A Calculation Method of the Total Efficiency of Wind Generators

AKIRA INOUE,1 RION TAKAHASHI,1 TOSHIAKI MURATA,1 JUNJI TAMURA,1 MAMORU KIMURA,2 MOTO-O FUTAMI,2 and KAZUMASA IDE2

1Kitami Institute of Technology, Japan2Hitachi, Ltd., Japan

SUMMARY

The spread of wind energy converters is progressingin recent years and its capacity is becoming larger andlarger. In order to capture more energy from the wind, it isimportant to analyze loss characteristics of wind generatorsfor the operating speed which is determined dependent onthe wind speed. This paper presents a method to evaluatevarious losses in a wind generator as a function of windspeed, which is based on steady-state analysis and thus thecalculations can be performed quickly. By using the pro-posed method, wind turbine power, generator output, vari-ous losses, and the total energy efficiency are calculated forthree types of wind speed data which are represented by aWeibull function. © 2006 Wiley Periodicals, Inc. ElectrEng Jpn, 157(3): 52–62, 2006; Published online in WileyInterScience (www.interscience.wiley.com). DOI10.1002/eej.20426

Key words: wind generator; induction generator;power loss; efficiency; capacity factor.

1. Introduction

In recent years wind power generation has gainedmomentum around the world and the number of installa-tions is rising dramatically. Effectiveness as a countermea-sure against global warming and a reduction in the cost ofpower generation due to larger size and mass production arethought to be the reasons, and further increases in the sizeof power generation facilities are expected. However, windelectric power obtained from wind power generation cannotbe considered stable; the generated power and loss varyregularly and are dependent on wind speed. Furthermore,because features such as output and loss in a wind generatorinclude highly nonlinear elements, predicting power levels

based on average wind speed results in large errors. Inparticular, in Japan, which has complex topography andincludes many mountains, complex changes in features canbe expected. Evaluating solutions for predicting such fea-tures is important not only for economic and operationalplanning of future wind generators, but also for improvingperformance and the spread of such generators.

The authors have evaluated methods to calculate vari-ous features during normal operation, in particular windturbine output, generator output, and various forms of loss,as a basis for a wind turbine characteristics equation and agenerator equivalent circuit using the idea of a wind gener-ator with an induction generator. In this paper, the authorsshow the results of analysis of the characteristics for thegenerator features and the wind turbine when using windspeed as input. This method represents the basis for asteady-state equivalent circuit for an induction generator.When the focus is natural wind with its substantial vari-ations, the electrical system time constant for the generatorand the wind variation time constant converge, and theeffects of electrical transient phenomena cannot be ignored.Thus, the authors perform an analysis that includes tran-sient phenomena by using the commercial power systemanalysis software PSCAD/EMTDC [1], and compare itsresults with those from the proposed method; the differencebetween the two is found to be very small.

As a practical example of the proposed method, theauthors used as input data on wind conditions representedusing a probability density distribution function (Weibullfunction) based on data for the NEDO local wind conditionsmap [2] (Local Area Wind Energy Prediction System) madepublic recently. They then calculated the capacity factor andannual total efficiency for a wind generator. In wind powergeneration, in general there are large fluctuations in outputfrom the generator depending on wind conditions. As aresult, the total efficiency and capacity factor found usingthe wind condition data and generated energy, and not theinstantaneous efficiency, are important as a measure to

© 2006 Wiley Periodicals, Inc.

Electrical Engineering in Japan, Vol. 157, No. 3, 2006Translated from Denki Gakkai Ronbunshi, Vol. 125-D, No. 10, October 2005, pp.946–954

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obtain more output from limited input (the kinetic energyin the wind). These measures are very significant for deter-mining the nature of the calculations and the type of windgenerator to use. In Japan with its limited land mass, thereare few regions characterized by good wind conditions, andas a result, evaluation of a method to measure the totalefficiency is vital for promoting the use of wind generationin the future.

