Unbalanced Voltage Sag Ride-Through of A Doubly Fed Induction Generator Wind Turbine with Series

Grid Side Converter

Patrick Flannery & Giri Venkataramanan Dept. of Electrical & Computer Engineering

University of Wisconsin – Madison Madison WI, USA

patrick.flannery@ieee.org, giri@engr.wisc.edu

Abstract— Regulatory standards for grid interconnection require wind generators ride-through disturbances such as faults and support the grid during such events. Conventional accommodations for providing voltage sag ride-through for doubly fed induction generator (DFIG) wind turbines result in compromised control of the turbine shaft and grid current during unbalanced faults. This paper presents analysis and control design of a DFIG wind turbine with series grid side converter for ride through during unbalanced voltage sag events. A dynamic model and control structure is developed for unbalanced operating conditions. Experimental results from 2kW laboratory hardware are used to verify the proposed concepts. Hardware results illustrate excellent ride through response of the DFIG system under various sag conditions.

Keywords- doubly fed induction generator; voltage sag; voltage dip; unbalance; low voltage ride-through; wind turbine

I. INTRODUCTION As the penetration of large scale wind turbines into the

electric power grid increases, connection codes are requiring turbines ride through a short-term low or zero voltage event at the point of common coupling (PCC) [1]. In the most prevalent utility scale wind turbine architecture, the stator windings of a doubly fed induction generator (DFIG) are connected to the grid PCC via collection and/or transmission transformers and excited at the grid frequency, along with back-back power converters in the rotor circuit [2,3].

During deep balanced voltage sags high per unit currents and shaft torque pulsations are known to occur in the standard DFIG wind turbine architecture [3,4,5]. Solutions to provide voltage sag ride through include resistive rotor crowbar circuits [4, 6, 7], temporary disconnection of the stator windings [5], a modified control scheme for the machine side converter [8], and a DVR type architecture with an inverter in series with the stator windings, referred to as a series grid side converter (SGSC) [9, 10] each with varying degrees of performance. The authors of [11, 12, 13, 14] demonstrate operation of a DFIG during a sustained shallow unbalanced,

that is, the amplitude of the negative sequence component does not exceed 10% or so. However, with the exception of the modified rotor control scheme [8], these approaches have not been demonstrated to respond to deep unbalanced sag events due to 1 or 2 phase-to-ground or phase-to-phase faults described in [15]. In these cases the negative sequence component of the voltage seen at the DFIG terminals can approach 50% for the most severe unbalanced sags, depending on the sag type.

The purpose of this paper is to characterize the capabilities of a DFIG wind turbine system with series grid side converter (SGSC) during generalized voltage sag events. In previous publications dynamic analysis and control design for balanced sags have been presented [9, 10]. The approach is extended here to provide ride-through during unbalanced sag events. Unbalanced sags are broken into sequence components to illustrate their effect on the DFIG response. Closed form results from constant speed transient analysis guides control law formulation. Experimental results from 2 kW laboratory hardware test bed are used to demonstrate the operation of the system under selected fault conditions.

II. TOPOLOGY AND DYNAMIC MODEL

A. System Description & Dynamic Model A single-line schematic of the DFIG with SGSC is

presented in Figure 1. As in a conventional DFIG, the rotor windings of the machine are accessed via slip rings, and connected to a three phase IGBT-diode inverter referred to as the machine side converter (MSC).

DFIG

Stator Windings

RotorWindingsDC Link

MSC

SGSC

Gearbox

Series InjectionTransformer

PGSC

PCC

Δ:YΔ:Y

Y:Y

Figure 1. Schematic doubly fed induction generator (DFIG) wind turbine with series grid side converter (SGSC).

This work was supported by the Wisconsin Electric Machine and PowerElectronics Consortium (WEMPEC) and Link Foundation Energy Fellowship.This work made use of ERC shared facilities supported by the NationalScience Foundation under Award number EEC-9731677.

