selective harmonic elimination in a solar powered multilevel inverter
TRANSCRIPT
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Harmonic Elimination in a Solar Powered Multilevel Inverter
Dr. Shimi S.L
Assistant Professor, EE
NITTTR, Chandigarh
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Chandigarh 1
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Global Solar Potential
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(maximum efficiency)= P(maximum power output)/(E(S,)(incident radiation flux)*A(c)(Area of collector))
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Dr. Shimi S.L, Assistant Professor, NITTTR, Chandigarh12/4/2017 4
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MAXIMUM POWER POINT TRACKING
(MPPT)
There are two basic approaches in maximizing the power extraction:
(a) Using automatic sun tracker
(b) Searching for the MPP conditions
Perturb and Observe method
Incremental Conductance method
Artificial intelligence (AI) methods
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The height of a projectile that is fired straight up is given by the motion equations
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Partial Shading of Solar Panels
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MPPT of a PV System
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Switching Mode Regulator (Buck Converter)
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Equivalent Circuit (a) Switch ON (b) Switch OFF
= =(1 )
2
= =1
162
For a switching frequency of 80 KHz and inductance current ripple () of 10% the and are approximated as 1mH and 100F respectively
=(1 )
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Parameters of Buck Converter
Sr. No. Parameter Value
1 Inductor (L) 1mH
2 Inductor series resistance (RL) 80 m
3 Output capacitor (Co) 100 F
4 Output capacitor ESR (Rco) 30 m
5 Input capacitor (Ci) 100 F
6 Input capacitor ESR (Rci) 30 m
7 Switching frequency (fs), 80 KHz
8 Input voltage 20 V
9 Duty-ratio (D) Variable
10 Load resistance 9 Ohm
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MATLAB/SIMULINK Model of Buck Converter
Components of PWM Block Subsystem
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PWM with 0.5 Value of Duty-cycle
Input and Output Voltages Waveforms of Buck Converter
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PERFORMANCE EVALUATION OF
VIKRAM SOLAR MODULE
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Performance Characteristics Outdoor Efficiency 9.95%
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Performance of 37W PV Module at Laboratory and Outdoor Conditions
Co
nd
itio
n
Angle of PV
Panel Tilt
Irradiation
W/m2
Temperature
oC
Voc
(V)
Isc
(mA)
Vm
(V)
Im
(mA)
Pm
(W)
(%)
Lab
00 450 30 18.71 129 17.93 126 2.254 1.446
450 450 30 18.99 255 17.96 183 3.291 2.111
Ou
tdo
or 00 923 32 18.20 1071 14.33 1043 14.94 7.640
450 923 32 19.07 1904 14.77 1777 26.26 11.25
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PCI Port
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Specification of DS1104 R&D Controller BoardParameter Characteristics
Processor MPC8240 processor with PPC603e core and on-chip
peripherals
64-bit floating-point processor
250 MHz CPU
2 x 16 KB cache; on-chip
On-chip PCI bridge (33 MHz)
Memory Global memory: 32 MB SDRAM
Flash memory: 8 MB
ADC
1 x 16-bit ADC with mux
4 x 12-bit ADC
