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Optimum design of a photovoltaic powered pumping system
Energy Convers. Mgmt Vol. 35, No. 12, pp. 1123 1130. 1994
~
Pergamon
0196-8904(94)00018-2
OPTIMUM
DESIGN
OF
Copyright c~')1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0196-8904/94 $7.00+ 0.00
A PHOTOVOLTAIC
PUMPING
POWERED
SYSTEM
WAGDY R. ANISt and M. A. NOURZ# 'Electronics and Communication Department, Faculty of Engineering, Ain Shams University, I Sarayat St., Abbasia, Cairo, Egypt and 2Electronics Department, Yanbou Industrial College, P.O. Box 30436, Yanbou AI Sinaiyah 21477, Kingdom of Saudi Arabia (Received 28 June 1993: receit,ed for publication 14 June 1994)
Abstract--Photovoltaic (PV) powered pumping systems are relatively simple and reliable, hence they are applied worldwide. Two conventional techniques are curently in use; the first is the directly coupled technique where a PV array is directly coupled to a d.c. motor-pump group, and the second is the battery buffered PV pumping system where a battery is connected across the array to feed the d.c. motor driving a pump. Recently, a third system is proposed to make use of the advantages of the previously mentioned conventional systems. It is the switched mode PV powered pumping system. The switched mode PV powered pumping system couples the pumping system to the PV array directly when the storage battery is fully charged as explained in Ref. [5]. The objective of such a system is the maximum utilization of available solar radiation to minimize the cost per pumped cubic meter from a given water depth. For a given location, four main parameters affect the design of this system; (1) d.c. motor-pump group parameters, (2) PV array size, (3) battery storage size and (4) water storage tank size. The system designer has to determine the previously mentioned four parameters so that the minimum cost per pumped cubic meter is achieved. It is found that some factors are more effective in reducing the cost than others. The PV array size is the predominant factor, while the battery storage and water tank sizes have relatively less effect. The system installation cost is considered in the detailed economic analysis discussed in this work. Photovoltaic
Pumping
Simulation and design
INTRODUCTION P h o t o v o l t a i c (PV) p u m p i n g systems m a y be classified as follows: (1) Directly c o u p l e d systems where the PV a r r a y is directly c o u p l e d to a d.c. m o t o r - p u m p group. Such a system is simple a n d reliable, but the m o t o r is n o t o p e r a t i n g c o n t i n u o u s l y at its o p t i m u m o p e r a t i n g p o i n t due to the c o n t i n u o u s v a r i a t i o n o f solar irradiance. References [1-3] have a n a l y s e d the steady state p e r f o r m a n c e o f this system, while the d y n a m i c p e r f o r m a n c e is studied in Ref. [4]. (2) Battery buffered systems where a storage b a t t e r y is connected across the PV array, a n d the d.c. m o t o r is o p e r a t i n g at a l m o s t c o n s t a n t voltage (note that the b a t t e r y voltage varies a r o u n d its n o m i n a l value), a n d as a rcsult, the d.c. m o t o r is o p e r a t i n g at a l m o s t its o p t i m u m o p e r a t i n g point. This system has two a d v a n t a g e s over the directly c o u p l e d one. Firstly, w a t e r m a y be p u m p e d d a y a n d night, thus the water discharge is larger. Secondly, the d.c. m o t o r is o p e r a t i n g at its o p t i m u m o p e r a t i n g point, a n d consequently, the system efficiency is enhanced. A m a j o r d i s a d v a n t a g e o f such a system is the extra system cost due to the a d d e d b a t t e r y cost. Thus, a b a t t e r y buffered system allows m o r e water p u m p i n g but at higher system cost. Again, the criterion d e t e r m i n i n g which system is better e c o n o m i c a l l y is the cost o f a p u m p e d cubic meter. A n o t h e r d i s a d v a n t a g e o f this system is the energy loss due to a r r a y disconnect when the b a t t e r y is fully c h a r g e d d u r i n g high solar r a d i a t i o n p e r i o d s as explained in Ref. [5]. (3) Switched m o d e PV p u m p i n g systems which are designed to o v e r c o m e the p r o b l e m o f the energy loss. This system uses a storage b a t t e r y as a buffer between the PV a r r a y a n d the p u m p i n g system, b u t a novel b a t t e r y voltage r e g u l a t o r is designed to connect the PV a r r a y directly to tTo whom all correspondence should be addressed. 1123
1124
ANIS and NOUR:
PHOTOVOLTAIC
POWERED PUMPING SYSTEM
d.c. motor
D -+
7%’ PV array
Water distribution network Fig. 1. Schematic diagram of a PV powered pumping system.
