Rana Choumane

Sophie Peulon
email: sophie.peulon@cnrs.fr

/or separation of soluble heavy metals

Keywords: Water pollution, Thin films, Metal oxides, Electrochemical treatment, Electrodeposition

Innovative electrochemical process for a total removal and

Introduction

Due to the particular intrinsic properties of heavy metals and associated compounds (e.g. oxides, hydroxides and oxyhydroxides), these materials are widely used in industries and new technologies such as metal processing, metal plating, electronics, textiles, paper, pesticides, etc. In this context, wastewater produced containing heavy metals and their direct or indirect discharge into the environment are relatively recent, and begin serious problems due to these vast anthropogenic sources and amount of heavy metals (mining and associated industries) [START_REF] Callender | Heavy Metals in the Environment-Historical Trends[END_REF][START_REF] Sukandar | Metals leachability from medical waste incinerator fly ash: A case study on particle size comparison[END_REF][START_REF] Chai | A review on conventional and novel materials towards heavy metal adsorption in wastewater treatment application[END_REF][START_REF] Deniz | Green purification of heavy metal pollution from aquatic environment by biorefinery waste biomass of Nigella sativa L.: A novel and effective treatment agent[END_REF]. In addition, there are also extrinsic environmental factors controlling pollution such as climate, precipitation, air temperature, hydrogeological conditions, etc. [START_REF] Paktunc | Characterization of Mine Wastes for Prediction of Acid Mine Drainage[END_REF][START_REF] Chen | Capacitive deionization and electrosorption for heavy metal removal[END_REF].

Once the heavy metals are released into the environment either by anthropogenic activities from their source either by natural processes, they can pollute the air and water, with possible great consequences on the production of drinking water, which is an essential resource for life. The most common heavy metals found in wastewater coming from industrial effluents and/or terrestrial ecosystems are cadmium (Cd), copper (Cu), zinc (Zn), lead (Pb), chromium (Cr), nickel (Ni) Vanadium (V), Platinum J o u r n a l P r e -p r o o f (Pt) and Titanium (Ti) [START_REF] Marella | Diatom mediated heavy metal remediation: a review[END_REF][START_REF] Ali | Environmental chemistry and ecotoxicology of hazardous heavy metals: environmental persistence, toxicity, and bioaccumulation[END_REF]. In complement, the concentrations are also an important parameter for characterizing their impact on environment, terrestrial and aquatic organisms, and human health [START_REF] Alloway | Chemical Principles of Environmental Pollution[END_REF]. This is particularly true for the most toxic heavy metals such as Pb, Cd, Cr, Ni and Ti. That is why their concentrations in produced wastewater before discharges into the environment are controlled and must be in coherence with the defined guideline for the acceptable concentration limits set by the World Health Organization (WHO) for drinking water and the environment standards [START_REF]Chemicals of Health Significance as described by World Health Organization Guidelines (WHO) for Drinking-water Quality in third edition[END_REF].

Different methods are frequently applied for removing heavy metals from wastewater including adsorption, ion exchange, membrane filtration, chemical precipitation, inverse osmose, electrochemical treatments, etc. [START_REF] Feng | Electrochemical technologies for wastewater treatment and resource reclamation[END_REF]. However, some of these largely used methods can be (i) energy intensive and/or expensive, (ii) lead to incomplete removal of metals, (iii) present low efficiencies for very high or low metals concentrations, (iv) require high consumption of reagents, more or less toxic or expensive or scarce, (v) produce toxic sludge or other wasted products that need complement treatments, (vi) require regeneration steps more or less complex or energy-intensive, (vii) need complex implementation and maintenance, etc. To ensure a less negative impact of these issues, constant improvements are necessary to respect the acceptable concentrations [START_REF] Choumane | Electrodeposited birnessite thin film: An efficient eco-friendly sorbent for removing heavy metals from water[END_REF][START_REF] Foong | A review on nanofibers membrane with amino-based ionic liquid for heavy metal removal[END_REF][START_REF] Sulaiman | Application of porous membrane bag enclosed alkaline treated Y-Zeolite for removal of heavy metal ions from water[END_REF][START_REF] Mameda | Electrochemical filtration process for simultaneous removal of refractory organic and particulate contaminants from wastewater effluents[END_REF][START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF].

In this context, we have recently developed an innovative electrochemical process for a high efficient lead removal from wastewater in very easy conditions [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. The mean idea is to remove lead in the form of adherent electrodeposited lead oxide(s) thin films onto conductive support at room temperature without addition of toxic reagents and / or complexing agents, and only based on the effect of an adequate applied potential at a given pH, with classical electrochemical materials. Even if the J o u r n a l P r e -p r o o f electrodeposition of pure oxides thin films, and lead in particular, is already largely reported in the literature for synthesis and/or various applications, because lead oxides are particularly interest compounds, no study focusses on the depollution of aqueous solutions by this way. Moreover, our electrochemical process is particularly efficient since it allows the decontamination of aqueous solutions (e.g. model or effluents), loaded with Pb(II) until elimination of 99.99% with reached concentration level acceptable for the environment and drinking water standards [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. Therefore, no reagent was used, no waste was produced, and the development at large scales with low maintenance at low costs, since the electrical energy inputs are low, appears possible.

Considering the real advantages and interests of this innovating electrochemical process for eliminating lead, compared to other classical methods, the aim of the present article was to extend our studies to other toxic heavy metals such as Cu(II), Ni(II) and Cd(II), which are largely present in wastewater, industrial effluents and terrestrial ecosystems [START_REF] Marella | Diatom mediated heavy metal remediation: a review[END_REF][START_REF] Ali | Environmental chemistry and ecotoxicology of hazardous heavy metals: environmental persistence, toxicity, and bioaccumulation[END_REF].

First, the adequate electrochemical conditions were researched for each heavy metal present alone in pure water. Then, systematic analyses of the solutions coupled to the characterizations of the recovered thin films by XRD and SEM were performed. In a second part, this treatment was applied on a model solution containing a mixture of these all heavy metals (e.g. Pb(II), Cu(II), Ni(II), and Cd(II)), present at equivalent concentrations for studying the possibility of their total removal and/or separation. Finally, the same procedure was applied on effluents coming from wastewater treatment plants (WWTP) and containing these heavy metals for evaluating the efficiency and the real interests of this innovative electrochemical treatment. The possibility to have a total elimination and separation of heavy J o u r n a l P r e -p r o o f metals in these complex solutions in simple and eco-compatible conditions is very promising for future applications in many fields.

Materials and methods

Chemicals

Standard solutions of Cu(II), Ni(II), Cd(II) and Pb(II) (1002 ± 4 mg. L -1 , 5% HNO 3 ) (Alfa Aesar), intended for use as certified reference materials or calibration standard for inductively coupled plasma optical emission spectroscopy (ICP-OES), were used for preparing all model solutions. NaOH (1M) and nitric acid (1M) (ACS Reagent Sigma Aldrich) were used for adjusting the pH and for the treatment of real effluents. All synthetic solutions were prepared by using Milli-Q water.

Experimental methodology

All electrochemical measurements were performed by using a microautolab potentiostat piloted by its associated software GPES (General Purpose for Electrochemical System).

All electrochemical studies were performed into a conventional electrochemical setup with three electrodes: a commercial glass plate covered with tin dioxide SnO 2 :F (FTO Fluorine-doped Tin Oxide, Solems, noted SnO 2 ), with a delimited surface to 3 cm 2 by an adhesive mask, as a working electrode, a platinum wire wound spirally, for having a higher surface to the working electrode, as a counter electrode, and a mercurous sulphate electrode (MSE, E = 0.6513 V/SHE) as a reference electrode. All values of potential reported in this study are referred to this reference electrode. All experiments were realized at room temperature, in the air at atmospheric pressure with a gentle agitation of the solution (250 rpm).

In first, cyclic voltammetry measurements (v = 10 mV.s -1 ; five successive scans) were performed for determining the potential ranges corresponding to the oxidation and/or J o u r n a l P r e -p r o o f reduction reactions of the soluble metal studied alone according to the pH value. Then, the electrochemical treatment for the elimination of heavy metals was carried out by chronoamperometry for different durations by imposing the adequate potential determined by cyclic voltammetry according to the pH value.

The experiments with model solutions were performed on 50 ml of milli-Q water at different pH adjusted by adding NaOH (1M) if necessary (no buffer), and containing 6.5 μmol of heavy metal, alone or in mixture, as soluble form (e.g. M(II), such as Cu(II), or Ni(II) or Cd(II)). In all cases, no precipitate was present, initially in the bulk solution and at the end of the treatment. The solutions being always clear, no filtration step was required and the analyses for determining the concentration of each heavy metal were directly performed without any preparation. Each condition was repeated several times for confirming the good repeatability and reproducibility of the treatment in terms of elimination and/or separation of heavy metal studied alone or in mixture. In complement of these experiments performed on model solutions, some tests were realized in similar experimental conditions on effluents coming from wastewater plants (WWTP).

The concentrations of heavy metals present in the aqueous solutions as soluble cation (noted M(II)), were determined by using the appropriate Spectroquant® test for each heavy metal: Cu(II) (1.14767.0001; 0.10 mg. L -1 to 6.00 mg. L -1 ), Ni(II) (1.14785.0001; 0.10 mg. L -1 to 5.00 mg. L -1 ), Cd(II) (1.01745.0001; 0.01 mg. L -1 to 0.50 mg. L -1 ) and Pb(II) (1.09717.0001; 0.10 mg. L -1 to 5.00 mg. L -1 ). Absorbance measurements were performed at the adequate wavelength by a spectrophotometer (Varian Cary® 50 UV-visible Agilent): 600 nm for Cu(II), 450 nm for Ni(II), 520 nm for Pb(II) and Cd(II).

