A Rule-Based Fuzzy Logic Controller for a PWM Inverter ... - IEEE Xplore

51

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 1, JANUARYIFEBRUARY 1996

A Rule-Based Fuzzy Logic Controller for a PWM Inverter in a Stand Alone Wind Energy Conversion Scheme Rohin M. Hilloowala, Member, IEEE, and Adel M . Sharaf, Senior Member, IEEE

Abstruct- The paper presents a rule-based fuzzy logic controller to control the output power of a pulse width modulated (PWM) inverter used in a stand alone wind energy conversion scheme (SAWECS). The self-excited induction generator used in SAWECS has the inherent problem of fluctuations in the magnitude and frequency of its terminal voltage with changes in wind velocity and load. To overcome this drawback the variable magnitude, variable frequency voltage at the generator terminals is rectified and the dc power is transferred to the load through a PWM inverter. The objective is to track and extract maximum power from the wind energy system (WES) and transfer this power to the local isolated load. This is achieved by using the fuzzy logic controller which regulates the modulation index of the PWM inverter based on the input signals: the power error e = (Pref - Po) and its rate of change e. These input signals are fuzzified, that is defined by a set of linguistic labels characterized by their membership functions predefined for each class. Using a set of 49 rules which relate the fuzzified input signals (e, 6) to the fuzzy controller output U , fuzzy set theory and associated fuzzy logic operations, the fuzzy controller's output is obtained. The fuzzy set describing the controller's output (in terms of linguistic labels) is defuzzified to obtain the actual analog (numerical) output signal which is then used to control the PWM inverter and ensure complete utilization of the available wind energy. The proposed rule-based fuzzy logic controller is simulated and the results are experimentally verified on a scaled down laboratory prototype of the SAWECS.

Radius and swept area of wind turbine. Tip speed ratio (A = R w T / V ~ ) . Rotor speed of wind turbine. Average torque conversion coefficient. Average torque at wind turbine shaft. Average torque at induction generator shaft. Gear box ratio.

I. INTRODUCTION

IND energy conversionhnterface scheme (WECS) using a wind turbine driven self-excited induction generator and line commutatedPWM inverter have been modeled, analyzed, and implemented [11-[4]. In remote locations where the utility grid does not exist, stand alone wind energy conversion scheme (SAWESCS) can be used to feed the local electrical load. However, thene is an appreciable amount of fluctuation in the magnitude and frequency of the generator terminal voltage due to its dependence on the rotor speed which is governed by the wind velocity and the pulsating input torque from the vertical axis wind turbine. This is objectionable to sensitive loads. Hence, the variable magnitude, variable frequency voltage at the self-excited induction generator terminal is first rectified and the dc power is then transferred to the local load NOMENCLATURE through a PWM inverter. It has been shown that the power available from a WES can be approximated as a cubic function dc voltage at rectifier output. VR of the wind veloci1,y [4], [ 5 ] . To ensure complete utilization dc voltage at inverter input. VI of available wind energy under varying wind velocities, most ZDC dc link current. of the schemes reported use a PID controller to track and Po Rectifier output power. Maximum output power of wind energy system. extract maximum energy. The conventional PID controller P,, requires quite a bit of tuning to obtain a fast and dynamically TG Efficiency of induction generator. acceptable response. Again, it is generally implemented using rlR Efficiency of rectifier. operational amplifier circuits whose parameters are adjusted Rotor speed of induction generator. Wm for an operating point based on a piece wise linear model of Synchronous speed of induction generator. ws the nonlinear system. These circuits have the tendency to drift d-axis component of stator current. ids with age and temperature causing degradation of the system q-axis component of stator current. alp performance. In this paper, an alternative controller based on d-axis component of stator voltage. vds fuzzy set theory [6] is proposed. The fuzzy logic controller Modulation index of PWM inverter. Minv does not require a detailed mathematical model of the system vw Wind velocity. and its operation 11s governed by a set of rules. Thus, it is Paper MSDAD 95-19, approved by the Industrial Automation and Control easy to implement and the same performance is ensured over Committee of the IEEE Industry Applications Society for presentation at the 1993 Industry Applications Society Annual Meeting, Toronto, ON, Canada, the years. The rule-based fuzzy logic controller to track and October 3-8. Manuscript released for publication June 15, 1995. extract maximum power from the WES under varying wind The authors are with the Electrical Engineering Department, University of conditions, uses two real time measurements, namely the error New Brunswick, Fredericton, NB, Canada E3B 5A3. e = (Pr,f - Po) and the rate of change of error 6, as the Publisher Item Identifier S 0093-9994(96)00328-3. 0093-9994/96$05.00 0 1996 IEEE

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 1, JANUARY/FEBRUARY 1996

WIND TURBINE

INDUCTION GENERATOR

DIODE BRIDGE

PWM

HALL EFFECT CURRENT SENSOR LOAD

ISCILATIUN AMPLIFIER

Fig. I.

