Energy and Power Engineering, 2011, 3, 276284 doi:10.4236/epe.2011.33035 Published Online July 2011 (http://www.SciRP.org/journal/epe) Copyright © 2011 SciRes. EPE Comparative Study between Different Modulation Strategies for Five Levels NPC Topology Inverter Noureddine Ould Cherchali1, Abdelhalim Tlemçani1, Mohemed Seghire Boucherit2, Linda Barazane3 1Laboratoire de Recherche en Electrotechnique et Automatique, Université de Médéa, Médéa, Alger 2Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, Algiers, Alger 3Faculté d’Electronique, Université des Sciences et de la Technologie Houari Boumediene, Algiers, Alger Email: nocherchali@yahoo.fr Received April 29, 2011; revised May 15, 2011; accepted May 23, 2011 Abstract The object of this paper is the study of various modulation strategies applied to the fivelevel inverter neu tralpointclamped NPC topology. Firstly we presented the structure of the voltage inverter threephase fivelevel NPC topology. After that we model the inverter and the inverter are controlled by different strate gies and then we made a comparative study between the results given by different strategies. Keywords: Multilevel, Five Levels, NPC, SHEPWM, SPWM, Hysteresis Control 1. Introduction In recent years, electrical industries have expanded and the variety of loads has increasingly grown. Recently, the industry has begun to apply highvoltage highpower equipment that has reached the megawatt range. Today, the direct connection of a single semiconductor switch to a system with medium sized voltage grids (2.3, 3.2, 4.16 and 6.9 KV) is too difficult. To overcome the limitations on semiconductor voltage and current ratings, some type of series connection will be necessary. Therefore, multi level inverters have been introduced. Due to their ability to synthesize waveforms with a better harmonic spec trum and attain a higher voltage without transformers, they have been receiving increasing attention in the past few years. There is several structure of multi levels inverter. in this work, we chose NPC topology [1] with five levels. Today, there are many switching strategies which are applied to multilevel inverter topologies. The most known are [1]: the sinusoidal pulsewidth modulation SPWM strategy, the selective harmonic eliminated pulse width modulation method SHEPWM and hysteresis current control. These strategies modulations, which are very effective methods for controlling the multilevels inverters, will be presented here to control a threephase voltage inverter fivelevel NPC topology [17]. In the first part, we will present the structure of the voltage inverter threephase fivelevel NPC topology. Secondly, we will apply four strategies [1]: The sinusoidal pulse width modulation strategy with a one carrier; The four carriers sinusoidal pulse width modulation strategy; The selective harmonic eliminated pulse width modulation method SHEPWM strategy; The hysteresis current control. In the third part we made a comparative study between these four strategies in several ways 2. Modeling of ThreePhase Inverter a FiveLevel NPC Topology The topology modeled in this study is the voltage in verter Three phase fivelevel topology NPC (Neutral Point Clamp) [2,3]. Figure 1 shows the voltage three phase fivelevel NPC topology inverter. The symmetry of threephase fivelevel inverters can model them by leg. So we begin by defining a global model of q leg without a priori on the control (Figure 2). A topological analysis of q leg of the fivelevel inverter NPC topology shows seven configurations (Table 1 and Figure 3). For a leg k, several complementary control laws are possible for the ﬁvelevel NPC. The optimal control law of this inverter is:
