Modeling of DFIG Based Wind Generator and Transient Characteristics Analysis

G.H. Li, B.H. Zhang, Z.G. Hao, J. Wang School of Electrical Engineering, Xi’an Jiaotong University

Xi’an, China gofeilee@gmail.com

Z.Q. Bo, David Writer, Tony Yip ALSTOM T&D Ltd

Stafford ST17 4LX, UK

Abstract— As a renewable, clean energy, wind energy has attract more and more attention. It has become a common understanding of the world to vigorously develop wind energy. In order to guarantee the safety and reliability for wind power integration operation, it is of great significance to establish an appropriate wind power generator system model and analyze its electromagnetic transient characteristics. This paper analyzes the control strategy of doubly-fed induction generator (DFIG) based wind generator. Vector decoupling control technology has been adopted to establish the mathematical model of DFIG based wind generator. Furthermore, an electromagnetic dynamic simulation model of DFIG based wind generator is established based on the platform of PSCAD/EMTDC. A short circuit fault is simulated to study the dynamic response of DFIG based wind generator. Finally, transient characteristic of DFIG is analyzed by this paper.

Keywords-DFIG; Vector decoupling control; dynamic model; transient characteristic

I. INTRODUCTION Energy depletion and pollution problems compel us to find

a clean and renewable energy. The end of 2008, the global total installed capacity of wind power had reached 120 000MW. At present, wind power still keeps the fastest growth rate in the renewable energy industry. Commonly used wind turbines can be divided into 4 types, as is mentioned in [1]. As an economical wind power generation, doubly-fed induction generator (DFIG) based wind generator has become the most widely used wind turbine. To further study the impact of wind turbine on the existing power grid, the electromagnetic transient modeling of DFIG based wind generator has become a research hotspot in recent years. Complete mathematical model of DFIG based wind generator is analyzed in this paper and an electromagnetic dynamic simulation model based on the PSCAD/EMTDC platform is established by adopting vector decoupling control method. A severe three-phase short circuit fault is simulated to study the response of DFIG wind generator and the transient characteristic is analyzed.

II. DFIG BASED WIND GENERATOR MODEL

A. Overall Structure of DFIG Based Wind Generator The DFIG based wind generator model can be divided into

five parts: wind speed model, aerodynamic model, pitch angle control model, mechanical drive model and DFIG model with

its control system [2]. Overall structure of DFIG based wind generator is shown in Fig. 1.

Mω

gP

Gω

GP

βrateP

MTGT

sU

GP

GQ

wV

Figure 1. Overall structure of DFIG based wind generator model

In order to describe the random and intermittent characteristics, wind speed Vw is constituted by basic wind, gust wind, ramp wind and random wind. The process of capturing wind energy and converting it to mechanical energy is simulated by aerodynamic model. Mechanical drive model includes low-speed shaft, gearbox and high-speed shaft. It can be simulated by a one-order inertial link. Aerodynamic model simulates the wind turbine to capture and convert wind power to mechanical energy.

B. Pitch Angle Control System Model In order to improve the wind energy utilization ratio, almost

all the wind turbines are equipped with the pitch angle control system. When the wind speed falls in between the start wind speed and rated wind speed, pitch angle is always zero and the wind turbine tracks the maximum wind power. When the wind speed is greater than the rated wind speed, pitch angle is adjusted to keep the wind turbine running on a constant speed [3]. Pitch angle control system model macro is shown in Fig. 2.

βrefβ

PΔ 1

sTddtβ

minddtβ

maxddtβ

1s

minβ

maxβ

βrateP

GP

wV wrateV

Figure 2. Pitch angle control system

This work is supported by the Major State Basic Research Development Program of China (973 Program) (2009CB219704)

978-1-4244-8782-0/11/$26.00 ©2011 IEEE

C. Vector Decoupling Control System of DFIG Vector decoupling control method is the core technology of

DFIG based wind generator. The method is achieved by controlling the grid VSC and rotor VSC, as is shown in Fig. 3.

Figure 3. Schematic diagram of DFIG wind turbine

1) The Grid VSC Control System Power grid voltage oriented vector control scheme is

adopted in grid VSC to achieve power decoupling control between the grid VSC and power grid. The two main control targets are to keep the DC bus voltage stable and adjust the reactive power exchange with power grid.

a) Mathematical Model of Grid VSC

ai

bi

ci

L R

CdcU

ae be ce

avbv

cv

Figure 4. Grid VSC macro

From Fig. 4 above, the grid-side voltage source converter (VSC) can be described by (1) under synchronous reference frame [4].

)1(

1

1

⎪⎪⎩

⎪⎪⎨

⎧

+++=

+−+=

qdq

qq

dqd

dd

vLidtdi

LRie

vLidtdiLRie

ω

ω

In the equations above, subscript “d” stands for d-axis component and subscript “q” stands for q-axis component; ω1 is the angular frequency of the power grid voltage. The power exchange between the power and the grid VSC can be calculated in (2).

