performance. I INTRODUCTION: Solar energy conversion/interface schemes using a photo- voltaic solar array and line commutated/PWM inverter have been.
A RULE-BASED FUZZY LOGIC CONTROLLER FOR A PWM INVERTER IN PHOTO-VOLTAIC ENERGY CONVERSION SCHEME. ROHIN. M. HILLOOWALA Student Member, IEEE
ADEL. M. SHARAF Senior Member, IEEE
ELECTRICAL ENGINEERING DEPARTMENT UNIVERSITY OF NEW BRUNSWICK FREDERICTON NEW BRUNSWICK CANADA E3B5A3
150,
ABSTRACT: The paper presents a Rule based controller based on fuzzy set theory to control the output power of a PWM inverter in PhotoVoltaic Energy conversion interface scheme. The objective is to track and extract maximum available solar power from the PV array under varying solar irradiation levels. To achieve this the power error e = (Pref - Ppy) and the rate of change of this error e are used as the input signals to the rule-based fuzzy controller and the output signal is used to control the PWM inverter. The input signals are defined by a set of linguistic variables or labels characterised by their membership functions which are preassigned for each class. A fuzzy relation matrix relates the input signals (e, e) to the fuzzy controller output U and using Fuzzy set theory and associated fuzzy logic operations, the desired fuzzy controller output is obtained. The fuzzy output (in terms of linguistic variable or label) is defuzzified to obtain the actual numerical (analog) output signal of the controller. This output (analog) signal is then fed to the PWM inverter to control only the output voltage (output frequency being fixed at 60 Hz.) and hence power drawn from the PV array. The proposed rule based controller is simulated and the results are experimentally verified on a PV energy conversion scheme consisting of an emulated PV array and a Pulse width modulated Inverter and is found to give a good power tracking performance.
I INTRODUCTION:
I
2 4 Ipv (Amps)
-0
Solar energy conversion/interface schemes using a photovoltaic solar array and line commutated/PWM inverter have been modelled, analyzed and implemented [1,2]. For a given solar insolation level and ambient temperature the voltage versus current and output power versus current characteristics are as shown in Fig: 1. It is seen that there is a particular operating point (IoptVopt) at which maximum output power Poptis obtained. Most of these schemes use a PID controller to track and extract maximum power under varying solar insolation levels. The conventional P D controller requires quite a bit of tuning to obtain a fast and
SI= 0.1 Wkm2
-
SI= 0.08W/cm2
-.-.-
SI= 0.06W/cin2 ........Figure:l
6
SI= 0.04 WIcm2
-----
SI= 0.02 W/cm2
-
C h a r a c t e r i s t i c s of PV a r r a y a t T=28'C and d i f f e r e n t s o l a r i n s o l a t i o n levels
dynamically acceptable response and are usually implemented using analog circuits which have the tendency to drift with age and temperature. This causes degradation of the system performance. In this paper a new type of controller using Fuzzy set theory is proposed. The rule based fuzzy controller to track and extract maximum power Poptfrom the solar m a y under varying conditions of solar irradiation, uses two real time measurements namely error e=(P, - PPJ and the rate of change of error e as the control input sign&. These input signals (e, e) are first expressed in terms of linguistic variables or labels such as LP (large positive), M P
0-7803-0634-1/92$03.OO OIEEE 762
-1.0
-.8
-.6
-.4
-.2
0.0
0.2
0.4
KORMALISED INPUT VARIABLES Figure:2
en
, Bn
1.0
__z
Reference fuzzy s e t s t o represent input variables in l i n g u s t i c l a b e l s characterised by membership grades.
(medium positive), SP (small positive), VS (very small), LN (large negative), MN (medium negative), SN (small negative) using fuzzy reference sets. The fuzzy reference sets are defined for each variable to cover the entire range of interest, with considerable amount of overlap between reference sets, as shown in Fig:2. This considerably simplifies the problem of fuzzy set definition. The input signals are nonfuzzy (crisp) values which must be fuzzified to be used as input signals to the fuzzy controller. The result of fuzzification will be a set of grades of membership of each of the linguistic label involved, as shown in Fig:2. Since the reference sets are overlapping, each nonfuzzy value of the variable will belong to at least two reference sets and the grade of membership to the other sets (labels) will be zero. Next, the relationship between the input signals expressed as linguistic labels and the fuzzy controller output is developed using fuzzy set theory and described as a fuzzy relation matrix using assigned membership functions. Finally using fuzzy logic operations, the fuzzy controller output is found, defuzzified (changed from linguistic label to numerical values) and used to control the pulse width of the PWM inverter. The proposed scheme with fuzzy rule-based controller is simulated and experimentally verified and found to give good power tracking performance.
