Data-Driven Estimation of Transmission Loss Coefficients via Linear and Quadratic Programming Under Linear Constraints

This paper presents a robust data-driven methodology for estimating transmission loss coefficients (B-coefficients) in power systems using linear and quadratic programming (LP and QP), both of which belong to the family of convex optimization models. The first model employs a linear objective function with linear constraints, ensuring computational efficiency for simpler scenarios. The second model utilizes a quadratic objective function, also under linear constraints, to better capture more complex nonlinear relationships. By framing the estimation problem as a parameter identification task, both methodologies minimize the cost functions that quantify the mismatch between measured and modeled power losses. By considering a broad range of operational scenarios, our approach effectively captures the stochastic behavior inherent in power system operations. The effectiveness of both the LP and QP models is validated in terms of their ability to accurately extract physically meaningful B-coefficients from diverse simulation datasets. This study underscores the potential of integrating linear and quadratic programming as powerful and scalable tools for data-driven parameter estimation in modern power systems, especially in environments characterized by uncertainty or incomplete information.