Dynamic Response of Wind Turbine with Double-Fed Induction Generator during Grid Voltage Dip

Kao-she Zhang Ping Su Lian-hui Ning Xin-wei Zhang

The Faculty of Water Resources and Hydraulic Power Xi’an University of Technology

Xi’an,China zhangks@263.net suping-1214@163.com

Abstract—Based on the transient model of double-fed induction generator (DFIG) under synchronous rotating reference frame, the electromagnetic transient simulation system of DFIG is implemented under PSCAD/ EMTDC. This paper deliberates the dynamic responses of stator and rotor voltage and current, active and reactive power, electromagnetic torque, rotor speed and DC link voltage both during the grid voltage dip and after the clearance of the fault and analyses the reason of the responses. Then, the dynamic response intensity of the above-mentioned variables under two typical voltage dip conditions is compared. Finally, the simulation results validate the research conclusion.

Keywords- double-fed induction generator (DFIG); voltage dip; dynamic response

INTRODUCTION

At present, the Double-Fed Induction Generator (DFIG) has a large proportion in variable speed and constant frequency wind power generation System, with the increasing of the single-unit capacity and installed capacity of the DFIG unit, the reaction between the generator and grid becomes more and more important [1]. According to the new requirement of grid regulation, when power failure occurs such as voltage dip (in a certain range), the wind turbine shall remain to be connected with the Main-Grid, therefore Low Voltage Ride Through(LVRT) of DFIG has become one of the domestic and foreign scholar’s hot research subjects. The leading country of the wind power generation technology has issued the quota standard about through fault in succession.

The voltage dip is referred to the sudden voltage drop by 10% -90% in a single point and lasts for a half cycle to 1 minute. The voltage dip is classified in three categories according to the reason which it forms: voltage dip caused by power failure, voltage dip caused by large-scaled generator’s start-up, voltage dip caused by generator’s reacceleration. As to the voltage dip caused by the power failure, the time of the voltage dip and voltage recovery is comparatively short, so it is a usual form of voltage tip. In order to reduce the harm to the DFIG caused by power failure, ascertain the related method of passing through fault on low voltage and protective measure, so it is very important to make clear the dynamic respond of the DFIG during Grid voltage dip and the reason which it produced. Literature [5] has established the precise model for DFIG in the stator winding dynamic’s process, and the voltage dip fault response simulation is implemented on the basis of improved vector control strategy. Literature [6], the response of DFIG during symmetrical grid faults is simulated by time

domain simulation model, and at the same time it puts forward power failure excitation control to guarantee that the system can recover from failure to steady operation rapidly. Literature [11] compare the dynamic responses of DFIG under three different degrees of voltage dip and put forward the corresponding LVRT control strategy, but has not analyzed the principle by which it produced. Literature [13]: Considering the crowbar protection and the current instantaneous trip protection, the analysis of the dynamic response of DFIG has been conducted, which brings about a certain error to the response result.

On the basis of the rotor flux linkage vector control of DFIG, the paper analyses the influences of flux linkage changes on characteristic quantities of the generator during the voltage dip process according to the principle of conservation of flux linkage. Two kinds of typical voltage dip are chosen to be simulated, one is 50% voltage dip of symmetrical three-phase with the duration of 0.5s, the other is 80% voltage dip of symmetrical three-phase with the duration of 0.25s. The simulation result can validate the correctness of theoretical analysis.

I. THE TRANSIENT MATHEMATICAL MODEL OF DFIG Diagram 1 is the schematic diagram of DFIG wind power

generator of variable speed and constant frequency.

