Pergamon o196-s9o4(95)oo355-x

Energy Convers. Mgmt Vol. 38, N6. I, pp. I-II, 1997 Copyright © 1996 Elsevier Science Lid

Printed in Great Britain. All rights reserved 0196-8904/97 $t5.00 + 0.00

P E R F O R M A N C E A N A L Y S I S O F PV P U M P I N G S Y S T E M S

U S I N G S W I T C H E D R E L U C T A N C E M O T O R D R I V E S

H A M I D M. B. METWALLyI"[ • and WAGDY R. ANIS 2 ~Electrical Engineering Department, Faculty of Engineering, Zagazig University, Zagazig and 2Electronics and Communications Department, Faculty of Engineering, Ain Shams University, 1 Sarayat Street,

Abbasia, Cairo, Egypt

(Received 25 January 1995; received for publication 6 November 1995)

Abstract--A PV pumping system using a switched reluctance motor (SRM) is thoroughly investigated in this work. This motor is supplied by a d.c. voltage through a simple switching circuit. This drive circuit is much simpler than the normal d.c./a.c, inverter required to supply the induction motor. The efficiency of this motor is considerably higher than that of the equivalent d.c. or induction motors. In addition, because of the simple construction, the SRM is cheaper than these conventional drives. Because of the above advantages oftbe SRM, the proposed system has higher efficiency and lower cost as compared with other systems. A design example is studied in detail to explore the advantages of PV pumping systems based on this new drive. The study of the performance of the proposed system showed that the operating efficiency of the motor is about 85% during most of its working time. The matching efficiency between the PV array and the proposed system approaches 95%. The major part of the losses takes place in the pump and the riser pipes. This loss represents one third of the total available energy. Copyright © 1996 Elsevier Science Ltd

Pumping systems Photovoltaic systems PV system simulation Performance of PV pumping systems

I. INTRODUCTION

Water pumping is one of the most popular applications of solar energy now-a-days. The pumping system consists of three basic components, a PV array, an electric motor, and a water pump. In addition, in some cases, there are storage batteries and power conditioning equipment. Generally, the electric motor used in these systems is one of two main types, either induction motor or d.c. motor.

The squirrel cage induction motor is a well developed motor. It is one of the simplest forms of motors available. Because of its simplicity, it is cheap, robust, and reliable. An electronic inverter is necessary to convert the d.c. power generated by the array to an a.c. power for the motor. For variable speed operation, a variable frequency supply is required. The supply must also be of variable voltage if a constant torque is to be obtained throughout the speed range. The requirements of variable voltage and frequency supply, as well as an a.c. waveform of minimum harmonics, necessitate the use of a complex and, hence, expensive inverter. As the inverter becomes complex, the reliability in service decreases. Hilloowala and Sharaf[l] investigated the design, modeling, and simulation of a PV powered pump irrigation system using a single phase induction motor drive.

The d.c. motor, on the other hand, is the most complicated and, hence, expensive motor. It has all the common disadvantages associated with the sliding brush contacts and commutator, such as the need for routine inspection and periodic maintenance. Brush contacts are also unsuitable for hazardous environments, and the associated arcing problem limits motor size and speed range. Direct current motors are not suitable for high speeds because of the wear and tear of the commutator and brushes, which limit the life of the motor. In spite of all these disadvantages, d.c. motors are used extensively in PV pumping systems. This is because they can be coupled directly

tTo whom all correspondence should be addressed at: Yanbu Industrial College, P.O. Box 30436, Yanbu AI Sinalyah 21477, Kingdom of Saudi Arabia.

2 METWALLY and ANIS: PV PUMPING SYSTEMS

to the PV array, giving a simple and inexpensive system. The design and performance of directly coupled PV pumping systems are investigated in many publications, some examples are found in Refs [2-10].

In order to avoid the complex electronic inverter needed for the induction motor and the brushes and commutator in conventional d.c. motors, brushless d.c. motors are used in pumping systems, but at limited scale. The brushless d.c. motor has a rotating permanent magnet and a stationary armature winding, thus avoiding brushes and commutator. Commutation of electric current in the stationary armature is done by an electronic circuit in accordance with the rotor position. This is why brushless d.c. motors are called electronically commutated d.c. motors. The design of a photovoltaic pumping system based on this drive is reported by Longrigg [11].

