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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014) Wavelet Modulation for Neutral Point Clamped Multilevel Inverters Umabati Laishram1, A.M. Nagaraj2 1 M Tech Student, DSCE Bangalore, 2Associate Professor, DSCE Bangalore Abstract— This paper implements a new type of modulation known as Wavelet Modulation (WM) based on non-uniform sampling and wavelet theory in a multilevel neutral-point clamped inverter. The proposed scheme is compared with other modulation techniques such as Sinusoidal Pulse Width Modulation (SPWM) and Squarewave Pulse Width Modulation (SQPWM). Simulation results show that the WM technique produces smoother current output, better output voltage, and lesser Total Harmonic Distortion (THD) as compared with the other modulation techniques. II. NEUTRAL-POINT CLAMPED MULTILEVEL INVERTER The neutral-point clamped (NPC) multilevel inverter was first introduced by [10] and generalization was done by [11]. A 3-level neutral-point clamped multilevel inverter is designed with 12 unidirectional active switches and 6 neutral point clamping diodes. Each switch blocks half of the full dc voltage. In each phase leg, only 2 out of the 4 switches must be on at any particular instant. Two series connected capacitors of the same rating splits the supply voltage into 3-levels. The diodes are all similar so that the same voltage level is clamped across the switch. A 3-level neutral-point clamped multilevel inverter is shown in figure I. The structure of the NPC multilevel inverter provides less voltage stress across the switch. The purpose of producing different levels of voltage is to sequentially activate only 2 switching elements in each leg. One of the main advantages of neutral-point clamped multilevel inverter is that they have twice the number of switching elements as the six pulse 3- inverters, where each switching element blocks only half the dc bus voltage. Also, the increased number of switches guarantees reduced switch utilization [7]. Keywords—modulation, neutral-point clamped multilevel inverter, THD, wavelets, wavelet modulation. I. INTRODUCTION A wavelet is a waveform of limited duration that has an average value of zero. Wavelets are mathematical functions that group data into varied frequency components and study each component with a resolution matched to its scale. The fundamental idea behind wavelets is to analyze according to scale [3]. S.A. Saleh, C.R. Moloney, and M.A. Rahman developed a special wavelet-based non-dyadic MRA for implementing wavelet modulation in single-phase voltage source Hbridge inverters [2]. The non-uniform recurrent sampling model of single-phase inverters provided the framework for 3 inverters [1]. A non-uniform recurrent sampling model for a 3 inverter is required for non-uniform recurrent sampling and reconstruction of three CT signals with the same frequency and shifted from each other by radians from each other. WM technique for 3 inverter requires establishing a unique non-dyadic MRA where each subspace is time and frequency shifted to support the nonuniform recurrent sampling reconstruction of three CT signals. This paper presents using the backbone of WM technique in 3 VS inverter [1] in implementing WM technique in a neutral-point-clamped multilevel inverter. Furthermore, this paper provides the effects of WM technique on the output voltage, current and THD of the neutral-point-clamped multilevel inverter. Furthermore, it also provides comparisons in the basic output parameters of WM technique with other PWM techniques such as SPWM and SQPWM. Figure I. Neutral-point clamped multilevel inverter. 61 International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014) III. SALEH AND RAHMAN’S WAVELET The output of an inverter is usually composed of trains of periodic rectangular pulses that have different durations and the overall period is equal to the period of the fundamental component of the inverter output. Such rectangular pulses can be accorded as the successive stages of interpolation to synthesize a CT signal from its samples. This type of sampling is known as non-uniform recurrent sampling. Single-phase inverters was modeled using nonuniform sampling where a sinusoidal CT signal is sampled in a non-uniform recurrent manner so that groups consisting of two samples each are created [2]. The sampling model of single-phase inverters was extended to the model of three-phase inverters [1], where three sinusoidal CT signals are sampled in a non-uniform recurrent manner. This sampling is to be applied to the model of a 3-phase neutral-point coupling inverter. The three sinusoidal signals have the same frequency with a phase shift of radians from each other. ( ) ( ( ) ( ⁄ ) ( ) ( ) ( ⁄ ) ( ) ) ( ) ( ( ( ) ( ( ( ) ( ) )( ( ) ) )( ( ) ) )( ( ) ∏( ) ( ) ( ) ∏( ) ( ) ( ( )) ∑∑ ( ) ( ) ( ( )) ∑∑ ( ) ( ) ( ( )) ∑∑ ( ) ( ) ( ) ( ) ( ( ) ( ) ( ( ) )( ( ) ) )( ( ) ) )( ( )) , ( ( )) and ( ( )) are the Where ( reconstructed versions of the three sinusoidal CT signals. Equations (10)-(12) relates the ac output voltage to its dc input voltage VDC through stages of periodic and timelocalized interpolating functions. The time-localization property of the interpolating function implies that each interpolating function is defined for one group of nonuniform recurrent samples. IV. IMPLEMENTING THE WAVELET MODULATION TECHNIQUE FOR A NPC MULTILEVEL INVERTER ( ) ) The WM