Robust Vector Controllers for Brushless Doubly-FedWind Turbine Generators

Sul Ademi 1, Milutin Jovanovic 2

Faculty of Engineering and Environment, Northumbria University NewcastleNewcastle upon Tyne NE1 8ST, United Kingdom

1 sul.ademi@northumbria.ac.uk2 milutin.jovanovic@northumbria.ac.uk

Abstract—The paper is concerned with field-oriented control(FOC) and vector control (VC) of a promising brushless doubly-fed reluctance generator (BDFRG) technology for adjustablespeed wind turbines with maximum power point tracking. TheBDFRG has been receiving increasing attention because of thelow capital and operation & maintenance costs afforded by usingpartially-rated power electronics and the high reliability of brush-less design, while offering performance competitive to its well-known slip-ring counterpart, a doubly-fed induction generator(DFIG). The preliminary studies have evaluated the performanceof the two parameter independent control algorithms on acustom-made BDFRG under the maximum torque per inverterampere (MTPIA) conditions for the improved efficiency of thegenerator and the entire wind energy conversion system (WECS).

Index Terms—Wind Power, Brushless, Doubly-Fed ReluctanceMachines, Wind Power Generation, Vector Control.

NOMENCLATURE

vp,s primary, secondary winding phase voltages [V]

ip,s primary, secondary winding currents [A]

Rp,s primary, secondary winding resistances [Ω]

Lp,s primary, secondary 3-phase inductances [H]

λp,s primary, secondary winding flux linkages [Wb]

λps, Lps mutual flux [Wb] and 3-phase inductance [H]

ωp,s primary, secondary winding frequencies [rad/s]

ωrm rotor angular velocity [rad/s]

ωsyn synchronous speed = ωp/pr [rad/s]

Pm mechanical (shaft) power [W]

Pp,s primary, secondary mechanical power [W]

Te electro-magnetic torque [Nm]

P,Q primary real [W] and reactive [VAr] power

T ∗e , Q

∗ control reference values for Te and Qσ leakage factor = 1− L2

ps/(LpLs)

I. INTRODUCTION

The brushless doubly-fed reluctance generators (BDFRGs)

have been considered as a viable alternative to conventional

slip-ring doubly-fed induction generators (DFIGs) for grid-

connected wind turbines where only a limited variable speed

capability is required (e.g. typically, a 2:1 range or so around

the synchronous speed) [1]–[3]. The BDFG would provide the

same DFIG cost benefits as obtainable using a smaller inverter

(e.g. around 25% of the machine rating), however, with

additional advantages of higher reliability and maintenance-

free operation by the absence of brush gear.

Fig. 1. A structural diagram of the BDFRG based WECS

Unlike the DFIG, the BDFRG has two standard stator

windings of different applied frequencies and pole numbers,

and a cageless reluctance rotor [4] with half the total number

of stator poles to achieve the rotor position dependent magnetic

coupling between the windings, a pre-requisite for the torque

production [5], [6]. The primary (power) winding is grid-

connected, and the secondary (control) winding is supplied

from a bi-directional (‘back-to-back’) dual-bridge power con-

verter (Fig. 1). The BDFRG offers the prospect for higher

efficiency [7] with simpler modeling and control than its

‘nested’ cage rotor form, the brushless doubly-fed induction

generator (BDFIG) [8]–[11]. Field-oriented control of the pri-

mary reactive power and electromagnetic torque is inherently

decoupled in both the BDFRG and DFIG [12], but not in the

BDFIG [9], [11]. Another important BDFR(I)G merit is the

seemingly superior low-voltage-fault-ride-through capability

to the DFIG, which may be accomplished safely without a

crowbar circuitry owing to the larger leakage inductances and

thus the lower fault current levels [13], [14].

Various control methods have been developed for the BD-

FRG(M) including scalar control [1], [15], field-oriented con-

trol (FOC) [1], [12], [15], [16], direct torque control [15], [17],

torque and reactive power control [18], [19], and direct power

control [20]. Although their comparative qualitative analysis

has been partly made in [15], no similar quantitative study has

been reported specifically on FOC vs VC, and there has been

no or very little work published on true vector control (VC)

of the machine side converter of the BDFRG. In the BDFRG

case, the ‘FOC/VC’ are commonly being referred to as the

primary winding flux/voltage oriented control by analogy to

the stator flux/voltage oriented control of the DFIG [21].

