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Microsoft Word - 01-10-015.docJ Electr Eng Technol.2015;10(1):
261-270 http://dx.doi.org/10.5370/JEET.2015.10.1.261

261Copyright The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/

licenses/by-nc/3.0/)which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Optimal Harmonic Stepped Waveform Technique for Solar Fed Cascaded Multilevel Inverter

S.Albert Alexander† and Manigandan Thathan*

Abstract – In this paper, the Optimal Harmonic Stepped Waveform (OHSW) method is proposed in order to eliminate the selective harmonic orders available at the output of cascaded multilevel inverter (CMLI) fed by solar photovoltaic (SPV). This technique is used to solve the harmonic elimination equations based on stepped waveform analysis in order to obtain the optimal switching angles which in turn reduce the Total Harmonic Distortion (THD). The OHSW method considers the output voltage waveform as four equal symmetries in each half cycle. In the proposed method, a solar fed fifteen level cascaded multilevel is considered where the magnitude of six numbers of harmonic orders is reduced. A programmable pulse generator is developed to carry the switching angles directly to the semiconductor switches obtained as a result of OHSW analysis. Simulations are carried out in MATLAB/Simulink in which a separate model is developed for solar photovoltaic which serves as the input for cascaded multilevel inverter. A 3kWp solar plant with multilevel inverter system is implemented in hardware to show the effectiveness of the proposed system. Based on the observation the OHSW method provides the reduced THD thereby improving power quality in renewable energy applications.

Keywords: Multilevel inverter, Pulse width modulation, Photovoltaic systems, Power conversion harmonics, Total harmonic distortion.

1. Introduction Harmonics is an important concern in all utility sectors.

However, the electric utilities are recently designed to monitor and analyze the existence and effects of distortion on system and customer devices. The factors contribute the harmonic distortion on distribution systems are increased application of capacitors and non linear devices [1]. In order to improve the power quality and to maintain stable power supply performance, an inverter control strategy with harmonic reduction techniques can be employed [2]. Unlike conventional inverters, the multilevel inverters (MLI) can be employed because these converters are based on the series connection of single phase inverters and widely applied to interface to renewable energy sources, flexible AC transmission systems (FACTS), electrical drives and power-quality devices [3-5]. There are three types of MLI topologies such as diode clamped, flying capacitor and cascaded H Bridge. Amongst the three topologies, diode clamped multilevel inverters are widely used in industrial drive applications but it requires the number of diodes when the levels are increasing [6-7] whereas in flying capacitor, the number of capacitors are required when the level exceeds three [8]. Hence the

cascaded multilevel inverter (CMLI) is an ideal choice to synthesize the desired output voltage from several separate DC sources (SDCs) like solar photovoltaic’s with reduced number of components when compared to other topologies [9]. In addition CMLI has no unbalance problem since each DC link is fed by an isolated DC source [10].

The performance of multilevel converter (MLC) can be improved by Harmonic elimination, control strategies and new multilevel converter topologies [11]. Several methods are put forth for the harmonic elimination in literature. The methods proceeds from the basic sinusoidal pulse width modulation (SPWM) which are not able to eliminate lower harmonics completely [12] and space vector modulation (SVM) where the application of SVM in cascaded topologies is usually limited to a small number of levels due to the large number of switching vectors [13]. Selective harmonic elimination pulse width modulation (SHE PWM) is employed in multilevel inverters which require solving the non linear harmonic equations in order to eliminate the certain harmonic orders by the generation of switching angles corresponding to harmonic elimination.

Theory of resultant is proposed in [14] to derive the mathematical model, but this method is complicated, time consuming and not suitable for the varying input sources. Moreover the resultant theory is limited to find up to six switching angles for equal DC voltages and up to three switching angles for non equal DC voltage cases [15]. Homotophy algorithm provides only one set of solution [16]. Evolutionary concepts such as Bee algorithm (BA),

† Corresponding Author: Dept. of Electrical and Electronics Engi- neering, Kongu Engineering College, Perundurai, Tamilnadu, India. ([email protected])

* Principal, P.A.College of Engineering and Technology, Pollachi, Tamilnadu, India. ([email protected])

Received: September 19, 2013; Accepted: September 24, 2014

ISSN(Print) 1975-0102 ISSN(Online) 2093-7423

Optimal Harmonic Stepped Waveform Technique for Solar fed Cascaded Multilevel Inverter

262 J Electr Eng Technol.2015;10(1): 261-270

Genetic algorithm (GA) and particle swarm optimization (PSO) methods are used to obtain the optimal switching angles in which additional to objective function the variables such as pheromone formation and its trail function in BA, crossover and mutation factors in GA, weighting function and random factors in PSO are required which makes the system complex [17-18].

Waveform synthesis is used to suppress the harmonics and also to reduce the filtering requirement. Use of stepped waveform technique provides trade off between harmonic cancellation and equipment complexity [19]. Calculating switching angles which minimize the total harmonic distortion (THD) using step modulation and stair case modulation in a seven level inverter is proposed in [20-21]. Half wave symmetry for SHE is proposed for a five level inverter in [22] where 20 switching angles are considered in a half cycle incorporating its rising and falling edges, so 20 equations can be formulated. The number of switching angles for half-wave symmetry SHE-PWM is twice that of quarter wave symmetry SHE-PWM [23].

Damoun et al., developed an equal area criteria based four equation method for five level inverter with unbalanced dc sources [24]. The line search trust region interior point algorithm to calculate the optimal switching angles in offline for a five level inverter is presented in [25]. All the methods referred deals with the minimum number of levels and the input DC other than solar PV is considered as the source for the multilevel converter.

A single phase grid connected photovoltaic inverter topology with boost converter, a low voltage three level inverter with an inductive filter and a step up transformer for interfacing the grid is considered in [26]. SHE for an eleven level inverter with Artificial Neural Network (ANN) based technique is proposed in [27] which requires an extensive data set required under various conditions which possess combinational problem.

