Re-generative Asymmetrical Multi-level Converter for ... - IEEE Xplore

Re-generative Asymmetrical Multi-level Converter for Multi-Megawatt Variable Speed Drives Joseph Song-Manguelle, Tobias Thurnherr, Stefan Schröder, Alfred Rufer and Jean-Maurice Nyobe-Yome

3

Abstract—This paper is focused on the design, modulation and control of a re-generative non-symmetrical multi-level converter for high-power applications such as oil and gas or mining. The converter is based on standard IGBT modules and the DC-link voltages are chosen in order to be easily implemented for real industrial motor drives. The modularity of the suggested topology can help to drive up to 60 MW using PWM strategies in normal mode of operation. The output voltage has 23 levels, enabling nearly no torque ripple and avoiding to use an output sine filter. A new control strategy is suggested to reduce power-switch losses and to increase the availability of the proposed converter. Index Terms—LNG, Medium-voltage, Megawatt drive, Multilevel converter, Oil and Gas, VSI.

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978-1-4244-5287-3/10/$26.00 ©2010 IEEE

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Slave: Thread control ler

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I. I NTRODUCTION

J. Song-Manguelle was with GE Global Research, Munich, Germany and GE Oil and Gas, Le Creusot, France. He is currently with GE Global Research, Niskayuna, NY, USA, [email protected] T. Thurnherr was with GE Global Research, Munich, Germany. He is currently with ABB Advanced Power Electronics, Turgi, Switzerland. S. Schröder is with GE Global Research, Munich, Germany. A. Rufer is with The Swiss Federal Institute of Technology, Lausanne, Switzerland. J.M. Nyobe-Yome is with ENSET, the University of Douala, Cameroon. He is currently a visiting Senior Research Associate with the University of Quebec in Abiti-Temiscamingue, Rouyn-Noranda, QC, Canada.

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Slave: Thread controller

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As the power demand increases, power converter topologies are facing a huge challenge to fulfill the industry requirements. In the oil and gas industry for example, load-commutatedinverter (LCI) technology is still the preferred variable frequency drive at a power level above 15 MW, predominantly due to its high-reliability and high number of reference applications since the 80𝑠. Voltage source inverter (VSI) technology is mainly limited to power range below 15 MW. For some applications such as gas reinjection, pipeline recompression and refrigeration processes in liquefied natural gas (LNG), the motor power rating can easily exceed 30 MW for a motor speed below 3600 rpm. In such power range and speed, LCI technology has been preferably selected. However, there is a substantial risk of mechanical failures, mainly due to the inter-harmonic torques generated by the LCI, [1]-[4]. Therefore there is an increasing industrial request to extend the power rating of VSI above 30 MW. VSI may provide significant reduction of shaft torque ripple, and expectations are a perceptible reduction of mechanical failures due to torsional excitation. A parallel connection of three-level neutral-point-clamped (NPC) converters has been proposed for a power range up to 35 MW. This solution operates with interleaved pulse-widthmodulation strategy, improves the motor current waveform, hence achieves very low-torque ripple [5].

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Slave: Thread controller

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Slave: Thread controller

Master controller

Fig. 1.

Overall system architecture with 4 threads: 60 MW 5.5kV

5.5kV

5.5kV

0.5kV 1kV 1kV

1.5kV 1.5kV

Fig. 2. One thread: Investigated re-generative asymmetrical multilevel power converter, 20 MW

According to [6], existing designs of a cascaded multi-level topology have gone as high as 60 MW. Symmetrical seriesconnection of H-bridge topology needs a complex power transformer to improve the grid side current [7] and a huge number of cells to increase the voltage resolution [8]. As a result, the system availability and reliability are reduced. Some structures to simplify the drive configuration have been proposed [9]. And several alternative power converter topologies for drive applications have been investigated [10], including open winding machines [11].

3683

The asymmetric multilevel converter has been investigated [12]-[20]. It is shown that, a high-resolution voltage phasor can be generated with reduced part count of power switches, by feeding partial cells with unequal DC voltages. The voltage phasor resolution can be increased through interpolation of the converter three-phase voltages in the 𝛼 − 𝛽 reference frame, by seeking and reducing redundant switching states [16]. Designs suggested in [13], [14] are theoretical approaches. Existing power switches cannot be used to design a reliable high-power drive for industrial application. The theoretical approach suggested in [18] requires a voltage phase-shift of 16.3 deg, which is very challenging and unrealistic for transformer manufacturers. The line-side harmonics will not be cancelled for a phase-shift of 16.0 deg. To overcome these issues, a re-generative configuration of the asymmetrical multilevel converter shown in Fig.2 is investigated in this paper. The proposed system is suitable for three-phase 15 MW industry applications. When using a multiphase machine, the system can drive up to 60 MW drive train, suitable for liquefied natural gas applications (LNG), with a dedicated control strategy. The possible IGBT to be used in a real industrial product are listed. In case of component failure, a new control strategy is developed in order to enhance the availability of the system. II. A SYMMETRICAL MULTILEVEL POWER CONVERSION A. Definitions and preliminary considerations Assuming a series connection of 𝐾- partial cells (H-bridge) in each phase of a three phase system. The 𝑗 𝑡ℎ cell is fed by the dc-link voltage 𝑈𝑑𝑗 (j=1..K). Choosing the supply voltage of the smallest cell as 1 𝑝.𝑢. According to [13], in order to design a uniform step multilevel converter, the conditions given in Eq. 1 should be fulfilled: ( 𝑢𝑑𝑗 ≤

