Model of DFIG Wind Farm and Study on Its LVRT Capability

He Guo,Ding-Zhong Huang,Li-Gang Gu,and Fang-Yuan Wu

1.Introduction

Under the background of energy crisis and environmental pollution,clean distributed energy(DG)has been widely used in recent years.With abundant reserves and relatively mature technology,wind power stands out.Developing at a fast speed of over 30% per year,wind power has obvious advantages in prospect of commercial and scale application[1].Among them,the doubly-fed induction wind generator is superior in variable speed operation and low capacity of converter,which makes it popular in wind generator operators.

The double-fed induction wind generator cluster,ordered in certain rules,is adopted by most grid-connected wind farms to achieve more electricity.However,considering wind power’s fluctuation and intermittent,the current power grid has been faced with serious problems.Not only the generator terminal voltage decreases under system faults and difficulties are gained in power transmission,but also the fluctuate power brings steep rise fault currents,charging capacity,and rapid direct voltage rise,as well as the speeding-up rotator and mutation of electromagnetic torque.Besides,current fault-handling methods could not cope with the increasing wind power capacity and wind farm scale,so low voltage ride through(LVRT)capability should be possessed by wind farms,which can provide voltage support by splitting wind generators from the grid.

Relevant investigation has been made by both domestic and abroad scholars,mainly focusing on modeling wind farms and the study of LVRT capability,thus properties of the double-fed wind generator under fault conditions have been analyzed[1]-[3].Based on the indices of cluster classification and K-means clustering algorithm,this paper builds a dynamic model of doubly-fed induction generators(DFIG)under network fault conditions.Then simulation is carried out to study the corresponding LVRT ability.

2.Dynamic Model of DFIG Wind Turbine under Network Fault Condition

Among the aggregation mode of wind turbines,common equivalent methods include the single machine representation method and multiple machine representation method.In the former method,an equivalent wind turbine is obtained,which is suitable in the wind farm with constant speed.In the latter one,on the basis of the coherency method of a power system,similar operation points are adopted as the cluster classification principle,achieving better accuracy in modeling.Thus,the multiple machine representation concept is considered in dynamic modeling of DFIG,and the pitch operation condition is considered as a classification method.To define relative variables,parameter identification is involved.

2.1 Cluster Classification Based on K-means Clustering Algorithm

As one of the most widely used clustering algorithms,the K-means algorithm regards the minimization of the standard measurement function as the principle,dividing N sample points into K clusters.As a result,samples in the same cluster share much more similarity,while less among various clusters.The standard measurement function is described as

where miis the sample expectation of the ith cluster; Ciis sample points set of the ith cluster ; Niis the number of sample points for the ith cluster; E is the standard measurement function; τ is the sample point.

The flow chart of the K-means clustering algorithm is shown as Fig.1.

According to the pitch operation condition in DFIG,clusters are sorted into three types:1)the pitch operation occurs before system faults,2)the pitch operation occurs during system faults,and 3)no pitch operation occurs neither before nor in faults.Affected by the active power,generator terminal voltage,and wind speed in pre-fault circumstances,the pitch operation could be reflected by supporting vector machine(SVM)classification devices.Then based on sorting indices in SVM,K could be set as 3,which represents the number of sort types.Afterwards,clustering classification results can be achieved.

2.2 Calculation of Parameters in Equivalent Model

In terms of parameter calculation,both the function-based method and parameter identification method are well-known.The former is applicable for the same type generators and can only calculate basic parameters,and the calculation could be finished for variable speed constant frequency generators with easy operation and accurate results.But in this paper,the parameter identification method is chosen.

A.Principle of Parameter Identification

The core of parameter identification is to achieve optimal parameters through various identification algorithms.In identification of DIFG,both nonlinear factors in the pitch control model and interactions between wind turbine elements should be included.Due to relatively long transaction time,identification results should be much more accurate.

The elaborate theory means presented as Fig.2,where WT is a wind turbine.

Define the cost function(or equivalent criterion)as E(θ).Then under the same wind speed Vw(t),the output signal can be generated by the detailed wind turbine model and equivalent wind turbine model P(tk)and Peq(t),respectively.

where tkis sample time,while N is the number of samples.

Modification is made on identification calculation until the error e(t)satisfies the minimized cost function.Then corresponding θeis the very parameter of equivalent model.B.Solutions to Parameter Identification

As a nonlinear system,the power system can not be well-solved through the fast Fourier transform(FFT),least square method in frequency domain,and piecewise linear polynomial function(PLPF)approach in time domain.Based on this,the artificial algorithm particle swarm optimization(PSO)is employed in this paper,because of its simple operation and strong robust.

PSO was proposed by Kennedy and Eberhart first in 1995.It is generated from the simulation of birds predator-prey behaviour,which seeks food by searching surroundings of birds that are the nearest to the current food location.A solution to a certain optimization problem is the optimal solution of a bird at certain speed.For every iteration,the speed and location are updated according to(3)and(4):

Considering that local optimization tends to reach in traditional PSO,this paper adopts an adaptive adjustment strategy with inertia coefficients to enhance its properties,solving model calculation in the multiple nodes system.Based on(5),adjustment in an adaptive degree can be finished for each iteration:

where i is iteration times,n is the maximum iteration times,and inertia weight decreases from ωmaxto ωminlinearly.

