Three-Phase Multilevel Bidirectional DC-AC Converter ... - Ivo Barbi

Three-Phase Multilevel Bidirectional DC-AC Converter Using Three-Phase Coupled Inductors Romeu Hausmann

Ivo Barbi

Student Member, IEEE University of Blumenau Department of Electrical and Telecommunication Engineering Blumenau – SC – Brazil [email protected]

Senior Member, IEEE Federal University of Santa Catarina Power Electronics Institute Florianopolis – SC- Brazil [email protected]

Abstract – A new three-phase multilevel DC-AC converter with three-phase coupled inductors is presented in this work. The related converter is employed only as an inverter here. Initially the power stage diagram is shown and discussed. Their main characteristics are described and the more relevant waveforms, generated by simulation, are shown. After that, the converter operation is presented and all topological states are shown. The vectorial interpretation of the line load voltage is shown to all available vectors of load voltage in the new structure. Next, the operation of the converter with sinusoidal PWM modulation is discussed and some relevant figures are presented. In the sequence, the presence of the three-phase coupled inductor to provide significant reduction in harmonic distortion is discussed. Finally, experimental results obtained from the implemented prototype are presented and briefly discussed. Index Terms- Coupled inductor; DC-AC bidirectional converter; multilevel inverter; three-phase inverter.

I.

INTRODUCTION

Several techniques are used to increase the amount of energy processed from static converters, amongst which the interleaving technique, multilevel converters and the use of inductive coupling cells. The interleaving technique is widely treated in the literature and consists of connecting converters in parallel, with synchronized and complementary operation, connected to the same load and with the same power source. Interleaved converters can be classified in two ways: without magnetic coupling and with magnetic coupling. The analyses of some interleaved converters with coupled inductors are presented in [13-15]. In [16-17] interleaved converters using intercell transformers are presented. It can be emphasizes the reference [14] who presents a generic model for interleaved multiphase boost converter, with coupled inductors. The mathematical development is presented considering “2N” boost converters, and the number of converters is always multiple of 2. The use of coupled inductors to improve the current capacity in inverters is presented in [7]. In this structure, techniques are proposed for paralleling the inverters, always in pairs. Beyond reducing the current stresses in the power devices, the structure also provides the reduction of the harmonic content in the output voltage. The proposal topology can be applied in three-phase inverters and be generalized for a bigger number of converters in parallel,

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with the disadvantage of only allowing converters in pairs. In the other hand, the use of coupled inductors can provide multilevel output voltage in power converters and improve the dynamic performance [8]. The use of multilevel coupled inductors in single-phase boost rectifiers is presented in [10 and 12]. These works presents a comparison between the inductors in converters using interleaving and multilevel coupled inductors. Structures with 3, 4 and 5 levels are shown, and the structure with 4 levels are emphasized because it is possible the use of a commercial three-phase core. Other related works are presented in [9 and 11]. Another solution for high power static converters is the use of multilevel converters. As characteristic, these converters present reduction of the voltage/current stresses on the switches and have output multilevel voltage. Theoretically, they can produce high-voltage output with infinite output voltage levels. This can be obtained through three techniques: the series and/or parallel association of the switches, the use of multilevel commutation cell and the converters association [13-24]. The concept of three-state commutation cells is presented in [3-5], and it is based on the two-state switching cell shown in [1-2]. The main characteristics of the three-state cell are the division of the current who flows through the switches and the frequency multiplication of the load voltage. These characteristics allow improvement of the losses distribution and the volume reduction of the output filter. The four-state switching cell is shown in [4] and [6] and consists of three switches, three diodes and a three-phase Y connected transformer. In this structure the frequency at the output filter is triple the switching frequency and the switches current is balanced divided and equal to 1/3 of the output current. The switching cell is formed with the substitution of the 2 states cell, shown in [1-2], for a 3, 4 or “n” states cell, maintaining the other elements of the converter. This work present a three-phase inverter based on the four-state switching cell. The four-state switching cell is applied to the three-phase full-bridge converter. The middlepoint of each leg of the three-phase converter is connected to each winding of a three-phase coupled inductor to form a phase of the converter. The proposed structure is a highcurrent middle-voltage converter and provides multilevel output voltage with three-times the switching frequency.

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II.

TOPOLOGY PRESENTATION

III. CONVERTER OPERATION

+

The topological states for a phase are shown in Fig. 3.

V3

+

Fig. 2. Simulation results: (a) load line voltage “Vab”; (b) total current in phase “a”; (c) current in one winding of the threewinding inductor.

