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Abstract--This paper presents the measured results and

harmonics generated by a commercial wind power generation

system (WPGS) consisting of four identical 660 kW wind-turbine

induction generators (WTIGs). The studied WPGS is connected

to an 11.4 kV bus inside a large petroleum-chemical industrial

mill located around the middle coast of Taiwan. The field

measured results of total harmonic distortion (THD) in the

current and voltage contributed by the WPGS are analyzed using

a probabilistic approach since the measured quantities arerandom in nature. The IEEE harmonic limit is employed to check

the level of penetration due to the WPGS. It is found that the

THD in the current at the point of common coupling (PCC)

connecting four WTIGs is larger than the 5% limitation of IEEE.

Index Terms--wind power generation system (WPGS), total

harmonic distortion (THD), probabilistic models.

I. INTRODUCTION

HE research of summation of randomly varying

harmonics of the same order can be dated back to [1].

Rowe examined the sum of randomly varying harmonic

currents of the same order. He assumed that the harmonicvectors or phasors had either fixed or random magnitudes and

the uniformly distributed phase angles were resolved into real

and imaginary components. The central limit theorem was

applied to the real and imaginary sums of the studied

harmonic currents in [1] and the analyzed outcomes

concluded that the magnitude of the sum of the harmonic

current would approach to a Rayleigh distribution when the

number of random vectors was large enough. Pierrat [2]

extended the work of Rowe to form a general case through

revising the phase angle of a phasor to be uniformly

distributed in the range of [-, ] and it proved that Rowe's

work was a special case. It should be noted that the magnitude

and the phase angle of each harmonic vector in [1] and [2]

were assumed to be independent. Since the real part and the

imaginary part of harmonic currents of the same order were

respectively summed up, the sum of the two resolved

components would approach to a normal distribution as the

number of random vectors was sufficiently large. A bivariate

This work was supported by the National Science Council of Taiwan, ROC,

under Grant NSC 94-2213-E-006-008.

Kuo-Hua Liu and Li Wang are with the Department of Electrical

Engineering, National Cheng Kung University, Tainan, 70101 Taiwan, Republic

of China (e-mail: liwang@mail.ncku.edu.tw).

normal distribution (BND) [3] model was applied to some

studied cases and the BND model contained five parameters,

i.e., the mean values and variances of the two resolved sums

and their correlation coefficient, which were employed by

Kazibwe, et al. [4]. The same BND model was employed to

determine the magnitude of harmonic contents generated by

ten independent power converters in a distribution system and

Monte Carlo simulation was performed to verify their

theoretical results [5]. The BND approach was also used topredict voltage distortion in a distributed power system and

the analyzed results were examined by using both simulation

and field measurements [6].

This paper is organized as follows. Section II describes

the configuration of the studied system. The measured results

are presented and analyzed in Section III. Statistic analysis of

measured harmonic data at the PCC of the studied WPGS is

depicted in Section IV. Specific conclusions are summarized

in Section V.

II. DESCRIPTION OF THE STUDIED SYSTEM

The one-line diagram of the studied commercial windpower generation system (WPGS) is shown in Fig. 1, where

the stator windings of the studied four identical 660 W, 690-V

induction generators (IG1, IG2, IG3, and IG4) are connected to

an equivalent utility grid (Grid) of 11.4 kV through individual

excitation capacitor banks (C), step-up transformers (RTr +

jXTr), and underground cables (RLine + jXLine). The rotor shaft

of each IG is coupled to the turbine blades through individual

gearbox (GB) with variable transmission rations for

transforming variable low turbine speeds to near-constant

high generator rotor speeds. The distance between two

neighboring wind turbines is about 300 m. The equivalent

capacitances Cline1 and Cline2 of the underground cables

connected between generators are calculated from fieldmeasured reactive power.

The point A shown in Fig. 1 is the point of common

coupling (PCC) connecting four wind generators on the high-

voltage side of the transformers. The three-phase line currents

and voltages at the point A were recorded from the outputs of

current transformers (CTs) and potential transformers (PTs)

every five-second interval. The measured data were recorded

from December 3-19, 2004 for about 16 days or 25,000

minutes. Since the wind speeds of the northeast seasonal wind

of Taiwan were high during the measurement period, the

Analysis of Measured Harmonic Currents and

Voltages Contributed by a Commercial Wind

Power SystemKuo-Hua Liu and Li Wang, Senior Member, IEEE

T

1-4244-1298-6/07/$25.00 2007 IEEE.

