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.
