International Journal of Emerging Researches in Engineering Science and Technology, Volume 1, Issue 2, December 14

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1 CONTROL STRATEGIES FOR A HYBRID MULTILEEL INERTER BY GENERALIZED THREE- DIMENSIONAL SPACE ECTOR MODULATION J.Sevugan Rajesh 1, S.R.Revathi 2 1. Asst.Professor / EEE, Kalaivani college of Techonology, Coimbatore, Tamilnadu. sevugan.rajesh@gmail.com 2. Asst.Professor / EEE K.P.R Institute of Engineering and Technology, Coimbatore, Tamilnadu. revthir@gmail.com Abstract A space vector pulse width modulation (SPWM) for multilevel inverters are developed to improve factors such as the computational cost and voltage distortion but has problems when multilevel inverters present unbalances in the dc voltages. This paper proposes a new algorithm for hybrid multilevel inverters with unequal voltage steps under the 3-D space vector pulse width modulation (3-D SPWM). The 3-D SPWM can be applied practically in hybrid multilevel inverters with different voltage steps; it can be applied to most multilevel topologies. The reference space vector is mapped to the innermost cube, using the center of the cube. The algorithm offers an intuitive method for minimizing the total harmonic distortion (THD) of the output voltage of the inverter and the proposed techniques lead to a significant reduction in THD. Finally, the algorithm was implemented on a Field programmable gate array and the scheme is explained for a five level inverter, and experimental results are presented to validate the proposed modulation technique. Keywords: Hybrid multilevel inverter, Power conversion, 3-D space vector modulation, Total harmonic distortion. 1. Introduction Multilevel inverter technology finds significant applications in the area of high-power mediumvoltage energy control [1]-[3]. Modulation methods for hybrid multilevel inverter can be classified according to the switching frequencies methods. The most widely used techniques for implementing the pulse width modulation (PWM) strategy for multilevel inverters are sine-triangle PWM (SPWM) and space vector PWM (SPWM). In multilevel SPWM, the reference sine wave is compared with a number of level-shifted carriers to decide the switches to be turned on [2]-[4]. In the SPWM scheme, the sampled value of the reference voltage space vector which is the combined effect of the threephase voltages is realized by switching the nearest voltage space vectors among the inverter voltage vectors [9]. There are different techniques available for implementing SPWM for multilevel inverters [11]. Fig.1. Topology of multilevel inverter.

2 SPWM is considered as a better technique of PWM implementation, due to its associated advantages as follows: 1) Better fundamental output voltage; 2) Better harmonic performance; and 3) Easier implementation in digital signal processor and microcontrollers. The topology of a cascade multilevel inverter is shown in Fig. 1. The SPWM methods using the principle of equivalence with SPWM, which can generate the SPWM signals directly from the instantaneous reference phase voltages for multilevel inverters without using lookup tables [7]. However, PWM and SPWM techniques for three-phase systems have problems when multilevel power inverters present unbalances in the dc voltages. A perfect balance of the dc voltages of a multilevel inverter cannot be achieved in all loading conditions. Load imbalances and nonlinear or transient loads have a significant impact on the multilevel inverter dc voltage ripple [4]. In this case, both modulation techniques are not prepared for this unbalance because they do not take it into account to carry out the modulation process. In this way, errors appear in the output modulated voltages because they do not match to the desired ones when they are averaged over a switching period. This fact leads to an increase of the harmonic distortion of the output voltages and currents of the multilevel inverters [6]. The proposed algorithm 3-D SPWM for multilevel inverters permits calculation of the sequence of the nearest space vector for generating the reference voltage vector [8]-[9]. This generalized method provides the nearest switching vectors sequence to the reference vector and calculates the on-state durations of the respective switching state vectors without involving trigonometric functions, look-up tables or coordinate system transformations which increase the computational load corresponding to the modulation of multilevel inverters. A key issue in designing an effective multilevel inverter is to ensure that the THD in the voltage output waveform is small enough. An algorithm for 3-D SPWM is presented to minimize THD for cascaded multilevel inverter with equal voltage steps. In this paper, it is shown how the method can be extended for the case of unequal and varying voltage steps. An algorithm to generate 3-D SPWM signals for multilevel inverters is presented, taking into account the actual unbalance of the power inverter to carry out the necessary calculations, avoiding errors in the modulation process. Using the proposed 3-D SPWM, unbalanced systems can be modulated with balanced or unbalanced dc voltages. 2. DESCRIPTION OF MODULATION TECHNIQUE The SPWM for unbalanced operation of a multilevel power inverter can be obtained with the neutral of the load connected to the middle point of the dc link or to a new phase of the power inverter. Using the multilevel inverter topologies, the gamma component of the voltage is not zero, and the three dimensions have to be used in the modulation to generate the reference vectors [11]-[12]. The 3- D SPWM techniques carry out a fast geometrical search of the four nearest state vectors to determine the switching sequence. Using abc coordinates, the control region is a triangle for three phase system. The state vectors of the power inverter are denoted by xyz, which means that phases a, b, and c, respectively, takes values between zero and N-1 for an N-level inverter. The coordinates of the reference space vector is normalized through division by the normalization constant DC / n 1. State zero means that the phase is connected to the lowest dc voltage level and N-1 is the highest possible dc voltage. In 3-D SPWM technique, initial process is to find the subcube where the reference vector is located [9]. Once this subcube is determined, it is divided into triangles, and the 3- D SPWM has to calculate the triangle where the reference vector is pointing. Finally, depending on the triangular region the switching sequence and the corresponding duty cycles are determined [11]- [12]. The switching sequence consists of four vectors and 6 different cases. The 3-D SPWM techniques can be applied to balanced and unbalanced systems and can be used for any multilevel power inverter with or without neutral connection. In addition, the algorithm provides the switching sequence that minimizes the total harmonic distortion. 3. THREE DIMENSIONAL SPWM FOR SWITCHING SEQUENCES A generalized 3-D SPWM is presented for multilevel inverters, which can be used for any number of levels of multilevel power inverter. In general, the SPWM techniques are used to generate an average voltage vector equal to the reference voltage vector. Each switching state of the inverter is represented by a switching voltage vector. The method is to choose the vectors that, applied during a certain time over the switching period, produce a voltage vector equal to the reference or desired voltage vector Determination of 3-D Control Region:

