A new linearization method of unbalanced electrical distribution networks

With increasing penetration of distributed generation in the distribution networks (DN), the secure and optimal operation of DN has become an important concern. As DN control and operation strategies are mostly based on the linearized sensitivity coefficients between controlled variables (e.g., node voltages, line currents, power loss) and control variables (e.g., power injections, transformer tap positions), efficient and precise calculation of these sensitivity coefficients, i.e. linearization of DN, is of fundamental importance. In this paper, the derivation of the node voltages and power loss as functions of the nodal power injections and transformers' tap-changers positions is presented, and then solved by a Gauss-Seidel method. Compared to other approaches presented in the literature, the proposed method takes into account different load characteristics (e.g., constant PQ, constant impedance, constant current and any combination of above) of a generic multi-phase unbalanced DN and improves the accuracy of linearization. Numerical simulations on both IEEE 13 and 34 nodes test feeders show the efficiency and accuracy of the proposed method.