N. O. CHERCHALI ET AL.277 D13 D12 D11 D14 D15 D16 T13 T12 T11 T14 T15 T16 D18 T18 T23 T22 T21 T24 T25 T26 T33 T32 T31 T34 T35 T36 D23 D22 D21 D24 D25 D26 D33 D32 D31 D34 D35 D36 D28 T28 D38 T38 D17 T17 D27 T27 D37 T37 DD11 DD21 DD31 DD10 DD20 DD30 UC2 UC1 UC3 UC4 VA VB VC N M i1 i2 i3 id0 id1 id2 id3 id4 Figure 1. Threephase inverter a fivelevel NPC topology. Tk3 Tk2 Tk1 Tk4 Tk5 Tk6 UC2 UC1 UC3 UC4 Dk3 Dk2 Dk1 Dk4 Dk5 Dk6 Dk7 Tk7 Dk8 Tk8 DD11 DD10 M Umk3 Umk2 Umk1 Umk4 Umk5 Umk6 ik Umk8 Umk7 UDk0 UDk1 Figure 2. Leg of threephase inverter a fivelevel NPC. Table 1. Electrical quantities for each configuration of one leg k. configuration electrical quantities E0 Ik = 0 E1 VkM = UC1 + UC2 = 2UC E2 VkM = UC1 = UC E3 VkM = 0 E4 VkM = −UC3 = −UC E5 VkM = −UC3 − UC4 = −2UC E6 VkM = 0 Figure 3. The different configurations for q leg k of the inverter. 42 5 63 1 1 1 kk k kk 1k F F F (1) for the leg k, We deﬁne a half leg connection function where k = 1, 2, 3: where b = 1 refers to the lower half leg and b = 0 to the upper half leg 1123 0 456 b kkkk b kkkk FF F FFF (2) Connect functions for switches in parallel are defined as follows: 712 3 845 6 1 1 kkk k kkkk FF F FF F (3) The potentials of nodes A, B and C of Three phase fivelevel inverter relatively to the middle point M in the case UC1 = UC2 = UC3 = UC4 = UC are given by the following system: 1711 1810 2721 2820 37313830 22 22 22 bb AM bb MC bb CM FFFF V VFFFF VFFFF U (4) The simple voltages at the boundaries of the load are given by the following system: Copyright © 2011 SciRes. EPE
N. O. CHERCHALI ET AL. 278 1711 1810 2721 2820 37313830 22 211 112 122 3112 22 bb A bb C bb C FFFF V VFFFF VFFFF U (5) 3. Control Strategies of the Five Levels Inverter 3.1. Sinusoidal Pulse Width Modulation Strategy with One Carrier The principle of this method [3,8] is to impose on the machine terminals voltage pulses so that the fundamental tension is nearest the reference sinusoidal voltage. The moments of impulse control switches are determined by the intersection of the signal voltage reference called “modulator” with one triangular high frequency signal called a carrier. The characteristics of the method are: Modulation index m: m (6) Modulation ratio r: 2 m m V rU . (7) Figure 4 shows the reference voltages and the carrier. The algorithm of this strategy for arm k of this inverter is that 12 3 1: 0& 1;0; 0; refk pmrefk p kk k CVUVU FF F 123 2: 0&&0 1; 1;0; refk pmrefk prefk kk k CVUVUV FFF 123 3: 0&&0 0;0; 1; refk pmrefk prefk kk k CVUVUV FFF 123 4:2& '&0 1; 1;0; pm refkpmrefkprefk kk k CU VUVUV FFF 123 5:2& '&0 1; 1;0; pm refkpmrefkprefk kk k CU VUVUV FFF 123 6:2& '&0 1;1; 1; pm refkpmrefkprefk kk k CU VUVUV FFF 123 7:2& '&0 0;0; 0; pm refkpmrefkprefk kk k CU VUVUV FFF ;if 0 with ';if 0 refk pmrefk refk refk pmrefk VU V VVU V Figure 4. Different signals for the sinusoidal pulsewidth modulation strategy with a one carrier (m = 6, r = 0.8). Figures 5(a), 5(b) and 5(c) represent the voltage VA of a single inverter arm controlled by the sinusoidal pulse width modulation strategy with a one carrier 3.2. The Four Carriers Sinusoidal Pulse Width Modulation Strategy In this section we will present the strategy sinusoidal pulse width modulation with four triangular bipolar carriers [3,9] (Figure 6). Where we use four triangular carriers bipolar (Up1, Up2, Up3, Up4) dephased one quarter of the period (Tp/4) one relative to another. As SPWM strategy with a one carrier, this strategy is characterized by the modulation index m, m m m (8) and the modulation ratio r: m m V rU (9) Algorithm of this strategy is as follows: Step 1: determination of intermediate voltages (VK1, Vk2, VK3, Vk4): 44 44 33 33 22 22 11 11 2 0 0 2 refk pkC refk pkC refk pkC refk pk refk pk refk pkC refk pkC refk pkC VUV U VU VU VU VU VU V VU V VU VU VU VU VU VU (10) Copyright © 2011 SciRes. EPE
