Decentralized Analytic Bayesian Probabilistic Composite Load Modeling: Sensitivity, Identifiability and Interpretability

With the widespread deployment of phasor measurement units (PMUs), data-driven composite load modeling has gained increasing attention among researchers. Existing approaches mainly rely on optimization-based methods to produce point estimates, which lack the capability to quantify estimation uncertainty. Alternatively, sampling-based techniques can provide confidence intervals (CIs) but are computationally expensive for real-time applications. In addition, the theoretical interpretability of such CIs is still limited. To address these issues, we propose a decentralized Bayesian load modeling strategy utilizing trajectory sensitivity that achieves structural decoupling between the load model and the external network. It eliminates the effects associated with external uncertainties in the system while effectively providing a probabilistic description of the load parameters, without resorting to time-consuming sampling. Moreover, for the first time we derive an analytical relation between trajectory sensitivities, measurement Jacobians, priors, noise, and confidence levels, theoretically demonstrating the rationale of key parameter screening in a statistical manner. The simulation results for multiple load modeling cases reveal the excellent performance of the proposed method.