In this work, we develop a polynomial-chaos-expa- nsion (PCE)-based approach for decentralized dynamic parameter estimation through Bayesian inference. Using this approach, the non-Gaussian distribution of the inverted parameters is obtained. More specifically, we first represent the decentralized generator model with the PCE-based surrogate. This surrogate allows us to efficiently evaluate the time-consuming dynamic solver at parameter values through Metropolis-Hastings (M-H)-based Markov chain Monte Carlo (MCMC). Then, we propose a two-stage hybrid Markov chain Monte Carlo (MCMC) to recover a posteriori distribution of the decentralized generator model parameters. In the first stage, we use the gradient-enhanced Langevin MCMC algorithm to characterize an intermediate posterior parameter distribution. This algorithm is computationally scalable to the high-dimensional parameter space. Based on the intermediate posterior distribution, during the second stage, we use the adaptive MCMC algorithm to fine-tune the strong correlations between the parameters. Finally, the fully recovered a posterior distribution is obtained in the end. The simulation results show that the proposed PCE-based hybrid MCMC algorithm can accurately and efficiently estimate the high-dimensional generator dynamic model parameters with full probabilistic distribution provided.

中文翻译：

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使用 PMU 测量进行实时动态参数估计的贝叶斯方法

在这项工作中，我们开发了一种基于多项式混沌扩展 (PCE) 的方法，用于通过贝叶斯推理进行分散动态参数估计。使用这种方法，可以得到反演参数的非高斯分布。更具体地说，我们首先用基于 PCE 的代理来表示分散的生成器模型。该代理允许我们通过基于 Metropolis-Hastings (MH) 的马尔可夫链蒙特卡罗 (MCMC) 有效地评估参数值处的耗时动态求解器。然后，我们提出了一个两阶段混合马尔可夫链蒙特卡罗 (MCMC) 来恢复分散生成器模型参数的后验分布。在第一阶段，我们使用梯度增强的 Langevin MCMC 算法来表征中间后验参数分布。该算法在计算上可扩展到高维参数空间。基于中间后验分布，在第二阶段，我们使用自适应 MCMC 算法对参数之间的强相关性进行微调。最后得到完全恢复的后验分布。仿真结果表明，所提出的基于PCE的混合MCMC算法能够准确有效地估计高维发电机动态模型参数，并提供全概率分布。