2. Creating the Method to Calculate the Features [3]

2.1 Overview of the proposed method

In general, induction motors or synchronous motorsare used in wind generators. Induction motors are morewidely used because they are small, light weight, easy tomaintain, and can be connected directly to the power sys-tem. Given this, in this paper the authors perform an evalu-at ion of an induction generator, and assume asquirrel-cage-type induction motor with a simple structure.The authors propose below a method to calculate accuratelythe features using an ordinary steady-state equivalent cir-cuit. In other words, they attempt to calculate the featureswhile ignoring transient phenomena. However, in the proc-ess the following issues must be resolved.

(1) The features of the induction motor are easilyfound when the number of rotations, that is, the slip, isdefined. However, the slip depends on the input torque, andfinding the slip from the input torque is not easy.

(2) The net input obtained from the generator basedon mechanical loss created in the wind generator is reducedby that amount, and at this point the slip is determined.However, the mechanical loss then becomes a function ofthe number of rotations (slip), and so finding the mechani-cal loss and the slip at the same time is not easy.

(3) Stray load loss and iron loss are difficult to meas-ure, and are difficult to deal with quantitatively.

In this paper, the authors propose a method to calculate thefeatures accurately while taking the above factors intoconsideration.

2.2 Flow of energy in a wind generator

The energy available in the wind is given by

(A: surface area receiving wind [m2]; ρ: air density [kg/m3];VW: wind speed [m/s]).

In a wind generator, the kinetic energy of the windrepresented by this equation is converted to rotation torque

by the wind turbine, and then that is converted to electricalenergy in the generator. The calculation of efficiency in thispaper is based on the mechanical torque generated by thewind turbine, and the analysis is based on the efficiency ofthe generator. Note that several forms of loss occur in thepower generation process in a wind generator, and a portionof the energy is lost as heat. However, accurate analysis ofall these factors is important for calculating efficiency. Thelosses in an induction generator are classified as shown inTable 1. These losses are represented using the calculationsfor the equivalent circuit shown in Fig. 1 and analyticalequations. Moreover, for wind power generation using aninduction generator, step-up gears are present before trans-mitting the power for the generator shaft, and in this paperthese are assumed to be ideal gears with no loss. Based onthe circuit configuration in Fig. 1, the voltage equationshown in Eq. (2) holds. As a result, the electrical loss(primary winding copper loss and secondary winding cop-per loss) can be found using the equivalent circuit.

2.3 Analytical equations to be used in theproposed method

(1) Wind turbine power

The authors used the MOD-2 model [4] developed inthe United States as a wind turbine model. The powercoefficient Cp for the wind turbine output in Eq. (3) isrepresented in Eqs. (5) and (6). As can be seen in Fig. 2, thisis nonlinear with respect to the speed ratio, and providescharacteristics close to those in a real wind turbine.

Table 1. Losses in an induction machine

(2)

(3)

(4)

(5)

(1)

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(λ: speed ratio; R: wind turbine radius [m]; ωwtb: windturbine angular velocity [rad/s]; β: blade pitch angle [deg]).

In this paper, Eq. (3) is converted to a pu repre-sentation by dividing Eq. (3) by the rated amount. The windturbine’s characteristics can then be represented in a simu-lated fashion by multiplying any wind turbine capacity tobe evaluated by the pu representation and then using theproportional relationship.

(2) Generator input

The generator input is represented in the equivalentcircuit as the power consumed in a variable resistance in therotating machine circuit. Because during power generationthe input is entirely negative, it becomes the input power.

In this method, the authors calculate the slip for which thepower entering the generator in reality (the value of the losssubtracted from the wind turbine output) matches the powerin the equivalent circuit found using Eq. (7). The windturbine power is then treated using the elements and currentin the electrical circuit.