In this work, a PV pumping system based on a new drive is investigated. The new drive is called a Switched Reluctance Motor. Although this motor is a new entrant to the field of variable speed drives, it has gained acceptance worldwide in many applications. As reported by Jones [12], this motor is used in a wide range of general industrial and domestic applications, such as fans, blowers, conveyors and pumps, and it may earn the title of the motor of the 1990s.

2. SWITCHED RELUCTANCE MOTOR

Recently, the interest in using SRMs as variable speed drives has increased remarkably. This is because this motor has many advantages over the other types of motors. It is robust, reliable, cheap, and of higher efficiency. During the last 15 yr or so, many publications concerning the design and performance prediction of this motor appeared. Among those important publications are Lawrenson et al. [13, 14] who investigated the design and performance aspects of the motor. Davis et al. [15] studied the drive circuit design.

A brief review of the construction, principle of operation and figures of merit of this motor is given here. Figure 1 shows the lamination profile of an 8/6 slotted motor as an example. Also, the elementary drive circuit of one phase is shown in the figure for the purpose of illustration. The construction of the motor is very simple with the following features:

(1) there are salient poles (teeth) on both stator and rotor, i.e. it is doubly salient (2) concentrated simple windings mounted on the stator poles (3) there are no windings of any type on the rotor (4) the number of poles (teeth) carried on the stator and the rotor are different (5) the windings on diametrically opposed poles are connected in series and/or parallel to form

one phase, and the number of phases and poles are open to a wide variety of choices.

The operation of this motor is based on the production of reluctance torque, that is, the torque produced by the forces tending to align the stator and rotor teeth when a particular phase is excited.

4 } -

Fig. I. Cross-section of an 8/6 slotted SRM with simplified drive circuit for one phase.

METWALLY and ANIS: PV PUMPING SYSTEMS 3

Solar

PV array

S 2

- ©i%ieVCit ::

Battery SR motor Pump

Fig. 2. Block diagram of the system.

These forces are independent of the direction of the excitation current. By switching the excitation current between phases, in an appropriate manner, continuous rotation is achieved. Although the motor can operate in the open loop mode, the closed loop mode of operation is usually preferred. This is to avoid the difficulties which could arise during starting or during load disturbances. In the open loop mode, it is not necessary to sense the rotor angle at the instant of switching-on, and the rotor adjusts itself according to the mechanical load imposed on it. In the closed loop mode, the phase switching can be controlled via a simple shaft-mounted position transducer, so that the stator windings are switched on and off in accordance with the rotor position.

Simplicity of construction makes the motor cheap, robust, and reliable. Unidirectional currents in stator windings allow the use of cheap and simple power converters. In addition, this motor has better thermal characteristics than other types of motors because of the absence of windings on the rotor. The above features produce a motor with a high specific output and high efficiency over a wide range of speeds and output powers.

3. SYSTEM MODEL

The block diagram of the system is shown in Fig. 2. It consists of a PV array, a storage battery connected to the array through a battery voltage regulator, a switched reluctance motor together with its drive circuit, and a centrifugal pump. In the following subsections, each component is introduced and the mathematical models for the main components are given.

3.1. The P V array

The PV array I - V characteristic is given by:

I = ILoG -- I0[exp((V + IRs) /VT) - 1] - (V + IRs)/Rsh (1)

where I is the PV array current (A), IL0 is the light generated current of the PV array at G = 1 kW/m 2, G is the solar irradiance (kW/m2), I0 is the PV array reverse saturation current (A), V is the PV array operating voltage (V), V T is the thermal voltage of the PV array (V), R s is the series resistance of the PV array (f~) and Rsh is the shunt resistance of the PV array (f]).

