stator flux

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2014 Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER)

A Comparative Study of Rotor Flux position- and

Stator Flux Position-based Direct Power Control

Method in a DFIG Wind Turbine System

Mona Valikhani, Constantinos Sourkounis

Power Systems Technology and Power Mechatronics line

Ruhr-University Bochum

Bochum, GermanyEmail: [email protected], [email protected]

AbstractToday, direct control strategies are more and more

demanded in high dynamic performances, since they offer

superior dynamic response. One of the major concerns in these

methodologies is the estimation of rotor flux which plays an

important role in conventional rotor flux position-based directpower control (DPC) methods. Recently there have been more

interests on stator flux position-based DPC and different direct

control strategies are accordingly developed. The aim of this

paper is thus to analyse the dynamic behaviour and robustness of

rotor flux position- and stator flux position-based DPC methods

for a DFIG-based wind system under the same operating

conditions and to develop a comparative study based on the

simulation results.

Keywords Direct Power Control (DPC); Doubly Fed

Induction Generator (DF IG).

I. NOMENCLATURE

Parameter Definitions Parameter Definitions

rs, lsStator resistanceand inductance

s Synchronous speed

rr,lrRotor resistance

and inductancem Rotor angular position

lmMagnetizinginductance

rRotor electricalangular position

Flux linkage Ps, QsStator active and

reactive power

s,r Stator, rotor,u,i Complex vector(space

vector)

u.ivoltage and

current

II. INTRODUCTION

Since the mid-1980s the ac drives have gone through directcontrol techniques: Direct torque control (DTC) and direct

power control (DPC). Direct torque control of doubly fedinduction generator (DFIG) was first developed in [1]-[2].Today, direct control strategies are more and more demandedin high dynamic performances, since they offer superiordynamic response while decoupling control signals such asactive and reactive power in case of DPC. On the other hand,these methods are independent of the machine parametervariations as this was inevitable in the conventional vectorcontrol methods. However, in the conventional rotor flux

position-based DPC, by variations in rotor resistance

degradations in dynamic response appear. One of the otherconcerns referring to the rotor flux position-based DPC is theestimation of rotor flux due to the rotor circuit parametervariations as a result of variations in slip frequency.

The aim of this paper is thus put on utilizing the stator fluxposition instead of rotor flux position and to compare thesimulation results of each method. For this purpose, a reviewof conventional DPC method is provided and thereafter themethodology of the stator flux position-based DPC will bediscussed.

III. ROTOR FLUX POSITION-BASED DPC

The first step for a better understanding of rotor fluxposition-based DPC in a DFIG system is to firstly grasp thestator power formulation based on the flux functionality. Fromthe basic power equations, it can be understood that statoractive and reactive powers can be obtained directly from themeasured stator current and voltage as follows:

(1)

With the stator voltage being rather constant, it followsfrom the above equations that the stator current takes over in

power control task such that changes in the stator current willhave impacts on active and reactive power values. However,stator current itself can be altered by the rotor voltage vectors.In a more general form, by injection of different rotor voltage

vectors, stator active and reactive powers are controlled.However, this assertion needs to be more clarified, since thelast two expressions dont provide enough information. In thisregard, the power equations of (1) can be rewritten as below:

(2)

(3)

978-1-4799-3787-5/14/$31.00 2014 IEEE


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Where is the phase angle between rotor and stator fluxvectors, which depending on the generating or motoring modeit adopts positive or negative values, respectively. Theseequations show the stator active and reactive powerdependency on the fluxes. Since the stator voltage andfrequency are kept constant and the stator resistance being alsoneglected, it will lead thus to a constant stator flux.

