Comparative Study between Different Modulation Strategies for Five Levels NPC Topology Inverter

Noureddine Ould Cherchali, Abdelhalim Tlemçani, Mohemed Seghire Boucherit, Linda Barazane Laboratoire de Recherche en Electrotechnique et Automatique, Université de Médéa, Médéa, Alger Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, Algiers, Alger Faculté d’Electronique, Université des Sciences et de la Technologie Houari Boumediene, Algiers, Alger E-mail: nocherchali@yahoo.fr Received April 29, 2011; revised May 15, 2011; accepted May 23, 2011


Introduction
In recent years, electrical industries have expanded and the variety of loads has increasingly grown.Recently, the industry has begun to apply high-voltage high-power 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, multilevel inverters have been introduced.Due to their ability to synthesize waveforms with a better harmonic spectrum 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 three-phase voltage inverter five-level NPC topology [1][2][3][4][5][6][7].
In the first part, we will present the structure of the voltage inverter three-phase five-level 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

Modeling of Three-Phase Inverter a Five-Level NPC Topology
The topology modeled in this study is the voltage inverter Three phase five-level topology NPC (Neutral Point Clamp) [2,3].
Figure 1 shows the voltage three phase five-level NPC topology inverter.The symmetry of three-phase five-level 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 five-level inverter NPC topology shows seven configurations (Table 1 and Figure 3).
For a leg k, several complementary control laws are possible for the five-level NPC.The optimal control law of this inverter is: 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 Connect functions for switches in parallel are defined as follows: The potentials of nodes A, B and C of Three phase five-level inverter relatively to the middle point M in the case U C1 = U C2 = U C3 = U C4 = U C are given by the following system: The simple voltages at the boundaries of the load are given by the following system:

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: Modulation ratio r: Figure 4 shows the reference voltages and the carrier.The algorithm of this strategy for arm k of this inverter is that

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 (U p1 , U p2 , U p3 , U p4 ) dephased one quarter of the period (T p /4) one relative to another.As SPWM strategy with a one carrier, this strategy is characterized by the modulation index m, and the modulation ratio r: Algorithm of this strategy is as follows: Step 1: Copyright © 2011 SciRes.EPE
After analyzing the Fourier series will be a system of nonlinear Equations (13).We must solve this system by a numerical method (Newton-Rafson [10,11] or Genetic Algorithms [12][13][14][15].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 improved fitness produced using genetic operators.A more complete discussion of GAs including ex-tensions 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 V km and control orders B ks switches    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 required 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 Algorithm [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 V A and its spectrum of an inverter arm controlled by the SHEPWM strategy.

The Hysteresis Current Control
The principle this method [20][21][22][23] is based on determination 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 current slide into a sliding surface.
If one considers k the difference between the real current ik and reference current i refk .( k = i k − i refk with k = 1.2 and 3).
The switches control commands B ks for the arm k are given by the following algorithm if not the command doe no change

Comparative Study
The comparative study between the different strategies for controlling the inverter three-phase five-level 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  easily be filtered.For The sinusoidal pulse width modulation strategy with a one carrier, we have for m even only the odd harmonics exist, for m odd, we have odd 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 characterized by hysteresis band i.From Figures 12 and 13 it is observed that the hysteresis current control is characterized 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 negligible compared to that of the fundamental especially for i = 0.1.
Figures 14 show the total harmonic distortion THD of the voltage V A , 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)).
For The four carriers sinusoidal pulse width modution 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 = 1.00About 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.

Conclusions
In our work we presented and modeled the three-phase five-level inverter NPC structure then we applied to it different strategies: 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 and at the end we saw The hysteresis current control.
After this study, we can note the following: Copyright © 2011 SciRes.EPE 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 modulation 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.

Figure 2 .
Figure 2. Leg of three-phase inverter a five-level NPC.

Figure 3 .
Figure 3.The different configurations for q leg k of the inverter.

Figure 4 .
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 V A of a single inverter arm controlled by the sinusoidal pulse width modulation strategy with a one carrier

Figures 7 (
Figures 7(a), 7(b) and 7(c) represent the output voltage V A and its spectrum of three-phase five-level inverter controlled by the strategy sinusoidal pulse width modulation with four triangular carriers (b) U c : supply voltage.

Figure 5 .
Figure 5.The simple voltage V A and its spectrum of Threephase five-level 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.

Figure 8 .
Figure 8.The waveform of the first quarter of tension V AM .

Figure 12 andFigure 9 .
Figure12 and Figure13show respectively the reference and real currents with the difference between them two, the output voltage of the inverter and the harmonic

Figure 12 .Figure 13 .
Figure 12.(a) reference and real currents and the difference between the two currents ε A ; (b) The simple voltage V A and its spectrum of three-phase five-level inverter controlled by the hysteresis current control (Δi = 0.5 A).