2∗

𝑗−1 ∑

𝑈𝑑1 ≤ 𝑈𝑑2 ≤ ... ≤ 𝑈𝑑𝐾

(1a)

𝑢𝑑𝑙 + 1; 𝑢𝑑𝑗 = 𝑈𝑑𝑗 /𝑈𝑑1

(1b)

)

𝑙=1

In that case, the number of level of the output voltage, 𝑁 , can be calculated as follow: 𝑁 =2

𝐾 ∑

𝑢𝑑𝑗 + 1

(2)

𝑗=1

For a particular case of a symmetrical converter, all the dclink voltages are equal to 1 𝑝.𝑢. Therfore the number of level of the output voltage is calculated as follow: 𝑁𝑠𝑦𝑚 = 2 (1 + 1 + ... + 1) +1 = 2𝐾 + 1   

From the uniformity condition given in Eq. 1a, it can be seen that the theoretical maximum dc-link voltage of the partial cells are in a geometric progression with a factor of three.

𝑢𝑑 2 2 1 2 1

𝑢𝑑 3 2 3 3 4

N 11 11 13 13 𝑢𝑑 1 1 1

𝐾02 1 4 3 9 𝑢𝑑 2 3 2

𝑢𝑑 1 1 1 1 1 1 𝑢𝑑 3 5 6

𝑢𝑑 2 3 2 1 3 2

𝑢𝑑 3 3 4 5 4 5

N 15 15 15 17 17

𝐾02 4 7 16 7 13

𝐾02 7 16

N 19 19

TABLE I S ET OF REDUNDANT SOLUTIONS TO FEED A SERIES - CONNECTION OF THREE PARTIAL CELLS PER PHASE

In that particular case, the converter is able to generate an output voltage with the maximum number of level, 𝑁𝑚𝑎𝑥 𝑁𝑚𝑎𝑥 = 3𝐾

(5)

B. Redundant design solutions on asymmetrical multilevel power converters The design condition given in equation Eq. 1b has redundant solutions which satisfy equation Eq. 2. Therefore many combinations of the DC-link voltages can be found in order to design an asymmetric multilevel converter which generates an output voltage with the same number of levels. Assuming a series connection of three partial cells per phase in a three-phase asymmetrical multilevel converter configuration. Assuming a unidirectional power flow from the grid to the converter load. The possible secondary voltages of a multiwinding transformer can be written as follows: ( ) 𝜋 2𝜋 (𝑥 − 1) − 𝑢𝑥𝐴 = 𝛿𝐴 𝑈𝑚𝑎𝑥 sin 𝜃 − 3 9 ) ( 2𝜋 (𝑥 − 1) 𝑢𝑥𝐵 = 𝛿𝐵 𝑈𝑚𝑎𝑥 sin 𝜃 − 3 ( ) 𝜋 2𝜋 (𝑥 − 1) + 𝑢𝑥𝐶 = 𝛿𝐶 𝑈𝑚𝑎𝑥 sin 𝜃 − 3 9

(6a) (6b) (6c)

Where 𝑥 = 1, 2, 3; 𝐴, 𝐵 and 𝐶 correspond to the threephase voltage sets of the transformer, with a voltage phaseshift of 20 deg. 𝛿𝐴 , 𝛿𝐵 , 𝛿𝐶 are scaling factors which can be referred to a common value. There is no predefined position of the transformer secondaries. An asymmetry quality factor can be defined as shown in Eq. 7. The smallest asymmetry quality factor will generate the smallest current harmonics distortion on the grid side; 𝐾0 = 0 for symmetrical converters [16]. √( 𝐾0 =

(3)

𝐾−𝑡𝑖𝑚𝑒𝑠

𝑢𝑑1𝑚𝑎𝑥 = 1, 𝑢𝑑2𝑚𝑎𝑥 = 3, ..., 𝑢𝑑𝐾 𝑚𝑎𝑥 = 3(𝐾−1)

𝑢𝑑 1 1 1 1 1

𝛿𝐵 −

1 (𝛿𝐴 + 𝛿𝐶 ) 2

)2 +

3 2 (𝛿𝐴 − 𝛿𝐶 ) 4

(7)

