【正文】 ion of induction motors for transient stability load modeling， ” IEEE Trans. Power Syst.， ， pp. 1096– 1102， Nov. 1987. [17] D. P. Molenaar， “Cost effective design and operation of variable speed wind turbines， ” . dissertation ， Delft Univ.， Delft， The Netherlands，2021 附錄 Ｂ FixedSpeed WindGenerator and WindPark Modeling for Transient Stability Studies Abstract Increasing levels of windturbine generation in modern power systems is initiating a need for accurate windgeneration transient stability models. Because many wind generators are often grouped together in wind parks， equivalence modeling of several wind generators is especially critical. In this paper， reducedorder dynamic fixedspeed windgenerator model appropriate for transient stability simulation is presented. The models derived using a model reduction technique of a highorder finiteelement model. Then， an equivalency approach is presented that demonstrates how several wind generators in a wind park can be bined into a single reducedorder model. Simulation cases are presented to demonstrate several unique properties of a power system containing wind generators. The results in these paper focuson horizontalaxis turbines using an induction machine directly connected to the grid as the generator. Index Terms—Transient stability simulation， windgenerator modeling， windpark modeling， windturbine modeling. I. INTRODUCTION RECENTLY， windenergy development has experienced significant level of interest. The rise in the use of wind generators is acpanied by a need to evaluate their impaction powersystem dynamics for electrical power transmission planning. The first goal of this paper is to present an accurate loworder dynamic model of a wind generator which inpatible with modern electromechanical transient simulation puter programs. The model developed here focuses on horizontalaxis， upwind， or downwind machine directly connected to the synchronous grid using an induction generator. This enpasses many modern largescale systems. Because large wind installations consist of many wind generators， windparkmodeling is a critical need. Consequently， the second goals to present a methodology for bining several wind generators connected to the grid through a mon bus into a single equivalent model. Wind generators are primarily classified as fixed speed or variable speed. With most fixedspeed units， the turbine drives an induction generator that is directly connected to the grid. The turbine speed varies very little due to the steep slope of the generator’s torquespeed characteristic； therefore， it is termed fixedspeed system. With a variablespeed unit， the generator is connected to the grid using powerelectronic converter technology. This allows the turbine speed to be controlled to maximize performance (.， power capture). Both approaches are Manuscript received February 3， 2021. This work was supported in part by the Western Area Power Administration. Paper no. TPWRS003882021. The authors are with Montana Tech， University of Montana， Butte， MT59701 USA ( ).Digital Object Identifier ， we focus on modeling the fixedspeed unit and an equivalent model of several Fixedspeed units in a wind park. The firstmode mechanical frequency of a typical wind turbines in the 0 to 10Hz range； This is also the range for electromechanicaloscillations. Consequently， the mechanical vibrations of the wind turbine interact with the electromechanical dynamics. Examples of this interaction are shown in this paper. Therefore， in order to create an accurate model of a wind generator to be used in transient stability studies， the firstmode mechanical turbine dynamics must be accurately represented. The windgenerator model presented here is derived by conducting model reduction on a detailed 650thorder finiteelement model of a typical horizontalaxis turbine. Aerodynamic and mechanical dynamics are reduced resulting in a nonlinear4thorder twoinertia turbine model bined with a standard generator model. Simulations are presented to demonstrate the accuracy of the model. A wind park consists of several wind generators connected toothed transmission system through a single bus. Because modeling each individual turbine for transient stability is overly cumbersome， our goal is to lump the wind park into a minimal setoff equivalent windgenerator models. Our approach for equivalence modeling of a wind park involves bining all turbines with the same mechanical natural frequency into a single equivalent turbine. Simulation results demonstrate this approach provides accurate results. II. PREVIOUS RESULTS A representative example of published results for modeling wind generators for transient stability is contained in [2]–[10].Results for modeling fixedspeed wind generators have focused on two primary approaches. The first approach represents the turbine and generator rotor as a single inertia thus ignoring the system’s mechanical natural frequency [2]–[5]. The second approach represents the turbine blades and hub as one inertia connected to the generator inertia through a spring [6]–[9]. In all of these papers， the spring stiffness is calculated from the system’s shaft. Our research indicates that representing the firstmode mechanical frequency is critical to an accurate model. Finiteelement analysis has shown that the firstmode dynamics are primarily a result of the flexibility of the turbine blades not the shaft as assumed by others [11]. The modeling approach presented in this paper centers on the fact that the primary flexible mechanical ponent is the turbine blade. The results in [7] focus on reducedorder windpark modeling. The authors use a standard induction generator equiva08858950/04$