International Journal of Applied Engineering Research
ISSN 0973-4562 Vol.2, No.1 (2007), pp. 15–30
© Research India Publications
http://www.ripublication.com/ijaer.htm
Simulation of Directly Grid-Connected Wind
Turbines for Voltage Fluctuation Evaluation
Hassan H. El-Tamaly*, Mohamed A. A. Wahab and Ali H. Kasem
Faculty of Engineering, EL-Minia University, EL-Minia 61111, EGYPT.
*Corresponding author. Address: Faculty of Engineering
EL-Minia University, EL-Minia 61111, EGYPT
Email: dr_h_tamaly@yahoo.com
Abstract
Power and voltage generated by a wind turbine are more variable than that
produced by conventional generators. Therefore, with the increasing
penetration of wind energy into the grid, it is very important to simulate
precisely the wind turbine/grid interaction to evaluate voltage fluctuation and
other power quality aspects. In this paper, the wind turbine instantaneously
generated power and voltage at the point of common connection (PCC) with
grid are simulated by considering all the aerodynamical and mechanical
effects, which could affect them. The inherent effect of the wind speed on the
entire blade swept area is simulated in the model of the wind speed. This
model takes into account the effects of tower shadow and the rotational
sampling of turbulence. The generated power is obtained by the simulation of
the wind speed time series into a wind turbine model. The proposed wind
turbine model includes detailed sub-models of aerodynamic rotor, drive train
and ac generator. A dq arbitrary reference frame is used for modeling of
asynchronous generator. The flux variations in the stator circuit are involved.
The flickermeter model which expresses voltage fluctuations is simulated
according to the IEC standard 61000-4-15. The wind speed, wind turbine and
flickermeter models are simulated in Matlab/Simulink software. Both of grid
and site parameters, which affect voltage fluctuation, are investigated. These
parameters have a wide influence on voltage fluctuation and flicker emission
levels.
Introduction
Wind turbine generators are increasingly becoming among the prominent components
of power systems. Due to the stochastic nature of wind, electrical power delivered by
16
Hassan H. El-Tamaly et al
this type of generation possesses similar features. Furthermore, wind turbines are
usually integrated with the grid at remote terminals, far from central loads or
conventional generation. This is raising certain reluctance on the part of utility
companies to inject that source of power with unknown behavior and to evaluate the
accompanied power quality considerations. Due to the importance of wind-turbine
power quality considerations, standard IEC 61400-21 [1] provides procedures for
determining the power quality characteristics of wind turbines.
The sources of fluctuations in the generated power are due to stochastic aspects
that determine wind speed at different times and heights, and to deterministic or
periodic effects. The largest periodic effect known as the tower shadow is at the
frequency at which rotor blades pass by the tower. In the common three bladed
horizontal axis wind turbines, this frequency is known as a 3p frequency which is
three times the rotational frequency [2]. The reactive power consumption of the wind
turbine asynchronous generator depends on the active generated power. The drawn
reactive power increases with the increase of the generated active power. Therefore,
the reactive power consumption of the generator fluctuates as the wind speed
fluctuates. Due to the fluctuations in the active and reactive power, the voltage at PCC
fluctuates.
Voltage fluctuation is a serious issue particularly for direct-connected wind
turbines because these turbines produce power dependent on the variations of the
wind speed and inject it without conditioning into the grid. Voltage fluctuation
disturbs the sensitive electric and electronic equipment. This may lead to a great
reduction in the life span of most equipment [3]. The lighting flicker level is generally
used to measure voltage fluctuation. A case studying the voltage level profile when
the power system is integrated with wind generation is given [4]. The influence of
wind turbines on consumer voltage quality is studied [5]. A frequency domain
approach to wind turbines for flicker analysis is presented [6].
The need to accurately simulate the wind turbines and investigate their interaction
with the grid is becoming so important, since the penetration of wind in certain areas
reaches significant levels. A suggested nonlinear simulation depending on the
collected measured data is presented [7]. This simulation employs the neural network
technique to predict the wind turbine output power. The modeling of wind turbines for
power system studies is presented [8]. The aerodynamic loads of the wind turbines are
represented and simulated in frequency domain [9]. A comprehensive model of
mechanical part consists of a number of lumped inertias, elastically coupled to each
other is presented [10], [11]. The problem in this model that it needs more
manufacturer’s design data about turbine elements which is not available in most
cases. Soft tools and techniques used for modeling and design simulation of wind
turbines are reviewed [12]. A simple approach to aggregated wind farm equivalent for
the analysis of power system operation is presented [13].