Table I provides all redundant feeding possibilities and the corresponding number of level of the generated output voltage, and the asymmetry quality factor in each case. Three sets of feeding solutions can be found in order to generate an output voltage with 15 levels:

(4)

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(𝑢𝑑1 , 𝑢𝑑2 , 𝑢𝑑3 ) ∈ {(1, 3, 3) ; (1, 2, 4) ; (1, 1, 5)}

(8)

The set of dc-voltage values (1, 1, 5) represents the worst case selection to generate an output voltage with 15 different levels. The set of dc-voltage value (1, 3, 3) has the advantage to have two identical partial cells, compared to the set (1, 2, 4).

up5

1.5 0 −1.5 up4

1.5 0 −1.5 p3

1 u

III. TARGETING 20 MW WITH FIVE CELL RE - GENERATIVE

0 −1

ASYMMETRICAL MULTILEVEL CONVERTER u

p2

1

B. Load side performance assessment Considering the 500 𝑣 dc-link voltage of the flying cell as the voltage reference, the following 𝑝.𝑢. characteristics can be deducted: 𝑢𝑑1 = 1, 𝑢𝑑2 = 2, 𝑢𝑑3 = 2, 𝑢𝑑4 = 3, 𝑢𝑑5 = 3. The uniform step conditions Eq.1 are fulfilled and the number output voltage value at the nominal operating frequency is 𝑁 = 2(1 + 2 + 2 + 3 + 3) + 1 = 23. For reference, a symmetrical converter configuration needs a series-connection of 11 cells per phase to achieve the same result. Therefore the suggested drive shows a part count reduction of 65% to achieve a comparable output voltage waveform. Using the switching function approach, each cell 𝑗 fed by a dc-link voltage 𝑢𝑑𝑗 can generate an output voltage 𝑢𝑝𝑗 , such that: 𝑢𝑝𝑗 = 𝑠𝑗 ∗ 𝑢𝑑𝑗 , where 𝑠𝑗 ∈ {+1, 0, −1}

(9)

The partial cells will generate output voltages as follow: 𝑢𝑝1 ∈ {+1, 0, −1} ; 𝑢𝑝2 , 𝑢𝑝3 ∈ {+2, 0, −2} , and 𝑢𝑝4 , 𝑢𝑝5 ∈ {+3, 0, −3}

(10)

Redundant switching states can be used to optimize the control strategy of the inverter.

0 −1

0.5 0 −0.5

5 upha

The proposed asymmetrical multilevel converter is shown in Fig.2 with a series connection of five H-bridges per phase in a three-phase converter configuration. Four cells are fed through a re-generative three-phase bridge. One cell is not connected to the grid. It provides only reactive power to the load, and contributes to have a uniform step output voltage. It has a DC capacitor voltage of 500 𝑣, which needs to be kept stable across the converter operating range. Two cells have a DC-link voltage of 1000 𝑣, and two other 1500 𝑣. There are several possibilities to improve the grid side current harmonic contain of that converter. The simplest one is to feed each cell through a regular three-phase transformer without voltage phase-shift. Harmonics cancellation could be done through a phase-shift of the reference voltage of each active rectifier, with an expectation of 36-pulse grid current. The 𝐹 𝐹 1200𝑅12𝐾𝐸3 power module of INFINEON is selected for the 1 𝑝.𝑢 cells; the 𝐹 𝐹 1200𝑅17𝐾𝐸3 module for the 2 𝑝.𝑢 cells. And the 𝐹 𝑍1200𝑅33𝐾𝐹 2𝐶 module for the 1.5 𝑝.𝑢 cells. Parallel connection of modules is needed to attempt to drive a 15 𝑀 𝑊 motor at 6.6 𝑘𝑣, with redundancy to achieve 20 𝑀 𝑊 in case of failure of a full thread. The possible challenge on this converter is the dc-link voltage stabilization of the smallest cell. The availability of the system can be increased with a control and modulation strategy, which allow the converter to operate with faulty partial cells.

up1

A. Power part topology

0 −5 0

Fig. 3.

5

10 time(ms)

