用扩散模型解决电力系统参数估计的非唯一性难题
Diffusion Model-based Parameter Estimation in Dynamic Power Systems
- 基于联合条件扩散模型生成符合观测数据的参数分布
- 相比单条件模型误差降低58.6%，故障响应误差低于4×10⁻³
- 适用于动态电力系统建模，可推广至其他科学领域的反问题
参数估计作为经典逆问题，常因不同参数组合产生相同输出而面临非唯一性，严重阻碍准确识别。本文提出联合条件扩散模型驱动的逆问题求解框架，利用扩散模型的随机性生成与观测数据一致的参数候选解，并通过多观测联合条件进一步压缩不可辨识参数的后验分布。在复合负荷模型参数化这一动态电力系统中的挑战性任务中，该方法相较单条件模型将参数估计误差降低58.6%，并在多种电气故障下准确复现系统动态响应，均方根误差低于4×10⁻³。其数据驱动特性使其成为可广泛应用于跨学科反问题的通用参数估计框架。
原文摘要 · Abstract (English)
Parameter estimation, which represents a classical inverse problem, is often ill-posed as different parameter combinations can yield identical outputs. This non-uniqueness presents a critical barrier to accurate and unique identification. Here we introduce a parameter estimation framework to address such limits: the Joint Conditional Diffusion Model-based Inverse Problem Solver. By leveraging the stochasticity of diffusion models, it produces candidate solutions that capture underlying parameter distributions conditioned on the observations. Joint conditioning on multiple observations further narrows the posterior distributions of non-identifiable parameters. For composite load model parameterization, a challenging task in dynamic power systems, the proposed method achieves a 58.6% reduction in parameter estimation error compared to the single-condition model. It also accurately replicates system's dynamic responses under various electrical faults with root mean square errors below $4 \times {10^{ - 3}}$, exhibiting comprehensive advantages in calibration and efficiency over existing methods. Given its data-driven nature, it provides a general framework for parameter estimation while effectively mitigating the non-uniqueness problem across scientific domains.
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