This paper describes a new class of system identification procedures that are tailored to electric power systems, in particular to synchronous generators (SGs) and other dynamic components. Our procedure builds on computational advances in differential geometry, and offers a new, global characterization of challenges frequently encountered in system identification of electric power systems. The approach also benefits from increasing availability of high-quality measurements. While the proposed procedure is illustrated on SG example in a multimachine benchmark (IEEE 14-bus and real-world 441-bus power systems), it is equally applicable to identification of other system components, such as loads.