(3) Copper loss

This represents loss in the primary and secondarycoils, and the value resulting from tripling the value ob-tained using the following equation represents the generatorcopper loss for all three phases:

(4) Iron loss

In general iron loss in an induction machine is treatedas ohm loss in the iron loss resistance in the equivalentcircuit. However, real iron loss is a loss resulting fromchanges over time in the flux in the iron core. As a result,in representations that use a constant resistance in theequivalent circuit, accurate calculations cannot be per-formed. In general, iron loss is proportional to the eddycurrent loss and frequency, which are proportional to thesquare of the frequency and flux density, and can be repre-sented as the sum of the hysteresis loss proportional to theflux density raised to the 1.6 to 2nd power. Moreover,because the flux density varies greatly in the continuousiron area and the area with gear teeth in a rotating machine,these fluxes must be considered separately. Thus, in theproposed method, first the flux density is found, and thenthe iron loss is calculated using the mass based on Eq. (9)in which the design calculations are used [5, 6]. Then, inorder to unify this result with the copper loss, the copperloss resistance value given by the equivalent circuit andidentical to the iron loss obtained is found using a conver-gence calculation:

Below, the method for finding the analytical equationfor iron loss and the flux density are given for the authors’method. Equation (9) represents the iron loss per kilogramof iron core. The iron loss for the entire generator is foundby multiplying this by the mass of the iron core. B, σH, andσE represent the flux density [T] for the regions withcontinuous iron or with teeth, the hysteresis loss coefficient,and the eddy current loss coefficient. Moreover, f representsthe frequency [Hz] and d, the thickness of the steel plate[mm]. The relationship between the flux and the internalelectromotive force is given in general by Eq. (10). As aresult, the internal electromotive force is proportional to the

(6)

Fig. 2. Power coefficient.

Fig. 1. Equivalent circuit for an induction generator.

(8)

(7) (9)

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flux, and so consequently is proportional to the flux densitybecause the number of coil windings is constant. By usingthis relationship, the flux density can be found from theinductive electromotive force obtained in the equivalentcircuit, and the iron loss can be calculated by using Eq. (9).In other words, the flux density when the generator is atrated output is set, and this is used as the reference value B0

(set for the teeth and continuous iron areas). The fluxdensity B is then determined because it is proportional tothe changes in the induced electromotive force E as shownin Eq. (11).

(kw: winding coefficient; w: coil windings; φ: flux)

(E0: internal electromotive force during rated output of thegenerator). Next, the masses of the continuous iron andteeth areas are multiplied by Eq. (9), and the sums are taken,and the total iron loss Wf is found. Then, rm is adjusted usingEq. (12) so that this value matches the loss Wr generated bythe iron loss resistance rm in the equivalent circuit. Note thatfor rm when the calculations begin, the flux density startsits convergence with the value of B0 as the initial value.

By repeating this procedure, rm for which the iron loss Wf

found from the flux density and the resistance loss in theiron resistance in the equivalent circuit match can be deter-mined using convergence calculations.

In the equivalent circuit in Fig. 1, to be precise, theexcitation reactance xm also varies depending on the fluxlevel, and its effects can be easily taken into considerationusing the computational flowchart (Fig. 5) to be describedlater. However, when performing these calculations in prac-tice using the standard saturation characteristics, it is clearthat the effect is extremely small in the example calcula-tions (Table 5) for the total efficiency to be given later. Asa result, the changes in xm are ignored here.

(5) Brush friction loss

Brush friction loss is mechanical friction loss thatoccurs as a result of the axis of the rotating machine turning.In general, it is represented using Eq. (13). KB is a parameterthat is determined using the mass applied to the bearings,the diameter of the axis, and the peripheral velocity of theaxis [5], and ωm is the speed of the angle of rotation:

(6) Wind loss

Because accurate calculations of wind loss are ingeneral very difficult, in this evaluation the approximation[6] shown in Eq. (14) is used. KW is a parameter that isdetermined using the external shape and length of the rotor,and the peripheral velocity of its surface.