the pumping system when the storage battery is fully charged. Thus, the energy loss due to array disconnect is drastically reduced [5]. The block diagram of this system is indicated in Fig. 1. This work considers the design of a switched mode PV pumping system and discusses the effect of different parameters influencing the system design. The design objective is to determine the optimum design leading to minimum cost. SYSTEM
PARAMETERS
Figure 1 shows a block diagram of a switched mode PV pumping system. The pinciples of operation, as well as the modelling, of this system are fully explained in Ref. [5]. The developed model takes into consideration the following factors: (1) (2) (3) (4) (5) (6) (7)
The The The The The The The
instantaneous variation of solar irradiance in Cairo city (30”N) effect of ambient temperature on the PV array performance effect of both series and shunt resistors of PV array effect of charging and discharging current on battery voltage effect of the instantaneous state of charge on battery voltage effect of battery capacity on battery performance dc. motor-pump group characteristics
To develop a general design, regardless of motor-pump following parameters are defined: (1) The array factor (F,) is defined as
size or the site under consideration, the
F _ Peak power of the PV array (kW) aLoad power (kW) F, = Pp 1PL
(1)
where Pp is the peak power of the array and PL is the load power, both expressed in kilowatts. (2) The storage factor (F,) is defined as F = Battery storage capacity (kWh) s Daily load energy (kWh) F, = S/24P,
(2)
where S is the battery storage expressed in kWh. The factor 24 represents the hours of the day. If both load power and daily load energy varies from day to day, then equations (1) and (2) consider the annual average daily load demand and the annual average daily load consumption. Note that I;, and F, are dimensionless since they are ratios. For the PV pumping system, the designer may consider one of the following alternatives to achieve his ultimate goal of minimum cost. (1) Continuous 24 h operation of the motor pump. This choice requires a relatively large battery storage size and larger amount of pumped water. If the water demand is continuous, such a design will reduce the water storage tanks.
ANIS and N O U R :
P H O T O V O L T A I C P O W E R E D P U M P I N G SYSTEM
1125
(2) Daily operation only. Hence, the water is pumped only whenever solar radiation is available. If the load demand is continuous, then one has to pump more water during the day to supply the load demand during the night. Such a design necessitates a larger motor-pump group, larger array size and larger water storage tanks. On the other hand, this design does not need a large battery storage. The preference between the two alternatives depends on (1) load water demand througout a complete year and (2) system economics, the lower the cost of 1 m 3 pumped, the better the design. From the above discussion, it is necessary to define a water storage factor Fw Water tank storage size (m 3) Sw Fw = Daily load water demand (m 3) --- bPL"
(3)
The daily load water demand is proportional to load power PL and Sw is the water storage tank size. In equation (3), b is a constant whose units are (m3/kW). Again, Fw is a dimensionless parameter. Another factor to be considered to achieve the minimum cost is the pump installation cost. To express this parameter as a dimensionless factor, let us define the pump installation cost parameter (Fp) as follows: Fp = Pump installation cost ($) (4) PV array cost ($) The pump installation cost depends mainly on the geology of the site where the pump is to be installed. If water is to be pumped from a well in a rocky area, the pump installation cost will be high, while if water is pumped from surface water, the pump installation will be low and so on. The above mentioned parameters enable one to determine the optimum solution of a given case. ECONOMIC ANALYSIS Since the economics is the predominant parameter in the system design, one defines the unit cost function Cu as follows Cu=
Overall system cost during system's lifetime Total amount of pumped water during the same period"
The total amount of daily pumped water is proportional to the load power PL. If the overall system cost is denoted by CT, one may write
Cu = CT/365NbPL
(5)
where N is the expected lifetime of the system (expressed in years). The factor 365 is simply the number of days per year. Overall system cost includes: PV array cost including its installation, battery storage cost including wiring and battery voltage regulator costs, water storage tank cost including piping and installation costs and operation and maintenance cost during a given period. The expected lifetime of the PV array is 20 yr. Thus, the economic analysis given hereafter is based on a 20 yr period. The storage batteries lifetime does not exceed 5 yr for commercial industrial lead acid batteries. The operation and maintenance costs include the d.c. motor brushes change, storage battery maintenance (addition of distilled water or acid and checking of battery cells voltage) and water storage tank cleaning. Since most of the system cost is paid at the system installation time, while the amount of water is produced during the system's expected lifetime, the economic analysis should consider this factor. The parameters to be considered are the money discount rate (d) and the inflation rate of battery storage (is). Let us now develop the economical model to be used to determine the optimum solution. The major constraint of the solution is that the load water demand throughout the year is assumed to be constant day and night. Thus, even during cloudy days, the water tank should be capable of delivering the load water demand. Assume that the PV array expected lifetime is N yr (usually considered 20 yr) and that of the battery storage is k yr (usually considered 5 yr). Thus, the cost of the storage battery is paid at the beginning of system installation (considered zero time) and partially paid each k years. If the
1126
ANIS and NOUR: PHOTOVOLTAICPOWERED PUMPING SYSTEM
cost of 1 kWh of storage batteries is Cs, the present value of the storage battery replacement cost CR is given by [6] CR = S{Cs[1 + (Is - d)] k + Cs[1 + (Is - d)] 2k+ ' "
+ Cs[1 + (Is - d)] N-k}
where S is the battery storage capacity expressed in kWh. Since, from equation (2), S = 24FsPL, then manipulating, one may write CR = 24FsPLC~[1 + ( I s - d)]k{[1 + (ls- d)] u k _ 1}/{[1 + (Is--d)] k - 1}.
(6)
The initial cost of the system C~ (paid at the installation time) is composed of the array cost, the cost of the initial storage battery whose capacity is S and the cost of the water storage tank. If the cost of 1 kW (peak) of the PV array is Ca($/kWp), the array cost is C, Pp. Using equation (1), the array cost will be CaFaPL . If the cost of water storage is Cw($/m3), then using equation (3), the water tank cost will be bFwCwPL. Thus, the initial system cost is Ci
=
CaFaPL -I- 24FsPL Cs + bFwCwPL + Cins.
(7)
The last term in equation (7) is the pump installation cost. From equations (1) and (4), one can write ci.s = rpr~ CaeL. (8) The total system cost CT is CT = Ci + CR.