Figure 1. Schematic Diagram of the DFIG Wind Energy Generation System

The DFIG voltage equation under synchronized revolving

coordinate system is [5-6]:

⎪⎪⎩

⎪⎪⎨

⎧

+++=

++=

rss

momrrrrr

smom

sss

jdtLdIL

dtdILIRV

jdtdILIRV

ψωσ

ψω2

1

(1)

The flux linkage equation is:

978-1-4244-4813-5/10/$25.00 ©2010 IEEE

⎪⎩

⎪⎨⎧

+=

=+=

rrs

momr

momrmsss

ILLIL

ILILIL

σψ

ψ2

（2）

The active and the reactive power of the stator respectively is:

[ ][ ]⎩

⎨⎧

−=−=

*

*

Im5.1Re5.1

ss

ss

IVQIVP

（3）

In the formula: rm

ssmo LL

ILI+

= ，sr

m

LLL2

1−=σ 。 sV 、

rV are respectively the stator and rotor voltage vector; sI 、

rI are respectively the stator and rotor current vector; sψ 、

rψ are respectively the stator and rotor flux linkage vector;

sR 、 rR are respectively the stator and rotor resistance;

mss LLL += σ ， mrr LLL += σ are respectively stator and

rotor winding entire self inductance, mL 、 sLσ and rLσ are respectively are respectively stator and rotor mutual inductance and stator leakage inductance and rotor leakage inductance；the variable above is the value that has been converted; 1ω is

the synchronous angular speed, rω is rotor angular speed;

rωωω −= 1s is slip angular speed.

II. ANALYSIS OF THE TRANSIENT PROCESS DURING THE VOLTAGE DIP

The process of the voltage dip is divided into two stages: The first stage is that wind turbine transitions from steady operation to faulty operation during voltage dip; the second stage is that wind turbine recovers from faulty operation to steady operation after voltage recovery; the paper mainly analyzes the first stage.

According to the principle of conservation of flux linkage, the generator stator flux remains constant in the fault instant. In order to maintain the constant flux leakage during faulty time, transient DC component will appear in the flux leakage.

When the grid voltage is normal, generator stator flux linkage and stator voltage can be express by space vector:

dtd

iRu ssss

ψ+−= （4）

In the formula: where su 、 si 、 sψ are respectively the voltage space vector of the stator voltage in static coordinates, stator current and stator flux, the sR is the stator winding resistance. According to the formula (4), we can deduce the relationship between the generator stator flux linkage components and the stator voltage components after the fault. The relationship can be expressed:

ωωωωω

ψψψψ

τ

ju

jue

jU

jU

jU sNsP

tsNsPs

sNsPsDCs

s

−′

+′

+⎟⎟⎠

⎞⎜⎜⎝

⎛ ′−

′−

=′+′+′=′− （5）

Where sψ ′ is the space vector of the generator stator flux

linkage after the fault and sDCψ ′ is the space vector of the generator stator flux linkage transient DC component after the fault, sPψ ′ and Nsψ ′ are the space vector of generator stator flux positive and negative sequence components after the fault;

sU is the space vector of the generator stator voltage before

fault; sPU ′ and sNU ′ are the space vector of the generator stator voltage of positive and negative sequence components after the fault; ω is the stator angular frequency; sτ is the attenuation

time constant of stator flux transient DC component; sPu′ and

sNu′ are the space vector of the positive and negative sequence components of generator stator voltage after the fault.

When DFIG-side three-phase symmetrical short-circuit fault occurs, due to the exhausted function of stator resistance, the stator flux DC component will gradually decrease, and the attenuation rate depends on the motor stator resistance and leakage. Since the generator rotor rotates with high speed during the voltage dip, the stator magnetic DC component with angular speed rω rotate against rotor winding, at the same time rotated frequency current component can be induced in the rotor winding (relative to the rotor), and then rotor flux transient DC component (relative to the stator) can be generated. Rotor flux DC component and stator flux DC component phase offset to maintain the rotor flux conservation during the fault. After the fault, under the effects of the stator resistance, the stator flux DC component will gradually attenuate, and the corresponding rotor speed frequency current component will attenuate, the attenuation rate depends on generator parameters. Because the momentary rotor transient magnetic components can only cross the stator winding magnetic leakage, when the stator flux DC component is large, the rotor winding induces a large current that produces enough magnetic flux which balances the stator flux linkage. This will lead to the rotor flow.

After the removal of the fault, generator stator voltage returns to be normal, the generator transient process is similar to the moment of fault, the stator flux still appears transient DC component, and this will also lead to the rotor flow.