N. O. CHERCHALI ET AL. Copyright © 2011 SciRes. EPE 279 123 123 12 3 123 123 21;1; 1; 1;0 01;0; 0;0; 1 20;0; km Ckkk km Ckkk kmk kk km Ckkk kmC kkk VUF FF VUF FF VFFF VUF FF VUFFF 1 0 0 (12) Figures 7(a), 7(b) and 7(c) represent the output voltage VA and its spectrum of threephase fivelevel inverter controlled by the strategy sinusoidal pulse width modulation with four triangular carriers (a) 3.3. The Selective Harmonic Eliminated Pulse Width Modulation SHEPWM Strategy The principle of control by elimination of harmonics [5,815] is to predetermine the moments of switching of Semiconductors in order to eliminate one harmonic or many harmonics of the desired row. To eliminate the harmonics of the following ranges: 5, 7, 11, 13 and 17, it will take 6 angles (α1, α2, α3, α4, α5 and α6) (Figure 8). After analyzing the Fourier series will be a system of nonlinear Equations (13). We must solve this system by a numerical method (NewtonRafson [10,11] or Genetic Algorithms [1215]. (b) Uc: supply voltage. i: switching angles. The required solution must satisfy the following condition 0 < α1 < α2 < α3 < α4 < α5 < α6 < /2 (14) As mentioned, the system equations are nonlinear. In order to solve these equations the genetic algorithm (GA), which is based on natural evolution and populations, is implemented. This algorithm is usually used to reach a near global solution. In each iteration of the GA a new set of trings, which are called chromosomes, with im proved ﬁtness produced using genetic operators. (c) Figure 5. The simple voltage VA and its spectrum of Three phase fivelevel inverter controlled by The sinusoidal pulse width modulation strategy with a one carrier, (a) m = 6, r = 0.8; (b) m = 9, r = 0.8; (c) m = 36, r = 0.8. A more complete discussion of GAs including ex ten sions o the general algorithm and related topics can be found in books by Davis [16], Goldberg [17], Holland [18], and Deb [19]. Step 2: determination the signal Vkm and control orders Bks switches Vkm = Vk1 + Vk2 + Vk3 + Vk4 (11) 123456 123456 123456 123456 123 π cos coscoscoscoscos4 cos5 cos5cos5cos5cos5cos50 cos 7cos7cos 7cos 7cos 7cos 70 cos 11cos 11cos 11cos 11cos 11cos 110 cos 13cos 13cos 13 C r U 456 123456 cos 13cos 13cos130 cos 17cos 17cos 17cos 17cos 17cos 170 (13)
N. O. CHERCHALI ET AL. Copyright © 2011 SciRes. EPE 280 Figure 6. Different signals for the four carriers sinusoidal pulsewidth modulation strategy (m = 6, r = 0.8). (a) (b) (c) Figure 7. The simple voltage VA and its spectrum of Three phase fivelevel inverter controlled by the four carriers sinusoidal pulse width modulation strategy; (a) m = 6, r = 0.8; (b) m = 9, r = 0.8; (c) m = 36, r = 0.8. 0 1 2 3 4 5 6 /2 2Uc Uc VAM rad Figure 8. The waveform of the first quarter of tension VAM. The structure of a simple GA consists mainly of three operators: a selection operator, a crossover operator which acts on a population of strings to perform the re quired reproduction and recombination, and a mutation operator which randomly alters character values, usually with a very low probability. The effect of these random alterations is to maintain diversity within the population, thereby preventing an early convergence of the algorithm to a possibly false peak. Figure 9 represents the flowchart of Genetic Algo rithm [12]. Figure 10 represents the values of the six switching angles obtained after the resolution of the system (13) as function of r. Figures 11(a)(c) represent the single voltage VA and its spectrum of an inverter arm controlled by the SHEPWM strategy. 3.4. The Hysteresis Current Control The principle this method [2023] is based on deter mination the switching angles of switches so that the variation of current in each phase follows a sinusoidal current reference with a range of error i where the cur rent slide into a sliding surface. If one considers k the difference between the real current ik and reference current irefk. ( k = ik − irefk with k = 1.2 and 3). The switches control commands Bks for the arm k are given by the following algorithm 123 123 123 123 1: 20;0;0; 2:20;0; 1; 3: 21;1;0; 4;21;1;1; if not the command doe no change kik kk ikikkk iki kkk kikkk CFFF CFF CFF CFFF F F (15) Figure 12 and Figure 13 show respectively the refe rence and real currents with the difference between them two, the output voltage of the inverter and the harmonic