-

V2 -

-

V1

+

The three-phase DC-AC converter with coupled inductor is presented in Fig. 1. The use of the three-phase coupled inductor allows the division of the load phase current through the switches, in a balanced way so that the current in each arm of the structure is equal to 1/3 of the load current in one phase, reducing the current values for the switches. Another characteristic of this structure is the increasing of the voltage load levels, thus contributing to reduce the common mode voltage, when compared with standard structures. The load voltage frequency is three times the switch frequency; this results in a reduction of the size and the cost of the output filter. The presented converter has 18 controllable switches and their respective freewheeling diodes that, for the sake of simplification, are represented by bidirectional switches. Switches S11 to S16 constitute the phase “a”, transistors S21 to S26 constitute the phase “b” and switches S31 to S36 constitute the set of active switches of phase “c”. Each set of switches that constitutes one of the three-phase leg is connected to the load through a symmetric three-phased coupled inductor. The employed modulation is the sinusoidal PWM.. The three-phase converter was simulated and the simulation results are presented in Fig. 2. From the results of simulation shown in Fig. 2(a), it is possible to verify that the line voltage has 7 levels; this favors the harmonic content reduction and minimizes the size of the output filter.

windings of the coupled inductor. Each part of the current is processed for one arm of the converter. This allows the use of the switch with smaller current capacity and easier dissipation of the heat produced by the semiconductors.

Fig. 1. Power structure of the three-phase converter.

The simulation results shown in Fig. 2 were obtained from the simulation of the circuit shown in Fig. 1, with modulation index equal to 0.9, switching frequency of 9 kHz and symmetrical triangular carriers shifted by 120°. The voltages applied to the coupled inductor have two components: one of them is a zero-sequence voltage in the low frequency; the other voltage forms a balanced three-phase system which operates at switching frequency. This brings about a null impedance of the inductor for the zero-sequence component voltage. It is verified from the simulation results in Fig. 2(c) that the load current is divided in a balanced way in the three

Fig. 3. Topological possible states for one phase of the converter.

Each arm of the converter has two possible states, therefore the command of the switches is complementary and it will always have a switch commanded to conduct in each

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arm. This implies in 8 possible topological states for the structure of one of the phases of the converter, and 512 possible topological states when considering the 9 arms of the three-phase structure. The 8 different topological states result in 4 distinct levels of Va0 voltage, therefore some topological states are redundant in terms of the line load voltage. The average value voltage of the winding must be null in each topological state of operation of the converter, so that there is no saturation of the inductor or significant unbalance in the winding currents. From the presented topological states shown in Fig. 3 it is possible to determine the values of the load and inductor winding voltages. Table 1 presents all the voltages for each topological state for one phase of the converter. TABLE I VA0 VOLTAGE FOR THE DIFFERENT TOPOLOGICAL STATES. Topological Va0[V] Simbol Windings voltages state V1 V2 V3 1 -Vcc/6 2Vcc/3 -Vcc/3 -Vcc/3 X 2 -Vcc/6 Vcc/3 Vcc/3 -2Vcc/3 X 3 -Vcc/6 -Vcc/3 2Vcc/3 -Vcc/3 X 4 Vcc/6 -2Vcc/3 Vcc/3 Vcc/3 X 5 Vcc/6 -Vcc/3 -Vcc/3 2Vcc/3 X 6 Vcc/6 Vcc/3 -2Vcc/3 Vcc/3 X 0 0 0 7 Vcc/2 Y 8 -Vcc/2 0 0 0 Y

Fig. 4. Available vectors in the three-phase structure.

The three-phase coupled inductor core design is shown in Fig. 5. To prevent unbalances in the winding currents it is necessary to build a symmetrical three-phase inductor and generate the converter switches signal commands accurately.

Ac c

Table II presents the summary of all available line voltage vectors for the three-phase converter. The vectors are divided into 11 groups, 10 groups of 6 vectors and 1 group with 4 null vectors. The groups are formed considering the module and phase of the resulting vector. Thus the vector A1 has the same magnitude of the vector A2 and is delayed by 60°.

g

e f

b

Aw

TABLE II SUMMARY OF THE AVAILABLE VECTORS FOR THE THREE-PHASE STRUCTURE. Group Vector 1 Vector 2 Vector 3 Vector 4 Vector 5 Vector 6 (Y Y Y ) (Y Y Y ) (Y Y Y ) (Y Y Y ) (Y Y Y ) (Y Y Y ) A

a

d Fig. 5. Three-phase coupled inductor core design.

