風力發(fā)電中的自我激勵與諧波@中英文翻譯@外文翻譯

rugged,egenerationcurrguidelines2 Power System Network Descriptionbine can enter self-excitation operation. The voltage and fre-quency during off-grid operation are determined by the balancebetween the systems reactive and real power.Downloaded 28 Mar 2008 to 0. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmWe investigate a very simple power system network consistingof one 1.5 MW, fixed-speed wind turbine with an induction gen-erator connected to a line feeder via a transformer H208492 MVA, 3phase, 60 Hz, 690 V/12 kVH20850. The low-speed shaft operates at22.5 rpm, and the generator rotor speed is 1200 rpm at its syn-chronous speed.A diagram representing this system is shown in Fig. 1. Thepower system components analyzed include the following:An infinite bus and a long line connecting the wind turbineto the substationA transformer at the pad mountOne potential problem arising from self-excitation is the safetyaspect. Because the generator is still generating voltage, it maycompromise the safety of the personnel inspecting or repairing theline or generator. Another potential problem is that the generatorsoperating voltage and frequency may vary. Thus, if sensitiveequipment is connected to the generator during self-excitation,that equipment may be damaged by over/under voltage and over/under frequency operation. In spite of the disadvantages of oper-ating the induction generator in self-excitation, some people usethis mode for dynamic braking to help control the rotor speedduring an emergency such as a grid loss condition. With theproper choice of capacitance and resistor load H20849to dump the energyfrom the wind turbineH20850, self-excitation can be used to maintain thewind turbine at a safe operating speed during grid loss and me-chanical brake malfunctions.The equations governing the system can be simplified by look-ing at the impedance or admittance of the induction machine. ToContributed by the Solar Energy Division of THE AMERICAN SOCIETY OF MECHANI-CAL ENGINEERS for publication in the ASME JOURNAL OF SOLAR ENERGY ENGINEERING.Manuscript received: February 28, 2005; revised received: July 22, 2005. AssociateEditor: Dale Berg.Journal of Solar Energy Engineering NOVEMBER 2005, Vol. 127 / 581Copyright 2005 by ASMEE. MuljadiC. P. ButterfieldNational Renewable Energy Laboratory,Golden, Colorado 80401H. RomanowitzOak Creek Energy Systems Inc.,Mojave, California 93501R. YingerSouthern California Edison,Rosemead, California 91770Self-ExcitationWind PowerTraditional wind turbinesthey are inexpensive,tion generators requiris often used. Becausethe capacitor compensationamong the wind turbine,tant aspects of windcontent in the outputena and gives someH20851DOI: 10.1115/1.20475901 IntroductionMany of todays operating wind turbines have fixed speed in-duction generators that are very reliable, rugged, and low cost.During normal operation, an induction machine requires reactivepower from the grid at all times. Thus, the general practice is tocompensate reactive power locally at the wind turbine and at thepoint of common coupling where the wind farm interfaces withthe outside world. The most commonly used reactive power com-pensation is capacitor compensation. It is static, low cost, andreadily available in different sizes. Different sizes of capacitorsare generally needed for different levels of generation. A bank ofparallel capacitors is switched in and out to adjust the level ofcompensation. With proper compensation, the power factor of thewind turbine can be improved significantly, thus improving over-all efficiency and voltage regulation. On the other hand, insuffi-cient reactive power compensation can lead to voltage collapseand instability of the power system, especially in a weak gridenvironment.Although reactive power compensation can be beneficial to theoverall operation of wind turbines, we should be sure the compen-sation is the proper size and provides proper control. Two impor-tant aspects of capacitor compensation, self-excitation H208511,2H20852 andharmonics H208513,4H20852, are the subjects of this paper.In Sec. 2, we describe the power system network; in Sec. 3, wediscuss the self-excitation in a fixedspeed wind turbine; and inSec. 