[00] levi, e. a six-phase wind energy induction generator system with series-connected dc-links

A Six-Phase Wind Energy Induction Generator System with Series-connected DC-links

H.S. Che1,2, W.P. Hew2, N.A. Rahim2, E. Levi1, M. Jones1, M.J. Duran3 1Liverpool John Moores University, Liverpool, United Kingdom ([email protected], [email protected])

2University of Malaya, Kuala Lumpur, Malaysia ([email protected], [email protected], [email protected]) 3University of Malaga, Malaga, Spain ([email protected])

Abstract—The paper presents a study of a six-phase wind

energy conversion system (WECS) with series-connected dc-links. The structure of the generation system requires the dc-link voltages to be balanced at the generator’s side. To achieve this, it is shown that a dc-link voltage balancing controller can be realised by exploiting the extra degrees of freedom provided by the xy plane of the six-phase machine. To facilitate the controller’s implementation, an alternative modified transformation matrix is also suggested. The feasibility of the studied system, including the operation of the dc-link voltage balancing controller, is verified using Matlab/Simulink simulations.

Keywords—multiphase machines, six-phase, wind energy conversion system, asymmetries.

I. INTRODUCTION

Compared with conventional three-phase machines, multiphase machines with sinusoidal spatial magneto-motive force distribution have lower space harmonics, greater fault tolerance, lower pulsating torque, and lower per phase power ratings for given power [1]. Multiphase generators have been studied much less than multiphase variable-speed drives and this remains to be an interesting topic, especially for WECS. In particular, multiphase machines with multiple three-phase windings are very convenient for WECS and several studies, employing asymmetrical six-phase [2–5] and nine-phase generators [6], have been conducted recently. There is also a commercialised wind energy conversion system offered by Gamesa, using eighteen-phase generator with six back-to-back three-phase converters [7]. The modularity of three-phase windings in multiple three-phase winding machines can take advantage of the well established three-phase technology, allowing the use of off-the-shelf three-phase converters.

Due to the modularity of the converters, different configurations are possible, giving generation systems of different topologies. Fig. 1 shows several structures for wind energy generation systems based on a six-phase generator. Conventional multiphase generation systems [2–4] have the generator side-converters connected in parallel, as depicted in Fig. 1(a). In [5], a generation system with series-connected dc-links, as shown in Fig. 1(b), was presented. Two three-phase converters are cascaded in series to give a higher dc-link voltage, and a three-phase three-level neutral point clamped (NPC) converter is used as the grid-side converter in back-to-back manner with the generator-side converters. The use of the back-to-back topology allows balancing of dc-link voltages directly by the grid-side NPC converter.

As discussed in [8], remote offshore wind farms favour the use of dc grids for power transmission. In such a case, the generator-side converters and the grid-side converter are located far apart, and interconnected by a dc-grid consisting of HVDC transmission lines with several dc-dc converter stages [9]. Generator-side converters with series dc-links are still advantageous due to the elevated voltage. However, the structure in Fig. 1(b) requires three conductors between the generator-side and the grid-side converters. For this reason, the configuration without the third conductor, shown in Fig. 1(c), is elaborated. This structure requires dc-link voltage balancing to be incorporated into the control of the generator-side converter. The paper shows that this can be achieved by exploiting the additional degrees of freedom, available in a six-phase generator. The grid-side converter is for simplicity taken here as two-level, although it will normally be three-level. This does not affect the validity of the study reported in the paper.

The paper is organised as follows. Section II gives general description of the system, including the control strategies of the generator-side converter and the grid-side converter. Analysis of the generation system with series-connected dc-links and the possible reasons for voltage unbalance are then

Fig. 1. Structures of multiphase (six-phase) wind generation systems.

3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG) 2012

978-1-4673-2023-8/12/$31.00/ ©2012 IEEE 26

given in Section III. In Section IV, an alternative modified transformation matrix, which facilitates implementation of the dc-link voltage balancing controller, is introduced. Finally, simulation results and conclusions are presented in Sections V and VI, respectively.

