【正文】 ig. 2). If the blade is not broken at the correct position， then the mechanical mode shape will not be correct. The break point is primarily a function of the blade mechanics and can be determined from finiteelement analysis or testing of the blade and seems to occur at the second bending node of the blade. In the example cases studied in [12]， the reducedorder system’s sensitivity to improper placement of the break point is significant. This is demonstrated in the example section. Fortunately， most modern blade manufactures or blade testing facilities (such as the facility at the National Renewable Energy Laboratory in the United States) have the required information to determine the blade break point. The power engineer simply needs to request this information. Once one has the blade break point， the inertia parameters can easily be calculated from typical manufacture’s data. The stiffness in (1) can be calculated from knowledge of the system’s firstmode mechanical natural frequency using(2)where is the firstmode mechanical leadlag natural frequency with the system connected to infinite bus. For example， in the system in the previous section， .Typically， manufactures can provide this frequency. It can be easily calculated by applying a brake pulse on the turbine and analyzing its response (for example， Fourier analysis of the generator’s speed). In most cases the blade damping is very small and assumed to be zero. The spring stiffness is a measure of the blade’s stiffness in the rotational plane which is a bination of the blade’s edge stiffness and flat stiffness [12]. Relating to the edge and flat results in(3)where is the edge stiffness， is the flat stiffness， and is the pitch angle. Both and are constant. As can be seen in(3)， is dependent on the pitch angle . Typically， is limited to be between zero and ten degrees. Analysis of (3) under this restriction shows that varies very little for different pitch set points. This implies， and experiments support， that the accuracy of the turbine model has very small sensitivity to variations in the system’s pitch angle [12].The wind torque is calculated assuming an ideal rotor disk from the equation [13](4)where is the velocity of the blade tip sections reflected through the gearing， is the air density， is the sweep area of the blades， is the free wind velocity， and is the turbine’s power coefficient. Unfortunately， is not a constant. However， the majority of turbine manufactures supply the owner with a curve. The curve expresses as a function of the turbine’s tipspeed ratio. Tipspeed ratio is defined to be the ratio of the turbine blade’s tip speed to the free winds velocity； it is expressed as(5)where is the unit less tipspeed ratio and is the blade sweep radius. Fig. 3 shows a curve for a typical wind turbine. Our research has shown that for transient stability studies， can be assumed constant except under extremely high wind conditions [14]. This is because the typical variation of the tipspeed ratio under a 10 second transient simulation is very small [14]. This1914 IEEE TRANSACTIONS ON POWER SYSTEMS， VOL. 19， NO. 4， NOVEMBER 2021 assumes that the wind does not significantly change over the simulation time period. The torque that is induced on the turbine shaft is actually a modulated version of (4). The modulation is well known and is caused primarily by tower shadowing and unbalanced mechanics. Typical modulation frequencies are at the 1P and 3Pmodes (note: 1P is once per revolution of a turbine blade) [6].We do not include these effects as we assume that the torque induced from the transient fault is much larger than the modulation torque. This assumption has been made by many other researchers (for example， [7]). Future research will focus on testing this assumption. In general， the twoinertia turbine model proposed here is a relatively robust model that covers many turbine operating conditions. All model parameters are relatively constant with very little sensitivity to the pitch angle. Because the main ponent of energy in a transient is due to turbine inertial energy， stallcontrolled turbines can be accurately modeled using this approach’s. Generator Model Standard practices are well established for modeling the generator [1]. A standard detailed twoaxis induction machine model is used to represent the induction generator [1]. The resulting equations are(6a) where is the transient opencircuit time constant， is the slip speed， is the synchronous reactance， is the transient reactance， and are the daxis and qaxis stator voltages， and are the daxis and qaxis perunit stator currents. The torque is calculated from(6b) TRUDNOWSKI et al.: FIXEDSPEED WINDGENERATOR AND WINDPARK MODELING FOR TRANSIENT STABILITY STUDIES where is the sweep area， is the free wind velocity， and is the turbine’s power coefficient for turbine .B. Equivalent Generator Model The equivalence induction generator parameters are obtained using the weighted admittance averaging method in [16]. With this method， the equivalent machine parameters ， ， and are calculated by taking the weighted average admittances of each branch of the induction machine equivalent circuit. The weighting for the averages are calculated using the rated power of the generators. I. SIMULATION RESULTS Many example test cases have been studied to evaluate the properties of the modeling approach； these are contained in [12]， [14]， [15]. A select few are presented in this section. A. Example 1 For this example， we pare the response of the twoinertia reducedorder turbine in (1) to the response of the finiteelement model and a detailed fiveinertia model. Each model is connected to an infinite bus through an。 外文翻譯 附錄 A 固定風(fēng)力發(fā)電機和風(fēng)力集成園建模系統(tǒng)暫態(tài)穩(wěn)定性的研究 緒論 抽象程度越來越高的風(fēng)力 發(fā)電 渦輪機 ，在現(xiàn)代電力系統(tǒng) 中 需要 一項 準(zhǔn)確的風(fēng)力發(fā)電