The fact is that with a proper selection of the reference

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frames, the two control techniques indeed become very similar

in nature and dynamic response, especially with larger ma-

chines having lower winding resistances [2], [3]. Nevertheless,

they have differences and performance trade-offs to be pointed

out in this paper using the maximum torque (power) per

inverter ampere (MTPIA) strategy [1], [5], [22] as a ground

for their comparison on a custom built BDFRG prototype. The

motivation for looking at this control objective is the efficiency

gain that can be achieved in wind energy conversion systems

(WECS) by reducing both the secondary winding copper and

inverter switching losses [1], [5] of the generator. Extensive

realistic simulation results taking into account the usual practi-

cal effects (e.g. transducers’ DC offset, noise in measurements,

and a four-quadrant power converter model with space-vector

PWM) are presented to support the discussions.

II. BDFRG OPERATION

The basic angular velocity relationship for the electro-

mechanical energy conversion in the machine with pr rotor

poles and ωp,s = 2πfp,s applied frequencies (rad/s) to the

respective 2p-pole and 2q-pole windings (Fig. 1) is [6]:

ωrm =ωp + ωs

pr=

(1− s) · ωp

p+ q= (1− s) · ωsyn

· · · ⇐⇒ nrm = 60 · fp + fspr

(1)

where the primary and secondary winding are denoted by

the subscripts ‘p’ and ‘s’ respectively, the generalized slip is

s = −ωs/ωp, and ωsyn = ωp/pr is the synchronous speed (for

ωs = 0 i.e. a DC secondary) as with a 2pr-pole wound rotor

synchronous turbo-machine. Notice that ωs > 0 for ‘super-

synchronous’ operation, and ωs < 0 at ‘sub-synchronous’

speeds (i.e. an opposite phase sequence of the secondary to the

primary winding). It is interesting that the two speed modes of

the BDFRG are equivalent to a 2pr-pole induction generator

(i.e. s < 0) despite the quite distinct operating mechanism [6].

The machine instantaneous and acceleration torques, taking

into account friction terms, can be expressed as follows [6]:

Te =3prLps

2Lp(λpdisq + λpqisd) =

3pr2

(λpsdisq − λpsq isd)

· · · = 3pr2

(λpdipq − λpqipd) (2)

Ta = J · dωrm

dt= Te − TL(ωrm)− F · ωrm (3)

where λps is the primary flux linking the secondary winding

(i.e. the mutual flux linkage). The definitions of the 3-phase

self (Lp,s) and mutual (Lps) inductances can be found in [6].

While the primary flux and current space vectors in (2) are in

ωp rotating frame, the corresponding secondary counterparts,

including the λps dq components, are in prωrm − ωp = ωs

frame according to (1) and the BDFRM theory in [6]. This

selection maps the variables into their natural reference frames

where they appear as DC quantities which are easier to control.

Given that λp and λps in (2) are approximately constant by

the primary winding grid connection, torque control can be

achieved through the secondary dq currents in the ωs frame.

Using (1), one can derive the mechanical power equation

showing individual contributions of each machine winding:

Pm = Te · ωrm =Te · ωp

pr︸ ︷︷ ︸Pp

+Te · ωs

pr︸ ︷︷ ︸Ps

= Pp · (1− s) (4)

The operating mode is determined by the power flow on the

primary side i.e. to the grid for the BDFRG when Te < 0in (4). The secondary winding can either take or deliver real

power (Ps) subject to its phase sequence: it would absorb

(produce) Ps > 0 at sub (super)-synchronous speeds. Note

also that (1) and (4) are the same form expressions used for

classical induction machines with Pp and ωs playing the role

of electro-magnetic power and slip frequency, respectively.

III. CONTROLLER DESIGN

A structural block-diagram of the primary voltage/flux angle

and frequency estimation technique in discrete form for real-

time implementation of VC/FOC is shown in Fig. 2. The entire

BDFRG drive system configuration with a generic controller

design is presented Fig. 3. The necessary computations and

sequential control actions being made are largely self-evident

from both the schematics. The functionality of the frame angle

calculation blocks ( A© and B©) in Fig. 3 has been detailed in

Fig. 2. An angular form of (1), which provides a crucial link

between the reference frame d-axis positions (θp,s) and shaft

encoder measurements (θrm) for control is:

ωr = prωrm = ωp + ωs ⇐⇒ θr = prθrm = θp + θs (5)

where ωrm = dθrm/dt is the rotor angular velocity.