The procedure of system parameter identification based on advanced PSO is as follows.

1)Build the original model and the model to be identified,then define parameters to be identified.

2)Initialize the location and speed of the particle cluster at random.

3)Calculate the fitness value of each particle.

4)Compare the fitness value of xiand that of the best location it has ever experienced.If xiis better,xiwill be regarded as a history optimal value,and the corresponding location is the optimal one.

5)Compare the fitness value of a particle and that of the best location that the cluster has ever experienced.If better,the location of the particle will be regarded as a history optimal value,and the corresponding location is the optimal one.

Update speed and location of particles(adaptive adjustment is done at the same time),and consider the maximum iteration times achieved or a good enough adaptive value gained as the termination condition.Once it is satisfied,print out the results.If not,return to 3).

2.3 Steps of Multiple Representation Method in DFIG

The steps to the multiple representation method in DFIG are detailed as follows.

a)Record the active power,terminal voltage,and wind speed in pre-fault conditions,and then generate indices of clustering classification through an SVM selector.

b)Achieve cluster classification results based on the classification indices and K-means clustering algorithm.

c)Based on the principles of parameter identification descried in Section 1.2,equivalent wind turbines in the same cluster are achieved.

d)Calculate the equivalent capacity,transformer parameters,and cable specifications between the equivalent wind turbine and the point of common connection(PCC)of the wind farm,thus the corresponding wind farm model can be achieved.

3.Study on LVRT Capability of DFIG Wind Turbine

Ruled by power system operators,the LVRT capability has to be affiliated by a wind farm when grid connected.When voltage sags in a certain range,the wind turbine with LVRT is able to operate without affecting the stability of the power system,and provide support of active power(related to frequency)and reactive power(related to voltage)[5].

Since the stator is directly connected to the grid,DFIG’s stator voltage can reflect the grid voltage.Large DC and negative sequence components of the stator is generated by the flux,because the flux is unable to mutate when the voltage sag happens[6].Eliminating the unharmonious sequence lies in enhancing the LVRT ability.When it comes to hardware solutions,the most widely used methods include the crowbar circuit,energy storage system(ESS),and stator switcher.

3.1 Crowbar Circuit

The principle of crowbar circuit is that the path is provided for rotator current by short-circuiting the rotator winding with resistance,to bypass the rotator converter,when the grid voltage decreases.There are mainly two types:active crowbar and passive crowbar.

The function realization of passive crowbar mainly is rooted in self-protection of a wind turbine.Once a fault appears,DFIG is converted into a squirrel cage asynchronous motor(SCAM)through short-circuiting the silicon controlled rectifier(SCR).After the stator of DFIG slips from the grid,SCR is turned off,and the stator accesses to the grid again.However,the reactive power demand is increasing during this process.Passive crowbar is mainly adaptive in a small-scale wind turbine under grid connected condition.The structure chart of the passive crowbar circuit is shown in Fig.3.

The SCR,gate turn-off thyristor(GTO),and insulated gate bipolar transistor(IGBT)with a forced converter function are allocated in the active crowbar circuit,which makes it possible to turn off the crowbar protection circuit at any time.Then the rotator converter can go back to work without the wind turbine off the grid,satisfying demands of power system operators.This paper employs the typical active crowbar,and its typical structure is presented in Fig.4.It is in the reverse-parallel type,and can connect the bypass resistance with the rotator circuit by three pairs of reverse-parallel linking switch devices.Continuous connections between the transformer,rotator,and grid guarantee DFIG’s synchronism with the grid in the whole process of faults and failure recovery.When fault is cleared out,the bypass resistance is cut off,making DFIG access to the grid.

3.2 Alternative Hardware Realization Methods[3]

Alternative realization methods mainly include the ESS and stator switcher.

When ESS is active,energy is stored during a fault and rejected to the grid after the fault.Although the frequent modes-switching problem raised by the crowbar has been avoided,large rotator current is increased by the out of control of the rotator,bringing damages to devices.

Fig.3.Typical structure of the passive crowbar.

Fig.4.Typical structure of the active crowbar.

The stator switcher refers to the reverse parallel SCR between the rotator and grid per phase.Short-circuiting current is limited and torque oscillation is avoided,for rotator-grid’s fast separation is achieved.

In a word,the crowbar circuit stands out for its control ability and incomparable advantages,being the most commonly used devices for LVRT.Simulation in this paper investigates the effects of crowbar on enhancing the LVRT capability of wind farms.

4.Study Case Simulation and Analysis

Based on the theory of multiple representation and crowbar circuit mentioned above,this paper builds a multiple machine model of wind farm made up by four identical DFIG wind turbines in DigSILENT.The system structure is presented in Appendix.