(9)
Combining equations (5)-(9) yields: Cu = (1/365Nb){CaFa(1 + Fp) + 24FsCs + bFwCw
+ 24FsCs[1 + (Is - d)]k{[1 + (Is -- d)] N-k - 1}/{[1 + (ls - d)] k - 1}}. (10) Equation (10) gives the per unit cost in terms of the system parameters Fa, Fs, Fp and Fw. The other parameters in equation (10) are the unit costs of PV array Ca, battery storage Cs, water storage tank Cw and installation Fp. WATER TANK SIZE It is assumed that the load water demand is constant day and night throughout the year. The load water demand will be denoted by QL (ma/day). The PV pumping system pumps a varying amount of water according to the available solar radiation and the energy stored in the batteries. For a PV pumping system, one may identify three parameters for the pumped water. They are the annual average daily water discharge Qa, maximum daily water discharge Qm,x and minimum daily water discharge Qmi,. The previously mentioned water discharge parameters are computed on an annual basis and their units are (m3/day). Since the load requires QL (m3/day), if the amount of pumped water by the system is smaller than QL, the difference should be obtained from the water tank. The worst condition takes place during cloudy days where the system depends mainly on the storage energy in the batteries. During cloudy days, the system's water discharge is Qm~n. If the number of successive cloudy days is m, the minimum tank storage size (Sw)mi, is
(Sw)min
=
(m + I)(QL -- Qmi,).
(11)
In equation (11), the term (m + 1) is used instead of m because the cloudy days start with the night of the previous sunny day and end with the night of the last cloudy day, hence there is an extra day of storage required. Actually, a cloudy day represents about 12 h of the night before and the night after, representing almost 24 h, hence the duration of insufficient solar energy for a single cloudy day is 36 h or 1.5 days. For m cloudy days, there should be enough stored energy or water for (m + 0.5) days. For conservative design, we consider this factor to be (m + 1). The load demand determines the size of the d.c. motor-pump to be used in the system. If the rated discharge of a motor-pump group is Q0 (m3/h), the load demand should not exceed 24Q0 (m3/day). Practically, when the load demand is determined, the motor-pump group rating is computed from the following inequality: Q0 > QL/24.
(12)
ANIS and NOUR:
PHOTOVOLTAIC POWERED PUMPING SYSTEM
1127
Note that the factor 24 in the inequality (12) arises from the fact that Q0 is an hourly discharge, while QL is the daily load water demand. To convert the inequality into an equation, one may assume a factor of safety R (greater than unity), and hence, the inequality (12) may be rewritten as
Qo = QL R/24.
(13)
The safety factor R is used because the motor-pump group cannot operate at its optimum operating point continuously due to battery voltage and, temperature continuous variations. To determine the load power PL (expressed here in watts) required, one has to know the overall water head h (m) of the system which is the sum of the water depth and the water tank height. The load power is related to the overall water head h and rated discharge Q0 (expressed here in ma/s) through t/PL(W) = Qo (m3/s)pg h (14) where ~/ is the pump efficiency p is the water density (1000 kg/m 3) g is the earth's gravitational acceleration (9.8 m/s2). If it is required to keep PL expressed in (kW) and Q0 in (m3/h), one has to add a constant 'a' in equation (14) to rectify the equation according to the required dimensions, hence equation (14) may be rewritten as r/e L (kW) = aQo (m3/h)pgh. (15) Equations (13) and (15) enable the designer to determine both PL and Q0. INTERDEPENDENCE
OF S Y S T E M
PARAMETERS
Let us consider a load demanding 100 m3/day and the water is pumped from a well of 25 m depth. Assume that the water tank height is 5 m, then the overall water head of the pump is 30 m. Assuming that R = 2, equation (13) gives the value of Q0 = 8.33 m3/h. Making use of equation (14) and assuming 80% pump efficiency, one obtains PL = 868 W. A d.c. motor operating at 48 V and 18 A would be a reasonable choice. The forthcoming analysis is based on this selected system. Now one has to determine the optimum array, battery storage and water tank sizes leading to meet the load demand at minimum cost. The pump installation factor Fp is considered to be 0.15, this means that the installation cost is assumed to be 15% of the PV array cost. The water storage factor Fw, according to equations (3) and (11), depends on the number of successive cloudy days at the site under consideration (m) and the battery storage and array sizes that determine the amount of pumped water during cloudy days Qmin. For Cairo city (30°N), the number of successive cloudy days is considered to be 2, i.e. m = 2. If the battery and array sizes are designed to supply the load water demand for two successive days, a water storage tank of minimum size may be sufficient. The expected PV array lifetime is 20 yr, i.e. N = 20, while the storage battery lifetime is 5 yr only, i.e. k = 5. The money discount rate is considered 10%, i.e. d = 0.1 and the storage battery inflation rate is is considered to be 12%. The constant b in our example is estimated to be 0.1. The cost of 1 kW peak of PV