research article coordinated stability control of wind

Research ArticleCoordinated Stability Control of Wind-ThermalHybrid ACDC Power System

Zhiqing Yao1 Zhenghang Hao2 Zhuo Chen2 and Zhiguo Yan3

1School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China2School of Electrical Engineering Guizhou University Guiyang 550025 China3School of Electrical Engineering and Automation and Key Laboratory of Pulp and Paper Science ampTechnology of Ministry of Education of China Qilu University of Technology Jinan 250353 China

Correspondence should be addressed to Zhiguo Yan yanzg500sinacom

Received 12 August 2015 Accepted 16 September 2015

Academic Editor Xinguang Zhang

Copyright copy 2015 Zhiqing Yao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The wind-thermal hybrid power transmission will someday be the main form of transmitting wind power in China but suchtransmission mode is poor in system stability In this paper a coordinated stability control strategy is proposed to improve thesystem stability Firstly the mathematical model of doubly fed wind farms and DC power transmission system is established Therapid power controllability of large-scale wind farms is discussed based on DFIG model and wide-field optical fiber delay featureSecondly low frequency oscillation and power-angle stability are analyzed and discussed under the hybrid transmission mode ofa conventional power plant with wind farms A coordinated control strategy for the wind-thermal hybrid ACDC power systemis proposed and an experimental prototype is made Finally real time simulation modeling is set up through Real Time DigitalSimulator (RTDS) including wind power system and synchronous generator system and DC power transmission system Theexperimental prototype is connected with RTDS for joint debugging Joint debugging result shows that under the coordinatedcontrol strategy the experimental prototype is conductive to enhance the grid damping and effectively prevents the grid fromoccurring low frequency oscillation It can also increase the transient power-angle stability of a power system

1 Introduction

As one of the most efficient new energy sources that have thepotential of large-scale development wind power generationhas developed speedily in China Due to the limited abilityof electricity consumption wind power in northwest Chinanortheast China and north China should be transmittedto the load center by long-distance transmission line [1 2]Given that wind power is not constant and it is not econom-ical to transmit wind power alone there arises the necessityto ldquobondrdquo large-scale wind farms with thermal power plantso as to realize transregional transmission However hybridtransmission system easily triggers low frequency oscillationor angle instability [3 4]

Damping features and controllable strategy of flywheelenergy storage device [5] flexible power conditioner [6] andstatic series compensator [7] were studied to improve damp-ing of the power system in previous research But the cost of

large-scale power electronic equipment is so high that it limitsthe application In comparison doubly fed wind generatorcan realize decoupling control of active and reactive power[8] Excitation converter in the wind turbine system can beadjusted to control the active power in the transient processAs a result for large-scale wind farms active power in thewhole wind farms can be adjusted randomly and quicklythrough the communication networkmaking thewind farmscontrollable So long as the active power is able to be adjustedit is possible to enhance the stability of the power systemControllable power in the wind farms can not only helpincrease the damping and prevent low frequency oscillationbut also enhance transient angle stability of the power systemwhich is meaningful for ensuring grid safety

In this paper firstly structural features of hybrid powersystem of wind farms and thermal power plant are analyzedand problems about stability of the power transmissionsystem are pointed out Secondly the mathematical model of

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 591232 9 pageshttpdxdoiorg1011552015591232

2 Mathematical Problems in Engineering

Local load Northwest grid

Sanhua grid

B1

LAC

WG1 B2

WG2

B3

WG3

B4

WG4

B5

B6

WG5

SGsim

simsimsimsim

Figure 1 ACDC power system with wind farms incorporated

doubly fed wind farms and DC power transmission system isestablished And it is proved that active power in the large-scale wind farms is controllable Thirdly for the purpose ofincreasing damping of the system and enhancing angel sta-bility a coordinated control strategy for wind farms and DCpower transmission system is proposed Finally the experi-mental prototype is made and the control effect of the experi-mental prototype is also introduced in detail

2 ACDC Power Transmission SystemIncorporating Wind Farms

Chinese large-scale wind farms are usually located at remoteareas Due to small load capacity power generated by thelarge-scale wind farms cannot be consumed So long-distancetransmission is an inevitable solution But as the wind poweris not constant long-distance transmission is costly if windpower is the only thing to transmit And irregular fluctuationof the wind power would make the grid unstable So at thepresent time a hybrid transmission mode of wind farms andthermal power plant (also named as wind-thermal hybridpower system) [9] is the main form of transmission as isshown in Figure 1 To be more specific wind farms are con-nected with the thermal power plant nearby and the power istransmitted to other areas by extra high voltage (EHV) line

Wind-thermal hybrid power transmission mode is forlong-distance transmission But as the utilization hours ofwind power are lesser than the conventional thermal powerplant the transmission channel capacity of wind power isdesigned lower than the maximum power When large-scalewind power is generated the transmission line will be heavilyloaded and the thermal power plant also functions in aheavy-load state resulting in low frequency oscillation Inaddition vector control of the turbine may pose influence ondamping [10] It is also worth noticing that the thermal powerunit bonded with the wind farms is responsible for curbingwind power fluctuation So the adjustment for the unit isfrequent which would damage the power system stabilizer(PSS) [11] and hamper damping characteristic Thereforeeffective measures on damping should be taken to ensure safeoperation of the wind-thermal power transmission system

In addition the wind-thermal hybrid power system doesnot work in a conventional way The dynamic behaviors ofwind farms may weaken the angle stability of the thermalpower plant even the whole power system Thus the windfarms and the ACDC power transmission system should be

subjected to coordinated control in order to erase negativeeffect caused by the wind farms