5 ADC channels (1 x 16-bit + 4 x 12-bit) can be
sampled simultaneous
16-bit resolution
10 V input voltage range
2s conversion time, 12-bit resolution
10 V input voltage range
800 ns conversion time
Slave DSP subsystem Texas Instruments TMS320F240 DSP
16-bit fixed-point processor
20 MHz clock frequency
64 K x 16 external program memory
28 K x 16 external data memory
4 K x 16 dual-port memory for communication
16 K x 16 flash memory
1 x 3-phase PWM output, 4 x 1-phase PWM output
13 mA maximum output current
Host interface 32-bit PCI host interface
5VPCI slot
33MHz5 %
Power supply +5 V 5 %, 2.5 A
+12 V 5 %, 0.3 A
Power consumption 18.5 W
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(a)
(b)
(c)
Parameter Settings for (a) ADC, (b) ADC Multiplexed and (c) PWM Blocks
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Efficiency of MPPT Algorithm
(a) Short-circuit Current Isc
(b) Open-circuit Voltage Voc
(c ) Fill Factor FF
MPPT =0tPMPPT t dt
0tPmax t dt
(2)
Maximum Power (Pmax ) Prediction Model
Isc = IscoG
G0
(3)
=0
1+0
0
(4)
= 0 1
(5)
0 =ln(+0.72)
1+(6)
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(d) Maximum Power Output (Pmax)
voc =Voc
nKT q(7)
Pmax = FF Voc Isc (8)
Pmax =ln(+0.72)
1+ 1
0
1+0
0
0
(9)
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MATLABTM / SIMULINKTM Model of Maximum Power Output (Pmax)
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Sub-System for Fill Factor
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Sub-system for Short Circuit Current
Sub-system for Open Circuit Voltage
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Response of Pmax, Voc , Isc , FF & Irradiance
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Fig. Experimental Result of PO with Delta D=0.01
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MPPT ALGORITHM COMPARISION
Maximum Power Point
Techniques Method
( %)
Peak
Overshoot
( %)
Settling
time
( sec)
Dynamic
Response
Delay
( sec)
Steady
State Error
( %)
Sensors
Voltage -V
Current -I
Perturb & Observe (D=0.1)77.60 - 79.39 No 0.48 0.06 15.14 V, I
Perturb & Observe (D=0.01) 81.00 - 81.60 No 0.41 0.039 12.77 V, I
Perturb & Observe (D=0.001) 81.23 - 84.37 No 0.40 0.04 12.03 V, I
Incremental Conductance 86.32 - 87.25 3.35 1.78 0.001 7.35 V, I
Neural Network 87.35 - 90.10 2.185 0.6439 0.038 3.88 V, I
Adaptive Neuro Fuzzy Inference
System (ANFIS)87.15 - 93.31 6.56 5.35 0 3.55 V, I
ANFIS &
CVT
12V NA 7.28 0.18 0.1 9 V
12V 87.15 - 93.31 6.56 5.35 0 3.55 V, I
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Selective Harmonic Elimination in a Solar Powered Multilevel
Inverter
Dr. Shimi S.L
Assistant Professor, EE
NITTTR, Chandigarh
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Weight, Cost, Power Loss and Harmonics
Comparison for Different Inverter Topologies Ty
pe
of
inve
rte
r
No
. of
swit
che
s
No
. of
cap
acit
ors
No
. of
dio
de
s
We
igh
t
Co
st
Po
we
r Lo
ss
(W)
Har
mo
nic
s
2-level12 0 0
Light
Weight
Cheap Very low THD > 40%
5-level diode
Clamped24 12 36
Medium Weight Costly Low 5th harmonics Eliminated
THD >15%
5-level capacitor
clamped24 30 0
Heavy Very Costly Low 5th harmonics Eliminated
THD >15%
5-level cascaded24 0 0
Light
Weight
Cheap Low 5th harmonics Eliminated
THD >15%
9-level diode clamped48 24 42
Medium Weight Costly medium 5th , 7th & 11th harmonics Eliminated
THD >7%
9-level capacitor
clamped48 60 0
