【英文】波动转矩下风电厂的短路研究.pdf

1 Abstract Wind power plants are now being paid more and more attention from the environmental point of view They are sometimes built remote from other power plants which implies that the fault current distribution becomes different from before Although induction generators which still cover major part of wind power plants do not have independent back voltage they behave as transient sources of fault current during the critical time range From this point of view fault analysis considering the contribution of wind farm is an important issue Recently many wind power plants take form of wind farms groups of many wind power sources which compensates non deterministic random variation inherent in wind fluctuation But most of the research works done in the field of electrical characteristics of wind power plants do not consider this effect This paper studies short circuit current fed from induction generators taking into account the random fluctuation of wind and its compensation by grouping them Index Terms wind farm short circuit calculation power system probabilistic variation I INTRODUCTION ind power generation has now become the center of public attention due to its low environmental cost They are steadily being built mostly at the site of good wind condition such as seaport isolated island etc According to the Ministry of Land Infrastructure and Transport of Japan in March 2005 the total output capacity of them built near harbor facilities has reached as much as 76MW 1 In respond to this trend vigorous efforts are being made also in the field of their research In the field of power systems technical analysis or control generally speaking attention has been paid mostly to the following two points so far One is the starting problem and the other is their steady state characteristics The starting problem occurs in case of application of induction generators which require large reactive power in the starting process leading to severe voltage sag A grid friendly connection method has been proposed using external resistors which enabled installation of constant apeed wind turbines to weaker systems 2 One of the most important difficulties in treating wind power in steady state power systems is always its fluctuation Variation in wind the primary driving power makes the output power T Kumano e mail kumano isc meiji ac jp is with Meiji University Kawasaki 214 8571 Japan vary and voltage quality deteriorates in case of weak connection The effect of variable speed wind turbines on the operation of weak distribution networks are studied on simulation basis 3 which concludes that the variable speed turbines can make power quality higher in the sense of voltage fluctuation and harmonic content Not so many works have been done in short circuit analysis of wind power plants except those for the purpose of protection 4 and fatigue life evaluation in the mechanical sense 5 As far as the author knows big efforts have not been made so far to clarify the short circuit current contribution of wind power plants from the viewpoint of power system analysis One of the reasons might be that the majority of the wind power plants tend to be constructed remote from the demand center which means that electrical distance between them and the other part of the power system is rather long Needless to say long electrical distance makes voltage variation bigger but short circuit problem smaller However wind power plants will be able to give more and more significant effects on the calculation of short circuit current in future power system operation The reason is twofold One is the above stated fact that wind generation site is usually apart from the conventional electrical power center It implies that the distribution of short circuit current might make a drastic change leading to a completely different short circuit capacity map The other reason is the fact that more and more wind power plants are being built today particularly in the form of so called wind farm In wind farms a substantial number of individual units are connected together and the total generation capacity will greatly rise up This paper studies the short circuit current fed from a wind farm Although variable speed or double fed types and synchronous machine AC link types have begun to be adopted more and more this paper assumes induction generator type because it is still the majority of the wind generation plants Unlike a conventional short circuit calculation of an induction generator the effect of different mechanical input variation in individual unit is taken into account It is often said that the total output from wind farm is to some extent better than the output from a single generation unit However in the sense of short circuit study the above stated effect will be called group effect in the present paper is not firmly established It is also studied how and on what condition such a group effect can be observed in short circuit current Calculation is based on simulation but the actually obtained power variation A Short Circuit Study of a Wind Farm Considering Mechanical Torque Fluctuation Teruhisa Kumano Member IEEE W 1 4244 0493 2 06 20 00 2006 IEEE 2 data 6 are used In the present paper neglecting the mechanical controls such as pitch control the shaft input torque is assumed to be given for the purpose of focusing on the electric characteristics of the generators II SHORT CIRCUIT CURRENT FED FROM INDUCTION GENERATOR A Model System A three node model system depicted in Fig 1 is used throughout the present paper A wind farm consists of n individual induction generators the electrical constants of which are identical Each units is connected together at the lower voltage terminal of the step up transformer the leakage reactance is Xt assumed 0 08pu of its own capacity which is 1 1 times larger than total capacity of the generating units The transformer is connected to the main system via tie line the impedance of which is Rs jXs Short circuit