For clarification sake, one should also be aware of the

following important points in relation to Figs. 2 and 3:

• A standard phase-locked-loop (PLL) algorithm from the

Simulink� library has been used to retrieve the primary

voltage/flux angular velocities (ωp), but not the respective

stationary α − β frame angles (θ/θp), from the measured

voltages and/or currents (Fig. 2). While a band-pass filter

inside the PLL blocks undoubtedly helps deal with mea-

surement noise and DC offset, it has a well-known down

side of causing inevitable phase delays and inaccurate θ/θpvalues. Better results can be achieved by estimating these

angles directly from the voltage/flux αβ components using

an ‘atan’ function. Despite the noisy instant estimates, the

simplicity and ease of implementation of the latter approach

have been given a preference over optimum performance

obtainable by adaptive, but more complicated, compensa-

tion schemes [23], [24]. The ωp estimation, on the other

hand, is immune to this drift problem as being affected by

incremental and not absolute positions (i.e. ωp ≈ Δθp/Δt).• The starting circuitry is not shown in Fig. 3. If a partially-

rated power converter is used then an auxiliary contactor is

required to short the secondary terminals directly or through

external resistors to avoid the inverter transient over-currents

and allow the BDFRM start as an induction machine. After

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reaching the no-load speed, the contactors are opened and

the converter is connected. Note that this conservative self-

starting method may be feasible in a laboratory environment

on small-scale WECS, like the one considered in this paper,

as in-rush current levels that may occur on the inverter

interchange are acceptable in most cases. However, a large

BDFRG would be accelerated to the synchronous speed

by a pitch controlled wind turbine and a special start-up

procedure, similar to commercial DFIGs [25], should be

followed to provide conditions for smooth synchronization

in order to comply with the stringent grid regulations.

• A conventional vector controller with space-vector PWM of

the active rectifier (e.g. the line-side IGBT converter) has

been implemented (Fig. 3) for control of DC link voltage at

unity line power factor [26], [27].

• The primary real (P ) and reactive (Q) power, as being

reference frame invariant, have been calculated using the

stationary frame voltage (vαβ) and current (iαβ) components

(Fig. 3). This is the least computationally intensive approach

for the controller as unnecessary conversions of vαβ and iαβinto their ds−qs equivalents and the use of time-consuming

trigonometric functions, can be avoided with higher control

rates and superior performance achievable in practice.

• The Y-connected windings have been derived with an iso-

lated neutral point allowing the use of only two current

sensors (e.g. in phases ‘a’ and ‘b’ so, ic = −ia − ib) on

each side (Fig. 3). However, as the primary supply voltages

may not be balanced, having three rather than only two line

voltage transducers is recommended for higher accuracy.

• The Q reference is often set to zero (Q∗ = 0) for the

unity primary power factor but can be any other value of

interest (e.g. for maximum torque per secondary ampere in

this paper) for a given real power setting (P ∗) in open-

loop speed (i.e. power or torque) mode of the machine (Fig.

3). In variable speed drive or generator systems, ω∗rm is the

desired angular velocity. For example, either P ∗ or ω∗rm may

correspond to the Maximum Power Point Tracking (MPPT)

operating point of a wind turbine [1], [3], [25], [26].

IV. CONTROL PRINCIPLES

A. Vector Control (VC)

The control form expressions can be derived from the

BDFRM space-vector model [6] written in ωp (e.g. dp−qp for

primary winding) and ωs (e.g. ds− qs for secondary winding)

rotating frames (Fig. 2). The following relationships for the

primary mechanical (i.e. electrical power minus losses) and

reactive power can be developed:

Ppvc= Ppel

− 3

2Rpi

2p =

3

2ωp(λpsdisq − λpsq isd)

= Ppfoc− 3

2ωpλpsq isd (6)

Qpvc=

3

2ωp

(λ2p

Lp− λpsdisd − λpsq isq

)

= Qpfoc− 3

2ωpλpsq isq (7)

Fig. 2. Identification of primary voltage and flux vectors in a stationary α−βframe

Fig. 3. Structure of a BDFRG drive setup with power electronics control

Note that (6) could have also been derived using (2) and (4).

