Pattern similarity-based phase identification problem formulation for medium voltage distribution networks

In this work, we propose an enhanced phase identification method to support distributed energy resources management in a medium voltage network. The problem is formulated with the objective function of minimizing the sum of the modified Kirchhoff’s Current Law at the branch node and power-current pattern similarity. This combined objective function is then linearized by introducing auxiliary variables and subsequently resolved through Mixed-Integer Linear Programming. A permutation matrix is employed to establish a correlation between the magnitudes of electrical currents across distinct phases, achieved through manipulation based on empirical data. Subsequently, by comparing this matrix with the observed magnitudes of currents, the approach facilitates the deduction and identification of phase information inherent in the electrical signals. Consequently, the permutation matrix functions as decision variables to identify the phases of currents for wye-connected loads, delta-connected matrices for delta-connected loads, and percentage matrices for aggregated multi-phase loads. The proposed method is applied to a dataset obtained from real power consumption with one-hour resolution, and validation is conducted through several case studies considering scenarios with and without power pattern similarity on IEEE 13, IEEE 34, and IEEE 123 test feeders, followed by comparative analysis against the correlation coefficient and Euclidean based methods. This demonstrates the robustness and practicality of the proposed method by exhibiting superior accuracy compared to the state-of-the-art method across diverse environments.