B

(Y X Y ) (Y X Y ) (Y Y X ) (Y X Y ) ( X Y Y ) (Y Y X )

IV. EMPLOYED MODULATION

C

(Y X Y ) ( X Y Y ) (Y Y X ) (Y X Y ) ( X Y Y ) (Y Y X )

D

(Y X X ) (Y Y X ) ( X Y X ) ( X Y Y ) ( X X Y ) (Y X Y )

E

( X Y Y ) ( X X Y ) (Y X Y ) (Y X X ) (Y Y X ) ( X Y X )

The employed modulation is the sinusoidal PWM with symmetrical triangular carriers shifted by 120°. The modulator for the three-phase structure is formed by nine comparators, which schematic diagram is presented in Fig. 6.

F

(Y X X ) ( X Y X ) ( X Y X ) ( X X Y ) ( X X Y ) (Y X X )

G

( X X Y ) ( X X Y ) (Y X X ) (Y X X ) ( X Y X ) ( X Y X )

H

(Y X X ) (Y Y X ) ( X Y X ) ( X Y Y ) ( X X Y ) (Y X Y )

I

( X X X ) ( X X X ) ( X X X ) ( X X X ) ( X X X ) ( X X X )

J

( X Y Y ) ( X X Y ) (Y X Y ) (Y X X ) (Y Y X ) ( X Y X )

Z

(Y Y Y ) ( X X X ) ( X X X ) (Y Y Y )

The representation of the available vectors is presented in Fig. 4. Each group of vectors is formed by 6 vectors shifted by 60° between them. Only vectors “1”are identified for each group, vectors “2” come to 60° in the counter-clockwise direction thus and successively.

Fig. 6. Modulator for the three-phase structure

In Fig. 7 it is possible to observe three waveforms groups market by three brackets. At the first group, the carriers and sinusoidal modulating signals are shown to a switching period. In the second group, the upper switches signal commands are presented. In the last group, the load line

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TABLE III SWITCHING SIGNAL COMMAND AND RESPECTIVE VECTOR.

voltages “Vab” and “Vca” are presented. It is possible to observe in Fig. 7 that the converter posses 18 operating stages. In each operating stage occurs only a commutation and the total commutations in a switching period are distributed in a balanced way. These facts provide a reduction on electromagnetic interference and improve the heat distribution in the converter. Figure 7 shows the load line voltage with Vcc/3 steps. The lower steps values contribute to the reduction of the electromagnetic interference and the output filter size.

{

Upper switches signals command Operating stages [S11;S12;S13] [S21;S22;S23] [S31;S32;S33]

{ {

vector

1

[0;1;1]

[0;0;0]

[0;1;1]

( X Y X ) E6

2

[1;1;1]

[0;0;0]

[0;1;1]

(Y Y X ) B6

3

[1;1;1]

[0;0;0]

[0;0;1]

(Y Y X ) C6

4

[1;1;1]

[0;0;1]

[0;0;1]

(Y X X ) D1

5

[1;1;1]

[0;0;0]

[0;0;1]

(Y Y X ) C6

6

[1;1;1]

[0;0;0]

[1;0;1]

(Y Y X ) B6

7

[1;0;1]

[0;0;0]

[1;0;1]

( X Y X ) E6

8

[1;1;1]

[0;0;0]

[1;0;1]

(Y Y X ) B6

9

[1;1;1]

[0;0;0]

[1;0;0]

(Y Y X ) C6

10

[1;1;1]

[1;0;0]

[1;0;0]

(Y X X ) D1

11

[1;1;1]

[0;0;0]

[1;0;0]

(Y Y X ) C6

12

[1;1;1]

[0;0;0]

[1;1;0]

(Y Y X ) B6

13

[1;1;0]

[0;0;0]

[1;1;0]

( X Y X ) E6

14

[1;1;1]

[0;0;0]

[1;1;0]

(Y Y X ) B6

15

[1;1;1]

[0;0;0]

[0;1;0]

(Y Y X ) C6

16

[1;1;1]

[0;1;0]

[0;1;0]

(Y X X ) D1

17

[1;1;1]

[0;0;0]

[0;1;0]

(Y Y X ) C6

18

[1;1;1]

[0;0;0]

[0;1;1]

(Y Y X ) B6

Representative waveforms are shown in Fig. 9 to evidence two important characteristics of this structure. The first one is that the Va0 voltage has a three times higher frequency compared with the switching frequency; this allows the reduction of the size of the output filter. The second important characteristic is that the V10 voltage has two levels and the Va0 has four levels of voltage; thus a change of 2 to 4 levels in the output voltage.

Fig. 7. Representative waveforms for a switching period.

Figure 8 shows the vectorial form from all employed vectors in the 16 operating stages presented in Fig. 7.