(7) Stray load loss

Electrical equipment experiences losses that cannotbe calculated using simple computations during design.This is stray load loss, and includes iron loss that occurs asa result of a conductor with leak flux, eddy current loss dueto adjacent metal parts, and flux density distortions in thegap. In this evaluation, Eq. (15), which is used as a generalrepresentation, is employed [5]:

(P: generated power [W]; Pn: rated output [W]).

2.4 Flow of the calculation method overall

The procedure to determine the generator states isgiven using the generator steady-state equation shown inEq. (2) and the losses represented in Eqs. (7) through (15).If the slip can be obtained when the wind turbine output(wind turbine torque [N ⋅ m] × wind turbine rotating angularvelocity [rad/s]) is added to the generator, then the variouscurrents in the equivalent circuit can be found, and basedon this, the generated power and loss can be determined. Inthis fashion, the various states can be readily found basedon the slip in an induction machine, but in the reversesituation, the calculations are complex. Thus, the authorsdecided to use a search method to determine the slip whichcreates a generator electromagnetic torque equivalent to thewind turbine torque using slip and torque characteristicsprepared beforehand. Figure 3 shows the generator torque(opposing torque) as positive. This represents the slip–

(11)

(12)

(13)

(10)

(14)

(15)

Fig. 3. Slip–torque curve.

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torque characteristics corresponding to the induction ma-chine constants used in the analytical example given later.

The generated output from the wind turbine is ob-tained from Eq. (3). It is a function of the slip because thewind turbine is connected to the generator via gears. Thus,in the authors’ method, the number of rotations (slip) forwhich the wind turbine output and the input in the generatorequivalent circuit are balanced is calculated using conver-gence with the search method and with the synchronousspeed (slip 0) as the initial value. At this point, the mechani-cal loss (brush friction loss + wind loss) and the stray loadloss cannot be represented in the generator equivalent cir-cuit. As a result, in the authors’ method this is treated as aloss which occurs before generator input, and the calcula-tion is performed by applying to the generator the result ofsubtracting the losses obtained in Eqs. (13) through (15)from the wind turbine generated output. Here, each form ofmechanical loss is a function of the generator speed of theangle of rotation (slip), and the stray load loss is propor-tional to the square of the output. As a result, these lossesare a function of the slip, and so convergence calculationsmust be performed such that all of these components arebalanced in the search process for the slip. The losses givenabove are shown in the power flow in Fig. 4.

2.5 Flowchart

Figure 5 illustrates a flowchart for the proposedmethod. The detailed procedure is given below.

(1) The input value is the wind speed, and calculatingthe state of the slip from the wind speed is the goal here.

(2) The wind turbine generated power is calculatedusing Eq. (3). Note that the initial value for the angularvelocity at the start of the calculations is the synchronousangular velocity.

(3) The mechanical losses, the brush friction loss andthe wind loss, are subtracted from the wind turbine outputcalculated in (2), and then the stray load loss is subtracted.Note that these losses are zero during the first cycle ofcalculations.

(4) The slip is found based on the characteristics inFig. 3. In other words, the slip for when the generator inputequivalent to the power found in (3) is reached is found.

(5) The current in the equivalent circuit is found usingEq. (2) and the slip determined in (4), and then the states,including generator output, copper loss, and iron loss, arecalculated. Here, the loss Wf is calculated based on the fluxdensity using the iron loss calculation method describedpreviously. Moreover, the iron loss resistance rm in theequivalent circuit is found such that this is the same as theloss generated.

(6) The brush friction loss and the wind loss arecalculated using Eqs. (13) and (14), using the generatorstates obtained in (5). Then, the stray load loss is calculatedbased on Eq. (15).

(7) The process is continued as the various lossesconverge, and unless they do, it returns to (2).

Fig. 4. Expression of power flow in the proposedmethod.