J o u r n a l P r e -p r o o f

The amount of each removed metal cations (n M(II) removed ) was calculated by the difference between the initial amount and the equilibrium one using Eq. 1, and the percentage of M(II) removed from the solution after the electrochemical treatment using Eq.2:

n M(II) removed = n M(II) initialn M(II) at t

Eq.1

( ) ( ) ( ) ( ) ( )

Eq.2

With n in mol, and t, corresponding to a fixed duration (h).

The values reported for each condition in the figures correspond to the mean value of several experiments with the associated incertitude.

After each electrochemical treatment, in the case of recovered adherent deposits onto the working electrode (e.g. SnO 2 ), X-Ray Diffraction (XRD) was performed with classical measurements (θ/2θ) by a BRUKER θθ diffractometer equipped with a copper anode (λ Cu =1.540600 Å) and a LYNXEYE detector. In addition, the thin films were observed by a MEB-FEG MERLIN Zeiss Scanning Electron Microscopy (SEM). All characterizations were carried out directly without any preparation step since the thin films were well adherent and sufficient conductive. The characterization by XRD and the observations by SEM of the deposits are reproducible for each eliminated metal for similar experimental conditions (pH and applied potential) and whatever species present in solution.

Results and discussion

Recently, we have developed an innovative electrochemical process for removing soluble Pb(II) present in wastewater as adherent thin films deposited onto a conductive substrate, at room temperature without addition of toxic reagents and/or complexing agents J o u r n a l P r e -p r o o f [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. The general principle is based only under the effect of an applied potential and at a given pH for inducing the change of the lead oxidation state. Initially, lead is soluble in solution (State 1, e.g. Pb(II)) and under the effect of the potential, it can be more or less oxidized (State 2), and precipitated onto the electrode as adherent thin films of oxide(s). It was found that Pb(II) can be quantitatively eliminated as a mixture of oxides (e.g. mainly of β-PbO 2 with few amount of Pb 3 O 4 ) under an imposed potential of 0.7 V at pH adjusted to 4.2, or as pure β-PbO 2 in acidic solution (pH≈ 2) under imposed potentials equal to 1.0 V or 1.2 V [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. This process is so effective that it achieves a depollution percentage up to 99.99%

with concentrations reached that meet environmental norms and even those of drinking water [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. In view of the real potentialities of this elimination process, it seemed very interesting to extend studies to other heavy metals.

Cu(II) and Ni(II) present different oxidation states and their eliminations in the form of adherent films deposited onto a conductive substrate seem theoretically possible according to the same principle and methodology already developed for lead. However, this is not the case for Cd(II), which possess only one soluble oxidation state that is why its elimination by this process will not be possible. Nevertheless, it was important to validate this assumption, for scientific rigor, and to study in the same time its possible effect on the elimination of the other heavy metals in the case of mixtures since they are often present together in wastewater. Each heavy metal having a specific chemistry in solution that is why it was necessary to study them separately before studying mixtures.

J o u r n a l P r e -p r o o f

Extension of the innovative electrochemical treatment on other heavy metal present alone in model solution

Case of Cu(II)

Copper has three oxidation states (0, +I and +II), and can form different solid compounds, either in metallic form (Cu(0) (s)), either in oxidized form such as CuO and Cu 2 O, according to pH and/or potential, as reported on the diagram of Pourbaix in the absence of complexing agent [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF]. In accordance to the copper chemistry, it should be possible to eliminate it by this electrochemical process but the main difference compared to the case of lead is that copper, present initially in solution as soluble Cu(II), must be reduced.

Although many research papers report the electrodeposition of copper oxides and the studies of key parameters on their nanostructures for different applications (e.g. solar energy conversion, catalysis) [START_REF] Raziyeh | The influence of bath temperature on the one-step electrodeposition of non-wetting copper oxide coatings[END_REF][START_REF] Mezine | Electrodeposition of copper oxides (CuxOy) from acetate bath[END_REF], never in the aim to have a total elimination of soluble Cu(II) as adherent electrodeposited thin films for water depollution. For that, cyclic voltammetry measurements were performed for determining the best potential(s) in reduction. Measurements were carried out with the conventional electrochemical cell, equipped with the three electrodes cited above, and containing 50 mL of milli-Q water and 6.5 μmol of Cu(II) (corresponding to 8.2 mg. L -1 ) at different pH (free pH ≈ 2, 4.2 and 7) by the addition of NaOH (1M) (no buffer). Only in the case of pH = 7, two different cathodic signals were observed with significant intensities: a small first peak between -0.35 V and -0.5 V, and a large second peak between -0.55 V and -1 V, Table 1. These signals could correspond to the reduction reactions of Cu(II) into Cu(I)

and/or Cu(0) according to the thermodynamic data and the diagram of Pourbaix [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF].

For testing the possibility to eliminate soluble copper, two electrochemical treatments were carried out by chronoamperometry on similar Cu(II) solutions (6.5

J o u r n a l P r e -p r o o f μmol into 50 mL of milli Q water at pH 7) under a potential imposed respectively at -0.45 V and -0.85 V. In both cases, an adherent deposit was formed onto the SnO 2 substrate with a visual aspect of these two thin films clearly different according to the value of potential, pinkish brown for -0.45 V and yellowish for E = -0.85 V, suggesting possible differences in nature and/or crystallinity of these electrodeposited materials.

In addition, the solutions were analysed by using the Spectroquant® test for Cu(II) after different durations and for these two values of potential. It appears that the elimination of copper is largely quicker at -0.45 V than at -0.85 V, Figure 1, since 91 % of the initial amount of copper was already eliminated after only 24 h compared to experiments performed at -0.85 V that required 72 h to obtain equivalent results. The total elimination of Cu(II) was reached after 48 h at -0.45 V and 96 h under a potential of -0.85 V, according to the detection limit of the Spectroquant® test (0.10 mg. L -1 ), which is largely inferior to the limit value fixed for drinking water (e.g. 2 mg.L -1 ) [START_REF]Chemicals of Health Significance as described by World Health Organization Guidelines (WHO) for Drinking-water Quality in third edition[END_REF].

These results appear coherent with the difference of current intensities observed during the electrodeposition, which could be due to the nature of the electrodeposited oxide(s) copper, with electrical properties more or less pronounced, their crystallinity, and/or the covering rate of the substrate causing possible parasitic electrochemical reactions, Insertion Figure 1. However, in these two conditions, the intensities of currents stay always very low, and the elimination was total with concentrations reached directly acceptable for drinking water standards [START_REF]Chemicals of Health Significance as described by World Health Organization Guidelines (WHO) for Drinking-water Quality in third edition[END_REF].

Case of Ni(II)

The chemistry of nickel is complex since nickel have many degrees of oxidation (0, + II, + III and + IV), with the possibility of forming different solid compounds, as reported by the Pourbaix diagram of nickel in the absence of complexing agent [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF]. In accordance to the chemistry of nickel, it appears possible to envisage its elimination from aqueous solutions according to the same principle (e.g. oxidation state change). However, it was necessary to define the adequate potential ranges and pH since different types of oxides can be formed by oxidation reactions (e.g. Ni 2 O 3 and NiO 2 ) in addition to NiO(OH), which can be also electrodeposited as thin films [START_REF] Girolamo | Investigating the electrodeposition mechanism of anodically grown NiOOH films on transparent conductive oxides[END_REF].

While many research papers in the literature report the electrodeposition of nickel oxides and the studies of parameters on the nanostructure for different applications [START_REF] Sonavane | Efficient electrochromic nickel oxide thin films by electrodeposition[END_REF][START_REF] Xi | Electrodeposition for antibacterial nickel-oxide-based coatings[END_REF], never in the aim to have a total elimination of soluble Ni(II) for depollution context.

For that, cyclic voltammetry measurements were carried out on Ni(II) model solutions with different pH (2.5, 4.2 and 7) as cited above. In the case of pH 4.2, an anodic peak was observed in the potential range comprised between 0.5 V and 0.8 V in contrary to the other values of pH (no significant peak), Table 1. For confirming this result, an electrochemical treatment was carried out at room temperature by chronoamperometry on a Ni(II) solution (6.5 μmol in 50 mL prepared with milli-Q water corresponding to 7.6 mg. L -1 ) at pH 4.2 by adding NaOH (1M), under an imposed potential of 0,7 V, with gentle stirring. After 24 h, an adherent deposit was recovered onto the SnO 2 substrate with a removal of 26 % of the initial amount of Ni(II) according to the analyses performed by the specific Spectroquant® kit. A total elimination of Ni(II), according to the detection limit of the Spectroquant® test (0.10 mg. L -1 ), was obtained after 72 h, associated to the obtention of a deposit, which has a colour between yellow and orange. The intensity of the current is low (inferior to 10 In our previous study, we have reported that lead can be eliminated under these same experimental conditions (e.g. pH and potential), and even in the presence of Ni(II), which stayed quantitatively in solution [START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. Therefore, it appeared important to test inversely the possibility to eliminate Ni(II) in the presence of Pb(II) and for that complementary measurements were performed. Based on these results, an equivalent treatment was made on a solution containing Pb(II) and Ni(II), at the same initial concentration (6.5 µmol each in 50 ml in milli-Q water at fixed pH = 4.2) but for a longer time (e.g. 7 days). After this duration, it appears that Pb(II) was totally eliminated, but Ni(II) remained quantitatively in solution, while previously nickel present alone in solution can be eliminated.

It appears therefore that the presence of lead in solution and its elimination as thin film seems to hinder the elimination of nickel, due to possible chemical interferences in solution.

However, this could be due also to the evolution of the working electrode, which was modified during the electrochemical treatment by the presence of the adherent lead oxide thin film electrodeposited. To verify this latter assumption, the working electrode was changed during the treatment of such mixture. For that, the working electrode of SnO 2 covered with the deposit of lead oxides, was thus exchanged by a novel working electrode of SnO 2 . In these conditions, Ni(II) was totally eliminated in the form of an adherent film after 72 h, exactly like previously observed in the absence of lead. Consequently, it appears that the removal of Ni(II) seems more difficult to carry out than lead or copper, and that it requires a specific surface such as SnO 2 to be able to be electrodeposited as an adherent thin film. This could be due to the necessity to have a specific crystalline structure for initiating the germination process.