(a)

Vs11

t

(b)

Vs12

(c)

Vs13

Ts

Vcc/2 Vcc/6 Va0

3Ts

(d)

t t

t

-Vcc/6 -Vcc/2 Fig. 9. Relevant wave forms: (a) S11 signal command; (b) S12

signal command; (c) S13 signal command and (d) Va0 voltage.

Fig. 8. Switching period employed vectors.

In Table III are shown the upper switches gate signals and the associate vector for each operating stage. It is possible to verify that the adjacent vector is always selected and this follows a sequence.

Other relevant waveforms are shown in Fig. 10. The phase load voltage “Van” has 11 levels, and each step has Vcc/9 value. The common mode voltage “Vn0” has 5 levels with Vcc/9 steps value. This implies in reduced electromagnetic

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interference.

The circuit shown in Fig. 11 can be represented by the equivalent circuit shown in Fig. 13. Voltages V10, V20 and V30 have rectangular form as shown in Fig. 12 and can be expressed as a fundamental sinusoidal component plus the sum of harmonic. V1h V1 + V1 0

V1

V2h

V1

V3h

+

V2

+

V3

-

a

-

Va0

Fig. 13. Equivalent circuit of Fig. 11

Fig. 10. Relevant wave forms: (a) Phase load voltage Van; (b)

Common mode voltage Vn0; (c) Line load voltage Vab.

The three-phase converter, composed of three singlephase structures, is able to power balanced or unbalanced loads connected in Δ or Y. V.

The circuit of Fig. 13can be represented by two separate circuits: one containing the sinusoidal voltage sources and another one containing the voltage sources of the harmonic components. The sources of sinusoidal voltage "V1" have the same amplitude, frequency and phase. In this situation the three-phase coupled inductor is subjected only to the zero sequence voltage V1 + V1

HARMONIC DISTORTION

The presence of the three-phase coupled inductor provides significant reduction in harmonic distortion; this fact is due to the harmonic cancellation. Fig. 11 presents the circuit for one phase of the proposed converter. The modulator for one phase of the converter consists of three comparators. The carriers Vtri1, Vtri2 and Vtri3 are symmetrical triangular carriers shifted by 120° and the sinusoidal modulate signal is Vsin1.

0

V1 V1

+

V2

+

V3

-

a

-

Va0

Fig. 14. Circuit containing only the sinusoidal voltage sources.

Since the system is symmetric and considering the absence of dispersion, the three-phase coupled inductor behaves as a short circuit to the zero sequence voltage component. The output voltage is shown in (1).

Va 0 = V1 (1)

Fig. 11. Structure of a phase of the converter.

The waveforms produced in the midpoint of each arm of the converter with respect to the midpoint of DC power supplies are given by Fig. 12. The three-phase voltages applied to the inductor have two components: a zero sequence voltage in low frequency, and another one that forms a three-phase balanced system at the switching frequency

Fig. 15 represents the equivalent circuit with the harmonic voltage sources V1h I1h + Vx -

0

V2h I2h +

Vy

V3h I3h +

Vz

-

Iht

a Va0h

Fig. 15. Circuit containing only the harmonic voltage sources. From the circuit of Fig. 15 the output current is according

with (2).

I ht = I1h + I 2 h + I 3h (2) Where Iht – total harmonic current;

Fig. 12. Voltage waveforms V10, V20 and V30.

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I1h, I2h e I3h – harmonic currents in the coils 1, 2 and 3 of the coupled inductor respectively. The equations of the inductor coil voltages are shown in (3), (4) and (5).

be represented as (14), (15) and (16).

V10 (t ) = V11 + ∑ V1h (14) V20 (t ) = V21 + ∑ V2 h (15)

Ld Mdi 2 Mdi 3 (3) Vx = i1 + + dt dt dt Vy =

Mdi1 Ldi 2 Mdi 3 + + dt dt dt

Vz =

(4)

Mdi1 Mdi 2 Ldi 3 + + (5) dt dt dt

Where Vx, Vy e Vz – voltages in coils 1, 2 and 3 of the coupled inductor respectively; L – inductance of each coil of the coupled inductor; M – mutual inductance between the coils of the coupled inductor. The load voltage can then be written as shown in (6).