ANALOG MULTIPLIER

Block schematic of the proposed stand alone wind energy conversion scheme with a fuzzy logic controller.

control input signals. These input signals are first “fuzzified” and expressed in fuzzy set notation using linguistic labels characterized by membership grades [6]-[8] before being processed by the fuzzy logic controller. Using a set Qf rules and fuzzy set theory (the AND operator, the OR operator and the rule of composition) the fuzzy logic controller’s output is obtained. This output, expressed as a fuzzy set using linguistic labels characterized by membership grade, is defuzzified and converted to an analog signal before being applied to the PWM inverter under control. By controlling the pulse width of the PWM inverter, it is possible to control its output voltage and the power transferred to the local load, indirectly controlling the power extracted from the WES. Also, a supplementary control loop is incorporated to exercise control on the dc link voltage in spite of using a diode bridge rectifier. The proposed SAWECS with the fuzzy logic controller is simulated and the results experimentally verified on a scaled down laboratory prototype consisting of an emulated wind turbine, a selfexcited induction generator, a diode bridge rectifier and a PWM inverter. The proposed controller is found to give good power tracking performance.

11. SYSTEMCONFIGURATION The proposed scheme consists of a self-excited induction generator driven by an emulated wind turbine, a diode bridge rectifier and a PWM inverter feeding a local load as shown in Fig. 1. A brief description of each of the subsections is as follows. A. Vertical A d s Wind Turbine

The vertical axis wind turbine acts as a prime mover to drive the self-excited induction generator. In practice, the wind turbine is coupled to the generator shaft through a step-up

gear-box (1 : ngear-box)so that the generator runs at a higher rotational speed w, in spite of the low speed WT of the wind turbine. The torque TT at the turbine shaft is a function of its rotor speed and wind velocity [5] and can be expressed as

where CT is the average torque conversion coefficient (averaged over one revolution of the wind turbine rotor) and is a nonlinear function of the tip speed ratio X = WT . R/Vw [SI. The torque at the generator shaft T, can be related to TT by the gear-box ratio. The vertical axis wind turbine characteristics are emulated using a separately excited dc machine fed from a power amplifier controlled by an analog computer [lo]. The torque speed characteristics of the wind turbine are as shown in Fig. 2. It is seen that there is good agreement between the experimental and predicted results. B. Self-Excited Induction Generator It is essentially an induction machine driven by a prime mover (wind turbine) and having a source of reactive power (self-excitation capacitor bank). The dynamics of the selfexcited induction generator can be represented by the follow-

59

HILLOWALA AND SHARAF: A RULE-BASED FUZZY LOGIC CONTROLLER FOR A PWM INVERTER

I

...

,

* * * * +V.I1

-VI11

............... '"I.-.

...................

Fig. 3. Double edge sinusoidal pulse width modulated waveforms of the inverter. (a) Carrier waveform. (b), (c), (d) Modulated phase voltage waveforms. (e) Modulated line voltage waveform. ROTOR SPEED

NI

(rem)

Fig. 2. Experimental and predicted characteristics (T, - N m ) of the vertical axis wind turbine. (All variables referred to the high-speed (generator) side.)

where R D and ~ L D ~are Z the dc link reactor's resistance and inductance respectively, ZDC is the dc link current (neglecting the small charging/discharging filter capacitor current) and VI is the dc voltage at the inverter input. The dc power transferred over the dc link to ihe local load is given by

Po = V R i D C

(10)

E. PWM Inverter

K2

= Lm/(L1L2 - L L ) .

The above equations were derived assuming that the initial orientation of the q-d synchronously rotating reference frame is such that d-axis is lagging q-axis and aligned with the stator terminal voltage phasor (i.e. wqs = 0).

C. Uncontrolled Rectifier It is a 3-phase diode bridge rectifier which is used to convert the variable magnitude, variable frequency voltage at the induction generator terminal to dc. The dc voltage VR at its output can be expressed in terms of the peak phase voltage 'uds = V, of the generator and the input transformer's turns ratio 1 : n,

VR = (3J2/r)(J3/J2)vds * m a .