3 Mathematical Model for Wind-ThermalHybrid Power Transmission

31 Wind Turbine System The mechanical part of the windturbine system includes wind turbine transmission shaftand gearbox Wind turbine is used to capture wind energythrough the turbines and transform it to the mechanicaltorque on the wheel hub The shaft and gearbox is used topass the driven force of the wind turbine to the generator andincrease the revolving speedThe gear ratio can reach 100 Tosimplify calculation themechanical part is regarded as a con-centrated mass expressed by first-order inertial element [8]

d119875119898

d119905=

1

119879119889

(119875119879minus 119875119898) (1)

where 119875119898and 119875119879refer to mechanical power and electromag-

netic power respectively on the rotor of the generator 119879119889

refers to inertia time constant

32 MathematicalModel for DFIG DFIG is actually the rotorasynchronous motor There are symmetrical three-phasewindings on the stator and the rotor The modeling processis similar to that of asynchronous motor and synchronousgenerator in which the primitive equation is confirmed in thethree-phase static coordinate system and then coordinates aretransformed Unlike the modeling of synchronous generator119889119902 coordinates of DFIG can be oriented in different modessuch as stator flux mode rotor flux mode and stator voltagemode And orientation of 119889119902 coordinates of synchronousgenerator is only to take physical location of the rotor In thispaper the stator vector voltage of DFIG is taken as axis 119902In the 119889119902 coordinates system the stator flux (120595

119889119904 120595119902119904) and

rotor current (119894119889119903 119894119902119903) are taken as the state variablesThe state

equation is expressed as follows [11]

119901120595119889119904

= minus119903119904

119897119904

120595119889119904+ 11989710158401015840

119903119904119894119889119903

+ 1205961120595119902119904

119901120595119902119904= minus

119903119904

119897119904

120595119902119904+ 11989710158401015840

119903119904119894119902119903minus 1205961120595119889119904+ 119906119902119904

1199011198971015840

119894119889119903

= minus119903119903119894119889119903

+ 119906119889119903

+ 1205961199041198971015840

119894119902119903+ 12059611990411989710158401015840

120595119902119904minus 11989710158401015840

119901120595119889119904

1199011198971015840

119894119902119903

= minus119903119903119894119902119903+ 119906119902119903minus 1205961199041198971015840

119894119889119903

minus 12059611990411989710158401015840

120595119889119904minus 11989710158401015840

119901120595119902119904

(2)

where 1198971015840

= (119897119903minus 119897119898119897119898119897119904) and 119897

10158401015840

= 119897119898119897119904 119897119904 119897119903 and

119897119898

being stator self-inductance rotor self-inductance andmutual inductance respectively 119903

119904and 119903119903are stator and rotor

resistance respectively 1205961and 120596

119904are synchronous speed

and slip respectively 119906119889119903

and 119906119902119903are vertical and horizontal

vector of excitation respectively 119906119902119904is stator voltage and 119901

is differential operator

33 UHVDC Power Transmission System Model UHVDCpower transmission refers to DC transmission based onthyristor inverter It consists of the inverter DC line and

Mathematical Problems in Engineering 3

the auxiliary equipment [12 13] Quasi steady state modelis used to simulate the UHVDC primary system DC com-mutation is described by algebraic equation DC line andsmoothing reactor are described in the T-equivalent-circuitmodel [14ndash16] Substitute the algebraic equation for thedifferential equation and get the mathematical model forUHVDC power transmission system expressed by [17 18]

119868119889119903

=1

119871119889119903Σ

(minus119877119889119868119889119903

minus 119880119888+3radic2

120587119880119889119903cos120572 minus

3

120587119883119903119868119889119903)

119868119889119894=

1

119871119889119894Σ

(minus119877119889119868119889119894minus 119880119888+3radic2

120587119880119889119894cos120573 minus

3

120587119883119894119868119889119894)

119880119888=

1

119862(119868119889119903

minus 119868119889119894)

(3)

where 119868119889119903 119868119889119894 and 119880

119888are state variable 119868

119889119903and 119868119889119894are DC

current of rectifier and inverter 119880119888refers to the voltage

in the middle of DC line 119877119889is direct current resistance

119862 is earth capacitance equivalent to DC line 119880119889119903

and 119880119889119894

are DC voltage of rectifier and inverter 119871119889119903Σ

and 119871119889119894Σ

areequivalent inductance of rectifier and inverter119883

119903and119883

119894are

commutation reactance of rectifier and inverter and 120572 and 120573

are trigger delay angle of rectifier and trigger angle of inverter

4 Conditions for Quick Adjustment ofthe Wind Farms

41 Quick Adjustment of the Active Power of Single Turbinein Transient Process Before the wind farms realize theeffectively quick adjustment it ismade sure that every turbineis highly controllable From (2) the rotor current can becontrolled by rotor voltage But 119894

119889119903and 119894119902119903are cross-coupled

so feedforward compensation scheme is usually adopted torealize decoupling control The feedforward compensation iscalculated from rotor current and internal flux variables

119890119889119903

= 119896 (1205961199041198971015840

119894119902119903+ 12059611990411989710158401015840

120595119902119904)

119890119902119903

= minus119896 (1205961199041198971015840

119894119889119903

+ 12059611990411989710158401015840

120595119889119904)

(4)

Add 119890119889119903

and 119890119902119903to 119906119889119903

and 119906119902119903 and get the new control

variable For the state equation of rotor current in (2)substituted feedforward compensation item the relationshipbetween rotor current and control command (119906lowast

119889119903 119906lowast119902119903) is

1199011198711015840

119894119889119903

= minus119903119903119894119889119903

+ 119906lowast

119889119903

1199011198711015840

119894119902119903

= minus119903119903119894119902119903+ 119906lowast

119902119903

(5)

Equation (5) shows that the response of active currentand reactive current to the control command is the first-orderinertial link Time constant of inertial element is 120591 Typicalparameters of DFIG are substituted into 120591 and we can get it isabout 10ms This means that the single turbine can respondat the level of ms under external control command

42 Quick Adjustment of the Active Power of Wind Farms inTransient Process In the previous research the wind farmswere usually equaled to a single wind turbine [8 11] Obvi-ously they are different Section 41 has already proved thatthe single turbine can respond at the level of ms but whetherthis holds true to the wind farms still needs to be proved