I1 SYSTEM CONFIGURATION: The proposed scheme consists of an emulated PV solar array, a DC link and a Pulse Width Modulated Inverter feeding some local load as shown in Fig:3. A brief description of each system subsection is as follows.
A. PHOTO VOLTAIC ARRAY: The solar m a y is emulated using the characteristic equation relating the solar cell's voltage and current as is shown below; V, = (AKT/q)*ln[
0.8
016
equivalent series resistance of the cell, 'p. is the array current, Vp is the array voltage, Np is the number of strings in parallel, N, is the number of cells in series in a string. The photo current $h is a function of the solar insolation level S, and its variation with S, is given by $h = K*S,
where K is a constant of value 0.56 Amps/w/cm2 and S, is the solar insolation in w/cm2. The characteristic equation relating the PV cell's voltage and current and associated parameters such as Np, N,, etc. are programmed into a digital computer and used to control a power amplifier whose output characteristics are made to match those of the PV array. Using a data translation board DT2821, the solar insolation level S, and the array current computer and used to compute $h and 4. 4 and using the above characteristic equation, the cell's output voltage V, and hence the array's output voltage Vp are computed and a voltage reference signal is fed to the power amplifier through D/A converter of the data translation board DT2821. By appropriately setting the gain of the power amplifier, the solar array's voltage-current characteristic can be obtained at it's output. This PV array simulator is used to experimentally verify the fuzzy rule-based controller in the lab.
B. INPUT FILTER AND DC LINK: The input filter consists of a series reactor and a shunt capacitor as shown in Fig:3. The series reactor reduces the current ripple content in the array current and the shunt capacitor reduces the ripple content in the DC link voltage and provides a relatively stiff voltage source for the PWM inverter. The DC link current is governed by the following differential equation
P 'py =
(Gh - DI, - Io)flo 1 - $I.,
where, V, is the cell voltage, I, is the cell current, q is the charge of an electron, K is Boltzman's constant, A is completion factor and its value is in the range 1 to 3 [l], T is the absolute temp, is the photo current, b is the reverse saturation c m n t , R, is
k
(2)
[ Vpv
- VI - R x$. 1
(3)
where Rx and are the DC link reactor's resistance and inductance respectively,+=IX is the DC link current, Vp is the PV array's voltage and I is the DC voltage at the inverter input. The output power of the PV array is given by (4)
I
PV
PV
P
$C
RULE BASED CONTROLLER (DIGITAL COMPUTER)
PWM INVERTER
GENERATOR (HEF4752V)
PV
Figure:3
B l o c k s c h e m a t i c of p r o p o s e d s o l a r e n e r g y c o n v e r s i o n scheme w i t h f u z z y Rule-based
C. PWM INVERTER:
The DC power available at the output of the PV array is converted to AC power using a Pulse width modulated (PWM) inverter employing double edged modulation. The PWM signal used to switch the transistors in the inverter is generated using a purpose designed LSI circuit type HEF4752V. The IC provides three complementary pairs of output drive waveforms which when applied to a three phase six-element bridge inverter, produces a symmetrical three phase output. The output waveforms 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:4 (courtesy Signetics application manual for HEF4752V [SI)for a carrier wave having 15 pulses for each cycle of the inverter output. Fig:4a shows the 15-fold carrier, Fig:4b the double edged modulated R phase, and Fig:4c and 4d show the double edged modulated Y and B phases respectively. The line to line voltage waveform obtained by subtracting Y-phase from Rphase is shown in Fig:4e. Each edge of the carrier wave is modulated by a variable angle 6, as shown in Fig:5, and can be mathematically represented by
6, = M*sin(a,)*6,,
(x = 1, 2,... 2r+1)
(5)
where, M is the modulation index, subscript x denotes the edge being considered, r is the ratio of carrier wave frequency to fundamental frequency at the inverter output, a, is the angular displacement of the unmodulated edge and 6is the maximum displacement of the edge for the chosen frequency ratio r. In the chosen PV energy conversion scheme, the inverter output frequency is held constant at 60 Hz. In this range of inverter output frequency, the PWM generator HEF4572V generates a carrier wave with frequency 15 times that of the fundamental frequency at inverter output. Such a choice, results in 15 pulses per
controller.