VC of Pp and Qp is coupled as both the isd and isq appear

in (6) and (7). The degree of cross-coupling can be reduced by

aligning the qp-axis to the primary voltage vector as proposed

in Fig. 2. The primary flux vector (λp) would then be leading

the magnetizing dp-axis, this phase shift being dependent on

the winding resistance values. For such a frame alignment

choice, VC should be similar to FOC as λpsd >> λpsq i.e.

λpsd ≈ λps so that (6) and (7) become:

Ppvc≈ Ppfoc

=3

2ωpλpsisq =

3

2

Lps

Lpωpλpisq (8)

Qpvc≈ Qpfoc

=3

2

ωpλ2p

Lp− 3

2ωpλpsisd

· · · = 3

2

ωpλp

Lp(λp − Lpsisd) =

3

2ωpλpipd (9)

With the λp, and thus λps, magnitudes being fixed by the

primary winding grid connection at line frequency (ωp), the Pp

vs isq and Qp vs isd relationships are nearly linear according

to (8) and (9), which justifies the use of PI power controllers

in Fig. 3. Feed-forward compensation for coupling terms in

(6) and (7) may lead to decoupled control similar to FOC but

at the expense of having to know the machine inductances.

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B. Field-Oriented Control (FOC)

The primary flux oriented (e.g. with the dp-axis aligned to

λp as in Fig. 2) form of (2) becomes [6], [12], [15]:

Te =3prLps

2Lpλpisq =

3pr2

λpsisq =3pr2

λpipq (10)

The corresponding real and reactive power can now be ex-

pressed by (8) and (9). Looking at (8)-(10), the most important

advantage of FOC over VC of the BDFRG (and the DFIG) is

the inherently decoupled control of Pp (or Te) and Qp through

isq and isd variations, respectively. This fact greatly facilitates

the FOC design as most AC machines, and especially if

vector controlled, need model-based decoupling schemes for

enhanced performance. In favor of VC, it is fair to say that

these appealing FOC properties come at the cost of the λp

angle estimation (θp in B© block of Fig. 2) and difficulties

with suppressing the detrimental DC offset effects on the

voltage integration accuracy. In addition, the primary winding

resistance (Rp) needs to be known. As parameter independent,

the VC concept does not suffer from these FOC constraints

but has compromised load disturbance rejection abilities.

Another interesting observation from Fig. 2 is that if the

dp-axis lies along the λp, then the respective ds-axis of

the secondary frame (where the control is actually being

executed), will get aligned to λps by default. Such an unusual

frame-flux mapping is inherent with the decoupled FOC, but

surely does not take place under the VC conditions.

V. BDFRG OPERATING AND TEST CONDITIONS

The preliminary performance comparisons of the FOC/VC

schemes in Fig. 3 have been made for a small proof-of-

concept BDFRG. The machine ratings and remaining parame-

ters (obtained by off-line testing as described in [7]) used for

simulation studies are given in Table I. Details of the dedicated

experimental system can be found in Figs. 4 and 5.

TABLE ITHE BDFRG MEASURED AND NOMINAL PARAMETERS

Rotor inertia [J ] 0.1 kgm2

Primary resistance [Rp] 11.1 ΩSecondary resistance [Rs] 13.5 ΩPrimary inductance [Lp] 0.41 HSecondary inductance [Ls] 0.57 HMutual inductance [Lps] 0.34 HRotor poles [pr] 4

Primary power [Pr] 1.5 kWRated speed [nr] 750 rev/minStator currents [Ip,s] 2.5 A rmsStator voltages [Vp,s] 415 V rmsStator frequencies [fp,s] 50 HzWinding connections Y/YStator poles [p/q] 6/2

A Simulink� programme has been built as a platform for

the subsequent code generation, compiling and uploading on

dSPACE� processing hardware for real-time implementation.

