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.

Typical formulations of the optimal power flow (OPF) problem rely on what is termed the "bus-branch" model, with network electrical behavior summarized in the Ybus admittance matrix. From a circuit perspective, this admittance representation restricts network elements to be voltage controlled and limitations of the Ybus have long been recognized. A fixed Ybus is unable to represent an ideal circuit breaker, and more subtle limitations appear in transformer modeling. In power systems parlance, more detailed approaches to overcome these limitations are termed "node-breaker" representations, but these are often cumbersome, and are not widely utilized in OPF. This paper develops a general network representation adapted to the needs of OPF, based on the Sparse Tableau Formulation (STF) with following advantages for OPF: (i) conceptual clarity in formulating constraints, allowing a comprehensive set of network electrical variables; (ii) improved fidelity in capturing physical behavior and engineering limits; (iii) added flexibility in optimization solution, in that elimination of intermediate variables is left to the optimization algorithm. The STF is then applied to OPF numerical case studies which demonstrate that the STF shows little or no penalty in computational speed compared to classic OPF representations, and sometimes provides considerable advantage in computational speed.