15

20

Partial cell commutations, amplitude modulation index 𝑚𝑎 = 1.11

Assuming stabilized dc-link voltages all over partials cells. Assuming an open-loop control strategy at nominal operating point, Fig.3 shows the output voltage of each partial cell, and the line-to-neutral with 23-levels. The simulated modulation strategy is the regular phase disposition sine-triangle PWM with homopolar component injection [21]; only the 500 𝑣cell has a high-switching frequency; the remaining cells are switching at fundamental frequency. C. Estimation of semi-conductor dynamic and static losses Assuming an output frequency of 50 𝐻𝑧 at nominal operating point and switching frequencies of 1200 𝐻𝑧 for partial cell fed by a 1 𝑝.𝑢 cell, 500 𝐻𝑧 for the other cells. Assuming a maximum junction temperature of 125𝑜 𝐶 and a case temperature of 80𝑜 𝐶 at unity power factor, possible dynamic and static losses of the converter can be approximated, using IPSOSIM [22]. The results on the load and grid sides are summarized in tables Tab. II and Tab. III. The redundant switching states of the converter can be used to optimize the switching sequence of the overall converter and to stabilize the capacitor voltage of the 1 p.u cell. The switching losses of the 3 p.u cell could also be minimized using the same degree of freedom. IV. C ONTROL STRATEGY A. Optimized inverter switching strategy The overall high-level control management architecture is shown in Fig.4. The optimal future state for minimal switching losses for a given operating point is calculated. All possible states, which produce the desired output voltage are precalculated and arranged in a state matrix, where each row represents one state. The difference between the actual and the desired state matrices contains integers between −2 and +2. Each entry in the matrix indicates whether the corresponding cell will change its output voltage assuming the corresponding future state is chosen. However for the losses, it does not matter if the output voltage of a cell changes from negative to positive or from positive to negative, therefore the absolute value of each entry is taken.

3685

3 𝑝.𝑢 44 117 113 1670 1944

p5

1.5 0

u

2 𝑝.𝑢 26 65 75 941 1107

−1.5 1.5 p4

1 𝑝.𝑢 16 218 86 785 1105

0

u

DC-voltage Dynamic losses Diode(w) Dynamic losses IGBT (w) Static losses diode (w) Static losses IGBT (w) Total losses (w)

−1.5 p3

1 0 −1 1 u

p2

3 𝑝.𝑢 260 791 1102 167 1430

0 −1

p1

0.5 0 −0.5

u

2 𝑝.𝑢 88 199 729 92 912

5 pha

DC-voltage Dynamic losses Diode(w) Dynamic losses IGBT (w) Static losses diode (w) Static losses IGBT (w) Total losses (w)

u

TABLE II L OAD SIDE DYNAMIC AND STATIC LOSSES

0

u

TABLE III G RID SIDE DYNAMIC AND STATIC LOSSES

−5 0

Local controller

10 time(ms)

15

20

Partial cell commutations, amplitude modulation index 𝑚𝑎 = 0.85

Fig. 5. Local controller 1

5

Local controller p5

1.5 u

0 −1.5

p4

1.5 u

0 −1.5

Local controller

Local controller X

1 u

p3

Local controller

Thread controller (Slave) + Modulation

0 −1

u

p2

1

B. Small cell capacitor voltage stabilization method Grid connected converters can be controlled using dqcontrol strategies as shown in Fig. 7. For the floating cell, the power required to charge the capacitor comes from the other cells or from the machine. That cell delivers only reactive power. Table IV shows all the possibilities of power flow

u

pha

The resulting matrix is multiplied with a weighting column vector. The values of the vector are chosen such that the states of the cells that are preferably switched are multiplied with a small number, and the cells that are preferably not switched are multiplied with a higher number. From this calculation, a vector with the quality of the future output state is found. To find the optimal future state, the position with the smallest number in the vector has to be found. The weighting vector can dynamically be adjusted to meet different cost functions. As an example, if the temperature of a converter cell is too high, the priority of the concerned cell is changed by adjusting the weighting vector. Simulation results shown in Fig. 3, have been obtained using the described switching strategy, with the weighting vector chosen such that the 1 p.u. cell is switched preferably. As it can be seen only the 1 p.u. cell has a high switching frequency, and the other cells are switching at rated frequency. Figures 5 and Fig. 6 show supplementary results for modulation indexes 𝑚𝑎 = 0.85 and 0.56. These results also highlight the reduced commutation of partial cells with higher dc-link voltages.

p1

High-level control management architecture

u

Fig. 4.

0 −1

0.5 0 −0.5

2 0 −2 0

Fig. 6.

5

10 time(ms)

15

20

Partial cell commutations, amplitude modulation index 𝑚𝑎 = 0.56

according to switching states and the current direction. The cell has an intrinsic redundant state to deliver an output voltage equal to zero. For a given current flow direction, the only controlled parameter is the output voltage of the cell, which can be adjusted to keep the power flow within a desired fluctuation limit. The limit can be defined by upper and lower boundaries of the cell voltage as shown in Fig.8. If the measured voltage requests no power variation, the only criterion is to switch preferably the small cell. To control the voltage tendency, redundant states are used. Thus, from all possible states that generate the desired converter output voltage, the ones with the desired 1 𝑝.𝑢.-cell output voltage are picked out. However, sometimes there is no state that can generate the desired 1 𝑝.𝑢.-cell output voltage. In that case, all the available states are used. Once the states are chosen, the algorithm to minimize the switching losses of

3686

510

Eb Ec

L ~

L

~

L

p1

icap

~

u

Ea

500

VDC 490 0.14

0.142

0.144

0.146 Time (s)

0.148

(a) DC-link voltage of the 1 𝑝.𝑢 cell 1.5

Gate Drive

p5

PLL

VDC

abc

0 −1.5

i ed1

Current Controller

p4

1.5 0

u

Vgrid

i eq1

u

dq

Reactive Power Controller

*

−1.5

i ed1

1

DC-link voltage Controller

up3

*

i eq1

0 −1

V *dc

1 up2

Q*

0 −1

Implemented grid side controller configuration u

p1

Fig. 7.