array (Ca) is about U.S. $5000. The storage cost Cs is about U.S. $50/kWh of storage batteries. The cost of a water tank is considered to be U.S. $25/m 3, i.e. Cw = 25. The remaining two parameters are array factor Fa and storage factor Fs. It is seen from equation (10) that the per unit cost Cu increases as Kd or Fs increases. Thus, the optimum economical solution is obtained at the minimum values of K~ and Fs satisfying the load requirements. Note that there is an interdependence between the water tank size and array and battery sizes. This fact may be explained as follows. As battery and array sizes increase, the amount of pumped water during cloudy days increases, hence Qmin increases and consequently (Sw)mm decreases, as seen from equation (i 1). The increase in battery storage and array sizes leads to a decrease in water tank size. The reason is that, if battery storage and array are increased to the extent that the load energy is totally supplied by the storage battery during cloudy days, then Qmin= QL, and from equation (11), one can deduce that the water tank size becomes zero. Table 1 shows 10 groups of system parameters satisfying the load requirement. It is observed from Table 1 that, as Fa and F~ E C M 35/12
I
1128
ANIS and NOUR: PHOTOVOLTAIC POWERED PUMPING SYSTEM Table 1. Systemparameters satisfyingthe load demand and the associated cost in each case System parameters Fa 2.83 3.54 4.55 5.05 5.56 6.06 6.57 7.07 7.58 7.38
F~ 0.37 0.44 0.84 0.95 1.15 1.26 1.47 1.57 1.68 1.76
Fw 1.80 1.70 1.09 0.85 0.78 0.75 0.59 0.40 0.19 0.00
Cu(c/m3) 2.51 3.12 4.23 4.71 5.26 5.74 6.30 6.77 7.26 7.52
increase, Fw decreases as expected. However, the minimum cost is obtained at the minimum value of Fa, since the array cost is the dominant factor in the cost analysis. R E S U L T S AND A N A L Y S I S To obtain the optimum design, all system parameters are kept constant except one parameter only. Thus, a family of curves is obtained. Figure 2 indicates the system water discharge for a constant storage factor Fs and different array factors during a complete year. It is clear that, as Fa increases, the amount of pumped water increases significantly. The directly coupled water discharge is shown in Fig. 3 where it is also seen that it is appreciably affected by the array factor. Figure 4 shows the effect of battery storage factor Fs on the amount of pumped water for a constant array factor. It is clear that the storage factor has a minor effect on the water discharge. Thus, the storage factor should be kept at the minimum value that satisfies the system design constraint. Figure 5 indicates that the effect of storage factor on the system performance is that, when Fs increases, the state of charge of the battery (SOC) is kept generally higher except during cloudy
300
,
Fs=I'9
250
..........
, {{~
'
......' .... ,-I-:.-
[............
r: !.q ..... r
200
{. . . . . . . ~--.--.'7,'['-
--~ . . . . . . . . . . . . . . ~ ~
I 01
{ i {
-'-,-,--
.
K:~-"
~ ,
I. . . . gl
/
I
JJiL
150 Fa4 = 1.8 ] I
100
50 I 0
50
I00
150
200
25O
Day
Fig. 2. Daily water discharge (fixed storage factor).
300
3~o
400
AN1S and N O U R : 180
PHOTOVOLTAIC
POWERED
PUMPING
,
!
140
i F.1=74
I
1129
,
!
I
I!1 J t ~.~., : - - . ; ...................... !!i............ "'-
F s = 1.9 ................
160 '
SYSTEM
~i - . - t
L I
'
....* Ig t15..
II !
120
100 d
C~ 80 F,3 - 3.7 60
I
N!
40
i li
20 0 . 0
100
50
,~.......................i...................... i..........t.
.
........... ................:!/?i
"'i............
F~'t = 1.8
150
.
.
~. rr.................
'
........ [...............
I:i
!
200
tii,,
250
350
300
400
Day Fig. 3. Directly coupled daily water discharge (fixed storage factor).
days where all curves coincide. O f course, when SOC is kept high, the battery lifetime is prolonged, however this advantage doesn't justify enlarging the battery storage factor. T o check, if given values o f Fa, Fw and F~ satisfy the load requirement, one has to run a complete year detailed simulation p r o g r a m . The p r o g r a m gives the daily water discharge; if it is larger than the load requirement
300
.
i
i,
i.,~
,
:
~ , : ~'IL%_".tL
F,=7.4
• ]'ittt![i"t~' . . . . . . . .;. . . . .i . . . -. ' I~ ~""~!
250 ~('I~
• '
"
U:
--
di,,t]ltli,l 1,
O'
150
] . . . . 4""" ": .................. ;'l ............ :".......
,
•
[
I
'
tl
:
'
i
: ~_~r~
~
'/ . . .~ ~! ' : , .... t ::'ii.... ~.-4.~........ ~...~t,i ....... I ...... ] :'-....... 11 F~2 = 2 " 8
2 0 0 A ! i ][ ~1 ~
!
Fvt=0"9
I
i::i
:
F.~
~ F,~
i
,
!'~
"
! F.3
~ :
.. . . .
'"
:
~1~
*
50
0
! 50
100
150
I
~"~
!lilt
.......... ]................. "':' ............ i " ' t . . . . . . . . . . . . . .
:
200
'
:=7, '~i
[
:
'
:
I
'1 ,
izl
, t ~!!
I!i !! '
i
uftlilJl
i"1 [
*
I *. ' F *L ' i i It...................... g!.......... t. lli i"" ~' ................... tl
:
~oo-~-~-!-r-¢-l,!..................................
'
~ ,~~' ' ' ' ' ~i ! l*"'+Lt
r
1
250
Day Fig. 4. Total daily p o w e r discharge (fixed array factor).
300
i
:
i
350
400
1130
ANIS and NOUR:
0.9
PHOTOVOLTAIC POWERED PUMPING SYSTEM
•
0.8
i
0.7
7.4
.................. i
..11:1 ........
F. I l l : ,
ill!
0.6
0
F~l = 3.7
0.5
I"fii i i i i il
... ,w
Fs2 = 2.8
0.4
Fs3 = 1.9
0.3
I
i
0.2
........
..................;..............i....
Fs4 = 0.9
I ,. i ...................