4, we discuss harmonics. Finally, our conclusions are pre-sented in Sec. 5.and Harmonics inGenerationare commonly equipped with induction generators becauseand require very little maintenance. Unfortunately, induc-reactive power from the grid to operate; capacitor compensationthe level of required reactive power varies with the output power,must be adjusted as the output power varies. The interactionsthe power network, and the capacitor compensation are impor-that may result in self-excitation and higher harmonicent. This paper examines the factors that control these phenom-on how they can be controlled or eliminated.H20852Capacitors connected in the low voltage side of the trans-formerAn induction generatorFor the self-excitation, we focus on the turbine and the capaci-tor compensation only H20849the right half of Fig. 1H20850. For harmonicanalysis, we consider the entire network shown in Fig. 1.3 Self-Excitation3.1 The Nature of Self-Excitation in an InductionGenerator. Self-excitation is a result of the interactions amongthe induction generator, capacitor compensation, electrical load,and magnetic saturation. This section investigates the self-excitation process in an off-grid induction generator; knowing thelimits and the boundaries of self-excitation operation will help usto either utilize or to avoid self-excitation.Fixed capacitors are the most commonly used method of reac-tive power compensation in a fixed-speed wind turbine. An induc-tion generator alone cannot generate its own reactive power; itrequires reactive power from the grid to operate normally, and thegrid dictates the voltage and frequency of the induction generator.Although self-excitation does not occur during normal grid-connected operation, it can occur during off-grid operation. Forexample, if a wind turbine operating in normal mode becomesdisconnected from the power line due to a sudden fault or distur-bance in the line feeder, the capacitors connected to the inductiongenerator will provide reactive power compensation, and the tur-Downloaded 28 Mar 2008 to 0. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmoperate in an isolated fashion, the total admittance of the induc-tion machine and the rest of the connected load must be zero. Thevoltage of the system is determined by the flux and frequency ofthe system. Thus, it is easier to start the analysis from a node atone end of the magnetizing branch. Note that the term “imped-ance” in this paper is the conventional impedance divided by thefrequency. The term “admittance” in this paper corresponds to theactual admittance multiplied by the frequency.3.2 Steady-State Representation. The steady-state analysisis important to understand the conditions required to sustain or todiminish self-excitation. As explained above, self-excitation canbe a good thing or a bad thing, depending on how we encounterthe situation. Figure 2 shows an equivalent circuit of a capacitor-compensated induction generator. As mentioned above, self-excitation operation requires that the balance of both real andreactive power must be maintained. Equation H208491H20850 gives the totaladmittance of the system shown in Fig. 2:YS+ YMH11032 + YRH11032 =0, H208491H20850whereYSH11005 effective admittance representing the stator winding, thecapacitor, and the load seen by node MYMH11032H11005 effective admittance representing the magnetizing branchas seen by node M, referred to the stator sideYRH11032H11005 effective admittance representing the rotor winding asseen by node M, referred to the stator sideH20849Note: the superscript “ H11032” indicates that the values are referred tothe stator side.H20850Equation H208491H20850 can be expanded into the equations for imaginaryand real parts as shown in Eqs. H208492H20850 and H208493H20850:R1L/H9275H20849R1L/H9275H208502+ L1L2+RRH11032/SH9275H20849RRH11032/SH9275H208502+ LLRH110322=0 H208492H20850whereFig. 1 The physical diagram of the system under investigationFig. 