J o u r n a l P r e -p r o o f [START_REF] Lee | Electrodeposition of PbO2 onto Au and Ti substrates[END_REF] , and ZnO in particular [START_REF] Peulon | Mechanistic Study of Cathodic Elecfrodeposition of Zinc Oxide[END_REF][START_REF] Peulon | Cathodic Electrodeposition from aqueous solution of dense or open-structured zinc oxide films[END_REF].

Even if we expected theoretically the non-removal of Cd(II) according to this depollution process, it was important for scientific rigor to study its behaviour alone.

Particularly, it was important to validate the absence of precipitation onto the working electrode, which could modify the efficiency of the treatment for the other heavy metals in the case of a mixture (nature change and/or conductivity of the working electrode).

According to the same experimental procedure, cyclic voltammetry measurements were carried out into the conventional electrochemical cell with the three electrodes described before. Different Cd(II) solutions, with various pH as cited above (2, 4.2 and 7), were studied, and in all cases, no peaks were reported. Moreover, the values of the oxidation and reduction potentials of water were not modified, in comparison to the other cyclic voltammetry measurements for similar pH, confirming the absence of the modification of the working electrode due to possible precipitation reaction. In addition, the SnO 2 working electrode was not visually modified. Clearly,

J o u r n a l P r e -p r o o f

Cd(II) cannot be eliminated from the solution in this way, whatever the pH and / or potential conditions.

Characterization of the recovered films by XRD and SEM

Case of Cu(II)

For confirming the nature of the solids, the adherent deposits obtained after a total elimination of Cu(II) at pH = 7 under imposed potentials fixed to -0.45 V or -0.85 V respectively, were characterized by XRD and SEM.

Figure 3 reports the X-ray diffractograms of these deposits. According to the observed peaks, and based on JCPDS 00-005-0667 card, it appears that Cu(II) was electrodeposited in the form of Cu 2 O (cuprite, cubic structure) in the two experimental conditions. The colour of the natural cuprite can be varied between yellow, red or brown, which is in good agreement with the visual aspect of the obtained thin films reported previously (e.g. pinkish brown for -0.45 V and yellowish for E = -0.85 V).

Moreover, the characteristic peaks of Cu 2 O are particularly intense for the treatment performed under a potential of -0.45 V compared to -0.85 V, meaning that the sample under these conditions must be more crystallized since the total amount was equivalent (total elimination). This result is also in good coherence with the difference of colour observed for each thin film.

The formation of Cu 2 O is particularly in good agreement with the diagram of Pourbaix as thermodynamic compound expected in this range of pH and value of applied potential (e.g. pH = 7 and E = -0.45 V), [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF]. In contrary, the treatment performed at -0.85 V is slightly lower to the limit of the Cu 2 O formation zone, according to the diagram of Pourbaix, which can justify the difference of the efficiency of treatment observed in this case. Indeed, the electrical energy input required must be more important for initiating the germination process. Moreover, this value of potential

J o u r n a l P r e -p r o o f

is close to the reduction potential of water, which can be also a parasitic electrochemical reaction. This can justify why the intensity of current was largely higher in this case.

Figure 3 reports also the associated SEM images of these two thin films. These observations show that the soluble copper was eliminated in the two cases as cubic crystals but with different sizes according to the experimental conditions. Therefore, the removal Cu(II) mechanism by this electrochemical treatment, made by reduction reaction, is a nucleation process according to the model of Volmer-Weber [START_REF] Palmer | The solubility of crystalline cupric oxide in aqueous solution from 25 °C to 400 °C[END_REF][START_REF] Seel | Tensile stress evolution during deposition of Volmer-Weber thin films[END_REF], as already reported for the elimination of lead [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. Indeed, whatever the conditions, the growth of the electrodeposited thin films was performed with the formation of 3D islands and not as a uniform thin film. This observation is relatively classical for electrodeposition process that begins generally from surface or nucleation site defects.

The cubes have very large sizes for the deposit formed at -0.45 V, which vary between 2 and 3 μm, compared to those obtained at -0.85 V (well below the micrometer). However, in both cases the cubes are well homogenously distributed onto the surface of the SnO 2 working electrode. These observations are in good coherence with the more or less intense peaks obtained by XRD measurements and the difference of intensities of current observed during their elimination by electrodeposition.

Based on literature studies, Cu 2 O is a p-type semiconductor with a reported resistivity varying from a few Ω.cm to 1014 Ω.cm depending on the synthesis conditions [START_REF] Seel | Tensile stress evolution during deposition of Volmer-Weber thin films[END_REF]. Cu 2 O preparation techniques include thermal oxidation, chemical oxidation, anodization, vacuum evaporation and electrochemical methods [START_REF] Mezine | Electrodeposition of copper oxides (CuxOy) from acetate bath[END_REF][START_REF] Seel | Tensile stress evolution during deposition of Volmer-Weber thin films[END_REF][START_REF] Luo | Copper nanocubes and nanostructured cuprous oxide prepared by surfactant-assisted electrochemical deposition[END_REF].

Thus, it is possible to suppose that the resistivity of the materials electrodeposited could change according to the value of potential, which can explain also these differences in term of the values of intensities, sizes of crystals, and covering rate J o u r n a l P r e -p r o o f during the total elimination of Cu(II). Cu 2 O has potential applications in solar energy conversion and catalysis [START_REF] Luo | Copper nanocubes and nanostructured cuprous oxide prepared by surfactant-assisted electrochemical deposition[END_REF]. This compound is also often used as an absorbent layer or hole transport layer in solar cells, [START_REF] Liu | Shape control in Epitaxial electrodeposition: Cu2O nanocubes on InO (001)[END_REF][START_REF] Yang | Potentiostatic and galvanostatic two-step electrodeposition of semiconductor Cu2O films and its photovoltaic application[END_REF][START_REF] Mahmood | Photoelectrochemical Characteristics of CuO films with different electrodeposition time[END_REF]. Synthesizing Cu 2 O deposits with very different crystal sizes according to the experimental conditions can be an asset for possible applications of these materials [START_REF] Raziyeh | The influence of bath temperature on the one-step electrodeposition of non-wetting copper oxide coatings[END_REF][START_REF] Mezine | Electrodeposition of copper oxides (CuxOy) from acetate bath[END_REF] obtained moreover within the framework of the total depollution of solutions loaded with copper.

Case of Ni(II)

The deposit recovered after the total Ni(II) removal with a yellow/ orange colour was characterized by XRD. The observed peaks correspond to the characteristic peaks of SnO 2 substrate but they can also well matched to γ-NiO(OH) according to the JCPDS 00-006-0075 card, compounds such as NiO(OH), could be also possible [START_REF] Girolamo | Investigating the electrodeposition mechanism of anodically grown NiOOH films on transparent conductive oxides[END_REF]. Therefore, we cannot conclude formally on the structural form of the Ni electrodeposited solid by XRD measurements, however, it is classical that Ni compounds are difficult to be identified by XRD [START_REF] Greenwood | Alan Earnshaw Chemistry of the Elements[END_REF]. For that, specific other measurements and/or change of the substrate nature would be required.

In complement, the thin film was observed by SEM but the morphology was not really defined with two different types of crystals, Figure 4. Other complementary techniques such as infrared spectroscopy or XPS would be interesting to identify precisely the nature of the compound electrodeposited, but this is out of the scope of this work.

J o u r n a l P r e -p r o o f

Determination of the Faraday efficiency and the yield of experimental energy consumption (R) for the elimination of each heavy metal present alone in solution.

After the electrochemical treatment, each heavy metal, e.g. Cu(II) and Ni(II), present alone in model solution was totally eliminated based on the analyses of solution. As a result, the faradic efficiency of recovered soluble metal in solution in the form of metal oxide is 100%.

However, it was interesting to compare the experimental electrical charge, calculated according to Eq. 3, in relation to the theoretical electrical charge, calculated according to the Faraday's law, Eq. 4, to estimate the yield of the experimental energy consumption for having a total elimination of each heavy metal, Eq. 5:

Eq. 3

Where I (A) the average current recorded during the elimination by electrodeposition of each heavy metal, and t (s) the time needed for the total elimination.

Eq. 4

Where n (mol) the molar number of the heavy metal eliminated from the started solution (6.5 10 -6 mol), z the electrons transferred for the oxidation (Ni(II) case) or the reduction (Cu(II) case) to produce the solid (NiO(OH) and Cu 2 O respectively), F Faradaic Constant (96485 C mol -1 ).

( )

Eq. 5

All values required for these calculations are regrouped in Table 2. As reported previously, Cu(II) can be eliminated at pH = 7 under an applied potential of -0.45 V or -0.85 V, and the yields of energy consumption for each case are 136 % and 3312 % respectively.

J o u r n a l P r e -p r o o f

This means that the experimental energy consumption is more than the theoretically expected by a factor of 1.3 and 33 respectively.

These results confirm clearly that the elimination of Cu(II) is largely more efficient and easy for an applied potential equal to -0.45 V, in good agreement with the diagram of Pourbaix. The difference of energy consumption is relatively low, given that the duration and the reactor were not optimized yet. In contrary, the elimination of Cu(II) in the case of an applied potential fixed to -0.85 V is clearly unfavourable. As already reported above, this is probably due to the presence of parasitic reactions and/or the requirement of more energy for initiating the nucleation process. By consequently, the most effective removal of Cu(II) for depollution purposes must be performed in priority under an applied potential of -0.45V.

Likewise, Ni(II) was removed under an applied potential of 0.7V at pH = 4.2. The yield of experimental energy consumption is 100 % and close to the theoretical value expected one, without parasite reaction.

Application of the electrochemical treatment on a synthetic solution containing a mixture of heavy metals: Determination of the separation efficiency and energy costs.

