  There is an opportunity in modern power systems to explore the demand
flexibility by incentivizing consumers with dynamic prices. In this paper, we
quantify demand flexibility using an efficient tool called time-varying
elasticity, whose value may change depending on the prices and decision
dynamics. This tool is particularly useful for evaluating the demand response
potential and system reliability. Recent empirical evidences have highlighted
some abnormal features when studying demand flexibility, such as delayed
responses and vanishing elasticities after price spikes. Existing methods fail
to capture these complicated features because they heavily rely on some
predefined (often over-simplified) regression expressions. Instead, this paper
proposes a model-free methodology to automatically and accurately derive the
optimal estimation pattern. We further develop a two-stage estimation process
with Siamese long short-term memory (LSTM) networks. Here, a LSTM network
encodes the price response, while the other network estimates the time-varying
elasticities. In the case study, the proposed framework and models are
validated to achieve higher overall estimation accuracy and better description
for various abnormal features when compared with the state-of-the-art methods.