In this paper, the optimized harmonic stepped waveform technique (OHSW) is applied to minimize low-order harmonics in a solar photovoltaic fed fifteen level CMLI, as well as to satisfy the desired fundamental component. Experimental results are presented to confirm the simula- tion results.

2. Problem Formulations The cascaded multilevel inverter consists of a series

connection of single phase full bridge inverter units as shown in Fig. 1. Each full bridge units known as ‘stages’ can generate three different voltages output: +Vpv, 0, -Vpv. For the seven stage inverter the output waveform is illustrated in Fig. 2. The level and stage relation is given by the Eq. (1).

2 1m Ns= + (1)

Fig. 2. Seven stage fifteen level output voltage waveform

S.Albert Alexander and Manigandan Thathan

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where m is the number of levels and Ns is the number of inverter stages. Hence for a fifteen level output, seven inverter stages are required.

By using Fourier series the staircase output of multilevel inverter with non equal input sources is described in Eq.(2).

1 1

2 21,3,5

nπ k nα

. (2)

where kiVpv is the ith DC voltage, Vpv is the nominal DC voltage and the switching angles α1 to αm must satisfy the following condition.

α1 ≤ α2 ≤ α3 ≤………..≤ αm ≤ 2 π

The number of harmonics which can be eliminated by

the multilevel inverter is (m-1). For a seven stage inverter, six numbers of harmonic orders can be minimized or eliminated. The equation governing the SHE for a fifteen level inverter is given in Eq. (3). Here the objective is to determine the switching angles α1 to α7. The elimination of triple harmonics for the three-phase power system applications is not necessary, because these harmonics are automatically eliminated from the line-line voltage [17].

In CMLI based photovoltaic systems, the operating DC voltages of standard PV cells range from 15 to 35 V and from the CMLI based energy-storage system with batteries, the voltages of batteries also change due to their states of charge [21]. Hence, the different voltages arrive at the inverter stages will cause unregulated fundamental with higher magnitude of low order harmonics which also to be considered.

11 2

33 4

( ) sin( ) cos( ) cos( 6)

∞

=

+ +

+ + = ∑

+ +

3. Optimized Harmonic Stepped Waveform The harmonic stepped waveform technique employing

the quarter wave symmetry concept is much suitable for the multilevel inverter to determine the optimal switching angles inorder to provide the output voltage waveform with reduced total harmonic distortion (THD). Switching losses can also be minimized by turning the switch on and off only once per cycle.

There are three possible optimization techniques for reducing the low-order harmonics: 1) step heights are optimized with equally spaced steps, 2) step spaces are

optimized with the steps of equal height and 3) optimizing both heights and spaces. In the variable-input scheme, the third optimization technique is more feasible than the other two techniques. The Fourier series expression for this method is given in Eq. (3). OHSW technique with equal input sources is given in [28].

The OSHW is depicted as quarter wave symmetry where the first half cycle of the output waveform is given in Fig. 3. Considering the switching angles for the complete cycle as α1 to α28, in which each set of α can be obtained by sampling the given waveform into four set of quarter. In the first quarter, from the interval zero to α1 the output voltage is zero and at α1, the output voltage approaches to Vpv1. At α2, the output voltage changes from Vpv1 to (Vpv1+Vpv2) and the process continues upto π /2 where the voltage becomes (Vpv1+Vpv2 + Vpv3+Vpv4+ Vpv5+Vpv6+ Vpv7). In the second quarter the level of output voltage decreases to (Vpv1+Vpv2 + Vpv3+Vpv4+ Vpv5+Vpv6) at π -α7. The process will be repeated upto π -α1 where the output voltage again approaches to zero to complete a half cycle. In the next half cycle the same process will be continued in the same manner other than the amplitude of the input voltage changes from positive to negative.

First quarter: Considering the switching angles α1 to α7

during the interval 0 to π /2. Second quarter:

α8= π -α7

Third quarter:

M α27=2 π -α7 α28=2 π +α1

While considering the harmonic contents in the output

waveform, the amplitude of DC components and all even

Fig. 3. Quarter wave symmetry waveform for 15 level

Optimal Harmonic Stepped Waveform Technique for Solar fed Cascaded Multilevel Inverter

264 J Electr Eng Technol.2015;10(1): 261-270

order harmonics approaches near zero. Hence the odd harmonic in the quarter wave symmetric CMLI to be estimated. The set of non linear equations to obtain optimal switching angles is given in the Eqs. (4) to (10).

1 7 71 2 2cos( ) cos( ) ........ cos( ) 4pvpv pv MV V V+ + + = πα α α

7 71 1 2 2cos(3 ) cos(3 ) ........ cos(3 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(5 ) cos(5 ) ........ cos(5 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(7 ) cos(7 ) ........ cos(7 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(9 ) cos(9 ) ........ cos(9 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(11 ) cos(11 ) ........ cos(11 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(13 ) cos(13 ) ........ cos(13 ) 0pvpv pvV V Vα α α+ + + = (4) - (10)

where 1

(1 7)pv

h M

h1 is the amplitude of the fundamental component. As

the proposed method involves the variable input sources, the Vpv is taken at the left hand side in the above expressions.

From Eq. (4), varying the modulation index value can control the amplitude of the fundamental component. The other nonlinear equations listed from (5) to (10) are the undesirable harmonic components can be eliminated which are set to be zero. Therefore, in an m level inverter, the lowest m-1 odd harmonics can be removed.

The Newton-Raphson (NR) method is used to solve the non-linear equation systems using successive approximation procedure which is suitable for implementing computer program. The following algorithm describes the steps involved to calculate switching angle.

Step 1: Formation of switching angle matrix is given in

the equation (11) where the unknown switching angles α1 to α7 to be determined.

1 2 3 4 5 6 7, , , , , ,

Tj j j j j j j jα α α α α α α α = (11)

Step 2: Formation of nonlinear system matrix is given in

the Eqs. (12) and (13).

