Figure 3: Smallest singular value of the observability matrix.
• Figure 4: Smooth saturation function and its derivative.
• Figure 5: Smooth deadband function and its derivative.

Theorems & Definitions (1)

• Remark 1