)2()(5.1

)(5.1

⎪⎩

⎪⎨⎧

−=

+=

qddqr

qqddr

ieieQ

ieieP

b) Control Scheme of Grid VSC Set the d-axis on the direction of the grid voltage vector, q-

axis ahead of the d-axis 90 degrees, which results in ed = e, eq=0, where e is the voltage vector of the power grid. The power equation turns into:

)3(5.1

5.1

⎩⎨⎧

−==

qr

dr

eiQeiP

The exchanged active power is only related to the d-axis current id, and reactive power is only related to the q-axis current iq. Power decoupling control can be easily achieved if id and iq can be adjusted respectively. But the current can’t be directly controlled by the grid VSC. It must be transformed into voltage variable which can be directly controlled by the grid VSC. By substitution of the equations ed=e, eq=0, (1) can be expressed in (4).

)4(

1*

1*

⎪⎪⎩

⎪⎪⎨

⎧

−−−=

++−−=

dq

qq

qd

dd

Lidtdi

LRiv

eLidtdiLRiv

ω

ω

In (4), vd* and vq

* are the reference voltage vectors of grid VSC in synchronous reference frame. The grid VSC control system macro is shown in Fig. 5.

*capv

capv

*rQ

rQ

*di

di

*qi

qi

qie 1ω+

di1ω−

*dv

*qv

Figure 5. Grid VSC control system macro

A double closed loop structure is adopted. External loop PI regulator is used to keep the DC bus voltage stable, adjust the reactive power exchange with power grid and produce reference current for the inner loop. Inner loop PI regulator is used to track given current in real time.

2) The Rotor VSC Control System Stator flux oriented vector control scheme is adopted in

rotor VSC to achieve power decoupling control between the stator and power grid. The main control target is to realize maximum power tracing, cooperating with wind turbine. Another target is to adjust the reactive power exchange with power grid, to maintain a suitable power factor of the wind generator [5].

a) Mathematical Model of DFIG Assuming that stator and rotor windings are three-phase

symmetrical, the air gap distributes in the circumference of the motor uniformly, the electronic and magnetic circuits are symmetrical. The mathematical model of DFIG in synchronous reference frame can be described with the following equations [6].

Voltage equations:

)5(

1

1

1

1

⎪⎪

⎩

⎪⎪

⎨

⎧

++=

+−=

++=

+−=

rqrrdrqrq

rdrrqrdrd

sqssdsqsq

sdssqsdsd

iRspu

iRspuiRpu

iRpu

ψωψψωψ

ψωψψωψ

Flux equations:

)6(

⎪⎪

⎩

⎪⎪

⎨

⎧

+=+=

+=+=

sqmrqrrq

sdmrdrrd

rqmsqssq

rdmsdssd

iLiLiLiLiLiLiLiL

ψψψψ

Electromagnetic torque equation:

(7) )( sdrqsqrdme iiiiLT −=

Stator power equations:

)8(⎪⎩

⎪⎨⎧

−=

+=

sqsdsdsqs

sqsqsdsds

iuiuQ

iuiuP

In the equations above, subscript “s” stands for stator; subscript “r” stands for rotor; “p” is the differential operator; ω1 is the angular frequency of power grid voltage.

b) Control Scheme of Rotor VSC The stator of DFIG is directly connected to the power grid.

For stator resistance is much smaller than the reactance, it can be neglected. Thus the stator flux and the stator voltage vector is approximate perpendicular to each other. Set the d-axis on the direction of the stator flux vector, q-axis ahead of the d-axis 90 degrees [7]. Under this condition, d-axis component of the stator voltage is zero and q-axis component is constant. The result is expressed as in:

)9(,0,0, ssqsdsqssd uuu ==== ψψψ

Where, ψs is the stator flux vector; us is the stator voltage vector. Conclusion can be obtained by joining (6) and (9).

)10(

⎪⎪⎩

⎪⎪⎨

⎧

−=

−=

s

rqmsq

s

rdmssd

LiL

i

LiLi ψ

By joining (8), (9) and (10), the output power of the stator can be calculated in (11)

)11()(

⎪⎪⎩

⎪⎪⎨

⎧

−==

−==

rdmss

ssdss

rqs

mssqss

iLLuiuQ

iLLuiuP

ψ

The stator active power is only related to the rotor q-axis current irq, and reactive power is only related to the rotor d-axis current ird. Power decoupling control can be easily achieved if irq and ird can be adjusted respectively. Similar to the grid VSC control method, control variables must be transformed from current to voltage which can be directly controlled.

By joining (5), (6) and (9), the reference voltage of rotor VSC can be calculated in (12).