As to the asymmetric grid fault, the stator flux linkage not only contains DC component but also contains negative sequence component. As the wind turbine speed is usually higher than the thermal power units, the speed of the stator flux leakage with a great rated slip that is relative to the DC component and negative sequence component causes the increasing of rotor circuit voltage and current significantly.

III. DFIG DOUBLE PMW TRANSDUCER CONTROL METHOD

A. Generator Side PWM Converter Control DFIG control is implemented by the converter on the rotor

side, therefore whether converter control on the rotor side is effective or not directly determines the DFIG system performance. DFIG has two main operational targets, The first is to achieve maximum wind power capture, the control of active power and DFIG speed is the core; The second is the control of DFIG stator output reactive power[14]. The active and reactive power of DFIG are closely relative with the rotor current, so we can control the rotor current of the DFIG by generator side converter to achieve these two goals. Thus, the control system of PMW converter on the generator side can be divided into two links, one is the speed control on the outer loop, the other is the current control in the inner loop, which forms double loop vector control mode, and the control principle is shown in figure 2.

dqabc

refω

refQ

Q

*qri

r qr r dr m dsR i L i L iω ω+ +

*eT s

m s

LL ψ

*dri

*dru

dru

*qruqru

dqabc

dqabc

,dr qri i

,ds qsi i

,ds qsu u

θ

r qr r qr m qsR i L i L iω ω− −

*1au

*1bu

*1cu

Figure 2. Diagram of Generator Side Rectifier Control

B. Grid Side PMW Converter Control The main functions of the grid-side PMW converter are to

keep DC bus voltage stable, the input current sinusoidal, and to control input power factor. Whether the DC bus voltage is stable or not depends on whether active power on the AC and DC side is balanced. If we can effectively control the input of AC-side active power, we can maintain DC bus voltage stable. As the grid voltage is basic constant, we can keep the stability of the DC-bus voltage by effectively controlling the input active power on DC side, the input power factor control is

dqαβ abc

αβ

abcαβ

*di

*qi

eθ

abcu

abciabc

αβdqαβ

dqαβ

e Lω

*dv

*qv

di qieLω

du

dcu

*dcu

Figure 3. Diagram of Grid Side Inverter Control

actually identical with the control of the input current reactive power component. And whether the input current waveform is sinusoidal or not is related to the main current control and modulation method. Thus, the PMW converter control system on grid side can be divided into two links: one is the speed control on the outer loop, the other is the current control in the inner loop, control principle is shown in figure 3.

IV. SIMULATION ANALYSIS OF THE DFIG RESPONSE DURING THE VOLTAGE DIP

In order to verify the result of theoretical analysis, based on the PSCAD/EMT DC platform, we can establish a simulation model for DFIG and control system and do the research during the voltage dip. The specific simulated parameters are as follows:

DFIG parameters: rated power is 500 kVA, stator rated voltage is 13.8Kv, rated frequency is 50 Hz, rated speed is 380rad/s, stator resistance is 0.0054pu, stator leakage is 0.102pu, rotor resistance is 0.0607pu, rotor leakage is 0.11pu, the moment of inertia is 0.7267s, the mechanical damping is 0.001pu.

This paper selects two ways of typical voltage dip to simulate and analyze, one is 50% voltage dip of symmetrical three-phase with the duration of 0.5s, the other is 80% voltage dip of symmetrical three-phase with the duration of 0.25s.Suppose the reason of voltage dip is that the three-phase short circuit fault that occur son grid side and rated power converter is large enough to withstand fault current.