Fig. 5. Flowchart.

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2.6 Results of calculations

Table 2 lists the wind power generator parametersused in this paper. The authors assumed a large windgenerator and conceived of a 5-MW generator. The iron lossresistance is the resistance equivalent to the iron loss in thesteady state. Figure 6 shows the characteristics of the gen-erator state variables calculated using the proposed methodwith the wind speed as input. The cut-in wind speed was5.8 m/s, the rated wind speed was 12.5 m/s, and beyond thatrated output was achieved through pitch control. As a result,

it is clear that the output varies depending on the windspeed. Because the variations in the mechanical loss andiron loss are difficult to see, expanded views are given.These show that the mechanical loss rises along with anincrease in the wind speed, as is the case with the variousother losses. Moreover, iron loss falls as the wind speedrises (generator output rises). This is because the generatorinternal voltage drops and the flux density decreases as aresult of an increase in reactive power received from thecontrol side in accordance with a rise in the generatoroutput.

3. Comparison with Analysis that IncludesTransient Phenomena

As has already been explained, in the authors’ methodcalculations are performed fundamentally based on asteady-state equivalent circuit. However, when real fluctua-tions in wind speed are considered, there is a possibility thattransient phenomena will occur in the generator. Thus,below the authors check the difference between calcula-tions that take transient phenomena into consideration andthe results from the proposed method. PSCAD/EMTDCwas used as a tool for the analysis of transient phenomena.PSCAD/EMTDC was created based on theory identical tothe commercially available software EMTP [7] for theanalysis of electromagnetic transient phenomena, and iswidely acknowledged as being very precise for the analysisof transient phenomena in various rotating machines, inparticular synchronous generators in electric power sys-tems. As one example, it is used in the analysis of inductionmotor-type wind generators [8] and in the analysis of tran-sient phenomena in variable speed flywheel generators [9]based on winding-type induction machines.

The authors compared the results calculated using theproposed method using three wind speed turbines as inputwith the analytical results which included transient phe-nomena calculated using PSCAD for the amount of energyproduced during one cycle from the wind speed. In theproposed method, transient phenomena cannot be simu-lated because the calculations are steady state. As a result,in order to clarify whether or not the effect is greater ingeneral, the authors performed the evaluation for changesin the time constant. In other words, the generator rotorresistance was calculated at 1/2 and 1/5. This is because ofthe assumption that the difference in the steady-state analy-sis will increase, and the time constants (the transient timeconstant T ′ for shorts with respect to the parameters inTable 2 is 0.062 s) will rise along with a drop in the rotorresistance (r2

g). When the rotor resistance was 1/5, thetransient time constant for a short was 0.3 second, which isextremely large for an induction machine, and is virtuallya boundary value. Note that iron loss resistance cannot be

Table 2. Generator parameters

Fig. 6. State variables for the generator.

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varied in PSCAD. As a result, here, the authors varied theequivalent circuit that formed the foundation of the pro-posed method in the form of the fixed iron resistance thatcan be calculated in PSCAD.

The authors created the three wind speed patternsshown in Fig. 7 using 20-, 5-, and 1-second period wave-forms for changes in the wind speed. Wind1 had a 20-sec-ond period (ordinary wind speed fluctuations), wind2 hada 5-second period (powerful or chaotic winds) added to the20-second period, and wind3 had a further 1-second periodadded. The wind in the 1-second period may seem to bevery brief when considering natural wind, but was set up to

confirm the precision of the proposed method. Figure 8shows the responses of the generated output calculatedusing PSCAD and the proposed method with the threevariations in wind speed as input. In the PSCAD calcula-tions, transient phenomena are generated because of theneed for a process that drives the generator in less than 1second. After that the values are virtually the same as seenin the results for the proposed method. Given this, it is clearthat the results of calculations that include transient phe-nomena and the results from the proposed method areessentially the same. Table 3 lists the energy obtained usingintegration over one period (20 seconds) after 20 seconds

Fig. 8. Output power of IG.