(8)

D. DC Link and Input Filter The input filter consists of a series reactor and a shunt capacitor as shown in Fig. 1. The series reactor reduces the current ripple content in the rectifier output current and the shunt capacitor reduces the ripple content in the dc link voltage providing a relatively stiff voltage source for the PWM inverter. The dc link current is governed by the following differential equation P ~ D C=

( ~ / L D c ) (-~ VI R - RDC~DC)

(9)

The dc power available at the rectifier output is filtered and converted to ac power using a PWM inverter employing double edge sinusoiidal modulation. The PWM signals used to switch the transistors in the inverter are generated using a purpose designed LSI circuit type HEF4752V. The IC provides three complimentary pairs of output drive signals which in conjunction with a three phase six-element bridge inverter produces a symmetnical three phase output. The output consists of sinusoidally modulated train of carrier pulses, both edges of which are modulated such that the average voltage difference between any two of the output three phases varies sinusoidally. This is illustrated in Fig. 3 (courtesy Signetics application manual for HEF47.52V [ll]), for a carrier wave having 15 pulses for each cycle of the inverter output. Fig. 3(a) shows the 15-fold carrier, IFig. 3(b), (c), and (d) shows the modulated R, Y, and B phases respectively. The line voltage waveform obtained by subtracting Y-phase from R-phase is shown in Fig. 3(e). Each edge of the carrier wave is modulated by a variable angle 6, as shown in Fig. 4 and can be mathematically represented by

6, = Msin(a,)G,,

(x = 1 , 2 , 3 , .. . ,2r + 1)

(11)

where M is the modulation index and ranges from 0 to 1, subscript x denotes the edge being considered, r is the ratio of carrier to fundamental frequency at the inverter output, a, is the angular displacement of the unmodulated edge and b, is the maximum displacement of the edge for the chosen frequency ratio T . In the proposed scheme (SAWECS), the inverter output voltage is controlled, while its frequency is held constant at 60 Hz. In this range of operation, the PWM generator HEF4752V generates a carrier wave with frequency 15 times the fundamental frequency at the inverter output. Such a choice

IEEE TRANSACTIObIS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 1, JANUARYFEBRUARY 1996

60

0.9

SMUSOiDAL PULSE WtDTH MODULAllON

CARRIER VAVEfORX I

a, = 0

a2

a,

a,

cl,

a6

a,

( I S PULSES)

c

a .

4k-w

&+P-

6,= 0

Fig. 4.

6,

6,

6,

s,

..

- ..

.

k c ( h

6,

67

Carrier waveform and double edge modulated phase voltage wave-

form.

results in a line voltage waveform with 15-pulses per half cycle at the inverter output. By modulating the carrier wave and hence the phase voltages, the fundamental and harmonic voltage content can be varied. There are 15 pulses and 15 slots of 12' each as shown in Fig. 4. In each slot two edges are modulated. For 100% modulation ( M = 1) the maximum = 6". amount by which the edge can be modulated is,,,S Any further displacement of the edge will cause the pulses in the modulated phase voltages to merge, resulting in a reduction of the number of pulses in the line voltage waveform (pulse dropping phenomenon). Fourier analysis of the modulated phase voltage shown in Fig. 4(b) indicates that the peak amplitude of the nth harmonic voltage component is given by

- cos(n&,k

+ nMSm,

+ cos(n83,k - nMS,,, - cos(n&,k + nMSm,

= ( 2 k - 2)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MODULATIONINDEX M Fig. 5. Variation of the nth harmonic line voltage (peak value) with modulation index.

where ipinv is the q-axis component of the inverter phase current I,,, 4 is the load power factor angle between the fundamental voltage and current at the inverter output, and f(1,M) is a nonlinear function of the modulation index 111, relating the rms, fundamental line voltage to the dc input voltage V I of the inverter. The above equation is derived assuming that the synchronously rotating q-axis is initially aligned with the voltage phasor Knv.

111. sin(63,k)) sin(Oa,k)) (12)

* r / r ; 0 2 , k = ( 2 k - 1) * x / r ; 63,k = ( 2 k ) * r / r ;

(13)

and the peak value of the nth harmonic component of the line voltage waveform is

Vn line = J3vn phase.

