Comparison of Fuzzy Logic and Digital PI Controllers ...

Comparison of Fuzzy Logic and Digital PI Controllers for an Induction Generator Drive in Wind Energy Conversion System Tolga Sürgevil*, Eyüp Akpınar*, Sinan Pravadalıoğlu** *Dokuz Eylül University **Dokuz Eylül University Department of Electrical and Electronics Engineering IMYO Control Syst. Dept. Kaynaklar Kampusu Buca, 35160 Izmir, Turkey Buca 35170 İzmir Turkey Abstract – This paper presents a comparison of fuzzy logic and PI controllers, which are employed in a variable-speed gridconnected wind energy conversion system (WECS). The system basically consists of an induction generator, back-to-back voltage-source PWM converters, horizontal axis 3-blade turbine. Two TMS320F240 16-bit fixed point digital signal processors are used to manage the power conversion. The performance of the controllers are investigated by using detailed computer simulations in Matlab and experimental results obtained on the WECS.

II. MODELING OF THE WECS A. Line-side Converter Assuming that the lossless converter is fed from a balanced three-phase voltage source without a neutral connection, the mathematical model of the converter can be derived in state-space form as follows [6]:

I. INTRODUCTION The maximum available power is extracted from the wind over a wide speed range by providing a power electronic interface between the generator and the utility grid. The use of PWM voltage source converters (VSC) in grid-connected wind energy applications is a suitable option since they allow bidirectional power flow and variable speed operation of the wind turbine. Also, due to their advantages of unity power factor operation and low total harmonic distortion of the ac supply currents, the back to back PWM converter topology has advantages [1-2] for low power rated WECS. The main disadvantage is that the converters should be rated at the power rating of wind turbine, if they are used between the grid and the armature of generator. A 5kW wind energy conversion system has been implemented with the converters shown in Fig.1. The hysteresis current controller is used in the line side converter [3]. This converter supplies regulated dc voltage and draws sinusoidal currents at unity power factor from utility grid. The inverter on the machine side provides the speed control of the induction machine based on constant V/f ratio with slip regulation method [4]. Both converters are designed to control the power extracted from the wind using two separate TMS320F240 16-bit fixed point DSP. A mathematical model of the complete system has been obtained and solved in Matlab [5]. The analysis of the system has been performed for conventional digital PI controllers designed for both PWM converters and repeated for the fuzzy logic controller replacing the PI controller of the line-side converter. The performance of the system under these controllers is also experimentally investigated. The rest of the paper is organized as follows: In the second part, the mathematical model of the generator, converters and wind turbine are given. In the third part, the fuzzy logic control used in the system is briefly described. In part four, the speed control of the induction machine is discussed. The fifth part contains the simulation and experimental results. The conclusions of this study are discussed in last section.

Ls C

di k u + R s i k = ek − (u dc d k − dc dt 3 du dc = dt

3

∑d

k)

(1)

k =1

3

∑d i

k k

− i dc

(2)

k =1

B. Generator-side converter The d, q transformation from phase variables to d, q axes fixed in the stator is applied to phase voltages, phase currents and switching status of switching devices (IGBTs) as follows:

Vqs = u dc d q'

(3)

Vds = u dc d d' 3 idc = (i qs d q' + i ds d d' ) 2

(4)

where

(5)

iqs , ids and d q' , d d' are the transformed machine

currents and inverter switching signals, respectively.

C. Induction Machine The 3-phase induction machine used in the system has a double-cage rotor and its mathematical model has been obtained from [7] and used in computer simulations. In that model magnetic saturation is neglected and machine windings are assumed to be balanced and sinusoidally distributed. Machine parameters can be found in [8].

D. Wind Turbine The wind turbine in the system is a horizontal axis, three-bladed, fixed pitch angle turbine. The turbine is coupled to the shaft of induction machine through a gearbox. The mechanical power developed by the turbine is as follows [9]:

Fig.1 The scheme of variable-speed WECS Pt = 0.5 C p (λ ) ρπR 2 v 3 (Watts)

(6)

Table I. Rule matrix for PI based fuzzy controller

II. FUZZY LOGIC CONTROL The closed-loop control scheme of the dc link voltage is shown in Fig.1. The dc link voltage is regulated by the control of ac supply currents, hence the voltage controller generates the required magnitude of these currents ( I cm ). Both PI and fuzzy logic controllers (FLC) have been implemented in order to maintain the dc link voltage constant at the reference level. The PI and FLC voltage controllers are incremental type, hence the controller output at the kth sampling instant in (7) is calculated from its previous value and the change of output ( ∆I cm ) as follows: I cm (k ) = I cm (k − 1) + ∆I cm (k )

