A FUZZY-PI CONTROLLER FOR WIND TURBINE DRIVEN DFIG

OPTIMIZED USING GENETIC ALGORITHMS

Lawrence K. Letting

, Josiah L. Munda

and Yskandar Hamam

1,2

Tshwane University of Technology, Pretoria, South Africa

ESIEE-Paris, Paris-Est University, LISV, UVSQ, Paris, France

Keywords:

DFIG, Fuzzy-PI control, Optimization, Genetic algorithms.

Abstract:

This paper presents the design of optimal TSK-fuzzy PI controller for the rotor side converter (RSC) of a

doubly fed induction generator (DFIG) in a grid connected wind generation system. The optimization strategy

is based on binary genetic algorithms. The controller is used to regulate the active and reactive power and hence

extract maximum energy from the system under varying wind speeds. Pitch angle control is used to regulate

the rotor angular speed while the active and reactive power are controlled by the rotor voltage supplied by the

RSC. The stator ﬂux oriented reference frame is adopted. A fuzzy-PI controller with a minimum rule base

of nine rules is realized. The controller is implemented in C code as a dynamic linked library and simulated

using LabVIEW. Simulation results are presented.

1 INTRODUCTION

Wind energy is the fastest growing and the most

promising renewable energy source in the world to-

day. It is non-polluting, free and economically vi-

able. In addition, there has been a rapid technological

development in wind turbine technology (Munteanu

et al., 2008). In the recent past there has been an in-

creased use of DFIG’s in small power plants due to

their unique capabilities (Abedi et al., 2010). The

special features of DFIG are: it can supply power

at constant voltage and frequency; the rotor can op-

erate in both sub-synchronous or super-synchronous

speeds; the rating of the power converter is approxi-

mately 30% of the rated wind turbine power and; the

generated active and reactive power can be indepen-

dently controlled (Abo-Khalil et al., 2007).

To ensure maximum utilization of wind energy

in variable speed power plants, the stator active and

reactive power are controlled separately by varying

the rotor current of the DFIG using a vector control

scheme. A power converteris used to control the rotor

voltage. The control of power converters connected to

the DFIG is traditionally accomplished using propor-

tional and integral (PI) controllers. However, wind

energy conversion systems (WECS) are highly non-

linear with time-varying system parameters such as

wind speed and reference power values. This makes

it difﬁcult to design optimal PI-controller gains using

either modern or classical control theory (Abedi et al.,

2010).

Artiﬁcial intelligence based methods using ge-

netic algorithms, particle swarm optimization (PSO),

and fuzzy logic have been introduced in order to im-

prove controller performance in WECS (Elshafei and

Azzouz, 2011), (Lin et al., 2011), (Ren et al., 2009),

(Leite et al., 2009), (Vieira et al., 2008). (Lin et al.,

2011) presents a particle swarm optimized recurrent

fuzzy neural network used to track the maximum

wind energy with reference values obtained from an

adaptive model reference observer. In (Leite et al.,

2009) PI controller gains are tuned using PSO with

aim of improving DFIG performance under network

faults. (Vieira et al., 2008) optimizes the PI-controller

gains using genetic algorithms in order to improve

active power control and dc-link voltage regulation.

(Ren et al., 2009) presents a 49-rule fuzzy controller

used to control the rotor speed and is shown to give

better performance than PI-control. (Elshafei and Az-

zouz, 2011) reports the design of a 9-rule adaptive

fuzzy controller (AFLC) for regulating the dc-link

voltage. The AFLC is shown to give better perfor-

mance compared to a classical PI controller and a 9-

rule non-adaptive FLC. It has therefore been estab-

lished that fuzzy control offers a great potential in

control of WECS.

This paper proposes an automated strategy for

tuning two fuzzy controllers used in regulation of ac-

348

K. Letting L., L. Munda J. and Hamam Y..

A FUZZY-PI CONTROLLER FOR WIND TURBINE DRIVEN DFIG OPTIMIZED USING GENETIC ALGORITHMS.