N. O. CHERCHALI ET AL.281 Generate Initial Population Calculation Reproduction Termi nate End Start Crossover Mutation Evaluation Ye s No Figure 9. Flowchart of genetic algorithm. i = 0.5 A and i = 0.1 A. 4. Comparative Study The comparative study between the different strategies for controlling the inverter threephase fivelevel NPC structure is performed to: *The same frequency of output voltage (f = 50 Hz) *The same the modulation ratio (r = 0.8) for both strategies sinusoidal pulse width modulation strategy with a one carrier and four carriers. According to Figures 5 and 7, we note that the increasing of the modulation index m can be pushed the harmonics to the higher frequencies and therefore can 0.55 0.60.65 0.7 0.75 0.80.85 0.9 0.9511.05 0 10 20 30 40 50 60 70 80 90 r angles (°) Alpha1Alphja2Alpha3 Alpha4Alpha5Alpha6 Figure 10. Six switching angles as function of modulation rate r, for the SHEPWM strategy to eliminate 5 harmonics (5, 7, 11, 13 and 15). (a) (b) (c) Figure 11. The simple voltage VA and its spectrum of three phase fivelevel inverter controlled by for SHEPWM strategy to eliminate 5 harmonics (5, 7, 11, 13 and 17). (a) r = 0.6; (b) r = 0.8; (c) r =1. easily be filtered. For The sinusoidal pulse width modu lation strategy with a one carrier, we have for m even only the odd harmonics exist, for m odd, we have odd Copyright © 2011 SciRes. EPE
N. O. CHERCHALI ET AL. 282 0.9 0.92 0.94 0.96 6 4 2 0 2 4 6Ia & Irefa (A) time (s) 0.9 0.92 0.94 0.96 1 0.5 0 0.5 1 time (s) IaIrefa (A) Ia Irefa (A)IaIrefa (A) (a) (b) Figure 12. (a) reference and real currents and the dif ference between the two currents εA; (b) The simple voltage VA and its spectrum of threephase fivelevel inverter controlled by the hysteresis current control (Δi = 0.5 A). 0.90.92 0.94 0.96 6 4 2 0 2 4 6Ia & Irefa(A) time (s) 0.9 0.92 0.94 0.96 0.4 0.2 0 0.2 0.4 time (s) IaIr e fa (A) Irefa Ia ( A)IaIrefa (A ) (a) (b) Figure 13. (a) reference and real currents and the dif ference between the two currents εA; (b) The simple voltage VA and its spectrum of threephase fivelevel inverter controlled byThe hysteresis current control (Δi = 0.1 A). harmonics and even harmonics too. For the strategy sinusoidal pulse width modulation four carriers it has only even harmonics. Figure 11 shows the existence of only odd harmonics and the magnitudes of first eliminated har monics are null. We note for the hysteresis current control is charac terized by hysteresis band i. From Figures 12 and 13 it is observed that the hysteresis current control is charac terized by a variable frequency modulation. This change will be even higher than the hysteresis value of (i) will be low. The spectrum of the voltage VA, has even and odd harmonics, the magnitudes of harmonic nearly neg ligible compared to that of the fundamental especially for i = 0.1. Figures 14 show the total harmonic distortion THD of the voltage VA, and the magnitude of the fundamental harmonic. The characteristic of adjustment strategy for the sinusoidal pulse width modulation strategy with a one carrier is linear for r = 0 to 0.5, and 0.56 to 1 but for r = 0.5 to 0.56 it’s constant because of the condition (16). And total harmonic distortion is decreasing function of r (Figure 13(a)). 2 mrefk p UV U m (16) For The four carriers sinusoidal pulse width modu tion strategy the modulation ratio r are like for the strategy with a one carrier, we have a linear adjustment of the magnitude of the fundamental r = 0 to 1. The total harmonic distortion THD decreases when r increases (Figure 14(b)), this strategy is better than with a one carrier. The modulation ratio r of the SHEPWM strategy is linear from 0.6 to r = 1.02 (Figure 14(c)) beyond this interval the system of nonlinear equation has no solutions after condition of angles (14). We note that the THD decreases as r increases. And we see also the best value for r which gives a low total harmonic distortion is 0.9 and r = 1.00 About The hysteresis current control, it is usefully than other strategies, more it can be controlled in closed loop, but we have to make an optimal control for low values of range (I). And the output voltages are asynchronous and no periodical. 