978-1-4244-2279-1/08/$25.00 © 2008 IEEE 1

The MSC shares a dc bus with a second inverter connected in parallel with the grid and DFIG stator, referred to as the parallel grid side converter (PGSC). The shared dc link enables power flow between the rotor circuit of the DFIG and the grid connection. The proposed topology includes an additional inverter connected in series with the stator windings of the DFIG, referred to as the series grid side converter (SGSC).

The DFIG can be modeled with complex dq space vectors [16] in an arbitrary rotating reference frame. The conventional T circuit DFIG model can be converted into a more convenient Γ circuit (Figure 2), including the effects of the SGSC transformer as described in detail in [10] with the following change of variables:

( )2

2

m m

ls i m st

rR R r

rR st s i

st Lst s R stR R

lr ls ist ls i m L

L L

L L L L

vv i i

RR R R R

L i i L i

L L LL L L L L

η

ηη

η

λ λ λ

η η

= + = +

+= + + = +

=+ +

= =

= = +

=

. (1)

In this case the stator referred dynamic state equations are

( )( )

( )

( )

1

/

1

32

st sst R f ist

st

RR R st r L

L

st R f ist st r

jj j fj Lj

j

dcj j i s R R

dc dc

Rd j i R v vdt L

di i R R j Ldt L

R L j v v v

dii j L R v v

dt L

dv v i v i v idt C v

λ λ ω

ω ω

λ ω

ω

⎛ ⎞= − + + + +⎜ ⎟

⎝ ⎠

⎡= − + + − +⎣

⎤+ + − − ⎦

⎡ ⎤= − + + −⎣ ⎦

− ⎡ ⎤= + +⎣ ⎦i i i

. (2)

The subscript “st” designates the total stator flux, voltage, inductance or resistance, which includes the DFIG stator and series injection transformer and inductive choke. The SGSC voltage space vector, vi, adds to the wind farm collector terminal voltage, vf, to affect the net voltage at the stator circuit, vst. The change of variables in (1) allows the use of the familiar expression for torque,

{ }†3

4e st R

PT iλ= ℑ , (3)

without compensating factors for the added injection transformer and inductor.

Mech.System

2JmT m(uw,β,ωr)

p Gm

jωλst

DFIG&Injection

Xfrmr

LL RR

Ls

Rst

is

Cdcvdc

iR

+ _ +_j(ω-ωr)λR

T eωr

+

_

+

_

vst

vi

vi

+ _

ip

+_

+_

ij Lj

vp+_

vj vR+_

vR

3 vR .iR2 vdc

3 vi .is2 vdc

3 vj .ij2 vdc

SGSCPGSC MSC

+

_

1

jωCjvf

Cj

+

_

vf

vj

Figure 2. Γ-circuit model of DFIG with series grid side converter (SGSC) and injection transformer, including parallel grid side convert (PGSC), machine side converter (MSC) and dc link in arbitrary dq reference frame.

B. Response of DFIG to Voltage Sags 1) Excitation The voltage seen at the stator terminals of a DFIG in a

typical wind farm during voltage sags has been characterized in [15]. The presence of Δ-Y transformers between the PCC and stator terminals prevents the occurrence of a zero sequence component voltage at the DFIG terminals during a sag event.

Absent a zero sequence component, any three phase quantity can be represented with positive and negative sequence components expressed in the stationary reference frame as

( ) ( )

†e e

e e

s ss j t j tp n

j t j ts s s sqp dp qn dn

x X e X e

X jX e X jX e

ω ω

ω ω

−

−

= +

= − + +. (4)

In the positively rotating synchronous reference frame (PRSRF – superscript “p”) this equals

† 2 ep j tp nx X X e ω−= + . (5)

The four different types of faults (single phase, 2 phase, 2 phase-to-neutral, and 3 phase-to-neutral) produce different voltage phasors at the wind turbine terminals, depending on the nature of the transformer connections between the fault and the wind turbine [15]. It has been shown that the voltage sags observed at wind turbine machine stator terminals fall under the four types, namely A, C, D & G, as classified in [15,17]. The different voltage sag types seen at the DFIG terminals vs. fault type at PCC with two intermediate Δ-Y transformers are presented in Table I.