3.2. The battery voltage regulator

The function of the battery voltage regulator (BVR) is to protect the battery against overcharging and deep discharging. If the battery is overcharged, the BVR opens switch SI, in Fig. 2, to disconnect the PV array, and the load is supplied from the battery and, hence, it is partially discharged. On the other hand, if the battery is deeply discharged, the BVR opens switch $2, and hence, the load is disconnected to allow the PV array to charge it. Thus, the BVR controls the battery charge and, hence, the battery voltage within the allowed limits. Such controlled performance ensures long life for the battery. The detailed design and performance characteristics of one such battery voltage regulator are given by Anis [16].

3.3. The storage battery

The function of the battery is to keep the operating voltage of the motor within certain allowed limits. This is necessary in order to operate the motor at high efficiency. Allowing a wide range

4 METWALLY and ANIS: PV PUMPING SYSTEMS

of variations in the operating voltage, as in the case of directly coupled systems, results in an inefficient motor operation. As shown in Fig. 2, the battery is connected across the array, while the battery voltage regulator controls switches SI and $2 as discussed in the previous section. This means that the voltage (V) in equation (1) is equal to the battery voltage (VB) and, at the same time, equals the motor voltage.

The battery voltage is affected by the following factors:

(1) its instantaneous state of charge (SOC), (2) its capacity expressed in ampere hours (Ah), (3) its instantaneous current (Ib) and whether it is charging or discharging, (4) the number of series cells (n), (5) the charging efficiency (~/ch) which is defined according to equation (2), (6) the discharging efficiency (~/dis) which is defined in equation (4).

The battery efficiency is simply/'/ch times ~/dis" For lead-acid batteries, the efficiency is about 80%. The characteristics of lead-acid storage batteries are given by Macomber [17]. During charging,

the state of charge (SOC) of the battery is given by:

SOC = SOC0 + ~/ch lb tch/Ah (2)

where SOC0 is the initial state of charge, and tch is the charging period. The battery voltage (VB) during charging is given by:

VB = Vao[1 + (Ib/Ah)(O.189/(1.142 - SOC) + 0.15)] (3)

where VBo is the nominal battery voltage. For lead-acid batteries, VRo = 2.094n V. During discharging, the SOC of the battery is given by:

SOC = SOC0 - Ib tdi~/Ah~/di~ (4)

where /dis is the discharge period. During discharge, the voltage V B is given by:

VB = VBo[1 -- (Ib/Ah)(O.189/SOC + 0.15)]. (5)

Consider now how the operating voltage of the motor is determined? At a given instant, the solar irradiance (G) is computed according to the climatic conditions of Cairo on a plane facing south and tilted at an angle equal to the latitude angle. The second step is to determine whether the array current (I) is smaller or larger than the motor current (i). The battery voltage is assumed to be the value determined in the previous moment. Substituting for the voltage (V) in equation (1) by the battery voltage, the array current (I) is determined. If the array current (I) is greater than the motor current (i), then the battery is charging and Ib is equal to (I -- i ). On the other hand, if the array current (I) is smaller than the motor current (i), then the battery is discharing with current (Ib) equal to (i -- I). Thus, the state of charge of the battery is calculated from equation (2) or (4) according to whether it is charging or discharging, respectively. Then, the battery voltage is calculated using either equation (3) or (5) depending on the state of charge. Then, the cycle of computation is repeated after the predetermined interval, in the simulation program, elapses.

3.4. The drive circuit

The switched reluctance motor operates well from a switched voltage supply. Unlike conven- tional motors, a square wave of voltage is a better excitation waveform than a sine wave. This is because the square wave voltage helps to build up the phase current quickly and, hence, produces more torque. The general shape of this voltage waveform is shown in Fig. 3. The voltage is switched on at instant t~ and off at instant t2, and the negative voltage is used for commutation. Hence, the drive circuit is simple, and its main task is to switch the voltage on and off in an appropriate way. Many drive circuit configurations are possible as reported by Lawrenson et al. [14] and Ray et al. [18]. Figure 1 shows a schematic for the most common one. There are two main power switches per phase, gate turn off (GTO) thyristors are used here, only the circuit for one phase is shown in this figure. Power is drawn from the supply when the two thyristors are turned on and is returned to it when the two thyristors are turned off. Thus, the commutation power is returned

METWALLY and ANIS: PV PUMPING SYSTEMS 5

0

0

/ ~ i I t 3

I Complet~ cycle -'~

Time

Fig. 3. Typical voltage and current waveforms of switched reluctance motors.

to the supply instead of being wasted in the freewheeling resistance as is the case of the induction motor. This increases the efficiency of the motor.