71 2

71 2

71 2

71 2

71 2

α α

the Eq. (14).

TMT π× × = ⋅ ⋅ ⋅ ⋅ ⋅ (14)

Eq. (4) and (14) can be rewritten as per the following

Eq. (15).

F(α)=T (15) Using the matrices given in the Eqs. (11) - (15) and NR

method the statement of algorithms is as follows to incorporate in the program using MATLAB software.

Step 1: Guess for initial values of α as per Eq. (16). The

process of finding the initial guess through equal area criterion is given in [29].

0 0 0 0 0 0 0 0 1 2 3 4 5 6 7, , , , , ,α α α α α α α α = (16)

Step 2: This step includes the Eqs. (17)-(20).

F(α0) = F0 (17) Linearizing the Eq. (15) at α0 we get

0

(18)

and

0 0 0 0 0 0 0 0 5 71 2 3 4 6, , , , , ,d d d d d d d dα α α α α α α α = (19)

Solving the Eq. (19) using the inverse of the matrix

given in the Eq. (20).

0 0

α ∂ = − ∂ (20)

Step 3: Updation of initial values is made as per the

Eq. (21).

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1j j jdα α α+ = + (21) The steps (2) - (3) is repeated until jdα is fulfilled and

the condition to be satisfied is α1, α2, α3………α7 < π /2.

4. Simulation and Results Simulations are carried out in MATLAB / Simulink. In

order to provide the source for a fifteen level inverter, a solar photovoltaic source model according to the specifica- tion of the commercial PV panel is used. The solar PV model comprises of many individual solar cells connected in series and parallel to obtain the required rating. The solar cell model consists of parallel combination of a current source, two exponential diodes, series (Rs) and parallel (Rp) resistances. The output current equation is given in Eqs. (22)-(24). The PV array input to the each inverter stage is 48V, 7A. A single solar cell of rating 0.5V and 7A with standard test conditions of 1000W/mm2 and 250C of 96 numbers in series connection is chosen.

2 s p1ph /I = I K K (V 1*R ) R+− − − (22)

where

s* *

*K = I (e 1)+ − (23)

2* *s 2 s2

(V 1 R )/(N Vt) *K = I (e 1)+

− (24) Is and Is2 are the diode saturation currents, Vt is the

thermal voltage, N and N2 are the quality factors (diode emission coefficients) and Iph is the solar-generated current. The quality factor is in the range of 1 to 2. The solar generated current Iph is given in the Eq. (25).

Iph= Ir*(Iph0/Ir0) (25)

where Iph0 is the measured solar-generated current for irradiance Ir0. In order to verify the model, the P-V and V-I characteristics is plotted and shown in Fig. 4 and 5. The design is to generate the output peak voltage of 336V to deliver power to consumer loads as given in Eqs. (26)-(27).

Vout = 48V x 7 stages = 336V (26) Vrms = 336/ 2 = 230Vac (27)

The simulation and analysis of optimal harmonic stepped

waveform technique for solar fed CMLI is developed. The set of harmonic orders considered are 3, 5, 7, 9, 11 and 13. The initial guess values utilized are {0.01; 0.2989; 0.4387; 0.6950; 0.9240; 1.170; 1.52} and the process is repeated until all elements in jdf matrix are less than 0.0000001. A programmable pulse generator is developed which will carry the switching angles directly to the semiconductor

devices which summarily reduces the complexity of the system.

Fig. 6 shows the output voltage waveform of OHSW based solar fed fifteen level inverter and Fig. 7 shows the

Fig. 4. P-V Characteristics of the solar panel

Fig. 5. I-V Characteristics of the solar panel

Fig. 6. Fifteen level output voltage waveform with OHSW

Fig. 7. FFT Analysis for the output waveform with OHSW

Optimal Harmonic Stepped Waveform Technique for Solar fed Cascaded Multilevel Inverter

266 J Electr Eng Technol.2015;10(1): 261-270

Fast Fourier transform (FFT) analysis of the waveform which shows the THD value of 8.55. Table 1 shows the various sets of switching angles obtained for the modulation index M = 0.36 and M = 1.

The OHSW is compared with the conventional pulse width modulation (PWM) technique. Fig. 8-9 shows the corresponding output voltage waveform and FFT analysis for a solar fed fifteen level multilevel inverter with PWM. Fig. 10 shows the comparison of harmonic orders magnitude obtained using OHSW and PWM techniques. Based on the result it is observed that the OHSW technique improves the output quality of the waveform with reduced THD and magnitude of harmonic orders.

Table 1. Switching angles determination

M=0.36 α 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter α1 8.857 171.1143 188.8857 351.1143 α2 14.8027 165.1973 194.8027 345.1973 α3 27.9257 152.0743 207.9257 332.0743 α4 47.2589 132.7411 227.2589 312.7411 α5 57.27771 122.7229 237.2771 302.7229 α6 72.8232 107.1768 252.8232 287.1768 α7 87.8539 92.1461 267.8539 272.1461

M=1 α1 5.0126 174.9874 185.0126 354.9874 α2 14.2451 165.7549 194.2451 345.7549 α3 25.9953 154.0047 205.9953 334.0047 α4 37.6040 142.3960 217.6040 322.3960 α5 52.0406 127.9594 232.0406 307.9594 α6 65.0413 114.9587 245.0413 294.9587 α7 86.2279 93.7721 266.2279 273.7721

Fig. 8. Fifteen level output voltage waveform with PWM

Fig. 9. FFT Analysis for the output waveform with PWM

Fig. 10. Comparison graph for harmonic order magnitudes

5. Experimental Results A 3kWp solar PV power supply unit is designed and

implemented for the seven stage fifteen level solar fed CMLI with the above mentioned algorithm. In India, much of the domestic loads operate from single phase 230V, 50Hz AC system. Hence the output voltage of the system is designed for the 230V AC supply. In order to achieve this, the input supply used in the setup is 48V. Table II shows the rating of the complete hardware setup. Each photovoltaic panel has a rated power of 115W with voltage variation of 16 to 21 volts (nominal 12V) depending on the operating conditions such as light intensity and so on. Four photovoltaic panels are connected in series to get a nominal voltage of 48V which constitutes as single individual source for CMLI. Four numbers of 12V, 100Ah battery packs are connected in series to get a nominal DC bus of 48 volts. These batteries are charged from the photovoltaic unit through a controlled charging circuit. There are seven sets of individual PV supply source used for the hardware implementation as they produce 48 x 7=336Vp (230Vrms).