TABLE I VOLTAGE SAG TYPE AT DFIG TERMINALS VS. FAULT TYPES AT PCC [15,17]

φn 2φ 2φn 3φ D C G A

∗ A notational list of symbols and parameters is provided in the Appendix.

2

When studying the effect of voltage sags on wind turbines, it is sufficient to know the sag type and value of the per unit characteristic voltage phasor, NV [15]. In general the characteristic voltage can be complex for phase jumps, but these are not common for faults in transmission systems [15].

For all fault types the characteristic per unit voltage is assumed to correspond directly to the voltage envelopes of the grid code ride through requirements (i.e NV = 0.15 corresponds to a sag down to 15% voltage remaining between either the smallest two phase or phase to neutral). The positive and negative sequence sag per unit voltage phasors can be determined from the abc phasors given in [13] and abc to sequence component transformation

0

2

2

1 1 11

13

1

a

p b

n c

V V

V a a V

a aV V

=

⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

(6)

as given in [18]. Positive and negative sequence sag per unit phasors for each sag type seen at wind turbine terminals, as a function of per unit characteristic sag voltage, NV, are listed in Table II, where the per unit ratios of the positive and negative sequence sag voltages are defined as

p

p

nom

VN

V= and

nn

nom

VN

V= . (7)

In the positively rotating synchronous reference frame (PRSRF) a positive sequence sag appears as a step change in the positive sequence voltage vector, which has a Laplace transform of

( )p

p f nompfp

N VV p

p−= . (8)

A negative sequence stator voltage excitation has the a Laplace transform in the PRSRF of

( ) 0†

2

( )2

ep

n f nompfn

e

j tN VV p

p j

e ω

ω

−

=+

, (9)

where t0 is the time delay between the alignment of the PRSRF and NRSRF, and the occurrence of the sag at t = 0.

TABLE II

PER UNIT SEQUENCE PHASORS FOR SAG TYPE AS A FUNCTION OF PER UNIT CHARACTERISTIC VOLTAGE, NV .

Sag Type

pN nN

A 0VN j+ 0 0j+

C ( )11 0

2 VN j+ + ( )11 0

2 VN j− +

D ( )11 0

2 VN j+ + ( )11 0

2V

N j− +

G ( )11 2 0

3 VN j+ + ( )11 0

3 VN j− +

2) Stator Flux Dynamic Solution A constant speed transient analysis [16] is used to

determine the effects of a voltage sag on the total stator flux. Considering first a case with the SGSC dormant, the dynamic state equation for the stator flux in positively rotating synchronous reference frame (PRSRF), with the q-axis aligned with the positive sequence component of the collection transformer voltage is

p

p p pst stst R fe st

st

Rd j i R vdt Lλ λ ω

⎛ ⎞= − + + +⎜ ⎟

⎝ ⎠ (10)

Neglecting ohmic drop which is typically quite small and taking the Laplace transform (with ωe as a constant) yields

0( ) ( )p p pst

st st fest

Rp j p V pL

ω λ⎛ ⎞

Λ + + − =⎜ ⎟⎝ ⎠

, (11)

where p is the Laplace variable and the initial condition

( 0)p

p p f nom f nomst nom st

e e

jVjVtω ω

− −−

−−Λ = Λ = ≈ = . (12)

The time domain response of the stator flux is

( )/1 ( )( )

/st st e

ppp R L j tfst nomst

st st e

V pt e

R L j pωλ

ω− +−

−⎧ ⎫⎪ ⎪= + Λ⎨ ⎬+ +⎪ ⎪⎩ ⎭

L . (13)

From linear system theory, the response of the DFIG electrical circuit to an unbalanced sag is determined from superposition of negative and positive sequence solutions. Using the excitations defined in (8) and (9), the total stator flux response to an unbalanced voltage sag is