II. GENERATION SYSTEM DESCRIPTION

A. System Overview In the studied system, Fig. 1(c), the generator used is an

asymmetrical six-phase induction machine, i.e. its two three-phase windings are mutually shifted in space by 30°. The neutral points of the two windings are isolated. As shown in Fig. 1(c), the generator is controlled using the generator-side converters, which consist of two series-connected three-phase two-level voltage source converters. For the grid-side, a two-level voltage source converter is employed. The generator-side and grid-side converters are interconnected via a dc-link. B. Generator Model

Using vector space decomposition (VSD) method [10], the machine’s six phase variables (a1b1c1a2b2c2) can be transformed into stationary reference frame quantities (��xy), which appear in two mutually orthogonal planes. Power invariant transformation is used,

��

�

�

��

�

�

−−

−−−

−−

−−−

=

10

01

10

01

31][

21

21

23

23

23

23

21

21

21

21

23

23

23

23

21

21

yx

Tβα

(1)

The torque and flux producing components are mapped into the �� plane, while the loss-producing components map into the xy plane. Zero-sequence components have been omitted because zero-sequence currents cannot flow due to the isolated neutral points. A rotational transformation is then used to transform the stationary reference frame variables into a synchronously rotating reference frame (dqxy), suitable for vector control:

[ ]��

�

�

��

�

�−

=

11

cossinsincos

ss

ss

yxqd

Dθθθθ

(2)

Here �s is the angle of rotational transformation. The xy quantities are not transformed. Assuming that the reference frame is rotating at an arbitrary speed of �, the model of the induction generator can be described using the following voltage and flux equations in the dq plane (indices s and r indicate stator and rotor quantities, respectively; motoring convention for the positive stator current flow is used):

( )( ) drrqrqrr

qrrdrdrr

dsqsqssqs

qsdsdssds

dtdiR

dtdiR

dtdiRv

dtdiRv

ψωωψψωωψ

ωψψωψψ

−++=

−−+=

++=

−+=

/0

/0

/

/

(3)

qrmqsmlsqs

drmdsmlsds

iLiLLiLiLL

++=++=

)()(

ψψ

(4a)

qsmqrmlrqr

dsmdrmlrdr

iLiLLiLiLL

++=++=

)()(

ψψ

(4b)

Rs and Rr are stator and rotor resistance, while Lls, Llr and Lm are stator- and rotor leakage inductance, and magnetising inductance. Additional stator equations, which describe machine in the xy plane, are:

//dtd�iRvdtdiRv

ysyssys

xsxssxs

+=+= ψ

(5)

yslsys

xslsxs

iLiL

==

ψψ

(6)

For a machine with p pole pairs, the electrical torque, which solely depends on the dq components, is given by:

[ ]qrdsqsdrme iiiipLT −= (7) Finally, equation of rotor motion is

dtdJTT m

meω

=− (8)

where �m is the rotor mechanical speed, J the inertia, and Tm is the mechanical (prime mover) torque.

C. Indirect Rotor Flux Oriented Control (IRFOC) With the VSD model, the six-phase generator can be

controlled using indirect rotor flux oriented control method in a similar manner as a three-phase induction generator [1]. The rotor flux angle, required for the rotational transformation, is calculated from the estimated slip speed and the measured rotor position. With the d-axis aligned to the rotor flux vector, the flux and torque of the machine are controlled by regulating the d- and q-axis currents, respectively. Using a maximum power point tracking (MPPT) algorithm similar to that in [4], the generator’s torque can be controlled according to the varying wind speed, to generate maximum power.