This paper presents the comprehensive time-domain modeling of wind speed,
wind turbine and flickermeter and investigates the influence different factors on
voltage fluctuation caused by wind turbines. The wind speed model considers the
effects of tower shadow and the interaction of blade rotation with wind turbulence.
The wind turbine model is composed of three sub models connected together,
Wind Turbines for Voltage Fluctuation Evaluation
17
aerodynamic rotor, drive train and induction generator models. A soft shaft along with
the mass inertia of both the generator and wind turbine rotors is simulated in a 2-mass
drive train model. The induction generator model, in the dq0 arbitrary reference
frame, involves the transients in the stator circuit. The flickermeter is implemented
according to the IEC standard 61000-4-15 [14]. The wind speed, wind turbine and
flickermeter models are implemented in Matlab/Simulink. The wind speed produced
from wind speed model is applied to the aerodynamic model to extract the
aerodynamic torque. This torque is fed to the drive train/generator models to simulate
the electrical power from wind turbine.
Modeling
The wind speed, wind turbine and flickermeter models are explained in the following
sub-sections.
Wind Speed Model
The main idea in the wind speed model is to represent the interaction of turbine blades
with wind speed distribution over the rotor swept area by an equivalent time series
data at hub level. The equivalent time series data simulates the wind and when it is
applied to a specific aerodynamic model, it reproduces the aerodynamic torque from a
wind turbine.
Equivalent wind speed (Weq), produced from wind speed model, takes into
account the deterministic and stochastic wind speed actions on the rotor area. The Weq
is given as follows [15];
Weq ( t , ψ ) = U eq −det (ψ ) + U eq −sto ( t , ψ )
(1)
where:
Ueq-det is the deterministic part of the wind speed;
Ueq-sto is the stochastic part of the wind speed;
ψ is swept angle of the rotor blades; and
t is the time.
Deterministic Part
The deterministic part of the wind is time independent and it depends only on the
rotor position, ψ. It consists of the mean wind speed, tower shadow and wind shear.
The wind shear is very important to the analyses of blade loads but it is not
transmitted to the electrical power so it is neglected. The deterministic part
components are explained in the following items.
a) Mean wind speed
The mean wind speed is estimated from the site wind data or wind Atlas. It is
converted from its measuring level to the wind turbine hub level according to the
following formula [16];
18
Hassan H. El-Tamaly et al
h
U o =  o
 h1
g*

 ⋅ W1

(2)
where: W1 is the average wind speed measured at height h1;
Uo is the mean wind speed at hub level, ho;
g* is an exponent varying from (0.16 to 0.40).
(g* = 0.16 for open land with a few obstacles and g* = 0.4 for land with big
obstacles).
b) Tower shadow
Towers, in horizontal axis wind turbines, are obstacles to the free wind that
modifies the wind flow. The upstream flow, which is interested in this paper, is
reduced in front the tower and increased laterally. The model is limited to the
effects on horizontal, up-wind, and three-bladed wind turbines. When the rotor
blade crosses the tower, a drop in the aerodynamic torque will be occurred.
Consequently, the Fourier transformation of the aerodynamic torque influenced by
tower shadow shows the 3np (i.e., 3p, 6p, 9p,….) components included in it. The
wind turbine dynamics remove the higher 3np frequency components from the
electrical output power and the dominant frequency of tower shadow is 3p [15].
Hence, the simulation of deterministic part of wind speed model is illustrated as
block diagrams in Fig. 1 [15]. Where “Udet-3” is the contribution amplitude of the
tower shadow, “Uo” is the mean wind speed and “Ueq-det” is the output
deterministic wind speed.
T o w e r sh a d o w e ffe ct
In te g e ra to r
ψ
D e te rm in istic
p a rt
c o s( 3ψ )
U eq- det
X
X
ωw tr
E ffe c t d u e
to w e r
sh a d o w
+
Ud e t3 -
W in d tu rb in e
ro to r sp e e d
M e a n W in d S p e e d
Uo
Figure 1: Simulation of the deterministic part of wind speed model.