Therefore, it is just needed to keep andunder control to achieve active and reactive power regulation

purposes. In other words, either the rotor flux amplitude or theflux angle has to be varied in order to control the stator

powers. To determine the rotor flux, the voltage model [3] willbe used, considering the rotor reference frame as follows:

(4)

Neglecting the drop voltage over the rotor resistance, wemay have the final rotor flux in terms of rotor voltage injected

by the converter at the h time interval of the voltage injectionas can be seen in (5):

(5)

The first two terms of Eq. (5) are final and initial rotor fluxamplitudes respectively. If the converter injects constant rotorvoltage during the injection time interval, the equation abovecan be simplified as:

(6)

It follows from (6) that injecting different rotor voltagevectors influences the rotor flux, thus from (2) and (3) leadingto changes in stator active and reactive powers. However, in[36], it has been proved that, the impact of initial rotor fluxamplitude and position on the active and reactive powerchanges can be neglected.

As a final result, the appropriate and optimal choice ofeach of the rotor voltage vectors depend not only on the rotorflux position but also on the active and reactive power errors.In Table I, the relation between rotor flux position, powererror on-off values and rotor voltage vector selection (theconverter switching states) is well depicted.

Table I. Rotor Voltage Vector Selection based on the power errors and

rotor flux position (k=section)Ps

1 0

Qs

1 u(k+1) u(k-1)

0 u(k+2) u(k-2)

Where K is the section, at which the rotor flux space vectoris positioned. Fig.1 shows the overall scheme of the rotor flux

position-based DPC method.

Fig. 1. An overall scheme of the rotor flux position-based DPC

IV. STATOR FLUX POSITION-BASED DPC

In DPC method based on the rotor flux position, anoptimal switching table was developed using active andreactive power errors and the rotor flux position, that is, therotor flux has to be estimated. However, since the slipfrequency might be very low and on the other hand since thewind speed varies and the rotor frequency may not be fixed,this would affect the machine parameters significantly andhence the rotor flux estimation might lose accuracy. Until2006, direct control method was mainly implemented usingrotor flux position. However, there have been some researchesfocusing on obtaining rotor voltage vectors independent fromrotor flux estimation [4]-[6].

Recently there have been more interests on usingstator flux position in DPC methods instead of rotor flux

position [7]-[8]. The reason behind this refers to the fact thatsince the stator voltage is rather fixed in frequency andharmonics-free, hence the accuracy of the estimated stator fluxis no more susceptible. On the other hand, the need to estimatethe rotor flux is totally eliminated hence resulting in reducedcomputation efforts. In this method, the same procedure ofconventional DPC method is accomplished except that insteadof estimating the rotor flux, the stator flux is estimated, whichmakes the DPC process easier to implement. For this purpose,the stator flux is transformed using rotor reference frame andfrom the estimated rotor flux position, the required sector forthe rotor voltage vector selection process can be obtained.That is, the stator flux in the stationary reference frameobtained from (7) has to be transformed into the rotorreference frame using the transformation equation given in (8).


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For this purpose using the , components of the stator fluxwould facilitate the transformations as shown in Eq. (9-10)

(7)

where0 represents the stationary reference frame.

(8)

(9)

(10)

The rotor voltage vectors can be then optimally obtainedusing a switching table based on the stator power errors and thestator flux position. This model is to a large extent simpler thanthe conventional DPC and excessive computations could be

also omitted .On the other hand, due to the fact that statorfrequency is fixed and stator voltage is relatively harmonic-free, this method would result in more accurate responses. Fig.2 shows an overall scheme of the stator flux position-basedDPC method.

V. SIMULATION RESULTS

The simulation results of a 40KW DFIG are shown in fig.(3-6). Fig. 3 shows the active and reactive power curves of astator flux position-based DPC under normal condition. Toevaluate the robustness, the rotor resistance is varied to 150%of its rated value and the simulation results are shown in fig. 4.

In order to achieve a comparative view, the rotor flux-basedDPC is also simulated under the same condition and thecomparative results are shown in fig. 5. The outstandingadvantage of the stator flux-based DPC can be well seen in fig.6, where the rotor flux DPC degrades to a large extent in caseof variations in rotor resistance while the stator flux-DPC triesto keep its robustness.

