Download weighted total harmonic distortion

WEIGHTED TOTAL HARMONIC DISTORTION AND POWER
QUALITY ANALYSIS OF SPACE VECTOR MODULATED
VOLTAGE SOURCE INVERTERS FOR WECS
1
NAIK R. L., 2JANGAMSHETTI SURESH.H.
1
Member IEEE, 2Senior Member IEEE
Department of Electrical and Electronics Engineering, Basaveshwar Engineering College, Bagalkot
Abstract- This paper presents harmonic and power quality analysis of two level and three level Diode Clamped Voltage
Source Inverter (DCVSI). Purpose of analysis is to investigate performance of VSI in WECS in terms of power quality fed to
grid, filter requirement and DC bus utilization. Modulation strategy used is Space Vector PWM (SVPWM) for two levels
and three levels DCVSI as it is readily available for digital implementation. Performance evaluation of VSI is measured
through Weighted Total Harmonic Distortion (WTHD), IEC 1000-3-4 Regulation and Filtering Ratio (FR). Voltage Source
Inverter and LCL filter are modeled in terms of switching function and state space technique respectively. These models
integrated and simulated using MATLAB-SIMULINK. It is observed from simulation that DCVSI has better WTHD and
higher DC Bus Utilization. Further it is also observed that DCVSI experiences lower switching loss and less filtering
requirement.
Index terms- Diode clamped voltage source inverter, Weighted Total Harmonic Distortion, Filtering Ratio
I.
harmonic component as its weight factor. Further
Inverter Interfaces wind turbine to grid is guided by
IEC 1000-3-4 Regulation. However selection of
inverters for WECS in terms of WTHD, IEC 1000-34 Regulation and Filtering Ratio (FR) is not focused
in literatures.
INTRODUCTION
Wind energy is undergoing a rapid development in
size and capacity, as a result modern wind turbine
power rating is exceeding up to 5 MW. Grid
interaction and grid impact of wind turbines has been
in focus during the past few years. Grid connected
variable speed wind turbine generator invariably use
power electronic devices to supply fixed voltage and
frequency shown in Fig.1. Presently two level
Inverters are used to interface a variable speed wind
turbine to the grid at a required voltage and
frequency[1-4]. However two level Inverters are
produce distorted output and switching losses for
high rated wind turbines. Further quality of output
voltage of two levels VSI is improved with increase
in the switching frequency. Higher switching
frequency can be employed only for low power
levels, managing switching losses at high power wind
turbine will be a difficult task. This makes the
multilevel inverter suitable for modern wind-turbines
applications with higher ratings.
In view of this there is need of harmonic and power
quality analysis of two levels VSI and three levels
DCVSI for WECS application. This paper presents
modeling of two level VSI and three level DCVSI
connected to grid. Modulation strategy used is Space
Vector PWM (SVPWM) as it is readily available for
digital implementation. Further LCL-grid filter is
designed to satisfy IEC 1000-3-4 regulation and
filtering capability is measured through FR. This
model helps designer for selection of appropriate
Inverter interfaces wind turbine to grid in terms of
power quality and filter requirement.
Multilevel-inverter topologies viz. Diode clamps,
Flying capacitors and Cascaded H-bridge inverters
were developed and employed in grid connection [23], each one will have its own relative advantages and
disadvantages. Generally Total harmonic distortion
(THD) and Weighted Total Harmonic Distortion
(WTHD) are two important Indices to measure
quality of output voltage fed to grid. Presence of
inductances in power systems causes higher order
current harmonics to damp out more quickly. THD
disregards this difference and treats all harmonics
equally. However WTHD gives a better measure of
harmonic pollution by using the order of each
Fig.1 Voltage Source Inverter Interfaces for WECS
II. SPACE VECTOR MODULATION OF TWO
LEVEL VOLTAGE SOURCE INVERTER
Wind turbine connected to grid through two level
voltage source inverter is shown in Fig 1. Space
Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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Weighted Total Harmonic Distortion and Power Quality Analysis of Space Vector Modulated Voltage Source Inverters for WECS
Vector PWM (SVPWM) method is used to control
inverter by sensing grid voltages and DC Bus voltage
VDC. The principle of SVPWM for two level inverter
has been proposed in many literatures [ ].


