Linear optimal power flow (LOPF) formulations use a linearization of the AC load flow equations. The common formulation uses voltage angles at the buses as auxiliary optimization variables, but alternatives can be computationally advantageous.
It is possible to circumvent the auxiliary voltage angle variables by expressing Kirchhoff’s voltage law based on a cycle basis of the network graph. In computationally challenging benchmarks such as multi-period LOPF with storage dispatch and generation capacity expansion, this formulation incurred speed-ups by an order of magnitude.
Including transmission expansion planning (TEP) adds to the problem complexity as it is bilinear (unless using a big-M disjunctive relaxation) due to the dependence of line expansion on line impedance and nonconvex because of a discrete set of line expansion options.
This talk will guide through a derivation of a cycle-based mixed-integer linear formulation of the transmission expansion planning (TEP) problem instead of using an angle-based formulation and will motivate why it is necessary for spatially and temporally resolved energy system models that co-optimize generation, transmission and storage infrastructure.