A large-scale wind farm has hundreds of wind turbinesControlling them depends on wide-field communicationtechnology The control system of the wind farms has amaster-slave structure There are two methods of commu-nication (1) one-to-multiple answering transmission and(2) one-to-multiple global broadcast For method (1) as allturbines (200 sets) are slave turbines it means 200 messagesare sent in a controlling cycle For method (2) as everyturbine receives the same message only 1 message is sent in acontrolling cycle

Message transmission presents the following featuressuppose the length of the message is 200 bits and the serialcommunication baud rate is 1Mbps It is calculated that itcosts 02ms to send the message If fiber communicationis adopted for long-distance transmission 15ms should beused in photovoltaic conversion So the total time which isthe delay time of the fiber communication for long-distancetransmission is 17ms Therefore time delay in a controllingcycle in method (1) is 200ms and that in method (2) is17msObviouslymethod (2) is suggested as 17ms timedelaywill not pose significant influence on the closed-loop controlsystem

According to the analysis in Sections 41 and 42 based onglobal broadcast fiber communication technology the windfarms can be an active power source which is able to beadjusted quickly

5 Coordinated Control Strategy of WindFarms and DC Power Transmission System

51 Basic Ideas and Purposes of Coordinated Control Eventhough it may weaken the damping of conventional powerplant and angle stability when the wind farms are con-nected with the thermal power plant the ability of poweradjustment of the wind farms would increase the dampingof synchronous generator and enhance angle stability Basicideas of coordinated control of wind farms and DC powertransmission system are mainly described as follows therevolving speed or the frequency of synchronous generatorof the conventional power plant is fed back to the controllerthen the controlled quantity that can activate small-scaledynamic active power in the wind farms is produced throughgain calculation and phase correction and the dynamic activepower of the wind farms propels the synchronous generatorto produce electromagnetic torque with damping character-istic So the damping can be increased and oscillation canbe restrained The key to supply the synchronous generatorswith the positive damping is that the wind farms must becontrollable and can be controlled quickly

52 Technical Framework of Coordinated Control Based onthe controllability of the wind farms and DC transmissionsystem the damping control principle of the thermal power


DC power controlsystem

Wide-field fiber network

Wind farms

Wide-field reactivepower control

Inputoutput of control

word

Inputoutput of controlword

Inputoutput of controlwordSmooth

Smooth

Scaling

Scaling

Scaling

Integral

K2

K1

K3

1

1 + sT1

1

1 + sT3

Δff0

fAC

ΔU

UAC

U0

ΔPDCΔPDCmax

ΔPDCmin

0

0

0

Ctrl = 0

Ctrl = 0

Ctrl = 0

Wide-field active powercontrol

Wind farms


Δudrmax

Δudrmin

Δudr

ΔuqrΔuqrmax

Δuqrmin

minus

+

minus

+ +

+

Ctrluarr

Ctrluarr

Ctrluarr

(t)dtX1

T2int

Figure 2 Coordinated control strategy framework

plant is described in Figure 2 Firstly the frequency ofcommon DC-bus of the wind farms (Δ119891

119901119888119888) or speed or

angle of the synchronous generator is collected Secondlythe collected signal passes smooth block and scaling blockand integral link Then the controlled signal of the 119894th windturbine (Δ119906

119902119903119894) is confirmed according to its working state

and the allocation algorithm This controlled signal is sentto the active circuit of each wind turbine through wide-fieldfiber communication network (excitation voltage referencepoint at axis 119902 of 119889119902 decoupling control of the excitationconverter) so that the wind turbines can adjust the activepower synchronically As a result the active power in thetransient process can increase the damping of the syn-chronous generator and prevent low frequency oscillation

Parameter design of damping controller is expressed asfollows the value of 119879

1is set up under the condition that the

low frequency signals are able to pass through and the anglefor compensation is figured out by calculating the dynamicfrequency before adjustment and the values of 119879

2and 119879

3are

calculated based on these values the value of119870 is confirmedaccording to the expected dynamic frequency

When the power transmission system is disturbed themost important thing is to extract fault characteristic quantityand analyze the type and the place of the fault in other wordsto judgewhether it occurs in theDC systemor theAC systemIf the fault occurs in the DC system DC block results in thegreat reduction of power At this moment the active output

of the wind farm should be lowered within controllable timeto protect the synchronous generator from instability Andthe reactive output is captured to prevent abrupt rise of thevoltage and the instability of the wind turbine

When the fault occurs in the AC system the powerreduces substantially The output power of the DC systemshould be increased within set time But the sudden supplyof DC power may increase the demand of reactive power anddecrease AC bus voltage at the converter station Thus thereactive output of the wind farms should be adjusted quicklyto prevent voltage fall At the same time the reactive powerdemand in the transient process is calculated according to theoutput power of DC system and the reactive power is sentfrom the wind farms

6 Modeling and Prototype TestBased on RTDS

An experimental prototype is designed according to the coor-dinated control strategy frameworkmentioned in Section 52To test the coordinated control strategy and verify the effec-tiveness of the experimental prototype ldquohardware in-the-loop simulationrdquo is conducted The experimental prototypeis the real object and the wind-thermal power transmissionsystem is the visual object based on Real Time Digital System(RTDS)


Field busDFIG

ComputerAdditional active power

controlling signal Photoelectricmodule

Local load

Northwest grid

Sanhua grid

B1

B2

B3B4

B5

B6

sim

sim

middot middot middot



220 kV

069kV35kV

LAC

simsimsimsim

Figure 3 Simulation case

61 Simulation of the Wind-Thermal Power Transmission Sys-tem The wind-thermal power transmission system is simu-lated and tested as shown in Figure 3 Compared to the con-ventional power plant each wind turbine has small capacityand the wind farms have a large number of wind power units[19] It is impossible to simulate every turbine set [14] There-fore ldquoequivalent similitude ratiordquo method is adopted in thesimulation In other words the large-scale wind turbine sys-tem is replaced by a relatively small DFIG in which there aremany wind turbine sets closely related to each other Parame-ters are scaled down to a proper proportion Thus a large-scale wind farm is divided into sections and each sectionis simulated by DFIG As a result electromagnetism andtransient process can be better reflected and the process issimplified to make the simulation close to the real situation