2 Per phase equivalent circuit of an induction generatorunder self-excitation mode582 / Vol. 127, NOVEMBER 20051LMH11032+L1LH20849R1L/H9275H208502+ L1L2+LLRH11032H20849RRH11032/SH9275H208502+ LLRH110322=0 H208493H20850R1L= RS+RLH20849H9275CRLH208502+1L1L= LLSCRLH20849H9275CRLH208502+1RSH11005 stator winding resistanceLLSH11005 stator winding leakage inductanceRRH11032H11005 rotor winding resistanceLLRH11032H11005 rotor winding leakage inductanceLMH11032H11005 stator winding resistanceS H11005 operating slipH9275 H11005 operating frequencyRLH11005 load resistance connected to the terminalsC H11005 capacitor compensationR1Land L1Lare the effective resistance and inductance,respectively, representing the stator winding and the load as seenby node M.One important aspect of self-excitation is the magnetizing char-acteristic of the induction generator. Figure 3 shows the relation-ship between the flux linkage and the magnetizing inductance fora typical generator; an increase in the flux linkage beyond a cer-tain level reduces the effective magnetizing inductance LMH11032 . Thisgraph can be derived from the experimentally determined no-loadcharacteristic of the induction generator.To solve the above equations, we can fix the capacitor H20849CH20850 andthe resistive load H20849RLH20850 values and then find the operating points fordifferent frequencies. From Eq. H208492H20850, we can find the operating slipat a particular frequency. Then, from Eq. H208493H20850, we can find thecorresponding magnetizing inductance LMH11032 , and, from Fig. 3, theoperating flux linkage at this frequency. The process is repeatedfor different frequencies.As a base line, we consider a capacitor with a capacitance of3.8 mF H20849milli-faradH20850 connected to the generator to produce ap-proximately rated VAR H20849volt ampere reactiveH20850 compensation forfull load generation H20849high windH20850. A load resistance of RL=1.0 H9024 isused as the base line load. The slip versus rotor speed presented inFig. 4 shows that the slip is roughly constant throughout the speedrange for a constant load resistance. The capacitance does notaffect the operating slip for a constant load resistance, but a higherresistance H20849RLhigh=lower generated powerH20850 corresponds to alower slip.The voltage at the terminals of the induction generator H20849pre-sented in Fig. 5H20850 shows the impact of changes in the capacitanceFig. 3 A typical magnetization characteristicTransactions of the ASMEDownloaded 28 Mar 2008 to 0. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmand load resistance. As shown in Fig. 5, the load resistance doesnot affect the terminal voltage, especially at the higher rpmH20849higher frequencyH20850, but the capacitance has a significant impact onthe voltage profile at the generator terminals. A larger capacitanceyields less voltage variation with rotor speed, while a smallercapacitance yields more voltage variation with rotor speed. Asshown in Fig. 6, for a given capacitance, changing the effectivevalue of the load resistance can modulate the torque-speedcharacteristic.These concepts of self-excitation can be exploited to providedynamic braking for a wind turbine H20849as mentioned aboveH20850 to pre-vent the turbine from running away when it loses its connection tothe grid; one simply needs to choose the correct values for capaci-tance H20849a high valueH20850 and load resistance to match the turbinepower output. Appropriate operation over a range of wind speedscan be achieved by incorporating a variable resistance and adjust-ing it depending on wind speed.3.3 Dynamic Behavior. This section examines the transientbehavior in self-excitation operation. We choose a value of3.8 mF capacitance and a load resistance of 1.0 H9024 for this simu-lation. The constant driving torque is set to be 4500 Nm. Note thatthe wind turbine aerodynamic characteristic and the turbine con-trol system are not included in this simulation because we aremore interested in the self-excitation process itself. Thus, we fo-Fig. 4 Variation of slip for a typical self-excited inductiongeneratorFig. 5 Terminal voltage versus rotor speed for different RLandCJournal of Solar Energy Engineeringcus on the electrical side of the equations.Figure 7 shows time series of the rotor speed and the electricaloutput power. In this case, the induction generator starts from rest.The speed increases until it reaches its rated speed. It is initiallyconnected to the grid and at t=3.1 seconds H20849sH20850, the grid is discon-nected and the induction generator enters self-excitation mode. Att=6.375 s, the generator is reconnected to the grid, terminatingthe self-excitation. The rotor speed increases slightly during self-excitation, but, eventually, the generator torque matches the driv-ing torque H208494500 NmH20850, and the rotor speed is stabilized. When thegenerator is reconnected to the grid without synchronization, thereis a sudden brief transient in the torque as the generator resyn-chronizes with the grid. Once this occurs, the rotor speed settles atthe same speed as before the