Each input source to the CMLI provides the variation upto ±10%, the voltage sensors are provided at each source level. These inputs are given to the FPGA processor SPARTAN3E. Based on the OHSW algorithm incorporated in the processor, it generates the switching angles to the inverter switches MOSFET IRF840 through a driver circuit considering the sequences at each four quarters in the complete cycle. Fig.11 shows the 3 kWp Solar PV plant and in Fig.12, the complete hardware setup comprising of charge controllers, battery and the proposed inverter is given. Fig.13 shows the power and control circuit of inverter and Fig.14 shows the FFT analysis using the Power Quality Analyser (PQA) WT3000 where the THD obtained in this method is about 9% with the possible minimisation of low order harmonics considered in this work. The variation of input PV voltage is measured at every instant which is used for solving OHSW equations. The comparison of the proposed method with the existing works is reported in Fig.15 and Fig.16 which shows that the proposed method provides higher voltage levels with V fundamental by considering more number of harmonic

S.Albert Alexander and Manigandan Thathan

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orders and results in lesser THD. In addition this method is implemented with solar

photovoltaic’s as the input and also considered the variations of the solar panels with respect to temperature

and irradiance. Based on the variations in the input Vpv1 to Vpv7 the necessary switching angles will be generated based on the equations given in (4) - (10). The advantage of the proposed method needs to satisfy the condition α1, α2, α3 …… α7 < π /2 rather than the condition α1 ≤ α2 ≤ α3

≤……….≤ αm ≤ 2 π

for the other SHE problems.

Table 2. Experimental setup specifications

Solar PV Model Solectric 9000 Pmpp 115Wp Voc 21.2V Isc 7.4A

Vpm 16.5V Ipm 6.95A

No. of panels 28 Total power 3220Wp

Charge Controllers (CC) Make Sukaam

V-I Rating 48V,10A No. of CC 7

Battery bank Make & Model EXIDE 6LMS100L

Rating 12V, 100Ah No. of batteries 28

Power Quality Analyser (PQA) Make Yokogawa Model WT3000

Fig.15. Comparison graph for performance parameters

Fig. 16. Comparison graph for Vfundamental considered

Fig. 11. Solar plant of rating 3kWp

Fig. 12. Hardware set up

Fig. 13. Power circuit and control circuit of MLI

Fig. 14. Output voltage waveform and FFT analysis

Optimal Harmonic Stepped Waveform Technique for Solar fed Cascaded Multilevel Inverter

268 J Electr Eng Technol.2015;10(1): 261-270

Fig. 17. Power Quality Analysis with WT3000

Adopting OHSW technique in [30], the THD obtained is

about 32.78 for a seven level inverter whereas for a fifteen level solar fed inverter the THD obtained in the proposed paper is 9.5. In both simulation and hardware, a solar fed fifteen level inverter of same specification and rating is taken into consideration. The correlation between the simulation and hardware results are made based on the THD analysis illustrated in Fig. 17 which is related to the Fig. 7 obtained through simulation.

6. Conclusion A fifteen level solar fed cascaded multilevel inverter for

the elimination of certain harmonic orders is developed for the power quality improvement. The method is compared with the conventional PWM approach, which shows that OHSW based method is much suitable and an ideal choice for implementing selective harmonic elimination cases. The advantages of this method include simple computational algorithm and no requirement of filters, detailed look up tables and output transformers. Moreover, this technique can be implemented in both standalone and grid interacted PV systems.

Acknowledgements The authors acknowledge and thank the Department

of Science and Technology (Government of India) for sanctioning the research grant for the project titled, “Design and Development of Multilevel Inverters for Power Quality Improvement in Renewable Energy Sources” (Ref.No.DST/TSG/NTS/2009/98) under Technology Systems Development Scheme for completing this work.

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[27] Faete Filho, Helder Zandonadi Maia, Tiago H. A. Mateus, Burak Ozpineci, Leon M.Tolbert and João O. P. Pinto, “Adaptive Selective Harmonic Minimization Based on ANNs for Cascade Multilevel Inverters with Varying DC Sources”, IEEE Transactions on Indust- rial Electronics, vol. 60, no. 5, pp. 1955-1962, May 2013.

[28] Siriroj Sirisukprasert, “Optimized harmonic stepped waveform for multilevel inverter”, Thesis, Virginia Polytechnic Institute and State University, pp. 40-56, 1999.

[29] Jin Wang, and Damoun Ahmadi, “A precise and practical harmonic elimination method for multilevel inverters”, IEEE Transactions on Industry Appli- cations, vol. 46, no. 2, pp. 857-865, March/April 2010.

[30] Fanghua Zhang and Yangguang Yan, “Selective harmonic elimination PWM control scheme on a three phase four leg voltage source inverter”, IEEE Transactions on Power Electronics, vol. 24, no. 7, 1682-1689, July 2009.

[31] Faete Filho, Leon M. Tolbert, Yue Cao and Burak Ozpineci, “Real-time selective harmonic minimize- tion for multilevel inverters connected to solar panels using artificial neural network angle generation”, IEEE Transactions on Industry Applications, Vol. 47, No. 5, pp. 2117-2124, September/October 2011.

[32] Nima Yousefpoor, Seyyed Hamid Fathi, Naeem Farokhnia and Hossein Askarian Abyaneh, “THD minimization applied directly on the line-to-line voltage of multilevel inverters”, IEEE Transactions on Industrial Electronics, Vol. 59, No.1, 373-380, January 2012.