D. Suppression of Asymmetries One important consideration when operating six-phase

generator is the suppression of xy currents. Ideally, if the two windings are supplied with two sets of balanced sinusoidal three-phase voltages, which are symmetrical and phase-shifted by 30°, two sets of balanced three-phase currents of the same amplitude would flow in each winding. In this case, there will be no current flowing in the xy plane (except for the switching harmonics related ripple current). However, if there are some phase and/or magnitude deviations from this ideal condition, xy currents will flow, and the machine is considered to have asymmetries. As shown in [11], asymmetries due to pulse width modulation (PWM) of the voltage source converter can be minimised by choosing suitable modulation technique, such as double zero-sequence injection method. However, the compensation of asymmetries due to machine and/or supply is not so straightforward. A comprehensive analysis of the operation of a six-phase induction machine with machine and/or supply asymmetries was presented in [12]. Conventional control method which utilises only one pair of dq current controllers is incapable of suppressing the xy currents, so additional current controllers must be added.

Several methods have been proposed in line with this. In [13] and [14], it was suggested to control a six-phase machine based on dual-dq model: the two windings are treated as


27

separate three-phase windings and two sets of dq current controllers are used. Some other authors prefer to control the machine based on the VSD model (3)-(6), with two sets of controllers used: one for the dq plane, and another for the xy plane. In [15], xy current control was done in the stationary reference frame, with the xy currents regulated by two additional resonant controllers. In [16], synchronous reference frame xy current controllers for five-phase induction machine were considered. A modified rotational transformation matrix

[ ]��

�

�

��

�

�

−

−=

ss

ss

ss

ss

dq

dqdq

yxqd

D

θθθθ

θθθθ

cossinsincos

cossinsincos

(9)

was introduced to rotate the xy plane at the same synchronous speed as the dq plane. PI controllers are then used to compensate the asymmetries, making this method intuitively simple and easy for implementation. The references for xy controllers are set to zero to eliminate the asymmetries. Structure of the current control scheme, based on (9), is shown in Fig. 2, where ed , eq are the feed-forward terms for IRFOC.

In this investigation, this synchronous xy current control method is adopted, with some modifications to the transformation matrix and an addition of a dc-link voltage balancing controller. Details of the controller are described in Section IV.

qe

deqsi

*dsi

dsi

*qsi

[ ] 1−dqD [ ] 1−T

[ ]dqD [ ]T

xdqsi

ydqsi

111 cbai

0** == ydqsxdqs ii

222 cbai

Fig. 2. Current control with modified transformation (9) and additional PI

controllers for xy current suppression [16].

E. Voltage-oriented Control (VOC) For the grid-side converter, the well known voltage-oriented

control (VOC) method is employed [17]. With the d-axis of the control reference frame aligned to the grid voltage vector, active and reactive powers delivered to the grid can be controlled by regulating d-axis and q-axis currents, respectively. The dc-link voltage can then be kept constant by controlling the active power.

III. ANALYSIS OF SERIES-CONNECTED DC-LINKS

To explain the operation of the generation system with series-connected dc-links, the system can be simplified as shown in Fig. 3, with the converters represented as controllable current sources. By using Kirchhoff’s current law for points W and Z, the generator-side converters’ currents can be written as

232131 capdcdccapdcdc IIIIII −−=−−= (10)

The currents Idc1 and Idc2 consist of two components: a common component (-Idc3) and a differential component (Icap1 and Icap2). At any time instant, the common current component will be drawn from both generator-side converters, while the instantaneous difference between the converters’ currents and the common current will be supplemented by each of the converter’s capacitors. Ideally, the two sets of machine windings are identical, so the average converter current should be the same despite the spatial difference. Hence, the average capacitor currents should also be the same.

The dc-link voltage balancing depends on the active power balancing between the two converters. The equations for the active powers of the generator-side converters are:

222

111

dcdc

dcdc

VIPVIP

==

(11)

During steady state, the average converters’ currents will be equal. Hence,

2

1

2

1

dc

dc

VV

PP = (12)

If the grid-side converter provides perfect control, the total dc-link voltage will be maintained at a constant value of Vdc. Each individual dc-link voltage is expressed as a sum of its ideal balanced value (Vdc/2) and a deviation from the ideal value (�Vdc1 and �Vdc2). Since the sum of two dc-link voltages is equal to Vdc, the voltage deviations must be equal but of opposite sign, i.e. �Vdc1 = −�Vdc2 = �Vdc. Hence the power equation (12) can be written as:

dcdc

dcdc

VV

VV

PP

Δ−

Δ+=

2

22

1 (13)

Rearranging (13), the voltage deviation can be expressed as a function of the active powers,

221

21 dcdc

VPPPPV ��

��

+−=Δ (14)

As can be seen from (14), the voltage deviation is a direct result of the power imbalance between the two generator-side converters. Under normal circumstances, there should be no

Fig. 3. Simplified circuit diagram for generation system with series-connected

dc-links.