half cycle in the line to line voltage waveform at 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 F i g 5 In each slot two edges are modulated. For 100 % modulation (i.e. M=l) the maximum amount by which the edge can be modulated is 6". Any further displacement of the edge will cause the pulse in the modulated phase voltage waveform to merge, resulting in a reduction of the number of pulses in the line to line voltage waveform. Fourier analysis of the modulated phase voltage waveform shown in Fig:Sb shoys that the amplitude (peak value) of the n* voltage harmonic component is given by
( cos(nOl - nM6-
VI
- cos(n02 +
sin(O1))
nM6-
sin(@,))
cos(n0, - nM6-
sin@,))
- cos(n0,
+
+
nM6-
sin(8,))
(6)
11
where, VI is the input DC voltage, n is the harmonic number, r is the carrier to fundamental frequency ratio (-15 in this case),, ,6 is the maximum displacement of the edge (6-=6" in this case) and O,, 0,and 0, are defined as follows 0, = (2k-2)*~/15; 0, = (2k)*~/15 0, = (2k-1)*~/15;
(7)
and the peak value of the nth harmonic component of the line to line voltage waveform is Vn line = '3*vn
phe
(8)
CARRIER
VR
VY
v0
VR-Y
Figure:4
K
12
X
12
15
-
pulse double edge sinusoidal pulse width modulaced waveforms.
Y
It 0.8
-
I
n=ll-----n=13... . .....
0.6 - n=17
- -.-
0.5
0
1
MODULATION INDEX M + Figure:6 Variation of nth harmonic amplitude
Figure:5 Carrier waveform and double edge modulated
(peak) with modulation index M.
phase voltage waveform.
where we is the electrical frequency at the inverter output, RL and are the r e s h n c e and inductance of the Wr Phase load, q is the power factor angle between fundamental components of VOlQe and current, f(1, M) is a non-linear function of the modulation index M,relating the peak fundamental line to line Voltage to the DC input VI of the inverter.
The variation of the n* harmonic component of the line to line voltage waveform (expressed as a per unit of the input DC voltage VI) with modulation index M is shown in Fig:d It is to be n o t 4 that triplen harmonics are present in the modulated phase voltage the three waveform. However, since the triplen harmonics in phases have zero phase displacement, they will cancel out and not appear in the line to line voltage waveform. Assuming the inverter to be lossless, and equating the input DC power to the output AC power, the following relation is obtained
v,
III FUZZY RULE BASED CONTROLLER: objective is to Uack and maximum power fmm the PV array for a given solar insolation level. The maximum power corresponds to the optimum operating point (P , ITt) which is determined for different solar insolation levels using off-line simulations. The data obtained is used to relate Pref (Pr&Pqt) to S, using second order polynomial c w e fit as shown below
The
3;
(9)
=
f2U, MI
COSW
Pd 765
= -11.575 + 4785.7*Sr+ 4706.8*S:
(10)
Step :6 Using Fuzzy set theory (4,5], the decision matrix is converted to the fuzzy relation matrix R shown in Table:& which gives the relationship between the fuzzy set characterising controller inputs and fuzzy set characterising controller output (U). The controller output obtained by applying a particular rule is expressed in linguistic labels characterised by membership grades. For example, Rule 7 is now expressed as Rule 7’: if e, is LP and e, is LP then the controller output U is described by the fuzzy set ((LN, 01, (MN, 01, (SN, 01, (VS, O), (SP, O), ( M P , 0.51, (LP, 1.0)) Step :7 The membership grade of the condition part is determined using fuzzy set theory. The condition part consists of two predicates ’e, is LP’ and ’e, is LP’ combined by an ’AND’ operator. Using law of intersection of two fuzzy sets the grade of membership of the condition part is determined.