I
, 0.1
0
50
100
I
150
I
J
I
200
250
300
350
400
Day Fig. 5. Final daily SOC (fixed array factor).
throughout the year, without a single day exception, the solution is accepted, otherwise the solution is refused. Table 1 indicates that the optimum parameters are Fa=2.83,
Fs=0.37
and
Fw=l.8.
This optimum solution results in a water pumping cost of 2.65 c/m 3 pumped from 30 m depth. CONCLUSIONS The optimum design of a PV powered pumping system leading to minimum cost of pumping 1 m 3 has to consider the three basic parameters, namely, PV array size, battery storage size and water tank size. It is found that the optimum solution is that which minimizes the PV array size. This is because the array cost is the major one. Increasing the battery storage without increasing array size has a non-significant effect on system performance. The designer has to choose one of two alternatives, either to increase the water tank size or to increase both array and battery storage sizes simultaneously. The former choice is economically justified. REFERENCES I. J. Appelbaum and J. Bany, 1st Commission of European Communities Conf. on Photovoltaic Solar Energy, Luxembourg, 27-30 September, Reidel, Dordecht (1979). 2. J. Appelbaum and J. Bany, SoL Energy 22, 439 (1979). 3. J. Roger, SoL Energy 23, 193 (1979). 4. W. Anis and H. Metwally, Dynamic performance of photovoltaic pumping systems. To be published. 5. W. Anis and M. Nour, Switching mode photovoltaic pumping system. A M S E International Conf. on Signals and Data, Moscow, 30 June-2 July (1993). 6. W. Anis, R. Mertens and R. van Overstraeten, Sol. Wind Technol. 2, 9 (1985).
~
Pergamon
0196-8904(94)00018-2
OPTIMUM
DESIGN
OF
Copyright c~')1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0196-8904/94 $7.00+ 0.00
A PHOTOVOLTAIC
PUMPING
POWERED
SYSTEM
WAGDY R. ANISt and M. A. NOURZ# 'Electronics and Communication Department, Faculty of Engineering, Ain Shams University, I Sarayat St., Abbasia, Cairo, Egypt and 2Electronics Department, Yanbou Industrial College, P.O. Box 30436, Yanbou AI Sinaiyah 21477, Kingdom of Saudi Arabia (Received 28 June 1993: receit,ed for publication 14 June 1994)
Abstract--Photovoltaic (PV) powered pumping systems are relatively simple and reliable, hence they are applied worldwide. Two conventional techniques are curently in use; the first is the directly coupled technique where a PV array is directly coupled to a d.c. motor-pump group, and the second is the battery buffered PV pumping system where a battery is connected across the array to feed the d.c. motor driving a pump. Recently, a third system is proposed to make use of the advantages of the previously mentioned conventional systems. It is the switched mode PV powered pumping system. The switched mode PV powered pumping system couples the pumping system to the PV array directly when the storage battery is fully charged as explained in Ref. [5]. The objective of such a system is the maximum utilization of available solar radiation to minimize the cost per pumped cubic meter from a given water depth. For a given location, four main parameters affect the design of this system; (1) d.c. motor-pump group parameters, (2) PV array size, (3) battery storage size and (4) water storage tank size. The system designer has to determine the previously mentioned four parameters so that the minimum cost per pumped cubic meter is achieved. It is found that some factors are more effective in reducing the cost than others. The PV array size is the predominant factor, while the battery storage and water tank sizes have relatively less effect. The system installation cost is considered in the detailed economic analysis discussed in this work. Photovoltaic
Pumping
Simulation and design
INTRODUCTION P h o t o v o l t a i c (PV) p u m p i n g systems m a y be classified as follows: (1) Directly c o u p l e d systems where the PV a r r a y is directly c o u p l e d to a d.c. m o t o r - p u m p group. Such a system is simple a n d reliable, but the m o t o r is n o t o p e r a t i n g c o n t i n u o u s l y at its o p t i m u m o p e r a t i n g p o i n t due to the c o n t i n u o u s v a r i a t i o n o f solar irradiance. References [1-3] have a n a l y s e d the steady state p e r f o r m a n c e o f this system, while the d y n a m i c p e r f o r m a n c e is studied in Ref. [4]. (2) Battery buffered systems where a storage b a t t e r y is connected across the PV array, a n d the d.c. m o t o r is o p e r a t i n g at a l m o s t c o n s t a n t voltage (note that the b a t t e r y voltage varies a r o u n d its n o m i n a l value), a n d as a rcsult, the d.c. m o t o r is o p e r a t i n g at a l m o s t its o p t i m u m o p e r a t i n g point. This system has two a d v a n t a g e s over the directly c o u p l e d one. Firstly, w a t e r m a y be p u m p e d d a y a n d night, thus the water discharge is larger. Secondly, the d.c. m o t o r is o p e r a t i n g at its o p t i m u m o p e r a t i n g point, a n d consequently, the system efficiency is enhanced. A m a j o r d i s a d v a n t a g e o f such a system is the extra system cost due to the a d d e d b a t t e r y cost. Thus, a b a t t e r y buffered system allows m o r e water p u m p i n g but at higher system cost. Again, the criterion d e t e r m i n i n g which system is better e c o n o m i c a l l y is the cost o f a p u m p e d cubic meter. A n o t h e r d i s a d v a n t a g e o f this system is the energy loss due to a r r a y disconnect when the b a t t e r y is fully c h a r g e d d u r i n g high solar r a d i a t i o n p e r i o d s as explained in Ref. [5]. (3) Switched m o d e PV p u m p i n g systems which are designed to o v e r c o m e the p r o b l e m o f the energy loss. This system uses a storage b a t t e r y as a buffer between the PV a r r a y a n d the p u m p i n g system, b u t a novel b a t t e r y voltage r e g u l a t o r is designed to connect the PV a r r a y directly to tTo whom all correspondence should be addressed. 1123
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ANIS and NOUR:
PHOTOVOLTAIC
POWERED PUMPING SYSTEM
d.c. motor
D -+
7%’ PV array
Water distribution network Fig. 1. Schematic diagram of a PV powered pumping system.