DOI: 10.5220/0003601403480353

In Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2011), pages

348-353

ISBN: 978-989-8425-78-2

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

tive and reactive power in the rotor side converter of

WECS. The FLCs are based on the ﬁrst order Takagi-

Sugeno-Kang (TSK) model with two inputs: error

and integral of error. This proposed method shows

that it is possible to optimize a fuzzy-PI controller and

meet the desired performance with a minimum rule

base of only 9 rules. An optimized fuzzy-PI controller

gives performance similar to a classical PI controller

with adaptive gains.

2 SYSTEM CONFIGURATION

The system is conﬁgured as shown in Fig. 1. The

stator of the induction machine is directly connected

to the three- phase grid while the rotor winding is

supplied through the back-to-back converters. The

system is implemented with PI control in LabVIEW

control design and simulation module (NI LabVIEW,

2009). A master controller is used to regulate the ro-

tor angular speed by varying the pitch angle in order

to the ensure operation is maintained at an optimal

tip-speed ratio. The generator controller uses PI con-

trollers to regulate the active and reactive power. Vec-

tor control scheme is applied using the stator ﬂux ori-

ented reference frame (Pena et al., 1996). The dc-link

voltage is ﬁxed while the rotor side converter is mod-

eled as a voltage source. Grid-side converter control

is therefore not considered.

(NI LabVIEW, 2009) presents a WECS control

system model where the rotor-side converter regulates

the the stator active and reactive power through rotor

voltage components V

and V

which are indepen-

dently controlled by PI controllers. In this paper the

same model is adopted and the PI controllers are re-

placed by two fuzzy-PI controllers as shown in Fig.

2. FLC1 controls the rotor d-axis voltage while FLC2

controls the q-axis voltage. The two fuzzy controller

outputs V

∗

and V

∗

are used as the reference values

for the PWM controller connected to the rotor side

converter.

Detailed modeling of the DFIG and the vector

control scheme is available in (Pena et al., 1996). The

modeling of the wind-turbine and calculation of the

maximum active power reference values can be found

in (NI LabVIEW, 2009).

3 fuzzyPI CONTROLLER

STRUCTURE

The structure of the fuzzy-PI controller is presented

in Fig. 3. It comprises of four parts: fuzziﬁcation,

Pitch angle

control

Pitch angle

control

Drive train

Wind

DFIG

Grid

Converter control

Rotor side

converter

Grid side

converter

Figure 1: DFIG wind turbine conﬁguration.

Calculation of

rotor current

reference values

_ _

s ref s ref

P Q

s r

I I

rq ref

rd ref

−

FLC1

1 /

FLC2

1 /

∆

Figure 2: DFIG vector control scheme using fuzzy logic.

knowledge base, inference engine, and defuzziﬁca-

tion. There are two input variables, error e(t

), and

the integral of error ie(t

) at the k

simulation step

deﬁned as:

e(t

) = i

ref

) − i(t

) (1)

ie(t

) = e(t

k−1

) +

k−1

e(t)dt (2)

where i

ref

) and i(t

) are the reference and actual

values of the rotor dq-currents respectively.

The fuzzy control algorithm was developed in

C++ based on ﬁrst order TSK-inference system. The

TSK fuzzy model is more compact with a computa-

tionally efﬁcient representation than a Mamdani sys-

tem (Bose, 2002). The input membership functions

are encoded as shown in Fig. 4 using trapezoidal

membership functions. Each input is fuzziﬁed using

three membership functions: Negative (N), Zero (Z),

and Positive(P). The FLC has nine rules and the out-

put of each rule is given by (3).

v(t

) = K

· e(t

) + K

· ie(t

) + K

(3)

Where K

, K

, and K

are constants to be determined

for each output MF in the inference engine of Fig. 3.

A FUZZY-PI CONTROLLER FOR WIND TURBINE DRIVEN DFIG OPTIMIZED USING GENETIC ALGORITHMS

349

e(k)

Inputs

Knowledge base

Fuzzification

interface

Inference engine

(decision making logic)

Defuzzification

interface

Output

ie(k)

Figure 3: Structure of the fuzzy-PI controller.

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

error (or integral of error)

Degree of membership

N Z P

Figure 4: Encoding of input membership functions.