Heavy Very Costly medium 5th , 7th & 11th harmonics Eliminated
THD >7%
9-level cascaded48 0 0
Light
Weight
Cheap medium 5th , 7th & 11th harmonics Eliminated
THD >7%
11-level diode
clamped 60 30 90
Medium Weight Costly High 5th , 7th , 11th &13th harmonics
Eliminated
THD
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Cascaded H-bridge Inverter
Va
(b)
Va[(m-1)/2]
(a)
(a) Single Phase Cascaded H-bridge Inverter Topology with m Levels (b) Output Phase Voltage with Non Equal dc Source
n
Vdc1 S1S2
S3 S4
VaVdcm S1
S2
S3 S4
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Block Diagram of the Harmonic Elimination System
GRID
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Selective Harmonic Elimination Technique
(10)
(11)
(12)
(13)
(14)
(16)
(17)
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f 1 = cos 1 +cos 2 +cos 3 +cos 4 +cos 5 = mi
f 2 = cos 51 +cos 52 +cos 53 +cos 54 +cos 55 = 0
f 3 = cos 71 +cos 72 +cos 73 +cos 74 +cos 75 = 0
f 4 = cos 111 +cos 112 +cos 113 +cos 114 +cos 115 = 0
f 5 = cos 131 +cos 132 +cos 133 +cos 134 +cos 135 = 0
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f 1 = [Vdc1cos 1 +Vdc2cos 2 +Vdc3cos 3 +Vdc4cos 4 +Vdc5cos 5 ]=mi
f 2 = [Vdc1cos 51 +Vdc2cos 52 +Vdc3cos 53 +Vdc4cos 54 +
Vdc5cos 55 ] = 0
f 3 = [Vdc1cos 71 +Vdc2cos 72 +Vdc3cos 73 +Vdc4cos 74 +
Vdc5cos 75 ] = 0
f 4 = [Vdc1cos 111 +Vdc2cos 112 +Vdc3cos 113 +Vdc4cos 114 +
Vdc5cos 115 ]=0
f 5 = [Vdc1cos 131 +Vdc2cos 132 +Vdc3cos 133 +Vdc4cos 134 +
Vdc5cos 135 ] = 0
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The cost function for SHE problem is given by,
= 100 ( 2 + 3 + 4 + 5 )
1
-
Newton Raphson - SHE The algorithm for the Newton-Raphson method is as follows:
Step 1 Assume any random initial guess for switching angles (say 0 ) The switching angle matrix is :
= [1 + 2
+ 3 + 4
+ 5 ]
Step 2 Set modulation index to zero.
Step 3 Evaluate the non-linear system matrix , the Jacobian matrix
and
the harmonics amplitude matrix represented below: The non-linear system matrix,
= cos 1 + cos 2
+ cos 3 + cos 4
+ cos 5
cos 51 + cos 52
+ cos 53 + cos 54
+ cos 55
cos 71 + cos 72
+ cos 73 + cos 74
+ cos 75
cos 91 + cos 92
+ cos 93 + cos 94
+ cos 95
cos 111 + cos 112
+ cos 113 + cos 114
+ cos 115
(18)
(19)
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the Jacobian matrix,
=
sin 1 sin 2
sin 3 sin 4
sin 5
5sin 51 5sin 52
5 sin 53 5sin 54
5 sin 55
7sin 71 7sin 72
7 sin 73 7sin 74
7 sin 75
9sin 91 9sin 92
9sin 93 9sin 94
9sin 95
11sin 111 11sin 112
11 sin 113 11sin 114
11 sin 115
and the corresponding harmonic amplitude matrix,
= [3
40 0 0 0]
The solutions must satisfy the following condition:
0 1 2 3 4 5
2
Step 4 Compute correction during the iteration using relation,
=
(-
)
Step 5 Update the new switching angles as,
+ 1 = + ()
Step 6 To obtain a feasible solution of switching angles by executing the following
transformation: + 1 = cos1(abs(cos( + 1 )))
(20)
(21)
(22)
(23)
(24)
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Step 7 Repeat steps (3) to (6) for sufficient number of iterations to attain error
goal.
Step 8 Increment modulation index by a fixed step.
Step 9 Repeat steps (2) to (8) for whole range of modulation index .
This algorithm can be implemented using MATLABTM programming. Aftersuccessfully executing and running the program the optimal firing angles1, 2, 3 , 4 and 5 can be obtained.