( ) ( )0

0

† /2

† 2 2

( ) (1 ) ...s s ee

e e

pp R L j tj tst nom p p nst

j t j tn

t N N N e e

N e e

ωω

ω ω

λ − +−

−

⎡= Λ + − +⎢⎣⎤− ⎥⎦

.(14)

3) Equivalent Rotor Voltage Requirement As derived similarly in [19,20], the open circuit rotor

voltage is driven directly by the stator flux. From KVL of the rotor circuit, this is approximately equal to

p

p pstR stsl

de j

dtλ ω λ= + (15)

The physical rotor circuit (T model) voltage required by the MSC to counter this EMF, and maintain regulation of rotor current is equal to

p

p p pstr R stsl

de e j

dtλ

η η ω λ= +⎛ ⎞⎜ ⎟⎝ ⎠

= (16)

Under steady state conditions the derivative of the stator flux vector is equal to zero in the PRSRF yielding the commonly known expression for the rotor voltage of p p

r f nomE s Vη −≅ . (17) This requires a rotor voltage (in per unit) approximately equal to the range of the slip, plus any additional dynamic headroom. However, during a sag event this EMF is non-constant, and is equal to

3

( ) ( )0

0

† /2

† 2 2

( ) (1 ) ...s s ee

e e

pp R L j tj trf nom p p nr

e

j t j tslnn

e

e t V sN N N e e

N e e

ωω

ω ω

ωηω

ωω

− +−

−

⎡= − − +⎢

⎣⎤

− ⎥⎦

.(18)

4) Principle of Ride Through From (18), it may be deduced that in the case of a balanced

sag ( 0nN = ) there are two components of the rotor EMF response. The first is a constant DC component proportional to the slip, s, and remaining positive sequence voltage, pN . The second piece of stator flux is proportional to the “missing” 1 pN− piece of the grid. From faraday’s law, this piece of stator flux appears “frozen” in the stationary reference frame. In the PRSRF frame this “frozen” piece appears to produce a transient oscillatory EMF in the rotor circuit, that decays with the stator time constant. The amplitude of the oscillatory component is scaled by the rotor speed, yielding worst case sag response at maximum speed and deepest sags.

It is important to note, that the imbalance due to the “missing” positive sequence piece is transient. Once the positive sequence flux is brought into equilibrium with the positive sequence sag voltage, the oscillatory component will be eliminated without any further correction required, pending the resolution of the sag event.

On the other hand, in the case of unbalanced sags, the negative sequence component adds a second term to the transient oscillatory response. The timing of the sag event, t0, will affect the phase of the negative sequence sag component relative to the positive sequence component. In addition, the negative sequence component adds a new forced response at twice synchronous frequency (relative to the PRSRF). The forced component of EMF is scaled by the negative sequence slip (max magnitude of 2.30 per unit) and the per unit negative sequence component phasor, (max magnitude of 0.5 per unit [15]) for a combined worst case product of 1.15 per unit.

For the MSC to maintain regulation of the rotor currents during a sag event, it is necessary to eliminate the large oscillatory components of the rotor EMF. This can be achieved by nulling the “missing” 1 pN− positive sequence component of the stator flux. This is equivalent to scaling the positive sequence stator flux in proportion the positive sequence grid voltage. To be sure, the negative sequence component of the grid voltage must be rejected throughout the sag event.

III. IMPLEMENTATION OF RIDE THROUGH

A. MSC and PGSC The MSC and PGSC of the DFIG are controlled in a

conventional manner. A high bandwidth current regulator on the MSC and grid flux aligned field orientation allows decoupled control of torque and stator reactive power [3]. Likewise the PGSC current is controlled with a high bandwidth proportional regulator aligned with the farm collector terminal voltage. An outer PI loop on the PGSC controls the dc link voltage and net reactive power through

changing the PGSC current commands. A phase locked loop generates a stable reference angle of the positive sequence component of the farm collector terminal voltage for grid flux and voltage alignment.

