The Formulation of a Power Flow Using <inline-formula> <tex-math notation="LaTeX">$d-q$</tex-math> </inline-formula> Reference Frame Components—Part I: Balanced <inline-formula> <tex-math notation="LaTeX">$3\phi$ </tex-math> </inline-formula> Systems

Abstract

This paper develops a new approach for formulating the power flow for power systems. The developed approach is based on expressing the active and reactive power injections at each bus in a power system using the d-q-axis components of bus voltages and admittance matrix. The new power flow formulation produces a scaled Jacobian matrix, which can offer a fast convergence to the solution. The proposed power flow formulation can also model bus type conversions without affecting its accuracy or fast convergence. In addition, the d-q-axis power flow (DQPF) offers a simplified and reliable representation of photovoltaic buses that have distributed generation units (DGUs). The DQPF is implemented with a step-by-step procedure for performance evaluation on several power systems operated at different conditions. Performance results demonstrate fast convergence, reduced computations, and minor sensitivity to the number of buses, loading conditions, and levels of DGU penetration. Furthermore, performance results show that DQPF power flow can attain solutions in less iterations than Newton-Raphson, Fast Decoupled, and Iwamoto power flow methods.