The proposed wind-thermal power transmission systemmodel based on RTDS consists of six wind turbines and onesynchronous generator set Wind-thermal capacity is in ratioof 1 15 According to the principle of ldquoequivalent per-unitvalue of parameterrdquo the capacity of the synchronous gener-ator is scaled down to the level of MW The rated capacity ofa DFIG is 22MVA and the rated frequency is 60Hz

In Figure 3 parameters of the DFIG are as follows statorwinding resistance is 000462 pu stator leakage inductanceis 0102 pu rotor winding resistance is 000736 rotor leakageinductance is 011 pu and stator and rotormutual inductanceis 262 pu parameters of synchronous generator are (refer toliterature [16] for name and physical definition)

119909119889= 051 pu

1199091015840

119889= 0042 pu

11990910158401015840

119889= 0032 pu

119909119902= 0375 pu

11990910158401015840

119902= 0011 pu

1198791015840

119889= 033 s

11987910158401015840

119889= 003 s

1198791015840

119902= 003 s

119867 = 698 s(6)

and parameters of the additional damping controller are

1198791= 532 s

1198792= 006 s

1198793= 038 s

119870 = 129

(7)

62 RTDS Hardware Requirement and Calculation Assign-ment RTDS hardware has the following requirement 10processors (GPC-PB5) of 2 RACKs and 1 12-channel analoginput card (GTAO) are used in the whole model RTDS isthe real time simulation equipment and the processors mustbe properly allocated whenmodeling To enhance simulationaccuracy small-step (lt2 us) RTDSRSCAD system is used asthe carrier ofDFIG systemmodel Eachmodel includesDFIGandPWMfrequency converter and transformer Small-step isset up in the VSCmodule in the small-step model base EachVSC module has a corresponding processor (GPC-PB5) Soamong 10 processors 6 of them correspond to 6 DFIGsrsquomodels respectively and the remaining 4 are for controllingcalculation and the synchronous generator simulation andthe grid simulation

63 Experimental Prototype and Interface of RTDS Thewindfarms the thermal power system and the ACDC powertransmission system shown in Figure 3 are simulated byRTDSAs the analog state variables the frequency of the com-mon bus of wind farms the speed of synchronous generatorand the power-angle are the output from GTAO of RTDSand they are put into the data collection module of theexperimental prototype by the signal cable To simulate actual


Figure 4 Joint debugging of the experimental prototype and RTDS

fiber channel the photoelectric conversion module and the3 km single-mode fiber are set up in the experimental deviceThe additional damping control signals are produced after thesignals collected from RTDS are processed through the datamanagement module and the algorithm producing moduleThen the additional damping control signals are connectedto GTAI of RTDS through profibus and photoelectricmoduleto control the stability of the system

In Figure 3 the first-order part of DC power transmissionsystem is simulated by RTDS and the controller of DCpower transmission system is a special controlling systemdeveloped on DPS3000 platform It is connected with RTDSthrough signal cable After the connection RTDS and theexperimental device construct a closed controlling system inwhich the experimental device is the controller and RTDS isbeing controlled as is shown in Figure 4

7 Joint Debugging of ExperimentalDevice and RTDS

71 Experiment Analysis of Damping Characteristic Theexperiment is described as follows rectify excitation param-eters and active power of the synchronous generator to pro-duce weak damping set up three-phase transient circuit faultat the common DC-bus to activate low frequency oscillationand record the speed of the synchronous generator activepower of the wind turbine stator current and rotor current

(1) Record the speed of the synchronous generator andobserve the additional damping control The speed is shownin Figure 5(a) under the condition that the experimentalprototype is not put into operation Compare Figures 5(a)and 5(b) and it is clear that the amplitude of the curve underadditional damping control is smaller and smaller whichpresents good damping characteristic This indicates thatunder additional damping control the damping characteris-tic of the system gets improved

(2) Record the active power of DFIG and analyze theactive power regulation ability of the wind turbine in thetransient process Figure 6(a) shows the real time activepower of DFIG without damping control strategy when shortcircuit occurs Figure 5(b) shows the active power of DFIGunder damping control Compare two figures and it is seenthat when low frequency oscillation occurs in the systemDFIG rectifies its active power according to additional con-trolling signals sent by the experimental device to activate

additional damping control When the experimental deviceis not connected DFIG outputs constant active power onlyaccording to the given value and does not provide anydamping for the synchronous generator

(3) Record the stator current and rotor current of theDFIG and observe the variation of current under additionaldamping control Figures 6(a) and 6(b) show rotor currentof DFIG when the experimental prototype is not put intooperation and when it is Figures 7(a) and 7(b) show thestator current of the DFIG when the experimental prototypeis not put into operation and when it is Compare these foursituations and it is found that the rotor current does not showsignificant change when there is experimental prototype andwhen there is not Although the stator current increasessubstantially when the experimental prototype is availablethe current changes within safe range because it is not directlyconnected with other power electric devices It indicates thatadditional damping control would not bring negative effectto the wind turbine and the system

From the results it is seen that the active power of eachwind turbine in the wind farms can be concentrated to beadjusted based on the integrated control platform of thewind farms and the technology of wide-field communicationWhen the system is working under weak damping theaction of additional damping control is excited to increasethe damping of the system and prevents low frequencyoscillation At the same time there is no negative influenceon the wind turbine and the system which proves thatthe method is available In addition wind-thermal ratio isan important factor influencing the damping effect If theratio is too small the damping effect is limited Compulsorydamping may lead to overload of the rotor