The following actions have been taken in the development

of the realistic controller simulator: (i) The readily available

Fig. 4. A photo of the BDFRG laboratory test facility for WECS emulation

Fig. 5. A schematic diagram of the BDFRG test rig

power electronics models from the SimPowerSystems� library

have been used; (ii) High-frequency uncorrelated white noise

and unknown slowly varying DC offset have been superim-

posed to the ideal signals to account for practical effects of the

measurement noise and current/voltage transducers resolution;

(iii) It has been assumed that both the rotor position and speed

information has been provided by an incremental encoder.

A. Maximum Torque per Inverter Ampere (MTPIA)

The MTPIA strategy [1], [5] has been implemented in Fig.

3 by setting: (i) i∗sd = 0, or (ii) Q∗p value for isd = 0

and λp ≈ up/ωp in (9), subject to the Qp controller status

i.e. (i) disabled or (ii) active. The advantage of the first

control option is one fewer PI regulator to tune and machine

parameter independence. The second choice has the limitations

of model-based approaches but allows Qp to be controlled

directly, which should make it more robust if, say, power

factor control was of immediate interest. The overall tuning

process also gets more difficult with Qp control by adding an

extra PI regulator to the existing three (two for the secondary

dq currents and one for the speed). Either way, the primary

winding would be almost entirely responsible for the machine

magnetization with most of the secondary current being torque

producing. This implies the minimum current loading for a

given torque, reduction of resistive and inverter switching

losses, and therefore an overall efficiency improvement.

B. Wind Turbine Characteristics

A geared BDFRG wind turbine has been usually operated in

a variable speed range of 2:1 or so. For the 6/2-pole example

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machine (Table I), this is [nmin = 500, nmax = 1000] rev/min

i.e. 250 rev/min around a synchronous speed of nsyn = 750rev/min for a fp = 50 Hz supply, the boundary secondary

frequencies of fs = ±fp/3, and the respective ‘slip’ limits of

s = −fs/fp = ∓1/3 according to (1). It can be easily shown

using (4) that Ps ≈ 0.25Pm meaning that the inverter would

need to handle at most 25% of the mechanical power (plus

total losses on the secondary side).

The turbine output torque on the generator side for the

maximum wind energy extraction in the base speed region

(i.e. between the minimum ‘cut-in’, umin, and the rated wind

speed, ur), can be represented as [1], [3]:

Topt =A · ρ · Cp(λopt, γ) ·R3

2 · g3 · λ3opt

· ω2rm = Kopt · ω2

rm (11)

where ρ is the air density, Cp(λ, γ) is the power (performance)

coefficient (i.e. the maximum turbine efficiency as λ = λopt

in this case), λopt = Rωt/u is the optimum tip speed ratio for

a given wind speed u, ωt is the turbine rotor angular velocity,

γ is the pitch angle (normally fixed to zero to maximise Cp),

R is the blade length (i.e. the radius of the circular swept

area, A = πR2), and g = ωrm/ωt is the gear ratio. The

main task of the gear-box is to provide mapping of the actual

wind and generator operating speed ranges i.e. [umin, ur] and

[nmin, nmax] through an appropriate g value. In practice, the

latter is normally chosen to allow matching of the respective

mid-range speeds, (umin+ur)/2 and (nmin+nmax)/2 (= nsyn

for the BDFRG or DFIG). At gusty wind speeds beyond ur

and up to the ‘cut-out’ limit, Cp has to be sacrificed to avoid

generator overloading. However, issues related to constant

power control of the turbine are out of scope of this paper.

The simulated BDFRG (Table I) has been assumed to have

a shaft torque-speed profile of the same form as (11) to be

used in (3) for computer studies:

TL = −Tr ·(

ωrm

ωmax

)2

≈ −19.1 ·( nrm

1000

)2

Nm (12)

VI. SIMULATION RESULTS

The plots below have been generated by running the FOC

and VC algorithms in Fig. 3 in speed mode at 0.1 ms sampling

time i.e. the 10 kHz switching rate of the IGBT converter using

the MTPIA strategy as a case study. The DC link voltage has

been maintained at ≈ 600 V by the PWM rectifier (i.e. the

line-side bridge) supplied at 415 V, 50 Hz.

Fig. 6 demonstrates an excellent speed tracking with

no overshoot of the BDFRG operating at synchronous

(750 rev/min), super-synchronous (900 rev/min) and sub-

synchronous (600 rev/min) speeds in the secondary frequency

range of fs = ±10 Hz. The reference speed trajectory has

been set as a ramp for dynamically less demanding target ap-

plications such as wind turbines. Note that the speed response

is virtually identical for either the FOC or VC.