Cell power

0.5 0 −0.5 0.14

0.142

0.144

P>0

0.146

0.148

Time(s)

P=0

(b) Corresponding cell output states

Cell voltage

Fig. 9. Small cell voltage control with 𝑉𝑙𝑖𝑚− = 495 𝑉 and 𝑉𝑙𝑖𝑚− = 505 𝑉 . Between the two limit values, the voltage is not controlled.

P0 Fig. 8.

Concept of the floating cell (1𝑝.𝑢. cell) voltage control

I0 𝑃𝑐𝑒𝑙𝑙 < 0, 𝑉 ↘ IL

𝑃𝑐𝑒𝑙𝑙 > 0, 𝑉 ↗ IL Vout

Vout

V 0, 𝑉 ↗ IL

𝑃𝑐𝑒𝑙𝑙 < 0, 𝑉 ↘ IL Vout

Vout

V=0 𝑃𝑐𝑒𝑙𝑙 = 0, 𝑉 →

𝑃𝑐𝑒𝑙𝑙 = 0, 𝑉 →

TABLE IV P OWER FLOW IN 1 P. U . CELL

C. Challenges of the proposed topology 1) Operating range challenge: If the fluctuation window is taken too tight, the switching solicitation of the IGBT will increase. That behavior points out one limitation, if the converter is operating at maximum modulation index. In that particular case, there is no redundancy to generate the two extreme voltage levels of the converter: +/ − 5.5 𝑘𝑉 and +/ − 5 𝑘𝑉 . For 5.5 𝑘𝑉 output voltage, all cells have a positive output voltage. For 5 𝑘𝑉 , the 3 𝑝.𝑢. and the 2 𝑝.𝑢. cells have a positive output voltage, and the 1 𝑝.𝑢. cell output voltage is zero. In motoring mode, the current is positive when the voltage is maximum. The cell voltage therefore decreases. This is primarily the case for a power factor close to one. And there

is only one possible switching sequence to two extreme values of the output voltage. When the voltage is minimum, the current is also negative. The 1 𝑝.𝑢. cell output voltage is either zero or negative, and hence the voltage also decreases. If the modulation index is increased, the converter output voltage is pushed towards the maximum and the minimum output voltage. The cell output voltage of the 1 𝑝.𝑢. cell can be chosen during a small fraction of one period only. Therefore, if the voltage magnitude becomes too high, the voltage decreases (increases) if the machine is in motoring (generating) mode.

3687

500

Line-to-neutral output voltage (kV)

1p.u. cell voltage

6 495 490 485 0.14

0.141

0.142

0.143

0.144

0.145 0.146 Time (s)

0.147

0.148

0.149

2

0

-2

1 0 −1 0.14 1

-4

0.142

0.144

0.146

0.148

0.142

0.144

0.146

0.148

0.142

0.144

0.146

0.148

0.142

0.144

0.146

0.148

0

-6

−1 0.14 1 0 −1 0.14 1

0

0.2

0.4

0.6

0.8

1

Time

Fig. 11. chosen

During the time colored in gray, the 1p.u. output voltage can be

0 −1 0.14 1

500 1p.u. cell DC−link voltage

switching state 1p.u. cell

switching state 2p.u. cell

switching state 2p.u. cell

switching state 3p.u. cell

switching state 3p.u. cell

(a) DC-link voltage of the 1 𝑝.𝑢 cell

4

0 −1 0.14

0.142

0.144

0.146

0.148

450

400

time(s) 350

0

0.05

0.1

0.15

Time (s)

(b) Corresponding cell output states

1p.u. cell DC-link voltage with 𝑚𝑎 = 1.1547

Fig. 12.

Fig. 10. Small cell voltage control where the voltage is kept constant between the two limits if possible

15

BC

Figure 11 shows the output waveform for maximum modulation index (𝑚𝑎 = 1.1547). During the time colored in green, the 1 𝑝.𝑢. output voltage can be chosen because there are redundant states. However, during the time limits colored in red, the 1 𝑝.𝑢. cell voltage is fixed by the output voltage of the converter. The 1 𝑝.𝑢. cell DC-link voltage with a modulation index of 𝑚𝑎 = 1.1547 = 𝑚𝑎𝑚𝑎𝑥 is shown in Fig. 12. Based on this behavior, we therefore recommend to operate this converter at reduced modulation index, where the extremum output voltage values are not needed. 2) Availability Challenge: The part count of the proposed asymmetrical converter is high, therefore, the probability of failure is also high. Equation 2 can be written in term of contribution of each partial cell 𝑗, such that:

10

AB

AC

2 beta

5

3

1

0

−5

−10

−15 −15

−10

Fig. 13.