28

power difference between the two windings. However, as discussed in [12], in an event of machine and/or supply asymmetries, power imbalance will occur. This causes the dc-link voltages to drift apart.

IV. DC-LINK VOLTAGE BALANCING CONTROLLER

A. An Alternative Modified Transformation Based on the discussions above, two additional control

aspects must be included in the control of the generator-side converters, i.e. suppression of asymmetries and dc-link voltage balancing. Both objectives are achieved by applying suitable control in the xy plane. In particular, balancing of dc-link voltages is achieved by controlling the power difference between two windings via proper injection of the xy currents. As will be shown in the section with simulation results, suppression of asymmetries is still possible although the xy currents are injected by the dc-link voltage balancing controller.

To develop the dc-link voltage balancing controller, it is important to establish the relationship between xy currents and the power in each winding. With the VSD model, the quantities in the two windings are not explicitly expressed, while the powers of the two three-phase windings now need to be controlled separately. In order to achieve separate power control with the VSD model, it is insightful to at first establish the relationship between dqxy components in the VSD model and the d1q1−d2q2 components in the dual-dq model, which enables separate formulation of winding powers.

To start with, according to the stationary transformation of the dual-dq model, the �� components of the two windings are separately treated as �1�1 and �2�2 currents, which can be given with:

( )( )( )( )222

122

132

2

123

123

32

1

223

223

32

2

121

121

132

1

cba

cb

ba

cba

iiii

iii

iii

iiii

−+=

−=

−=

−−=

β

β

α

α

(15)

Comparison of (15) with (1) shows that the following holds true:

( )( )( )( )212

1

2121

2121

2121

ββ

αα

βββ

ααα

iii

iii

iii

iii

y

x

+−=

−=

+=

+=

(16)

For control purpose, it is more useful to have the control variables in the dq synchronous reference frame, so that they appear as dc quantities and can hence be easily dealt with using PI controllers. For dual-dq model, currents in synchronously rotating frame are given as:

ssqssq

ssdssd

iiiiii

iiiiii

θθθθθθθθ

βαβα

βαβα

cossin cossin

sincos sincos

222111

222111

+−=+−=

+=+= (17)

For the VSD model, using the modified rotational transformation defined in (9), the following is obtained:

( )( )

( ) ( )[ ]( ) ( )[ ]sqqsddydq

sqqsddxdq

qqq

ddd

iiiii

iiiii

iii

iii

θθ

θθ

2cos2sin2/1

2sin2cos2/1

2/1

2/1

2121

2121

21

21

+−++−=

−−−=

+=

+=

(18)

As can be seen from (18), the resulting xdqydq components are not dc quantities. Hence, an alternative modified transformation matrix is introduced,

[ ]��

�

�

��

�

�

−−

=

ss

ss

ss

ss

yxqd

D

θθθθ

θθθθ

cossinsincos

cossinsincos

''

' (19)

Instead of rotating the xy plane at the synchronous speed in the same direction as the dq plane using (9), (19) provides rotation in the inverse (anti-) synchronous direction. With this alternative modified rotational transformation, a more suitable form of xy components can be obtained,

( )( )( )( ) qqqy

dddx

qqq

ddd

iiii

iiii

iii

iii

Δ−=−=

Δ=−=

+=

+=

2/12/1

2/12/1

2/1

2/1

12'

21'

21

21

(20)