fault is assumed to take place at the high voltage terminal of the transformer because it is the severest fault for the wind farm occurring in transmission system and also because it suffices the objective of the present analysis to study the group behavior In many cases reactive compensation such as shunt capacitors are installed near the induction generators in order to supply reactive power required but they are neglected for simplicity Neglecting them does not make any considerable effects in the discussion unless they cause instability such as electrical resonance B Short Circuit from a Single Induction Generator A single induction generator case is studied in order to examine the short circuit current maximum and time constant large power system jXtRs jXs 1 2 n VsV Rs 0 143pu 1000MVAbase Xs 1 608pu 1000MVAbase Fig 1 Model system Note that Vs is constant because the power system is very large 0 0 5 1 1 5 2 2 5 3 3 5 4 00 511 5 Time sec Current pu Fig 2 An example of short circuit current fed from a single induction generator In calculating the short circuit current the following equations are solved which is directly given by the two axis theory 7 under the condition that the transformer voltage is negligibly small compared to the speed voltage 2 22 2 22 2 11 2 2 22 2 22 2 11 2 2 22 2 22 0 0 m RXRR mlml ml olXR ml m XRXX mlml ml olRX ml m RoXRR mlml XoR R XR vi XX XX X X X iRi XX R XR vi XX XX X X X iRi XX R XR p i XX XX p 2 22 2 22 m XX mlml R XR i XX XX 1 where R i and X i stand for the stator current of the induction generator The last two equations describe electrical dynamics inside the generator The obtained result is shown in Fig 2 The maximum short circuit current is as much as 3 5pu which is equal to internal voltage 0 89pu see Fig 3 series reactance where series reactance is 0 251pu as easily calculated from the data given in Table I The decaying time constant can be easily observed to be around 0 1sec which is near the calculated value 0 127sec 0 0 2 0 4 0 6 0 8 1 00 511 5 Time sec Internal voltage pu Fig 3 Internal voltage obtained in the same case as in Fig 2 TABLE I MACHINE CONSTANTS rated capacity MVA 1 14 rated output MW 1 0 nominal slip 0 91 primary resistance R1 pu 0 0063 primary leakage reactance X1 pu 0 089 secondary resistance R2 pu 0 0095 secondary leakage reactance X2 pu 0 092 mutual reactance Xm pu 2 85 inertia constant sec 2 0 3 From this result the following two remarks can be easily obtained 1 Time constants are fixed even when the mechanical input power varies because they are determined by the configuration of the wind farm 2 Maximum magnitude of short circuit current can be changed in proportion to the variation of internal voltage III NUMERICAL EXAMPLE CONSIDERING WIND VARIATION IN A BASE CASE A Assumed variation Numerical calculation is conducted using the wind variation data given in 6 Reference 6 gives spectrum of wind variation whose period ranges from 1 sec to several hundred sec The present paper picks up six typical frequency components and the simulations are done under the condition as shown in TABLE II in which phase diff stands for the difference between the phases of each component measured at the both units located at the very ends of the wind farm The phase difference data is not given in 6 and the present paper assumes these values on the basic consideration that the rapid component can take various phases in the same wind farm but not in slow components Fig 4 shows the waveforms of the assumed variation in mechanical input torque at four locations in the wind farm As shown in Fig 4 the variation of the mechanical input torque is almost in phase or coherent The resultant internal voltage variation is shown in Fig 5 TABLE II ASSUMED COMPONENTS OF WIND VARIATION period sec magnitude pu phase diff deg 200 0 0 1 0 100 0 0 025 10 50 0 0 01 20 20 0 0 003 30 10 0 0 00075 60 5 0 0 0002 180 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0100200300400500600 Time sec Mechanical torque pu Fig 4 Assumed variation in mechanical torque due to wind fluctuation 0 86 0 865 0 87 0 875 0 88 0 885 0 89 0 895 0 9 390440490540590 Time sec Internal voltage pu Fig 5 Obtained variation in the internal voltage at 4 different locations 0 0 5 1 1 5 2 2 5 3 3 5 4 443443 5444444 5445 Time sec Current pu Fig 6 Short circuit current in case of short circuit at t 444sec 0 0 5 1 1 5 2 2 5 3 3 5 4 555555 5556556 5557 Time sec Current pu Fig 7 Short circuit current in case of short circuit at t 556sec 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 390490590 Time sec Electrical power pu Fig 8 Electrical output power variation in the studied case 4 B Result Based on the result of the preliminary study in chapter II we have only to take a close look into the variation of the internal voltage Fig 5 It can be expected that the minimum and maximum short circuit currents would be obtained when fault occurs at t 444sec internal voltage takes minimum value and t 556sec internal voltage takes maximum value respectively It is true that the current in the former case Fig 6 is somewhat less than the latter Fig 7 but the difference effect is very small This is because the variation in the internal voltage is too small to produce considerable effects In fact the difference between the maximum and the minimum internal voltages in this case is only around 1 7 This corresponds to the result that the magnitude of the short circuit current in the two cases are 3 52pu and 3 46pu Here observed is that the internal voltage does not vary much even when the output power greatly varies Fig 8 leading to the small effects on short circuit current magnitude The variation of the internal voltage is affected by the series reactance In case of heavily loaded long transmission line it can be expected that the internal voltage changes considerably IV PARAMETER STUDIES A Objective of the study From the discussions given above it has been clarified that the short circuit current does not differ much no matter when