the pumping system when the storage battery is fully charged. Thus, the energy loss due to array disconnect is drastically reduced [5]. The block diagram of this system is indicated in Fig. 1. This work considers the design of a switched mode PV pumping system and discusses the effect of different parameters influencing the system design. The design objective is to determine the optimum design leading to minimum cost. SYSTEM
PARAMETERS
Figure 1 shows a block diagram of a switched mode PV pumping system. The pinciples of operation, as well as the modelling, of this system are fully explained in Ref. [5]. The developed model takes into consideration the following factors: (1) (2) (3) (4) (5) (6) (7)
The The The The The The The
instantaneous variation of solar irradiance in Cairo city (30”N) effect of ambient temperature on the PV array performance effect of both series and shunt resistors of PV array effect of charging and discharging current on battery voltage effect of the instantaneous state of charge on battery voltage effect of battery capacity on battery performance dc. motor-pump group characteristics
To develop a general design, regardless of motor-pump following parameters are defined: (1) The array factor (F,) is defined as
size or the site under consideration, the
F _ Peak power of the PV array (kW) aLoad power (kW) F, = Pp 1PL
(1)
where Pp is the peak power of the array and PL is the load power, both expressed in kilowatts. (2) The storage factor (F,) is defined as F = Battery storage capacity (kWh) s Daily load energy (kWh) F, = S/24P,
(2)
where S is the battery storage expressed in kWh. The factor 24 represents the hours of the day. If both load power and daily load energy varies from day to day, then equations (1) and (2) consider the annual average daily load demand and the annual average daily load consumption. Note that I;, and F, are dimensionless since they are ratios. For the PV pumping system, the designer may consider one of the following alternatives to achieve his ultimate goal of minimum cost. (1) Continuous 24 h operation of the motor pump. This choice requires a relatively large battery storage size and larger amount of pumped water. If the water demand is continuous, such a design will reduce the water storage tanks.
ANIS and N O U R :
P H O T O V O L T A I C P O W E R E D P U M P I N G SYSTEM
1125
(2) Daily operation only. Hence, the water is pumped only whenever solar radiation is available. If the load demand is continuous, then one has to pump more water during the day to supply the load demand during the night. Such a design necessitates a larger motor-pump group, larger array size and larger water storage tanks. On the other hand, this design does not need a large battery storage. The preference between the two alternatives depends on (1) load water demand througout a complete year and (2) system economics, the lower the cost of 1 m 3 pumped, the better the design. From the above discussion, it is necessary to define a water storage factor Fw Water tank storage size (m 3) Sw Fw = Daily load water demand (m 3) --- bPL"
(3)
The daily load water demand is proportional to load power PL and Sw is the water storage tank size. In equation (3), b is a constant whose units are (m3/kW). Again, Fw is a dimensionless parameter. Another factor to be considered to achieve the minimum cost is the pump installation cost. To express this parameter as a dimensionless factor, let us define the pump installation cost parameter (Fp) as follows: Fp = Pump installation cost ($) (4) PV array cost ($) The pump installation cost depends mainly on the geology of the site where the pump is to be installed. If water is to be pumped from a well in a rocky area, the pump installation cost will be high, while if water is pumped from surface water, the pump installation will be low and so on. The above mentioned parameters enable one to determine the optimum solution of a given case. ECONOMIC ANALYSIS Since the economics is the predominant parameter in the system design, one defines the unit cost function Cu as follows Cu=
Overall system cost during system's lifetime Total amount of pumped water during the same period"
The total amount of daily pumped water is proportional to the load power PL. If the overall system cost is denoted by CT, one may write
Cu = CT/365NbPL
(5)
where N is the expected lifetime of the system (expressed in years). The factor 365 is simply the number of days per year. Overall system cost includes: PV array cost including its installation, battery storage cost including wiring and battery voltage regulator costs, water storage tank cost including piping and installation costs and operation and maintenance cost during a given period. The expected lifetime of the PV array is 20 yr. Thus, the economic analysis given hereafter is based on a 20 yr period. The storage batteries lifetime does not exceed 5 yr for commercial industrial lead acid batteries. The operation and maintenance costs include the d.c. motor brushes change, storage battery maintenance (addition of distilled water or acid and checking of battery cells voltage) and water storage tank cleaning. Since most of the system cost is paid at the system installation time, while the amount of water is produced during the system's expected lifetime, the economic analysis should consider this factor. The parameters to be considered are the money discount rate (d) and the inflation rate of battery storage (is). Let us now develop the economical model to be used to determine the optimum solution. The major constraint of the solution is that the load water demand throughout the year is assumed to be constant day and night. Thus, even during cloudy days, the water tank should be capable of delivering the load water demand. Assume that the PV array expected lifetime is N yr (usually considered 20 yr) and that of the battery storage is k yr (usually considered 5 yr). Thus, the cost of the storage battery is paid at the beginning of system installation (considered zero time) and partially paid each k years. If the
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ANIS and NOUR: PHOTOVOLTAICPOWERED PUMPING SYSTEM
cost of 1 kWh of storage batteries is Cs, the present value of the storage battery replacement cost CR is given by [6] CR = S{Cs[1 + (Is - d)] k + Cs[1 + (Is - d)] 2k+ ' "
+ Cs[1 + (Is - d)] N-k}
where S is the battery storage capacity expressed in kWh. Since, from equation (2), S = 24FsPL, then manipulating, one may write CR = 24FsPLC~[1 + ( I s - d)]k{[1 + (ls- d)] u k _ 1}/{[1 + (Is--d)] k - 1}.
