Unbalanced Control System Design for DFIG-Based Wind Turbines

Shuying Yang, Long Zhan, Changxi Huang, and Zhen Xie School of Electrical Engineering and Automation

Hefei University of Technology Hefei, China

yangsyhfah@163.com

Abstract—To achieve high performance operation of doubly fed induction generator (DFIG) based wind turbines under unbalanced voltage conditions, a well designed control system is important, otherwise wind turbines will take a risk of being cut out of the power grid. Meanwhile, without proper designed control the power ripples generated from wind turbines will further aggravate the power grid. Under unbalanced conditions, DFIG was modeled in dual synchronous reference frame (SRF), namely the positive one and the negative one, based on which the dual PI current controllers were designed. To implement the dual current control, the sensing variables were divided into positive and negative sequence components with the designed generalized filters, and then the corresponding control in positive and negative SRF were designed respectively. At the same time, to get the dual SRFs oriented to the positive and negative sequence voltage components, a notch filter based phase latch loop (PLL) control was designed. Experimental results on 11kW DFIG wind turbine test bed validated the control system design.

Keywords- DFIG; dual current control; unbalanced input voltages

I. INTRODUCTION Variable-speed wind turbines, as a dominant wind turbine

type, not only can improve wind power capture efficiency, but also can reduce system mechanical stresses [1]. Compared with full rated converter based ones, DFIG-based wind turbines only need partially rated driving converters to excite them, which would be beneficial for driving converter design and cost efficient [2-3]. However, it is also the partially rated converters that make the control for DFIG-based wind turbines be more complicated, especially under abnormal or distorted power grid conditions, such as voltage dip, voltage unbalance, and so on.

Under unbalanced input voltage conditions, the operation performance of DFIG-based wind turbines would be deteriorated, such as shaft tremble, windings hot, and so on [4]. At the same time, the unbalanced currents and power pulsation would further aggravate the input voltage unbalance. With the unbalance degree increasing, the rotor terminal voltages would even go beyond the driving converter voltage ratings, which would compel wind turbines to cut out of the power grid [5].

Symmetrical component method based dual synchronous reference frames (SRF), namely the positive one and the negative one, are usually and conveniently adopted to model and design the control system of DFIG[4,5]. So in this paper the mathematical models of DFIG were built in dual SRF,

firstly, and then based on which the DFIG operation characteristics under unbalanced conditions were analyzed, simply. To control the positive and negative sequence components effectively, a dual current control scheme was designed. In the control scheme, the positive and negative sequence components of currents and voltages were divided through notch filter based generalized filters. And to orient the dual SRFs to the positive and negative sequence voltage components, a notch filter based phase latch loop (PLL) control was designed. The experimental results on 11kW DFIG test bed validated the control system design.

II. MATHEMATICAL MODELS OF DFIG The sketch of DFIG-based wind turbines is shown in Fig.1.

Under unbalanced input voltage conditions, DFIG can be modeled in positive and negative SFR, based on symmetrical component theory.

For convenience, space vectors are defined for voltages, currents, fluxes in positive and negative SRF, as (1).

dqqd xx j−=X (1)

Where, p n p n p nqd qd qd qd qd qd qd∈X U U I I ψ ψ、 、 、 、 、 ; U , I and

ψ represent voltage, current and flux space vectors, respectively; superscript p and n denote the positive and negative components; subscript qd denotes the SRF. In this paper, the variables in positive and negative SRF only refer to the positive and negative sequence components unless specification.

With the space vector definition, (1), variables about DFIG can be divided into positive and negative components and expressed in positive and negative SRF. And then, DFIG can be modeled as (2) and (3), respectively.