3.5. The switched reluctance motor

The mathematical model of the switched reluctance motor consists of the electrical and mechanical equations which govern its behavior under given operating conditions. In general, there is one voltage equation for each phase of the motor. In addition, there is one mechanical equation representing the motor dynamics. Assuming an n-phase motor, the mathematical model is given by the following (n + 1) equations:

Vj = ijRj + dtPJ where (j = 1, 2, 3 . . . . n) (6) dt

dco 1 dt - J [T - Tin] (7)

where j represents the phase number, V is the phase applied voltage (V), i is the phase current (A), R is the phase resistance (f~), W is the phase flux-linkage (Wb-turn), co is the rotor speed (rad/s), J is the rotor and load moment of inertia (Nm. s ~), T is the electromagnetic torque developed by the motor (Nm) and Tm is the load torque including the effects of motor and load friction (Nm).

The flux-linkage function (tp), given in the above equations, depends on both the rotor angle (0) and the phase current (i) in a complicated nonlinear manner and is usually written in the form tP(0, i). In order to solve the motor model, the function tP(0, i) must be known: either in an analytical form or in the form of tabulated measured data. Once this function is known, the electromagnetic torque developed by the motor can be calculated using the coenergy function as follows:

W'(O, i ) = ~(0, i ) dilo . . . . . t.~t (8)

and ~gW'

T(O,i)=--~-I~=¢o.~.~ (9)

where W'(0, i) is the coenergy function and T(O, i) is the electromagnetic torque function. The (n + 1) equations (6) and (7), together with the flux-linkage function ~P(0, i) and the static

torque relationships (8) and (9), represent the complete mathematical model of the n-phase switched reluctance motor.

6 METWALLY and ANIS: PV PUMPING SYSTEMS

The following assumptions are made to obtain the steady state performance:

(1) all motor phases are symmetrical, (2) the mutual flux-linkage between phases is small enough to be neglected, and (3) the motor is running at constant speed.

The above assumptions reduce the model of the motor to one voltage equation in the following form:

dV - - = V - i R . (10) dt

By differentiating the function ud(O, i ) partially with respect to (0) and (i), equation (10) takes the following form:

dt-O~p/Oi V - i R - c o - ~ . (11)

It should be noted here that, although the model is a steady state one, it contains a differential equation. This is because all the parameters of the motor are time dependent and not constant, as is the case with d.c. motors. In order to solve this model, the function ~(0, i) must be obtained either experimentally or by using the finite element method. The solution of equation (11) for a given voltage waveform produces the motor phase current (i) as a function of time (t), and hence, the torque produced by the motor can be calculated using equations (8) and (9). Equation (11) can be solved using the well known Runge-Kutta 4th order method for solving differential equations.

3.6. The pump

Braunstein and Kornfeld [4] have reported that the torque required to drive the centrifugal pump is given by:

rp = KpOJ 2 (12)

where Tp is the torque required to drive the pump (Nm) and Kp is a constant for a given pump.

4. DESIGN EXAMPLE

In the following subsections, the detailed calculations of an illustrative design example are given. Assume that it is required to pump water from a depth of 28 m at a rate of 150 m3/day. This amount of water is enough to irrigate a vegetable farm of two acres area.

4. I. The pump

Assuming that the PV pumping system operates for 10 h daily, the required discharge (Q) is Q = 4.167 x 10 -3 m3/s. The relationship between the diameter of the riser pipe (D) and the speed of water (v) is given by the continuity equation:

ltO2v Q = 4 (13)

If a 2 in. dia. riser pipe is used, then from equation (13), the water speed (v) is equal to 2.056 m/s. From the friction charts given by Karassik et al. [19] and considering a smooth pipe, the friction factor ( f ) is estimated to be f = 0.018. The friction head (Hf) is given by:

fLy 2 Hf -- (14)

2Dg

where L is the length of the riser pipe (m), 28 m in this example and g is the gravitational acceleration (m/s2).

