  This letter first explores the solution uniqueness of the data-driven
modeling of price-responsive flexible loads (PFL). The PFL on the demand side
is critical in modern power systems. An accurate PFL model is fundamental for
system operations. Yet, whether the PFL model can be uniquely and correctly
identified from operational data remains unclear. To address this, we analyze
the structural and practical identifiability of the PFL model, deriving the
condition for the solution unique-ness. Besides, we point out the practical
implications of the results. Numerical tests validate this work.