As a classic DFIG wind farm,4 kinds of voltage class are set in the system.The DC bus is charged by the grid inverter,maintaining the voltage level of DFIG,while the output voltage and current frequency are controlled at the same time.The grid inverter is connected to the low voltage winding of three-winding step-up transformer through 690 V branches,the middle winding is connected with the generator stator by the 3.3 kV bus,while the 20 kV high voltage winding transferring active and reactive power to the infinite-bus system.

According to the properties of wind turbines with constant speed,a test on transient performance is carried out in the wind farm.The constant wind speed is regarded as the test signal,and the conditions of active power,reactive power,wind coefficient,and pitch angle are observed.

Simulation conditions are set as follows:the initial active power of each DFIG is 4.5 MW,the reactive power is 0.2 MVar,and the constant wind speed is 14 m/s.Then each DFIG’s conditions of active power,reactive power,wind coefficient,rotate speed,pitch,and bus voltage are observed.Among them,the operation curves of a certain DFIG is shown in Fig.5 and Fig.6（the lateral axis represents time,which is the same in Fig.8 to Fig.11）.

4.1 Simulation and Analysis on Equivalent DFIG Wind Farm Model

Based on the cluster classification indices and K-means clustering algorithm,wind turbines in the same cluster is equivalent to one wind turbine.Then the multiple generator system(as presented in Appendix),the four DFIGs could be equivalent to a single wind turbine,by adding their mechanical power together.Then the system can be described as Fig.7.

Fig.7 shows the wiring structure of DFIG equivalent wind farm,which has only one equivalent DFIG model,covering four voltage classes.Since the structure is similar to that of one DFIG system,details are not described here.By using identical test ways,conditions of active power,reactive power,wind coefficients,rotate speed,pitch,and bus voltage are observed as presented in Fig.8 and Fig.9.

Fig.5.Operation curves of DFIG wind turbine under constant wind speed.

Fig.6.Grid voltage curves of DFIG wind farm under constant wind speed.

Fig.7.Equivalent system structure of DFIG wind farm.

Fig.8.Operation curves of equivalent DFIG wind turbine under constant wind speed.

Fig.9.Grid voltage curves of equivalent DFIG wind farm under constant wind speed.

Comparing Fig.5 and Fig.6 with Fig.8 and Fig.9,it is obvious that the conditions of active power,reactive power,wind coefficient,rotate speed,pitch,and bus voltage between the four identical DFIGs and the equivalent DFIG could be considered sharing the same values and curve trend,within acceptable errors.As a result,the accuracy of the equivalent method is verified.

4.2 Analysis on LVRT Capability of Crowbar Circuit

Considering the single and equivalent DFIG shares the same LVRT ability,the single DFIG presented in Section 3.1 is selected to have a better observation on crowbar properties under the system fault.The steady active power is set as 4 MW,reactive power 0 MW.Two cases are studied as follows.

Case 1.Without the crowbar,a symmetric fault of three phase voltage drop happens at 0 s,and the fault is cleared up at 0.15 s.

Case 2.With crowbar,a symmetric fault of three phase voltage drop happens at 0 s,the crowbar operates at 0.005 s,and the fault is cleared up at 0.15 s,then the crowbar is cut off at 0.5 s.

Simulation of the above cases is carried out respectively with DigSILENT.Simulation time is 2 s,while active power and reactive power curves of DFIG are described in Fig.10 and Fig.11.

Fig.10 and Fig.11 show that the steady state of 4 MW/0 MVar is reached by both cases,following the transaction period.For Case 1,since no crowbar is allocated,the peak value of active power fluctuation is above 12 MW,while that of the reactive power is -14 MW.Namely,large amount of reactive power is consumed.Besides,the transaction time is relatively longer and obvious fluctuations are presented.For Case 2,with a mild fluctuation,the peak value of active is about 6 MW and that of the reactive power is -10 MW.So conclusions can be achieved that the crowbar circuit plays a crucial part in periods of both faults and faults recovery,making the output power much smoother.

Fig.10.Curves of active power and reactive power under Case 1.

Fig.11.Curves of active power and reactive power under Case 2.

Because the low rated power is possessed with the tested DFIG,advantages of the crowbar circuit have not been so apparent.Nevertheless,qualitative verification has been demostrated in valuating crowbar’s effect on the capability improvement of LVRT.

5.Conclusions

On the basis of study on modeling the double-fed wind farm and LVRT ability,research findings are presented as follows:

1)The dynamic modeling theory of DFIG wind farm under the fault conditions is proposed,which realizes the clustering classification by using the K-means algorithm and considering the pitch control operation first,then the optimal parameter identification is done by adopting the advanced PSO algorithm.Finally,the multiple generator representation model is built.

2)Feasibility of the multiple representation method is verified in the study cases,which can describe the properties of multiple generators in an effective way.

3)The crucial role of crowbar circuit in improving the LVRT ability is analyzed in the study cases,which shows that it smoothes the output power both in the period of faults and faults recovery.

Future work will focus on the further study in more optimized modeling methods of DFIG wind farm,as well as the optimal resistance of crowbar circuit and other factors that affect its performance.

Appendix

Fig.12 shows the typical system structure of DFIG wind farm(presented in DigSILENT).

Fig.12.Typical system structure of DFIG wind farm.

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