The monitored primary electrical power (P ) and estimated

electro-magnetic torque (Te) in Fig. 6 reflect the BDFRG input

conditions represented by (12) in the control region following

the machine start-up. Except for a difference in losses, and

considering that ωp ≈ const by the primary winding grid-

connection, P and Te are directly related as follows from

(4) and (6) which explains a close resemblance in shape of

the two waveforms. The Te deviations from the desired load

profile during the speed transients refer to the acceleration

or deceleration torque term in (3) depending on whether the

machine is to speed-up (Ta > 0) or slow-down (Ta < 0). One

can also hardly see any disparity between the FOC and VC

results for either P or Te given (6) and (8) for i∗sd = 0.

The primary reactive power (Q) has been controlled at ≈1340 VAr (Fig. 6) to minimize the is magnitude for a given

torque and meet the desired MTPIA objective. Note that the Qbehavior with the decoupled FOC is largely unaffected by the

P variations. However, the VC waveform is rather distorted

and looks like a scaled mirror image of the P counterpart due

to the uncompensated cross-coupling (isq) term in (7).

The secondary current components (isd,q) and their primary

winding equivalents (ipd,q) under the MTPIA conditions are

presented in Fig. 7. The transient over-currents are avoided by

the PI regulators not having to be saturated to allow accurate

tracking of the desired trajectories for the moderately varying

command speeds in a trapezoidal manner (Fig. 6). The isd ≈0 as expected for the minimum secondary current loading,

while the ipd is required to establish the machine flux and

to satisfy the specific Qp demand according to (9). A close

analogy between the active q currents and the complementary

real power (torque), as well as the magnetising d currents and

Q, is immediately visible from the relevant waveforms in Figs.

6 and 7. The uncompensated cross-coupling effects of the isqclearly manifest themselves as speed dependent disturbance in

the respective non-controllable ipd profiles (Fig. 7) in the VC

case similarly to the P and Q situation in Fig. 6 considered

above. The corresponding FOC ipd (and Q) levels are however

constant in average sense throughout the entire speed range.

Fig. 8 shows the PWM sector change of the modulated

secondary voltage vector (vs) during the speed reduction from

900 rev/min to 600 rev/min. In the super-synchronous mode,

vs rotate anti-clockwise as indicated by the ascending sector

numbers for the same phase sequence of the windings when

ωs > 0 in (1). At sub-synchronous speeds, on the other hand,

vs rotate clockwise with the sector numbers descending which

comes from the opposite phase sequence of the secondary

to the primary winding since ωs < 0 in (1). Notice that vsbecomes stationary at synchronous speed (750 rev/min) as the

secondary currents are then DC i.e. ωs = 0 in (1).

Finally, it should be mentioned that the ‘proof-of-concept’

BDFRM(G) under consideration (Table I) has been built

for electric drives control prototyping and is by no means

optimized. The moderate power factor values in Fig. 6 can

be partly attributed to the MTPIA conditions when most of

the reactive power for the machine magnetization comes from

the primary side [22]. Nevertheless, another contributing factor

is certainly the relatively weak magnetic coupling between the

windings of the machine with an axially-laminated rotor [1],

[5], [28]. However, recent studies have reported that advanced

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4 5 6 7 8 9 10 11 12 13 14 15 16500

600

700

800

900

1000VECTOR CONTROL

Time [s] + offset

Spe

ed [r

pm]

ωrm

Actual

ωrm

* Ref

4 5 6 7 8 9 10 11 12 13 14 15 16500

600

700

800

900

1000FIELD−ORIENTED CONTROL

Time [s] + offset

Spe

ed [r

pm]

ωrm

Actual

ωrm

* Ref

4 5 6 7 8 9 10 11 12 13 14 15 16−30

−25

−20

−15

−10

−5

0

5

Time [s] + offset

Te, T

load

[Nm

]

Te

Tload

4 5 6 7 8 9 10 11 12 13 14 15 16−30

−25

−20

−15

−10

−5

0

5

Time [s] + offset

Te, T

load

[Nm

]