[33] Naeem Farokhnia, Hadi Vadizadeh, Seyyed Hamid Fathi and Fariba Anvariasl, “Calculating the formula of line-voltage THD in multilevel inverter with un- equal DC sources”, IEEE Transactions on Industrial Electronics, vol. 58, No. 8, pp. 3359-3372, August 2011.

[34] M.G. Hosseini Aghdam, S.H. Fathi, G.B. Gharehpetian,

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270 J Electr Eng Technol.2015;10(1): 261-270

“Comparison of OMTHD and OHSW harmonic optimization techniques in multi level inverter with non equal DC sources”, International Journal of Electrical and Electronics Engineering, vol. 2, No.10, pp. 600-606, 2008.

S.Albert Alexander He received B.E. degree in Electrical Engineering from Bharathiar University, India. He re- ceived M.E. degree (Power Electronics and Drives) and Ph.D. degree from Anna University, India in 2007 and 2014 respectively. His research interests are multilevel inverters, renewable

energy systems and soft computing techniques. He is the principal investigator for the major research projects of worth Rs.0.62 crores sponsored by Government of India.

Manigandan Thathan He received B.E. degree in Electrical Engineering from Government College of Tech- nology, Coimbatore in 1996. He received M.E. degree in control systems from PSG College of Technology, Coimbatore, India in 1998 and Ph.D. degree from Anna University, India in

261Copyright The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/

licenses/by-nc/3.0/)which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Optimal Harmonic Stepped Waveform Technique for Solar Fed Cascaded Multilevel Inverter

S.Albert Alexander† and Manigandan Thathan*

Abstract – In this paper, the Optimal Harmonic Stepped Waveform (OHSW) method is proposed in order to eliminate the selective harmonic orders available at the output of cascaded multilevel inverter (CMLI) fed by solar photovoltaic (SPV). This technique is used to solve the harmonic elimination equations based on stepped waveform analysis in order to obtain the optimal switching angles which in turn reduce the Total Harmonic Distortion (THD). The OHSW method considers the output voltage waveform as four equal symmetries in each half cycle. In the proposed method, a solar fed fifteen level cascaded multilevel is considered where the magnitude of six numbers of harmonic orders is reduced. A programmable pulse generator is developed to carry the switching angles directly to the semiconductor switches obtained as a result of OHSW analysis. Simulations are carried out in MATLAB/Simulink in which a separate model is developed for solar photovoltaic which serves as the input for cascaded multilevel inverter. A 3kWp solar plant with multilevel inverter system is implemented in hardware to show the effectiveness of the proposed system. Based on the observation the OHSW method provides the reduced THD thereby improving power quality in renewable energy applications.

Keywords: Multilevel inverter, Pulse width modulation, Photovoltaic systems, Power conversion harmonics, Total harmonic distortion.

1. Introduction Harmonics is an important concern in all utility sectors.

However, the electric utilities are recently designed to monitor and analyze the existence and effects of distortion on system and customer devices. The factors contribute the harmonic distortion on distribution systems are increased application of capacitors and non linear devices [1]. In order to improve the power quality and to maintain stable power supply performance, an inverter control strategy with harmonic reduction techniques can be employed [2]. Unlike conventional inverters, the multilevel inverters (MLI) can be employed because these converters are based on the series connection of single phase inverters and widely applied to interface to renewable energy sources, flexible AC transmission systems (FACTS), electrical drives and power-quality devices [3-5]. There are three types of MLI topologies such as diode clamped, flying capacitor and cascaded H Bridge. Amongst the three topologies, diode clamped multilevel inverters are widely used in industrial drive applications but it requires the number of diodes when the levels are increasing [6-7] whereas in flying capacitor, the number of capacitors are required when the level exceeds three [8]. Hence the

cascaded multilevel inverter (CMLI) is an ideal choice to synthesize the desired output voltage from several separate DC sources (SDCs) like solar photovoltaic’s with reduced number of components when compared to other topologies [9]. In addition CMLI has no unbalance problem since each DC link is fed by an isolated DC source [10].

The performance of multilevel converter (MLC) can be improved by Harmonic elimination, control strategies and new multilevel converter topologies [11]. Several methods are put forth for the harmonic elimination in literature. The methods proceeds from the basic sinusoidal pulse width modulation (SPWM) which are not able to eliminate lower harmonics completely [12] and space vector modulation (SVM) where the application of SVM in cascaded topologies is usually limited to a small number of levels due to the large number of switching vectors [13]. Selective harmonic elimination pulse width modulation (SHE PWM) is employed in multilevel inverters which require solving the non linear harmonic equations in order to eliminate the certain harmonic orders by the generation of switching angles corresponding to harmonic elimination.

Theory of resultant is proposed in [14] to derive the mathematical model, but this method is complicated, time consuming and not suitable for the varying input sources. Moreover the resultant theory is limited to find up to six switching angles for equal DC voltages and up to three switching angles for non equal DC voltage cases [15]. Homotophy algorithm provides only one set of solution [16]. Evolutionary concepts such as Bee algorithm (BA),

† Corresponding Author: Dept. of Electrical and Electronics Engi- neering, Kongu Engineering College, Perundurai, Tamilnadu, India. ([email protected])

* Principal, P.A.College of Engineering and Technology, Pollachi, Tamilnadu, India. ([email protected])

Received: September 19, 2013; Accepted: September 24, 2014

ISSN(Print) 1975-0102 ISSN(Online) 2093-7423

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262 J Electr Eng Technol.2015;10(1): 261-270

Genetic algorithm (GA) and particle swarm optimization (PSO) methods are used to obtain the optimal switching angles in which additional to objective function the variables such as pheromone formation and its trail function in BA, crossover and mutation factors in GA, weighting function and random factors in PSO are required which makes the system complex [17-18].

