Bayesian Inertia Estimation via Parallel MCMC Hammer in Power Systems

The stability of modern power systems has become critically dependent on precise inertia estimation of synchronous generators, particularly as renewable energy integration fundamentally transforms grid dynamics. Increasing penetration of converter-interfaced renewable resources reduces system inertia, heightening the grid’s susceptibility to transient disturbances and creating significant technical challenges in maintaining operational reliability. This paper addresses these challenges through a novel Bayesian inference framework that synergistically integrates PMU data with an advanced MCMC sampling technique, specifically employing the Affine-Invariant Ensemble Sampler. The proposed methodology establishes a probabilistic estimation paradigm that systematically combines prior engineering knowledge with real-time measurements, while the Affine-Invariant Ensemble Sampler mechanism overcomes high-dimensional computational barriers through its unique ensemble-based exploration strategy featuring stretch moves and parallel walker coordination. The framework’s ability to provide full posterior distributions of inertia parameters, rather than single-point estimates, helps for stability assessment in renewable-dominated grids. Simulation results on the IEEE 39-bus and 68-bus benchmark systems validate the effectiveness and scalability of the proposed method, with inertia estimation errors consistently maintained below $1\%$ across all generators. Moreover, the parallelized implementation of the algorithm significantly outperforms the conventional M-H method in computational efficiency. Specifically, the proposed approach reduces execution time by approximately $52\%$ in the 39-bus system and by $57\%$ in the 68-bus system, demonstrating its suitability for real-time and large-scale power system applications.