Table 3. Calculation results (I)

Fig. 7. Wind speed variation.

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has passed. The output and lost energy for this one periodshow little difference between the two methods with respectto the fluctuations in the three types of wind. There was onlya small difference for the complex wind speed variationsseen in wind3.

Table 3 also shows the calculated results for theamount of energy in one period when the rotor resistanceis varied. Based on these results, it is clear that the differ-ence between the two approaches is minimal. As a result, itis evident that even when the input to a generator with alarge time constant is a wind speed with major fluctuations,such as wind3, there is virtually no difference in the calcu-lation error resulting from transient phenomena. On theother hand, it is clear that the energy generated by the windturbine decreases as the rotor resistance drops even whenthe wind speed input is the same (wind3). This is becausethe number of rotations in the wind turbine falls a little evenfor the same wind speed as the rotor resistance drops. Giventhe above, the effects of transient phenomena in generalclearly are small, sufficiently precise calculation results canbe obtained using calculations based on steady-state analy-sis, and the proposed method is general.

4. Calculation of Total Efficiency Using aProbability Distribution Function

Applying the wind condition data represented by aprobability distribution function to the proposed method,the authors calculated the total efficiency of a wind gener-ator. Based on the evaluation in the previous section, it isclear that the wind generator state can be calculated rapidlyand without performing calculations of transient phenom-ena by using the proposed method. However, for instance,calculating the total efficiency by representing the windcondition data over a year as a time function is not practical.Thus, the authors propose representing the wind conditionsduring a year using a probability density function, and usingthe method below to calculate efficiency. In general thecurve for the distribution of the appearance frequency ofwind speed is not symmetrical, and the number of timesmaximum speed is reached is a feature that is biased towardslower wind. One function that resembles this kind of curveis a Weibull function, and it can be considered optimal forthe analysis of wind conditions.

(k: form constant; c: factor constant; v: wind speed). f(v) isthe probability density function for which the wind speed(v) will appear, k is the form constant (a parameter thatindicates the shape of the wind speed stepped distribution),and c is a factor constant (the relative cumulative frequencyfor the wind speed is equivalent to a wind speed at 63.2%).

The appearance frequency for a particular wind speedcan be calculated using Eq. (16). Moreover, even when theannual average wind speed is the same, if two of theparameters (c and k) are different, then the wind conditionsare different, and variations in the amount of power willappear. In the calculations in this paper, the NEDOLAWEPS (Local Area Wind Energy Prediction System) [2]was used to determine the parameters. LAWEPS includesnonlinear fluid dynamical calculations in order to representcomplex topography, but here the authors directly used theresults of a weather model calculation (minimum 500 mmesh) made available on their Web site. The two Weibullfunction parameters obtained there were used, the appear-ance frequency of the wind speeds found, the total powergenerated and the loss for 1 year, as well as the totalefficiency and the capacity factor were all calculated. Thegenerator model uses the induction generator shown inTable 2, with a cut-in wind speed of 5.8 m/s and a ratedwind speed of 12.5 m/s. When the rated wind speed isexceeded, the wind turbine pitch angle is varied so thatoperation continues at the rated output. Note that the cut-outwind speed is 20.1 m/s [4], and above that power generationis halted. In the current calculations, regardless of whetheror not a wind generator was actually set up, three areas withthe differing Weibull parameters shown in Table 4 wereselected. In this instance, the authors assumed a 5-MWgenerator, and so used wind condition data for a height of70 m to match the height of the assumed nacelle. Also,because the appearance probability for the wind directionis publicly known, in this paper the authors performed theircalculations by assuming that the wind was coming in at anoptimal angle for the wind generator at all times. A (KitamiCity) is an inland region with relatively weak winds, B(Erimo Cape) is a region with strong winds located at theend of a cape, and C is the slope of Mount Fuji. Figure 9shows the probability density curves calculated using Eq.(16). It is clear that the appearance probability for the windspeed is very different for the three regions.