72 Experimental Analysis of Angle Stability

721 Fault Analysis of the Wind Farms After the large-scalewind farms are connected to the power system the overallstability of the power system declines greatly An experimentis carried out to find out reasons The wind farms in Figure 3are replaced by a thermal power plant (SG1) of the same levelSG and SG1 constitute a large-scale thermal power plantFault simulation is compared between the single thermalpower plant and the wind-thermal hybrid power system tosee how the wind farms affect the stability of the powersystem Assume that short circuit fault occurs on AC (B3-B4) for 03 s Simulation results under two power modes areshown in Figures 8(a) and 8(b)

From Figure 8(a) it is seen that after short circuit faultoccurs two thermal power plants have experienced an abruptdecline of power The active power of SG and SG1 is reducedto 011 pu respectively It suggests that the power decline isshared between two thermal power plants From Figure 8(b)it is found that after short circuit fault happens the powerof SG is decreased to 022 pu but that of the wind farmsremains unchanged It suggests that the power decline occursonly in the thermal power plant rather than both This is notconductive to the thermal power plant and may result in itspower-angle instability Thus a coordinated control strategyis proposed to address the power imbalance during the fault


Spee

d (r

admiddotsminus

1)

375

376

377

378

379

08 17 250 33 5042t (s)

(a) Experimental prototype not put into operation

Spee

d (r

admiddotsminus

1)

08 17 25 33 42 500t (s)

375

376

377

378

(b) Experimental prototype put into operation

Figure 5 The speed of the synchronous generator

0

1

2

3

P(M

W)

08 17 25 33 42 500t (s)


08 17 25 33 42 500t (s)

0

1

2

3

P(M

W)


Figure 6 Rotor current of the doubly fed generator

08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


Figure 7 Stator current of DFIG

SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)

(a) Thermal power plant power

SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)

(b) Wind-thermal hybrid power

Figure 8 Power comparisons under fault

722 Angle Stability under Coordinated Control In order totest the effectiveness of coordinated control strategy a shortcircuit default simulation is carried out based on the experi-ment in Figure 4 Fault occurs on the AC circuit Results areshown in Figure 9 Figure 9(a) shows the variation of power-angle of SG due to 03 s fault without the coordinated strategyIt shows that the stability of the synchronous generator isviolated Under the same fault condition Figure 9(a) shows

the variation of power-angle of SG due to 03 s fault withthe coordinated strategyThemaximum oscillation of power-angle is 69∘ which indicates that the synchronous generatoris within its stability

The duration of fault can reflect how bad the fault isThus the duration is increased to 041 s And the variationof power-angle is shown in Figure 9(c) It shows that themaximum oscillation of angle is 79∘ which indicates that


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)

(a) Without coordinated control 119905 = 03 s

Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)

(b) With coordinated control 119905 = 03 sA

ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)

(c) With coordinated control 119905 = 041 s

Figure 9 Analysis of the influence of coordinated control strategy

the synchronous generator maintains its stability Conse-quently the coordinated control strategy proposed in thispaper is proved to enhance the transient stability of the windfarms thermal hybrid power system

8 Conclusion

Conclusions can be drawn as follows

(1) The active power and the reactive power of DFIGhave quick responses Under the support of wide-fieldoptical fiber network doubly fed wind farms can beadjusted quickly

(2) Quick adjustment of the active power of doubly fedwind farms is accomplished which can restrain thelow frequency oscillation of the thermal power unitand can supply the positive damping to the unit

(3) Through coordinated control for wind farms and DCpower transmission system the transient stability ofthe hybrid power system can be enhanced

(4) The experimental prototype and RTDS are connectedfor joint debugging Results show that the experi-mental prototype can pose significant damping effecton thermal power plant and lower the risk of lowfrequency oscillation of the grid The experimentalprototype can also enhance the transient stability ofhybrid ACDC power transmission system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge the support of Scienceand Technology Project of Henan Province (112101210700)the Introduce Talents Research Fund of Guizhou University(2014-07) the National Natural Science Fund of China(51467003 61403221) Open Foundation of Key Laboratoryof Pulp and Paper Science and Technology of Ministry ofEducation of China underGrant nos KF201419 and 08031347and the Social Development Research Project of GuizhouProvince (SY[2011]3081)

References

[1] S Wang D Yu and J Yu ldquoA coordinated dispatching strategyfor wind power rapid ramp events in power systems with highwind power penetrationrdquo International Journal of ElectricalPower amp Energy Systems vol 64 pp 986ndash995 2015

[2] H Li S Guo L Cui J Yan J Liu and B Wang ldquoReviewof renewable energy industry in Beijing development statusobstacles and proposalsrdquo Renewable and Sustainable EnergyReviews vol 43 pp 711ndash725 2015

[3] A A Eldesouky ldquoSecurity constrained generation schedulingfor grids incorporating wind photovoltaic and thermal powerrdquoElectric Power Systems Research vol 116 pp 284ndash292 2014

[4] Y Zhang F Yao H H C Iu T Fernando andH Trinh ldquoWind-thermal systems operation optimization considering emissionproblemrdquo International Journal of Electrical Power and EnergySystems vol 65 no 2 pp 238ndash245 2015

[5] Y Yubisui S Kobayashi R Amano and T Sugiura ldquoEffectsof nonlinearity of magnetic force on passing through a criticalspeed of a rotor with a superconducting bearingrdquo IEEE Trans-actions on Applied Superconductivity vol 23 no 3 pp 338ndash3402013


[6] B Basu A Staino and M Basu ldquoRole of flexible alternatingcurrent transmission systems devices in mitigating grid fault-induced vibration of wind turbinesrdquoWind Energy vol 17 no 7pp 1017ndash1033 2014

[7] A Moharana R K Varma and R Seethapathy ldquoSSR allevi-ation by STATCOM in induction-generator-based wind farmconnected to series compensated linerdquo IEEE Transactions onSustainable Energy vol 5 no 3 pp 947ndash957 2014

