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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: [email protected]).
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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