3 In 3-D SPWM, three different dc voltages Dc1, Dc2, and Dc3 have to be considered for a three-bridge fourteen-level cascaded multilevel inverter. The various possible phase-0 voltages of the multilevel inverter are zero, DC1, DC1 + DC2 and DC1 + DC2 + DC3. The phase states can be represented using generalized dc voltages DC1, DC2 and DC3. The 3-D control region formed will be cube with size DC1 + DC2 + DC3, which forms several triangles with different sizes, depending on the voltages of different dc sources. The 3-D control region of a fourteen-level power inverter having DC1- < DC2 < DC3 is represented in Fig.2. The δ i values are the size of the triangle that form the 3-D control region, is as follows: DCtotal DC 1DC 2... DCN (1) Di i (2) DCtotal Fig. 2. Three-dimensional control region of a five level inverter with voltage unbalance in the dc link DC1 < DC2 < DC3 The actual output voltages of the multilevel inverter is determined from the vector o. The elements of the vector o are in increasing order from zero to the positive value. In the N-level inverter, the vector is represented as: o 0, DC 1, DC 1 DC 2,..., DC 1... DCN 1 (3) Normalizing the vector o with respect to the total dc voltage generating vector on o on (4) DCtotal on... 0,,,..., DCtotal DCtotal DCtotal DC1 DC1 DC 2 DC1 DCN 1 0,,,...,... N ,,,...,1 (5) 3.2. Reference ector Normalization: The reference vector calculated is defined as ref = { a, b, c }, where j is the voltage of phase j with respect to point zero. The reference vector ref is normalized using the total dc voltage of

