Energy Systems manuscript No. (will be inserted by the editor) Optimal Power Flow: A Bibliographic Survey I Formulations and Deterministic Methods Stephen Frank · Ingrida Steponavice · Steffen Rebennack Received: date / Accepted: date Abstract Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and con- trol limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic opti- mization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF. Keywords electric power systems · optimal power flow · optimal power flow formulations · optimal power flow requirements · deterministic optimization · global optimization · nonlinear optimization · survey Stephen Frank Colorado School of Mines Division of Engineering 1500 Illinois St., Golden, CO, 80401, USA E-mail: stfrank@mymail.mines.edu Ingrida Steponavice University of Jyvaskyla Department of Mathematical Information Technology E-mail: ingrida.steponavice@jyu.fi Steffen Rebennack Colorado School of Mines Division of Economics and Business 1500 Illinois St., Golden, CO, 80401, USA E-mail: srebenna@mines.edu