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studied WPGS had at least 7 days under full-load generation

of about 2.5 MW. The values of total harmonic distortion

(THD) of both voltage and current were calculated from the

measured three-phase voltages and currents.

The point B shown in Fig. 1 is for filed measuring the

output quantities of a single WTIG. The output data of single

WTIG were recorded from 14:20 to 15:20 on January 21,

2005. The three-phase line currents and voltages were

recorded from the outputs of CTs and PTs at the 11.4-kV sideof the step-up transformer every five-second interval. During

the one-hour measurement, the wind speed is high and the

WTIG is generally under full-power generation.

It is worth noting that total 7680 data points for each

current or voltage signal are captured from the output

terminals of CTs or PTs in one second. These data points are

further processed to obtain 1024 data points for performing

fast Fourier transformation (FFT) in order to precisely

calculate the contents of current or voltage harmonics with

different orders. The calculated harmonic results are averaged

to obtain the required total harmonic distortions (THD) for

each second. Hence, the values of THD are determined by the

written software program in the power recorder. According tothe specifications of the power recorder, the highest harmonic

order that can be analyzed is the 63rd

order.

Fig. 1 One-line diagram of the studied wind power generation system.

III. ANALYSIS OF FILED MEASURED RESULTS

Fig. 2 shows the filed measured results at point B of the

WPGS shown Fig. 1 for one hour. It is seen from Fig. 2(a)

that the point B has line voltage around 11.65 kV which is

higher than the nominal value of 11.4 kV since this WTIG is

generating near full power to the system under high wind

speeds. The measured line current shown in Fig. 2(b) is

around full-load current of about 33 A while the line active

power shown in Fig. 2(c) is around an upper limit of 450 kW.

This active power reduction could be resulted from the action

of pitch control under high wind speed to limit the output

active power of the wind induction generator. The reactive

power shown in Fig. 2(d) also has higher negative limit of

about 500 kVAR under high wind speeds. The apparent power

shown in Fig. 2(e) reaches its upper bound of about 660 kVA

under high wind speeds. Combing the results of active power,

reactive power, and apparent power shown in Fig. 2, it is

realized that the rated 660 kVA apparent power is obtained

from the maximum active power output of 450 kW with

reactive power upper bound of 500 kVAR. The frequencyshown in Fig. 2(f) is severely varied between 59.9 Hz to

60.125 Hz due to randomly varying wind speeds. The power

factor shown in Fig. 2(e) has the lowest value of 0.68 lagging

and the highest value of 0.95 lagging. It is well known that the

power factor of a WTIG is controlled by the internal capacitor

bank inside the wind tower. Each capacitor bank has 5

capacitance values for maintaining output power factor. The

total harmonic distortion (THD) in the line current shown in

Fig. 2(h) is varied from 4% to 16% and the highest THD

value is due to very low wind speeds with low line currents.

Fig. 3 shows the measured voltage, current, active

power and reactive power at point A of the studied WPGS

shown in Fig. 1 for about 16 days. It is seen from Fig. 3(a)that the values of the line voltage are varied between 11 kV to

11.3 kV and these values are below nominal value of 11.4 kV.

Sudden voltage peak and dip on special dates can be clearly

observed from Fig. 3(a). The measured waveforms of both

current and active power are similar as shown in Figs. 3(b)

and 3(c). The total duration of full-power generation of about

2.5 MW and full line current output of 139 A is about 7 days.

The reactive power variation shown in Fig. 3(d) has a

maximum negative peak value of 600 kVAR under full power

generation since four induction generators require larger

reactive power for magnetizing under higher power output.

Comparing the maximum reactive-power value of 600 kVAR

at point A for 4 WTIGs with the maximum reactive-powervalue of 500 kVAR at point B for only one WTIG, it can be

found that the total reactive power supplied from the

combined underground cables with large capacitance and

switched capacitors inside the wind tower is not enough to

supply the required reactive power of four induction

generators under full power generation. Additional reactive

power could be supplied by the grid side to which the four

WTIGs are connected. Figs. 4 and 5 respectively show the

time-domain variations of THD in the measured current and

voltage shown in Fig. 3 for about 25000 minutes.