4 the multilevel inverter [8]. The normalized reference voltages v a,v b and v c take values between zero and one. The reference vector in the n th component is represented as a b c { v, v, v },, DCtotal DCtotal DCtotal refn a b c 3.3. Algorithm for generating switching angles: 1) Read the instantaneous magnitudes of phase voltages. 2) Determine the coordinates of the instantaneous space vector. 3) The coordinates of the reference space vector is normalized through division by the normalization constant DC / n 1. 4) Determine the triangular region enclosing the normalized cube for a two-level inverter. 5) Calculate the modulation index m, which is the number of iterations repeatedly applied to various triangles. 6) Identify the triangular region having m, calculated in step (5) 7) Determine the centroid of each of the four triangles. Also determine the triangles with centroid closest to the 16 triangles. 8) Each triangle gives three vectors and switching states. 9) If the number of application of step (5) gives the m, go to next step, else go to step (7). 10) The triangle is finally determined in step (10), represents the triangle enclosing the space vector. 11) Continue the process of identifying the voltage space vector in different triangles of the cube. 12) Select the zero vector from the vectors located at the vertices of the identified subcube Determination of the triangle from subcube: Several iterations are carried out over each component to find out the nearest centroid of the triangular region enclosing the normalized subcube. For example, iterations are carried out in phase a, to find where v a is located inside on vector, comparing with each element. Finally, the lower and upper closer elements in vector on of the range where v a is located can be determined. For instantaneous, for the three level stages as follows on 0,,, DC1 DC1 DC 2 DC1 DC 2 DC3 DC1 DC 2 DC3 DC1 DC 2 DC3 DC1 DC 2 DC3 0,,, ,,,1 3 3 If δ 1 < v a < 1, the factor v a is δ 1 and the factor S a is one. For each phase of the reference vector this process is repeated to calculate the vector abc = { a, b, c } which is the nearest centroid of the triangular region where the reference vector {v a,v b, v c } is located. Also, the vector S abc = { S a, S b, S c } is determined. ectors Δ = {δ a, δ b, δ c } and Δ={r a, r b, r c } can be calculated. = { a, b, c}={ Sa a, Sb b, Sc c} (8) = {r, r, r }={ v, v, v } (9) a b c a a b b c c The switching sequences and the duty cycles calculations are summarized in Table I and the parameters µ a, µ b, and µ c in the table are defined as r r r (10) a b c a b a a b c The proposed modulation technique finds out the four nearest state vectors to form the switching sequences to generate the reference voltage. The switching sequence consisting of four nearest state vectors have four triangles in each sub cube and six different cases is shown in Fig. 3. (6) (7)

5 Determine the centroid of each of the four triangles; each triangle gives three vectors and switching state. Fig. 3. Division of each triangular subcube of the 3D SPWM control region of a multilevel inverter with generalized dc voltages. TABLE I Switching sequence and Duty Cycles Determined by the 3DSPWM Technique S.No Cube Cases 1 Case 1 2 Case 2 3 Case 3 4 Case 4 5 Case 5 6 Case 6 State ector Sequences 210, 310, , 310, , 311, , 321, , 311, , 311, , 211, , 321, , 321, , 221, , 221, , 321, , 321, , 321, , 221, , 220, , 321, , 321, , 220, , 320, , 320, , 320, , 310, , 320, 321 Duty Cycles D = 1-µ a D = µ a - µ c D = µ c - µ b D = µ b D = 1-µ c D = µ c - µ a D = µ a - µ b D = µ b D = 1-µ c D = µ c - µ b D = µ b - µ a D = µ a D = 1-µ b D = µ b - µ a D = µ c - µ a D = µ a D = 1-µ b D = µ b - µ a D = µ a - µ c D = µ c D = 1-µ a D = µ a - µ c D = µ b - µ c D = µ c 4. EXPERIMENTAL RESULTS 4.1. Simulation Result The proposed algorithm is generated in front end with the aid of system generator editor, the 3D-SM blocks and the associated blocks for individual phases are interconnected and the sampling frequency is set to 5kHz. The entire system is shown in Figure 4.

6 The generated output pulses from the main 3D-SM blocks are converted in to nine numbers which is required to drive the devices in to ON state with the aid of pulse converter blocks and output voltages as shown in Figure 5. The simulation parameters for constant switching frequency Three dimensional Space vector pulse width modulation are as following, 2KW rating, three phase load R = 150 ohms, L = 10mH, each source DC1 = 50, DC2 = 75and DC3 = 100.The switching patterns adopted are applied at the cascaded multilevel inverter switches to generate five or three output voltage levels at different modulation indexes. Fig. 4. Circuit diagram for three-bridge Fourteen-level inverter. Fig.5. Output voltage for the Seven-level inverter using 3-D SPWM, when m is Hardware Result To verify the performance of the proposed method, a cascade multilevel inverter was developed in the laboratory. Three IGBT H-Bridges are used to form a single-phase five level hybrid multilevel inverter. The model of IGBT module is CM100DY-24NF. The dc sources of the H-Bridges are dc power supplies whose output voltages range from 0 to 30. The load is a 100Ω resistor and controller includes a TMS320C6701 DSP board and the 3-D SPWM is implemented in PRO XC2P30 FPGA board. The DSP board calculates the switching sequences based on dc source voltages and given modulation index with the 30 KHz sampling frequency. The voltages of dc supplies are 5, 10 and 15. The circuit diagram for three-bridge Five-level inverter is shown in Fig. 6 The total dc-link voltage 30, and a 50 Hz sinusoidal waveform is applied as the reference voltage to be generated by the inverter with a modulation index m is 0.8. In Figs. 7 and 8 show the output voltage for the five-level inverter using the proposed 3-D SPWM and its spectrum of the output phase voltage of the fourteen-

