Download mitigation of harmonics in seven level inverter by using pso

MITIGATION OF HARMONICS IN SEVEN LEVEL INVERTER BY
USING PSO ALGORITHM
B.Rajitha
M-tech Student Scholar
Department of Electrical & Electronics Engineering,
Shri Vishnu Engineering College for Women,
Bhimavaram
sources increases the output voltage will be pure closer to
ABSTRACT: In nowadays the multilevel inverters are
sinusoidal waveform. In this paper, an attempt has been
increased due to their ability to generate high quality
made to improve the quality of power. There are three
output wave forms with low switching frequency. The
types of conventional structures for multilevel inverters
different multilevel inverter structures are cascaded Hsuch as diode clamped multilevel inverter, flying
bridge, diode clamped and flying capacitor multilevel
capacitor multilevel inverter and cascaded multilevel
inverter. A cascaded H-bridge converter (CHB) is a
inverter.There are many popular methods are used to
multilevel topology which is formed from the series
reduce the harmonics in order to get an effective results.
connection of H-bridge cells. In this paper the selective
The methods for high switching frequency are Sinusoidal
harmonic elimination pulse width modulation strategy is
PWM and Space Vector PWM. For low switching
eliminating low-order harmonics by solving nonlinear
frequency methods are space vector modulation and
equations. The selective harmonic elimination method
selective harmonic elimination. The spwm, svpwm
(SHE-PWM) at fundamental frequency switching scheme
techniques are don’t eliminate low order harmonics. So
has been implemented using the Particle Swarm
theselective harmonic mitigation (SHM-PWM) technique
Optimization (PSO) Algorithm that produces all possible
for generating pwm signals that can be eliminate selected
solution sets when they exist. In comparison with other
lower order harmonics from voltage sources inverter. The
suggested methods, the proposed technique has many
Selective harmonic mitigation (SHM-PWM) is found out
advantages such as: it can produce all possible solution
the switching angles and these switching Angles are used
sets for any numbers of multilevel inverter without much
to amplitude of the fundamental harmonic component. In
computational burden; speed of convergence is fast etc.
this switching angles can be calculated by several
methods.
The first method is Newton–Raphson (N–R) method. The
This paper is to reduce the total harmonic distortion
disadvantage of iterative methods is their dependence on
(THD) and elimination of selective lower order harmonics
an initial guess and divergence problems are likely to
such as 5thand 7th order with minimum harmonic
occur for large numbers of inverter levels. Also, they can
distortion and obtain desired fundamental voltage. The
only find one set of solutions. Where low-order
results prove that the PSO algorithm converges
harmonics can be completely eliminated, but they can
successfully to the global solution faster than other
also find solutions for infeasible modulation index. The
algorithms. The simulation will be obtained by using
Optimization technique based on particle swarm
MATLAB/SIMULINK.
optimization Algorithm (PSO) was proposed for
computing switching angles for 7-level Inverter. The
Keywords- Multilevel inverters, Selective harmonic
implementation of this approach requires proper selection
elimination (SHEPWM), cascaded h bridge, particle
of certain parameters such as population size; Mutation
swarm optimization.
rate etc, there by its implementation becomes also
difficult for higher level inverters.
1. INTRODUCTION
In this paper we presented 7level cascaded h bridge
In recent years, multilevel inverters have received more
inverter with three H-bridges, solution of three
attention because of their ability to generate high quality
transcendental equations using PSO and elimination of
output waveforms with low switching frequency.
lower order harmonics such as 5thand 7th order with
Multilevel inverters have been considered as an optimum
minimum harmonic distortion and obtain desired
choice to provide better quality power to the load. In
fundamental voltage.
