  Distribution system state estimation (DSSE) plays a crucial role in the
real-time monitoring, control, and operation of distribution networks. Besides
intensive computational requirements, conventional DSSE methods need
high-quality measurements to obtain accurate states, whereas missing values
often occur due to sensor failures or communication delays. To address these
challenging issues, a forecast-then-estimate framework of edge learning is
proposed for DSSE, leveraging large language models (LLMs) to forecast missing
measurements and provide pseudo-measurements. Firstly, natural language-based
prompts and measurement sequences are integrated by the proposed LLM to learn
patterns from historical data and provide accurate forecasting results.
Secondly, a convolutional layer-based neural network model is introduced to
improve the robustness of state estimation under missing measurement. Thirdly,
to alleviate the overfitting of the deep learning-based DSSE, it is
reformulated as a multi-task learning framework containing shared and
task-specific layers. The uncertainty weighting algorithm is applied to find
the optimal weights to balance different tasks. The numerical simulation on the
Simbench case is used to demonstrate the effectiveness of the proposed
forecast-then-estimate framework.
