Benefits of Sparse Tableau Over Nodal Admittance Formulation for Power-Flow Studies

Assembly of power-flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit's behavior. Most power-flow formulations encapsulate network constraints in the bus admittance matrix, <inline-formula><tex-math notation="LaTeX">$Y_{\text{bus}}$</tex-math></inline-formula>. From a circuit perspective, this admittance representation restricts the network elements to be voltage controlled; resulting drawbacks treating zero-impedance branches in such applications as state estimation have long been recognized. This paper explores the advantages of the alternatives to <inline-formula><tex-math notation="LaTeX">$Y_{\text{bus}}$</tex-math></inline-formula>-based formulations in power flow. It proposes a sparse tableau formulation (STF), and it demonstrates its computational efficiency, robustness, and generality in detailed comparison to traditional <inline-formula><tex-math notation="LaTeX">$Y_{\text{bus}}$</tex-math></inline-formula>-based solution algorithms. In the examples of power networks ranging from 1888 to 82 000 buses, computational case studies indicate that STF provides comparable computational speed, while allowing simple treatment of zero-impedance branches and more reliably converging to solutions in many cases for which <inline-formula><tex-math notation="LaTeX">$Y_{\text{bus}}$</tex-math></inline-formula>-based Newton algorithms diverge.