Waveform synthesis is used to suppress the harmonics and also to reduce the filtering requirement. Use of stepped waveform technique provides trade off between harmonic cancellation and equipment complexity [19]. Calculating switching angles which minimize the total harmonic distortion (THD) using step modulation and stair case modulation in a seven level inverter is proposed in [20-21]. Half wave symmetry for SHE is proposed for a five level inverter in [22] where 20 switching angles are considered in a half cycle incorporating its rising and falling edges, so 20 equations can be formulated. The number of switching angles for half-wave symmetry SHE-PWM is twice that of quarter wave symmetry SHE-PWM [23].

Damoun et al., developed an equal area criteria based four equation method for five level inverter with unbalanced dc sources [24]. The line search trust region interior point algorithm to calculate the optimal switching angles in offline for a five level inverter is presented in [25]. All the methods referred deals with the minimum number of levels and the input DC other than solar PV is considered as the source for the multilevel converter.

A single phase grid connected photovoltaic inverter topology with boost converter, a low voltage three level inverter with an inductive filter and a step up transformer for interfacing the grid is considered in [26]. SHE for an eleven level inverter with Artificial Neural Network (ANN) based technique is proposed in [27] which requires an extensive data set required under various conditions which possess combinational problem.

In this paper, the optimized harmonic stepped waveform technique (OHSW) is applied to minimize low-order harmonics in a solar photovoltaic fed fifteen level CMLI, as well as to satisfy the desired fundamental component. Experimental results are presented to confirm the simula- tion results.

2. Problem Formulations The cascaded multilevel inverter consists of a series

connection of single phase full bridge inverter units as shown in Fig. 1. Each full bridge units known as ‘stages’ can generate three different voltages output: +Vpv, 0, -Vpv. For the seven stage inverter the output waveform is illustrated in Fig. 2. The level and stage relation is given by the Eq. (1).

2 1m Ns= + (1)

Fig. 2. Seven stage fifteen level output voltage waveform

S.Albert Alexander and Manigandan Thathan

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where m is the number of levels and Ns is the number of inverter stages. Hence for a fifteen level output, seven inverter stages are required.

By using Fourier series the staircase output of multilevel inverter with non equal input sources is described in Eq.(2).

1 1

2 21,3,5

nπ k nα

. (2)

where kiVpv is the ith DC voltage, Vpv is the nominal DC voltage and the switching angles α1 to αm must satisfy the following condition.

α1 ≤ α2 ≤ α3 ≤………..≤ αm ≤ 2 π

The number of harmonics which can be eliminated by

the multilevel inverter is (m-1). For a seven stage inverter, six numbers of harmonic orders can be minimized or eliminated. The equation governing the SHE for a fifteen level inverter is given in Eq. (3). Here the objective is to determine the switching angles α1 to α7. The elimination of triple harmonics for the three-phase power system applications is not necessary, because these harmonics are automatically eliminated from the line-line voltage [17].

In CMLI based photovoltaic systems, the operating DC voltages of standard PV cells range from 15 to 35 V and from the CMLI based energy-storage system with batteries, the voltages of batteries also change due to their states of charge [21]. Hence, the different voltages arrive at the inverter stages will cause unregulated fundamental with higher magnitude of low order harmonics which also to be considered.

11 2

33 4

( ) sin( ) cos( ) cos( 6)

∞

=

+ +

+ + = ∑

+ +

3. Optimized Harmonic Stepped Waveform The harmonic stepped waveform technique employing

the quarter wave symmetry concept is much suitable for the multilevel inverter to determine the optimal switching angles inorder to provide the output voltage waveform with reduced total harmonic distortion (THD). Switching losses can also be minimized by turning the switch on and off only once per cycle.

There are three possible optimization techniques for reducing the low-order harmonics: 1) step heights are optimized with equally spaced steps, 2) step spaces are

optimized with the steps of equal height and 3) optimizing both heights and spaces. In the variable-input scheme, the third optimization technique is more feasible than the other two techniques. The Fourier series expression for this method is given in Eq. (3). OHSW technique with equal input sources is given in [28].

The OSHW is depicted as quarter wave symmetry where the first half cycle of the output waveform is given in Fig. 3. Considering the switching angles for the complete cycle as α1 to α28, in which each set of α can be obtained by sampling the given waveform into four set of quarter. In the first quarter, from the interval zero to α1 the output voltage is zero and at α1, the output voltage approaches to Vpv1. At α2, the output voltage changes from Vpv1 to (Vpv1+Vpv2) and the process continues upto π /2 where the voltage becomes (Vpv1+Vpv2 + Vpv3+Vpv4+ Vpv5+Vpv6+ Vpv7). In the second quarter the level of output voltage decreases to (Vpv1+Vpv2 + Vpv3+Vpv4+ Vpv5+Vpv6) at π -α7. The process will be repeated upto π -α1 where the output voltage again approaches to zero to complete a half cycle. In the next half cycle the same process will be continued in the same manner other than the amplitude of the input voltage changes from positive to negative.

First quarter: Considering the switching angles α1 to α7

during the interval 0 to π /2. Second quarter:

α8= π -α7

Third quarter:

M α27=2 π -α7 α28=2 π +α1

While considering the harmonic contents in the output

waveform, the amplitude of DC components and all even

Fig. 3. Quarter wave symmetry waveform for 15 level

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264 J Electr Eng Technol.2015;10(1): 261-270

order harmonics approaches near zero. Hence the odd harmonic in the quarter wave symmetric CMLI to be estimated. The set of non linear equations to obtain optimal switching angles is given in the Eqs. (4) to (10).

1 7 71 2 2cos( ) cos( ) ........ cos( ) 4pvpv pv MV V V+ + + = πα α α

7 71 1 2 2cos(3 ) cos(3 ) ........ cos(3 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(5 ) cos(5 ) ........ cos(5 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(7 ) cos(7 ) ........ cos(7 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(9 ) cos(9 ) ........ cos(9 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(11 ) cos(11 ) ........ cos(11 ) 0pvpv pvV V Vα α α+ + + =

7 71 1 2 2cos(13 ) cos(13 ) ........ cos(13 ) 0pvpv pvV V Vα α α+ + + = (4) - (10)

where 1

(1 7)pv

h M

h1 is the amplitude of the fundamental component. As

the proposed method involves the variable input sources, the Vpv is taken at the left hand side in the above expressions.

