# Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis
## 1 Introduction  
Transients are the time intervals that occur when a system is transiting from one steady state to another. Such a time interval can be understood as the time of adaptation by all system parameters to the new conditions in the network. Electromagnetic transients occur in the windings of electrical machines after a disturbance, the activation of a protective system, or the interaction between electrical machines and the network. The duration of transients is from milliseconds to seconds. Electromechanical transients refer to changes in speed and torques in the rotating parts of electrical machines and turbines. These transients are slower, and last from a second to a few seconds. Understanding the details of transients is very important in the proper design of all parts of a power system, including synchronous generators, which are an integral part of a power system [1]. Early models for calculating parameters that occur during transients consisted of simple analytical expressions, included many simplifications, and were only used in some special cases. From a general model of electrical machines [2] that can be represented by equivalent circuits, dynamic models have been developed for certain types of electrical machines. These models consist of systems of differential equations that are solved numerically for given initial conditions, mainly in the time domain. The application of these systems became possible after computers reached a stage of development that provided the solutions in a relatively short time. Dynamic models have significantly increased the precision of the results. However, the accuracy of these models still dependson how precisely the parameters of the equivalent circuit are calculated. The parameters are still determined by analytical methods or measured on a built-in generator. In these models, it is usually assumed that the parameters of the electrical machine are constant. The variability of the parameters is considered only in models that are more complex. The variability in parameters is mainly caused by saturation and by the shape of the air gap; the skin effect in conductors could also have a significant influence. Nowadays, very sophisticated methods are used to calculate the parameters of electrical machines, including those in transient processes. These methods are based on numerical calculations in determining the electromagnetic field. Specialized software, such as the MagNet software package [3], was developed for such modeling using the finite element method (FEM), as presented here. The application of this software requires an approach that includes setting the electrical and magnetic characteristics of the materials from which the machine is made, building a solid model, and defining the conductors and their connections to the electrical circuits. Finally, it is necessary to define a finite element network, which can be a very time-consuming process. The parameter estimation of a model synchronous generator is analyzed in [4; 5; 6; 7; 8]. A two-dimensional (2D) time-stepped FEM is used to model three-phase short-circuit test responses on large hydro generators [4]. The authors in [5] describe the application of a 2D model based on the Gaussian Modulated Sinusoidal Pulse (GMSP), validated by comparing the simulation results with the experimental data from a sudden three-phase short-circuit fault. The parameters for standard test procedures, such as the three-phase short-circuit test, have been implemented in time-stepping finite element software in [6] and validated by comparison with test results from the commissioning of a large hydropower generator. The rotor of a large turbo generator is modeled using the FEM with solid, hollow, and tapered elements in [7; 8]. Different types of faults were simulated and analyzed in MATLAB: line-to-ground (L-G), line-to-line (L-L), three-phase (L-L-L), and loss of synchronism. The most severe outcomes occurred during three-phase short-circuit testing.