IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 1, MARCH 2003 121 Synchronous Generator Model Identification and Parameter Estimation From Operating Data H. Bora Karayaka, Ali Keyhani, Fellow, IEEE, Gerald Thomas Heydt, Fellow, IEEE, Baj L. Agrawal, Fellow, IEEE, and Douglas A. Selin, Senior Member, IEEE Abstract—A novel technique to estimate and model parameters of a 460-MVA large steam turbine generator from operating data is presented. First, data from small excitation disturbances are used to estimate linear model armature circuit and field winding pa- rameters of the machine. Subsequently, for each set of steady state operating data, saturable inductances and are identified and modeled using nonlinear mapping functions-based estimators. Using the estimates of the armature circuit parameters, for each set of disturbance data collected at different operating conditions, the rotor body parameters of the generator are estimated using an output error method (OEM). The developed nonlinear models are validated with measurements not used in the estimation procedure. Index Terms—Armature circuit and rotor body parameters, large utility generators, parameter identification. I. INTRODUCTION P ARAMETER identification from operating data for syn- chronous generators is a beneficial procedure which does not require any service interruption to perform. Thus, machine parameters, which can deviate substantially from manufacturer values during online operation at different loading levels, can be determined without costly testing [1]. These deviations are usually due to magnetic saturation [2]–[4], internal temperature, machine aging, and the effect of centrifugal forces on winding contacts and incipient faults within the machine. References [5]–[7] include investigations into modeling synchronous gen- erator parameters as a function of operating condition. In most of these studies, the independent variables used in modeling nonlinear variations of the parameters are primarily the terminal voltage, current, or a combination of these quantities including the phase angle. A similar study can be found in [7] and [8] for a small round rotor synchronous generator. In this study, disturbance data sets acquired online at dif- ferent loading and excitation levels of a large utility generator are used to identify the machine parameters. It is assumed that the machine model order is known (i.e., the number of differ- ential equations). Estimated machine parameters for each oper- ating point are then mapped into operating condition-dependent machine variables using nonlinear mapping functions. The non- Manuscript received July 17, 2000; revised October 26, 2001. This work is supported in part by the National Science Foundation, Grant ECS9722844. H. B. Karayaka and A. Keyhani are with Department of Electrical Engi- neering, Ohio State University, Columbus, OH 43210 USA G. T. Heydt is with Arizona State University, Tempe, AZ 85287 USA B. Agrawal and D. Selin are with Arizona Public Service Company, Phoenix, AZ 85062 USA Digital Object Identifier 10.1109/TEC.2002.808347 Fig. 1. Online model structure. linear mapping [7] can easily identify the shape of the nonlinear function from training data. Therefore, no apriori knowledge of the shape of the mapping is required. The effects of gener- ator saturation, rotor position, and loading are included in the mapping process. Finally, validation studies are conducted to investigate the performance of nonlinear mapping models and estimated parameters. II. MACHINE MODEL DESCRIPTION AND PROBLEM FORMULATION The structure of the synchronous machine model used in this study is a model 2.1. type [1], with one damper in the -axis and one damper in the -axis, given in Fig. 1. For continuous time systems, the state space representation of this model is (1) where and represent the process and measurement noise. Also, see the equation at the bottom of the next page. All parameters are in actual units. Also, it is assumed that the ma- chine power angle is available for measurement. Variables , , , and represent generator - and -axis terminal voltages and currents, respectively. The quantities and represent field current and field voltage, respectively, as measured on the field side of the generator and is the field winding resistance as measured on the field side. Terms , , and represent 0885-8969/03$17.00 © 2003 IEEE