International Journal nal of Research in Advent Technology, Vol.2, No.6, No. June 2014 E-ISSN: 2321-9637
Selective elective Harmonic Elimination for a Cascaded Multilevel Inverter Rohini Sharma1, Gagandeep Sharma 2, Prabhu Omer 3 Department of Electrical Engineering 1, 2, 3, ,Punjab Technical University1, 2 ,Chandigarh University 3 rohini.vasu23@gmail.com 1,gaggu246@gmail.com 2, prabhu.omer89@gmail.com3 Abstract-This This paper presents selective harmonic elimination technique intended ntended for cascade nine level multilevel inverter for both single and three phases to remove the specific harmonics in the output voltage. This new approach is presented to implement the Newton-Raphson Newton method for solving the transcendental equations which produces all probable solutions with any random initial guess and for any amount of levels of multilevel inverter. The angles obtain are re then used to choose the switching pulses for 9-level 9 level cascaded multilevel mult inverter. The simulation results expose that method can competently eliminate the selective lower order harmonics in the output waveform of the inverter, and as well as low THD (Total Harmonics Distortion). inverter1, Selective harmonic elimination2, Total harmonic elimination3 Index Terms- Cascaded multilevel inverter1, 1.
INTRODUCTION
The notion of multilevel converters has ha been introduced ever since 1975.. The word multilevel began with the three-level level converter. converter However, the basic idea of a multilevel converter to accomplish higher power is to use power semiconductor switches with several lower voltage dc sources to accomplish the power conversion by synthesizing a staircase voltage waveform [1]. As the number of dc sources is augmented, the output voltage waveforms obtained is nearer to the sinusoidal voltage waveform. These multilevel inverters found there relevance in induction motor drives, static var compensation, UPS system, laminators, mills, conveyors and compressors. To obtain the sinusoidal voltage waveform from multiple multipl dc sources the semiconductors switches such as MOSFET/IGBT are switched on and off in such a way to maintain the THD % to its least amount value. These semiconductor switches are of low power ratings but of high switching speed. The multilevel inverter configurations onfigurations contain; flying capacitor topology,, diode clamped topology and H-bridge topology. The commonly used switching technique is selective harmonics elimination method me at fundamental frequency [2]. Multilevel Modulation Lower Switching Frequency SHE
High Switching Frequency Hybrid Modulation
Multicarrier PWM
Phase Shifted
Since multilevel converter usually operated with low switching frequency, SHE-PWM PWM offers several advantages over the other methods such as low switching frequency with a wider converter’s bandwidth, direct control over low-order low harmonics and better DC source utilization. The main challenge related with SHE-PWM PWM techniques is to attain the systematic solution of the system of non-linear non transcendental equations that consist of trigonometric terms which in turn offer multiple sets of solutions. solutions Several algorithms gorithms have been reported in the open text relating methods of solving the consequential nonnon linear transcendental equations, which describe the SHE-PWM PWM problem. These algorithms contain the well-known known iterative approach, Newton–Raphson Newton method .This method od is derivative-dependent derivative and may finish in local optima; further, a well judged choice of the initial values only will give assurance of convergence [3]-[5]. The Multilevel inverter using cascaded-inverters cascaded with alienated dc sources, in future called a “cascade multilevel inverter” appears to be finer to other multilevel structures in expressions of its structure that is not barely simple and modular but also requires the least number of components. This modular structure makes it easily extensible for higher number of most wanted output voltage levels without excessive increase in circuit power complication. In addition, extra clamping diodes or voltage balancing capacitor are not compulsory [6].
Level Shifted
Figure1 Multilevel converter modulation methods.
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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 In this paper, a selective harmonic elimination technique is introduced to cascade multilevel converter. With the switching angles which are found out, it could be obtain that the low order harmonic of the output from the converter is minimize. An simulation model of 9-level Hbridge multilevel converter with secluded dc sources is engaged to authenticate the method presented in the paper. The results show that the method can in actual fact eliminate the specific harmonics, and the output voltage waveforms have low THD as anticipated in theory analysis [7]. 2. CASCADED H-BRIDGH INVERTER
is associated in series such that the synthesized voltage waveform is the sum of all of the entity inverter outputs. With enough levels and an appropriate switching algorithm, the multilevel inverter results in an output voltage that is approximately sinusoidal [8]. The main advantages and disadvantages of cascaded multilevel inverters are summarized as follows: Advantages: • •
The high number of phase output voltage levels base on the dc sources (k = 2m + 1). A suitable and cost-effective manufacturing process for the multilevel inverters by using the series of H-bridges.
Disadvantages: •
Separate dc sources are necessary for each of the H-bridges that limit the applications of the circuit based on the accessible sources [9].
