Output power control for large wind power penetration in small power system.pdf
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Output power control for large wind power penetration in small power systemTomonobu Senjyua, Toshiaki Kanekoa, Akie Ueharaa,*, Atsushi Yonaa,Hideomi Sekinea, Chul-Hwan KimbaUniversity of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami, Okinawa 903-0213, JapanbSungkyunkwan University, Suwon 440-746, Koreaa r t i c l ei n f oArticle history:Received 19 March 2008Accepted 2 April 2009Available online 8 May 2009Keywords:Frequency deviationPitch angle controlPower systemWind turbine generatora b s t r a c tNowadays, wind turbine generator (WTG) is increasingly required to provide control capabilitiesregarding output power. Under this scenario, this paper proposes an output power control of WTG usingpitch angle control connected to small power systems. By means of the proposed method, output powercontrol of WTG considering states of power system becomes possible, and in general both conflictingobjectives of output power leveling and acquisition power increase are achieved. In this controlapproach, WTG is given output power command by fuzzy reasoning which has three inputs for averagewind speed, variance of wind speed, and absolute average of frequency deviation. Since fuzzy reasoningis used, it is possible to define output power command corresponding to wind speed condition andchanging capacity of power system momentarily. Moreover, high performance pitch angle control basedon output power command is achieved by generalized predictive control (GPC). The simulation results byusing actual detailed model for wind power system show the effectiveness of the proposed method.? 2009 Elsevier Ltd. All rights reserved.1. IntroductionThere are a lot of isolated islands in the world and power isprovided mainly by diesel generation. Heavy oil for diesel gener-ated power needs fuel cost, transport cost and storage cost, which isexpensive compared with main island, and the environment isinfluenced harmfully by emissions of sulfur oxide and carbondioxide. Since many suitable regions of wind power generationexist in isolated island, wind power generation systems areinstalled to decrease usage of heavy oil, and it is possible todecrease generation costs. In addition, wind power generationsystems are environment-friendly because there is no emission ofsulfur oxide and carbon dioxide 1,2.However, wind energy is not constant and windmill output isproportional tothe cube of wind speed, which causes the generatedpower of wind turbine generator (WTG) to fluctuate. The generatedoutput power fluctuation increases relative to the increase ininstallation capacity of the WTGs. Therefore, a provision is neededin small power system for isolated island. Recently, a provisionusing power storage system has been proposed 3, however, it iscostly. Provisions for stand-alone WTG have also been proposed,such as variable-speed WTG and using pitch angle control 410.Inthese reports, it is intended thatoutput powerlevelingof WTG orwind farm is achieved. However, if the capacity ratio of powersource for WTG is small, the need for reduction of output powerfluctuation is low, and output power leveling decreases generatedpower of WTG or wind farm. Thus, if power system capacitychanges hourly, considering the load difference between seasons,or day and night, there is no need to reduce output power fluctu-ation of WTG system. In order to consider the effect of WTG outputpower for power system, a variety of control functions whichcontrol output power of WTG are proposed in 9, and outputpower command is decided by solving the optimal problem in 10.However, neither study considers the power system condition onan hourly basis. From the above-mentioned background, there isneed toformulate ways toachieve output powercontrol of WTG forpower system condition.Therefore, this paper presents output power control of WTGsystem using pitch angle control in small power system. Outputpower command of WTG is increased or decreased by the proposedmethod, and estimation of the increase or decrease is done bypowersystemcondition.Thus,outputpowercommandisdecreased in times that large frequency deviation continuouslyoccurs because the frequency deviation increases by output powerfluctuation of WTG due to rapid wind speed change, and outputpower command increases in times that frequency deviation issmall. Hence, it is possible by the proposed method to correspond* Corresponding author. Tel./fax: 81 98 895 8686.E-mail addresses: b985542tec.u-ryukyu.ac.jp (A. Uehara), (C.