The purpose was (i) to confirm first the real efficiency of this treatment to remove and to separate totally the different heavy metals present in a mixture for determining eventual interference problems, and in the second part (ii) to estimate the energy costs for the implementation of the elimination of each heavy metal by this electrochemical process [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF].

The consumption of the electrical energy consumed for the elimination of each heavy metal by this electrochemical treatment was estimated using the following equation:

E consumed = (I.V.t) / 1000
Eq. 6

J o u r n a l P r e -p r o o f

With E, the electrical energy consumed (kWh), I, the maximal intensity of the measured current (A), V, the imposed potential (V), t, the duration applied to have a total elimination of the metal present in soluble form in the solution (h).

Determination of the separation efficiency

After the determination of the adequate conditions for removal each metal cation, an electrochemical treatment was carried out by chronoamperometry on 50 ml of a solution under stirring containing 6.5 μmol of each soluble metal, Pb(II), Cu(II), Ni(II), and Cd(II), corresponding to 27 mg. L -1 , 8.2 mg. L -1 , 7.6 mg. L -1 and 14.6 mg. L -1 respectively. For that, the following protocol was performed at room temperature, and only by changing the pH and the imposed potential for each step as illustrated on Figure 5. After each step, a systematic analysis of the solution was performed to determine the concentration of the heavy metal studied, in complement to the observation by SEM of the recovered thin film and its characterization by XRD. In all cases, the presence of other heavy metals in solution has any effect on the nature, crystalline structure and/or the morphology of the recovered metal, confirming the absence of chemical interference problems.

 Step 1: Elimination of Pb(II)

According to our previous study, we have demonstrated that Pb(II) can be eliminated at pH = 4.2 but also in acidic medium (pH ≈ 2) under an imposed potential of 1.2 V for 24 h [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF][START_REF] Choumane | Method for decontaminating heavy metals in an aqueous solution[END_REF]. To avoid possible competition with Ni(II) at pH=4.2, as reported and discussed above (paragraph 3.1.2), we have chosen to eliminate lead the first in acidic conditions. After 24h, the solution analysis confirms that Pb(II) was totally eliminated from the solution as a brown adherent thin film. The crystalline structure of the deposit is pure β-PbO 2 , as observed in the case of its elimination alone in solution with the same morphology of branches (dendrites) as reported in our previous study. This result prove that soluble lead can be totally removed J o u r n a l P r e -p r o o f alone or in the presence of these other heavy metals with the same efficacy and without any effect on the nature and/or morphology of the deposit [START_REF] Choumane | Development of an efficient electrochemical process for removing and separating soluble Pb (II) in aqueous solutions in presence of other heavy metals: Studies of key parameters[END_REF]. Then, the separation of lead in the presence of these other heavy metals appears easy at room temperature, and this point is very interesting for future applications (depollution, separation).

 Step 2: Elimination of Ni(II)

A novel SnO 2 working electrode was put in the cell, and the pH of the solution was adjusted to 4.2 by adding NaOH. Under the imposition of a potential of 0.7 V, Ni(II) was quantitatively eliminated after 72 h as an adherent deposit with a yellow/orange colour onto the SnO 2 working electrode. In addition, the SEM observation shows that the deposit did not have a well-defined morphology, as observed previously, and in good agreement with the XRD characterization, which reports exactly a similar diffractogram obtained during its elimination alone in solution without characteristic peaks except those of the substrate, Figure 4. This result signifies then that the elimination of soluble nickel is total and easy at room temperature, even in the presence of Cu(II) and Cd(II).

 Step 3: Elimination of Cu(II)

Then, a novel SnO 2 working electrode was put in the cell and the pH of the solution was adjusted to 7 by the addition of NaOH (1M). Under a potential of -0.45 V for 48 h, Cu(II) was quantitatively eliminated from the solution as a pinkish brown adherent thin film onto the SnO 2 electrode. The characterizations by XRD and SEM show that the crystal structure is purely Cu 2 O with a cubic morphology as observed above in the case of its elimination alone in solution. This result signifies then that the elimination of soluble copper is total and easy at room temperature, even in the presence of Cd(II).

J o u r n a l P r e -p r o o f

At the end, the concentration of Cd(II) was analysed and it stays quantitatively in solution. These all result are important for future applications in order to separate Cd(II) to other heavy metals.

However, for obtaining a total depollution of the solution, it was possible to eliminate Cd(II) in a last step by only sorption reaction onto the eco-friendly sorbent based on electrodeposited manganese oxides thin films (birnessite), that we have recently developed and optimized particularly for the elimination of cadmium [START_REF] Choumane | Electrodeposited birnessite thin film: An efficient eco-friendly sorbent for removing heavy metals from water[END_REF].

Determination of the energy costs

For each case, the energy cost was estimated using Eq. 6 with the maximal current intensity (I max ) and not the average value over the entire period of the treatment meaning that the energy costs are largely overestimated. The parameters used for the energy consumption calculations were regrouped in Table 3.

According to these calculations, the estimations of energy consumptions for the depollution of this sample, after the different electrochemical steps are equal to 2.8 10 -6 kWh for Pb(II), corresponding to 2.1 kWh for one kg of lead, 2.6 10 -7 kWh for Ni(II), corresponding to 0.7 kWh for one kg of nickel, and 3.2 10 -7 kWh for Cu(II), corresponding to 0.8 kWh for one kg of copper. These overestimated values vary between 0.7 and 2.1 kwh/Kg of metal, which are largely inferior compared to the values reported in the literature for the recuperation of these metals [START_REF] Bru | Etat de l'art des procédés de récupération sélective et de valorisation des métaux présents dans les Drainages Miniers Acides des mines métalliques[END_REF]. Indeed, for example, the removal of Ni(II) and Cu(II) was reported in the literature by electrochemical processes (reduction reaction) by using Stainlesssteel sheets with surface area of 0.011 m 2 and titanium coated with ruthenium oxide used as cathode and anode respectively. The electrolyte was circulated at a constant flow rate and the pH was kept constant at 1. Applied current densities were 10 and 90 A/m 2 . More than 99% of metal reduction was achieved, with the energy consumptions estimated to 42.30 kWh/kg of metal [START_REF] Hunsom | Electrochemical treatment of heavy metals (Cu 2+ , Cr 6+ , Ni 2+ ) from industrial effluent and modeling of copper reduction[END_REF].

J o u r n a l P r e -p r o o f Therefore, we were able to eliminate and separate quantitatively heavy metals, which were initially present in solution at a non-negligible concentration by an easy electrochemical treatment based solely on change of pH and potential, with reduced electrical energy requirements. In addition, it is important to highlight that all treatments always took place in the same conventional reactor at ambient temperature and in the air (no degassing), without addition of reagents and without production of wastes. These results are very promising for future applications.

Application of the electrochemical treatment on real effluents coming from wastewater treatment plants (WWTP)

Until now, studies were performed with synthetic solutions to search the optimal conditions needed for the elimination and separation of these heavy metals. In this part, this electrochemical treatment was applied on two effluents coming from wastewater treatment plant (e.g. at the entrance and exit) for testing its real capacities in complex media (experimental conditions and efficiency).

Before applying the electrochemical treatment on such samples, chemical steps were carried out in the conventional way. Firstly, the pH of the sample was measured (7.3 for the entrance sample and 7.9 for the exit sample respectively), and then an acidification by the addition of nitric acid was carried out to reach pH ≈ 2, in the aim to dissociate all complexes formed between heavy metals and organic micro pollutants [START_REF] Fischer | Ionic liquids for extraction of metals and metal containing compounds from communal and industrial waste water[END_REF]. The filtration of the samples was then carried out using filters (0.2 μm; IC certified with hydrophilic PTFE membrane) to remove suspended solids. After this pre-treatment step, the concentrations of heavy metals, present in these two samples, were determined by UV-visible measurements using the Spectroquant® tests. Lead, Nickel and cadmium were highlighted and the values of the concentrations found for each sample (input and output) are regrouped in Table 4, in comparison to the limits defined for drinking water and environment standards [START_REF]Chemicals of Health Significance as described by World Health Organization Guidelines (WHO) for Drinking-water Quality in third edition[END_REF].

J o u r n a l P r e -p r o o f

The electrochemical treatment of these two samples was carried out following the same methodology as cited above for the mixture. In the first step, Pb(II) was eliminated by imposing a potential equal to E = 1.2 V since the pH = 2. For the two samples, a very thin yellowish film was electrodeposited onto the SnO 2 working electrodes, and lead was not detected in the solution after the electrochemical treatment. The recovered deposit was too thin to be controlled by XRD and SEM due to the very small quantity of Pb(II) present initially in the solution (0.64 mg.L -1 ). Then, in a second step, the pH was adjusted to 4.2, and a potential equal to 0.7 V was applied during 72 h, for eliminating Ni(II) present in the two samples. At the end, a very thin film was electrodeposited onto the SnO 2 electrodes, and nickel was not detected in the two samples after the electrochemical treatment. As previously, these very thin deposits did not have sufficient amount to be controlled by SEM and XRD. At the end, only Cd(II) stayed in solution, but complementary experiments confirmed its total elimination by sorption reaction with our eco-friendly sorbent based on electrodeposited manganese oxides thin films [START_REF] Choumane | Electrodeposited birnessite thin film: An efficient eco-friendly sorbent for removing heavy metals from water[END_REF].

These results therefore confirm that this easy electrochemical treatment is effective even on real samples to remove and to separate heavy metals such as Pb(II) and Ni(II) dissolved in complex media in the form of adherent films onto a conductive substrate, and even in the presence of Cd(II). These all result are important for future applications in order to separate Cd(II) to other heavy metals. Indeed, in the literature the processes developed for their separation are often complicated to implement and / or energy consuming, [START_REF] Fang | A novel method for the sequential removal and separation of multiple heavy metals from wastewater[END_REF][START_REF] Hu | Stabilization and separation of heavy metals in incineration fly ash during the hydrothermal treatment process[END_REF][42]. On the other hand, this result allowed us to confirm the principle of this innovative electrochemical process already developed.