Transformed x’y’ components in (20) are now both dc signals and the difference between dq components of the two windings can be controlled using x’y’ components. Positive ix’ will make id1 greater than id2, while positive iy’ makes iq1 smaller than iq2, and vice versa. Thus, power drawn from the two windings can be controlled by the proper injection of ix’y’. Moreover, since dq components are dc quantities, x’y’ will also be dc quantities which allow the use of simple PI controllers. It is also worth noting that, from (20), injecting ix’y’ changes the difference between idq1 and idq2 but does not change the overall flux and torque currents (idq). Hence the injection of ix’y’ will not adversely affect the overall operation of the generator. B. Strucutre of Dc-link Voltage Balancing Controller

There are several ways in which ix’y’ can be injected to change the power difference. Here, the following strategy is adopted: iy’ is injected to manipulate the difference in the active powers, while ix’ is kept at zero, to maintain the same flux current in both windings. Fig. 4 illustrates the current vector variation based on this strategy. Only the case with negative iq is considered, since iq is limited to take only negative values in the generator control.

From Fig. 4, increasing �iq increases iq1, and causes more power to be generated in winding 1. Decreasing �iq will in turn decrease iq1, and reduce power generated in winding 1. On the basis of this reasoning, �iq can be derived from the dc-link voltage difference (Vdc1 – Vdc2). The y’ current reference, iy’

*, is obtained by multiplying �iq with −1, based on (20). Overall structure of the x’y’ current controllers with dc-link voltage balancing controller is given schematically in Fig. 5. The ultimate controller outputs are the references for the x’y’ voltage components.


29

Fig. 4. Current vectors in dq plane (for machine in the generating mode with

motoring convention for positive current flow).

'xi

'yi1dcV

2dcV

*'yi

'xv

'yv

0*' =xi

qiΔ

Fig. 5. Structure of the xy current controllers (red dotted box) and dc-link voltage balancing controller (blue dotted box), based on (19). Decoupling

terms (not shown) can be added to x’-y’ current controllers.

V. SIMULATION RESULTS AND DISCUSSION

A. Matlab/Simulink Simulations The induction generation system is simulated using

Matlab/Simulink to examine the operation. Initially, the system is simulated with just dq current controllers, to visualise the operation of the WECS under ideal operating conditions. Next, asymmetries are introduced in the machine in the second simulation, and the effect on the dc-link voltage drift is observed. In the third simulation, the x’y’ current controllers and the dc-link voltage balancing controller are activated to suppress the asymmetries and achieve voltage balancing. The last simulation is then performed to examine the dc-link voltage balancing for the case when there are no machine/supply asymmetries but there is an initial deviation between the dc-link voltages. Parameters used for the simulation are listed at the Appendix. B. Simulation Results

The first simulation examines the ideal operation (no asymmetries) of the generator system with varying wind speed. With the use of MPPT controller, the generator’s speed reference is varied accordingly, to allow optimal power generation. Variation of the generator’s speed reference and the actual speed are shown in Fig. 6. Once the generator’s speed converges to the reference, the operation is considered to be at the maximum power point and the speed does not change until the next change in the reference. Fig. 7 shows the dq currents of the generator. The flux-controlling d-axis current is well regulated at its rated value, giving rise to a near constant rotor flux in the machine, as depicted in Fig. 8. The torque producing q-axis current is limited to take only negative values, to prevent the machine from operating in the motoring mode. When acceleration is required (in interval t =

0.9 s ~1.1s), the generating electrical torque is clamped to zero so that only the mechanical torque from the wind turbine is used to accelerate the machine.

Fig. 9 and Fig. 10 show the total and the individual voltages of the series-connected dc-links. Both the total and individual dc-link voltages are well regulated at their references (1200V and 600V, respectively). The two dc-link voltages are also well balanced under this ideal operating condition. Fig. 11 shows the balanced six-phase stator currents of the machine, while Fig. 12 shows the balanced three-phase current injected into the grid by the grid-side converter. In this simulation, the same two-level converters are used for machine-side and grid-side converters, but the machine-side converters are operating from a 600V dc-link, while the grid-side converter operates from a 1200V dc-link. This causes the higher ripple in the grid’s currents than in the generator’s currents.