National Natural Science Funds (51107025) and Fundamental Research Funds for the Central Universities (2010HGZY0015)

Figure 1. DFIG driving diagram in wind turbine

978-1-4577-1600-3/12/$26.00 © 2012 IEEE

p p ps s s m r

p p pr m s r r

p p p ps s s s s s

p p p pr s r r s r r

d jdd j( )d

qd qd qd

qd qd qd

qd qd qd qd

qd qd qd qd

L L

L L

Rt

Rt

ω

ω ω

⎧ = +⎪

= +⎪⎪⎪⎨ = + +⎪⎪⎪ = + + −⎪⎩

ψ I I

ψ I I

U I ψ ψ

U I ψ ψ

(2)

n n ns s s m r

n n nr m s r r

n n n ns s s s s s

n n n nr s r r s r r

d jdd j( )d

qd qd qd

qd qd qd

qd qd qd qd

qd qd qd qd

L L

L L

Rt

Rt

ω

ω ω

⎧ = +⎪

= +⎪⎪⎪⎨ = + −⎪⎪⎪ = + − +⎪⎩

ψ I I

ψ I I

U I ψ ψ

U I ψ ψ

(3)

Where, L, R, and ω represent inductance, resistance, and angular frequency; subscript s, r, and m denote the stator side, rotor side and mutual parameters; j is unit imaginary.

According the complex power theory, the stator active and reactive power and the electromagnetic torque can be derived as:

p n p ns s0 sc2 s0 ss2 s0

p n p ns s0 sc2 s0 ss2 s0

p n p ne p e0 ec2 s0 es2 s0

3( ) [ cos(2 ) sin(2 )]23( ) [ cos(2 ) sin(2 )]2

3 [ cos(2 ) sin(2 )]2

ω ϕ ϕ ω ϕ ϕ

ω ϕ ϕ ω ϕ ϕ

ω ϕ ϕ ω ϕ ϕ

⎧ = + + + + + +⎪⎪⎪ = + + + + + +⎨⎪⎪ = − + + − + +⎪⎩

P t P P t P t

Q t Q Q t Q t

T n T T t T t

(4)

Where,

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−−−−

−−=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

ns

ns

ps

ps

ps

ps

ns

ns

ps

ps

ns

ns

ns

ns

ps

ps

ps

ps

ns

ns

ps

ps

ns

ns

ns

ns

ps

ps

ss2

sc2

s0

ss2

sc2

s0

d

q

d

q

dqdq

qdqd

qdqd

qdqd

dqdq

dqdq

iiii

uuuuuuuuuuuuuuuu

uuuuuuuu

QQQPPP

,

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−−

−−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

ns

ns

ps

ps

ps

ps

ns

ns

ps

ps

ns

ns

ns

ns

ps

ps

0ses2

ec2

e0 1

d

q

d

q

qdqd

dqdq

dqdq

iiii

uuuuuuuuuuuu

TTT

ω.

Comparing (4), it can found that the 2nd order ripples in stator reactive power and electromagnetic torque are consistent, so they can be eliminated simultaneously.

According to above analysis, under unbalanced conditions several control targets can be achieved with DFIG rotor current control, namely the constant active power control, constant electromagnetic torque and reactive power control, balanced stator current control, and balanced rotor current control. However, these control targets can’t be realized simultaneously.

III. DUAL SRF CONTROL SYSTEM

A. Control System Design Under unbalanced conditions, DFIG stator voltages,

currents and fluxes all include positive and negative sequence components, so it’s convenient to control the positive and negative sequence components in the positive and negative oriented SRF, respectively [4,5]. In oriented SRF, the stator voltage can be written as:

⎪⎩

⎪⎨⎧

=

=

0ps

ps

ps

d

q

u

uu, and

⎪⎩

⎪⎨⎧

=

=

0ns

ns

ns

d

q

u

uu (5)

With (2), (3) and (5), the control equation in dual SRFs can be designed as:

⎪⎪⎩

⎪⎪⎨

⎧

−−+=

+−+=

prdc

pr

*pr

irIirP

*pr

prqc

pr

*pr

irIirP

*pr

))(s

(

))(s

(

uiiKKu

uiiKKu

ddd

qqq (6)