Multilevel inverters the desired output voltage is achieved
by Suitable low combination of multiple low dc voltage
sources used at the input side. As the number of dc
II. SEVEN LEVEL CASCADED H-BRIDGE
INVERTER
The cascaded H-bride multi level inverter is to use
capacitors and switches and requires less number of
components in each level. The combination of capacitors
and switches pair is called an H-bridge and gives the
separate input DC voltage for each H-bridge. It consists of
H-bridge cells and each cell can provide the three
different voltages like zero, positive DC and negative DC
voltages. The cascaded h bridge inverter is a series
connection of h bridge cells. The seven level cascaded h
bridge inverter diagram is shown in below. The number of
output phase (line-neutral) voltage levels in a cascade
multilevel inverter is then 2S+1, where S is the number of
dc sources. Cascaded h bridges typically use IGBT
switches. These switches have low block voltage and high
switching frequency.
Fig.2: phase voltage output of seven level inverter
III.SELECTIVE
HARMONIC
MITIGATION
TECHNIQUE
The Selective Harmonic Elimination Pulse Width
Modulation (SHEPWM) technique has proved to be
useful in eliminating some of the undesired harmonics
without increasing the switching frequency, leaving the
rest of them free. The solution to the rest of harmonics is
to add bulky and expensive filters. Pulse Width
Modulation (SHMPWM) has been introduced. The main
aim of this technique is mitigate the undesired harmonics
and find out the nonlinear equations are used to determine
switching angles of an Inverter. Switching angles play an
important role to produce the desired output by
eliminating selected harmonics.
Fig.1:Single phase Seven level cascaded h bridge
multilevel inverter
The Fourier series expansion for the above stair case
wave form is given bellow
The phase voltage output of seven level inverter as shown
in Fig.2, there are three switching angles and three nonlinear transcendental equations. Among s number of
switching angles, generally one switching angle is used
for fundamental voltage selection and the remaining (s-1)
switching angles are used to eliminate certain
predominating lower order harmonics. In three-phase
power system with isolated neutral, triplen harmonics are
cancel out automatically, and only non-triplen odd
harmonics are present.
∞
Van (wt) =∑𝑛=1 4vdc/nП[(cos(nӨ1) +cos (nӨ2) +cos
(nӨ3)] [sin (nwt)] ….
(1)
For a given desired fundamental peak voltageV1, it is
required to determine the switching angles such that
0<α1<α2<…. <αs<П/2
The expression for the fundamental voltage in terms
of switching angles is given by
V1 = 4vdc/П [(cos (α1) +cos (α2) +cos (α3)] … (2)
The switching angles are used to set the amplitude of the
fundamental harmonic and cancel a set of specific
harmonics.
value that is tracked by the PSO is the best value obtained
so far by any particle in the neighborhood of that particle.
This value is called gbest.
The maximum fundamental voltage is obtained when all
The basic concept of PSO lies in accelerating each
particle toward its pbest and the gbest locations, with a
random weighted acceleration at each time step as shown
in Fig.
the switching angles are zero and the V1max is given as
V1max=3*(4vdc/П)……. (3)
The modulation index is defined as the relationship
between the dc link voltage of the converter and the
amplitude of the generated fundamental component is
given as
M =V1 / [3*(4Vdc/п)] ………
(4)
The above stated conditions can be written in following
way by combining (1) and (4)
Cos (α1) + Cos (α3) + Cos (α3) = 3M…… (5)
Fig.3: Concept of modification of a searching point by
Cos (5α1) + Cos (5α2) + Cos (5α3) = 0…… (6)
Cos (7α1) + Cos (7α2) + Cos (7α3) = 0….. (7)
In this α1, α2and α3equations are unknown vales and
these angles can be calculated
1V.PARTICLE SWARM OPTIMIZATION
The particle swarm optimization is a population based
algorithm. The PSO methods have been employed
successfully to solve complex optimization problems and
eliminate low order harmonics and find switching angles.
PSO first introduced by Kennedy and Eberhart is one of
the modern heuristic algorithms; it has been motivated by
the behavior of organisms, such as fish schooling and bird
flocking.
