AC/DC Converters with Open-End Grid for ACMachine Conversion Systems

Joao P. R. A. Mello∗, Cursino B. Jacobina∗, Gregory A. A. Carlos∗† and Nady Rocha‡∗ Department of Electrical Engineering

Federal University of Campina Grande (UFCG)Campina Grande - 58429-900 - Paraıba - Brazil† Department of Control and Industrial Process

Federal Institute of Alagoas (IFAL)Palmeira dos Indios - 57601-220 - Alagoas - Brazil

‡ Department of Electrical EngineeringFederal University of Paraıba (UFPB)

Joao Pessoa - 58051-900 - Paraıba - Brazi

Abstract—This paper presents five configurations of AC/DCconverters for AC machine conversion systems. They interconnecta three-phase open-end winding grid supplier with DC/ACconverters and an AC machine. These configurations are dividedinto two groups. Group A is composed of configurations withtwo DC-links, and Group B has configurations with only oneDC-link. The discussion is focused on the AC/DC converters ofthe grid-side, since the arrangements for the machine-side arestandard in each case. Group A contains two configurations, andthe machine-side is composed of a six-phase AC machine withtwo conventional three-phase DC/AC converters. Group B hasthree configurations, and the machine-side can be composed ofa six-phase AC machine with one six-phase DC/AC converteror of a three-phase AC machine with one three-phase DC/ACconverter. The proposed configurations are employed to reducethe harmonic currents of the grid-side or the switching frequencyof the converters. They also guarantee feasibility when high-power applications are considered. Therefore, the analyses of thesystems are presented, including the PWM technique and thecontrol strategy. Simulation and experimental results are alsopresented and compared.

I. INTRODUCTION

Nowadays, multiphase induction machines have been usedfor high-power applications because of their inherent advan-tages, such as greater robustness, tolerance to faults, lowerper-phase power rating, higher degree of freedom, and highersystem redundancy [1]–[3]. On the other hand, AC/DC/ACconverters are employed in a large number of high power andhigh/medium voltage applications, as seen in [2]–[5]. In driveapplications for six-phase machines, the conventional back-to-back AC/DC/AC converter is composed of one three-phaseAC/DC converter and one six-phase DC/AC converter. Sincereliability is a crucial aspect for assessing the viability ofconversion systems [4], the use of multilevel converters appearas an interesting option to this kind of systems, as seen in [6]and [7].

Concerning multi-level configurations, they are particularlyattractive over two-level because they allow harmonic reduc-

(a)

(b)

Fig. 1: Proposed configurations of Group A with two DC-links. (a)Configuration A1 with 12 controlled power switches at the grid-side.(b) Configuration A2 with 6 controlled power switches at the grid-side.

tion, which improves both voltage and current THD at lowerfrequencies. Other advantages are stated in [1], [8]–[10]. Some

978-1-4799-5776-7/14/$31.00 ©2014 IEEE 1278

Fig. 2: Machine-side configuration for Group A.

disadvantages are related to high number of components [8],[9], which increases the total cost of the project and decreasesreliability.

The particular choice for the multi-level open-end configu-rations presented in this paper is grounded on some benefitsthey provide, such as the increased number of voltage levelsgenerated by the grid-side converters, which reduces the THDof its currents; higher tolerance to faults and lower powerrating in the individual converters. Furthermore, the DC-linkvoltages and harmonic distortion can be reduced, consideringa constant switching frequency [11], [12].

Thus, this paper presents five configurations of AC/DCconverters linking an open-end winding grid supplier withDC/AC converters and an AC machine. These configurationsare divided into two groups, labeled Group A and Group B.Group A is shown in Fig. 1 and it has configurations thatare part of conversion systems for six-phase AC machines.It is composed of configurations with two DC-links. GroupB is shown in Fig. 3 and it has configurations that can bepart of conversion systems for both six-phase and three-phaseAC machines. It contains configurations with only one DC-link. The configurations from both groups go from the mostexpensive, but versatile, to the cheaper, but more restrictive.The discussions in this paper will be focused on the systems’grid-side, as the machine-side is standard for each case.