Substituting in equation (14) gives He= 2.127 m. Hence, the total required head (H) is about 30 m.

From the above analysis, it can be concluded that a pump delivering 15 m3/h at a head of 30 m is required. The commercial, four stage centrifugal pump whose H/Q characteristic is shown in Fig. 4 is chosen. It delivers about 16.5 m3/h at 30 m head when driven at 1350 rpm. At this operating

M E T W A L L Y and ANIS: PV P U M P I N G SYSTEMS

50 - -

40

30

20

10

I I I I I I 5 10 15 20 25 30

Water discharge (m3/h)

Fig. 4. Water head/water discharge characteristics of the pump at 1350 rpm.

point, the mechanical power input to the pump is 3 h.p., hence the torque required to drive the pump is Tp -- 15.83 Nm, and the efficiency of the pump is 56.3%.

4.2. The motor

The motor used in this example is a 3 kW, 3-phase, switched reluctance motor. It has 12 teeth on the stator and 10 teeth on the rotor and, hence, is known as the 12/10 motor. The measured flux-linkage/phase current/rotor angle characteristics of the motor are shown in Fig. 5. More design details and the measured characteristics of this motor are given by Finch et al. [20, 21]. A simulation program is developed to calculate the performance curves of the motor using the measured flux-linkage data and the above discussed mathematical model. These curves are shown in Figs 6 and 7. Figure 6 shows the torque/speed characteristics at different values of d.c. voltages. Figure 7 shows the corresponding d.c. current/speed characteristics. Since the operating point of the pump is 15.83 Nm at 1350 rpm, the d.c. voltage required to drive the motor must be at least 84 V. Figure

2.O [- | ; m : -- = n - i - - , -

_ -- --m~l.. l~ ~--'-..i~w~i~--~..t~ ~w... I 1.6 t --'----. I ~ "~'-- -~'n "~-m "~'s - '~-

~--m--m--l..... m'~'m_ ""m_ ~i__ '~1__ '%ik %m%_ '~. l~l_m_l 10A ""l.~. ~'m %i ~'l %i --I m~.m.

1.2 L m~, m ~m_ ~'m ~m '~m ~m-. m m"'m--m--mm r ~'mm~'m "~'mm~m~m~im~m~m~mm~m_ '~'l"m--m--m-- m

~--l--m...m.~. m - - I~ ~m, ~ m ~m~ m~m--m--m = 0.8 ~ -~'i'~.l... " l ~ i --m~ "m~m m'm.m_l_ l_ m 5A

| mm"~m.~.mm ~m mm'~, m ki"-.i__ i

E [ m.~i~m ~m~ m ~m..m_m__m_m_l 0.4 r %'l%l "%m'm--l--m--l--l--i

) ~mm~ m'"m--lm--m--l--I -- m --I IA

I i i I i i I 0 30 60 90 120 150 180 210

Rotor angular position (elee. deg.)

Fig. 5. Measured flux-linkage/rotor angle/phase current characteristics of the SR motor (current = 1-I0 A in 1 A steps).

8 METWALLY and ANIS: PV PUMPING SYSTEMS

30 -

z o

O

25

20

15

10 -

5 -

0 500

A B C D E

C 96 V D 108 V

M o t o r o ~

I I I I I I 1000 1500 2000 2500 3000 3500

Sp¢¢d (rpm)

Fig. 6. Torque/Speed/d.c. voltage characteristics of the SR motor.

8 shows that the current drawn by the motor varies between 29 and 26 A (points C and D) according to the variations of the battery voltage, which changes according to the solar irradiance. Also, the efficiency of the motor varies between 86.7 and 83.6% (points A and B), but it is above 85% most of the time.