0.1

CONTROLLER FOR THE

PROPOSED SCHEME

sin(Bz,k))

where Vi is the input dc voltage, n is the harmonic number, T is the carrier to fundamental frequency ratio (r = 15 in is the maximum displacement of the edge this case), S, (S, = 6' in this case) and 1 9 l , k , Q2,k and Q3,k are defined as Ql,k

0

(14)

The variation of the nth harmonic component of the line voltage waveform (expressed as a per unit of the input dc voltage V I ) with modulation index M is shown in Fig. 5. It is to be noted that, since the triplen harmonics in all the three phases have zero phase displacement, they will cancel out and not appear in the line voltage waveform even though they (triplen harmonics) are present in the modulated phase voltage waveform. Assuming the inverter to be lossless and equating the input dc power to the output ac power, the following relation is obtained:

A. Maximum Power Tracking Controller In order to ensure complete utilization of the available wind energy, a fuzzy logic controller is used to track and extract maximum power from the wind energy system (WES) and transfer this power to the local load. A F u u y Logic Controller: The fuzzy logic controller unlike conventional controllers does not require a mathematical model of the systerdprocess being controlled. However, an understanding of the systerdprocess and the control requirements is necessary. The fuzzy controller designer must define what informatioddata flows into the system (controlhnput variable), 'now the informatioddata is processed (control strategy and decision), and what informatioddata flows out of the system (solutiodoutput variable). The fuzzy logic controller consists of three basic blocks. i) Fuzzifier; ii) Inference Engine; iii) Defuzzifier. i) Fuzzijer: The fuzzy logic controller requires that each control/solution (input/output) variables which define the control surface be expressed in fuzzy set notations using linguistic labels. Seven classes of linguistic labels ((Large Positive) LP, (Medium Positive) MP, (Small Positive) SP, (Very Small) VS, (Small Negative) SN, (Medium Negative) MN, (Large Negative) LN) characterized by membership grade are used to decompose each system variable into fuzzy regions. The membership grade denotes the extent to which a variable belongs to a particular class/label. This process

61


TABLE I MAC VICAR-WHELAM’S DECISIONMATRIX

NORMALISED VARIABLE

X

b --

Fig. 6. Fuzzy reference sets to represent normalized variables in linguistic labels characterized by membership grades.

ii)

of converting input/output variable to linguistic labels is termed as fuzzification. It is executed using reference fuzzy sets shown in Fig. 6 and used to create a fuzzy set that semantically represents the concept associated with the label. To have a smooth, stable control surface, an overlap between adjacent labels is provided such that the sum of the vertical points of the overlap should never be greater than one. In the proposed controller, the error in power e = (Pre,- Po) and its rate of change ei are normalized, fuzzified, and expressed as fuzzy sets. Inference Engine: The behavior of the control surface which relates the input and output variables of the system is governed by a set of rules. A typical rule would be

where the numbers represjent the Rule No.

Several methods of defuzzification are available. Of these, the most commonly used methods are i) Mean of Maxima (MOM) and ii) Center of Area (COA). Most control applications use the COA method. This method computes the centre of gravity of the final fuzzy space (control surface) and produces a result which is sensitive to all the rules executed. Hence, the results tend to move smoothly across the control surface. A rule-based fuzzy logic conroller is used as shown in Fig. 1, to track and extract maximum power from the WES for If (fuzzy proposition), then (fuzzy proposition). a given wind velocity, and to transfer this power to the local where the fuzzy proposition is of the type “ x is Y” load. The power tranisferred over the dc link (output power of or “ x is not Y,” LI: being a scalar variable and Y is a the rectifier Po) can be related to the maximum power output of the WES by the efficiency of the generator 736 and fuzzy set associated with that variable [12]. The set of P,, . mentioned earlier, the maximum rules for the fuzzy controller are based on MacVicar- that of the rectifier 7 1 ~ As Whelam’s decision table [8] shown in Table I, which power output of the WES is a function of the wind velocity proposes a definite control action for a given error e and the tip speed ratio A. The maximum power output P,, of the WES at different wind velocity V, is computed and the and its rate of change 6. As for example data obtained is used to relate P,,,, to V, using polynomial If ( ( e is LP) AND (ti is LP)), then curve fit as shown below (the controller output U is LP).

Thus, each entry in the table is a rule and there are 49 rules that form the knowledge repository of the fuzzy logic controller. These rules are used to decide the appropriate control action. When a set of input variables are read, each of the rule that has any degree of truth (a nonzero value of membership grade) in its premises is fired and contributes to the forming of the control surface by appropriately modifying it. When all the rules are fired, the resulting control surface is expressed as a fuzzy set (using linguistic labels characterized by membership grades) to represent the controller’s output. iii) Defuzzijer: The fuzzy set representing the controller output in linguistic labels has to be converted into a crisp solution variable before it can be used to control the system. This is achieved by using a defuzzifier.