B. SGSC The SGSC remains dormant (zero voltage vector) during

normal conditions to eliminate switching losses. When a sag event is detected the SGSC engages and controls the total stator flux as shown in Figure 3.

Starting at the top right of Figure 3 and moving counterclockwise, the three phase abc farm collector terminal voltages are sensed and transformed into the two axis αβ stationary reference frame. A phase locked loop, implemented as described in [12], is used to estimate the angle of the PRSRF and NRSRF. The total stator flux in the αβ stationary frame (superscript “s”) is readily estimated from the measured stator voltage (neglecting ohmic drop) as ( )s s s s

st st f iv dt v v dtλ = = −∫ ∫ . (19)

The farm collector terminal voltage and estimated total stator flux are input to positive and negative sequence component controllers, and sag detection logic. The SGSC voltage commands from each of these controllers is summed in the stationary reference frame and used to develop the modulation signals to the SGSC.

1) Sag Detection Logic The SGSC transitions from its dormant state to stator flux

control when the imbalance between the synchronous stator flux speed voltage and farm collector terminal voltage exceeds a prescribed limit. The rationale for this criteria is motivated by the relationship between the stator flux and rotor EMF described in the previous section. Thus the sag detection criteria is

e

ppf stv jω λ χ δ− ≥ + . (20)

where χ ± δ is a hysteretic threshold for engagement.

DC Link

SGSC Y:Y

DFIG

StatorWindings

RotorWindings

SeriesInjectionXfrmr

is,abc

To MSC

vi,abc

Δ:Y

++

vis*

PCCΔ:Y

θp,θn

vfs

abcαβ

λstestimator

λsts

SeqPLL

Positive SequenceStator Flux Controller

Negative SequenceStator Flux Controller

vips*

vins*

To PGSC

GateSignals

abc

zerovector

Modulatorαβ

SagDetect

vfs

λsts

vf,abc

Figure 3. Block diagram of total SGSC control system.

4

χ + δ sets the maximum allowable imbalance between the farm collector terminal voltage and the stator flux speed voltage, in units of volts, beyond which the SGSC controller engages. The SGSC disengages following a set time delay after this term drops below χ − δ. Typical values for χ and δ are 0.09 and 0.04 per unit, and 30 ms for the disengagement delay.

2) Stator Flux Commands From the constant speed transient analysis of the total stator

flux and rotor EMF, it is desirable to eliminate the “missing” positive sequence component of the stator flux. This is comparable to having the stator flux scale in proportion to the farm collector terminal voltage. It is desirable for the negative sequence stator flux to be rejected completely. This yields the following commands for the positive and negative sequence stator flux,

* *, 0p

p nfp

stp stn

e

v

jλ λ

ω= = . (21)

This stator flux command is chosen so as to synchronize the flux level in the DFIG (and injection transformer) such that it will be in equilibrium with the new farm collector terminal voltage during the sag. At the resolution of the sag event, when the PCC and farm collector voltage returns to nominal, the same total stator flux command acts to bring the total stator flux back up to a nominal level.

A second important property of this command is that the torque and power production of the DFIG will inherently scale with the remaining positive sequence voltage during the sag event. In principle, this directly scales power to/from the MSC and prevents the need for any braking resistor in the dc link and/or on the rotor circuit. This is consistent with the fact that the power processing capability of the PGSC is limited by its maximum current rating, and thus scales with the farm collector terminal voltage during a sag event.

3) Sequence Component Stator Flux Controllers When engaged, the SGSC controls the stator flux through a

pair of proportional controllers in the positively and negatively rotating synchronous reference frames aligned with the respective component of the farm collector terminal voltage. A block diagram of a sequence component controller (for either positive or negative sequence) is show in Figure 4. The letter “x” in subscripts and superscripts in the figure is a place holder for either the positive or negative sequence indicator.