Using a digital computer with data translation card DT2821, the solar insolation level and the power output of the PWM inverter are sampled at regular intervals (AT=3OOps). The reference power is computed using the above equation and compared to the actual measured power output of the PV array. The error in power and its rate of change are used to adjust the modulation index of the PWM inverter. This changes the output voltage of the PWM inverter and hence the power drawn from the PV array. As shown in Fig:3, the input signals to the fuzzy rule-based controller are solar insolation level S, and the power output of the PV array Ppv, and these are used to compute the error in power output e and its rate of change e. The fuzzy controller’s output is change in modulation index U=AM and is determined as follows: Step :1 Calculate the normalised power error at the k” instant
Step :2 Calculate the normalised rate of change of error
where AT is the sampling interval selected as 0.1 ms and K, is the scaling factor chosen such that AT*K, = 1 to allow normalisation in the range -1 to 1. Step :3 Use assigned membership functions shown in Fig2 to represent the normalised error e, and rate of change of error e, in fuzzy set notations using linguistic labels (LP, MP, SP, VS, SN, MN, LN). Step :4 Use the generalized decision table as proposed by Macvicar-Whelm [3] and shown in Table I, to determine the fuzzy controller output for a given error and its rate of change.
p(x7) = p(’e,, is LP’ AND ’e, is LP’) = min ( p(’e, is LP’) p(’e, is LP’) )
(1 3)
Step :8 Knowing the membership grade for the condition part and the fuzzy relation mamx, the membership grade for the controller output characterised by the linguistic labels LP, M P , SP, VS, SN, MN, LN can be obtained using the intersection rule of Fuzzy set theory. The membership grade for the linguistic label LP is computed as follows Pu,
=
min(p&7,LP) P(X7))
(14)
Step :9 This procedure is repeated for all the 49 rules and the final grade of membership is determined using the composition rule of fuzzy set theory. For example, the controller output characterised by the linguistic label ’LP’ can be evaluated as follows
Table:I MacVicar Whelm’s Decision table [3]
pu(LP) = max ( min(pR(xi,LP) p(xi)) ) i=1,2,..49
(15)
xi
Step :5 Using the decision mamx the fuzzy controller output in linguistic variable such as LP, MP, SP, VS, SN, MN, LN is decided. It is seen that there are (7*7) = 49 combinations of error e, and its rate of change e,,. Each combination corresponds to a particular rule. Hence there are 49 rules on the basis of which the fuzzy controller’s output is decided. A typical rule would be Rule 7 if e is LP and e is LP then the controller output U should be LP
Step :10 Step 9 is repeated for the controller output characterised by the other linguistic labels ( M P , SP, VS, SN, MN, LN) Step :11 The final controller output can be decided using (i) The Mean of Maxima (MOM) criteria (ii) The Center of Area (COA) criteria (iii) The Maximum algorithm In this paper the maximum algorithm is used wherein, the linguistic label with the highest membership grade is chosen as the controller’s output. To demonstrate the fuzzy controller’s action, let the controllers input signals be e, = 1.0 and e, = -0.2. Using reference fuzzy sets defined in Fig:2, the controller inputs can be described by the following fuzzy sets. e,: ((LP, l), ( M P , 0.7), (SP, 0.4), (VS, 0 2 , (SN, 01, (m,o), (LN, 0)) e,: ((LP, O), ( M P , 0), (SP, 0.2), (VS, O S ) , (SN, l.O), (MN, 0 4 , (LN, 1.0)) where the numbers correspond to the membership grade of the particular label. The membership grade of the condition part of rule 7 is given by p(x7) = p(’e, is LP’ AND ’e, is LP’) = min ( p(’e, is LP’) ~ ( ’ e ,is LP’) ) = min ( 1, 0) = 0 The membership grade for the linguistic label LP can be computed as follows PU, 7(Lp) = min(pR(x7,LP) p(x7)) = min(1, 0) = 0 766