Configuration A1 is bidirectional and has twelve controlledpower switches at the grid-side, being employed in drive andgeneration applications (see Fig. 1(a)). Configuration A2 isunidirectional and has six controlled power switches, beingemployed only in drive applications (see Fig. 1(b)). Config-urations B1 and B2 are the versions of the configurations ofGroup A with only one DC-link (shown in Figs. 3(a) and3(b) respectively). Configuration B3 (see Fig. 3(c)) has sixcontrolled power switches in converter Ag and a three-phasediode bridge is converter Bg . This last configuration can onlybe realized with one DC-link for the proposed application. Toour knowledge, the conversion systems proposed at configu-rations A1, A2, B2 and B3 are not found in the literature.

(a)

(b)

(c)

Fig. 3: Proposed configurations of Group B with one DC-link. (a)Configuration B1 with 12 controlled power switches at the grid-side. (b) Configuration B2 with 6 controlled power switches at thegrid-side. (c) Configuration B3 with 6 controlled power switches atConverter Ag and a three-phase diode bridge at converter Bg .

II. SYSTEM MODEL

In this paper, the level-shift PWM is proposed as the methodfor switching the converters of the grid-side (Ag and Bg). Thistechnique will be explained in section III, but in order to thisexplanation make sense it is first necessary to describe thegrid-side model. For the configurations of Group A (Fig. 1),considering j = {1, 2, 3} henceforward, the model can be

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(a)

(b)

Fig. 4: Machine-side configurations for Group B. (a) Configurationfor six-phase AC machine. (b) Configuration for three-phase ACmachine.

summarized by the following equation:

vgj = vgaj0a − vgbj0b − v0b0a = egj − Lgdigjdt−Rgigj (1)

where vgaj0a and vgbj0b are the pole voltages of the grid-side.The voltages egj are the grid’s source voltages, and vgj are theresultant voltages applied to each phase by the converters. Thecurrents of the grid are denoted by igj . Lg is the inductance ofthe grid-side inductors and their internal resistance is denotedby Rg . Assuming balanced systems, i.e., vg1 + vg2 + vg3 = 0and ig1 + ig2 + ig3 = 0, it is derived the following expressionfor v0b0a:

v0b0a =1

3

3∑j=1

(vgaj0a − vgbj0b) (2)

For the configurations of Group B (Fig. 3), there is no v0b0a

voltage (i.e., v0b0a = 0), hence the model is given by thefollowing equation:

vgj = vgaj0 − vgbj0 = egj − Lgdigjdt−Rgigj (3)

Within this group of configurations, it is not physicallyguaranteed that the system will be balanced. This means thatit is possible that vg1 + vg2 + vg3 6= 0 and ig1 + ig2 + ig3 6= 0.Then, the unbalancing should be minimized by the controlsystem, which will be discussed in section IV.

III. PWM TECHNIQUE

The superscript ”∗” will be used to denote a reference vari-able associated to a physical variable henceforward, e.g., v∗g1

is the reference of vg1. The level-shift PWM can be explainedby dividing the three-phase grid-side of the conversion systemsinto three single-phase circuits, shown as one generic circuitin Fig. 5(a) for the configurations of Group A and in Fig. 5(b)for the configurations of Group B. Furthermore, by (1) and(3), vgrj voltages can be defined for both groups, such that:

vgrj = vgaj0a − vgbj0b = vgj + v0b0a (4)

vgrj = vgaj0 − vgbj0 = vgj (5)

Where (4) is relative to Group A and (5) is relative toGroup B. Considering that for the intended application wemust have vCa = vCb in Group A, analyzing all possiblevoltage levels for vgrj at all configurations, it can be derivedthe diagrams presented in Fig. 6 for Configurations A1 troughB3, as indicated. Thus, it must be determined the referencesv∗grj that shall be used by the level-shift PWM. Thereby, from(4) and (5), we have respectively:

v∗grj = v∗gj + v∗0b0a (6)

v∗grj = v∗gj (7)