Stochastic part
The stochastic part depends on both the time and the rotor position, ψ. Low frequency
wind variations have large amplitudes and vice versa. To model this characteristic,
the Kaimal spectral description of turbulence signal, K(f), is commonly used [15],
[17]. Equation (3) defines the Kaimal turbulence filter model.
Wind Turbines for Voltage Fluctuation Evaluation
19
f .x L
Uo
f .K (f )
=
σ2

 f .x
1 + 1.5 *  L
 U

 o


 


(3)
5/3
Where: f is the frequency of the turbulence;
xL is the turbulence length scale; and
The interaction between the rotation of wind turbine blades and the variable wind
speed due to wind turbulences is called the rotational sampling of turbulence. The
rotational sampling of turbulence has been reported as the main cause of flicker from
wind turbines. Therefore, the contribution of rotational sampling of turbulence on
wind speed model is very necessary.
The stochastic part, which includes the rotational sampling turbulence, is
simulated by same way of deterministic component and depends mainly on (0p and
3p harmonic). However, the amplitudes are time dependent as shown in Fig. 2. The
turbulence is simulated by random numbers filtered by Kaimal filter to eliminate high
frequency components. Two second-order filters are employed as admittance
functions for the smoothing of the amplitudes of 0p and 3p harmonics after applying
Kaimal filter [17].
The Weq is the sum of the stochastic and deterministic parts as presented in Eqn.
1.The rotor position, ψ, is obtained from the integral of the angular rotor speed.
Random
In te g e ra to r
ψ
K a im a l
Filte r
0p
h a rm o n ic
Filte r
+
g eq -s to
S to c h a s tic
w in d s p e e d
c o s( 3ψ )
X
ωw tr
Random
W in d tu rb in e
ro to r s p e e d
ψ
Random
K a im a l
Filte r
3p
h a rm o n ic
Filte r
s in ( 3ψ )
K a im a l
Filte r
+
X
3p
h a rm o n ic
Filte r
Figure 2: Simulation of the stochastic part of wind speed model.
20
Hassan H. El-Tamaly et al
Wind Turbine Model
The wind turbine structure is generally composed of the rotor blades, a mean of drive
train, and the electrical generator. In this paper, the rotor blades have been connected
to an induction generator through a flexible coupling followed by gear box. The
induction generator is directly connected to the grid. The dynamic wind turbine
parameters of a fixed-speed, stall-regulated wind turbine are investigated. Figure 3
shows a layout of the proposed wind turbine model. Each sub-model presented in Fig.
3 will be given in the following sub-sections.
V at PC C
I1_a,b,c
C apacitor
M odel
-
+
I2_a,b,c
Grid M odel
V at PC C
Uo
T aer
W in d S p e e d
M odel
W eq
A e ro d y n a m ic
R otor M odel
ωg
D rive T rain
M odel
Induction
Generator
m odel
I1_a,b,c
Te
ωw tr
Figure 3: Fixed-speed, stall-regulated model structure
Aerodynamic Rotor Model
The aerodynamic rotor converts the wind into mechanical torque. The aerodynamic
model uses the Weq and the rotor speed as input data to compute the aerodynamic
torque on the wind turbine shaft. The aerodynamic torque, Taer, can be expressed in
(4) [11].
Taer =
ρ ⋅ π ⋅ R 2 ⋅ Weq3 ⋅ C p (λ)
2 ⋅ ω wtr
where:
ρ LVWKHDLUGHQVLW\
R is the rotor radius;
Cp(λ) is the power coefficient of stall regulated wind turbine;
ωwtr is the rotational rotor speed.
λ is the tip speed ratio (R. ωwtr / Weq).
(4)
Wind Turbines for Voltage Fluctuation Evaluation
21
Drive Train Model
The drive train model simulates the elastic connection between the low-speed wind
turbine shaft and the high-speed generator shaft. It consists of the inertia of both the
turbine and generator (2-mass system). The elastic coupling between the two masses
is modeled by spring, k, and damper, B. The equivalent model for the drive train of
the wind turbine referred to the generator side is shown in Fig. 4.