⎪⎪⎩

⎪⎪⎨

⎧

−−+=

+−+=

nrdc

nr

*nr

irIirP

*nr

nrqc

nr

*nr

irIirP

*nr

))(s

(

))(s

(

uiiKKu

uiiKKu

ddd

qqq (7)

Where, 2

p p p p psm m mrqc s s r s s0 r r r

s s s s2

p p p psm mrdc s r s s0 r r r

s s s

( ) ( )( )

( ) ( )( )

q d d

d q q

RL L Lu u L iL L L L

RL Lu L iL L L

ψ ω ψ ω ω

ψ ω ψ ω ω

⎧= − + + − −⎪

⎪⎨⎪ = + + − −⎪⎩

⎪⎪

⎩

⎪⎪

⎨

⎧

−+−+=

−+−+−=

nr

s

2m

rrs0nsr

ns

s

s

s

mnrdc

nr

s

2m

rrs0nsr

ns

s

s

s

mns

s

mnrqc

))(()(

))(()(

qqd

ddq

iLLL

LR

LLu

iLLL

LR

LLu

LLu

ωωψωψ

ωωψωψ

With above control equations, the DFIG dual SRF control scheme can be designed as Fig.2.

B. Voltage Orientation and Components Sensing In positive SRF, the total stator voltage space vector is

denoted as: p n

sj(2 )p p ns s sedq dq

ω ϕ ϕ− + += +U U U (8)

Obviously, in positive SRF, the total stator voltage is composed of the constant component and the 2nd order ripples. So, the voltage orientation for positive SRF and negative SRF can be designed as Fig.3, based on the notch filter with its resonance frequency at synchronous frequency [6].

In Fig.3, the notch filter transfer function is shown as (9), which is used to filter out the 2nd components.

200

2

20

2

/)(

ωωω

+++

=Qss

ssF (9)

Where, ω0 is the angular frequency, Q is the quality factor and s is complex variable.

Also with the notch filter, the stator current components and the rotor current components in positive and negative SRF can be achieved, shown as Fig.4 and Fig.5, respectively.

C. Implement of PLL and notch filter In fig.3, to get the positive and negative SFR oriented under

unbalanced voltage condition, the positive and negative voltage components are taken out, and then the conventional PLL is adapted to them respectively. In this paper the conventional PLL is modeled as (10), and the designed sketch is shown in Fig.6.

1

2

ˆ ˆ ˆ

ω ε

θ ω ε

=⎧⎪⎨

= +⎪⎩

s

s s

r

r (10)

Where θε −= sjseU .

To improve the robustness and to damp the oscillations, the character roots normally are designed to equal the same negative real value, noted as ρ− . And then the values of r1 and r2 can be valued as:

21 / mr Eρ= − , 2 2 / mr Eρ= − (11)

Figure 3. Voltage orientation for positive and negative SRF

Figure 4. Positive and negative SRF stator currents sensing

Figure 5. Positive and negative SRF rotor currents sensing

Figure 6 The sketch of conventional PLL

To discrete and implement the second order notch filter, (9) is structured as Fig.7[7].

1Q

0ωs

0ωs

+− +−

+−input output

Figure 7 The implement structure of notch filter

IV. EXPERIMENTS To validate the design presented in the paper, an 11kW

DFIG-based wind turbine test system was built. In the test system, the 11kW DFIG is driven by a 15kW squirrel cage induction motor. By control design of the driving induction motor, the driving system can operate as driven by wind turbine. The main parameters of DFIG are shown in Table I.