d 1  m sin    
3


(6)
d 2  m sin 
(7)
d 0  1  d1  d 2
(8)
Where, m  V V p n , is the modulation index and its
range is 0< m <1.
Symmetrical switching Sequence is to be performed
in order reduce distortion at the output voltage wave
form and switching losses. The symmetrical
switching strategy for sector 1 is shown in Fig.4.
Model of two level VSI is given in terms of switching
function and is given by
Fig. 2. Topology of conventional two level voltage source
inverter
Space vector modulation (SVM) is based on
conversion from three phase quantity to two phase.
This is obtained by orthogonal transformation from
abc- α-β , voltages in α-β are given by
V an 
1/ 2  
V   2 1  1 / 2
(1)
V bn
V    3  0
3 / 2  3 / 2   
 

V cn 
1
2
1
 1  s a 
 1  S b 
2   S c 
(9)
(2)
V ref  V  jV 
V ref  V ref e
V an 
 2
V   V DC   1
 bn 
3 
V cn 
  1
(3)
j
Referring to Fig.2, there are eight switching states V1V8, out eight switching states, V7 and V8 are zero
switching states. These vectors (V1 to V6) is used to
frame the vector plane as shown in Fig.3. The
rotating reference vector can be approximated in each
switching cycle by switching between the two
adjacent active vectors and the zero vectors.
Fig.4: Symmetrical switching strategy for sector-1
Inverter output phase currents injected to grid are
given by
di a
1

V an  i a R  e an 
dt
Ls
di b
1

Vbn  ib R  ebn 
dt
Ls
di c
1
Vcn  ic R  e cn 

dt
Ls
Fig. 3: Zero and Non-zero voltage vectors in

(11)
(12)
Where, Ls is inductance due to LCL filter, R
resistance due to filter, Van, Vbn and Vcn are phase
voltage of grid and ean, ebn and ecn are converter
voltages
plane
Duty cycle of vectors to be switched is calculated in
each sampling period Ts. Ts is divided into three
subintervals d1, d2 and d0. The inverter is switched so
as to produce the vector V1 for d1 period, vector V2
for d2 period and zero state vectors either V7 or V8 for
d0 period. Let d1, d2 and d0 denote the duty cycles of
V1, V2 and V7/V8 respectively. Then,
d 1V1  d 2V 2  V
(10)
III. SPACE VECTOR MODULATION OF
THREE
LEVEL
DIODE
CLAMPED
VOLTAGE SOURCE INVERTER
This section presents SVM of three level DCVSI
connected to grid [ ]. SVM has more computation
involved in identifying Nearest Three Vectors
(NTVs) for synthesizing reference vector. However
this paper gives simple procedure to identify NTVs
by solve linear equation, which reduces
computational burden on processor. Following are
steps to implement three level SVPWM method.
(4)
d1  d 2  d 0  1
(5)
Upon solving the above equations (4&5), we get
expressions for duty cycles as given bellow,
Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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Weighted Total Harmonic Distortion and Power Quality Analysis of Space Vector Modulated Voltage Source Inverters for WECS
1. The functional diagram of a three level DCVSI
switching network is shown in Fig.5. Each switch
will assume one of the positions like Sa may be
connected to positive DC rail i.e. point ‘p’ or
negative DC rail i.e. point ‘n’ or neutral point
(N.P) i.e. point ‘o’. There are totally 27 (33)
allowable switching state vectors which
corresponds to 6-large vectors, 6-medium vectors,
12-small vectors and 3-zerovoltage vectors. There
are totally 24 triangles and tip of the reference
vector may lie in any one of the triangle as shown
in Fig.6.
V
y 
y 
2
3
1
2
y 
(15)
pn
3
V

pn
3(x 
V
pn
6
)
V pn 

3  x 

3


(16)
(17)
(a)
(b)
Fig.7 (a) Hexagon space showing bigger triangles, (b) Division
of large sector into smaller triangles
.
4. Computation of Duty Cycles: Duty cycles of
NTVs are calculated for refrence vector lies in
OUTER and INNER SMALL TRIANGLEs as
shown in Fig.8 then,
Fig.5: Switching network of a three-level DCVSI
Fig.8: (a) Reference in outer triangle (b) Reference vector in
inner triangle.
The duty cycles of NTVs for outer triangle is given as
d so   3m cos    m sin    2
2.
d L  1  3m cos    m sin  
To synthesize the reference voltage vector, task
modulator is used to determine position the
switches and duration needed (duty cycle). This
is achieved using the nearest three vectors
(NTVs) as expressed by,
V REF  d 1V 1  d 2 V 2  d 3 V 3
(18)
d M  2 m sin  
Fig.6: Six sectors and 24-regions
The duty cycles of NTVs for inner triangle is given as
d so  m ( 3 co s    s in  )
d s1  1 
(13)
3 m co s    m sin 
d s  2 m s in 
where, d1, d2 and d3 are the duty cycles of the vectors
V1, V2 and V3 respectively. With additional constraint
on duty cycle.
d1  d 2  d 3  1
(14)
3. Identification of Nearest Three Vectors (NTVs):
The first step is to divide the large space into
smaller triangles a as shown in Fig.7a, knowing
reference vector magnitude |VREF| and its angle δ
bigger triangle located. Further smaller triangle is
identified by evaluating the sign linear equations
(15-16) as shown in Fig.7b.