Once desired v∗gj are set, the references v∗grj are alreadydetermined for the configurations of Group B, but for GroupA there is still the reference voltage v∗0b0a to be defined. Thischoice represents a degree of freedom for both ConfigurationsA1 and A2, and it is free once the voltage limits imposedby the DC-link voltages are respected. Then, it is possibleto calculate v∗grj using (6). Once v∗grj references are definedfor all configurations, the switching between the possiblevalues of vgrj must occur such that only the two closestvoltage levels with respect to the reference are used duringone determined period. The mean value of vgrj during thisperiod must be equal to v∗grj . These descriptions are translatedby the following expressions:

v∗0b0amin = −v∗Cm −min{v∗g1, v∗g2, v

∗g3} (8)

v∗0b0amax = v∗Cm −max{v∗g1, v∗g2, v

∗g3} (9)

v∗0b0a = µ0b0av∗0b0amax + (1− µ0b0a)v

∗0b0amin

0 ≤ µ0b0a ≤ 1(10)

vgrj =

{{0, vCm}, if v∗grj ≥ 0

{−vCm, 0}, if v∗grj < 0(11)

Where vCm = (vCa + vCb)/2 and v∗Cm = (v∗Ca + v∗Cb)/2in Group A. Once it is determined the two values of vgrj thatmust be applied, their times of application must be calculated,so that the switching states are defined accordingly to thediagrams of Fig. 6. This can be solved automatically if v∗grjis compared to appropriate triangular carriers, i.e., if v∗grj ≥ 0the carrier must vary between 0 and v∗Cm; if v∗grj < 0 thecarrier must vary between −v∗Cm and 0. Then, two carriersare defined, v∆gr+ and v∆gr−, such that 0 ≤ v∆gr+ ≤ v∗Cm

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(a)

(b)

Fig. 5: Circuits representing each phase of the grid-side for level-shift PWM analysis. (a) Circuit for the configurations of Group A.(b) Circuit for the configurations of Group B.

(a)

(b)

(c)

Fig. 6: Possible voltage levels for vgrj and correspondent switchingstates. (a) For Configurations A1 and B1. (b) For Configurations A2and B2. (c) For Configuration B3.

and −v∗Cm ≤ v∆gr− ≤ 0. These carriers are set in phasewith each other, and their frequency is labeled f∆, such thatf∆ = 1/T∆. T∆ is the carriers’ period, in which the meanvalue of vgrj must correspond to v∗grj . This description isrepresented in Fig 7.

So far, the PWMs for Configurations A2, B2 and B3 areresolved. But it still remains the ambiguity when vgrj = 0 inConfigurations A1 and B1 to be solved (see Fig. 6(a)). In thesecases, both qgaj = qgbj = 0 and qgaj = qgbj = 1 combinationsare allowed, and the choice of which will be applied is relatedto the three degrees of freedom, one for each phase, allowedby these configurations.

For Configuration A1, these degrees of freedom are parti-

Fig. 7: Representation of the level-shift PWM switching technique,by comparison with triangular carriers sorted by levels.

Fig. 8: Representation of the ambiguity resolution technique of thelevel-shift PWM.

cularly important. In terms of power balance, the combinationqgaj = qgbj = 1 favors the DC-link loading at the A side ifigj ≥ 0 and at the B side if igj < 0. On the other hand, thecombination qgaj = qgbj = 0 favors the DC-link loading at theB side if igj ≥ 0 and at the A side if igj < 0. Therefore, wecan define a µgx variable, such that 0 ≤ µgx ≤ 1, to determinethe time of application of each switching combination whenvgrj = 0, so that the desired power balance is generated,within certain limits.

This control is made by comparing µgx with a triangularcarrier v∆gx, in phase with v∆gr+ and v∆gr− and whosefrequency is f∆, such that 0 ≤ v∆gx ≤ 1. Thus, we canestablish the following rules:

- For v∗grj ≥ 0 and igj ≥ 0:

(qgaj , qgbj) =

(1, 0), if v∗grj ≥ v∆gr+

(1, 1), if v∗grj < v∆gr+ and µgx ≥ v∆gx

(0, 0), if v∗grj < v∆gr+ and µgx < v∆gx

(12)

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(a)

(b)

Fig. 9: Generic control diagrams. (a) Diagram for the configurationsof Group A. (b) Diagram for the configurations of Group B.