4.3. The battery and its voltage regulator

Since the voltage required to drive the motor is at least 84 V, the nominal voltage of the battery is taken equal to 96 V. During the winter solstice day, worst climatic conditions, the voltage will change according to the state of charge of the battery between a minimum value of 88.8 V and a maximum value of 103 V, as can be seen from Fig. 8. Accordingly, the current required to drive the motor at 1350 rpm and 15.83 Nm will vary between 29 and 26 A. The BVR controls the voltage between the above mentioned limits according to the state of charge of the battery, as explained earlier.

45 -

4 0

35

3 0

• 25

20

15 --

10

A B C D E

I I I I I I 1000 ISO0 2000 2500 3000 3500

Speed (rpm)

Fig. 7. Direct current/Speed/d.c, voltage characteristics of the SR motor.

METWALLY and ANIS: PV PUMPING SYSTEMS 9

4 0 - - - 9 0

t3

36

32

28

24

A

2o I I I I I I I 75 80 85 90 95 100 105 l l 0

D.C. voltage (V)

87

s4 o

sx ~ 0

78

75 15

Fig. 8. Variations of d.c. current and efficiency with d.c. voltage (at 1350 rpm and 15.83 Nm).

4.4. The P V array

To calculate the size of the PV array, the following assumptions are made:

(1) climatic conditions for Cairo (30°N) are considered (2) water discharge is guaranteed for sunny days only, thus it may be interrupted during cloudy

days. According to the Cairo climatic conditions, cloudy days take place only a few times during the winter when the water demand is a minimum. Hence, the system guarantees the water supply almost throughout the whole year

(3) the PV array tilt angle is 45 ° and facing south (4) the battery voltage is controlled by a conventional battery voltage regulator (5) the effect of ambient temperature variations on the PV array performance is considered (6) the minimum allowed state of charge of the battery is 25%.

4

3

1

0

-1

-2 I 6 18

Maximum p o w e r

I I I I I 8 l 0 12 14 16

T i m e (h)

Fig. 9. Variations of different powers during winter solstice day (21st of December).

10 M E T W A L L Y and ANIS: PV P U M P I N G SYSTEMS

Riser pipe loss 3.22%

Pun "" " loss los~ b 31.1

Mismatch loss 5.05%

Battel loss 0.72~

output

Fig. 10. Distribution of energy during winter solstice day (21st of December).

A detailed simulation program is developed to determine the PV array and the battery storage sizes. Using this program, the following results are obtained:

(1) the PV array size is 6.048 kW peak (2) the battery capacity is 1060 Ah.

5. SYSTEM PERFORMANCE

The proposed system operates 12 h daily most of the year. During spring, summer and autumn, the system delivers 180 m 3 of water per day. Winter is the exceptional season when the system delivers 150 m 3 per day. Thus, the annual average discharge exceeds 170 m 3 per day. Figure 9 shows the PV array maximum and utilized powers during the winter solstice day. The utilized power is slightly less than the maximum power, the difference represents the mismatch loss. It can be seen in Fig. 9 that the utilized power has two abrupt changes, at points E and F. At point E, the state of the battery changes from discharging to charging, and as a result, its voltage rises abruptly, leading to a better match with the PV array. Conversely, at point F, the battery state changes from charging to discharging, and hence, its voltage drops suddenly, leading to a poor matching with the PV array. Points E and F represent the moments when the utilized array power is just equal to the load power. Figure 9 also shows the battery power variations during the winter solstice day. In this figure, the battery power is considered positive during the discharging time and vice versa.

The energy distribution during the winter solstice day is shown in Fig. 10. The maximum energy available from the array is considered 100%. The mismatch loss is about 5%, and hence, the utilized energy is 95% of the maximum available energy. The motor loss is almost 14% of the total energy, this low loss is attributed to the high efficiency of the SRM drive. The largest part of the losses takes place in the pump because of its limited efficiency (-~ 56%). The useful hydraulic output of the system is 45.15% of the total available array energy which is significantly higher than that obtainable from the systems that use conventional motors. Since the pump loss represents a major part of the total loss of the system, choosing a more efficient pump, even if it is more expensive, would be the effective way to improve the overall efficiency and economics of the system.

6. CONCLUSIONS

The steady state performance of a PV pumping system employing a switched reluctance drive has been analyzed. This new drive has a number of advantages over conventional d.c. and induction drives. High efficiency and low maintenance requirements are among those advantages.