−5

0 alpha

5

10

15

Reduction due to failed cells

V. AVAILABILITY ENHANCEMENT 𝑁=

𝐾 ∑

𝑁𝑗 + 1, where 𝑁𝑗 = 2 ∗ 𝑢𝑑𝑗

(11)

𝑗=1

From equation 11, it can be seen that, each dc-link voltage 𝑢𝑑𝑗 (p.u value of the voltage 𝑈𝑑𝑗 in volts, referred to the smallest cell voltage 𝑈𝑑1 ) has a contribution 𝑁𝑗 to the final number of levels of the output voltage. This contribution is twice the p.u value of that dc-link voltage. The previous equation shows that in case of failure, the number of level in that phase will be reduced. This reduction has a very high impact if the fault occurs in the partial cell having the biggest dc-link voltage. The phase having a fault in one of the 3 𝑝.𝑢-cells will not be able to generate six values (three positives and three negatives). This limitation represents a huge drawback for industrial applications of the proposed topology. In the next section, a new control method is proposed, in order to compensate voltage reduction in case of failure and to enhance the availability of the converter.

A. Maximum modulation index with failed cells A converter with faulty cells reduces the number of possible output states. If the converter output voltages are not symmetric, the hexagon with the output phasor is not equilateral. To find the inner circle with the biggest radius, the distance between the center and the closest hexagon side has to be found. Details of that method are given in [24]. The 𝛼-𝛽 frame is divided in three sectors as shown in Fig.13. Failures in A and C reduce the size of the hexagon in sector one, failures in B and C reduce the sector two, and failures in A and B sector three. On the lower half of the hexagon, the sectors and the reduction of levels are exactly the same. Therefore only the upper half is considered. The maximum line-to-neutral voltage for a balanced system with faulty cells is calculated as follow [24]: 𝑚𝑎𝑥(𝑉𝐿𝑁 ) =

√

3 (𝑛 − 1 − 𝐹𝑚𝑎𝑥 ) 𝑉𝑚𝑎𝑥𝐿𝐿

(12)

𝐹𝑚𝑎𝑥 is the greatest inner circle of the hexagon such that:

3688

5.5kV

3kV

Avg(min, max)

Vmax -Vmax

DQ Vd,Vq

Fig. 14. phases

Vmax

Vabcref

ABC

Re-balancing method without online evaluation of angles between

1kV

1kV

1kV

1kV

1.5kV

1.5kV

1.5kV

1.5kV

LN Voltage

(13)

𝐹1 ..𝐹3 are the number of level reduction per sector; 𝑊𝑝 is the number of level lost in the phase 𝑝, 𝑝 = 𝑎, 𝑏, 𝑐:

5.5kV

Example of failures on leg A

5 0 −5

B. Re-balancing the three-phase system

C. Increasing availability by increasing the motor current In the design requirements, the converter has to feed a 60 𝑀 𝑊 12-phase machine. Therefore, each three-phase converter unit has to be able to deliver 15 𝑀 𝑊 . However, the system should be designed such that even if one thread fails,

2 0 −2

1 0 −1

LL Voltage

10 0 −10

0

5

10

15

20 25 Time (ms)

30

35

40

LN Voltage

Fig. 16. Top: LN voltage after failure as shown in Fig.15a; Middle left: Fist homopolar according to Fig.14a Middle right: second homopolar according to Fig.14; Bottom: Balanced line-to-line voltage after new modulation strategy. 5 0

Homopolar 2

Homopolar 1

−5

LL Voltage

A method to restore balanced voltage to a three-phase system is described in [25]. The voltage reference values are given on a rectangular reference system DQ. The magnitude of the DQ-voltage takes into account the limitation by the maximum modulation index calculated in the previous section. The angles between the A-phase and the B-phase vector and between the A-phase and C-phase vector are 𝛽 and 𝛾 respectively, and calculated according to [25], and they need to be evaluated in real time. In the proposed method, we avoided the online evaluation of the angles 𝛽-𝛾. A simple limitation is added to the converter reference voltages considering the unachievable number of levels at the converter output. A peak-reduction homopolar component is added. All the phase references still have the same magnitude, the phase leg with failed cells is not treated in a special way. Therefore in the phase leg with failed cells, the reference exceeds the maximum output voltage, whereas in the other cells, the reference does not attain the maximum output voltage. Another homopolar component is added, such that the instantaneous voltage in the phase leg with failed cells does not exceed the maximum output voltage. This is implemented with limitations, which measure the difference between the actual reference voltage and the maximum/minimum output voltage. If the reference value lies in the range between the maximum and the minimum output voltage, that difference is zero. The difference is finally added as an homopolar component to the three reference voltages. This method is summarized in Fig.14. Assuming a failure on leg A as shown in Fig.15 (left). The generated unbalanced line-to-neutral voltages are shown in Fig.16 (top), the two homopolar components added to the references are illustrated in the middle and finally, the re-balanced line-to-line voltage according to the method described in this section are shown on the bottom. Similar results are shown in Fig.17 for the failures in phase A as shown in the right of Fig.15.