In the second simulation, asymmetries are introduced at t = 0.1s, by adding a 5� resistor in phase a1 only (50% of stator resistance). Figure 13 shows that the total dc-link voltage

0 0.5 1 1.5500

1000

1500

2000

Gen

erat

or S

peed

(rp

m)

Time (s)

Reference speed

Actual speed

Fig. 6. Generator's speed reference and actual speed.

0 0.5 1 1.5-10

-5

0

5

Sta

tor

dq C

urre

nts

(A)

Time (s)

d-axis current

q-axis current

Fig. 7. Stator dq currents of the six-phase generator.

0 0.5 1 1.50

0.5

1

1.5

2

Rot

or F

lux

(Wb)

Time (s)

Fig. 8. Magnitude of rotor flux in generator.

0 0.5 1 1.51190

1195

1200

1205

1210

Tot

al d

c-lin

k V

olta

ge (

V)

Time (s) Fig. 9. Total dc-link voltage.

0 0.5 1 1.5590

595

600

605

610

Dc-

link

Vol

tage

s (V

)

Time (s)

Vdc1

Vdc2

Fig. 10. Individual dc-link voltages.


30

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2-4

-2

0

2

4S

tato

r C

urre

nts

(A)

Time (s) Fig. 11. Stator currents of the generator.

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2-4

-2

0

2

4

Grid

Cur

rent

s (A

)

Time (s)

Fig. 12. Grid-side currents. remains well regulated to the reference value. However, due to the asymmetry, the individual dc-link voltages drift apart, as seen in Fig. 14. The drift varies as the power changes. The additional resistance also causes the imbalance in the windings. Hence, stator currents are unbalanced and have different amplitudes, as depicted in Fig. 15.

Next, the same simulation is repeated, now with current control that includes x’y’ current controllers and the dc-link

voltage balancing controller. Fig. 16 indicates that the individual dc-link voltages are now well regulated and are close one to the other, without any significant drift. The additional control structure, while balancing the dc-link voltages, also suppresses the asymmetries within the system. This is shown in Fig. 17, where the stator currents are seen to be much better balanced, when compared to Fig. 15. The amplitude of currents in winding 1 (blue, green, red) is only very slightly different compared to winding 2 (magenta, cyan,

0 0.5 1 1.51190

1195

1200

1205

1210

Tot

al d

c-lin

k V

olta

ge (

V)

Time (s) Fig. 13. Total dc-link voltage (in the presence of asymmetry).

0 0.5 1 1.5500

550

600

650

700

Dc-

link

Vol

tage

s (V

)

Time (s)

Vdc1

Vdc2

Fig. 14. Individual dc-link voltages (in the presence of asymmetry).

1.4 1.405 1.41 1.415 1.42 1.425 1.43 1.435 1.44 1.445 1.45-4

-2

0

2

4

Sta

tor

Cur

rent

s (A

)

Time (s) Fig. 15. Stator currents showing unbalance due to asymmetries.

0 0.5 1 1.5590

595

600

605

610

Dc-

link

Vol

tage

s (V

)

Time (s)

Vdc1

Vdc2

Fig. 16. Individual dc-link voltages (with x’y’ current controllers and dc-link

voltage balancing controller as in Fig. 5).

1.4 1.405 1.41 1.415 1.42 1.425 1.43 1.435 1.44 1.445 1.45-4

-2

0

2

4

Sta

tor

Cur

rent

s (A

)

Time (s) Fig. 17. Stator currents (with x’y’ current controllers and dc-link voltage

balancing controller as in Fig. 5).

0 0.5 1 1.5-10

-5

0

5

Sta

tor

dq C

urre

nts

(A)

Time (s)

d-axis current

q-axis current

Fig. 18. Stator dq currents (with x’y’ current controllers and dc-link voltage

balancing controller as in Fig. 5).