J o u r n a l P r e -p r o o f 4 Conclusion

A very simple and innovative electrochemical process was developed in our previous study leading to a total removal of soluble lead present in aqueous solutions as adherent oxide(s) films by changing the oxidation states. In this study, and in order to extend this treatment on a wide range of toxic heavy metals, this electrochemical process of depollution was tested with success to remove Ni(II) and Cu(II), present alone or in mixture with other heavy metals in solutions, and to recover them in the form of adherent films according to the same principle. This study confirms also that this treatment cannot be applied to recover Cd(II) due to its own chemistry (only one soluble oxidation state). Indeed, it is required that the metal present different oxidation states to be eliminated by this electrochemical process, however its presence do not affect the efficacy of the elimination and the separation of the other heavy metals, which is a very important point for potential applications.

Firstly, the adequate conditions were determined on model solutions containing only one heavy metal before application with success on a synthetic mixture and real effluents.

This process shows a high efficiency for removing these heavy metals in the form of adherent films on the substrate. It appears also efficient for a total separation of the metals present in solution, which is very interesting for many applications.

All results are extremely encouraging because this efficient simple process can be done at room temperature with low energy consumption, without the addition of reagents and / or complexing agents, and consequently without the production of wastes. Moreover, it appears possible to be applied with success on wastewater.

J o u r n a l P r e -p r o o f

[42] E-B Son, K-M Poo, H.O. Mohamed, Y-JChoi, W-CCho, K-J Chae, A novel approach to developing a reusable marine macro-algae adsorbent with chitosan and ferric oxide for simultaneous efficient heavy metal removal and easy magnetic separation. 2018, Bioresource Technology, Vol. 259, pp. 381-387.

Tables:

Table 1: Potential range values of electrochemical signals observed following cyclic voltammetry analyses for a solution containing M(II) (6.5 µmol) in 50 mL of milli-Q water with different adjusted pH by adding NaOH (no buffer). J o u r n a l P r e -p r o o f

Potential range signals (V)

  J o u r n a l P r e -p r o o f According to this diagram, the thermodynamic expected compounds in function of pH and potential are nickel in metallic form (Ni (0)) or in oxidized form such as Ni(OH) 2 , Ni 2 O 3 and NiO 2 .

  -5 A), Figure 2, J o u r n a l P r e -p r o o f suggesting a relatively good electrical conductivity of the electrodeposited thin film, and no parasite electrochemical reactions.

3. 1 . 3 3 [ 25 ]

 13325 Case of Cd(II)As already mentioned, cadmium has only two degrees of oxidation, 0 and (+ II), with only one as soluble specie (+ II). According to the Pourbaix diagram in absence of complexing agent[START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF], cadmium forms a solid compound either in metallic form (Cd(0)) either in the oxide or hydroxide form. Therefore, it appears impossible to remove Cd(II) in solution according to the same methodology based on oxidation state changes. Only the formation of cadmium oxide or hydroxide is possible, however, under these conditions, it is only a precipitation reaction based on a local pH change as already reported for the electrodeposition of various materials such as AgO[START_REF] Switzer | Electrochemical synthesis of ceramic films and powders[END_REF] Y 2 O Cu 2 O [26], PbO 2

Figure 4 .

 4 According to the diagram of Pourbaix, at these potential and pH values, nickel can be expected rather in the form of NiO 2 , but the formation of Ni 2 O 3 cannot be excluded. Moreover, the electrodeposition of other

Figure 1 :

 1 Figure 1: Percentages of Cu(II) eliminated after electrochemical treatments carried out on a model solution of Cu(II) alone, and treated under different potentials and durations. Insertion: Variation of current during chronoamperometry for E imposed = -0.45 V and E imposed = -0.85 V during 24 h. J o u r n a l P r e -p r o o f

Figure 2 :

 2 Figure 2: Variation of current during chronoamperometry performed on a model solution of Ni(II) alone with adjusted pH = 4.2 for E imposed = 0.7V.

Figure 3 :

 3 Figure 3: X-ray diffractograms of the adherent films obtained after the total elimination of Cu(II) at pH = 7 for imposed potentials of -0.45 V (red curve) and -0.85 V (blue curve) for durations of treatment fixed to 48 hours and 96 hours respectively, with the SEM observations associated for each one. (x) SnO 2 (*) Cu 2 O.

Figure 4 :

 4 Figure 4: X-ray diffractogram of the adherent film obtained after the total elimination of Ni(II) alone in solution at pH 4.2 for imposed potential of 0.7 V during 72 hours ((+) -NiO(OH), (x) SnO 2 ) with the SEM observation associated.

Figure 5 :

 5 Figure 5: Schematic procedure of the recovery of each heavy metal separately in the case of a mixture containing Pb(II), Ni(II), Cu(II) and Cd(II) present in aqueous solution at equivalent concentrations.

Table 2 :

 2 Parameters used for the calculation of the yield of experimental energy consumption (R)

		E	I (A)	t(s)	Q exp (C)	Q theo	R (%)
		(V)				(C)
	2Cu 2+ +H 2 O+2e -	-	-1.0	172800	1.71	1.25	136
	Cu 2 O+2H +	0.45	10 -5
	2Cu 2+ +H 2 O+2e -	-	-1.2	345600	41.40	1.25	3312
	Cu 2 O+2H +	0.85	10 -4
	Ni 2+ +2H 2 O	0.70 2.4 10 -	259200	0.62	0.62	100
	NiO(OH)+3H + +1e -		6

Table 3 :

 3 Parameters used for the energy consumption calculations.

		I max (A)	E (V)	t (h)
	Lead	9.7 10 -5	1.2	24
	Nickel	5.1 10 -6	0.7	72
	Copper	-1.5 10 -5	-0.45	48

Table 4 :

 4 Concentrations of heavy metals measured (mg.L -1 ) in samples at the input and output of the WWTP, with the Environmental Quality Standards (EQS) for water of internal surfaces (in mg.L -1 ) and the quality standards of drinking water according to the World Health Organization (WHO) (in mg.L -1 ).

	Input	Output	EQS	WHO
	Lead 0.64	0.64	0.0072	0.01
	Cadmium 0.017	-	0.005	0.003
	Nickel 0.65	0.65	0.02	0.07
	Copper -	-	-	2

J o u r n a l P r e -p r o o f

Acknowledgements

Thanks go to O. Rouleau for XRD characterizations and R. Pires for SEM observations and EDS analyses (ICMPE -CNRS -UMR 7182), A. Masy for providing real samples from wastewater treatment plant (Evry-France).


Member, IEEE Arnaud Videt

Medhi Messaoudi

Member, IEEE Nadir Idir

Hocine Boulharts

Heu Vang

Mehdi Messaoudi

PWM Strategy for the Cancellation of Common-Mode Voltage Generated by Three-Phase Back-to-Back Inverters

Keywords: Pulse width modulated inverters, Variable speed drives, Rectifiers, Electromagnetic compatibility, Electromagnetic conductive interference

come

PWM Strategy for the Cancellation of Common-Mode

Voltage Generated by Three-Phase Back-to-Back Inverters

I. INTRODUCTION

T HREE-PHASE voltage-source inverters are a major source of electromagnetic interferences (EMI) due to the fast switching of their power semiconductors [START_REF] Ran | Conducted electromagnetic emissions in induction motor drive systems. I. Time domain analysis and identification of dominant modes[END_REF]. Especially, a common-mode (CM) voltage is generated between the input and output potentials of the converter, inducing CM currents because of parasitic capacitive coupling to the ground in power cables and electric motors in variable-speed drives (VSDs) applications [START_REF] Luszcz | Modeling of common mode currents induced by motor cable in converter fed AC motor drives[END_REF], [START_REF] Cacciato | Reduction of common-mode currents in PWM inverter motor drives[END_REF]. As a consequence, high levels of conducted perturbations are emitted toward the power grid, which exceed the limits imposed by electromagnetic compatibility (EMC) standards. As a consequence, costly and bulky EMI filters are usually necessary, at least on the grid side of VSDs [START_REF] Akagi | Attenuation of conducted EMI emissions from an inverter-driven motor[END_REF]. Another harmful effect of CM voltage is the generation of shaft voltage across the motor bearings that may cause destructive electric discharge machining [START_REF] Muetze | Practical rules for assessment of inverterinduced bearing currents in inverter-fed AC motors up to 500 kW[END_REF], [START_REF] Kalaiselvi | Bearing currents and shaft voltage reduction in dual-inverter-fed open-end winding induction motor with reduced CMV PWM methods[END_REF]. In order to prevent EMI on the load side, output EMI filters may be necessary, adding to the total cost and weight of the converter.

