Electric Machines and Power Systems, 28:761–777, 2000 Copyright c s 2000 Taylor & Francis 0731-356X/ 00 $12.00 + .00 Parameter Estimation Using A n Orthogonal Series Expansion J. RICO University of Michoac ´ an Morelia, M´ exico G. T. HEYDT Arizona State University Tempe, AZ This paper presents an innovative alternative to estimate parameters of a sys- tem for which a dynamic model is known. The focus of this paper is the esti- mation of the armature circuit parameters of large utility generators using real time operating data. Other applications are possible. The alternatives consid- ered are the use of orthogonal series expansions, in general, and the Hartley series, in particular. The main idea considers the use of orthogonal series ex- pansions for tting operating data ( e.g., voltage and currents measurements) . This allows writing a set of linear algebraic equations that can be “solved” in the least squares sense for the unknown parameters. The method shown utilizes the pseudoinverse in the solution. The essence of the approach is linear state estimation. Several alternative types of orthogonal expansions are briey dis- cussed. Although solutions are the same in all domains, one wishes to employ the expansion that gives the most e cient computation. The approach may be used for static as well as dynamic problems. The approach is tested for noise corruption likely to be found in measurements. The method is found to be suit- able for the processing of digital fault recorder data to identify synchronous machine parameters. 1 Introduction The use orthogonal series expansions are well-known alternatives for approximation and representation of functions. These series may also be used to establish algebraic methods for the solution of problems described by di Œerential equations, such as analysis of linear time-invariant and time-varying systems, model reduction, optimal control, and system identication. The problem of parameter identication using orthogonal includes linear time-invariant lumped and distributed systems [ 1 ] , linear time-varying lumped and distributed systems [ 2–3 ] , and nonlinear systems [ 4–5] . The utilization of this series has the common objective of representing models e ciently and calculating intermediate parameters rapidly for the given problem. Transformed domains are popular in engineering calculations. Mathematicians who rst proposed these domains referred to them as “ images” (in French) because the transformed functions were maps or images of the original (usually time) func- Manuscript received in nal form October 19, 1999. Address correspondence to Dr. G. T. Heydt. 761