grid disconnection.Figure 8H20849aH20850 plots per phase stator voltage. It shows that thestator voltage is originally the same as the voltage of the grid towhich it is connected. During the self-excitation mode H208493.1 sH11021tH110216.375 sH20850, when the rotor speed increases as shown in Fig. 7, thevoltage increases and the frequency is a bit higher than 60 Hz.The voltage and the frequency then return to the rated valueswhen the induction generator is reconnected to the grid. Figure8H20849bH20850 is an expansion of Fig. 8H20849aH20850 between t=3.0 s and t=3.5 s tobetter illustrate the change in the voltage that occurs during thattransient.4 Harmonic Analysis4.1 Simplified Per Phase Higher HarmonicsRepresentation. In order to model the harmonic behavior of thenetwork, we replace the power network shown in Fig. 1 with theper phase equivalent circuit shown in Fig. 9H20849aH20850. In this circuitrepresentation, a higher harmonic or multiple of 60 Hz is denotedFig. 6 The generator torque vs. rotor speed for different RLand CFig. 7 The generator output power and rotor speed vs. timeNOVEMBER 2005, Vol. 127 / 5834.1.2 Transformer. We consider a three-phase transformerwith leakage reactance H20849XxfH20850 of 6 percent. Because the magnetiz-Downloaded 28 Mar 2008 to 0. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmby h, where h is the integer multiple of 60 Hz. Thus h=5 indicatesthe fifth harmonic H20849300 HzH20850. For wind turbine applications, theinduction generator, transformer, and capacitors are three phaseand connected in either Wye or Delta configuration, so the evenharmonics and the third harmonic do not exist H208515,6H20852. That is, onlyh=5,7,11,13,17,., etc. exist.4.1.1 Infinite Bus and Line Feeder. The infinite bus and theline feeder connecting the wind turbine to the substation are rep-resented by a simple Thevenin representation of the larger powersystem network. Thus, we consider a simple RL line representa-tion.Fig. 8 The terminal voltage versus the time. a Voltage duringself-excitation. b Voltage before and during self-excitation,and after reconnection.Fig. 9 The per phase equivalent circuit of the simplified modelfor harmonic analysis584 / Vol. 127, NOVEMBER 2005ing reactance of a large transformer is usually very large com-pared to the leakage reactance H20849XMH11032 H11015H11009 open circuitH20850, only theleakage reactance is considered. Assuming the efficiency of thetransformer is about 98 percent at full load, and the copper loss isequal to the core loss H20849a general assumption for an efficient, largetransformerH20850, the copper loss and core loss are each approximately1 percent or 0.01 per unit. With this assumption, we can computethe copper loss in per unit at full load current H20849I1 FullH6018Load=1.0 per unitH20850, and we can determine the total winding resistanceof the primary and secondary winding H20849about one percent in perunitH208 Capacitor Compensation. Switched capacitors representthe compensation of the wind turbine. The wind turbine we con-sider is equipped with an additional 1.9 MVAR reactive powercompensation H208491.5 MVAR above the 400 kVAR supplied by themanufacturerH20850. The wind turbine is compensated at different levelsof compensation depending on the level of generation. The ca-pacitor is represented by the capacitance C in series with the para-sitic resistance H20849RcH20850, representing the losses in the capacitor. Thisresistance is usually very small for a good quality capacitor.4.1.4 Induction Generator. The induction generatorH208491.5 MW,480 V,60 HzH20850 used for this wind turbine can be repre-sented as the per phase equivalent circuit shown Fig. 9H20849aH20850. Theslip of an induction generator at any harmonic frequency h can bemodeled asSh=hH9275s H9275rhH9275sH208494H20850whereShH11005 slip for hth harmonich H11005 harmonic orderH9275sH11005 synchronous speed of the generatorH9275rH11005 rotor speed of the generatorThus for higher harmonics H20849fifth and higherH20850 the slip is close to 1H20849Sh=1H20850 and for practical purposes is assumed to be 1.4.2 Steady State Analysis. Figure 9H20849bH20850 shows the simplifiedequivalent circuit of the interconnected system representinghigher harmonics. Note that the magnetizing inductance of thetransformers and the induction generator are assumed to be muchlarger than the leakages and are not included for high harmoniccalculations. In this sec