P,,

= -3.0

$-l.OSV,

-

O.l25V,”

+ 0.842V:

(16)

To ensure maximum power tracking, the reference power at the rectifier output I>,,, is taken as

The actual power output of the rectifier Po is compared to the reference power P,,r and any mismatch is used by the fuzzy logic controller to change the modulation index M . As shown in Fig. 1, the input signals to the fuzzy logic controller are the wind velocity V, and the power output of the rectifier Po.Thew are sampled at regular intervals and used to compute the error in power output e and its rate of change 6. The controller’s output U = A M p (change in modulation index due to power mismatch) is determined as follows.

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 1, JANUARYFEBRUARY 1996

62

Step 1: Calculate the normalized power error and its rate of change at the mth instant

R W 3

e,(m) = [ P r e f ( m ) - Po(m)l/Pr,f(m) &(m)= [e,(m) - e,(m - l)l/(AT * K

)

where A T is the sampling interval selected as .33 ms and K , is the scaling factor chosen such that A T * K , = 1. This allows normalization in the range of -1 to +l. Step 2: The normalized input signals are expressed in fuzzy set notation (linguistic labels characterized by membership grade) using fuzzy reference sets shown in Fig. 6. Step 3: Using the set of 49 rules based on MacVicarWhelam' s decision table, the control action is decided. The controller output obtained by applying a particular rule is expressed in linguistic labels characterized by membership grades. For example, Ru1e:lO is expressed as If ((e, is MP) AND (e, is SP)), then the controller output U is given by the fuzzy set

{(LN 01, ( M N 01, (SN O), (ZZ, O), (SP, O), (MP, I), (LP, 0)) The membership grade of the condition part which consists of two predicates connected by an AND operator is determined using the intersection rule of two fuzzy sets. ~ ( 2 1 0= ) p((e, is MP) AND (& is SP)) = min(p(e, is MP), p(& is SP)) This is graphically represented in Fig. 7(b), where two premises connected by an AND operator are combined by taking the minimum of the two membership grades and assigning it to the associated label in the fuzzy set. Thus, the membership grade of the label MP as decided by Ru1e:lO is P U , lO(MP)

=4x10) = min(p(e, is MP), p(& is SP))

Step 4: This procedure is repeated for all the 49 rules (xi;i = 1 , 2 , . . . .49) and the final grade of membership is decided using the rule of composition. For example, the membership grade of the linguistic label MP representing the controller output can be evaluated as P u ( M P ) = In$PU,

WP));

where i = 1 , 2 , 3 , .. . , 49. This is graphically represented in Fig. 7(c), where two rules are combined by using the OR operator; that is by taking the larger of the two values and assigning it to each point on the premises.

4

U

Fig. 7. Rule implementation of fuzzy logic controller. (a), (b), AND operation. (c) OR operation.

Step 5: The above steps are repeated for the other linguistic labels (LP, SP, ZZ, SN, MN, LN) representing the controller output. The results are used to form a fuzzy set representing the controller output. Step 6: The fuzzy set representing the controller output is defuzzified (converted from linguistic labels to an analog signal) using the Centre of Area (COA) method. In this case the controller output (change in modulation index A M p ) is given by

where U k represents the normalized controller output (expressed numerically in per unit) for the kth interval and pug is the associated membership grade as shown in Fig. 7(c). The change in the modulation index AMp(m)at the mth time step is computed using (18) and this in conjunction with the current modulation index M p ( m )is used to compute the value for the next time step as follows:

M,(m

+ 1) = M p ( m )+ AM,(m).

(19)

An analog voltage of appropriate magnitude is then sent through the data translation card DT2821 to control the PWM inverter. B. Supplementary Control Loop

In the proposed scheme, a diode bridge rectifier is used in the asynchronous dc link. This reduces the reactive power burden on the self-excitation capacitor bank. However, the diode bridge rectifier has no control on the dc link voltage. Hence, during a wind gust, the rotor speed (wm), terminal voltage (vds), and the dc link voltage (VR) can rise to an unacceptably high value which can be harmful from voltage rating point of view. This is overcome by using a supplementary control loop (as shown in Fig. 1) which continuously monitors the dc link voltage VR.If VR tends to exceed the preset voltage threshold V R ~the~ supplementary ~ ~ ~ . control loop

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