(6)
The initial cost of the system C~ (paid at the installation time) is composed of the array cost, the cost of the initial storage battery whose capacity is S and the cost of the water storage tank. If the cost of 1 kW (peak) of the PV array is Ca($/kWp), the array cost is C, Pp. Using equation (1), the array cost will be CaFaPL . If the cost of water storage is Cw($/m3), then using equation (3), the water tank cost will be bFwCwPL. Thus, the initial system cost is Ci
=
CaFaPL -I- 24FsPL Cs + bFwCwPL + Cins.
(7)
The last term in equation (7) is the pump installation cost. From equations (1) and (4), one can write ci.s = rpr~ CaeL. (8) The total system cost CT is CT = Ci + CR.
(9)
Combining equations (5)-(9) yields: Cu = (1/365Nb){CaFa(1 + Fp) + 24FsCs + bFwCw
+ 24FsCs[1 + (Is - d)]k{[1 + (Is -- d)] N-k - 1}/{[1 + (ls - d)] k - 1}}. (10) Equation (10) gives the per unit cost in terms of the system parameters Fa, Fs, Fp and Fw. The other parameters in equation (10) are the unit costs of PV array Ca, battery storage Cs, water storage tank Cw and installation Fp. WATER TANK SIZE It is assumed that the load water demand is constant day and night throughout the year. The load water demand will be denoted by QL (ma/day). The PV pumping system pumps a varying amount of water according to the available solar radiation and the energy stored in the batteries. For a PV pumping system, one may identify three parameters for the pumped water. They are the annual average daily water discharge Qa, maximum daily water discharge Qm,x and minimum daily water discharge Qmi,. The previously mentioned water discharge parameters are computed on an annual basis and their units are (m3/day). Since the load requires QL (m3/day), if the amount of pumped water by the system is smaller than QL, the difference should be obtained from the water tank. The worst condition takes place during cloudy days where the system depends mainly on the storage energy in the batteries. During cloudy days, the system's water discharge is Qm~n. If the number of successive cloudy days is m, the minimum tank storage size (Sw)mi, is
(Sw)min
=
(m + I)(QL -- Qmi,).
(11)
In equation (11), the term (m + 1) is used instead of m because the cloudy days start with the night of the previous sunny day and end with the night of the last cloudy day, hence there is an extra day of storage required. Actually, a cloudy day represents about 12 h of the night before and the night after, representing almost 24 h, hence the duration of insufficient solar energy for a single cloudy day is 36 h or 1.5 days. For m cloudy days, there should be enough stored energy or water for (m + 0.5) days. For conservative design, we consider this factor to be (m + 1). The load demand determines the size of the d.c. motor-pump to be used in the system. If the rated discharge of a motor-pump group is Q0 (m3/h), the load demand should not exceed 24Q0 (m3/day). Practically, when the load demand is determined, the motor-pump group rating is computed from the following inequality: Q0 > QL/24.
(12)
ANIS and NOUR:
PHOTOVOLTAIC POWERED PUMPING SYSTEM
1127
Note that the factor 24 in the inequality (12) arises from the fact that Q0 is an hourly discharge, while QL is the daily load water demand. To convert the inequality into an equation, one may assume a factor of safety R (greater than unity), and hence, the inequality (12) may be rewritten as
Qo = QL R/24.
(13)
The safety factor R is used because the motor-pump group cannot operate at its optimum operating point continuously due to battery voltage and, temperature continuous variations. To determine the load power PL (expressed here in watts) required, one has to know the overall water head h (m) of the system which is the sum of the water depth and the water tank height. The load power is related to the overall water head h and rated discharge Q0 (expressed here in ma/s) through t/PL(W) = Qo (m3/s)pg h (14) where ~/ is the pump efficiency p is the water density (1000 kg/m 3) g is the earth's gravitational acceleration (9.8 m/s2). If it is required to keep PL expressed in (kW) and Q0 in (m3/h), one has to add a constant 'a' in equation (14) to rectify the equation according to the required dimensions, hence equation (14) may be rewritten as r/e L (kW) = aQo (m3/h)pgh. (15) Equations (13) and (15) enable the designer to determine both PL and Q0. INTERDEPENDENCE
OF S Y S T E M
PARAMETERS
Let us consider a load demanding 100 m3/day and the water is pumped from a well of 25 m depth. Assume that the water tank height is 5 m, then the overall water head of the pump is 30 m. Assuming that R = 2, equation (13) gives the value of Q0 = 8.33 m3/h. Making use of equation (14) and assuming 80% pump efficiency, one obtains PL = 868 W. A d.c. motor operating at 48 V and 18 A would be a reasonable choice. The forthcoming analysis is based on this selected system. Now one has to determine the optimum array, battery storage and water tank sizes leading to meet the load demand at minimum cost. The pump installation factor Fp is considered to be 0.15, this means that the installation cost is assumed to be 15% of the PV array cost. The water storage factor Fw, according to equations (3) and (11), depends on the number of successive cloudy days at the site under consideration (m) and the battery storage and array sizes that determine the amount of pumped water during cloudy days Qmin. For Cairo city (30°N), the number of successive cloudy days is considered to be 2, i.e. m = 2. If the battery and array sizes are designed to supply the load water demand for two successive days, a water storage tank of minimum size may be sufficient. The expected PV array lifetime is 20 yr, i.e. N = 20, while