7 level inverter with a modulation index of 0.8. The offline fast Fourier transform analysis of the simulation data shows the THD as 12.98%. Fig.6. Hardware setup of Single phase five level cascaded multilevel inverter Fig.7. Output voltage for the five - level inverter using 3-D SPWM, when m is 0.8. Fig.8. Harmonic spectrum of the output phase voltage of the five-level inverter with a 25- unbalance, using the proposed 3-D SPWM. 5. CONCLUSION The 3-D space vector modulation algorithm presented in this paper is very useful to calculate the switching sequence and the on-state durations of the respective switching state vectors

8 corresponding to the space vector modulation used in multilevel inverters. The proposed modulation technique directly allows compensation of a zero sequence in unbalanced systems with neutral and optimizing the switching sequence minimizing the number of switchings. This algorithm does not use trigonometric functions or look-up tables. Experimental results for a three-bridge five-level cascaded multilevel inverter are presented. Using the proposed algorithm, the voltage unbalance does not affect the THD of the waveform and also provides the switching sequence that minimizes the total harmonic distortion. This technique can be applied to multilevel power inverter with any number of levels. It has been implemented in a DSP, running at 30 khz frequency with dc supplies of 5, 10 and 15 olts. The computational cost of proposed technique is very low and can be applied to multilevel inverters of any number of levels. References Journal: [1] J. Rodriguez, J.-S. Lai, and F. Z. Peng, Multilevel inverters: A survey of topologies, controls, and applications, IEEE Trans. Ind. Electron.,2002 vol. 49, no. 4, pp , A. [2] J. Holtz, Pulsewidth modulation A survey, IEEE Trans. Ind. Electron., vol. 39, no. 5, pp [3] K. Zhou and D. Wang, Relationship between space-vector modulation and three-phase carrierbased PWM: A comprehensive analysis, IEEE Trans. Ind. Electron., vol. 49, no. 1, pp [4] A.S.Aneesh Mohamed, Anish Gopinath and M.R.Baiju, A Simple Space ector PWM Generation Scheme for Any General n-level Inverter, IEEE Trans. Ind. Electron., 2009 ol.56, no. 5, pp [5] J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, and Z. Du, Elimination of harmonics in a multilevel inverter using the theory of symmetric polynomials and resultants, IEEE Trans. Control Syst. Technol., vol. 13, no. 2, pp [6] C. Rech and J. R. Pinheiro, Hybrid multilevel inverters: Unified analysis and design considerations, IEEE Trans. Ind. Electron., vol. 54, no. 2, pp [7] L. Li, D. Czarkowski, L. Yaguang, and P. Pillay, Multilevel selective harmonic elimination PWM technique in series-connected voltage inverters, IEEE Trans. Ind. Appl., vol. 36, no. 1, pp [8] H. W. an Der Broeck, H.-C. Skudenly, and G.. Stanke, Analysis and realization of a pulse width modulator based on voltage space vectors, IEEE Trans. Ind. Appl., vol. 24, no. 1, pp [9] N. Celanovic and D. Boroyevich, A fast space-vector modulation algorithm for multilevel threephase inverters, IEEE Trans. Ind. Appl., vol. 37, no. 2, pp [10] A.R. Beig, G. Narayanan, and T. Ranganathan, Modified SPWM algorithm for three level SI with synchronized and symmetrical waveforms, IEEE Trans. Ind. Electron., vol. 54, no. 1, pp Proceeding: [11] M. M. Prats, L. G. Franquelo, J. I. Leon, R. Portillo, E. Galvan, and J. M. Carrasco, A SM-3D generalized algorithm for multilevel converters, in Proc. 29th Annu. IEEE IECON, 2003, vol. 1, pp [12] P. F. Seixas, M. A. Severo Mendes, P. Donoso Garcia, and A. M. N. Lima, A space-vector PWM method for three-level voltage source inverters, in Proc. IEEE APEC, 2000, vol. 1, pp