(7)

The PI and FLC differs only in the algorithm of calculation the change of output value. In digital implementation of the PI controller, this value is calculated from error ( E ) and change of error ( ∆E ) in dc link voltage with the scaling factors K E and K CE as follows; ∆I cm (k ) = K E E (k ) + K CE ∆E (k )

(8)

The error and change of error signals are processed in the FLC by a set of linguistic control rules. The crisp values of error and change of error are expressed in terms of 7 linguistic variables: NB (negative big), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), and PB (positive big). The linguistic variables are defined in the universe of discourse with overlapping symmetrical triangular and trapezoidal shaped membership functions as shown in Fig.2. During the implementation, the states of the system are scaled into the range of the 10-bit A/D converter on DSP and the controller inputs are defined in this range. The membership degrees of the linguistic variables are calculated for a given values of the inputs.

The inputs of the FLC are expressed in 7 linguistic variables and total 49 rules can be constructed with two antecedents and one consequent. These rules are used for control action and shown in Table I. The output of the fuzzy controller is also expressed in terms of 7 linguistic variables. The membership functions used to describe the output of the controller are shown in Fig. 3. During inference process, Mamdani max-min implication method is used for a disjunctive set of rules. Hence, the aggregated output of 49 rules can be obtained based on this method such that [10]

µ ∆I k ( y ) = max{min (µ E k ( E i ), µ ∆E k (∆E j ) )} cm

k

(9)

where k=1,2,…,49. The aggregated output is translated into a crisp value by using one of the defuzzification methods. The mostly used one is the center of gravity (COG) method. However, the weighted average method has been used in the implementation because it brings less computational burden to DSP. This method is valid for output membership function having symmetrical shape as shown in Fig.3 and gives approximately the same results with the COG. Also, in the universe of discourse there are at most two input membership functions overlapping, which means at most two membership values will have membership degree other than zero. As a combination of these input membership values, at most four rules will be fired and the others will be zero. In the calculation of the defuzzified output, only the

fired rules are taken into account and the others are omitted [11]. This results in a considerable reduction in the computational burden. Hence, the defuzzified output of the FLC is calculated as follows: 4

∆I cm =

∑ k =1 4

k =1

and change of error ( ∆E spd ) in rotational speed is calculated from (13) as follows: * ∆ω slip (k ) = K E , spd E spd (k ) + K CE , spd ∆E spd (k )

µ ∆I cm ( yk ) yk

∑µ

where the change of slip expressed in terms of error ( E spd )

(13)

(10)

V. RESULTS

∆I cm ( y k )

A. Simulation and Experimental Results of Lineside Converter

Fig.2 Membership functions for error (e) and change of error (ce)

The computer simulation of the system has been performed using MATLAB Simulink. The performance of the PI and fuzzy logic controllers are investigated on the line-side converter for the same scaling gains and sampling rate. The error and change of error gains are scaled to the range [-512, +511], by observing the open-loop responses of both signals under the rated load of the rectifier using the simulation program [12]. The PWM rectifier is fed by 3-phase voltage source at the level of 280 volts. The output of diode bridge rectifier (keeping all IGBTs off) with this input voltage is approximately 400 V. This dc link voltage is boosted up to its reference value of 500V under no-load. The dc link voltage responses of the line-side converter controlled by the PI and the FLC are given in Fig.4 and Fig.5, respectively.

Fig. 3 Membership functions for change of output ( ∆I cm )

IV. INDUCTION MACHINE SPEED CONTROL The closed-loop speed control scheme of the doublecage induction machine is shown in Fig.1. Inverter switches are controlled using the sinusoidal PWM. The operating frequency of the inverter is obtained via PI-controlled slip regulation method and calculated at the kth sampling instant as follows; * ω * (k ) = ω slip (k ) + ω r (k )

(11)

* is slip command, which is obtained from PI where ω slip

controller output, and ω r is the rotational speed of the machine. The output of the PI speed controller is in incremental form. Hence, the slip command is calculated from its previous value and the change of slip command as follows: * * * ω slip (k ) = ω slip (k − 1) + ∆ω slip (k )

(12)

