Decoupled three-phase load flow method for unbalanced distribution systems

This paper proposes a decoupled three-phase load flow analysis method for unbalanced distribution systems. The power flows are solved through nodal current injection mismatch equations written in rectangular coordinates. The voltage changes resulting from nodal current injection mismatches and nodal admittance matrix have been decoupled into one contribution from the real part, conductance matrix, and the other contribution from the imaginary part, susceptance matrix. The method determines voltage changes resulting from conductance and susceptance matrices respectively, and determines the voltages of a node as a linear combination of those voltage changes. The relative contributions are determined based on the diagonals of the conductance and susceptance matrices. The constant active power and voltage magnitude(PV) nodes have been converted into constant active and reactive power(PQ) ones based on a sensitivity matrix determined through Kron reduction of the nodal admittance matrix, and the corresponding reactive powers are adjusted after each solution has converged. The zero-impedance branches are merged with adjacent impedance branches, and the three phases of a balanced-voltage PV bus are merged into one single-phase PV bus to be modeled in the nodal admittance matrix. Numerical examples on IEEE 37 node test feeder and IEEE 123 node test feeder are presented to demonstrate the effectiveness of the proposed method.