4 OPTIMIZATION OF fuzzyPI

CONTROLLER

The conventional design of membership functions

and rule base of a fuzzy inference system is based on

expert knowledge. However, expert knowledge alone

is not enough to design a robust fuzzy controller for a

complex system such as WECS. In this design a ﬁxed

rule base size and and input MF type were selected as

explained in section 3. The total number of variables

that need to be optimized for each FLC are summa-

rized in Table 1. The variable limits were identiﬁed by

performing initial simulation runs in open-loop mode.

Each FLC has 35 optimization variables.

During optimization using GA, each FLC is mod-

eled as single chromosome with 35 genes where each

gene represents a parameter in Table 1. The initial

Table 1: Optimization variables.

No.of

Parameter variables Min. Max.

e 4 −30 30

ie 4 −10 10

9 −1 1

Table 2: GA parameters.

Parameter Value

Population 70

Number of iterations 50

No. of bits 8

Selection rate 0.5

Mutation rate 0.2

population is randomly generated using the param-

eters of Table 2. At the end of each iteration the

cost of each chromosome is evaluated and ranking is

done. An elitist strategy is adopted such that 50%

of the individuals with the least cost are selected to

form the next population. The remaining members

are reproduced through mating of the selected indi-

viduals. Parents for mating are selected using rank-

weighting and the offspring is generated using single-

point crossover. Random mutations are carried out on

the population with a mutation rate of 20%. Muta-

tions ensure that the entire cost surface is explored.

The best chromosome is not mutated due to elitism.

The mean-square-error (MSE) deﬁned in (4) and

(5) is used as the ﬁtness function for FLC1 and FLC2

respectively. Equations (4) and (5) measure the devia-

tion from the desired reactive(Q) and active power(P)

respectively. The optimization variables for the two

fuzzy-PI’s are encoded in one matrix where each row

represents the parameters of FLC1 and FLC2 which

are used to run the system during one iteration. The

ﬁtness of each row of the population is given by the

sum of the cost obtained in (4) and (5). Optimization

is carried out off-line before the start of the next iter-

ation. The simulation steps are illustrated in the the

ﬂowchart of Fig. 5.

ref

(t)− Q(t))

dt (4)

ref

(t)− P(t))

dt (5)

5 SIMULATION RESULTS

Optimal parameters for the fuzzy controllers is ob-

tained from the best chromosome at the end of the

simulation. The optimized input MFs for FLC1 and

FLC2 are presented Fig. 6 and Fig. 7 respectively.

The rule surface for FLC1 and FLC2 are shown in

Fig. 8 and Fig. 9 respectively. The contour maps are

shown at the bottom of each surface plot. The perfor-

mance of the fuzzy-PI was tested using the wind pro-

ﬁle of Fig.10. It is observedin Fig. 11 and Fig. 13 that

the proposed controller is able to track the maximum

SIMULTECH 2011 - 1st International Conference on Simulation and Modeling Methodologies, Technologies and

Applications

350

k>P?

(all FLCs

simulated?)

Simulate current FLC

and update cost,

Run genetic

algorithm

Max. no. of

iterations

reached?

Download results

to disk

Stop

Start

Initialization

Yes

Figure 5: Illustration of optimization procedure.

energy from the wind and maintain the stator reactive

power close to zero. The reference active power is

obtained from the rotor current q-axis reference com-

ponent (I

ref

−30 −20 −10 0 10 20 30

0.2

0.4

0.6

0.8

Degree of membership

N Z P

−10 −5 0 5 10

0.2

0.4

0.6

0.8

Degree of membership

N Z P

Figure 6: Optimized input MFs for FLC1.

−30 −20 −10 0 10 20 30

0.2

0.4

0.6

0.8

Degree of membership

N Z P

−10 −5 0 5 10

0.2

0.4

0.6

0.8

Degree of membership

N Z P

Figure 7: Optimized input MFs for FLC2.

Figure 8: Optimized rule surface for FLC1.

Figure 9: Optimized rule surface for FLC2.

A FUZZY-PI CONTROLLER FOR WIND TURBINE DRIVEN DFIG OPTIMIZED USING GENETIC ALGORITHMS

351

Figure 10: Wind proﬁle (base speed 12m/s).