Te
Ta e r
ωw tr
ωg
k
ϑw tr
ϑg
JT
JG
B
Figure 4: Equivalent diagram of the drive train model.
The dynamics of the drive train on the generator side can be written in (5) and (6)
[8]:
Taer = J T
dωwtr
+ k ⋅ ∆ϑ + B ⋅ ∆ω
dt
k ⋅ ∆ϑ + B ⋅ ∆ω = J G
Where:
dωg
dt
+ Te
(5)
(6)
∆ω = ωwtr − ωg
∆ϑ = ϑwtr − ϑg
dϑ g
dϑwtr
ωg =
and
dt
dt
JT (kg .m2) is the turbine moment of inertia,
JG (kg .m2) is the generator moment of inertia,
k ( N.m/rad) is the stiffness of the shaft,
B (N.m.sec/rad) is the absorption of the shaft,
Taer (N.m) is the wind turbine torque,
Te (N.m) is the electromagnetic generator torque,
&wtr, &g (rad s-1) are the angular speed of the turbine and of the generator,
respectively, and ϑwtr ϑg (rad) are the positions of the turbine and generator shafts,
ωwtr =
respectively.
22
Hassan H. El-Tamaly et al
Induction Generator Model
The asynchronous machine has been used as generator for many years in wind
turbines. This type of machine has high reliability, low price, and low maintenance.
The speed flexibility (slip), when compared to the synchronous machines reduces the
current spikes due to wind gusts. The main disadvantage is that asynchronous
machine consumes reactive power, which influences the wind turbine/grid integration
in normal and transient conditions. A dq arbitrary reference frame is extensively used
for modeling of several types of induction generators [18], [19], [20]. In this model
the dynamic equations of induction machine in the dq0 arbitrary reference frame are
employed. The variations in the stator circuit are involved.
Flickermeter Model
Flicker is defined as “impression of unsteadiness of visual sensation induced by a
light stimulus whose luminance or spectral distribution fluctuates with time” [21].The
flicker level depends on the amplitude, shape and repetition frequency of voltage
fluctuation. Flicker level is measured by the use of a flickermeter described in IEC
61000-4-15 [14]. The flickermeter takes voltage as input and gives the short-term
flicker index, Pst, as output. The flickermeter sequence consists of five steps;
- Step1: input voltage adaptor
- Step2: square law demodulator
- Step3: weighting filters
- Step4: squaring and smoothing
- Step5: statistical manipulation
The steps 1-4 are simulated in Matlab/simulink. The output of step 4 is the
instantaneous flicker level (IFL). Using the statistical manipulation over IFL for an
observation period of 10 min, the Pst, can be estimated. The normalized response of
the flickermeter (Fig. 5) shows that a quite small voltage fluctuation at certain
frequency (8.8 Hz) can be irritable.
Figure 5: Normalized flickermeter response (Pst =1) for voltage fluctuation [14].
Wind Turbines for Voltage Fluctuation Evaluation
23
The integration of wind turbines with the distribution networks may affect
different issues of power quality. The flicker level (Pst”FDQEHDOLPLWLQJFRQGLWLRQ
for connecting wind turbines to low voltage networks [21].
Voltage Fluctuation Caused by Wind Turbine
The wind turbine induction generator injects fluctuated active power into the grid and
correspondingly it draws fluctuated reactive power from the grid.
Figure 6 shows a simplified diagram of wind turbine generator connected to grid.
If the variation of the active power injected to the grid is ∆P and the corresponding
variation of the reactive power absorbed from the grid is ∆Q, then voltage fluctuation,
at PCC, ∆V/V, is given in (7). The nominal voltage is 1 pu.
∆V
≈ ∆P ⋅ R − ∆Q ⋅ X
V
(7)
which can be rewritten as follows;
∆V
≈ ∆S ⋅ Z ⋅ cos(θ + ϕ)
V
(8)
where:
R is the resistance of the grid impedance (pu);
X is the reactance of the grid impedance (pu);
∆S is the apparent power variation,
∆S = ∆P 2 + ∆Q 2 (pu);
Z is the grid impedance amplitude (pu);
is the grid impedance angle; and
3 is tan-1(∆Q/∆P).