)12(

1

2

11

2*

1

22*

⎪⎪⎩

⎪⎪⎨

⎧

−++−+=

−−−+=

rds

mrs

s

mrq

s

mrsrqrrq

rqs

mrsrd

s

mrsrdrrd

isL

LLLsLLpi

LLLLiRu

isL

LLLpiL

LLLiRu

ωψω

ω

In (12), urd* and urq

* are the reference voltages vectors of rotor VSC in synchronous reference frame. The rotor VSC control system macro is shown in Fig. 6.

rdi*rdu

*rqu

*sdi

*sqi

srefP

sP

srefQ

sQ

*rqi

rqird

s

mrss

s

m isL

LLLsLL

1

2

1 ωψω −+

rqs

mrs isL

LLL1

2

ω−

*rdi

sψ

Figure 6. Rotor VSC control system macro

A double closed loop structure is adopted. External loop PI regulator is used to realize maximum power tracing by cooperating with wind turbine, adjust the reactive power exchange with power grid, and produce reference current for the inner loop. Inner loop PI regulator is used to track given current in real time.

III. TRANSIENT CHARACTERISTICS ANALYSIS

A. EMTDC/PSCAD Simulation A 2 MW DFIG based wind generator is simulated in a

single-machine infinite-system. A three phase symmetrical short circuit fault occurs at the high voltage side of the package transformer at the time t=3s and lasts for 200ms. Curves of the stator voltage (Vs), electromagnetic torque (Te), mechanical torque (Tm), rotor speed (n), DC voltage (Vdc), stator current (is) and the rotor current (ir) are shown in Fig. 7.

Time [s]

Volta

ge [p

.u]

Time [s]

Torq

ue [p

.u]

(a) Stator voltage (b) Electromagnetic and

mechanical torque

Time [s]

Volta

ge [k

V]

Time [s]

Spee

d [p

. u]

(c) DC bus voltage (d) Rotor speed

Time [s]

Volta

ge [k

A]

(e) Stator current

Time [s]

Volta

ge [k

A]

(f) Rotor current

Figure 7. Curves of the DFIG based wind generator under short circuit fault.

B. Transient Characteristics Analysis DFIG terminal voltage drops to about 10% of the rated

voltage during three phase short circuit fault. Electromagnetic torque decreases because the stator can’t continue outputting active power. But the input mechanical torque keeps unchanged. Accumulated power makes the rotor accelerate. Meanwhile, Accumulated power will flow into rotor VSC. This will result in the increase of DC bus voltage. The analysis above is consistent with the simulation result. Simulation shows that, for the electromagnetic torque and rotor speed, the recoil phenomenon occurs on the fault instant. This is similar to synchronous machine.

The simulation also shows that there is a large DC component in stator short circuit current, while the power frequency component almost disappears. For the rotor current, the situation is quite the reverse. The phenomenon is explained as follows. The angular frequency of rotor current is calculated by ωψ-ωr, where ωψ is the angular frequency of stator flux and ωr is rotating angular frequency of rotor. The method to observe the stator flux is shown in Fig. 8.

s1

sss Riu αα −

s1

sss Riu ββ −

αse

βse

αψ s

βψ s

ψθ

ψ

ψω

Figure 8. Stator flux observer macro

In Fig.8, usα, usβ, isα and isβ are the voltage and current of stator in two-phase rotating frame and Rs is the stator resistance, which is so small that can be neglected. Under normal operation, ωψ is equal to synchronous angular frequency ω1. During severe three-phase fault as in the simulation, the stator voltage drops close to zero, i.e. usα≈0 and usβ≈0. After the integral part, ψsα and ψsβ basically keep unchanged during fault time. So the calculated θψ keeps unchanged. This will result

that the calculated angular frequency of stator flux ωψ is zero, which is close to synchronous angular frequency under normal situation. Compared to angular frequency of stator flux, the rotating angular frequency of rotor can still be correctly observed by rotor position detector, which is close to synchronous angular frequency because the slip is very small in DFIG. So the angular frequency of rotor current is ωψ-ωr≈ωr, approximately corresponding to power-frequency current. According to electromechanical theory, the angular frequency of the stator current will be close to zero, approximately corresponding to DC current.

IV. CONCLUSION Vector decoupling control method is the core technology of

DFIG based wind generator. A DFIG based wind generator model is established based on PSCAD/EMTDC in this paper, by adopting vector decoupling control method. The simulation result shows that in severe three-phase short circuit fault, the frequency of rotor current is close to power-frequency while the stator generates an approximate DC current. Thus the transient characteristic of DFIG based wind generator is completely inconsistent with the traditional synchronous machine. The phenomenon is analyzed in this paper. With the increasing popularity of DFIG based wind generator, power-frequency based protection relay can be no longer applied to wind farm. It is necessary to develop new, special protection system for wind farm.

ACKNOWLEDGMENT My deepest gratitude goes first and foremost to Inner

Mongolia Electric Power Research Institute. This work is finished by the selfless help of researchers in Inner Mongolia Electric Power Research Institute. Thank for their many useful advice and standpoints.

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