Homopolar 2

(14) Homopolar 1

𝐹1 = 𝑊𝑎 + 𝑊𝑐 ; 𝐹2 = 𝑊𝑏 + 𝑊𝑐 ; 𝐹3 = 𝑊𝑎 + 𝑊𝑏

5.5kV

3kV 0.5kV

Fig. 15.

𝐹𝑚𝑎𝑥 = max (𝐹1 , 𝐹2 , 𝐹3 )

5.5kV

0.5kV

2 0 −2

1 0 −1

8 0 −8 0

5

10

15

20 25 Time (ms)

30

35

40

Fig. 17. Top: LN voltage after failure as shown in Fig.15b; Middle left: Fist homopolar according to Fig.14b Middle right: second homopolar according to Fig.14; Bottom: Balanced line-to-line voltage after new modulation strategy.

the converter still delivers 60 MW. Therefore, each thread has to be able to deliver 20 MW. Each thread is a 15-cell converter. With the permutations, there is a total of 576 possibilities of failure of up to three cells. Out of the 576 possibilities, 78 will reduce the voltage under 5.24 𝑘𝑉 . All the possibilities in which the converter is not able to generate 5.24 𝑘𝑉 , have three faulty cells. In

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Ref.

1𝑝.𝑢. cell

2 𝑝.𝑢. cell

3 𝑝.𝑢. cell

Maximum voltage Chosen voltage

720𝑉 500𝑉

1080𝑉 1000𝑉

2160𝑉 1500𝑉

TABLE V DC- LINK VOLTAGE LIMITATIONS WITH CHOSEN IGBT’ S

all possibilities where one or two cells failed, the converter is still able to generate the required voltage. This is achieved by increasing the dc-link voltage fo the 3 𝑝.𝑢. cells from 1, 500 𝑉 to 2, 000 𝑉 . The chosen IGBT’s are able to conduct 1.1 𝑘𝐴. With two IGBT’s in parallel, the RMS-current is 2.2 𝑘𝐴. Therefore, the minimum fundamental RMS voltage needed to ensure the proper operation of the converter is 3.03 𝑘𝑉 . The corresponding line-to-line RMS voltage is 5.24 𝑘𝑉. The DC voltage of each IGBT is also chosen with some margin, as shown in V. This operating approach would be applicable to reduce the shutdown time of the converter. Supplementary results and details can be found in [26]. VI. C ONCLUSION This paper has shown an attempt to increase the penetration of the voltage source inverter technology in high-power variable speed applications, such as oil and gas. The proposed solution combined the multi-rectifier/inverter approach applied to LCI feeding multi-phase machines, and the multithread configuration of VSI based on interleaving approach. It also combined existing cascaded VSI topology and the hybrid asymmetrical multilevel to drive a motor up to 60 MW in normal operation. Several control solutions have been suggested to increase the availability of the system which can be built using commercially available IGBTs. R EFERENCES [1] C. Meckel Mechanical damage of a subsynchronous cascade drive due to torsional resonance, IEEE-IAS/PCA Cement Industry Technical Conf., pp. 133-150, 2001. [2] K. S. Smith, L. Ran, Torsional Resonance Risk Management in Islanded Industrial Power Systems Supplying Large VFDs, IEEE Trans. on Ind. Applicat. Vol. 44 no. 6, pp. 1841 - 1850, Nov.-Dec 2008. [3] S. Sihler, S. Schramm, J. Song-Manguelle, P. Rotondo, S. Del Puglia, E. Larsen Torsional Mode Damping For Electrically Driven Gas Compression Trains in Extended Variable Speed Operation Proc. of 38𝑡ℎ Annual Turbomachinery Symposium, Houston, TX, September 2009. [4] S. Schramm, S. Sihler, J. Song-Manguelle, P. Rotondo, Damping Torsional Interharmonic Effects of Large Drives IEEE Trans. on Power Elect. vol. 25 no. 4, pp. 1090 - 1098, Apr. 2010. [5] S. Schröder, P. Tenca, et al. Modular High-Power Shunt-Interleaved Drive System: A Realization up to 35 MW for Oil & Gas Applications, IEEEIAS 43rd annual meeting, Edmonton, Canada, Oct. 2008. [6] Asirobicon, Propulsion revolution, Marine News, no. 3, 2003.