The positive and negative sequence components of the farm collector terminal voltage and total stator flux are extracted using complex coefficient filters described in [21] and presented here as 1( )

2 ( )1( )e e

p e

G pj p j

K p jω ω

ω

± =⎛ ⎞

+ ⎜ ⎟⎜ ⎟±⎝ ⎠

∓. (22)

The sequence components are rotated into the PRSRF and NRSRF within their respective control loops.

Sequence Component Filter

vfs

λsts

vfxs

λstxs

+

λstxx*

vfxx

λstxx

vfxx

λstxx

σλx

Proportional Controller

Frame Trans.

θx

+/-jωe

++ vix

x*

Frame Trans.

vixs*

θx1( )

2 ( )1( )e e

p e

G pj p j

K p jω ω

ω

± =⎛ ⎞

+ ⎜ ⎟⎜ ⎟±⎝ ⎠

∓ dqαβ dq

αβ

Figure 4. Block diagram of the sequence component stator flux controller.

The difference between the stator flux sequence command and estimated stator flux is multiplied by a proportional gain, σλx. State feedback decoupling of farm collector terminal sequence component voltage and sequence component estimated stator flux speed voltage are further used to improve command tracking [22]. Decoupling of stator ohmic drop is omitted to simplify control and preclude the need for stator current sensors.

4) Controller Gains While it is possible to derive closed form analytical

solutions for the SGSC and MSC voltages as a function of the controller gains during sag events, these are only of modest value since such solutions commonly assume that the inverters are not overmodulated. In practice the MSC and SGSC would likely go into overmodulation during deep sag events (unless significantly oversized) necessitating the use of simulation methods and trial and error in controller gain selection. Nonetheless, several qualitative guidelines can be determined by considering ride-through objectives and the results of the previous constant speed transient analysis.

In general, increasing the positive or negative sequence stator flux controller gains will result in improved regulation of the stator flux during sag events, stability and signal noise limits aside. However, as expressed in (16) the rotor EMF in the PRSRF is approximately equal to the sum of a stator flux speed voltage term and the derivative of the stator flux. For balanced sags, this indicates that there is an upper acceptable bound to the speed of the stator flux response, which correlates directly to the controller gain, σλp. However, if the positive sequence controller gain produces too slow of a response in the stator flux, excess mechanical power, not delivered to the grid, will cause the dc link voltage to exceed safe limits. In the case of unbalanced sags, the negative sequence component of the stator flux has a large impact on the rotor EMF. Thus it is desirable to select the negative sequence stator flux gain, σλn, sufficiently high for a fast response. Typical values of controller gains are provided in the appendix.

IV. LABORATORY SCALE TEST RESULTS The proposed ride-through feature for DFIG using SGSC

under balanced conditions have been simulated in extensive detail for a candidate 2 MW system and presented in [9, 10]. Further simulation studies indicate excellent performance under unbalanced sags for the 2 MW system under a variety of sag conditions. However, in order to verify the operation of the system in hardware, a 2 kW laboratory scale system was developed as described further.

5

Y:Y

RotorTerminals

DFIG

StatorTerminals

PGSC MSC

Encoder

"PCC"

Lf

Cj

SGSC

Y:Δ

SeriesInjectionTransformer

Cdc

Lj

Li

vdc

Gate Signals

Control Boards (2x)TI TMS320C31 DSPXilinix XCS40 FPGA

Current & VoltageMeasurements

Encoder PositionPM Motor

SpeedControl

Allen BradleyUltra 3000iMotor Drive

vf,abc is,abc

ir,abc

Figure 5. Schematic of 2.0 kW experimental hardware setup

A. Experimental Hardware Setup An illustration of the experimental hardware setup is

presented in Figure 5. The shaft of the DFIG is driven by a permanent magnet ac motor drive. A grid emulator generates arbitrary ac voltages sags at the point of interconnection. The rotor windings of the DFIG are accessed via slip rings and connected to the machine side converter (MSC). The dc bus of the MSC is shared by the parallel grid side converter (PGSC) and series grid side converter (SGSC).