(19)

Similarly, duty cycles are calculated for middle and
other outer regions
5. Switching strategy: Switching strtegy is proposed
such as to minimising switching frequency,
uniform distribution of all conduction times
between the 12 switches and maintaing the neutral
point voltage into a narrow band around Vdc/2.
6.0 Three level DCVSI connected to grid is Modeled
based on switching functions and is given by
Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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Weighted Total Harmonic Distortion and Power Quality Analysis of Space Vector Modulated Voltage Source Inverters for WECS
 V an
V
 bn
 V cn

 S a1
  S

 b1

 S c 1
Sa2
S b2
Sc2

  V DC 1 

 V
  DC 2 
Cb  1
(20)
VDC1 and VDC2 is the DC link voltages of three level
DCVSI Inverter.
2. Choice of the capacitor is based on percentage of
reactive power absorbed at rated condition, ideally
5% of the base value
IV. LCL GRID FILTER DESIGN
3. Choice of the inductor L1 is based on the current
ripple, ripple attenuation from converter side to
grid and ICE 61000-3-4 regulation.
The selection of the grid filter is an important part, as
it has a significant effect on dynamic behavior,
commercial price and the quality of the energy
exchanged with the grid. Traditionally L –filter is
connected at every converter phase to obtain
sinusoidal voltage and reduce current harmonics
around switching frequency. However size of filter
becomes bulky and expensive for higher KWs. On
the contrary an attractive industrial solution to this
problem is to use an LCL-filter shown in Fig.9.
4. Choice of the inductor L2 is based on ripple current
attenuation ideally taken as 50 % that of converter
side.
L1=2L2
i g ( h sw )
V ( h sw )

i g (hsw )
i(hsw )
LCL filter is modeled using state space method and is
given by
5.
f0 
i
o

1
0
 i1
i2
 V c




6.
(22)
The procedure for design of LCL filter given is as
follows
En
2
Pn

Z LC
2
(25)
w 2 res  w 2 sw
L1  L 2
L1 L 2 C o
(26)
The attenuation introduced by the LCL filter is
effective only if the filter is properly damped.
This achieved by putting resistor in series with
the filter capacitor. Damping element is selected
as 1/3rd of filter capacitor impedance at
resonance frequency.
7.
Transfer function is derived neglecting the
values of R1 and R2 to check stability of filter.
This is verified using bode plot for the transfer
function as given below.
Rd C o S  1
(27)
H (s) 
1. The procedure for the choice of the LCL-filter
parameters has inputs the power rating of the
converter, line frequency and the switching
frequency. Filter values will be referred in % of the
base values:
Zb 
(24)
w sw L1 . w 2 res  w 2 sw
If fo is within the limit i.e. 10fb ≤ fo ≤ fsw/2. Where fb is
the base frequency. If this condition does not match
change percentage of reactive power absorbed and
current ripple attenuation.
Output current is grid current i2 can be obtained

2
Calculate resonant frequency using L1, L2 and C0
(21)
where, i1 is converter current, i2 is grid current and Vc
voltage across capacitor, V1 converter voltage and Vg
is grid voltage.
0
Z LC
Where, ig(hsw) is grid harmonic current at switching
frequency, V(hsw) is harmonic voltage at converter
side at switching frequency, ZLC is characteristic
impedance, i(hsw) converter harmonic current at
switching frequency.
Fig.9: Grid LCL- Filter
 di1 
 dt 
1/ L1
Rd / L1i1  1/ L1 0 
 di  (R1 Rd )/ L1
Vi 
 2    Rd / L2