0 0.5 1 1.50

0.5

1

1.5

2

Rot

or F

lux

(Wb)

Time (s) Fig. 19. Magnitude of rotor flux (with x’y’ current controllers and dc-link

voltage balancing controller as in Fig. 5).

yellow) due to the injected iy’ for dc-link voltage balancing. Fig. 18 and Fig. 19 depict the dq currents and rotor flux of the machine, respectively. These are in essence identical to those in Fig. 7 and Fig. 8, indicating that the overall generator operation has not been affected.

Finally, a simulation is conducted to examine the effect of the dc-link voltage balancing controller when there are no physical asymmetries in the machine/supply. For this purpose, the initial voltages of the dc-links are set to different values at the start of the simulation (640V and 560V, respectively), and dc-link voltage balancing controller is activated at t = 0.1s. Fig. 20 shows that, with the use of the controller, the dc-link voltages converge quickly to equal values and remain balanced afterwards. The x’y’ currents of the machine are depicted in Fig. 21. At t =0.1s, y’ current is injected to balance the dc-link voltages, while x’ current remains close to its reference (zero). After the dc-link voltage difference is eliminated, the y’ current returns to zero since there is no asymmetry in the machine/supply. This is confirmed by the enlarged view of the x’y’ currents in Fig. 22, showing average zero value with no observable low order harmonics (only switching harmonics related ripple is evident). These simulation results confirm that the dc-link voltage balancing


31

controller does not introduce any problems in the operation of the system and is in essence inactive if there are no asymmetries.

0 0.5 1 1.5560

580

600

620

640

Dc-

link

Vol

tage

s (V

)

Time (s)

Vdc1

Vdc2

Fig. 20. Individual dc-link voltages with dc-link voltage balancing controller

and x’y’ current control activated at t = 0.1s.

0 0.5 1 1.5-2

0

2

4

x ′y ′

cur

rent

s (A

)

Time (s) Fig. 21. x’y’ currents with dc-link voltage balancing controller and x’y’

current control activated at t = 0.1s.

0.5 0.502 0.504 0.506 0.508 0.51 0.512 0.514 0.516 0.518 0.52-1

-0.5

0

0.5

1

x ′y ′

cur

rent

s (A

)

Time (s)

x' current

y' current

Fig. 22. Enlarged view of the x’y’ currents.

VI. CONCLUSION An induction generator system with series-connected dc-

links has been discussed in the paper. The operation of the system with series-connected dc-links has been elaborated. It is shown that the power unbalance between machine windings, caused by asymmetries, may result in dc-link voltage unbalance. To design a dc-link voltage balancing controller, an alternative modified rotational transformation matrix is suggested, such that the xy plane is rotated in the inverse synchronous direction. It is shown, by using the analogy with the dual-dq model approach, that application of this transformation enables implementation of a dc-link voltage balancing controller as an integral part of the current control in the x’y’ plane. Simulation results confirm that the proposed controller is capable of performing dc-link voltage balancing and asymmetry suppression.

It should be pointed out that the topology of Fig. 1(c) does have some serious drawbacks. First of all, the series-connection of the dc links seriously affects fault tolerance of the system, since fault in any leg of a converter leads to single-phase operation of a three-phase winding. Hence the improved fault tolerance of the system in Fig. 1(a) is here completely lost. Secondly, since the two neutral points of the generator are isolated and dc links are connected in series, there are two different common mode voltages at different voltage levels. However, the choice of a suitable topology is always a trade-off between different features of the structure.

APPENDIX - SIMULATION PARAMETERS Machine parameters

Rs = 10 � Rr = 6.3 � Lls = Llr = 0.04 H Lm = 0.42 H p = 2 �r = 0.63 Wb (rms)

Controller gains Generator-side dq and x’y’ current controllers:

Kp = 77 Ki = 10000 Generator-side dc-link voltage balancing controller:

Kp = 0.01 Ki = 1.00 Grid-side dq current controllers:

Kp = 30 Ki = 500 Grid-side dc-link voltage controller:

Kp = 1100 Ki = 137500 Other parameters

Vdc = 600 V Cdc = 1500 �F

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[00] levi, e. a six-phase wind energy induction generator system with series-connected dc-links

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