3. SELECTIVE HARMONIC ELIMINATION Selective Harmonic Elimination is a pre-programmed modulation technique whereby the switching angles for the pulses in the output waveform are optimized to make sure decline or removal of chosen low order harmonics. The pre-determined switching points are considered from equations which are formulated using the Fourier examination of a ‘chopped’ square wave. Due to the transcendental and nonlinear character of these equations loads of methods have been formulated for finding their solutions, including extensions of Newton Raphson algorithms, Genetic Algorithms and minimization schemes [10]. The Fourier series expansion of the Van waveform obtained by a m-level cascaded inverter with s DC sources, is given by
Van (wt ) = 4Vdc / Π
∑ n[cos (nα 1) + cos (nα 2 ) + .......... ...... + cos (nαs )]
Figure 2 Nine-level cascaded H-bridge For a cascade multilevel inverter, separate dc sources are utilized by multiple full H-bridge to generate a staircase waveform for output voltage. Each inverter level can produce three different voltage outputs, +Vdc, 0, and –Vdc by dissimilar combinations of the four switches, S1, S2, S3, and S4. To find +Vdc, switches S1 and S4 are turned on, whereas –Vdc can be obtained by turning on switches S2 and S3. By turning on S1 and S2 or S3 and S4, the output voltage is 0.The ac output of each level’s full-bridge inverter
sin (nwt ) / n
(1) To determine the s switching angles it is required the condition:
0 ≤ α 1 ≤ α 2 ≤ .......... ... ≤ α s ≤ ∏ / 2
(2)
It is value notice that a m-level cascade inverter has s degrees of freedom: one degree is used to control the magnitude of the fundamental voltage while the 107
International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637
cos(α1) + cos(α 2) + ........... + cos(αs ) − sm1 = 0 cos(5α1) + cos(5α 2) + ....... + cos(5αs ) = 0 cos(7α1) + cos(7α 2)........... + cos(7αs ) = 0 . . .
40 30 20
L in e v o lt a g e
remaining s-l degrees can be used for eliminating assured predominating order harmonics: for instance 3Td, 5th, 7th, 11th, 13th, ... rth order harmonic components. In fact, these components usually govern the Total Harmonic Distortion. A transcendental equations system can be written as
10
-10 -20 -30 -40 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time(s) Figure 4 Line voltage of single phase nine level Selective harmonic elimination inverter.
. cos(rα1) + cos(rα 2) + ........... cos(rαs ) = 0 (3) There are several methods for solving this nonlinear system we used the Newton-Raphson one. The resolution of the system gives the switching angles suitable [11]-[12].
0
20 0
4. SIMULATION RESULTS -20 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (s)
Discrete, Ts = 2e-005 s. powergui
Fundamental (50Hz) = 38.43 , THD= 9.54% 5
Vabc A Iabc B
4
a Scope
b
M a g (% o f F u n d a m e n t a l)
Phase A
3
C c a
Three-Phase V-I Measurement
To Workspace
A Phase B
B
2 1
t
C Clock
Three-Phase Series RL Load
To Workspace1
0
0
100
200
300
400
500
600
700
800
900
Frequency (Hz)
Figure 5 THD contents in the output voltage of single phase Selective harmonic elimination has been obtained by using FFT analysis
Phase C
Figure 3 Simulation model
108
1000
International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 400 300
500
P h a s e v o lta g e
200 100
0
0
-500
-100 -200
0
-300
0.005
0.01
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Time(s)
0.03
0.035
0.04
Fundamental (50Hz) = 716.2 , THD= 7.83% 2.5
M a g ( % o f F u n d a m e n t a l)
800 600
2
400
L in e v o lt a g e
0.025
0.04
Figure 6 Phase voltage of three phase nine level Selective harmonic elimination inverter.
200
1.5
0
1
-200 -400
0.5
-600 -800 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Time (s)
0
0
100
200
300
400
500
600
700
800
900
Frequency (Hz)
Figure 7 Line voltage of three phase nine level Selective harmonic elimination inverter. 6
0.02 Time (s)
-400 0
x 10
0.015
Figure 9 THD contents in the output voltage of three phase Selective harmonic elimination has been obtained by using FFT analysis.
-4
Load current
4
5. CONCLUSION
2
0
-2
-4 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Time(s) Figure 8 Load current of three phase nine level Selective harmonic elimination inverter.
0.04
The selective harmonic elimination method for single and three phase at fundamental frequency switching scheme has been implemented using the NewtonRaphson method that produces all possible solution sets when they exist. and it is shown that a significant amount of THD reduction can be attained if all possible solution sets are computed. The Total Harmonics distortion is reduced to 9.59% for single phase and 7.88% for three phase and staircase voltage waveform is obtained which is much closer to sinusoidal waveform. Therefore, an effective reduction of total harmonics distortion is achieved.
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