Acting on the converter PWM strategy is an interesting solution to these issues. Indeed, with low overcost it is possible to reduce the source of perturbation by performing simultaneous commutations so that their effects on CM voltage A. Videt and N. Idir are with the Laboratory of Electrical Engineering and Power Electronics (L2EP), University of Lille, Cité Scientifique, 59655 Villeneuve d'Ascq, France (e-mail: arnaud.videt@univ-lille1.fr; nadir.idir@univ-lille1.fr) M. Messaoudi and H. Boulharts are with Schneider Toshiba Inverter, rue André Blanchet, 27120 Pacy-sur-Eure, France (e-mail: mehdi.messaoudi@schneider-electric.com, hocine.boulharts@schneiderelectric.com) H. Vang is with Toshiba Schneider Inverter, 1-19-30 Aoi, Higashi-ku, Nagoya, 461-0004, Japan (e-mail: heu.vang@schneider-electric.com)

M

Vi cm Vr cm Vcm Fig. 1. Three-phase back-to-back inverters VSD with CM path to ground cancel each other. Such CM-voltage-reducing PWM strategies have been proposed for three-phase matrix converters [START_REF] Espina | Reduction of output common mode voltage using a novel SVM implementation in matrix converters for improved motor lifetime[END_REF], [START_REF] Nguyen | An enhanced SVM method to drive matrix converters for zero common-mode voltage[END_REF], dual converters for open-end windings motors [START_REF] Baranwal | Carrier-based implementation of SVPWM for dual two-level VSI and dual matrix converter with zero common-mode voltage[END_REF], and single two-level [START_REF] Cacciato | Reduction of common-mode currents in PWM inverter motor drives[END_REF] and multilevel inverters [START_REF] Zhang | Multilevel inverter modulation schemes to eliminate common-mode voltages[END_REF]- [START_REF] Nguyen | A reduced switching loss PWM strategy to eliminate common-mode voltage in multilevel inverters[END_REF], usually with drawbacks regarding the DC bus utilization or output power quality (current ripple, motor overvoltages in long cable applications) [START_REF] Videt | Motor overvoltage limitation by means of a new EMIreducing pwm strategy for three-level inverters[END_REF], [START_REF] Wu | Optimized common-mode voltage reduction PWM for three-phase voltage-source inverters[END_REF]. Indeed, CM cancellation is performed by simultaneous switching in opposite direction of two legs, resulting in increased phase-to-phase voltage steps. In this regard, multilevel converters are interesting as they naturally improve the differential-mode voltage quality. On the other hand, little research has focused on the back-to-back voltagesource inverter topology [START_REF] De Broe | Neutral-to-ground voltage minimization in a PWM-rectifier/inverter configuration[END_REF]- [START_REF] Wang | A common-mode voltage reduction method for a back-to-back four-level hybrid-clamped converter[END_REF], where the typical diodebridge rectifier in VSDs is replaced with a PWM rectifier (active front-end, Fig. 1). In this case, simultaneous switching in the same direction of one inverter leg with one rectifier leg allows CM voltage cancellation of the whole association of two converters. This method has been applied for partial CM voltage reduction [START_REF] Lee | A common mode voltage reduction in boost rectifier/inverter system by shifting active voltage vector in a control period[END_REF], where two-level back-to-back inverters are synchronized at the same switching frequency, and zerosequence injection is performed so that one inverter voltage pulse exactly coincides with one rectifier voltage pulse.

This paper presents a new PWM strategy that theoretically provides full CM voltage cancellation for the whole converters association [START_REF] Videt | Control method and system for reducing the common-mode current in a power converter[END_REF], [START_REF] Videt | PWM strategy for common-mode voltage reduction in three-phase variablespeed drives with active front end[END_REF]. Its major degrees of freedom are studied to demonstrate the limitations and opportunities using this method. Finally, experimental results are provided to validate the effectiveness of this strategy.

II. ACHIEVING CM VOLTAGE CANCELLATION

A. Basic Principle

In the following, the study is focused on a VSD system where the grid-connected inverter is referred to as the active front-end (AFE) rectifier. The CM voltage generated by a converter can be defined as the difference between the average of its output potentials and the average of its input potentials. Thus, according to Fig. 1, the CM voltage generated by the inverter can be defined as:

V icm = 1 3 (V UO + V VO + V WO ) , (1)
and that generated by the rectifier is:

V rcm = 1 3 (V RO + V SO + V TO ) , (2)
where O is the average DC bus potential. However, in some cases it is more convenient to use the lower DC potential (M) as a reference and to define CM voltages according to this point:

V i M cm = 1 3 (V UM + V VM + V WM ) = V icm + E 2 V r M cm = 1 3 (V RM + V SM + V TM ) = V rcm + E 2 , ( 3
)
where E is the DC bus voltage. The total CM voltage generated by both converters may be defined as:

V cm = V icm -V rcm = V i M cm -V r M cm (4)
In case the inverter and rectifier are synchronized at the same switching frequency, and controlled by conventional PWM strategy, Fig. 2 shows an example of switching patterns and both the individual and total CM voltages as defined in equations ( 1) to [START_REF] Akagi | Attenuation of conducted EMI emissions from an inverter-driven motor[END_REF]. Note that the inverter and rectifier pulses are arbitrarily ordered by decreasing width, though they could as well be positioned in any other order (different operating points) without changing the overall observations on the CM voltage: since each commutation of a single leg induces one CM voltage step, the resulting V cm waveform naturally has 12 variations per switching period (6 legs with 2 commutations per leg per period). This voltage is responsible for bearing failures and its variations generate capacitive CM current circulating to the ground. In order to reduce CM emissions, the CM voltage can be reduced by making two commutations happen at the same time so that their simultaneous contribution to CM voltage cancel each other. This is easily achieved by making one inverter voltage rise simultaneously with one rectifier voltage rise (the same would stand for voltage falls), as shown in Fig. 3. This can be realized by acting on the PWM intrinsic degrees of freedom.

B. Use of the PWM Degrees of Freedom

In 2-level voltage-source converters, pulse-width modulation aims at building an arbitrary reference phase-to-DC-bus voltage (V * k M for phase k) by applying the DC voltage (E) during a fraction α k (duty cycle) of the switching period (T sw ), so that the average output voltage (V k M ) equals its reference:

V * k M = V k M Tsw = α k E with 0 α k 1 (5)
Since only the difference between two phase voltages of a given converter have to be controlled to feed the load, shifting all the phase references by the same amount of voltage (commonly called the zero-sequence component) is possible as long as all duty cycles remains in the [0, 1] interval. Indeed, the zero-sequence voltage has no effect on the average phaseto-phase voltage and can thereby be freely used as a degree of freedom. It can be regarded as a reference voltage between the AC neutral point and the average DC potential (O), and is thereby expressed as:

V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 ti 1 ti 1 ti 2 ti 2 ti 3 ti
V rk V ik -V rk E 0 E 0 0 V ik t t t non-simultaneous commutations V rk V ik -V rk E 0 E 0 0 V ik t t t simultaneous commutations E E

CM voltage cancellation

V * 0 = 1 3 k=1,2,3 V * k O (6)
Due to equations (1), ( 2) and ( 5), it is also the average value of the CM voltage generated by the considered converter.

In conventional sinus PWM, sinusoidal voltage references V * k O are centered around zero, which means that the zerosequence voltage is null. Modifying its value results in changing the reference phase-to-DC-bus voltages:

∀k ∈ {1, 2, 3}, V * k O = V * k N + V * 0 , (7)
where V * k N are reference voltages between the phases and the AC neutral point. As a consequence, zero-sequence injection widens or narrows all the converter pulse widths by the same amount of time. In [START_REF] Lee | A common mode voltage reduction in boost rectifier/inverter system by shifting active voltage vector in a control period[END_REF], this feature has been applied to the AFE/inverter association so as to equalize one rectifier pulse with one inverter pulse, thereby cancelling 4 CM voltage variations out of 12. Once the voltage references and the zero-sequence component are set, all six pulse widths of the VSDs are determined. Still, another degree of freedom is available as the pulses do not necessarily have to be stuck at the center of the switching period. Rather, they can be time-shifted inside the switching period while still satisfying equation [START_REF] Muetze | Practical rules for assessment of inverterinduced bearing currents in inverter-fed AC motors up to 500 kW[END_REF]. This pulse position can be used to move rectifier and inverter pulses so that their commutations coincide as shown in Fig. 4. Therefore, this possibility is yet another way to synchronize inverter and rectifier commutations.

V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 -E 3 t
The two aforementioned PWM degrees of freedom (zerosequence component and pulse position) will be studied hereafter to derive a PWM method that completely eliminates the resulting CM voltage of the whole system.

III. PROPOSED PWM STRATEGY

A. The Cyclic Pulse Sequencing

According to equation ( 4), full CM voltage cancellation is obtained when V i M cm and V r M cm have exactly the same waveform at each switching period, which means that:

• the inverter and the rectifier operate at the same switching frequency and are synchronized

• each upward (rising) commutation of an inverter leg coincide with an upward commutation of a rectifier leg

• likewise, downward (falling) commutations coincide between one inverter and one rectifier leg

For that means, the PWM degrees of freedom must be used, especially regarding the position of the pulses inside the switching period. For all constraints to be met whatever the converters operating points, a cyclic association between inverter and rectifier voltage pulses is necessary, as explained hereafter.

V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 ti 1 ti 1 ti 2 ti 2 ti 3 ti
V i1 V r1 V i2 V r2 V i3 V r3
inverter pulses rectifier pulses Fig. 6. Cyclic sequencing of pulses to achieve CM voltage elimination

Figure 5 presents such an association, where the rising and falling commutations of any pulse are always synchronized with commutations in the same direction in the other converter (for convenience, notation V ik stands for the k th inverter V k M voltage, and V rk likewise for the rectifier). As a consequence, V i M cm equals V r M cm and the resulting V cm voltage is kept null during the whole switching period. In order to avoid special cases that may not happen in the general case (such as equal pulse widths of inverter and rectifier legs), it can be noted that the commutations of one converter leg are always synchronized with commutations of two different legs in the other converter. This leads to a cyclic sequence in the way commutations are synchronized, as summarized in Fig. 6: the first inverter upward commutation (on V i1 ) is synchronized with the first rectifier one (on V r1 ), then the downward commutation of this leg is synchronized with that of a second inverter leg (V i2 ), and so on, until the last rectifier downward commutation (on

V r3 ) is synchronized with that of V i1 .
It is noteworthy that the feasibility of such pulse association is not dependant on the converters operating points nor related to any specific sector of the vector diagram. For instance, Fig. 7 presents the same association pattern as Fig. 5 in case the inverter operates with low output voltage (the three inverter pulses have about the same width, which could correspond to low motor speed) while the rectifier operates at high modulation index (both large and small pulses involved, indicating high phase-to-phase voltages). Furthermore, the sectors are changed since the largest pulses are now on the third leg for the inverter and the second for the rectifier. It can be verified that the V icm and V rcm voltages still have the same waveforms, resulting in zero V cm voltage.