Generally, PSO is characterized as a simple concept, easy
to implement, and computationally efficient. PSO is a
robust stochastic optimization technique based on the
movement and intelligence of swarms.PSO applies the
concept of social interaction to problem solving. It uses a
number of agents (particles) that constitute a swarm
moving around in the search space looking for the best
solution .Each particle is treated as a point in a
Ndimensional.Each particle keeps track of its coordinates
in the solution space which are associated with the best
solution (fitness) that has achieved so far by that particle.
This value is called personal best, pbest .Another best
PSO
The modification of the particle’s position can
bemathematically modeled according the following
equation:
V (n+1) = WV (n) + C1 rand (P best-Ө (n)) + C2 rand
(G best-Ө (n))… (8)
X (n+1) = X (n) + V (n+1)
…. (9)
V. THE PROPOSED PSO ALGORITHM
The minimization of THD in multilevel inverters is
achieved by using this PSO algorithm because of its
simple in nature and easy to implement, computational
efficient. The procedure for getting optimized results the
objective function is taken as the THD equation is as
follows
The proposed PSO algorithm is given as following steps:
Step1: create the random initial population size of
switching angles by considering their limitation is 0 to
π/2.
Step2: initialize the velocity, Pbest, Gbest, iteration count
for computing switching angles.
Step 3: update the iteration count.
Step 4: update the velocity and position according to the
equations (8) & (9) for moving of particles in search
space.
variation technique are simulated with the use of
MATLAB mfile. For seven level inverter three H-bridges
are needed for simulation. IGBT switches are used as
power switches. Figure 6 shows the simulation circuit for
seven level inverter using SHM- PWM technique.
From simulation results, PSO is advantage for compute a
large number of switching angles. The Modulation index
between MI=0 to 0.9653 are less than 5% or standard
requirement. The best THD=12.5%, MI=1.The table show
harmonic amplitude of multilevel inverter for modulation
index is 0.99.
Step 5: evaluate the fitness or objective function by using
equation (11)
TABLE 1
Step 6: update the values of Pbest and Gbest.
Step 7: Is criterion achieved then go for next step
otherwise repeat the step3 to step6 for best solution.
OPTIMUM SWITCHING ANGLES FOR SINGLE
PHASE 7-LEVEL INVERTER
M
Start
Initialize particles with random position and velocity
vectors
Switching angles
α2
α3
30.6
50.5
1
α1
30.5
0.9
50.5
30
30.5
0.99
50.5
30.4
50.7
THD
12.5%
For each particle’s position (p) evaluate
fitness
If fitness (p) better than fitness (Pbest)
then
best=P
Set best of Pbest as Gbest
Update particles velocity and position
Stop: Giving Gbest as optimal
solution
Fig.4: Particle swarm optimization algorithm flow chart
V1. SIMULATION AND RESULTS
The single phase cascaded H bridge seven level inverter
using SHM -PWM technique and switching angle
FIG.5: Simulation circuit of single phase7 level cascaded
multilevel inverter using SHM –PWMtechnique
Fig.6: Output waveform of seven level inverter
using SHM-PWM
The switching angles versus Modulation index, the final cost
of each solution, THD, and any individual harmonic
amplitudes in M=1.2 are shown in Fig. 7 to Fig.
9respectively.
Figure 9: Plot of switching angle (α3) Vs Modulation
index
Fig.10: THD values in Seven Level Inverter
Fig.7: Plot of switching angle (α1) Vs Modulation index
Fig.11: 5th harmonic reduction
Figure 8: Plot of switching angle (α2) Vs Modulation
index
VIII.REFERENCES
Fig.12: 7th harmonic reduction
VII. CONCLUSION
The selective harmonic elimination method can used to
eliminate the lower order harmonics and reduce the total
harmonic distortion. The PSO method gives the lower
%THD compared to the other classical Iterative methods.
In recent years the strategy for elimination of harmonics
in multilevel Inverters by using PSO method has been
done by taking better switching angles as the objective
function. In this work lower order harmonics have been
eliminated by using the equation for THD as the objective
function and have given better results in minimization of
THD for up to the 99th order of harmonics. The results
prove that the PSO algorithm converges successfully to
the global solution faster than other algorithms.
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