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{
initialize population;
evaluate population;
while Termination Criteria Not Satisfied
{
select parents for reproduction;
perform crossover and mutation;
evaluate population;
}
}
Genetic Algorithm (GA)
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The GA Cycle of Reproduction
reproduction
population evaluation
modification
discard
deleted
members
parents
children
modified
children
evaluated children
-
Consider the problem of maximizing the
function,
f(x) = x2
Where x is permitted to vary between 0 to 31.
(i) 0(00000) and 31(11111) code x into finite
length string
(ii) Select initial population at random (size 4)
(iii) Calculate fitness value for all strings
(iv) probability of selection by:
=()
=1 ()
,
-
Table 1. Selection
String
No.
Initial
population
X
Value
Fitness
value
Prob. %age
Prob.
Expected
Count
Actual
Count
1. 01100 12 144 0.1247 12.47% 0.4987 1
2. 11001 25 625 0.5411 54.11% 2.1645 2
3. 00101 5 25 0.0216 2.16% 0.0866 0
4. 10011 19 361 0.3126 31.26% 1.2502 1
Sum
Avg.
Max.
1155
288.75
625
1.0000
0.2500
0.5411
100%
25%
54.11%
4.0000
1.0000
2.1645
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Table 2. Crossover
String
No.
Mating
Pool
Crossover
point
Offspring
after
crossover
X value Fitness
value
1. 01100 4 01101 13 169
2. 11001 4 11000 24 576
3. 11001 3 11011 27 729
4. 10011 3 10001 17 289
Sum
Avg.
Max.
1763
440.75
729
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Table 3. Mutation
String
No.
Offspring
After
crossover
Mutation
chromosomes
Offspring
after
mutation
X value Fitness
value
1. 01101 10000 11101 29 841
2. 11000 00000 11000 24 576
3. 11011 00000 11011 27 729
4. 10001 00100 10101 20 400
Sum
Avg.
Max.
2546
636.5
841
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Minimize the following fitness
function including 2 variables:
= (
)+ ( )
Subject to the following linear
constraints and bounds:
12 + 1 2 + 1.5 010 12 00 1 1 and 0 2 13
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The function has one output y and two input variables x1 and x2.
We use the vector x to include both x1 and x2.
-
=
2 8 40 22
4
2 + + + 3 + + 3 + 2
2
1
24 + 12 = 360
2 + = 30
THD Equation
Constraint
Multilevel inverter with reduced ie. 15
number of switches and 4 sources
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Step 1 Initialize the system parameters for MATLABTM / GA toolbox such as
CrossoverFcn as @crossoverscattered, CrossoverFraction as 0.8, SelectionFcn as
@selectionstochunif , 'CreationFcn' as @gacreationlinearfeasible and 'MutationFcn'
as @mutationadaptfeasible. Assign the values of Generations as 100, Population
Size as 40 and PopInitRange as [0;1].
Step 2 Now evaluate the particles using the Fitness Function
= 100 ( 2 + 3 + 4 + 5 )
1for harmonic elimination.
Here the switching angles 1, 2, 3, 4and 5 are chosen in such a way that the
selective 5th, 7th, 11th and 13th harmonics can be eliminated.
Step 3 Check the constraints 0 1 2 3 4 5 /2.
Step 4 Select the parent chromosomes.
Step 5 Create the new offspring using crossover and mutation.
Step 6 Check if termination criteria ( the maximum number of iterations) is reached. If
not goto Step 2.
Step 7 If optimized switching angles are obtained, terminate the problem.
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PSO
vt
gbestt
pbestt
xt
xt+1
Ruben E. Perez
0 < C1 + C2 < 4
C1+C2
2< C0 < 1
+ 1 = 0 + 11 + 22
+ 1 = () + + 1
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Step 1: Initialize the system parameters such as Position Vector Xi, Velocity Vector Vi, Personal Best Particle Vector Pi, Global Best Vector Pg and Particle Inertia Weight C0 . Assign the values of Generations as 100, Population Size as 40, Cognitive Parameter C1 as 0.5 and Social Parameter C2 as 1.25.