For PI controller, the change of output ranges in [-1024, +1022]. After the dc link voltage is stabilized at 500V as it is seen from Fig. 4, the rectifier is loaded to 2.5kW by a resistance connected to the output of rectifier when t = 0.3 seconds. The controller responds to this step change of load by reducing the rectifier output voltage. This transient damps out in 0.1 seconds, and the output voltage settles down to its reference value again. When t=0.6 seconds, a back emf voltage in series with the resistance is applied at the level of 1000 V, therefore, the converter goes into regenerative mode and works as an inverter. After damping out this transient on output voltage, the back emf is set again to zero, when t=1 second. Hence the converter works in rectification mode as a rectifier. The output of the FLC is ranged between [-307, 307], and controller responds to the same step load changes with larger excursions as shown in Fig.5a. However, if the FLC output is scaled to the range of PI output by extending the output membership functions to a larger universe, the FLC gives better response than PI as shown in Fig 5b. The peak deviation from steady state output voltage and settling time are reduced. However, the ripples on the dc link output voltage are more significant.

Fig.4 Response of PI controller (KE=2, KCE=128)

Fig.6 Response of PI controller (KE=4, KCE=256)

Fig.5 Response of FLC a) output range [-307, +307] b) output range [-1024, +1022] (KE=2, KCE=128)

Fig.7 Response of FLC a) output range [-307, +307] b) output range [-1024, +1022] (KE=4, KCE=256)

The error and change of error parameters are increased twice, i.e., KE =4 and KCE=256 for both controllers, while the output universe is kept same as the intervals given in Fig.4 and Fig.5. By comparing Fig.4 and Fig.6 corresponding to the PI controllers, the deviation from steady-state value and settling time are considerably reduced. The dc voltage ripples are more significant in Fig.6. When Fig.5a and Fig.7a are compared, it can be clearly seen that there is no effective reduction on the dc link voltage excursions and settling times, in addition, the steady state error is increased. Comparing Fig.5b and Fig.7b, the steady-state error and dc link voltage oscillations are significantly increased, when the FLC output universe is scaled to the PI output range.

and Fig.9 show the experimental and simulation results of dc link output voltage and ac supply current during the voltage boost under no-load with FLC, respectively. In Fig.10 and Fig.11 presents the same results for the PI controller. The dc link voltage response is properly predicted by the computer simulation. The ac supply current is very close to experimental waveform. The difference is caused by the instantaneous values of the ac supply voltages when the switching signals are applied to the IGBTs. The sampling periods of the DSP in the FLC and the PI applications are measured to be Tsmp = 250 µs and

The results of mathematical model of the line-side converter are compared with experimental ones. Fig.8

Tsmp = 150 µs , respectively, hence these values are used in

the computer simulations. The line-side converter circuit parameters are as follows: L s = 50mH , R s = 0.8Ω , C = 1200 µF

Fig.8 DC link voltage and ac supply current with FLC during boost-up from experiments (upper trace: 160V/div, lower trace 4A/div, time/div: 50ms)

Fig.10 DC link voltage and ac supply current with PI controller during boost-up from experiments (upper trace: 160V/div, lower trace 4A/div, time/div: 20ms)

Fig.9 DC link voltage and ac supply current with FLC during boost-up from simulations

Fig.11 DC link voltage and ac supply current with PI controller during boost-up from simulations

A. Experimental Results on Wind Turbine

VI CONCLUSIONS

Some tests are performed on a horizontal axis, threebladed, fixed pitch angle wind turbine with a blade length of 2.75m. The wind speed, dc link current, and rotor speed are recorded over a long time range during the operation of the WECS. The recordings of the system in Fig.12 belong to the system controlled by two PI controllers in both converters. Fig.13 gives the results of the system with FLC in the lineside converter and PI in the machine side converter. The PI parameters of the induction machine speed controller are chosen as K E , spd = 1 / 8 , K CE , spd = 1 / 2 . The recordings show that both controllers are successfully holding the system stable during the change of wind speed.

A 5kW wind energy conversion system has been designed and implemented using PWM converters. The FLC and PI controllers have been employed for the PWM converters and their performances have been investigated. The results show that the FLC has a significant improvement on the dc link voltage response, if the inputoutput universe range of the controller is adjusted to the scale of the PI output range. However, the FLC reduces the sampling rate of the DSP since more mathematical calculations are required in the implementation. This leads to a tracking error of the ac supply currents, since a slow sampling rate causes ac supply currents to exceed the defined hysteresis band within one sampling period.

Fig.12 Records with two PI controllers on both converters

Fig.13 Records with FLC on line-side and PI controller on the machine-side

ACKNOWLEDGEMENT This work was carried out as a part of research project, “wind energy conversion system with induction generator using PWM converters”, sponsored by Turkish Scientific and Research Council under contract 101-E004.

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