the fault occurs under the existence of wind fluctuation in usual cases It implies that even in the case of incoherent wind fluctuation at individual generating unit short circuit current supply from each takes almost the same amount However from the last statement in Chapter III it is not always the case that the internal voltage does not vary largely particularly in case of long and heavily loaded transmission In this chapter short circuit study is generalized by setting parameters in a wider range so that the possibility of large internal voltage variation consequently considerable change in short circuit contribution is discussed B Equivalent circuit Since the study system is linear the electrical characteristics can be handily analyzed by equivalent circuit Fig 9 shows its Thevenin equivalent The equivalent internal voltage Es is calculated by n k kisi n k krsr E n EE n E 1 1 1 1 2 where the subscripts r and i stand for real and imaginary component k stands for the unit number large power system jXtRs jXsVsV Es Fig 9 Electrical equivalent of the studied case Equation 2 implies that the equivalent internal voltage source which generates the total short circuit current is nothing but the averaged value of each internal voltage C Effects of group behavior For the purpose of clearly showing the effect of wind fluctuation upon the resultant short circuit current magnitude various sinusoidal variations are assumed in each individual generating unit Numerical simulations have been done for these cases and the magnitude of the resultant equivalent internal voltage variation is plotted as shown in Fig 10 In this figure the horizontal axis or phase difference stands for the difference in phases of mechanical torque variations between the two units located at the very ends of the wind farm and the other units have corresponding phases uniformly distributed between these two extremes Zero phase difference means that the all generating units are driven by the same wind variation with the completely coherent sinusoidal wave In that case the short circuit current fed from each unit are accumulated each other to make a substantial value but in the case of 360 degrees difference they are canceled each other to make almost no variation in the equivalent internal voltage seen from the power system In case of the slower variation of the 1 sec period and more the internal voltage variation is bigger than that in the case of fast variation of the 0 5 sec period It is because the electrical transients in the rotor circuit in each induction generator play a certain role in smoothing the variation in this time domain This example shows how the induction generator group makes smoothing effects in short circuit current D Consideration on pre fault operating condition As mentioned in the previous chapters internal voltage variation gives the variation in short circuit current and in most cases the internal voltage does not change so much by the mechanical input torque Here the sensitivity of internal voltage with respect to the power is considered Electrical power is related to the internal voltage E by the formula sin st s xxx EV P 0 0 002 0 004 0 006 0 008 0 01 0 012 0 014 0100200300400 Phase difference deg Max internal voltage variation pu T 200sec 1sec T 0 5sec Fig 10 Equivalent internal voltage variation as a function of incoherency and the variation period 5 where Vs x xt xs and stand for the voltage of the large power system transient reactance of the induction generator leakage reactance of the transformer series reactance of the tie line and the phase difference between the internal and the large power system buses In a lightly loaded case E does not vary much but does corresponding to the variation in P However when heavily loaded which means becomes larger the sensitivity of P with respect to becomes small In such a case E needs to greatly vary to meet the required variation in P Fig 11 shows the result when the transmission length is taken five times longer and the initial slip is taken as much as 0 01pu Easily observed are 1 much bigger variation in the internal voltage 2 distortion in the waveform of the internal voltage 1 might give a potential effect on the short circuit current Here the slight change in fault occurrence time might bring about large difference in its magnitude 2 implies that the system cannot be regarded as linear which means the resultant waveform of the internal voltage takes a different shape which leads to the relation between the magnitude of the fault current and the fault timing complicated In this case two simulations are done changing the fault occurrence timing Their results are shown in Fig 12 and 13 As expected the maximum short circuit current is substantially different In case of the fault occurrence at the highest internal voltage instant the maximum is as much as 3 01pu whereas in the other fault occurrence at the lowest internal voltage as much as 2 499pu Fig 14 and 15 summarize the results As shown in them in case of heavily loaded condition larger negative slip the variation in the internal voltage and consequently the difference in the fault current magnitude become larger From these results obtained so far the group behavior of the wind farm in short circuit study should be examined in heavily loaded long transmission line system Next section is devoted to this study 0 0 2 0 4 0 6 0 8 1 020406080 Time sec Internal voltage pu Fig 11 Equivalent internal voltage variation in case of heavily loaded condition 0 0 5 1 1 5 2 2 5 3 3 5 020406080100 Time sec Current pu Fig 12 Steady state and fault current fed from the wind farm in case of heavily loaded condition and fault occurrence at t 95 65sec 0 0 5 1 1 5 2 2 5 3 3 5 020406080100 Time sec Current pu Fig 13 Steady state and fault current fed from the wind farm in case of heavily loaded condition and fault occurrence at t 86 55sec 0 0 02 0 04 0 06 0 08 0 1 0 12 0 14 0 011 0 01 0 009 0 008 0 007 0 006 initial slip magnitude of internal