Step 2: Check for the conditions 0
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NR Algorithms
GA Algorithms
PSO Algorithms
Optimized Switching Angles using NR, GA and PSO Algorithms for 11 Level Inverter
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THD Versus Modulation Index of 7, 9 and 11 Level Cascaded H-bridge Inverters for NR, GA and PSO Algorithms
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11 Level Cascaded H-bridge Inverter Applied with NR-SHE Algorithm for 0.8 Value of MI
Line Voltage Waveform
Phase Voltage Waveform
Current Waveform12/4/2017
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Harmonic Spectrum at 0.8 MI for NR-SHE Algorithm for a 11 level Cascaded H-bridge Inverter
Phase Voltage Spectrum
Line Voltage Spectrum
Current Spectrum 12/4/2017
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Tech
niq
ue
Use
d
11 Level Cascaded H-bridge Inverter
Magnitude of Harmonic Contents (%) up to 19th Order
Line Voltage
(THD 5.55%)
105.8 peak (74.83 rms)
Phase Voltage
(THD 7.93%)
61.14 peak (43.23 rms)
Current (THD 5%)
0.6063 peak (0.4287 rms)
Har
mo
nic
Ord
erEv
en
Har
mo
nic
Har
mo
nic
Ord
erO
dd
Har
mo
nic
Har
mo
nic
Ord
erEv
en
Har
mo
nic
Har
mo
nic
Ord
erO
dd
Har
mo
nic
Har
mo
nic
Ord
erEv
en
Har
mo
nic
Har
mo
nic
Ord
erO
dd
Har
mo
nic
NR
0th 0.00 1th 100 0th 0.00 1th 100 0th 0.01 1th 100
2nd 0.00 3rd 0.02 2nd 0.00 3rd 0.60 2nd 0.00 3rd 0.02
4th 0.00 5th 0.09 4th 0.00 5th 0.04 4th 0.00 5th 0.07
6th 0.00 7th 0.08 6th 0.00 7th 0.06 6th 0.00 7th 0.09
8th 0.00 9th 0.06 8th 0.00 9th 3.26 8th 0.00 9th 0.06
10th 0.00 11th 0.10 10th 0.00 11th 0.10 10th 0.00 11th 0.11
12th 0.00 13th 0.02 12th 0.00 13th 0.02 12th 0.00 13th 0.03
14th 0.00 15th 0.09 14th 0.00 15th 1.04 14th 0.00 15th 0.08
16th 0.00 17th 2.65 16th 0.00 17th 2.58 16th 0.00 17th 2.62
18th 0.00 19th 1.89 18th 0.00 19th 1.88 18th 0.00 19th 1.86
Magnitude of Harmonic Contents (%) up to 19th Order for 11 Level Cascaded H-bridge Inverter Applied with NR-SHE Technique
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1. Intelligent Power Module (Power Circuit)
2. Firing Pulse for H-bridge Inverter
(a) Optocoupler (b) Gate Driver
(c ) AND Gate (d) Schmitt Trigger
(e) FPGA Based Spartan 3A DSP Board
3. Protection Circuit
4. Regulated Power Supply
5. Signal Conditioning Circuit
6. Constant and Isolated dc Supply for MLI
7. 3 Induction Motor Load
8. Power Quality Analyzer
9. PC with MATLAB/SIMULINK and Xilinx Software Packages
Block Diagram of the Hardware
Implementation of 3 MLI
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Complete Laboratory setup of 3 11
Level Cascaded H-bridge Inverter
3 Induction Motor
Power Quality Analyzer
CHMLISpartan-3A
DSP FPGA CHMLI
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Experimental Results for 11 Level