The THD is a measure of the effective value of the

harmonic components in a distorted voltage or current

waveform and it can be calculated by

max

2

1

1

h

h

h

M

THDM

>=

(1)

whereMh is the rms value ofh-th harmonic component of the

quantityMandMcan be either voltage or current. The values

of THD in the measured voltage and current of the studied

WPGS are generally not constant and they depend on wind-

speed variations.

B A

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(a) Line voltage (b) Line current

(c) Active power (d) Reactive power

(e) Apparent power (f) Frequency

(g) Power factor (h) THD in the line current

Fig. 2 Filed measured results at point B of the studied WPGS.

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Consider a time-varying random process shown in Figs. 4

and 5, the definitions of basic statistical concepts are

employed. IfN independent measurements random variablesare X = X(t1), , Xi = X(ti), , XN= X(tN), the average or

mean value Xavg and standard deviation x can be written in

the following form [6-7]

1

N

i

iavg

X

XN

==

(2)

and

2

1

( )

1

N

i avg

iX

X X

N=

=

(3)

For a given mean value ofXavg and an associated standard

deviation ofx, a time-varying random variableXN whose data

spread according to the Gaussian distribution can be written

in the following form

22

( )1( ) ( )

22

avg

X

XX

X Xf x exp

= (4)

Fig. 4 Time-domain variation of THD in the measured current.

Fig. 5 Time-domain variation of THD in the measured voltage.

(a) Line voltage

(b) Line current

(c) Active Power

(d) Reactive power

Fig. 3 Filed measured results at point A of the studied WPGS.

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The cumulative frequency curve is computed to demonstrate

the computation of the 95th

percentile value. It is economical

to consider THD magnitude exceeding some level. These

levels can be used for comparison with the maximum levels

recommended by IEEE Standard 519 [11]. The probability of

the phasor magnitude Knot exceeding some harmonic level

Kmax can then be determined numerically:

max

max max 0( ) ( ) ( )

K

P K K cdf K pdf K dK = =

(5)

IV. ANALYSIS OF MEASURED DATA USING APROBABILISTIC

APPROACH

A computer program using statistical techniques is

employed in this section to determining the harmonic

contribution of the studied WPGS at the point A shown in Fig.

1. A useful method of summarizing the characteristics of the

THD results shown in Figs. 4 and 5 is to sketch histograms of

probability density that are respectively shown in Figs. 6 and

7. Once the histograms are plotted, the associated cumulative

probability graphs shown in Figs. 8 and 9 can be obtained.

The cumulative frequency curves are to demonstrate thecomputation of the 95

thpercentile value, known as 95%.

Table 1 lists the mean values and the standard deviations of

the associated THD in the measured current and voltage as

well as the corresponding 95th percentile values.

Fig. 6 Histogram of THD in the measured current.

Fig. 7 Histogram of THD in the measured voltage.

Fig. 8 Cumulative probability graph for calculating the 95% value of THD in the

measured current.

Fig. 9 Cumulative probability graph for calculating the 95% value of THD in the

measured voltage.

Table 1 Statistical computed results of THD in the measured current and voltage

at point A of Fig. 1.

X Xavg X 95%

Current THD(%) 0.7835 1.3155 3.543

Voltage THD(%) 1.6682 0.04312 1.747

It can be concluded from the statistical computed

results listed in Table 1 and shown in both Fig. 8 and Fig. 9

that the values of THD in the measured current and voltage

are evidently lower than 5% limitation using 95% cumulative

probability approach.

V. CONCLUSIONS

This paper has presented the field measured results

and probabilistic approach to evaluate the total harmonic

distortion in the measured current and voltage contributed by

a commercial wind power generation system with four

identical wind-turbine induction generators. Since wind speed

is a random quantity, the measured quantities are also random

varied with wind speeds. The proposed probabilistic method

is for analyzing the characteristics of measured harmonic data.

Statistical measurement techniques and histograms are the

most commonly used methods for random quantities. Such

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