the storage battery lifetime is 5 yr only, i.e. k = 5. The money discount rate is considered 10%, i.e. d = 0.1 and the storage battery inflation rate is is considered to be 12%. The constant b in our example is estimated to be 0.1. The cost of 1 kW peak of PV array (Ca) is about U.S. $5000. The storage cost Cs is about U.S. $50/kWh of storage batteries. The cost of a water tank is considered to be U.S. $25/m 3, i.e. Cw = 25. The remaining two parameters are array factor Fa and storage factor Fs. It is seen from equation (10) that the per unit cost Cu increases as Kd or Fs increases. Thus, the optimum economical solution is obtained at the minimum values of K~ and Fs satisfying the load requirements. Note that there is an interdependence between the water tank size and array and battery sizes. This fact may be explained as follows. As battery and array sizes increase, the amount of pumped water during cloudy days increases, hence Qmin increases and consequently (Sw)mm decreases, as seen from equation (i 1). The increase in battery storage and array sizes leads to a decrease in water tank size. The reason is that, if battery storage and array are increased to the extent that the load energy is totally supplied by the storage battery during cloudy days, then Qmin= QL, and from equation (11), one can deduce that the water tank size becomes zero. Table 1 shows 10 groups of system parameters satisfying the load requirement. It is observed from Table 1 that, as Fa and F~ E C M 35/12
I
1128
ANIS and NOUR: PHOTOVOLTAIC POWERED PUMPING SYSTEM Table 1. Systemparameters satisfyingthe load demand and the associated cost in each case System parameters Fa 2.83 3.54 4.55 5.05 5.56 6.06 6.57 7.07 7.58 7.38
F~ 0.37 0.44 0.84 0.95 1.15 1.26 1.47 1.57 1.68 1.76
Fw 1.80 1.70 1.09 0.85 0.78 0.75 0.59 0.40 0.19 0.00
Cu(c/m3) 2.51 3.12 4.23 4.71 5.26 5.74 6.30 6.77 7.26 7.52
increase, Fw decreases as expected. However, the minimum cost is obtained at the minimum value of Fa, since the array cost is the dominant factor in the cost analysis. R E S U L T S AND A N A L Y S I S To obtain the optimum design, all system parameters are kept constant except one parameter only. Thus, a family of curves is obtained. Figure 2 indicates the system water discharge for a constant storage factor Fs and different array factors during a complete year. It is clear that, as Fa increases, the amount of pumped water increases significantly. The directly coupled water discharge is shown in Fig. 3 where it is also seen that it is appreciably affected by the array factor. Figure 4 shows the effect of battery storage factor Fs on the amount of pumped water for a constant array factor. It is clear that the storage factor has a minor effect on the water discharge. Thus, the storage factor should be kept at the minimum value that satisfies the system design constraint. Figure 5 indicates that the effect of storage factor on the system performance is that, when Fs increases, the state of charge of the battery (SOC) is kept generally higher except during cloudy
300
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AN1S and N O U R : 180
PHOTOVOLTAIC
POWERED
PUMPING
,
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1129
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Day Fig. 3. Directly coupled daily water discharge (fixed storage factor).
days where all curves coincide. O f course, when SOC is kept high, the battery lifetime is prolonged, however this advantage doesn't justify enlarging the battery storage factor. T o check, if given values o f Fa, Fw and F~ satisfy the load requirement, one has to run a complete year detailed simulation p r o g r a m . The p r o g r a m gives the daily water discharge; if it is larger than the load requirement
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Day Fig. 4. Total daily p o w e r discharge (fixed array factor).
300
i
:
i
350
400
1130
ANIS and NOUR:
0.9
PHOTOVOLTAIC POWERED PUMPING SYSTEM
•
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i
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200
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300
350
400
Day Fig. 5. Final daily SOC (fixed array factor).
throughout the year, without a single day exception, the solution is accepted, otherwise the solution is refused. Table 1 indicates that the optimum parameters are Fa=2.83,
Fs=0.37
and
Fw=l.8.
This optimum solution results in a water pumping cost of 2.65 c/m 3 pumped from 30 m depth. CONCLUSIONS The optimum design of a PV powered pumping system leading to minimum cost of pumping 1 m 3 has to consider the three basic parameters, namely, PV array size, battery storage size and water tank size. It is found that the optimum solution is that which minimizes the PV array size. This is because the array cost is the major one. Increasing the battery storage without increasing array size has a non-significant effect on system performance. The designer has to choose one of two alternatives, either to increase the water tank size or to increase both array and battery storage sizes simultaneously. The former choice is economically justified. REFERENCES I. J. Appelbaum and J. Bany, 1st Commission of European Communities Conf. on Photovoltaic Solar Energy, Luxembourg, 27-30 September, Reidel, Dordecht (1979). 2. J. Appelbaum and J. Bany, SoL Energy 22, 439 (1979). 3. J. Roger, SoL Energy 23, 193 (1979). 4. W. Anis and H. Metwally, Dynamic performance of photovoltaic pumping systems. To be published. 5. W. Anis and M. Nour, Switching mode photovoltaic pumping system. A M S E International Conf. on Signals and Data, Moscow, 30 June-2 July (1993). 6. W. Anis, R. Mertens and R. van Overstraeten, Sol. Wind Technol. 2, 9 (1985).