V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 -E 3 t
Actually, the cyclic sequence is always effective regardless the individual pulse widths as long as a specific constraint is respected on the zero-sequence voltage. This constraint is detailed in the next section. It should also be noted that the inverter U, V, W and rectifier R, S, T phases can be substituted to the 1, 2, 3 indexes in any order: this degree of freedom will be discussed in section III-C.

B. Contraints Related to the Zero-Sequence Component

According to Fig. 5, with (t ik ; t i k ) respectively the rise and fall instants of the k th inverter leg, and (t rk ; t r k ) those of the k th rectifer leg, the following conditions should be satisfied:

t i1 = t r1 t i2 = t r2 t i3 = t r3 t r 1 = t i 2 t r 2 = t i 3 t r 3 = t i 1 . (8)
Thus, the widths T ik and T rk of the inverter and rectifier pulses verify:

k=1,2,3

T ik = (t i 1 -t i1 ) + (t i 2 -t i2 ) + (t i 3 -t i3 ) = t r 3 + (-t r1 + t r 1 ) Tr 1 + (-t r2 + t r 2 ) Tr 2 -t r3 = k=1,2,3 T rk (9)
Therefore, complete cancellation of the total CM voltage can always be achieved as long as the sum of the inverter pulse widths equals the sum of the rectifier ones. Indeed, starting from the V i1 rising edge in Fig. 6, each new synchronization involves a new pulse and thereby can always be realized until the final (6 th ) one, where the very last rectifier falling edge (on V r3 ) must exactly coincide with the very first inverter one (on V i1 ). Traveling this cycle by counting positively the rectifier pulse widths and negatively the inverter ones, it appears that this remaining synchronization is guaranteed when the sums of pulse widths are equal. This condition can be transposed as an equality between the sum of inverter and rectifier duty cycles, and thereby between the sum of the reference phaseto-DC-bus voltages according to equation ( 5):

k=1,2,3 V i * k = k=1,2,3 V r * k , (10)
which means that zero-sequence components of the inverter and rectifier should be equal in the considered AFE/inverter association. Fig. 8 presents an example of such zero-sequence addition that widens all rectifier and inverter pulses by the same amount, preserving the sum-of-widths equality and still achieving CM voltage cancellation. In contrast, Fig. 9 shows the result of the same cyclic association when the sum-ofwidths is different (unequal zero-sequence on inverter and rectifier): two commutations remain unmatching and the end of the cycle, leading to a non-cancelled CM voltage pulse. As a drawback, this zero-sequence-equality constraint prevents free use of this degree of freedom on each converter separately. This parameter usually allows to increase the conversion ratio between AC voltages and the DC bus voltage [START_REF] Hava | Simple analytical and graphical methods for carrier-based PWM-VSI drives[END_REF], so that the amplitude of the reference voltages between one phase and the AC neutral point ( V * k N ) can be increased above E 2 (linear voltage extension up to E √ 3 ), while keeping phase-to-DC-bus voltages V * k O below the E 2 physical limit. Figure 10 shows an example of such zero-sequence injection on the inverter side when

V * k N is equal to 1.1 × E 2 .
Actually, the equality constraint on zero-sequence components implies that any voltage extension in a given converter must be compensated by a similar decrease of the conversion ratio in the other converter (at least in the general case where motor and grid voltages are not synchronous). Figure 10 shows this limitation on the rectifier part because the zero-sequence voltage has been chosen for the inverter side and is not adapted to the rectifier reference voltages.

Thus, the limitations for input and output voltages are depicted in Fig. 11, where the example of Fig. 10 is identified as point "A". If no DC voltage boost is required, then the Fig. 9. PWM pattern from Fig. 5 with unequal zero sequence injection DC bus voltage is typically controlled to be as small as possible; therefore, the rectifier conversion ratio and thereby the reference phase-to-AC-neutral voltages should be as high as possible. However, in the worst situation when inverter and rectifier AC voltages have the same amplitude, then linear voltage extension is not possible and V * 0 should remain null. Compared with conventional PWM strategies where voltage extension could be performed on both converters, this results in a larger DC bus voltage by a factor of 2 √ 3 , which is about 15% higher and should be taken into account in the converters design. However, any input-to-output transfer ratio can still be obtained, and the aforementioned oversizing disappears when the output AC voltages are either higher than 1 √ 3-1 ≈ 1.366 times the input ones (starting from point "B" and below) or lower than √ 3 -1 ≈ 0.732 times the input voltages (left of point "C").

V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 ti 1 ti 1 ti 2 ti 2 ti 3 ti
V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 ti 1 ti 1 ti 2 ti 2 ti 3 ti

C. Multiplicity of the Possible Pulses Associations

The synchronization solution presented in Fig. 5 is not the only possibility to cancel all CM voltage variations. For instance, Fig. 12 presents other ways to synchronize all commutations in the same operating point (inverter and rectifier pulse widths). Indeed, several combinations exist depending on how the actual R, S, T and U, V, W legs are tied to the 1, 2, 3 indexes.

Once zero-sequence components are set equally for the two converters, the number of possible pulses associations can be determined based on Fig. 6, taking arbitrarily the inverter phase U as a starting point:

• its rising edge should be synchronized with the rising edge of either R, S, or T rectifier leg (3 choices)

V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 -E 3 t t t t t t t t t ti 1 ti 1 ti 2 ti 2 ti 3 ti 3 tr 1 tr 1 tr 2 tr 2 tr 3 tr 3 (a) (b) V i2 V i3 V r1 V r2 V r3 V i M cm V r M cm V cm E 0 E 0 E 0 E 0 E 0 E 0 E 0 E 0 0 E 3 V i1 -E 3 t

Fig. 12. Alternative PWM patterns cancelling all CM voltage variations

• having selected one of them, say R for instance, its falling edge should be synchronized with one falling edge among the two remaining inverter legs (V or W) (2 choices)

• assuming for example that leg V is selected, then rising edge should be synchronized with a rising edge among the two remaining rectifier legs (for instance, S or T in this case) (2 choices)

• no more choices are necessary since the falling edge of this rectifier leg (say, S) has to coincide with that of the last inverter leg (W), of which the rising edge must coincide with that of the last remaining rectifier leg (T), of which the falling edge will naturally coincide with the falling edge of the initial inverter leg (U).

Thus, there are in total 12 different possible choices (3 × 2 × 2) to perform a cyclic sequence that synchronizes all commutations of both converters. One possible formalism to identify these choices consists in naming the 3 selected legs in the 3 first steps above that involve a choice. In other words, the naming convention determines the physical legs associated with V r1 , V i2 , and V r2 respectively. For instance in the given example, the selected choice could be named "RVS". Likewise, the 12 possible solutions can be determined as: RVS, RVT, RWS, RWT, SVR, SVT, SWR, SWT, TVR, TVS, TWR, TWS. In order to choose from these possibilities, one simple implementation consists in avoiding situations like Fig. 12b where pulses are positioned far from each other, much different from the nesting effect obtained with conventional PWM strategies (Fig. 2). This could be achieved by selecting a synchronization solution that minimizes the standard deviation of the pulses positions. Indeed, grouping pulses as much as possible like in Fig. 12a is a good option to avoid degrading too much the current ripple in the AC line inductors or in motor windings. It is also possible to focus on the pulses of a given converter, for instance favouring the rectifier to prevent oversizing of the grid-side inductors. Thus, a possible implementation of the proposed PWM strategy is depicted in Fig. 13: once pulse widths are set in accordance with the instantaneous voltage references, the relative pulse positions (e.g. their center instant) can be determined for the 12 solutions so as to select the most grouping one. Note that the subsequent "modulator" part is detailed in section IV-B. The following section shows the effect of the proposed method on the quality of output voltages.

D. Impact on output voltages

Since the proposed PWM strategy modifies the pulses positions compared with conventional methods, a degradation of AC voltage quality can be expected. Figure 14 presents simulation waveforms when the rectifier operates at 50 Hz fundamental frequency and boosts the 230 V AC mains to a 540 V DC bus (modulation index is 0.7) while the inverter operates at 20 Hz and produces a 152 V phase-to-phase voltage (modulation index is 0.46). The VSD supplies a 11 kW induction motor (380 V, 50 Hz nominal) at full load with constant voltage/frequency ratio. The switching frequency is 4 kHz. Phase-to-phase voltages are plotted as well as line currents and both the individual and total CM voltages. Input power factor correction can be verified as the line current (Fig. 14c) is in phase with the mains voltage of the same line (Fig. 14a). The first part (until 50 ms) is obtained with a conventional PWM strategy. The phase-to-phase voltages exhibit typical positive and negative half waves where the reference voltage is synthesized by modulating between the two nearest voltage levels {0, +E} or {0, -E}. At time 50 ms, the modulation method is suddenly changed to the proposed PWM with pulses grouping (Fig. 13). As a consequence, the total CM voltage becomes zero starting from this time in Fig. 14g (assuming ideal commutations and thereby perfect cancellation). However, the phase-to-phase voltages are sometimes modulated using all three voltage levels {-E, 0, +E}, which is not as good as with the conventional strategy. The actual shape of the voltage pulses including 2-and 3-level modulation can be seen more clearly in the enlarged view over 16 switching periods in Fig. 15. It is noteworthy that places where 3-level modulation happen are only a consequence of non-nested phase-to-DC-bus voltages (Fig. 15a andd), and that the resulting average value still satisfies the voltage reference requirements. CM voltages are also more distinguishable, showing that the individual V rcm and V icm waveforms vary identically, resulting in zero V cm voltage.