Tab1e:II Fuzzy relation matrix R
7-zControUcr
0
0
0.5
0
0 0
0 0 0 0
0
0
0
0
0
0
0 0 0 0
0
0
0.5 0 0 0 0
0 0
0 0
0 0
1 0.5
0
0 0
0 0 0
0 0.5 0 0 0 0
0 0 0 0 1.o 1.o 0.5 0 0 0
0 0 0.5 0.5 0 0
0 0 0 1 05
0 0.5 1.0
1.o 0.5
0
0 0
0 0 0.5 1.o 0.5 0 0 0
1.o 0.5 0
0
0 0
0
0
0
0
0
0
0.5
0.5 1.o
0
0
0
0.5
0
0.5
0 0 0.5 0.5 1.o
0 0 0
0.5 1.o 1.o 0.5 0
1.o
0.5
0.5 0
0.5 0.5 1.0
0.5 0.5 11) 1.o
0 0 0 0.5 1.o 0 0 0
0 0.5
0
1.o 0.5 0
0 0 0 0.5
0
0
0 0.5 1.o 1.o
0 0 0.5 0.5 1.o 0.5
1.o 0.5 0.5 0 0
0.5 0 0 0 0 0.5 1.0 1.0 0 0
0
0
0
0 0.5 1.O 05 0 0
0 0 0.5 1.o 0 0
0 0
0 0 0
0 0 0 0
0.5 0
0
0
0
0 0
0.5 0 0
0.5
0
0
0.5 1.0 1.o
0 0.5 0.5
0 0
0.5 0.5 0
0.5
0 0
0 0
1.o 0.5 0
0.5 0.5 0.5 0.5 1.o 0.5
0 0 0 0 0.5 1.o
0
0.5
0
0 0.5 1.O 0.5
0 0 0 0 0 0.5 1.o
0.5 1.O 0 0 0 0
0.5 0
0 0
0
0 0
0
0
0.5
0
0 0 0.5 0.5 0 0
0 0.5 0 0 0 0 0
0 0 0 0 0
0 0 0 0
Using the 'maximum algorithm' the controller output in linguistic terms is "MP" since it has the highest membership grade. The reference signal representing the modulation index is an analog signal. Hence, the fuzzy linguistic label has to be defuzzified, that is converted to numerical value. Based on previous experience with power aacking controllers, defuzzification is done using the conversion table shown in Tab1e:III.
i=1,2,3,...49
xi
=
0 0 0.5 1.o
0.5 1.o 1.o 1.o 1.o
0.5
This is the membership grade of the controller output 'LP' for rule:7. Considering all the 49 rules, the final value of the membership grade for the linguistic label 'LP' is determined using the composition rule as follows pu(LP) = max ( rnin(pR(xi,LP)p(xi)) )
0
0 0
0
0.5 0.5
1.o 1.O 1.O 1.O 0.5 0 0
0
0.5 1.0 0.5 0.5 0.5 0.5 0 0 0.5 1.0 1.0 0.5 0.5 0
0 0
0 1.o 1.o
0.5 1.o 0.5 0 0
0.5
Table I11 Conversion from linguistic labels to numerical values LP MP SP VS SN MN LN
The same procedure is repeated for the six other linguistic variables representing the probable controller output and their membership grades are found to be as follows
U=AM P.U.
pu(MP) = 1.0; pu(SP) = 0.8; pu(VS) = 0.7; pu(SN) = 0.6; pu(MN) = 0.5; pU(LN) = 0.4;
Note: 1.0 p.u. corresponds to M=1.0 which is represented by 0 V 0.5 p.u. corresponds to M=0.5 which is represented by 10 V
(16) 167
0.1
0.05 0.025 0
-0.025
-0.05 -0.1
The modulation index M at any instant of time is given by
intervals (AT=300 ps). The array’s maximum power output Pref is computed for the insolation level S,. The actual power output of the array is computed as the product of the array voltage and current (Ppv=VPv$,). Knowing Prd and Ppv, the error e and the rate of change of error e are computed and used to deternine the fuzzy controller’s output which is then used to control the pulse width of the inverter’s output voltage waveform. The inverter’s output is fed to a three phase load which is either a resistive load bank or a 3phase induction motor driving a DC generator. By changing the pulse width of the PWM inverter, within limits (0-6”), it is possible to change the power drawn from the PV solar array, thereby making maximum utilization of the available solar energy. The experimental results shown in Fig9 indicate that the proposed controller is successful in tracking and extracting maximum solar power from the solar array under varying insolation levels by maintaining the output power as near as possible to the optimal (maximum) power POpr
M(k) = M(k-1) - Ud(k-1) where U, is the defuzzified output of the controller representing the actual change in the modulation index. Taking the change introduced by the fuzzy controller into account, the modulation index M is computed at regular intervals (AT=300 ps) and an analog signal of appropriate amplitude is sent to the PWM inverter to control it’s output voltage and power and hence the power drawn from the PV array.