(
R

R
)
/
L

1/ L2 i2   0 1/ L2  
2
d
2
Vg
 dt  
 Rd /C
0 Vc   0
0  
dVc   Rd /C
 dt 
wn Z b
Where, En is the line to line rms voltage, wn is the grid
frequency and Pn is the active power absorbed by
converter at rated condition.
L1 L 2 C 0 S 3  L1  L 2 R d C 0 S 2  ( L1  L 2 ) S
If system is not stable repeat the step 1 to 6 other wise
designed parameter meets designed constraints.
(23)
Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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Weighted Total Harmonic Distortion and Power Quality Analysis of Space Vector Modulated Voltage Source Inverters for WECS
V.
considered to evaluate the performance of voltage
source inverter for WECS are WTHD, Fundamental
Voltage, FR, IEC1000 3-4 and Power loss.
HARMONIC ANALYSIS
Grid operator imposes harmonic limit and power
factor control on wind farms to maintain power
quality feeding to grid. In order to reduce this effect,
study of harmonics generated by voltage source
inverter becomes prime importance. Traditionally
quality of output voltage is measured by THD,
reflects energy of the waveform harmonic content
and is defined as

1 
THD   V 2 n 
V1  n  2, 3.. 
Table-1: Parameter for simulation of Voltage source
converter with filter
Sl.No
Parameters
Values
Grid
1
Grid Voltage
400 Volts
2
Frequency
50 Hz
Inverter
1
DC Bus Voltage
700 Volts
2
Switching Frequency
5KHz
3
Rating of Inverter
100 KVA
LCL Filter
1
Converter Inductance 0.212mH
L1
2
Grid Inductance L2
0.106mH
3
Filter Capacitance C0
92.87µF
4
Damping element Rd
0.303
Ohms
1/ 2
(28)
Where V1 is rms value of fundamental component
voltage and Vn is rms value of the nth harmonic
component.
Presence of inductance in a transformer or filter
damps out higher order current harmonics quickly as
compared to lower order. This indicates that higher
order harmonics are not sever as lower one. However
THD does not consider severity of lower order
harmonics and treat all harmonic equally. In this
regard another measuring index is proposed in
addition to THD is weighted total harmonic distortion
(WTHD) [7-8]. This index gives a better measure of
harmonic pollution by using the order of each
harmonic component as its weight factor. Further
index considers the severity of lower order of current
harmonics and is defined by.
WTHD

2
1   Vn  


 

V 1  n  2 , 3 ..  n  
1/ 2
Line to line voltages of two level and three level
voltage source converter is obtained for modulating
index 0.57 and switching frequency is 5KHz as
shown in Fig.10 and Fig.11 respectively.
(29)
As there is no benchmark for WTHD, which will
consider the severity of lower order harmonics like
THD i.e. IEEE Standard 519 maximum permissible
THD for low voltage applications is 5% and the
maximum individual voltage harmonic is 3%. Some
more Indices are defined for the choice of Voltage
source Inverter for WECS
 IEC 1000-3-4 i.e. Ih < 0.6% of nominal current
for h ≥33
 Highest harmonic component around switching
frequency.
 Losses due to damping element in filter at
harmonic component
2
(30)
P  3R .
i(h )  i (h )
d
d