From Eq. (4), varying the modulation index value can control the amplitude of the fundamental component. The other nonlinear equations listed from (5) to (10) are the undesirable harmonic components can be eliminated which are set to be zero. Therefore, in an m level inverter, the lowest m-1 odd harmonics can be removed.

The Newton-Raphson (NR) method is used to solve the non-linear equation systems using successive approximation procedure which is suitable for implementing computer program. The following algorithm describes the steps involved to calculate switching angle.

Step 1: Formation of switching angle matrix is given in

the equation (11) where the unknown switching angles α1 to α7 to be determined.

1 2 3 4 5 6 7, , , , , ,

Tj j j j j j j jα α α α α α α α = (11)

Step 2: Formation of nonlinear system matrix is given in

the Eqs. (12) and (13).

71 2

71 2

71 2

71 2

71 2

α α

the Eq. (14).

TMT π× × = ⋅ ⋅ ⋅ ⋅ ⋅ (14)

Eq. (4) and (14) can be rewritten as per the following

Eq. (15).

F(α)=T (15) Using the matrices given in the Eqs. (11) - (15) and NR

method the statement of algorithms is as follows to incorporate in the program using MATLAB software.

Step 1: Guess for initial values of α as per Eq. (16). The

process of finding the initial guess through equal area criterion is given in [29].

0 0 0 0 0 0 0 0 1 2 3 4 5 6 7, , , , , ,α α α α α α α α = (16)

Step 2: This step includes the Eqs. (17)-(20).

F(α0) = F0 (17) Linearizing the Eq. (15) at α0 we get

0

(18)

and

0 0 0 0 0 0 0 0 5 71 2 3 4 6, , , , , ,d d d d d d d dα α α α α α α α = (19)

Solving the Eq. (19) using the inverse of the matrix

given in the Eq. (20).

0 0

α ∂ = − ∂ (20)

Step 3: Updation of initial values is made as per the

Eq. (21).

http://www.jeet.or.kr 265

1j j jdα α α+ = + (21) The steps (2) - (3) is repeated until jdα is fulfilled and

the condition to be satisfied is α1, α2, α3………α7 < π /2.

4. Simulation and Results Simulations are carried out in MATLAB / Simulink. In

order to provide the source for a fifteen level inverter, a solar photovoltaic source model according to the specifica- tion of the commercial PV panel is used. The solar PV model comprises of many individual solar cells connected in series and parallel to obtain the required rating. The solar cell model consists of parallel combination of a current source, two exponential diodes, series (Rs) and parallel (Rp) resistances. The output current equation is given in Eqs. (22)-(24). The PV array input to the each inverter stage is 48V, 7A. A single solar cell of rating 0.5V and 7A with standard test conditions of 1000W/mm2 and 250C of 96 numbers in series connection is chosen.

2 s p1ph /I = I K K (V 1*R ) R+− − − (22)

where

s* *

*K = I (e 1)+ − (23)

2* *s 2 s2

(V 1 R )/(N Vt) *K = I (e 1)+

− (24) Is and Is2 are the diode saturation currents, Vt is the

thermal voltage, N and N2 are the quality factors (diode emission coefficients) and Iph is the solar-generated current. The quality factor is in the range of 1 to 2. The solar generated current Iph is given in the Eq. (25).

Iph= Ir*(Iph0/Ir0) (25)

where Iph0 is the measured solar-generated current for irradiance Ir0. In order to verify the model, the P-V and V-I characteristics is plotted and shown in Fig. 4 and 5. The design is to generate the output peak voltage of 336V to deliver power to consumer loads as given in Eqs. (26)-(27).

Vout = 48V x 7 stages = 336V (26) Vrms = 336/ 2 = 230Vac (27)

The simulation and analysis of optimal harmonic stepped

waveform technique for solar fed CMLI is developed. The set of harmonic orders considered are 3, 5, 7, 9, 11 and 13. The initial guess values utilized are {0.01; 0.2989; 0.4387; 0.6950; 0.9240; 1.170; 1.52} and the process is repeated until all elements in jdf matrix are less than 0.0000001. A programmable pulse generator is developed which will carry the switching angles directly to the semiconductor

devices which summarily reduces the complexity of the system.

Fig. 6 shows the output voltage waveform of OHSW based solar fed fifteen level inverter and Fig. 7 shows the

Fig. 4. P-V Characteristics of the solar panel

Fig. 5. I-V Characteristics of the solar panel

Fig. 6. Fifteen level output voltage waveform with OHSW

Fig. 7. FFT Analysis for the output waveform with OHSW

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266 J Electr Eng Technol.2015;10(1): 261-270

Fast Fourier transform (FFT) analysis of the waveform which shows the THD value of 8.55. Table 1 shows the various sets of switching angles obtained for the modulation index M = 0.36 and M = 1.

The OHSW is compared with the conventional pulse width modulation (PWM) technique. Fig. 8-9 shows the corresponding output voltage waveform and FFT analysis for a solar fed fifteen level multilevel inverter with PWM. Fig. 10 shows the comparison of harmonic orders magnitude obtained using OHSW and PWM techniques. Based on the result it is observed that the OHSW technique improves the output quality of the waveform with reduced THD and magnitude of harmonic orders.