- For v∗grj ≥ 0 and igj < 0:

(qgaj , qgbj) =

(1, 0), if v∗grj ≥ v∆gr+

(0, 0), if v∗grj < v∆gr+ and µgx ≥ v∆gx

(1, 1), if v∗grj < v∆gr+ and µgx < v∆gx

(13)- For v∗grj < 0 and igj < 0:

(qgaj , qgbj) =

(0, 1), if v∗grj < v∆gr−

(0, 0), if v∗grj ≥ v∆gr− and µgx ≥ v∆gx

(1, 1), if v∗grj ≥ v∆gr− and µgx < v∆gx

(14)- For v∗grj < 0 and igj ≥ 0:

(qgaj , qgbj) =

(0, 1), if v∗grj < v∆gr−

(1, 1), if v∗grj ≥ v∆gr− and µgx ≥ v∆gx

(0, 0), if v∗grj ≥ v∆gr− and µgx < v∆gx

(15)Since Configuration B1 has only one DC link, we apply the

same rules to define the switches’ states, but µgx is definedas a constant such that µgx = 0.5, once there is no need toimpose a different power balance between the Converters Ag

and Bg .The technique of ambiguity resolution when vgrj = 0 is

represented in Fig. 8. In section IV it will be discussed howthis PWM technique is used to control the DC-link voltagesat Configuration A1.

IV. CONTROL STRATEGY

For all configurations, the role of the control system is tomaintain the DC-link voltages at desired values. The configu-rations of Group A have two DC-links, and their voltages mustbe such that vCa = vCb = v∗Cm. This is required because weneed to feed a six-phase machine, which has two three-phasesets, labeled set A and set B. Converter Ag feeds set A, andConverter Bg feeds set B. Therefore, to keep the machine’sbalance, it is required to maintain equivalent voltages andcurrents in both sets, considering only that they must be 60◦ offphase from their correspondents (α = 60◦). The configurationsof Group B have only one DC-link, and their voltages must besuch that vCm = v∗Cm. The control diagrams for each group ofconfigurations are generically represented in Fig. 9. In eithercases the control is executed in cascade. The external loopcontrols the voltage vCm, given by vCm = (vCa + vCb)/2 inthe configurations of Group A. The internal loop controls thecurrents igj . For the configurations of Group A there is stillone more control loop that is relative to the difference betweende voltages vCb and vCa, as seen in Fig. 9(a).

The following description is general for the control systemsof all configurations, unless otherwise noted. The controllerRCm is a conventional PI and it controls the (mean) voltageat the DC-links, receiving the error signal v∗Cm − vCm andproducing I∗g as output, which is the amplitude of the signalsi∗gj . These signals are the references of the grid currents,which are synchronized in the Sin block with the voltagesegj for configurations that contains only switches, and withvgj for configurations with diodes. This grants an unitarypower factor to the grid-side in the first case, and that thesystem works properly in the last. At the control diagramof the configurations of Group A (see Fig. 9(a)), the blockR12 represents two resonant PI controllers. They are able tocontrol sinusoidal signals, and their models are detailed in[13]. They control the currents ig1 and ig2 (ig3 is consequentlycontrolled), receiving the error signals i∗g1− ig1 and i∗g2− ig2,and producing v∗g1 and v∗g2 as outputs (v∗g3 = −(v∗g1 + v∗g2)).The resulting v∗gj signals are sent as inputs to the PWM,which will realize the switching of the grid-side convertersaccordingly to the technique described in section III. At thecontrol diagram of the configurations of Group B (see Fig.9(b)), the block R123 represents resonant PI controllers forthe igj likewise, but this time three of them are needed. Sincethere is no v0b0a voltage, the system is not naturally balanced,and thus this must be granted by controlling each currentindividually. These controllers generate the references v∗g1, v∗g2

and v∗g3 that serve the PWM as inputs, similarly to what waspreviously described.