[8] S-Y Yang Y-K Wu H-J Lin and W-J Lee ldquoIntegratedmechanical and electrical DFIG wind turbine model develop-mentrdquo IEEE Transactions on Industry Applications vol 50 no3 pp 2090ndash2102 2014

[9] H Hinz B Zuber and J Kilz ldquoDevelopment of a hybridpower generation systemrdquo in Proceedings of the InternationalExhibition and Conference for Power Electronics IntelligentMotion Renewable Energy and Energy Management (PCIMEurope rsquo14) pp 651ndash658 IEEENurembergGermanyMay 2014

[10] R Zhu Z Chen X Wu and F Deng ldquoVirtual dampingflux-based LVRT control for DFIG-based wind turbinerdquo IEEETransactions on Energy Conversion vol 23 no 1 pp 186ndash1922015

[11] T Surinkaew and I Ngamroo ldquoCoordinated robust control ofDFIG wind turbine and pss for stabilization of power oscilla-tions considering system uncertaintiesrdquo IEEE Transactions onSustainable Energy vol 5 no 3 pp 823ndash833 2014

[12] S Nouri E Babaei and S H Hosseini ldquoA new ACDCconverter for the interconnections between wind farms andHVDC transmission linesrdquo Journal of Power Electronics vol 14no 3 pp 592ndash597 2014

[13] Y Li Z Zhang Y Yang Y Li H Chen and Z Xu ldquoCoordinatedcontrol of wind farm and VSC-HVDC system using capacitorenergy and kinetic energy to improve inertia level of powersystemsrdquo International Journal of Electrical Power amp EnergySystems vol 59 pp 79ndash92 2014

[14] A Rabiee A Soroudi and A Keane ldquoInformation gap decisiontheory based OPF with HVDC connected wind farmsrdquo IEEETransactions on Power Systems vol 30 no 6 pp 3396ndash34062014

[15] I Erlich C Feltes and F Shewarega ldquoEnhanced voltage dropcontrol by VSC-HVDC systems for improving wind farm faultridethrough capabilityrdquo IEEE Transactions on Power Deliveryvol 29 no 1 pp 378ndash385 2014

[16] A Rabiee and A Soroudi ldquoStochastic multiperiod OPF modelof power systems with HVDC-connected intermittent windpower generationrdquo IEEETransactions on PowerDelivery vol 29no 1 pp 336ndash344 2014

[17] K E Okedu SMMuyeen R Takahashi and J Tamura ldquoEffec-tiveness of current-controlled voltage source converter exciteddoubly fed induction generator for wind farm stabilizationrdquoElectric Power Components and Systems vol 40 no 5 pp 556ndash574 2012

[18] A A Elserougi A S Abdel-Khalik A M Massoud andS Ahmed ldquoA new protection scheme for HVDC convertersagainst DC-side faults with current suppression capabilityrdquoIEEE Transactions on Power Delivery vol 29 no 4 pp 1569ndash1577 2014

[19] J-H Lee T-H Kim G-H Kim S Heo M Park and I-K YuldquoRTDS-basedmodeling of a 100MWclass wind farm applied toan integrated power control systemrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo12) pp 1441ndash1443 Seoul Republic of Korea October 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Local load Northwest grid

Sanhua grid

B1

LAC

WG1 B2

WG2

B3

WG3

B4

WG4

B5

B6

WG5

SGsim

simsimsimsim

Figure 1 ACDC power system with wind farms incorporated

doubly fed wind farms and DC power transmission system isestablished And it is proved that active power in the large-scale wind farms is controllable Thirdly for the purpose ofincreasing damping of the system and enhancing angel sta-bility a coordinated control strategy for wind farms and DCpower transmission system is proposed Finally the experi-mental prototype is made and the control effect of the experi-mental prototype is also introduced in detail

2 ACDC Power Transmission SystemIncorporating Wind Farms

Chinese large-scale wind farms are usually located at remoteareas Due to small load capacity power generated by thelarge-scale wind farms cannot be consumed So long-distancetransmission is an inevitable solution But as the wind poweris not constant long-distance transmission is costly if windpower is the only thing to transmit And irregular fluctuationof the wind power would make the grid unstable So at thepresent time a hybrid transmission mode of wind farms andthermal power plant (also named as wind-thermal hybridpower system) [9] is the main form of transmission as isshown in Figure 1 To be more specific wind farms are con-nected with the thermal power plant nearby and the power istransmitted to other areas by extra high voltage (EHV) line

Wind-thermal hybrid power transmission mode is forlong-distance transmission But as the utilization hours ofwind power are lesser than the conventional thermal powerplant the transmission channel capacity of wind power isdesigned lower than the maximum power When large-scalewind power is generated the transmission line will be heavilyloaded and the thermal power plant also functions in aheavy-load state resulting in low frequency oscillation Inaddition vector control of the turbine may pose influence ondamping [10] It is also worth noticing that the thermal powerunit bonded with the wind farms is responsible for curbingwind power fluctuation So the adjustment for the unit isfrequent which would damage the power system stabilizer(PSS) [11] and hamper damping characteristic Thereforeeffective measures on damping should be taken to ensure safeoperation of the wind-thermal power transmission system

In addition the wind-thermal hybrid power system doesnot work in a conventional way The dynamic behaviors ofwind farms may weaken the angle stability of the thermalpower plant even the whole power system Thus the windfarms and the ACDC power transmission system should be

subjected to coordinated control in order to erase negativeeffect caused by the wind farms