A numerical example is given to illustrate the design procedure. Starting from the required head and discharge, the rating of each component is calculated and a suitable component is chosen. Finally, the sizes of the storage battery and the PV array are computed.

METWALLY and ANIS: PV PUMPING SYSTEMS 11

It has been found that the voltage of the battery varies according to its state of charge, but this will not affect the speed of the motor because the speed of a given SRM is determined only by the switching frequency. The motor compensates for changes in battery voltage by changing the switch-on angle, but its speed and torque will remain constant. This affects, to some extent, its efficiency. The study showed that the efficiency of the motor is about 85% during most of its working time. The overall efficiency of the system is found to be above 45% which is higher than that of the other systems based on d.c. or induction motors. Further improvement in the efficiency of the system is still possible by choosing a more efficient pump.

R E F E R E N C E S

1. R. M. Hilloowala and A. M. Sharaf, Single phase induction motor drive scheme for pump irrigation using photovoltaic source. Proc. 1EEE 22nd Ann. N. Am. Power Syrup., Auburn Univ., pp. 415-427 (1990).

2. J. Appelbaum and J. Bany,. Performance analysis of d.c. motor photovoltaic converter system--I. Solar Energy 22, 439-445 (1979).

3. J. A. Roger, Theory of the direct coupling between d.c. motors and photovoltaic solar arrays. Solar Energy 23, 193-198 (1979).

4. A. Braunstein and A. Kornfeld, Analysis of solar powered electric water pumps. Solar Energy 27, 235-240 (1981). 5. J. Appelbaum, Performance analysis of d.c. motor photovoltaic converter system--II. Solar Energy 27, 421-431 (1981). 6. D. Weiner and A. Levinson, An optimal operation design of a photovoltaic d.c. motor coupled water pumping system.

Proc. IEEE Industry Applic. Soc. Ann. Meet., IAS-25, Seattle, U.S.A., pp. 268-274 (1990). 7. W. B. Lawrance and R. Troster, Dynamic simulation of a solar pumping system. Renewable Energy 2, 591-596 (1992). 8. A. Chaurey, P. M. Sadaphal and D. Tyagi, Performance evaluation of PV pumping systems. RERIC Int. Energy J.

14, 57~53 (1992). 9. P. K. Koner, A review on the diversity of photovoltaic water pumping systems. RERIC Int. Energy J. 15, 89-110 (1993).

10. W. R. Anis and H. M. B. Metwally, Dynamic Performance of a Directly Coupled PV Pumping System. Solar Energy 53, 369-377 (1994).

11. P. Longrigg, Use of solar photovoltaics to transport and desalt ground water supplies using brushless d.c. motors. Solar Cells 13, 231-252 (1985).

12. D. Jones, Current status of switched reluctance motors. J. Power Convers. & Intelligent Motion (PCIM) 15, 40-42 (1989).

13. P. J. Lawrenson, J. M. Stephenson, P. T. Blenkinsop, J. Corda and N. N. Fulton, Variable speed switched reluctance motors. Proc. lEE 127, 253-265 (1980).

14. P. J. Lawrenson, W. F. Ray, R. M. Davis, J. M. Stephenson, N. N. Fulton and R. J. Blake, Controlled-speed switched-reluctance motors: present status and future potential. Proc. 1st Europ. Conf. Electrical Drives~Motors~Controls, Univ. of Leeds, U.K., pp. 23-31 (1982).

15. R. M. Davis, W. F. Ray and R. J. Blake, Inverter drive for switched reluctance motors: circuits and component ratings. Proc. lEE 128, 126-136 (1981).

16. W. R. Anis, Design of a novel battery voltage regulator for photovoltaic systems. Solar Cells 28, 19-29 (1990). 17. H. L, Macomber, Photovoltaic Stand Alone Systems, Chap. 4. Manegan, Gaithersburg, Md (1981). 18. W. F. Ray, R. M. Davis, R. J. Blake, N. N. Fulton, J. M. Stephenson and P. J. Lawrenson, Industrial switched

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