Fig. 2. An overall scheme of the stator flux position-based DPC


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0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2x 10

4

Time (S)

ActivePowe

r(W)

reference

actual

0.985 0.99 0.995 1 1.005 1.01 1.015

-10000

-8000

-6000

-4000

-2000

0

Time (S)

ActivePowe

r(W)

reference

actual

(a) (b)

0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

23

4x 10

4

Time (s)

ReactivePower(Var)

reference

actual

1.49 1.5 1.51 1.52 1.53

-1

-0.5

0

0.5

1

x 104

Time (s)

ReactivePower(Var)

reference

actual

(c) (d)

Fig. 3. a,b) active power c,d) reactive power curves for Stator flux position-based DPC

0 1 2 3 4 5-5

-4

-3

-2

-1

0

1x 10

4

Time (s)

ActivePower(W)

0 1 2 3 4 5-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Time (s)

Rea

ctivePower(Var)

(a) (b)Fig. 4. a) active power b) reactive power curves for rotor resistance variation of 150% of rated in stator flux-based DPC


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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

-4

-3

-2

-1

0

1

2x 10

4

Rotor Flux Position-based DPC

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

-4

-3

-2

-1

0

1

2x 10

4

Time (S)

ActivePower

(W)

Stator Flux Position-based DPC

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5x 10

4


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

-4

-3

-2

-1

0

1

2

3

4x 10

4

Time (s)

ReactivePower(Var)


Fig. 5) Comparative results of stator flux and rotor flux position-based DPC for 100% of rated rotor resistance

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

0

5x 10

ActivePower(W)


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

-4

-3

-2

-1

0

1x 10

4

Time (s)


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.5

0

0.5

1x 10

5

Rotor Flux position-based DPC

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-4

-2

0

2

x 104

Time (s)

ReactivePower(Var)


Fig. 6) Comparative results of stator flux and rotor flux position-based DPC for 150% of rated rotor resistance

VI. CONCLUSION

This paper presents a comparative study between theconventional rotor flux position-based DPC and the statorflux position-based DPC methods for a DFIG wind turbinesystem. It can be seen that the latter provides a good dynamic

performance and a robust behavior when rotor resistancevaries to 150% of its rated value. On the other hand, thecomputational complexities which exist in the conventionalDPC due to the rotor flux estimation are then reduced andthe system model is more accurate and easier to implement.

REFERENCES

[1] I. Takahashi and T. Noguchi, A new quick-response and high-efficiency control strategy of an induction motor, IEEE Trans. Ind.Appl., vol. IA- 22, no. 5, pp. 820827, Sep.Oct. 1986.

[2] M. Depenbrock, Direct self control of inverter-fed inductionmachines, IEEE Trans. Power Electron., vol. 3, no. 5, pp. 420429,Oct. 1989.

[3] S. Engelhardt, Direkte Leistungsregelung einer Windenergieanlagemit doppelt gespeister Asynchronmaschine,Shaker, Aachen, 2011.

[4] T. Noguchi, H. Tomiki, S. Kondo, and I. Takahashi, Direct powercontrol of PWM converter without power-source voltage sensors,IEEE Trans.Ind. Appl., vol. 34, no. 3, pp. 473479, MayJun. 1998.

[5] M. Malinowski, M. P. Kazmierkowski, S. Hansen, F. Blaabjerg, andG. D. Marques, Virtual-flux-based direct power control of three-phase PWM rectifiers, IEEE Trans. Ind. Appl., vol. 37, no. 4, pp.10191027, Jul.Aug. 2001.

[6] G. Escobar, A. M. Stankovic, J. M. Carrasco, E. Galvan, and R.Ortega, Analysis and design of direct power control (DPC) for athree phase synchronous rectifier via output regulation subspaces,IEEE Trans. Power Electron., vol. 18, no. 3, pp. 823830, May 2003.

[7] L. Xu, P. Cartwright, Direct active and reactive power control ofDFIG for wind energy generation, IEEE Transactions on EnergyConversion, vol. 21, pp. 750 - 758, September 2006.

[8] L. Xu ;D. Zhi ;L. Yao, Direct Power Control of Grid ConnectedVoltage Source Converters, Power Engineering Society GeneralMeeting IEEE Digital Object Identifier IEEE, pp. 1-6, 2007.
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