3 Mathematical Model for Wind-ThermalHybrid Power Transmission

31 Wind Turbine System The mechanical part of the windturbine system includes wind turbine transmission shaftand gearbox Wind turbine is used to capture wind energythrough the turbines and transform it to the mechanicaltorque on the wheel hub The shaft and gearbox is used topass the driven force of the wind turbine to the generator andincrease the revolving speedThe gear ratio can reach 100 Tosimplify calculation themechanical part is regarded as a con-centrated mass expressed by first-order inertial element [8]

d119875119898

d119905=

1

119879119889

(119875119879minus 119875119898) (1)

where 119875119898and 119875119879refer to mechanical power and electromag-

netic power respectively on the rotor of the generator 119879119889

refers to inertia time constant

32 MathematicalModel for DFIG DFIG is actually the rotorasynchronous motor There are symmetrical three-phasewindings on the stator and the rotor The modeling processis similar to that of asynchronous motor and synchronousgenerator in which the primitive equation is confirmed in thethree-phase static coordinate system and then coordinates aretransformed Unlike the modeling of synchronous generator119889119902 coordinates of DFIG can be oriented in different modessuch as stator flux mode rotor flux mode and stator voltagemode And orientation of 119889119902 coordinates of synchronousgenerator is only to take physical location of the rotor In thispaper the stator vector voltage of DFIG is taken as axis 119902In the 119889119902 coordinates system the stator flux (120595

119889119904 120595119902119904) and

rotor current (119894119889119903 119894119902119903) are taken as the state variablesThe state

equation is expressed as follows [11]

119901120595119889119904

= minus119903119904

119897119904

120595119889119904+ 11989710158401015840

119903119904119894119889119903

+ 1205961120595119902119904

119901120595119902119904= minus

119903119904

119897119904

120595119902119904+ 11989710158401015840

119903119904119894119902119903minus 1205961120595119889119904+ 119906119902119904

1199011198971015840

119894119889119903

= minus119903119903119894119889119903

+ 119906119889119903

+ 1205961199041198971015840

119894119902119903+ 12059611990411989710158401015840

120595119902119904minus 11989710158401015840

119901120595119889119904

1199011198971015840

119894119902119903

= minus119903119903119894119902119903+ 119906119902119903minus 1205961199041198971015840

119894119889119903

minus 12059611990411989710158401015840

120595119889119904minus 11989710158401015840

119901120595119902119904

(2)

where 1198971015840

= (119897119903minus 119897119898119897119898119897119904) and 119897

10158401015840

= 119897119898119897119904 119897119904 119897119903 and

119897119898

being stator self-inductance rotor self-inductance andmutual inductance respectively 119903

119904and 119903119903are stator and rotor

resistance respectively 1205961and 120596

119904are synchronous speed

and slip respectively 119906119889119903

and 119906119902119903are vertical and horizontal

vector of excitation respectively 119906119902119904is stator voltage and 119901

is differential operator

33 UHVDC Power Transmission System Model UHVDCpower transmission refers to DC transmission based onthyristor inverter It consists of the inverter DC line and



119868119889119903

=1

119871119889119903Σ

(minus119877119889119868119889119903

minus 119880119888+3radic2

120587119880119889119903cos120572 minus

3

120587119883119903119868119889119903)

119868119889119894=

1

119871119889119894Σ


120587119880119889119894cos120573 minus

3

120587119883119894119868119889119894)

119880119888=

1

119862(119868119889119903

minus 119868119889119894)

(3)

where 119868119889119903 119868119889119894 and 119880


119889119903and 119868119889119894are DC




and 119880119889119894


and 119871119889119894Σ


119903and119883

119894are







119890119889119903

= 119896 (1205961199041198971015840

119894119902119903+ 12059611990411989710158401015840

120595119902119904)

119890119902119903

= minus119896 (1205961199041198971015840

119894119889119903

+ 12059611990411989710158401015840

120595119889119904)

(4)

Add 119890119889119903

and 119890119902119903to 119906119889119903



119889119903 119906lowast119902119903) is

1199011198711015840

119894119889119903

= minus119903119903119894119889119903

+ 119906lowast

119889119903

1199011198711015840

119894119902119903

= minus119903119903119894119902119903+ 119906lowast

119902119903

(5)












Wind farms



word



Smooth

Scaling

Scaling

Scaling

Integral

K2

K1

K3

1

1 + sT1

1

1 + sT3

Δff0

fAC

ΔU

UAC

U0

ΔPDCΔPDCmax

ΔPDCmin

0

0

0

Ctrl = 0

Ctrl = 0

Ctrl = 0


Wind farms


Δudrmax

Δudrmin

Δudr

ΔuqrΔuqrmax

Δuqrmin

minus

+

minus

+ +

+

Ctrluarr

Ctrluarr

Ctrluarr

(t)dtX1

T2int



119901119888119888) or speed or







2and 119879

3are








Field busDFIG



Local load

Northwest grid

Sanhua grid

B1

B2

B3B4

B5

B6

sim

sim




220 kV

069kV35kV

LAC

simsimsimsim





119909119889= 051 pu

1199091015840

119889= 0042 pu

11990910158401015840

119889= 0032 pu

119909119902= 0375 pu

11990910158401015840

119902= 0011 pu

1198791015840

119889= 033 s

11987910158401015840

119889= 003 s

1198791015840

119902= 003 s

119867 = 698 s(6)


1198791= 532 s

1198792= 006 s

1198793= 038 s

119870 = 129

(7)


















Spee

d (r

admiddotsminus

1)

375

376

377

378

379

08 17 250 33 5042t (s)


Spee

d (r

admiddotsminus

1)

08 17 25 33 42 500t (s)

375

376

377

378



0

1

2

3

P(M

W)

08 17 25 33 42 500t (s)


08 17 25 33 42 500t (s)

0

1

2

3

P(M

W)



08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)



SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)


SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)







Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)




8 Conclusion








Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119868119889119903

=1

119871119889119903Σ

(minus119877119889119868119889119903

minus 119880119888+3radic2

120587119880119889119903cos120572 minus

3

120587119883119903119868119889119903)

119868119889119894=

1

119871119889119894Σ


120587119880119889119894cos120573 minus

3

120587119883119894119868119889119894)

119880119888=

1

119862(119868119889119903

minus 119868119889119894)