-H. Kim).Contents lists available at ScienceDirectRenewable Energyjournal homepage: /locate/renene0960-1481/$ see front matter ? 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.renene.2009.04.004Renewable Energy 34 (2009) 23342343to power system condition. In addition, if more than rated windspeed occurs, WTG can output constant power which hardlycausesnegative effects for power system. Therefore, in order to avoiddecrease of generatedpower, it is important toconsiderwind speedcondition besides power system condition. By means of theproposed method, in general the conflicting objectives of bothoutput power leveling and acquisition power increase are achieved.Output power command of WTG is defined by fuzzy reasoningwhich has three inputs of average wind speed, variance of windspeed, and absolute average of frequency deviation. Since fuzzyreasoning is used, output power command can change flexiblycorresponding to wind speed condition and power system condi-tion. Moreover, high performance pitch angle control based onoutput power command is achieved by generalized predictivecontrol (GPC), in 7,8. The simulation results by using actualdetailed model for wind power system show the effectiveness ofthe proposed method.2. Small power system and WTG model2.1. Small power system modelThe concept of small power system in this paper is shown inFig.1. The small power system consists of the diesel generators andWTGs that generate power that supplies the demand. In addition,small power system is not connected to large power system whichis different from micro-grid, it is assumed that the isolated island isalways operated independently.Small power system model which consists of diesel generator,WTG system and load, is shown in Fig. 2 11. Diesel generator andWTG system feed power to the load. As a frequencycontrol methodof power systems, flat frequency control method which is used inmajority of stand-alone power system is adopted.The output power control of WTG system is done according tooutput power command Pgo. Output power command of WTG isdefined by output power command system, where inputs foroutput power command system are wind speed Vw, and frequencydeviationDf.2.2. Windmill and generator modelIn Fig. 3, WTG system using GPC for pitch angle control system isshown 68. Windmill output Pwis determined by the followingequation:PwCpl;bV3wrA2(1)where Vwis wind speed,ris air density, A is cross-section of rotorfor windmill, Cpis power coefficient,bis pitch angle of blade, andl Ru=Vwis tip speed ratio that includes the angular speeduofthe rotor.In this paper, a squirrel-cage induction generator is used.Generator output Pgcan be expressed byWind turbine generatorsDiesel generatorsLoadSmall power systemFig. 1. Concept of small power system.R11MsD1s+Tts+11Tgs+11Tr+Power system+sKIf+PgPLWTG systemOutput powercommand systemPgoVwPdPeDiesel generatorGovernor5Fig. 2. Small power system model.VwPgPgoePitch angle control systemWindmill and generatorHydraulicservo systemCMDIdentifierGPCu2u1STRFig. 