To satisfy the PWM with all needed variables, it is stillrequired to define other parameters for some configurations.For the configurations of Group A it is required to defineµ0b0a. For Configurations A1 and B1 it is also required todefine µgx. For Configurations B2 and B3 there is no degree offreedom left to be solved, hence the description of the controlsystem is concluded so far.

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(a) (b)

(c) (d)

(e)

Fig. 10: Simulation results. Current ig1 of the grid-side in steady statefor each configuration. (a) Current and voltage eg1 in ConfigurationA1. (b) Current and reference voltage v∗g1 in Configuration A2.(c) Current and voltage eg1 in Configuration B1. (d) Current andreference voltage v∗g1 in Configuration B2. (e) Current and referencevoltage v∗g1 in Configuration B3.

In Configuration A1 it is set µ0b0a = 0.5, so that it becomesa neutral parameter at the control system, i.e., it won’t interfereat the power balance between converters Ag and Bg . Thevariable µgx is set by the PI controller RCab, whose purposeis to control the difference between the voltages vCb and vCa.It receives the error signal vCb − vCa and generates µgx asoutput.

In Configuration A2 it is not possible to choose the valueof µgx, due to the physical limitations imposed by the diodes.Then, the control action set by the RCab controller is changedto define µ0b0a. This also allows the controlling of the DC-links voltages, as it is going to be shown in sections V and VI.The situation physically imposed by the diodes in this confi-guration is equivalent to always setting (qgaj , qgbj) = (0, 0)in Configuration A1 when vgrj = 0. Therefore, it is possibleto show that in this situation the power balance betweenconverters Ag and Bg can be changed by changing the valueof µ0b0a around 0.5.

In Configuration B1 the µgx variable does not influence thecontrol system, then µgx is set equal to 0.5 to keep an uniformpower distribution between the converters.

(a) (b)

(c) (d)

(e)

Fig. 11: Simulation results. Resultant voltage vg1 for each confi-guration. (a) Resultant voltage in Configuration A1. (b) Resultantvoltage in Configuration A2. (c) Resultant voltage in ConfigurationB1. (d) Resultant voltage in Configuration B2. (e) Resultant voltagein Configuration B3.

V. SIMULATION RESULTS

The simulations were made in order to obtain results for thedifferent grid-side configurations, considering the followingparameters:

• Continuous computation step: h = 100ns• Control system’s computation step: hdisc = 50µs• Triangular carriers’ frequency: f∆ = 10kHz• Nominal per phase voltage: VN = 220VRMS

• Nominal three-phase power (total load power): PN =600W

• egj amplitude: Eg = 0.25p.u.• Grid’s electrical frequency: fg = 60Hz; ωg = 120πrad• DC-link reference voltage in Group A: v∗Cm = 87V• DC-link reference voltage in Group B: v∗Cm = 100V

The simulation results are exposed in Figs. 10 through 12.In Fig. 10 the grid current ig1 is shown in steady state foreach configuration. The currents of Configurations A1 and B1are synchronized with the voltages egj , and the currents ofConfigurations A2, B2 and B3 are synchronized with voltagesvgj , which is better realized by comparing ig1 with the meanvalue of vg1, as shown in the figures. The currents of GroupA have a minor ripple in relation to Group B’s. This can bejustified by observing Fig. 11. Because the configurations of

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(a) (b)

(c) (d)

(e)

Fig. 12: Simulation results. DC-link voltages for each configuration.(a) Voltages vCa and vCb in Configuration A1. (b) Voltages vCa andvCb in Configuration A2. (c) Voltage vCm in Configuration B1. (d)Voltage vCm in Configuration B2. (e) Voltage vCm in ConfigurationB3.

Group A have two DC-links, thus allowing the use of thevoltage v0b0a to generate more voltage levels to vgj , theirresultant voltages vgj present a minor variation around theirreferences, which contributes to reduce the current’s ripple andTHD, as seen in Table I.