The method for calculating the total efficiency andthe capacity factor involves finding the energy generatedannually by multiplying the appearance probability for thewind speed in the operating region by 365 days (8760hours), and then integrating this over an operating windspeed range (5.1 m/s to 20.1 m/s) using the equation

Table 4. Weibull parameters

(16)

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(Etotal: power generated annually [Wh]; Pg: power gener-ated [W]; Vmax: cut-out wind speed; Vmin: cut-in windspeed). Given the above, the total energy generated annu-ally for a wind generator can be found. In addition, thelosses and the wind turbine energy are found using Eqs. (3)through (15) in place of Pg, and in the same fashion thecalculations are performed using integration. Also, the totalefficiency and the capacity factor can be found using theequations below.

Total efficiency = Power generated [Wh]

Wind turbine captured power [Wh] × 100%

(18)

Capacity factor = Power generated [Wh]

Rated output [W] × 365 × 24[h] × 100% (19)

Table 5 lists the results of the calculations. Theseresults are results for when power is generated at all timesin a region with a wind speed operating throughout the year.In practice, the results would be lower due to maintenanceand failures. Based on these results, it is clear that there isa major difference in the power generated in the three

regions, and that there is a substantial difference in thecapacity factor as well. Although the slope of Mount Fujihas a higher average wind speed than Erimo Cape, theannual power generated was lower. This is because theannual operation time there was lower due to the frequencyof winds that exceeded the cut-out wind speed. Table 6 liststhe operation time per year for each region as determinedby the Weibull function and the wind speed of the operatingregion.

As for loss, the copper loss and the stray load losswhich rose in accordance with the power output, as wasdetermined based on Fig. 6, varied greatly in the threeregions. Moreover, although there were no major fluctua-tions in the mechanical loss or the iron loss with respect togenerator output, differences in the regions appeared due todifferences in operation times.

5. Conclusion

In this paper the authors proposed a method to calcu-late the state of the generator’s output and loss, as well asthe wind turbine when using wind speed as input based ona steady-state equivalent circuit used for the purpose ofcalculating the total efficiency of the wind generator withan induction generator. Next, the authors calculated andcompared the generator output and loss response withrespect to patterns in wind speed fluctuation using bothPSCAD, software for analyzing transient phenomena, andthe proposed method. The results showed that the differencebetween the analytical results from the two methods wassmall, and that accurate results were obtained using theanalysis in the proposed method based on the steady state.Naturally, the wind generator’s state and efficiency can alsobe calculated using PSCAD, but this would require a time

(17)

Fig. 9. Probability density distribution.

Table 5. Calculation results (II)

Table 6. Operation times

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simulation with changes in the wind speed as input, and interms of calculation time, finding the capacity factor for ayear would be virtually impossible. On the other hand, animportant feature of the proposed method is that the gener-ator state and efficiency can be calculated very quicklyusing wind condition data. In Section 4, the authors calcu-lated the amount of power generated for a year using windspeed data represented by a Weibull function as an exampleof this, and then calculated the annual total efficiency andcapacity factor. As a result, if the Weibull parameters andother wind condition data can be obtained, then the annualtotal efficiency and the capacity factor can be estimatedrapidly for that location, which would be very useful in thedesign of generators based on specific wind conditions andthe selection of locations to set up wind generators.

Future topics include the importance of using theauthors’ method for variable-speed wind generators usingsynchronous motors, a type of generator that is becomingmore common. In this instance, the loss component gener-ated by the AC/DC/AC converter must be calculated. Theauthors are currently pursuing work in this area and willpublish results as they become available.