3. Wind turbine generator (WTG) system.T. Senjyu et al. / Renewable Energy 34 (2009) 233423432335Pg?3V2s1 sR2R2? sR12s2X1 X22(2)where V is phase voltage, s uo?u=uois slip that includessynchronous angular speeduoof rotor, R1is stator resistance, R2isrotor resistance, X1is stator reactance, and X2is rotor reactance.From the above expression, Pgis a function ofu, and from (1), Pwisfunction ofu, Vwandb. Therefore, the next expression is obtainedsince Pgand Pware equal in steady state.Pgu Pwu;Vw;b:(3)The pitch anglebis fixed at a certain value, and Pgis calculatedby eachu, which is discretely varied fromuoto the rated angularspeed. Since the left-hand side in (3) is calculated by determininguand right-hand side in (3) is a function of only wind speed Vw, therelation of Vwversus Pw Pg is obtained that is able to approxi-mate the polynomial equation:Pw d1b d2bV2w(4)whered1b a11a12ba13b2a14b3d2b a21a22ba23b2a24b3anda11wa24are constants.In Fig. 3, Pgo(k) is output power command, Pg(k) is output power,e(k) is output power error of generator, u2(k) is control input of STREq. (7) Fuzzy Iffs Fuzzy II+Eq. (17)Eq. (12)Pgo(k)VwEq. (8)Vw+2IIIZOHZOH : Zero-Order-Hold+z10.41.0uf(k)Fig. 5. Output power command system.Table 1Fuzzy rules of fuzzy I.DfsNBNMNSZOPSPMPBVwNBZONSNMNBNBNBNBNMPSZONSNMNBNBNBNSPMPSZONSNMNBNBZOPBPMPSZONSNMNBPSPBPBPMPSZONSNMPMPBPBPBPMPSZONSPBPBPBPBPBPMPSZO01NBNMNSZOPMPBPSHz0.015 0.0225 0.03 0.0375 0.045 0.0525 0.0601NBNMNSZOPMPBPSm/sV10.511.512.513.5 14.515.516.5PBPSNSPMZONMNB01-0.03-0.02-0.010.00.006 0.012 0.018fswIL1L2L3L4L5L6L7M1M2M3M4M5M6M7Z1Z2Z3Z4Z5Z6Z7Fig. 6. Membership functions of fuzzy I.Table 2Fuzzy rules of fuzzy II.DfsNBNMNSZOPSPMPBs2NBPBPBPBPBPMPSZONMPBPBPBPMPSZONSNSPBPBPMPSZONSNMZOPBPMPSZONSNMNBPSPMPSZONSNMNBNBPMPSZONSNMNBNBNBPBZONSNMNBNBNBNB00.81.01.2051015202530m/spuVwPwWindmill outputWind speedcut-inratedcut-out=90deg.=90deg.=1090deg.Fig. 4. Pitch angle control law for all operating regions.T. Senjyu et al. / Renewable Energy 34 (2009) 23342343233612,13, and k is the number of sampling. The error equation can beexpressed as:A?q?1?ek q?kmB?q?1?u2k xkD(5)withA 1 a1q?1 / anq?nB b0 b1q?1 / bmq?mwherekmis dead time, q?1is a backward shift operator,x(k) is whitenoise that is equal to average value of zero and decentralizations2,Dis differencing operator 1?q?1, and n and m are model orders.For (5), the GPC law is derived by minimizing a performance indexJ1, which is given byJ1 E24XNj1fek jg2XNUj1l2jfDuk j ? 1g235(6)where E$ is the expectation value (integral average) andl2(j) isa weighting function. In (6), the first term on the right-hand side issumming output power error e(kj) for predictive interval N, andthe second term is summing the difference of control inputDu forcontrol interval NU, which is multiplied by weighting functionl2(j).As a result, with the difference of control inputDu(kj?1) forcontrol interval NU, it is possible to minimize the output powererror e(kj) for interval j. Moreover, control input u2for GPC islimited byl2(j) to prevent divergence.3. Output power command system3.1. Pitch angle control law for all operating regionsConventional method for the pitch angle law is fixed betweencut-in wind speed and rated wind speed so that the output powerfor WTG is proportional to the fluctuation of wind speed betweencut-in wind speed and rated wind speed. Thus, in order to achieveoutput power control of WTG for all operating regions by pitchangle control, pitch angle control law has been extended as shownin Fig. 4, while the fixed rated output power command has beenconverted to variable output power command. The decision ofoutput power command is described in Section . Output power command of WTG consideringpower system conditionIn order to control output power of WTG considering powersystem condition, output power command Pgois decided by outputpower command system in Fig. 5. Output power command systemconsists mainly of two fuzzy reasoning, and the rate of rated outputpowerfor WTGisdecidedby these fuzzy reasoning. Fuzzy reasoningisdescribedbya set of ifthen rulesbased onfuzzy rules andso donot need a deterministic model. In addition, fuzzy reasoning iseffective when mathematical expressions are difficult by inherentcomplexity, nonlinearity, or unclarity.Firstly, fuzzy reasoning I is explained. There are two inputs offuzzy reasoning. One is absolute average of frequency deviationDfs,01NBNMNSZOPMPBPSHz0.015 0.0225 0.03 0.0375 0.045 0.0525 0.0601NBNMNSZOPMPBPSm/s3.054.04.254.5PBPSNSPMZONMNB01-0.008 -0.006 -0.004 -0.002 0.00.002 0.004fsII2H1H2H3H4H5H6H7I1I2I3I4I5I6I7Q1Q2Q3Q4Q5Q6Q7Fig. 