In terms of THD (Table I), Configuration A1 presents thebest performance, though the difference between its THDand that of Configuration A2 is slight. Configuration A1 isstill better in terms of performance because it is possible tooperate it with unitary power factor (igj synchronized withegj). Nevertheless, the power-factor of configurations usingdiodes is still close to 1, around 0.99. The situation is thesame comparing Configuration B1 with Configuration B2.Configuration B3 presents the worst performance, but is thecheapest.

TABLE I: THDs of the grid-side currents.

Conf.A1 Conf.A2 Conf.B1 Conf.B2 Conf.B3ig1 THD 0.91% 0.99% 2.33% 2.36% 3.29%ig2 THD 0.85% 0.86% 2.30% 2.31% 2.93%ig3 THD 0.85% 0.86% 2.30% 2.31% 3.07%

Mean 0.87% 0.90% 2.31% 2.33% 3.10%

Fig. 12 shows the controlled DC-link voltages in steadystate. In all cases, the voltages are properly controlled. It is

(a) (b)

(c)

Fig. 13: Experimental results. Currents ig1 and ig2 of the grid-side insteady state for configurations A1, B1 and B2. (a) Currents ig1 andig2 in Configuration A1. (b) Currents ig1 and ig2 in ConfigurationB1. (c) Currents ig1 and ig2 in Configuration B3.

(a) (b)

(c)

Fig. 14: Experimental results. DC-link voltages for configurationsA1, B1 and B2. (a) Voltages vCa and vCb in Configuration A1. (b)Voltage vCm in Configuration B1. (c) Voltage vCm in ConfigurationB3.

noted that the reference voltage v∗Cm set for Group A is lowerthan that of Group B. The reason is because it is possible to usethe voltage v0b0a to generate higher values of resultant voltagesin Group A. Then, it is required a lower voltage at the DC-links to make the systems operate in equivalent conditions toGroup B, i.e., with similar modulation index in the converters.Furthermore, it can be observed that Configurations A1 andB1 present the minor variation around the reference, whileConfiguration A2 presents the greater variation.

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VI. EXPERIMENTAL RESULTS

The experimental results are shown in Figs. 13 and 14. Theywere extracted at similar conditions to those of the simulations.The results for configurations A2 and B2 where not obtaineddue to momentary limitations of the laboratory. Fig. 13 showsthe controlled grid-side currents ig1 and ig2, it can be notedthat the currents are properly controlled for all configurations.For configuration B3 there is a very low distortion near tozero crossing. Fig. 14 shows the controlled DC-links voltages.It can be observed the proper functioning of the DC-linkcapacitor controls in the systems.

VII. CONCLUSIONS

The presented configurations can be evaluated in terms ofcost and performance. The performance is evaluated by theTHD of the grid currents shown in Table I, and the cost isindirectly evaluated by the number of DC-links and controlledpower switches at the grid-side converters.

Configuration A1 presents the best performance, but alsothe highest cost, because it employs twelve power switches atthe grid-side and two DC-links. The second best performanceis obtained from Configuration A2. Practically, it has thesame THD compared to Configuration A1, but it doesn’tallow the operation with unitary power factor, i.e., igj can’tbe synchronized with egj , even though it is still very closeto 1. Nevertheless, it is cheaper since it has less controlledpower switches. Its legs, which contain one IGBT and onediode, are available as a single module, cheaper than theusual module with two IGBTs. Configuration B3 has the worstperformance, but also the lowest cost, because it is possibleto acquire a single module with a three-phase diode bridgeat considerably lower prices than the IGBT modules. Plus,it contains only one DC-link. Configurations B1 and B2 areintermediate alternatives. In general, they are cheaper thanGroup A configurations, because they require only one DC-link, but they have considerably lower performances.

This evaluation was made considering the obtained resultsfor the proposed applications. It is also important to note thatthe configurations of Group B can be employed in a largervariety of applications than those of Group A, e.g., feedinga single DC load or a single six-phase or three-phase ACmachine.

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