3Va 0 h = V1h + V2 h + V3h − (Vx + Vy + Vz ) (6) The coils voltages of the inductor are described by (7).

d d ⎞ ⎛d Vx + Vy + Vz = L ⎜ i1 + i 2 + i 3 ⎟ + ⎝ dt dt dt ⎠ (7) ⎛ di1 di 2 di 3 ⎞ + 2M ⎜ + ⎟ ⎝ dt dt dt ⎠

V30 (t ) = V31 + ∑ V3h (16) The resulting voltage on the load considering one phase of the converter is then the sum of the voltages of the midpoint of each arm. The equation (17) shows that the harmonics contents in the load voltage will always be multiple of 3 when compared to the switching frequency. Va 0 h = V3 sin 3ω st + V6 sin 6ω st + V9 sin 9ω st + ... (17)

VI. EXPERIMENTAL RESULTS Experimental results were obtained from a three-phase prototype operating as inverter in open-loop and 15 kW output power. The switching frequency was 9 kHz and the DC link voltage was 300V. The switches gate signals were generated by the digital signal processor of TEXAS TMS320F2812. Fig. 16(a) presents the load current for one phase and Fig. 16(b) shows the current in one of the winding of the three-phase coupled inductor. The current in the winding is a bit higher than 1/3 of the load current due to the magnetizing current.

Or according related in (8).

0

For the ideal three-phase inductor the mutual inductance is given by (9):

-0.1

M =−

L (9) 2

-0.2 0.8

The total inductance is shown in (10).

1.4

1.6

1.8

2

2.2

2.4 5

Vx + Vy + Vz = 0 (11) The substitution of (11) in (6) results in (12):

V1h + V2 h + V3h (12) 3

Or generically according (13).

=

1.2

Fig. 16. a) line load current; (b) one winding current of the inductor. Fig. 17(a) shows the DC link voltage and Fig. 17(b)

L + 2 M = 0 (10)

Va 0 h =

1

x 10

The sum of the coils voltages is given by (11)

a0h

(b)

0.1

⎛d ⎞ Vx + Vy + Vz = ( L + 2M ) ⎜ iht ⎟ (8) ⎝ dt ⎠

∑V

(a)

0.2

∑V + ∑V 1h

2h

3

+ ∑ V3h

(13)

Voltages in the midpoint of each arm shown in Fig. 11 can

presents the Vab line voltage. The presence of many voltage levels can be observed, which maximum value is limited to the DC link voltage. The presence of the 7 voltage levels is verified clearly, thus proving the theoretical analysis and the simulation previously presented. The use of the three-phase coupled inductor in classics converters changes the number of the voltage levels of the load, consequently reducing the harmonic distortion and the filter size. Due to the presence of the symmetric three-phase coupled inductor, the current in each leg to one phase of the converter divides in a balanced

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way and is equal to 1/3 of the load phase current.

It is possible to verify the presence of three multiple frequencies in the line load voltage as shown in (1.17). The picture of implemented three-phase coupled inductor is shown in Fig. 20.

(a)

300

200

2Vcc/3

100

Vcc/3 (b)

0

-100

-200

-300 0

1

2

3

4

5

6

7

8

9

10 4

x 10

Fig. 17. a) DC link voltage; (b) Vab line voltage without output filter. In Fig. 18 the evolution of harmonic distortion in Vab line

voltage according to the index of modulation is shown. There is a great similarity between the results obtained with the evolution of harmonic distortion experimentally and from numerical simulation. THD of Vab line voltage (%)

70 60 50 40 30

Simulation result 20

Experimental result

10 0 0,5

0,55

0,6

0,65

0,7

0,75

0,8

0,85

0,9

Modulation index

Fig. 18. Evolution of the harmonic distortion of the Vab voltage according to the modulation index. In Fig. 19 is presented the harmonic spectrum of Vab line

voltage experimentally obtained. 20

15

10

Fig. 20. picture of the three-phase coupled inductor.

VII.

CONCLUSION

A new three-phase DC-AC multilevel converter is presented. The overall schematic diagram of the implemented structure is shown in Fig. 21. This converter uses a threephase coupled inductor to produce multilevel PWM voltage waveforms on the load. The more relevant waveforms are presented along with theoretical analysis. The results obtained from numerical simulation and experimentation confirm the theoretical analysis performed. It is possible to verify the low harmonic content on the load voltage from the multilevel voltage produced, and, as consequence, a major reduction in volume and cost of the output filter. Another factor that favors the reduction of the volume of the filter is the fact that the load voltage frequency is three times the switching frequency. It is shown the balanced current division of each phase in each arm of the converter, provided by the use of the three-phase coupled inductor, bringing as benefit the reduction of losses in the switches and allowing the use of semiconductors with lower current capacity. For applications such as drives, without output filter, there is a reduction of voltage steps in the machine windings, reducing isolation problems, iron losses, the ripple torque and bearing currents.

5

0

9KHz

27KHz

54KHz

Frequency(Hz)

81KHz

Fig. 19. Harmonic spectrum of Vab line voltage - experimental results.

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Fig. 21. Overall schematic diagram of the implemented structure.

VIII.

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