Harmonic performance can be quantified by the total harmonic distortion (THD) defined in eq. [START_REF] Benabdelghani | Use of extra degrees of freedom in multilevel drives[END_REF], where U k is the magnitude of the k th harmonic, which takes into account all harmonics with equal importance:

THD = k 2 U k 2 U 1 ; DF = k 2 U k k 2 U 1 . (11)
The weighted distortion factor (DF) can also be determined to give a better representation of low-order harmonics that will eventually be reflected in the line currents. These quantities are computed over one fundamental period of either converter. Since the common period for both converters is larger (100 ms in the simulation example for 20 ms rectifier and 50 ms inverter periods), their value may also depend on the relative phase shift between the rectifier and inverter reference voltages. It is also a function of the modulation depth. THD and DF values of the phase-to-phase rectifier and inverter voltages with various phase shifts have been computed up to 100 kHz and reported in Table I for three different inverter voltages (modulation index in the first line of the table) and for three different PWM strategies each time:

TABLE I HARMONIC PERFORMANCE OF RECTIFIER AND INVERTER PHASE-TO-PHASE VOLTAGES WITH DIFFERENT MODULATION STRATEGIES

"A" is the conventional one, "B" is the proposed method with pulses grouping, and "C" without grouping. First, it appears that the inverter/rectifier phase shift does influence much the resulting percentages. Second, as expected, it appears that the proposed PWM increases the harmonic content compared with a conventional strategy. However, the DF is kept small which indicates that the high THD values are due to high frequency components rather that low-order ones. Confirmation of this behavior can be obtained by frequency-domain analysis of the phase-to-phase voltage waveforms from Fig. 14, which is shown in Fig. 16: the new strategy mainly involves larger harmonic families around multiple times the switching frequency. Finally, comparing strategies "B" and "C" in Table I also reveals that the pulses grouping criteria is effective in limiting the harmonic degradation due to pulses positioning.

Note that apart from output voltages quality, another interesting criteria that may be impacted by the pulses positioning is current that flows in the DC-bus capacitor, which is chopped at the switching frequency. An RMS value of 10.5 A has been computed with the conventional strategy in the simulation conditions of Fig. 14. Due to non-optimal pulses positions, the proposed PWM slightly increases this value at 12.7 A. Again, the pulse grouping is effective regarding this criteria as the RMS current would rise above 20 A otherwise. Again, these figures validate the interest of the pulses-grouping implementation depicted in Fig. 13.

IV. EXPERIMENTAL RESULTS

A. Measurement Setup

The proposed PWM strategy has been implemented in an experimental setup (Fig. 17 Dead-time effects are known to reduce the effectiveness of simultaneous switching for CM voltage reduction [START_REF] Videt | A new carrier-based PWM providing common-mode-current reduction and DCbus balancing for three-level inverters[END_REF], [START_REF] Zhang | Impact and compensation of dead time on common mode voltage elimination modulation for neutral-point-clamped three-phase inverters[END_REF]. Therefore, the proposed PWM strategy has been tested both with and without a conventional dead-time compensation method based on the measured direction of input and output phase currents [START_REF] Mannen | Dead-time compensation method based on current ripple estimation[END_REF]. Basically, turn-on (diode-to-transistor) commutations are identified so that their logical signals are time-shifted by the dead-time value for the actual voltage transition to occur at the expected instant. Table II summarizes commutations in which dead times are involved depending on the current sign and the phase-to-DC-bus voltage variation. Finally, a conventional sinus PWM (SPWM) strategy has also been tested for comparison purposes of the drive EMC performance.

B. Carrier-based implementation

Once the control algorithm has determined the pulse association cycle, modulation signals can be sent to the modulator. The proposed method requires microcontroller PWM peripher-als that allow to freely position pulses within the switching period. In this experimental setup, the TI TMS320F28335 DSC has been used. Instead of generating a pulse by comparing only one modulation signal with the carrier wave (Fig. 18a), it can be configured to compare two modulation signals with a saw-tooth carrier, and to define the actions at the crossing instants so that the first modulation signal (m 1 ) determines the start of the pulse (upward commutation) while the second one (m 2 ) determines its end (downward commutation) as shown in Fig. 18b. Thus, pulse width can be controlled by their difference ∆m and its position can be controlled by m 1 , which is a convenient capability for the implementation of the proposed method.

C. Time and Frequency Domain Results

The measured individual motor-side and grid-side CM voltages (respectively, V icm and V rcm in Fig. 1) are presented in Fig. 19 along with the resulting total CM voltage (V cm ) during 5 switching periods. While the conventional strategy generates 12 CM voltage steps per switching period (Fig. 19c), the proposed PWM strategy cancels the total CM voltage (Fig. 19f) by achieving identical rectifier and inverter individual CM voltage waveforms (Fig. 19d ande). Meanwhile, voltage references are still satisfied and control functionalities such as unity input power factor are kept; indeed, Fig. 20 shows that the overall input current is not affected by the proposed method. This current actually has some harmonics (11.6 % and 12.0 % THD, respectively, with 2.22 % and 2.30 % DF), which is possibly due to the simplicity of the implemented AFE control loop that may not be able to compensate for the small unbalance and distortion of the practical three-phase network.

The preceding results where actually obtained using deadtime compensation as mentioned in section IV-A. In order to evaluate its effect, Fig. 21 presents the total measured CM voltage between motor-side and grid-side potentials during only one switching period. In the medium curve, it can be seen that the proposed method without dead-times compensation cancels the CM voltage except for thin pulses of the width of the dead time. These pulses are then suppressed using the dead-time compensation, resulting in a flat CM voltage in which some residual spikes remain at the commutations instants. This can be explained by the simultaneous switching waveforms that may not have the exact same dv/dt. Indeed, the voltage waveform may be influenced by the commutation kind (Table II) and the value of the phase current and temperature [START_REF] Bryant | Investigation into IGBT dv/dt during turn-off and its temperature dependence[END_REF], resulting in non-perfect CM voltage cancellation during the commutation process [START_REF] Messaoudi | Modeling the residual common-mode voltage generated by 3-phase inverters with simultaneous-switching PWM strategies[END_REF]. Still, the proposed PWM significantly reduces the CM voltage, so that in VSD applications, the converter operation should become safe for motor bearings. Furthermore, Fig. 22 presents the frequency-domain spectra of the CM voltage, obtained by performing FFT on the timedomain waveforms over the fundamental system period. Postprocessed envelopes are also plotted to facilitate comparisons. This experimental result confirms the relevance of dead-time compensation and shows that the proposed strategy reduces CM voltage by more than 15 dB at switching frequency and

V. CONCLUSION

A new PWM strategy is presented for the reduction of common-mode voltage generated by 3-phase back-to-back two-level voltage-source inverters used in variable-speed motor drive applications. This strategy theoretically cancels all CM voltage transitions of the whole converters association whatever its operating point, thereby allowing a better EMC behavior on both motor side (no bearing failure) and grid side (smaller EMI filter). The degrees of freedom of this strategy on zero-sequence component and cyclic pulse sequencing are studied, and an experimental implementation is performed to validate its effectiveness. It is shown that dead-time effect should be compensated to optimize EMC performance, and that more than 15 dB reduction is obtained from the switching frequency up to a few hundred kilohertz. Future work should focus on the PWM strategy impact on the design of the gridside EMI filter, which requires careful identification of CM currents propagation paths. Differential-mode power quality should also be analyzed to assess the possible trade-offs with common-mode performance when using the proposed PWM strategy.

Fig. 3 .

 3 Fig. 3. Effect of inverter/rectifier switching synchronization on CM voltage

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Zero-sequence injection for inverter voltage extension to the rectifier as well

  ) including two 15 kW-rated backto-back inverters switching at 4 kHz and a development control board based on DSPs. The dead time is set to 2 µs. A shielded, 4-wire, 25-meter cable is used to connect the VSD to a 11 kW induction machine of 380 V, 50 Hz nominal voltage. The 230 V mains are rectified to a 530 V DC bus from which the inverter supplies the motor at 150 V, 20 Hz in these tests.

Fig. 14 .

 14 Fig. 14. VSD time-domain waveforms comparison between conventional (before 50 ms) and proposed (after 50 ms) PWM strategy. (a) grid phase-R-to-neutral voltage; (b) U ST rectifier phase-to-phase voltage; (c) rectifier R-line current (A); (d) U VW inverter phase-to-phase voltage; (e) inverter U-line current (A); (f) Vr cm rectifier CM voltage; (g) V icm inverter CM voltage; and (h) V cm total CM voltage

Fig. 15 .

 15 Fig. 15. Enlarged view of time-domain voltage waveforms from Fig. 14 during application of the proposed PWM method. (a) V RM , V SM , and V TM rectifier phase-to-DC-bus voltages; (b) U ST rectifier phase-to-phase voltage; (c) Vr cm rectifier CM voltage; (d) V UM , V VM , and V WM inverter phase-to-DC-bus voltages; (e) U VW inverter phase-to-phase voltage; (f) V icm inverter CM voltage; and (g) V cm total CM voltage

Fig. 17

 17 Fig. 17. The experimental test bench

. The experimental test bench m m 1 m 2 ∆mFig. 18 .

 218 Fig. 17. The experimental test bench

Fig. 19 .Fig. 20 .

 1920 Fig. 19. Measured CM voltage waveforms with (a-c) the conventional PWM strategy: (a) V icm inverter (V); (b) Vr cm rectifier (V); (c) V cm total (V); and(d-f) with the proposed PWM method: (d) V icm inverter (V); (e) Vr cm rectifier (V); and (f) V cm total (V)

Fig. 21 .

 21 Fig. 21. Measured CM voltage waveform during one switching period

This is author's version of this paper. Final published version is available at: https://doi.org/10.1109/TPEL.2016.2573831 © 2016 IEEE. Personal use is permitted. For any other purposes permission must be obtained from IEEE.

© 2016 IEEE. Personal use is permitted. For any other purposes permission must be obtained from IEEE.

This is author's version of this Final published version is available at: https://doi.org/10.1109/TPEL.2016.2573831 © 2016 IEEE. Personal use is permitted. For any other purposes permission must be obtained from IEEE.