Fig.10. Line Voltage of two level VSI, Ma=0.57 and fs=5 KHz
Fig.11. Line Voltage of three level DCVSI, Ma=0.57 and fs=5
KHz
Magnitude of voltage harmonics for two level and
three level VSI are found through harmonic analysis.
Variations of THD and WTHD with modulating
index for two level and three level VSI are plotted as
shown in Fig.12 and Fig.13 respectively. It is
observed that THD and WTHD for three level
inverter are found to be much lower than two level
inverter for all range of modulating index.
Fundamental voltages of both inverters are found by
varying modulating index from 0.3 to 1.0 as shown in
Fig.14 and its found that DCVSI has higher DC Bus
utilization than two level Inverter
g
 Filtering Capability through Filtering Ratio (FR)
FR 
I hc ( sw )
I hg ( sw )
(31)
VI. SIMULATION RESULTS
Simulation is performed using MATLAB Simulink,
parameter considered for grid, voltage source inverter
and LCL filter are given in Table-1. Further indices
Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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Weighted Total Harmonic Distortion and Power Quality Analysis of Space Vector Modulated Voltage Source Inverters for WECS
3
4
6
7
Fig.12: Variation THD with Ma
8
(FR)
Converter
THD
Grid
Converter
WTHD
Grid
IEC 1000-3-4
Ih < 0.6% of In for h >=
33
Pd (Watts)
10.969
14.470
6.450
2.780
2.063
0.556
0.635
1.700
0.465
0.478
0.038
0.017
60.73
20.09
Inferences are drawn from the Table-II in selection
VSI are given below
 FR is low for DCVSI as compared to two level
VSI, with same designed parameter filtering
capability of the filter for three level is 58 %
higher than two level.
 Another index to measure quality of output
waveform is IEC 1000-3-4 Regulation; it is
found that for designed filter parameter
magnitude of 33rd harmonic are within limit for
both two level and three level VSI. However
DCVSI have much reduces value around 50%.
 Effectiveness of filter is achieved if there is
proper damping, it is found that three level
DCVSI has much lower damping than two level.
 Magnitude of current harmonics around
switching frequency are much lower as
compared to two level as shown in Fig.16.
 Designed filter is stable as shown in Fig.17, it is
observed that at crossover frequency, gain is
below zero, hence system is stable.
Fig.13: Variations of WTHD with Ma
Fig.14: Variations of Fundamental voltage with Ma
Variation of THD with switching frequency is plotted
as shown in Fig.15. It is observed that for same
harmonic performance switching frequency of three
level VSI is reduced to 45% that of two level VSI.
This advantage of three level DCVSI will have less
dv/dt and di/dt across the switch and reduced EMI
problem.
Fig.16: Comparison of grid side current harmonics magnitude
for two level and three level VSI
Fig.15: Variation THD with switching frequency (KHz)
This characteristics will improves efficiency of
inverter for high rated wind turbine. Performance
indices for the selection of VSI for WECS are listed
in Table-II.
Fig.17: Bode plot of LCL filter
CONCLUSIONS
Simulation of two level VSI and three level DCVSI
for WECS is performed using MATLABSIMULINK. Performance of VSI is evaluated by
different power quality indices. Further, LCL filter is
modeled using state space analyses and filtering
Table-II: Performance Indices for selection of VSI
Two
Three
Sl.No
Indices
Level
Level
1
Ihc(sw) (%)
1.697
0.420
2
Ihg (sw) (%)
0.155
0.066
Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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Weighted Total Harmonic Distortion and Power Quality Analysis of Space Vector Modulated Voltage Source Inverters for WECS
capability is obtained for two level and three level
voltage source inverter. It is observed from
simulation results that WTHD and THD are lower for
three level DCVSI as compared to the two level VSI.
Further, it is also observed that fundamental voltage
of DCVSI is higher than two level VSI This result in
better DC bus utilization, reduced switching loss and
less distorted output voltage for WECS. From
comparison it is found that three level DCVSI is
advantageous for WEC as it reduces filter
requirement connected to grid.
Overview of topologies and Modulation Strategies," in Proc.
of Optimization of Electrical and Electronic Equipments
OPTIM '98 Conf., May 14-15, 1998, vol. 2, pp 11-24.
[4]
Nikola Celanovic, “Space Vector Modulation and Control
of Multilevel Converters”, PhD thesis, Dept. of Electrical
and Computer engineering, Blacksburg, Virginia, 20th Sept.
2000
[5]
Bum-Soek Suh and Dong-Seok Hyun, “A new N level high
voltage inversion system", IEEE Transactions on Industrial
Electronics, vol.44,no.1, pp. 107-115, Feb. 1997.
[6]
Yo-Han Lee,Bum-Soek Suh and Dong-Seok Hyun, “A
novel PWM scheme for a three level voltage source inverter
with GTO thyristors," IEEE Transactions on Industry
Applications, vol.32 , no. 2, pp.260 - 268, March-April
1996.
[7]
Naik.R.L, .Udaykumar.R.Y ''A Novel Technique For
Control Of Cascaded Multilevel Inverter For Photovoltaic
Power Supplies'' ,IEEE Xplore & Proceedings of 11th
European Conference On Power Electronics and
Application (EPE 2005 ), Dresden Germany , Jan
2005, vol2, p1-7
[8]
Naik.R.L, Udaykumar.R.Y “''Photovoltaic Power Supply”,
Proceedings of ICERD3, Kuwait, Vol.2, November 2005,
pp.867-880.
REFERENCES
[1]
Koessler RJ, Pillutla S, Trinh LH. “Integration of large wind
farms into utility grids (Part 1-Modeling of DFIG)”. IEEE
Power Engineering Society general meeting, 2003; Toronto,
Canada.
[2]
Jih- Sheng Lai, Fang Zheng peng, “Multilevel converters A new breed of power converters," IEEE Trans. on Industry
Applications, vol.IA-32, no.3 pp 509-517, May/June 1996.
[3]
Bum-Seok Suh, Gautam Sinha. Madhav D. Manjrekar and
Thomas A. Lipo, “Multi- level Power conversion - An

Proceedings of International Conference on Research in Electrical, Electronics & Mechanical Engineering, Dehradun, 26th April-2014, ISBN: 978-93-84209-11-7
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