∆P
R
X
∆Q
V th =1pu.
IG
W ind T urbine
Generator
PCC
Figure 6: A simple equivalent circuit for wind turbine generator connected to grid.
24
Hassan H. El-Tamaly et al
Simulation Results
Samples of Results of Wind Speed and Wind Turbine Modeling
Using the parameters of the wind turbine generator, which are given in the appendix,
the wind speed and wind turbine models have been implemented under
Matlab/Simulink. The wind turbine ratings are taken as base quantities. The grid fault
level and X/R ratio are assumed 50 pu and 10 respectively. The no-load reactive
power demand of the induction generator under study is compensated by capacitor
banks installed at PCC. Figure 7 presents a sample of selected model outputs;
equivalent wind speed, active/reactive power and voltage at PCC.
Figure 7: Samples of the discussed modeling outputs (a)-wind speed in m/sec. (b)aerodynamic and electrical output power in pu (c)-absorbed reactive power in pu. (d)voltage fluctuation at PCC (∆V/V, %)
The wind speed variation, assuming turbulence intensity of 10%, and Uo=12
m/sec., is shown in Fig. 7(a). The corresponding aerodynamic power and electrical
output power are shown in Fig. 7(b). Not all variations in the aerodynamic power are
transmitted to the electrical power. It means that the soft shaft coupling and the inertia
of wind turbine rotor and generator rotor masses damp and smooth the variations of
the aerodynamic power. Figure 7(c) shows the variation of the absorbed reactive
power from grid. It is clear that the voltage fluctuation, in Fig. 7(d), is very small due
the high fault level of the grid.
Figure 8 traces the variation of the absorbed reactive power with the injected
active power for the integrated wind energy system and the induction generator under
study. The drawn reactive power increases with the increase of the generated active
power. This relation is known as Q-P characteristic of the induction generator.
Wind Turbines for Voltage Fluctuation Evaluation
25
Figure 8: The absorbed reactive power versus the injected active power for the
induction generator under study.
Influences of Grid Parameters on Flicker Caused by Wind Turbines
The grid parameters affecting the wind turbine flicker emission are the fault level, and
X/R ratio of the gird impedance.
Fault Level
Figure 9 shows the variation of the short-term flicker index with different grid fault
levels. This simulation test is carried out with two cases of grid impedance angles; 45Û
and 70Û 7KH PHDQ ZLQG VSHHG DW KXE OHYHO LV PDLQWDLQHG DW PVHF DQG VLWH
turbulence is 10%. From Fig. 9, it can be seen that the flicker level decreases with the
increase of fault levels.
Figure 9: Variation of Pst with the grid fault level.
26
Hassan H. El-Tamaly et al
X/R Ratio of grid impedance
The X/R ratio of the gird impedance is studied in terms of the impedance angle,
=tan-1(X/R). Figure 10 shows the variation of the short-term flicker index with the
impedance angle. The fault level is maintained at 10 pu. The mean wind speed at hub
level is 12 m/sec. and site turbulence is 10%.
From Fig. 6 it can be seen that the flicker decreases with the increase of XQWLOO
the minimXPSRLQWWKHQWKHVORSHLVUHYHUVHGDQGIOLFNHULQFUHDVHVZLWKLQFUHDVHRI
The 'V' curve trend for the relation of Pst with the grid impedance angle agrees with
those given in [22], [23]. However, in [24], there is no indication to the minimum
point and states that flicker increases with low X/R ratio.
The minimum point of voltage fluctuation is occurred when 3 =90Û7KHDQJOH
3 can be obtained according to the incremental variation, ∆Q/∆P, of Q-P
characteristic of the induction generator (Fig. 8). The Q-P characteristic of the
generator determines the 3-P relation. Then the mean generated power (operating
point) determines the value of3 and consequently =90Û-3 at the point of minimum
flicker emission.
Figure 11 shows the variation of angle 3 ZLWh the active generated power. The
mean active generated power is estimated accordance to the wind turbine power curve
at mean wind speed. In this case, it is approximately 0.6 pu. as shown in Fig. 7(b).