A. The Voltage Dip of 50%-0.5s Assume that the three-phase short circuit occurs at 4s, lasts

for 0.5s, generator operates in the rated wind speed, and the variables of generators during the voltage dip are shown in figure 4.

a) Stator Voltage and Electromagnetic Torque

b) Rotor Speed

c) DC Voltage

d) Rotor Current

e) The d, q Axis Current of The Rotor

f) The Active and Reactive Power of the Stator

Figure 4. Dynamic Response of DFIG during 50%—0.5s Voltage Dip

As shown in figure 4-a, electromagnetic torque reduces correspondingly during the voltage dip, the flux leakage reduces because the voltage reduces, then electromagnetic torque reduces. But the mechanical input torque keeps constant when the wind turbine operates at rated wind speed, so the generator speed increases. After the fault removal, as the reason for inertia generator speed goes continues to increase, but the input mechanical power of generator is less than the output electromagnetic power right now, then the generator begins to slow down, and the generator speed stabilizes again after short regulation, as shown in figure 4-b. As shown in figure 4-d, rotor current increases because of the coupling effect on the generator stator, so the rotor current of d, q-axis increases (as shown in figure 4-e). The increase of the rotor current can damage the converter since the converter is directly connected with the generator rotor. As the system adopts a reactive power control, the reactive power of generator basically remains unchanged during the voltage dip, the active power reduces as while. Stator flux reduces after fault, which causes that the stator reactive power deviates from the original operating point, as shown in figure 4-f. Generator absorbs the

reactive power from system on the stator side during the voltage dip, which diminishes reactive power on the stator side, as shown in figure4-f.The generator voltage on the DC side is shown in figure 4-c, the DC voltage increases, but a large capacitor which is regarded as a inertial element is installed between the DC bus, the inertial element slows down the speed of DC side response, so the change of DC bus voltage is small. Conversely, the DC voltage drops when the excitation power needed exceeds the maximum power provided by converter on the grid side [12], which is to meet the need of rotor excitation power, conversely the DC bus voltage rises.

B. 80%—0.25s Voltage Dip Assume that the three-phase short circuit occurs at 4s, lasts

for 0.25s, generator operates in the rated wind speed. The variables of generators during the voltage dip are shown in figure 5.

The variable changes of generator during the voltage dip are shown in fig.5 are similar to counterpart that is shown in figure 4, but the changes and peak amplitude in fig.5 are larger than the counterpart that is shown in fig.4, oscillation frequency increases, and the recovery time of generator’s variable has became longer after the fault disappears. The reason why it occurs is the further voltage dip, from 50% to 80%.

a) Stator Voltage and Electromagnetic Torque

b) Rotor Speed

c) DC Voltage

d) Rotor Current

e) The d, q Axis Current of the Rotor

f) The Active and Reactive Power of the Stator

Figure 5. Dynamic Response of DFIG during 80%—0.25s Voltage Dip

TABLE I. THE CHANGE TREND OF DFIG DURING GRID VOLTAGE DIP

Variables Change trend

Stator voltage reduction Electromagnetic torque reduction Active power of generator reduction Reactive power of stator side reduction rev acceleration Rotor current active component augment Rotor current reactive component augment Voltage on DC side augment

We can conclude from the simulation result that when system operates under rating wind speed when voltage dip occurs, the change tendency of each variable of the generator is shown in Table 1, when the voltage dip occurs, stator voltage, electromagnetic torque, active power of the generator, reactive power on the rotor side will reduce, whereas rev of generator, the rotor current, DC point voltage will increase.

V. CONCLUSION The dynamic response of the DFIG during two different

typical voltage dip conditions is simulated in the paper, and the dynamic response of the DFIG during grid voltage dip is comparably analyzed, as a result, the simulations indicates:

1) In order to maintain the flux linkage conservation during the grid voltage dip, the amplitude value of rotor current increase correspondingly, where the amplitude value of rotor current has a close relationship with the intensity of the grid voltage dip, the more serious the

voltage dip is, the more large the rotor current amplitude increases.

2) The variables of DFIG will produce an intense oscillation during grid voltage dip, which indicates that the grid voltage fault has an intense influence on DFIG connecting with the grid. The more serious the voltage dip degree is, the more intense the oscillation of the generator’s characteristic parameters are, accordingly, the power electronic devices and the mechanical parts of the system will suffer great impacts

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BIOGRAPHIES Kao-she ZHANG, (1965- ), male, Qianese county in Shaanxi Province, associate professor, doctor, mainly engaged in the study of the power system stability control and electrical market. Ping Su (1985- ), male, PingLiangnese in GanSu province, master graduated student, mainly engaged in the study of power system analysis and wind power.