Rectangular Branch-Based Load Flow

Power of constant impedance load is proportional to the square of bus voltage magnitude (SBVM). A solution space for a set of power balance equations (PBEs), constructed using SBVMs, has lower-order terms and less non-linearity. Such solution space yields faster solution. This work proposes a set of rectangular PBEs which uses SBVMs in conjunction with bus phase angles to relate branches power flow, a pair of real and reactive power equations for each branch for sending/receiving ends. Using an incidence matrix, branches power flows are related to bus powers with two set of equations for real and reactive powers. Another set of equations to relate rectangular form of voltages at generators to their voltage magnitudes, the total number of equations equals four times branches number, and two times buses number, less the two for unknown powers of slack bus. While the equations number is more than the node-based PBEs, order of Jacobian's terms is significantly lower. Testing the proposed algorithm on numerous case studies, up to a 9241-bus real system, showing the algorithm is precise, has superior convergence features, scales well for real systems and is up to thrice as fast as the rectangular node-based load flow for some cases.