  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.