technique developed for 3 VS inverter can be implemented in a similar fashion to a 3 NPC multilevel inverter. According to [1], the technique is divided into two parts: ( ), ( ) and ( ) in a nonPart 1) Sampling uniform recurrent manner by using a set of basis functions. The created samples in sample groups da, db, and dc are located at the boundaries of the intervals [ ], [ ] and [ ]. These time locations are determined as follows: ( ) ) ( ) ( ) ( ), ( ) and ( ) are the Lagrange Where interpolating function over the sample groups da, db and dc given by ( ) ∏( The intervals [ ], [ ] and [ ] are the time intervals for the three interpolating functions ( ), ( ) and ( ) respectively. The periodicity of the sample groups and the time localized feature of the interpolating functions ensure their periodicity with a period of Tm. The reconstructed version of the three sinusoidal CT signals are given as follows: Where and is the frequency of each sinusoidal signal. In general, the reconstruction of a CT signal from its non-uniform samples can be achieved using Lagrange’s Interpolating functions. In order to reconstruct three sinusoidal CT signals from groups of non-uniform recurrent samples, stages of periodic interpolating functions are employed. Each stage of these interpolating functions is defined for one sample group of each sampled sinusoidal signal. The interpolating functions for sample groups da of ( ), db of ( ) and dc of ( ) is as follows: ( ( ) ) ( ) 62 International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014) For SMa(t), VI. PERFORMANCE RESULTS Simulation is done using the following parameters: Output frequency, f =50 Hz. Switching frequency, Fs =250 Hz. For SMb(t), Pulse frequency, fp = 1080 Hz. No. of pulses, p = 10. For performance comparison purposes, the same inverter is activated using Sinusoidal Pulse Width Modulation (SPWM) and Square Pulse Width Modulation (SQPWM) techniques. For SMc(t), Where d=0,1,2……D-1 and D is the number of sample groups created over Tm; j=0,1,2……. Part 2) Generating switching pulses created as a dilated (by scale j) and translated (by shift value k) version of the synthesis scaling functions. Each of these generated switching pulses will have its duration determined in Part 1. Changes in the scale j and the translation k leads to a change in the time interval and location of each sample group of each CT reference modulating signal. V. SIMULATION USING MATLAB The step-by-step-procedure for implementing the WM technique in NPC multilevel inverter is realized using a MATLAB code that generates switching pulses to activate a SIMULINK model of a NPC multilevel inverter. The simulation model is as shown below: Figure III. Output waveform for SPWM NPC multilevel inverter. Figure IV. Output waveform for SQPWM NPC multilevel inverter. Figure II. Simulink model of NPC multilevel inverter. 63 International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014) Table I summarizes the performance simulation results for all the three modulation techniques tested. The comparative performance results in Table I clearly demonstrates that significant improvements in the outputs of a NPC multilevel inverter can be achieved using WM technique. VII. CONCLUSION In this paper, WM technique developed for VS inverters is implemented in NPC multilevel inverter using a simple switching pulse generation code. This pulse generation code is applied to a SIMULINK model of a 3level NPC multilevel inverter developed using MATLAB. Simulation results of the NPC multilevel inverter shows that outputs have high fundamental component magnitude and low harmonic components. Furthermore, a performance comparison between the WM technique and other PWM techniques such as SPWM and SQPWM shows that WM inverters produce outputs with lower harmonic content or improved THD than the other traditional inverter modulation techniques. The advantages of WM inverters can be listed as follows: The inverter function with non-uniform recurrent sampling reconstruction of reference modulating signal means that the output pulses have a quarter cycle symmetry. It is able to produce output voltages and currents with higher magnitudes of the fundamental component and lower harmonic contents better than the other types of modulation techniques. The effect of harmonics on the source is low and switching losses are low. Controllability is easy and implantation is simple. Figure V. Output waveform for WM NPC multilevel inverters. Figures III, IV and V demonstrate the output voltage waveforms of the NPC multilevel inverter on the implementation of SPWM, SQPWM and WM respectively. The quality of inverter output voltage and load current is usually expressed in terms of the THD factor defined as Where is the rms value of the fundamental component of the inverter output voltage or load current. is the summation of the rms values of all the other harmonic components, which is given by √ Where h=2,3,…..,n indexes of the harmonic component. THD factors can be evaluated using in-built MATLAB tools. REFERENCES TABLE I [1] SPW M SQP WM WM THDV 13.72 3.58 1.90 [2] THDI 7.54 13.42 1.94 [3] [4] 64 S. A. Saleh, C. R. Moloney, and M. A. Rahman, ―Analysis and development of wavelet modulation for three-phase voltage-source inverters,‖ IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3330–3348, Jul. 2009. S. A. Saleh, C. R. Moloney, and M. A. 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