5. Conclusions In our work we presented and modeled the threephase fivelevel inverter NPC structure then we applied to it different strategies: The sinusoidal pulse width modu lation strategy with a one carrier, The four carriers sinusoidal pulse width modulation strategy, the selective harmonic eliminated pulse width modulation method SHEPWM strategy and at the end we saw The hysteresis current control. After this study, we can note the following: Copyright © 2011 SciRes. EPE
N. O. CHERCHALI ET AL.283 (a) (b) (c) Figure 14. THD results and fundamental harmonic; (a) The strategy with a one carrier (m = 6); (b) The four carriers sinusoidal pulsewidth modulation strategy (m = 6); (c) The SHEPWM strategy to eliminate 5 harmonics (5, 7, 11, 13 and 17). The four carriers sinusoidal pulse width modulation strategy is more favorable than the sinusoidal pulse width modulation strategy with a one carrier, and it can be made with analog circuits. Selective harmonic eliminated pulse width modula tion method SHEPWM strategy is favorable to other control strategies in terms of number of switching (commutation energy dissipation) and noise nuisance. The hysteresis current control it perfectly follows the current reference, it can be controlled in closed loop. 6. References [1] B. S. Suh, G. Sinha, M. D. Manjrekar and T. A. Lipo, “Multilevel Power Conversion—An Overview of To pologies and Modulation Strategies,” IEEEOPTIM Con ference Record, Vol. 2, 1998, pp. 1124. [2] R. Guedouani, B. Fiala, E. M. Berkouk and M. S. Boucherit, “Control of Capacitor Voltage of Three Phase FiveLevel NPC Voltage Source Inverter. Application to Inductor Motor Drive,” International Aegean Conference on Electrical Machines and Power Electronics, Bodrum, 1012 September 2007, pp. 794799. doi:10.1109/ACEMP.2007.4510609 [3] R. Guedouani, B. Fiala, E. M. Berkouk and M. S. Boucherit, “Modelling and Control of ThreePhase PWM Voltage Source RectifiersFiveLevel NPC Voltage Source InverterInduction Machine System,” 18th Medi terranean Conference on Control & Automation, Marra kech, 2325 June 2010, pp. 533538,. [4] F. Bouchafaa, D. Beriber, M. S. Boucherit and E. M. Berkouk, “Enslavement and Control of the Multi DCBus Link Voltages Using Adaptive Fuzzy,” 8th International Symposium on Advanced Electromechanical Motion Sys tems & Electric Drives Joint Symposium, Lille, 13 July 2009, pp. 17. doi:10.1109/ELECTROMOTION.2009.5259075 [5] S. R. Pulikanti and V. G. Agelidis, “FiveLevel Active NPC Converter Topology: SHEPWM Control and Op eration Principles,” Australasian Universities Power En gineering Conference, Perth, 912 December 2007, pp. 15. doi:10.1109/AUPEC.2007.4548071 [6] R. Chibani, E. M. Berkouk and M. S. Boucherit, “Five Level NPC VSI: Different Ways to Balance Input DC Link Voltages,” ELEKTRIKA Journal, Vol. 11, No. 1, 2009, pp. 1933. [7] A. Nabae, I. Takahashi and H. Akagi, “A New Neu tralPointClamped PWM Inverter,” IEEE Transactions on Industrial Applications, Vol. 17, No. 5, 1981, pp. 518523. doi:10.1109/TIA.1981.4503992 [8] S. A. Mohamed, M. Dahidah and G. Vassilios Agelidis “SingleCarrier Sinusoidal PWMEquivalent Selective Harmonic Elimination for a FiveLevel Voltage Source Converter,” Electric Power Systems Research, Vol. 78, No. 11, 2008, pp. 18261836. doi:10.1016/j.epsr.2008.01.021 [9] P. K. Chaturvedi, J. Shailendra and P. Agrawal, “A Study of Neutral Point Potential and Common Mode Voltage Control in Multilevel SPWM Technique,” Proceedings of the 15th National Systems Conference, Bombay, 1618 December 2008, pp. 518523. [10] N. Ould Cherchali, N. Henini, S. Boulkhrachef, L. Bara zane and M. S. Boucherit, “Contribution of SHEPWM Copyright © 2011 SciRes. EPE
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