Te

Tload

4 5 6 7 8 9 10 11 12 13 14 15 16−2000

−1500

−1000

−500

0

500

Time [s] + offset

P [W

]

4 5 6 7 8 9 10 11 12 13 14 15 16−2000

−1500

−1000

−500

0

500

Time [s] + offset

P [W

]

4 5 6 7 8 9 10 11 12 13 14 15 160

500

1000

1500

2000

2500

Time [s] + offset

Q [V

Ar]

4 5 6 7 8 9 10 11 12 13 14 15 160

500

1000

1500

2000

2500

Time [s] + offset

Q [V

Ar]

Fig. 6. BDFRG speed, torque, and primary real/reactive power response to reference speed, and associated torque, variations in a limited range down tosynchronous speed

ENERGYCON 2014 • May 13-16, 2014 • Dubrovnik, Croatia

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4 5 6 7 8 9 10 11 12 13 14 15 16−6

−4

−2

0

2

4

6VECTOR CONTROL

Time [s] + offset

Prim

ary

dq c

urre

nts

[A]

Ipd

[A]

Ipq

[A]

4 5 6 7 8 9 10 11 12 13 14 15 16−6

−4

−2

0

2

4

6FIELD−ORIENTED CONTROL

Time [s] + offset

Prim

ary

dq c

urre

nts

[A]

Ipd

[A]

Ipq

[A]

4 5 6 7 8 9 10 11 12 13 14 15 16−6

−4

−2

0

2

Time [s] + offset

Sec

onda

ry d

q cu

rren

ts [A

]

Isq

Actual

Isq

* Ref

Isd

4 5 6 7 8 9 10 11 12 13 14 15 16−6

−4

−2

0

2

Time [s] + offset

Sec

onda

ry d

q cu

rren

ts [A

]

Isq

Actual

Isq

* Ref

Isd

Fig. 7. BDFRG dq currents in the respective frames complementing the results in Fig. 6

9 9.5 10 10.5 11 11.50

1

2

3

4

5

6

7VECTOR CONTROL

Time [s] + offset

Sec

tor

9 9.5 10 10.5 11 11.50

1

2

3

4

5

6

7FIELD−ORIENTED CONTROL

Time [s] + offset

Sec

tor

9 9.5 10 10.5 11 11.5−5

−4

−3

−2

−1

0

1

2

3

4

5

Time [s] + offset

Sec

onda

ry c

urre

nts

[A]

9 9.5 10 10.5 11 11.5−5

−4

−3

−2

−1

0

1

2

3

4

5

Time [s] + offset

Sec

onda

ry c

urre

nts

[A]

Fig. 8. BDFRG inferred secondary voltage positions and secondary current waveforms showing a phase sequence reversal during the transition from super-to sub-synchronous speed mode

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‘ducted’ reluctance rotor designs [4] can provide competitive

performance to large-scale DFIGs in terms of torque density

and efficiency [2], [29]. The latest work has confirmed that a

2 MW BDFRG based WECS can successfully meet the power

factor requirements stipulated by the grid codes [30].

VII. CONCLUSIONS

The main contribution of the paper is the comparative

development and performance analysis of field (primary flux)

oriented control (FOC) and vector (primary voltage oriented)

control (VC) for the optimum operation of the BDFRG. This

framework can serve as a benchmark for further research on

this emerging generator topology for wind power applications

where the cost advantages of partially-rated power electronics

and brush-less design can be fully realized.

The realistic simulation results have shown high control

potential using the MTPIA strategy for a typical variable

speed-torque profile of wind turbines. Despite the necessity

for the primary winding resistance knowledge and flux estima-

tion (which largely become obsolete with increasing machine

sizes), the FOC scheme allows seamless Q control quality in

an inherently decoupled fashion from power (torque). The VC

counterpart, on the other hand, does not require any machine

parameters for implementation, and as such is more robust

from this point of view than FOC, but has limitations of

uncompensated cross-coupling and inferior Q response as a

trade-off. Although the employment of decoupling techniques

may bring the VC performance enhancement, this direction has

not been taken to avoid the consequent model-based set-backs

(e.g. sensitivity issues and accuracy problems associated with

parameter identification uncertainties) and retain the entire

parameter independence in order to make a fair assessment

and valid comparisons with the FOC.

The experimental verification is currently in progress and

will be published in our future journal papers.

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