REFERENCES

1. PSCAD/EMTDC, http://www.hvdc.ca2. NEDO LAWEPS, http://www2.infoc.nedo.go.jp/

nedo/top.html3. Inoue A, Takahashi R, Murata T, Tamura J, Kimura

M, Futami M, Ide K. Calculation of the steady state

operating conditions of wind generators using induc-tion machines. Papers of Technical Meeting on Ro-tating Machinery, IEE Japan, RM-04-39, 2004. (inJapanese)

4. Wasynczuk O, Man DT, Sullivan JP. Dynamic behav-ior of a class of wind turbine generators during ran-dom fluctuations. IEEE Trans Power Apparatus Syst1981;100:2837–2854.

5. Communications and Education Group in the Insti-tute of Electrical Engineers of Japan. Electricalequipment design (2nd revised edition). IEEJ.

6. Takeuchi J. Electrical machine design (revised, 2ndedition). Ohm Publishing; 1993.

7. EMTP theory book. Japan EMTP Committee; 1994.8. Akagi H, Takahashi K, Sato H. Control strategy and

dynamic performance of a doubly-fed flywheel gen-erator-motor. Trans IEE Japan 1998;118-D:1308–1314. (in Japanese)

9. Sasaki Y, Harada N, Kai T, Sato T. A countermeasureagainst the voltage sag due to an inrush current ofwind power generation system interconnecting to adistribution line. Trans IEE Japan 2000;120B:180–186. (in Japanese)

10. Inoue A, Takahashi R, Murata T, Tamura J, KimuraM, Futami M, Ide K. Calculation of the total effi-ciency of wind generators in steady state operation.Papers of Technical Meeting on Rotating Machinery,IEE Japan, RM-04-99, 2004. (in Japanese)

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AUTHORS (from left to right)

Akira Inoue (student member) graduated from Kitami Institute of Technology in 2004 and enrolled in the first half of hisdoctoral studies in engineering research. He is pursuing research related to efficiency in wind power generators.

Rion Takahashi (member) graduated from the Department of Electrical and Electronic Engineering at Kitami Institute ofTechnology in 1998 and joined the staff of that Department. He is primarily pursuing research related to electric power systemsand variable speed generators.

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AUTHORS (continued) (from left to right)

Toshiaki Murata (member) graduated from the Department of Electrical Engineering at Hokkaido University in 1966 andjoined Godoyoki Co., Ltd. At present he is an assistant professor at Kitami Institute of Technology. He is primarily pursuingresearch on methods to create control systems for vector control systems using optimization control theory. He holds a D.Eng.degree.

Junji Tamura (member) completed his doctorate at Hokkaido University in 1984. At present he is a professor of electricaland electronic engineering at Kitami Institute of Technology. He was a visiting researcher at Texas University in 1991–92. Heis pursuing research related to synchronous motors and electric power system analysis. He holds a D.Eng. degree, and is amember of the Institute of Electrical Installation Engineers of Japan, the Japan Wind Energy Association, and a senior memberof IEEE.

Mamoru Kimura (member) completed the first half of his doctoral studies in electronics and communications engineeringat Tohoku University in 1999 and joined Hitachi, Ltd. He has been working in the Research and Development Laboratory, andis primarily pursuing research and development of rotating electrical machines.

Moto-o Futami (member) completed his master’s course in electrical engineering at Muroran Institute of Technology in1987 and joined Hitachi, Ltd. He has been pursuing research related to power electronics equipment and technology at theHitachi Laboratory.

Kazumasa Ide (senior member) completed the first half of his doctoral studies in electrical and communicationsengineering at Tohoku University in 1988 and joined Hitachi, Ltd. He has primarily worked on research and development ofrotating machinery. At present he is a lead researcher at the main Research and Development Laboratory. He received the 1993and 2001 Institute of Electrical Engineers of Japan Prize for Outstanding Paper and the 2002 Ohm Technology Award. He holdsa D.Eng. degree, and is a member of the Magnetics Society of Japan and IEEE.

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