[7] P. Lezana, J. Rodriguez, M. Perez, J. Escobar, Input Current Harmonics in a Regenerative Multicell Inverter With Single-Phase PWM Rectifiers, IEEE Trans. Indust. Elect., vol. 56 no. 2, pp. 408 - 417, Feb. 2009. [8] P. W. Hammond, A new approach to enhance power quality for medium voltage AC drives, IEEE Trans. on Ind. Applicat. vol. 33, no. 1, , pp. 202-208, Jan. Feb. 1997. [9] P. Lezana, J. Rodríguez, D. A. Oyarzun, Cascaded multilevel inverter with regeneration capability and reduced number of switches, IEEE Trans. Indust. Elect., vol. 55, no. 3, pp. 1059 - 1066, Mar. 2008. [10] K. Corzine, Y. Familiant, A new cascaded multilevel H-bridge drive, IEEE Trans. on Pow. Elect. vol. 17, no. 1, pp. 125-135, Jan. 2002. [11] P. N. Tekwani, R. S. Kanchan, K. Gopakumar, A Dual Five-Level Inverter-Fed Induction Motor Drive With Common-Mode Voltage Elimination and DC-Link Capacitor Voltage Balancing Using Only the Switching-State Redundancy - Part I & II, IEEE Trans. on Ind. Elect. vol. 54, no. 5, pp. 2600-2617, Oct. 2007. [12] A. Rufer, M. Veenstra, K. Gopakumar Asymmetric multilevel converter for high resolution voltage phasor generation, European Conf. on Power Elect. and Appl., Lausanne, Switzerland, Sept. 1999. [13] J. Song-Manguelle, S. Mariethoz, M. Veenstra, A. Rufer Generalized design principle of a uniform step asymmetrical multilevel converter for high power conversion, European Conf. on Power Elect. and Applications, Gratz, Austria, 2001. [14] S. Mariethoz, A. Rufer Design and control of asymmetrical multi-level inverters, Conf. IEEE Indust. Elect. Soc. IECON, 2002. [15] J. Song-Manguelle, A. Rufer Multilevel inverter for power system applications : Highlighting asymmetric design effects form a supply network point of view, IEEE Canadian Conf. on Elect. and Computer Eng., Montreal, Canada, proc. Vol. 1, pp. 435-440, May 2003. [16] J. Song-Manguelle, Asymmetric multilevel converters fed by multisecondary multi-winding low-frequency transformers: Reactions on the supply network PhD dissertation, Swiss Federal Institute of Technology, no. 3033, Lausanne, Switzerland, 2004. [17] C. Rech, J. R. Pinheiro, Hybrid Multilevel Converters: Unified Analysis and Design Considerations, IEEE Trans. Ind. Elect., vol. 54, no. 2, pp. 1092-1104, April 2007. [18] C. Rech, J. R. Pinheiro, Line current harmonics reduction in multipulse connection of asymmetrically loaded rectifiers, IEEE Trans. Ind. Elect., vol. 52, no. 3, pp. 640-652, Jun. 2005. [19] M. Veenstra, A. Rufer, Control of a hybrid asymmetric multilevel inverter for competitive medium-voltage industrial drives, IEEE Trans. on Ind. Appl., Vol. 41 no. 2, pp. 655-664, 2005. [20] M. Veenstra, A. Rufer, Non-Equilibrium State Capacitor-Voltage Stabilization in a Hybrid Asymmetric Nine-Level Inverter: Non-Linear ModelPredictive Control, EPE Journal : European Power Electr. and Drives Association Journal, Vol. 15, no. 1, pp. 28-35, 2005. [21] G. Carrara, S. Gardella, M. Marchesoni, R. Salutari, G. Sciutto A new multilevel PWM method: a theoretical analysis, IEEE Trans. Pow. Elect., vol. 7, no. 3, pp. 497-505, July. 1992. [22] Infineon, Dimensioning program IPOSIM for loss and thermal calculation of Infineon IGBT modules, www.infineon.com [23] N. Schibli, T. Nguyen, A. Rufer A Three-Phase Multilevel Converter for High-Power Induction Motors IEEE Trans. Pow. Elect., vol. 13, no. 5, pp. 978-986, Sept. 1998. [24] S. Wei, B. Wu, F. Li, X. Sun Control method for cascaded H-bridge multilevel inverter with faulty power cells APEC-03, Applied Power Elect. Conf. and Exibition proc.vol.1, pp. 261-267., 2003. [25] P. W. Hammond, Enhancing the reliability of modular medium-voltage drives IEEE Trans. Indust. Elect., vol. 9 no. 5, pp. 948 - 954, Oct. 2002. [26] T. Thurnherr, Modulation and control of re-generative asymmetric multilevel converter for high-power medium voltage variable speed drive system Master thesis, Swiss Federal Institute of Technology, EFPL, Lausanne Switzerland, 2006.

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