7. Membership functions of fuzzy II.Table 3Simulation parameters.Parameters of small power systemInertia constant M0.150 puMWs/HzDamping constant D0.008 puMW/HzGovernor time constant Tg0.10 sTime constant Tt0.25 sTime constant Tr8.0 sSpeed regulation R2.5 Hz/puMWParameters of windmillBlade radius R14 mInertia coefficient J62,993 kg$m2Air densityr1.225 kg/m3Parameters of induction generatorRated output Pg275 kWPhase voltage V400ffiffiffi3pVStator resistance R10.00397UStator reactance X10.0376URotor resistance R20.00443URotor reactance X20.0534UControl parameters for GPCWeighting factorL2diag50(j)Dead time order d1Model order n3Model order m3Maximum costing horizon N5Control horizon NU1T. Senjyu et al. / Renewable Energy 34 (2009) 233423432337and the other is average wind speed Vw. The former, which is anindex to estimate power system condition, is expressed byDfsZtt?TjDfjdtT(7)where t is present time and T is integral interval. Since absolutevalue of frequency deviationDf is used, absolute average offrequency deviationDfsincreases or decreases with increase ordecrease in frequency deviationDf of the power system. Therefore,(7) indicates frequency deviation quantitatively at any given time.Average wind speed Vwis defined byVwZtt?TVwdtT(8)where Vwis instantaneous wind speed. Output power control ofWTG for power system condition is accomplished byusing absoluteaverage of frequency deviationDfsfor inputs of fuzzy reasoning.However, if wind speed condition is not considered, the generatedpower may decrease within that period. Thus, wind speed condi-tion should be considered to determine output power command ofthe WTG. However, it is undesirable to increase output powercommand of WTG considerably by wind speed condition, becauseprobability of wind speed decrease at short times is high as can beseen from the frequency distribution of wind speed. Therefore, it isdesired to limit output power command using variance of windspeed in time with large fluctuation of wind speed. Fuzzy rules andmembership functions of fuzzy reasoning I are shown in Table 1and Fig. 6, respectively. The important thing is prevention ofdeviations of magnitude ?0.3 Hz for frequency deviationDf ratherthan increase of generated power of WTG. Thus, membershipfunctions are decided so that decreasing tendency is strongcompared with increasing tendency of output power command ofWTG. When frequency deviationDf deviates by more than ?0.2 Hzin certain times, fuzzy rules and membership functions that yield020040060080010001200140016001800510152025Time t sTime t sTime t sWind speed m/sVw0200400600800100012001400160018000.9Load puPL0200400600800100012001400160018000Output of WTG Pg puabcFig. 8. Simulation results with conventional method. (a) Wind speed Vw, (b) loadDPL, (c) output power of WTGDPg, (d) pitch angleb, (e) output of diesel generatorDPdand(f) frequency deviationDf.T. Senjyu et al. / Renewable Energy 34 (2009) 233423432338an output to decrease the output power command are defined bytrial-and-error. The ith of fuzzy rules is expressed asRule i : ifDfsis Lxand Vwis MythengIis Zl(9)where x1, 2,., 7, y1, 2,., 7, l1, 2,., 7. Lx, Mydenote theantecedents and Zlare consequent part. Fuzzy reasoninggIiscalculated bygIX49i1wiZl?X49i1wi(10)where widenotes the grade for the antecedent and is obtained bywi wDfsiwVwi(11)where wDfsiand wVwiare the grade of antecedents for each rule.Secondly, fuzzy reasoning II is explained. Absolute average ofDfsand variance of wind speeds2are used as inputs of fuzzy reasoningII, where variance of wind speeds2is expressed ass2Ztt?TVw? Vw2dtT:(12)Output power command that depends on power systemcondition rather than wind speed condition is decided by usingabsolute average of frequency deviationDfsfor both fuzzyreasoning I and fuzzy reasoning II as inputs. In addition, from theabove-mentioned, when wind speed fluctuations are large, thevariance of the wind speed,s2, is used, since the objective is todecrease output power command. Fuzzy rules and membershipfunctions of fuzzy reasoning II are shown in Table 2 and Fig. 7,respectively. Setup of fuzzy rules and parameters of membershipfunctions are determined by prioritizing to prevent reduction offrequency deviation. The oth of fuzzy rules is expressed asRule o : ifDfsis Hcands2is IzthengIIis Qh(13)020040060080010001200140016001800010203040Time t sTime t sTime t sPitch angle deg020040060080010001200140016001800020040060080010001200140016001800-0.5-0.4-0.3-0.2-dOutput of Diesel generator Pd puFrequency deviation f HzefFig. 