Each of the inverters is controlled by one of two DSP/FPGA control boards, and are sine-triangle modulated with 3rd harmonic injection. Switching and sample frequencies are both set to 5 kHz. For proper representation of the DFIG system’s response during voltage sags, it is necessary for the MSC to have an equivalent voltage rating in the range of 0.3 to 0.4 pu. Since the rotor to stator turns ratio in the hardware DFIG is 1:1, it is necessary to step down the PCC voltage for connection to the PGSC. The PCC voltage of 110 VRMS L-L is stepped down to 31.8 VRMS L-L via a Y:Δ transformer with 2:1 winding turns ratio. This allows the dc link to be regulated at 55 V, yielding a MSC voltage rating of approximately 0.33 pu.

The dc side of the SGSC shares the 55 V bus with the MSC and PGSC. Three single phase 100 to 115 V transformers (1:1.15 SGSC to stator circuit turns ratio) are connected in Y:Y configuration, yielding an equivalent SGSC voltage rating of approximately 0.38. A 3 phase 0.12 mH inductor between the SGSC phase terminals and transformers limits the voltage ripple at the transformers during SGSC operation.

The rotor position is determined from an encoder, and is also used for rotor speed estimation in state feedback decoupling terms. The angle of the voltage, vf, is estimated from a PLL as described in [12] for use in synchronous frame controllers for the MSC and PSGC, and the positive and negative sequence stator flux controllers of the SGSC.

B. Hardware Results Scope captures from balanced and unbalanced voltage sag

events on the 2kW laboratory scale hardware testbed are presented in Figure 6 to Figure 8. In each case the DFIG speed is 1.25 per unit, running near rated power at nominal voltage and frequency. The scope image captures show response to type C, D, and A sags representative of phase-to-

phase, phase-to-ground and 3 phase faults, each with a characteristic per unit voltage, Nv, of 0.4. Type G sags are not shown for brevity. As seen in each the figures, the synchronous frame stator flux d & q components (frame (c) of figures) scale in proportion to the remaining positive sequence component of the grid voltage during the sag events, and have little oscillation at 2ωe. The rotor currents (frame (b) of figures) have some second harmonic component, but are within the bounds of the MSC current rating.

(a)

(b)

(c)

(d)

Figure 6. Experimental results, voltage sag type “C” (φ-φ Fault), Nv = 0.4, ωr = 1.25 pu. From top to bottom: (a) vf,abc (25V/div); (b) ir,abc (5A/div); (c) ,

p pds qsλ λ (0.2Wb/div); (d)vdc (25V/div), is,ab(10A/div); 50

ms/div.

(a)

(b)

(c)

(d)

Figure 7. Experimental results, voltage sag type “D” (φn fault), Nv = 0.4, ωr = 1.25 pu. From top to bottom: (a) vf,abc (25V/div); (b) ir,abc (5A/div); (c) ,

p pds qsλ λ (0.2Wb/div); (d)vdc (25V/div), is,ab(10A/div); 50 ms/div.

6

(a)

(b)

(c)

(d)

Figure 8. Experimental results, voltage sag type “A” (3φ fault), Nv = 0.4, ωr = 1.25 pu. From top to bottom: (a) vf,abc (25V/div); (b) ir,abc (10A/div); (c) ,

p pds qsλ λ (0.2Wb/div); (d)vdc (25V/div), is,ab(10A/div); 50 ms/div.

V. SGSC VA RATING AND PRACTICAL REALIZATION The results presented herein point toward some important

practical issues to be addressed in further investigations. The most important of these is the requisite size, in terms of volts-amps product, of the SGSC and the accompanying injection transformer and choke. This will very likely depends on the exact requirements of the specific grid codes at the site in question, considered together with the electrical properties of the wind farm collection network, including leakage inductances and shunt capacitances.