The experiment results of the designed notch filter based PLL is shown in Fig.8. In the experiment, to validate the dynamic performance of the designed notch filter based PLL, the grid voltage is step changed, namely the unbalanced dip fault. Fig.8 shows the high dynamic performance of the

Figure 2. DIFG dual SRF control scheme

TABLE I. DFIG Parameters Rated power (kW) 11 Rotor current (A) 8.1Rated frequency (Hz) 50 Xs (Ω) 0.418Poles 4 Xm (Ω) 20.02Stator voltage (V) 380 Xr (Ω) 0.5627Stator current (A) 22.5 Rs (Ω) 0.2767Rotor voltage (V) 858 Rr (Ω) 0.3015

designed PLL.

Fig.9 and Fig.10 show the experimental results for the constant rotor current control case. Namely, in this case balancing rotor currents is set as the control target.

The rotor currents, under unbalanced input voltages, can be controlled very well, which is validated with Fig.9. To balance the rotor currents, the rotor current components in negative SRF are controlled zero. In this case, the DFIG operates just like its rotor windings open circuit for input voltage negative sequence components, so the stator current negative sequence components directly are decided by the input voltage negative sequence components, shown as Fig.10.

Fig.11 shows the constant stator current control case. Namely, in this case balancing stator currents is set as the control target.

From (3), the components of rotor currents in negative SFR follow the relationship as:

( )n n nr s s s m/qd qd qdL L= −I ψ I (12)

It can be found that to eliminate the stator current negative sequence components, the rotor current components in negative SRF should be controlled as:

n nr s m/qd qd L=I ψ (13)

In practical, the rotor current reference value, n*rqdI , in

negative SRF can be set either by (13) directly, or by closed control of the stator currents in negative SRF.

With the designed control scheme, the other control targets, such as constant active power control, constant reactive power or torque control will be easy to be implemented.

Figure 9. Rotor currents with balanced rotor current control target

Figure 10. Stator currents with balanced rotor current control target

Figure 11. Stator currents with balanced stator current control target

V. CONCULTIONS When DFIG operate under unbalanced input voltage

conditions, the special control system should be designed properly, otherwise, the 2nd order ripples will appear in stator currents, stator active and reactive power, electromagnetic torque, and so on. Based on the mathematical model of DFIG under unbalanced voltage conditions, the pulsation and the control targets are analyzed. To realize the control targets, a dual SRF control scheme and the notch filter based PLL are designed and discussed. Experiments on 11kW DFIG-based wind turbine test system validate the design.

REFERENCES [1] J. Morren and S.W.H de Haan, “Ridethrough of Wind Turbines with

Doubly-Fed Induction Generator During a Voltage Dip,” IEEE Trans. on Energy Conversion, Vol.20, No.2, pp.435-441, 2005.

[2] J. Lopez, E. Gubia, P. Sanchis, X. Roboam, and L. Marroyo, “Wind turbines based on doubly fed induction generator under asymmetrical voltage dips”. IEEE Trans. on Energy Conversion, Vol. 23, No.1, pp 321-330, March 2008.

[3] O. G. Bellmunt, A. J. Ferre, A. Sumper, and J. B. Jane, “Ride-through control of a doubly fed induction generator under unbalanced voltage sags”. IEEE Trans. on Energy Conversion, Vol. 23, No. 4, pp 1036-1045, Dec. 2008.

[4] L. Xu, and Y. Wang, “Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditions”. IEEE Trans. on Power Systems, Vol.22, No.1, pp 314-323, Feb. 2007.

[5] P. Zhou, Y. He, D. Sun, and J. Zhu, “Control and protection of a DFIG-based wind turbine under unbalanced grid voltage dips”, in Proc. of IEEE IAS, Oct. 2008.

[6] L. Shi, and M. L. Crow, “A novel PLL system based on adaptive resonant filter”, in Proc. of IEEE 40th NAPS, Sept. 2009.

[7] Mihai Ciobotaru, Remus Teodorescu, and Frede Blaabjerg, “A new single-phase PLL structure based on second order generalized integrator”, in Proc. of IEEE PESC, pp361-366, Jun. 2006.

Figure 8 The dynamic response of the designed notch filter based PLL