(3)

where 119868119889119903 119868119889119894 and 119880


119889119903and 119868119889119894are DC




and 119880119889119894


and 119871119889119894Σ


119903and119883

119894are







119890119889119903

= 119896 (1205961199041198971015840

119894119902119903+ 12059611990411989710158401015840

120595119902119904)

119890119902119903

= minus119896 (1205961199041198971015840

119894119889119903

+ 12059611990411989710158401015840

120595119889119904)

(4)

Add 119890119889119903

and 119890119902119903to 119906119889119903



119889119903 119906lowast119902119903) is

1199011198711015840

119894119889119903

= minus119903119903119894119889119903

+ 119906lowast

119889119903

1199011198711015840

119894119902119903

= minus119903119903119894119902119903+ 119906lowast

119902119903

(5)












Wind farms



word



Smooth

Scaling

Scaling

Scaling

Integral

K2

K1

K3

1

1 + sT1

1

1 + sT3

Δff0

fAC

ΔU

UAC

U0

ΔPDCΔPDCmax

ΔPDCmin

0

0

0

Ctrl = 0

Ctrl = 0

Ctrl = 0


Wind farms


Δudrmax

Δudrmin

Δudr

ΔuqrΔuqrmax

Δuqrmin

minus

+

minus

+ +

+

Ctrluarr

Ctrluarr

Ctrluarr

(t)dtX1

T2int



119901119888119888) or speed or







2and 119879

3are








Field busDFIG



Local load

Northwest grid

Sanhua grid

B1

B2

B3B4

B5

B6

sim

sim




220 kV

069kV35kV

LAC

simsimsimsim





119909119889= 051 pu

1199091015840

119889= 0042 pu

11990910158401015840

119889= 0032 pu

119909119902= 0375 pu

11990910158401015840

119902= 0011 pu

1198791015840

119889= 033 s

11987910158401015840

119889= 003 s

1198791015840

119902= 003 s

119867 = 698 s(6)


1198791= 532 s

1198792= 006 s

1198793= 038 s

119870 = 129

(7)


















Spee

d (r

admiddotsminus

1)

375

376

377

378

379

08 17 250 33 5042t (s)


Spee

d (r

admiddotsminus

1)

08 17 25 33 42 500t (s)

375

376

377

378



0

1

2

3

P(M

W)

08 17 25 33 42 500t (s)


08 17 25 33 42 500t (s)

0

1

2

3

P(M

W)



08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)



SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)


SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)







Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)




8 Conclusion








Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Wind farms



word



Smooth

Scaling

Scaling

Scaling

Integral

K2

K1

K3

1

1 + sT1

1

1 + sT3

Δff0

fAC

ΔU

UAC

U0

ΔPDCΔPDCmax

ΔPDCmin

0

0

0

Ctrl = 0

Ctrl = 0

Ctrl = 0


Wind farms


Δudrmax

Δudrmin

Δudr

ΔuqrΔuqrmax

Δuqrmin

minus

+

minus

+ +

+

Ctrluarr

Ctrluarr

Ctrluarr

(t)dtX1

T2int



119901119888119888) or speed or







2and 119879

3are








Field busDFIG



Local load

Northwest grid

Sanhua grid

B1

B2

B3B4

B5

B6

sim

sim




220 kV

069kV35kV

LAC

simsimsimsim





119909119889= 051 pu

1199091015840

119889= 0042 pu

11990910158401015840

119889= 0032 pu

119909119902= 0375 pu

11990910158401015840

119902= 0011 pu

1198791015840

119889= 033 s

11987910158401015840

119889= 003 s

1198791015840

119902= 003 s

119867 = 698 s(6)


1198791= 532 s

1198792= 006 s

1198793= 038 s

119870 = 129

(7)


















Spee

d (r

admiddotsminus

1)

375

376

377

378

379

08 17 250 33 5042t (s)


Spee

d (r

admiddotsminus

1)

08 17 25 33 42 500t (s)

375

376

377

378



0

1

2

3

P(M

W)

08 17 25 33 42 500t (s)


08 17 25 33 42 500t (s)

0

1

2

3

P(M

W)



08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)



SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)


SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)







Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)




8 Conclusion








Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Field busDFIG



Local load

Northwest grid

Sanhua grid

B1

B2

B3B4

B5

B6

sim

sim




220 kV

069kV35kV

LAC

simsimsimsim





119909119889= 051 pu

1199091015840

119889= 0042 pu

11990910158401015840

119889= 0032 pu

119909119902= 0375 pu

11990910158401015840

119902= 0011 pu

1198791015840

119889= 033 s

11987910158401015840

119889= 003 s

1198791015840

119902= 003 s

119867 = 698 s(6)


1198791= 532 s

1198792= 006 s

1198793= 038 s

119870 = 129

(7)


















Spee

d (r

admiddotsminus

1)

375

376

377

378

379

08 17 250 33 5042t (s)


Spee

d (r

admiddotsminus

1)

08 17 25 33 42 500t (s)

375

376

377

378



0

1

2

3

P(M

W)

08 17 25 33 42 500t (s)


08 17 25 33 42 500t (s)

0

1

2

3

P(M

W)



08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)



SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)


SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)







Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)




8 Conclusion








Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Spee

d (r

admiddotsminus

1)

375

376

377

378

379

08 17 250 33 5042t (s)


Spee

d (r

admiddotsminus

1)

08 17 25 33 42 500t (s)

375

376

377

378



0

1

2

3

P(M

W)

08 17 25 33 42 500t (s)


08 17 25 33 42 500t (s)

0

1

2

3

P(M

W)



08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)


08 17 25 33 42 500t (s)

minus2

minus1

0

1

2

I(k

A)



SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)


SG

SG1

Activ

e pow

er (p

u)

0

02

04

06

08

10

12

1 2 3 4 5 7 90 6 8 10t (s)







Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)




8 Conclusion








Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


Ang

le (d

eg)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)


ngle

(deg

)

minus20

020406080

100

1 2 3 4 5 7 90 6 8 10t (s)




8 Conclusion








Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article coordinated stability control of wind

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