Figure 11: DFIG active power (P

Figure 12: Control signal (V

′

Figure 13: DFIG reactive power (Q

6 CONCLUSIONS

In this paper an optimized fuzzy-PI controller for ac-

tive and reactive power control in the rotor side con-

Figure 14: Control signal (V

′

verter of a wind energy conversion system is pro-

posed. It is shown that it is possible to design and

optimize a fuzzy-PI controller with a minimum rule

base of nine rules using genetic algorithms. The ad-

vantage of the small rule base is that it requires less

memory space with faster execution speed. It is an

improvement from the standard fuzzy-PI controllers

with 49 rules. Comparison of the performance of the

proposed fuzzy-PI and other methods such as classi-

cal PI and PI with optimized gains is part of future

work.

REFERENCES

Abedi, A., Pishvaei, M., Madadi, A., and Kelk, H. M.

(2010). Analyzing vector control of a grid-connected

dﬁg under simultaneous changes of two inputs of con-

trol system. European Journal of Scientiﬁc Research,

45(2):221–231.

Abo-Khalil, A., Lee, D.-C., and Jang, J.-I. (2007). Con-

trol of back-to-back pwm converters for dﬁg wind tur-

bine systems under unbalanced grid voltage. In Indus-

trial Electronics, 2007. ISIE 2007. IEEE International

Symposium on, pages 2637 –2642.

Bose, B. K. (2002). Modern Power Electronics and AC

Drives. Prentice-Hall, Inc.

Elshafei, A. and Azzouz, M. (2011). Adaptive fuzzy regu-

lation of the dc-bus capacitor voltage in a wind energy

conversion system (wecs). Expert Systems with Appli-

cations, 38(5):5500 – 5506.

Leite, H., Barros, J., and Miranda, V. (2009). Evolutionary

algorithm epso helping doubly-fed induction genera-

tors in ride-through-fault. In PowerTech, 2009 IEEE

Bucharest, pages 1 –8.

Lin, W.-M., Hong, C.-M., and Cheng, F.-S. (2011). De-

sign of intelligent controllers for wind generation sys-

tem with sensorless maximum wind energy control.

Energy Conversion and Management, 52(2):1086 –

1096.

Munteanu, I., Bratcu, A. I., Cutululis, N.-A., and Ceangˇa,

E. (2008). Optimal Control of Wind Energy Systems,

Towards a Global Approach. Springer-Verlag, Lon-

don.

SIMULTECH 2011 - 1st International Conference on Simulation and Modeling Methodologies, Technologies and

Applications

352

NI LabVIEW (2009). Designing controllers

for a doubly-fed wind power system.

http://zone.ni.com/devzone/cda/epd/p/id/6272.

Accessed: 1st April 2011:

http://zone.ni.com/devzone/cda/epd/p/id/6272.

Pena, R., Clare, J., and Asher, G. (1996). Doubly fed induc-

tion generator using back-to-back pwm converters and

its application to variable-speed wind-energy genera-

tion. Electric Power Applications, IEE Proceedings -,

143(3):231 –241.

Ren, Y., Li, H., Zhou, J., An, Z., Liu, J., Hu, H., and

Liu, H. (2009). Dynamic performance analysis of

grid-connected dﬁg based on fuzzy logic control. In

Mechatronics and Automation, 2009. ICMA 2009. In-

ternational Conference on, pages 719 –723.

Vieira, J., Nunes, M., and Bezerra, U. (2008). Design of

optimal pi controllers for doubly fed induction gen-

erators in wind turbines using genetic algorithm. In

Power and Energy Society General Meeting - Con-

version and Delivery of Electrical Energy in the 21st

Century, 2008 IEEE, pages 1 –7.

APPENDIX

The parameters of the DFIG are given in Table 3.

Table 3: DFIG Parameters.

Parameter Value

Power base 4.8MW

Frequency base 60Hz

Stator resistance 0.003068pu

Rotor resistance 0.006068pu

Rotor leakage inductance 0.05783pu

Stator leakage inductance 0.05783pu

Mutual inductance 1.85068pu

Gear box ratio 55

A FUZZY-PI CONTROLLER FOR WIND TURBINE DRIVEN DFIG OPTIMIZED USING GENETIC ALGORITHMS

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