TKHQ3§8.6ÛZKLFKJLYHV§ÛDWPLQLPXPIOLFNHU emission as shown in Fig. 10
The minimum point of flicker emission cannot be zero because the power swings up
and down the mean value.
Figure 10: Variation of Pst with the
grid impedance angle.
Figure 11: Variation of the angle
3 with generated active power for
the induction generator under study.
Effects of Site Parameters on Wind Turbine Flicker Emission
The effects of mean wind speed and the site turbulence on flicker emission will be
discussed.
Wind Turbines for Voltage Fluctuation Evaluation
27
Mean Wind Speed
The flicker severity is calculated for the same site turbulence (Iu=10%) and different
mean wind speed, Uo. The fault level of the grid is 10 pu. The Pst values versus the
mean wind speed are estimated for two grid impedance angles, 45ÛDQGÛ
Figure 12: Variation of Pst with mean
wind speed for =45ÛDQGÛ
Figure 13: Wind turbine power curve
The Pst variation with the mean wind speed is illustrated in Fig. 12. It can be
explained by the wind turbine power curve, shown in Fig. 13. From Fig. 13, it can
concluded that the output power and its fluctuations in the low wind region are low
and therefore the induced voltage fluctuation is small. As the wind speed increases
from cut in speed to 13 m/sec., the output power fluctuations and Pst increase,
approximately in linear relation with the mean wind speed. However, in the stall
region (greater than 13 m/sec.), the rate of change of the aerodynamic power curve is
reduced, resulting in a corresponding reduction in the output electrical power
variability. Then Pst values vary in small range with the increase of the wind speed as
shown in Fig. 12. The trend of Pst versus the mean wind speed, shown in Fig.12,
agrees with this given in literature [22]. However, in [23], [25], the flicker emission
increases with increasing wind speed.
Turbulence Intensity
In this case, the mean wind speed at hub level is maintained at 12 m/sec., the fault
level is 10 pu., and the grid impedance angle is 45Û)LJXUHVKRZVWKHYDULDWLRQRI
Pst with the turbulence intensity. The increase in the wind speed turbulence increases
the power variability then the flicker emission increases with the increase of the
turbulence intensity as shown in Fig. 14.
28
Hassan H. El-Tamaly et al
Figure 14: Variation of Pst with wind speed turbulence.
Conclusion
The comprehensive wind speed and wind turbine models can be applied for voltage
fluctuation and power quality studies. The wind speed model involves the tower
shadow and the rotational sampling of turbulence. A 2-mass drive train model,
including soft shaft coupling, is used for damping and smoothing the output electrical
power variations. A dq arbitrary reference frame is used for modeling of the
asynchronous generator. The variations in the stator circuit are involved. The flicker
level caused by voltage fluctuation is evaluated by the flickermeter, described in IEC
61000-4-15.
From simulation results, voltage fluctuations are widely affected by the grid
strength and X/R ratio of grid internal impedance. The flicker emission is decreased
with higher fault levels. The risk of voltage fluctuation increases in the resistive grids.
The wind turbine operating point and the Q-P characteristic of the generator
determine the point of minimum flicker emission. The trend of flicker variation with
the mean wind speed depends mainly on the wind turbine power curve. The power
variability and consequently flicker emission increases with turbulence increase. A
wide look on the results indicates that grid parameters have more effect on flicker
emission than site parameters.
Appendix
The Wind Turbine Data, Drive Train Data and Generator Data are stated as follows:
- rated power 180 kW;
- hub height 30 m;
- rotor diameter 23.2 m;
- number of blades three;
- rotor speed 42 r/min;
- blade profile NACA-63 200;
- gearbox ratio 23.75.
- stall regulated.
Wind Turbines for Voltage Fluctuation Evaluation
29
---------------------------------------- turbine inertia 102.8 kg.m2 ;
- generator inertia 4.5 kg.m2 ;
- stiffness of the shaft 2700 N.m/rad;
(all data referred to the high speed shaft).
---------------------------------------- nominal voltage 400 V;
- number of pole-pairs three;
- stator resistance 0.0092 Ohm;
- rotor resistance (referred to the stator) 0.0061 Ohm;
- stator leakage inductance 0.186 mH;
- rotor leakage inductance (referred to the stator) 0.427 mH;
- magnetizing inductance 6.7 mH.
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