IV SIMULATION AND EXPERIMENTAL VERIFICATION: The complete model of the PV energy conversion/interface scheme is represented by equations (l), (3), (4), (6) and (8). To study the system response using a fuzzy rule-based controller, under varying solar insolation levels, these equations have to be solved. This is achieved by using a simulation software package TUTSIM. The various equations are solved at regular intervals (AT3.1 ms). The PV array’s output power Ppv is computed and compared to the Pref at the given solar insolation level S,. The error in power e=(PrerPpv) is used to change the modulating index M by U,=AM. This changes the DC voltage VI at the inverter input and alters the DC link current = IDc, thereby affecting the PV array’s output power. Simulation results depicting the variation of various variables for step changes in solar insolation level are shown in Fig:7. It is seen that as the solar insolation level increases, the modulation index M increases, which causes the PV array’s output power to increase. This continues till the PV array’s output power becomes equal to the Prefat which state, the array is operating at it’s optimum operating point. The proposed rule based fuzzy controller is implemented using a digital computer and the data translation card DT2821, for the simple PV energy conversion scheme as shown in Fig:3. Using the data translation card, the solar insolation level S,, the solar array voltage v and the array current & are sampled at regular
V CONCLUSIONS: An alternative rule-based controller based on Fuzzy set theory is proposed for a PV energy conversion scheme. The objective is to track and extract maximum available solar power from the PV array under varying solar insolation levels. To achieve this the power error e=(PrefPpv) and the rate of change of this error e are used as input signals to the fuzzy rule-based controller and it’s output signal is used to control the PWM inverter. The input error signals are fuzzified and expressed as linguistic labels characterised by their membership grades. Using a fuzzy relation matrix (which relates the input error signals to the fuzzy output signal expressed as a linguistic label), a set of 49 rules and fuzzy logic operations, the controller output is obtained. The fuzzy controller output expressed in linguistic labels is defuzzified to obtain the actual analog signal to control the PWM inverter. The proposed fuzzy rule-based controller is simulated and experimentally verified and is found to give good power tracking performance.
PV
0.055
1 05
9 0.05 -
100 -
20.045 -
O 0.8
lW 95&-
0.040.035
900 ~ 9 0
3
2.5
2
4 Time (sec.)
6
8
I
2-
I
i‘
O.’ 0.6 0
;
E
i 2
4
6
J
8
Time (sec.) 38
300
-
.
1
250 -
200 -
1.5
I5O
2
0
Figure:7
4 Time (sec.)
6
8
28 0
2
4
Time (sec.)
S i m u l a t i o n r e s u l t s d e p i c t i n g v a r i a t i o n of v a r i o u s v a r i a b l e s f o r s t e p change i n solar insolation level S
. 768
6
8
39.7
50.93
51.68
98.08
99.45
2Lf--=2.265
0.035
0.047
0.0532 I
I
1.79
n
1.98
2.29
I 0.552
v32 0.638
\ .
159.5
218.7
250.1
15.0 s
10.0 s
15.0 s
m
Figure:8
P
Y
Experimental r e s u l t s depicting variation of various variables f o r step change in
s o l a r insolation l e v e l S
.
References: H.S. Rauschenbach, 'Solar cell array design handbook the principles and technology of photovoltaic energy conversion', Van Nostrand Reinhold Company, New York, 1980. J. Appelbaum, 'The operation of loads powered by separate sources or by a common source of sola cells', IEEE Trans. Energy Conversion, Vol. 4, No. 3, pp.351-357, Sept. 1989. P.J.MacVicar - Whelan, ' Fuzzy sets 'for man machine interactions', Int. Journal Man-Machine Studies, Vol. 8, pp. 687-697, NOV. 1976. L. Zadeh, ' Outline of a new approach to the analysis of complex systems and decision processes', IEEE Trans. System Man Cybernetics, Vo1.28, pp. 28-44, 1978. Zh-nnennann H.J., ' Fuzzy set theory and its applications', Kluwer-Nijhoff Publishing Company, 1985. Hsu Y.Y. and Cheng C.H., 'Design of fuzzy power system stabilizer for multimachine power systems', E E proceedings, Vol 137, pt.C, N0.3, pp 233-238, May 1990. Hilloowala R.M. and Sharaf A.M., ' Single phase induction motor drive scheme for pump irrigation using photovoltaic source', Proceedings of 22nd Annual North American Power Svmuosium. DD 415-427, Auburn, Alabama, Oct 1990. [8] Signktics reference manual 'HEF4752V application guidelines Advance information', April 1981. 169
I
