On the Non-Uniqueness of Parameter Identification in ZIP-Based Dynamic Equivalents Under Disturbance

It is well recognized that dynamic equivalent modeling plays an important role in power system analysis, where ZIP-based structures are widely used to represent aggregated load behavior. However, parameter identification of such models under short-duration disturbances often suffers from limited excitation, which raises fundamental questions regarding parameter identifiability. This paper investigates the non-uniqueness of parameter identification in ZIP-based dynamic equivalents from a regression and excitation perspective. A unified identification framework is established to analyze how limited excitation affects the structure of the regression problem and leads to ambiguity in parameter estimation. In this context, conventional and learning-based methods are examined not as competing algorithms, but as representative solution-selection mechanisms within the same feasible parameter set. Quantitatively, all methods achieve high response reconstruction accuracy, where the errors are below 2%. The corresponding parameter estimation errors, meanwhile, remain significantly larger. These results demonstrate that accurate reproduction of active and reactive power responses does not imply unique parameter identification under limited excitation conditions. From a theoretical perspective, this phenomenon is explained by the ill-conditioned structure of the regression problem under limited excitation, where near-null directions in the regression matrix lead to strong parameter coupling and give rise to a feasible set of behaviorally equivalent parameter combinations. These findings reveal a fundamental characteristic of dynamic equivalent modeling in which the preservation of external behavior does not imply a unique internal parameter decomposition, and equivalent models should therefore be interpreted as behavior-preserving representations rather than structure-identifying models. Furthermore, the present results suggest that, under the studied disturbance scenarios, enhancing excitation diversity may be more effective than solely refining identification algorithms in improving parameter distinguishability.