As derived in the constant speed transient analysis, and noted by others [11-14], negative sequence excitation of the DFIG stator terminals produces a significant impact on the amplitude of the rotor circuit EMF. As noted in Table II, the negative sequence component of the grid voltage approaches a magnitude of 0.5 per unit, in a stiff voltage sag model. Reduction of the negative sequence component voltage seen at the stator terminals through either less stringent grid codes, or mitigation through negative sequence current from a wind farm STATCOM or the PGSCs of the wind turbines will obviously reduce the SGSC negative sequence loading.

On the other hand the effect of sags that produce changes in the positive sequence component of the stator terminal voltage are transient in nature. Thus the SGSC voltage requirements in this case is less severe, but likely also dependent on the specifics of the wind farm collection network and the control employed in both the SGSC and MSC.

In considering both the positive and negative sequence SGSC requirements, it is important to note that series injection transformers in dynamic voltage restorers can often see transient flux of twice the sustained value [23]. While this has not been specifically verified for the SGSC transformer, it must be considered. Finally, the presence of the SGSC during normal operation of the DFIG is undesirable due to the conduction in the inverter and the ohmic losses in the inductor and transformer. Thus it may be desirable to bypass the SGSC with a static SCR switch, and transition to SGSC control during sag events.

VI. CONCLUSIONS This paper has demonstrated the capability of a doubly-fed

induction generator equipped with series grid side converter to ride through both balanced and unbalanced voltage sag events typical of grid faults. Constant speed transient analysis of the native DFIG’s response to typical grid voltage during sag events were derived and used to formulate control objectives for successful ride through. During sag events, the positive sequence component of the stator flux is to scale in proportion to the positive sequence component of the remaining grid voltage, and the negative sequence component of the stator flux is to be kept at zero. The SGSC, which remains dormant (zero voltage vector) during normal conditions, engages during sag events to control the positive and negative sequence component of the stator flux.

A 2kW laboratory hardware demonstration of the proposed topology is described, and results from representative sag events verifying the performance of the proposed solution are presented. The SGSC is sized at approximately 0.4 per unit voltage in the 2 kW laboratory prototype.

The open issue of minimum SGSC volts-amps rating is discussed. It is expected that the exact voltage sag ride through requirements coupled with the specific electrical properties of the wind farm collection systems will have a significant impact on the required SGSC rating. Other issues such as transformer saturation, static bypass switch, and operation during other abnormalities are subjects of continuing investigations.

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APPENDIX

TABLE III: NOMENCLATURE

v Voltage space vector i Current space vector λ Flux space vector e Back EMF space vector t Time p Laplace variable j 1− T Torque P Poles s Slip θ Angle ω Speed

χ,δ SGSC logic threshold

TABLE IV: SUBSCRIPTS

s Stator st Total stator r Rotor (Γ circuit) R Rotor (T circuit) L Leakage dc Direct current e Electrical f Wind farm collector terminals i SGSC circuit j PGSC circuit sl Slip q Real axis d Negative imaginary axis p Positive sequence component n Negative sequence component

nom Nominal steady state value

TABLE V: SUPERSCRIPTS

s Stator reference frame p Positively rotating synchronous reference frame n Negatively rotating synchronous reference frame ^ Estimated quantity ~ Phasor quantity

TABLE VI: PARAMETERS USED IN HARDWARE SYSTEM

Base Parameters Values

Pb 2.0 kW Vb(L-L) 110 VRMS

Zb 6.05 Ω ωb 2 π 60 rad/s

Parameters Real Per Unit Lm 17.55 mH 1.096 Lls 0.525 mH 0.033 Llr 0.525 mH 0.033 Rr 0.080 Ω 0.013 Rs 0.104 Ω 0.017 P 4 Li 0.121 mH 0.008 Lj 0.70 mH 0.523 Lf 0.85 mH 0.053 Xcj 132 Ω 22.1 Nsr 1.0 Nsi 1.15 Nsj 3.46 (incl .Δ−Y) vdc 55 V Cdc 14.5 mF σpλ 2 π 50 σnλ 2 π 100 χ 0.09 δ 0.04

Tdelay 30 ms

8