Sparse Tableau Approach for Power System Analysis and Design

Textbook treatments of the power flow and related problems are almost universally based on the bus admittance matrix Y
_bus
, representing a choice of nodal analysis for the circuit equations. Many texts further simplify their presentation by insisting that all network components be represented in equivalents that are interconnections of two-terminal circuit elements; e.g., the pi-equivalent for transmission lines, the star-equivalent for three-winding transformers. The combined restrictions of nodal analysis and two-terminal elements disallow more general ideal circuit elements that could serve as useful modeling building blocks. This work will argue that these are unnecessary limitations that have outlived their usefulness in modern power system pedagogy. While research literature has often overcome these limitations with Modified Nodal Analysis, here we instead advocate Sparse Tableau Analysis (STA) as a general tool for power system instruction, with particular value in facilitating node-breaker models. Illustrative examples show that these concepts are easily accessible, and allow more systematic formulations to facilitate graduate research. As an application benefiting from this approach, STA is applied to Optimal Power Flow, with numerical examples to demonstrate that STA provides computational speed comparable to nodal analysis Y
_bus
based formulations.