8. (continued).T. Senjyu et al. / Renewable Energy 34 (2009) 233423432339where c1, 2,., 7, z1, 2,., 7, h1, 2,., 7. Hc, Izdenote theantecedents and Qlare consequent part. Fuzzy reasoninggIIisdefined bygIIX49o1woQh?X49o1wo(14)where wodenotes the grade for the antecedent and is obtained bywo wDfsows2o(15)where wDfsoand ws2oare the grade of antecedents for each rule.As can be seen fromFig. 5, the discrete value uf(k1) is obtainedby the sums of output of fuzzy reasoning I,gI, and fuzzy reasoningII,gII, through zero-order-hold, and the rate of current rated outputpower of WTG. Then, new rate of rated output power of WTGg(k1) becomes output power command by the followingequation:gk 1 gk ufk 1:(16)Moreover, since the rate obtained by (16) changes step, it isnecessary to convert it into a smooth output power command.Linear output power command is obtained in each sampling timeby using the following equation:Pgo Prated?gk gk 1 ?gkTsft?(17)Pgo Pratedgl:(18)Finally, (17) becomes output power command Pgoto WTGsystem, where Pratedis rated output power, Tsis sampling time, f(t)is periodic function such that f(t)t (0tTs) andglis linearoutput power command.4. Simulation resultsIn this paper, the effectiveness of output power control of WTGfor power system condition using the proposed method is exam-inedby simulation withsystemmodelandparametersasmentioned in 6. In order to use parameters of real machine in 6,020040060080010001200140016001800510152025Time t sTime t sTime t sAverage wind speed VwWind speed VwWind speed m/s Vw0200400600800100012001400160018000.9Load puPL0200400600800100012001400160018000Output of WTG puPgOutput of WTG PgOutput power command PgoCaptured maximum energy PmaxabcFig. 9. Simulation results with proposed method. (a) Wind speed Vw, (b) loadDPL, (c) output power of WTGDPg, (d) pitch angleb, (e) output of diesel generatorDPd, (f) frequencydeviationDf, (g) absolute average of frequency deviationDfs, (h) fuzzy reasoning I outputgI, (i) fuzzy reasoning II outputgIIand (j) output power commandgl.T. Senjyu et al. / Renewable Energy 34 (2009) 233423432340the rated output power of the WTG is 275 kW, however theproposed method can also be applied to a large WTG. Constantoutput power command using pitch angle control of conventionalsystemiscomparedwiththeproposedsystem.Simulationparameters of power system, windmill, induction generator, andcontroller are shown in Table 3. Integral time T is 100 s, samplingtime Tsto obtain discrete value of output power command is 10 s,sampling time of GPC is 1 ms, and parameterL2of GPC, values oforders m and n, maximum costing horizon N, and control horizonNU are based on simulation results that achieve good performance.Output power error parameters used in GPC are unknown atinitial condition. Unknown parameters are determined by least-square method 12,13, and used to control pitch angle.4.1. Simulation results with conventional methodThe simulation results with conventional method using constantoutput power command are shown in Fig. 8. As can be seen fromFig. 