Table 1. Switching angles determination

M=0.36 α 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter α1 8.857 171.1143 188.8857 351.1143 α2 14.8027 165.1973 194.8027 345.1973 α3 27.9257 152.0743 207.9257 332.0743 α4 47.2589 132.7411 227.2589 312.7411 α5 57.27771 122.7229 237.2771 302.7229 α6 72.8232 107.1768 252.8232 287.1768 α7 87.8539 92.1461 267.8539 272.1461

M=1 α1 5.0126 174.9874 185.0126 354.9874 α2 14.2451 165.7549 194.2451 345.7549 α3 25.9953 154.0047 205.9953 334.0047 α4 37.6040 142.3960 217.6040 322.3960 α5 52.0406 127.9594 232.0406 307.9594 α6 65.0413 114.9587 245.0413 294.9587 α7 86.2279 93.7721 266.2279 273.7721

Fig. 8. Fifteen level output voltage waveform with PWM

Fig. 9. FFT Analysis for the output waveform with PWM

Fig. 10. Comparison graph for harmonic order magnitudes

5. Experimental Results A 3kWp solar PV power supply unit is designed and

implemented for the seven stage fifteen level solar fed CMLI with the above mentioned algorithm. In India, much of the domestic loads operate from single phase 230V, 50Hz AC system. Hence the output voltage of the system is designed for the 230V AC supply. In order to achieve this, the input supply used in the setup is 48V. Table II shows the rating of the complete hardware setup. Each photovoltaic panel has a rated power of 115W with voltage variation of 16 to 21 volts (nominal 12V) depending on the operating conditions such as light intensity and so on. Four photovoltaic panels are connected in series to get a nominal voltage of 48V which constitutes as single individual source for CMLI. Four numbers of 12V, 100Ah battery packs are connected in series to get a nominal DC bus of 48 volts. These batteries are charged from the photovoltaic unit through a controlled charging circuit. There are seven sets of individual PV supply source used for the hardware implementation as they produce 48 x 7=336Vp (230Vrms).

Each input source to the CMLI provides the variation upto ±10%, the voltage sensors are provided at each source level. These inputs are given to the FPGA processor SPARTAN3E. Based on the OHSW algorithm incorporated in the processor, it generates the switching angles to the inverter switches MOSFET IRF840 through a driver circuit considering the sequences at each four quarters in the complete cycle. Fig.11 shows the 3 kWp Solar PV plant and in Fig.12, the complete hardware setup comprising of charge controllers, battery and the proposed inverter is given. Fig.13 shows the power and control circuit of inverter and Fig.14 shows the FFT analysis using the Power Quality Analyser (PQA) WT3000 where the THD obtained in this method is about 9% with the possible minimisation of low order harmonics considered in this work. The variation of input PV voltage is measured at every instant which is used for solving OHSW equations. The comparison of the proposed method with the existing works is reported in Fig.15 and Fig.16 which shows that the proposed method provides higher voltage levels with V fundamental by considering more number of harmonic

S.Albert Alexander and Manigandan Thathan

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orders and results in lesser THD. In addition this method is implemented with solar

photovoltaic’s as the input and also considered the variations of the solar panels with respect to temperature

and irradiance. Based on the variations in the input Vpv1 to Vpv7 the necessary switching angles will be generated based on the equations given in (4) - (10). The advantage of the proposed method needs to satisfy the condition α1, α2, α3 …… α7 < π /2 rather than the condition α1 ≤ α2 ≤ α3

≤……….≤ αm ≤ 2 π

for the other SHE problems.

Table 2. Experimental setup specifications

Solar PV Model Solectric 9000 Pmpp 115Wp Voc 21.2V Isc 7.4A

Vpm 16.5V Ipm 6.95A

No. of panels 28 Total power 3220Wp

Charge Controllers (CC) Make Sukaam

V-I Rating 48V,10A No. of CC 7

Battery bank Make & Model EXIDE 6LMS100L

Rating 12V, 100Ah No. of batteries 28

Power Quality Analyser (PQA) Make Yokogawa Model WT3000

Fig.15. Comparison graph for performance parameters

Fig. 16. Comparison graph for Vfundamental considered

Fig. 11. Solar plant of rating 3kWp

Fig. 12. Hardware set up

Fig. 13. Power circuit and control circuit of MLI

Fig. 14. Output voltage waveform and FFT analysis

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268 J Electr Eng Technol.2015;10(1): 261-270

Fig. 17. Power Quality Analysis with WT3000

Adopting OHSW technique in [30], the THD obtained is

about 32.78 for a seven level inverter whereas for a fifteen level solar fed inverter the THD obtained in the proposed paper is 9.5. In both simulation and hardware, a solar fed fifteen level inverter of same specification and rating is taken into consideration. The correlation between the simulation and hardware results are made based on the THD analysis illustrated in Fig. 17 which is related to the Fig. 7 obtained through simulation.

6. Conclusion A fifteen level solar fed cascaded multilevel inverter for

the elimination of certain harmonic orders is developed for the power quality improvement. The method is compared with the conventional PWM approach, which shows that OHSW based method is much suitable and an ideal choice for implementing selective harmonic elimination cases. The advantages of this method include simple computational algorithm and no requirement of filters, detailed look up tables and output transformers. Moreover, this technique can be implemented in both standalone and grid interacted PV systems.

Acknowledgements The authors acknowledge and thank the Department

of Science and Technology (Government of India) for sanctioning the research grant for the project titled, “Design and Development of Multilevel Inverters for Power Quality Improvement in Renewable Energy Sources” (Ref.No.DST/TSG/NTS/2009/98) under Technology Systems Development Scheme for completing this work.

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Optimal Harmonic Stepped Waveform Technique for Solar fed Cascaded Multilevel Inverter

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S.Albert Alexander He received B.E. degree in Electrical Engineering from Bharathiar University, India. He re- ceived M.E. degree (Power Electronics and Drives) and Ph.D. degree from Anna University, India in 2007 and 2014 respectively. His research interests are multilevel inverters, renewable

energy systems and soft computing techniques. He is the principal investigator for the major research projects of worth Rs.0.62 crores sponsored by Government of India.

Manigandan Thathan He received B.E. degree in Electrical Engineering from Government College of Tech- nology, Coimbatore in 1996. He received M.E. degree in control systems from PSG College of Technology, Coimbatore, India in 1998 and Ph.D. degree from Anna University, India in