Inverter (a) Output Line Voltage (b)
Phase Voltage and (c) Current at
M=0.8 (NR-SHE)
(a)
(b)
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(a)
(b)
Experimental Results for 11 Level
Inverter (a) Line Voltage FFT
Analysis (b) Phase Voltage FFT
Analysis and (c) Current FFT
Analysis at M=0.8 (NR-SHE)
(b)
(c)
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Optimum Switching Angles and Minimum THD using NR-SHE, GA-SHE
and PSO-SHE
Technique Method Mi Alpha 1 Alpha 2 Alpha 3 Alpha 4 Alpha 5
Line
Voltage
THD
(%)
Phase
Voltage
THD
(%)
Current
THD
(%)
NRSimulation
0.8 0.1147 0.3306 0.4744 0.7878 1.0864 5.55 7.93 5
Hardware 0.8 0.1147 0.3306 0.4744 0.7878 1.0864 4.8 6.7 3.3
PSO
Simulation0.9 0.0709 0.1466 0.3481 0.4505 0.7265 4.79 16.02 4.00
Hardware 0.9 0.0709 0.1466 0.3481 0.4505 0.7265 3.7 15 3
GA
Simulation0.91 0.0676 0.1637 0.3509 0.4871 0.7473 4.3 14.77 3.73
Hardware 0.91 0.0676 0.1637 0.3509 0.4871 0.7473 3.4 13.4 2.7
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Comparison of Harmonic (%) for 11 Level Inverter with NR, GA and PSO
Technique Harmonics
Line Voltage (%) Phase Voltage (%) Current (%)
Practical Simulation Practical Simulation Practical Simulation
NR
THD 4.8 5.55 6.7 7.93 3.3 5.00
3rd 1.7 0.02 1.8 0.60 0.8 0.02
5th 0.6 0.09 0.5 0.04 0.3 0.07
7th 0.9 0.08 0.6 0.06 0.2 0.09
9th 0.2 0.06 3.0 3.26 0.2 0.06
11th 0.4 0.10 0.3 0.10 0.1 0.11
13th 0.3 0.02 0.3 0.02 0.1 0.03
15th 0.1 0.09 1.4 1.04 0.1 0.08
PSO
THD 3.7 4.79 15 16.02 3.0 4.00
3rd 0.7 0.03 14.1 14.81 0. 6 0.01
5th 0.8 0.05 1.2 0.02 0.2 0.06
7th 0.3 0.01 0.5 0.06 0.1 0.01
9th 0.0 0.09 1.1 0.93 0.0 0.11
11th 0.2 0.09 0.3 0.05 0.1 0.02
13th 0.2 0.05 0.2 0.04 0.0 0.05
15th 0.1 0.05 1.8 1. 68 0.1 0.05
GA
THD 3.4 4.30 13.4 14.77 2.7 3.73
3rd 1.0 0.06 13.1 13.6 1.0 0.06
5th 0.7 0.67 1.7 0.66 0.4 0.68
7th 0.4 0.17 0.3 0.12 0.2 0.18
9th 0.1 0.02 1.3 1.20 0.2 0.00
11th 0.4 0.02 0.4 0.02 0.1 0.01
13th 0.2 0.09 0.2 0.09 0.1 0.10
15th 0.1 0.06 1.5 1.38 0.1 0.0712/4/2017 Dr. Shimi S.L, Assistant Professor, NITTTR, Chandigarh 73
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Comparison of Harmonics Content (%) up to 15th Order of Line Voltage for 11 Level Cascaded H-bridge Inverter Applied with Different Techniques
12/4/2017Dr. Shimi S.L, Assistant Professor, NITTTR,
Chandigarh 74
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Comparison of Magnitude of Line Voltage THD and Harmonics Content for CHMLI Applied with NR-SHE, PSO-SHE and GA-SHE Algorithms
THD
12/4/2017Dr. Shimi S.L, Assistant Professor, NITTTR,
Chandigarh 75
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Questions, Comments?
[email protected]/shimireji
9417588987
Thanks
12/4/2017Dr. Shimi S.L, Assistant Professor, NITTTR,
Chandigarh 76
mailto:[email protected]