8(a), (b), respectively, wind speed Vwand loadDPL. Outputpowerof WTG Pg, andpitch angleb, are shown in Fig.8(c), (d).Windspeed is above rated wind speed at t0400 s, pitch angle is welloperated by pitch angle control system using GPC, thus outputpower Pgis constant withrated output power. However, windspeedbecomes less than rated wind speed at t4001800 s, resulting inlarge output power fluctuation. When wind speed is below ratedwind speed, the pitch angle becomes 10?so that the windmill cancapture maximum energy.From Fig. 8(e), it is found that the diesel generator output powerDPdfluctuates highly in order to cancel out fluctuation of outputpower Pg, and loadDPL. Fig. 8(f) shows frequency deviationDf,which deviates by more than ?0.3 Hz frequently at t5001200 swith severe power system condition, and maximum frequencydeviationDf is 0.49 Hz. Therefore, if capacity ratio of the powersource for WTG is large, output power of WTG by constant outputpowercommandhas harmfuleffects onfrequencyof powersystem.4.2. Simulation results with the proposed methodThe simulation results with the proposed method are shown inFig. 9. Fig. 9(a) shows wind speed Vwand average wind speed Vw,020040060080010001200140016001800010203040Pitch angle deg020040060080010001200140016001800Output of Diesel generator Padj pu020040060080010001200140016001800-0.5-0.4-0.3-0.2-Time t sTime t sTime t sFrequency deviation f HzdefFig. 9. (continued).T. Senjyu et al. / Renewable Energy 34 (2009) 233423432341and loadDPLis shown in Fig. 9(b). Wind speed Vwand loadDPLareequal to simulation with conventional method. As can be seen inFig. 9(c), output power of WTG Pg, is controlled according to outputpower command Pgo. However, output power fluctuation occurswhen output power command Pgoexceeds utilizable energy forwindpower.Fig. 9(d) showspitch angleb, whichis controlled foralloperating regions at below rated wind speed. In addition, outputpower fluctuates a lot because of the difference of a little pitchangle in large-size and medium-sizewindmills. However, GPC givessuitable control input, and there is no effect of rapid wind speedturbulence. From Fig. 9(e), since output power Pg, is smooth, dieselgenerator output powerDPdis mainly controlled corresponding to02004006008001000120014001600180000.020.040.060.080.1Time t sAbsolute average of frequency deviation fs Hz020040060080010001200140016001800-0.03-0.02-0.0100.010.020.03Time t sTime t sTime t sOutput of fuzzy reasoning IIOutput of fuzzy reasoning II II020040060080010001200140016001800-0.01-0.00500.0050.01020040060080010001200140016001800020406080100Output power command l %ghijFig. 9. (continued).T. Senjyu et al. / Renewable Energy 34 (2009) 233423432342the fluctuation component for loadDPL. Thus, diesel generatoroutput powerDPdbecomes smooth compared with Fig. 8(e).Fig. 9(f) shows frequency deviationDf, which is maintained withinthe range of ?0.3 Hz. Because at t 6001000 s there occurs largefrequency deviation by loadDPL, output power command Pgoisreduced so that output power fluctuation of WTG does not occur byrapid wind speed decrease. At t 14001800 s, with small loadDPL,in order to achieve increased generated power, output powercommand Pgoincreases. As a result, frequency deviationDfincreases by wind turbulence below rated wind speed. However,further increase of frequency deviationDf is prevented bydecreasing output power command Pgo. Fig. 9(g) shows absoluteaverage of frequency deviationDfs. Output of fuzzy reasoning I, IIand the rate of rated output power of WTG,g, are shown inFig. 9(h), (i), (j), respectively. It is confirmed that output of fuzzyreasoning I, II change in response to each of the inputs which areabsolute average of frequency deviationDfw, average wind speedVw, and variance of wind speeds2. However, sum of fuzzyreasoning I, II is discretized, and this sum is smoothed by using (16)and (17). Output power control of WTG for power system conditionis achieved by the proposed method.5. ConclusionThis paper presents output power control of WTG using pitchangle control for power system condition. Output power commandis defined by fuzzy reasoning which has three inputs for absoluteaverage of frequency deviation, average wind speed, and varianceof wind speed. Setup of fuzzy rules and parameters of membershipfunctions are determined by prioritizing to prevent reduction offrequency deviation. It is possible to control output power of WTGby pitch angle control system using GPC for all operating regions ofWTG. Therefore, the WTG operates to level output power so as notto harmfully infl
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