- Email: [email protected]
PV pumping analytical design and characteristics of boreholes
Pergamon
PII: S0038 – 092X( 99 )00050 – X
Solar Energy Vol. 68, No. 1, pp. 49–56, 2000 1999 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X / 00 / $ - see front matter
www.elsevier.com / locate / solener
PV PUMPING ANALYTICAL DESIGN AND CHARACTERISTICS OF BOREHOLES ˜ L. NARVARTE†, E. LORENZO and E. CAAMANO ´ Solar, ETSI Telecomunicacion, ´ Ciudad Universitaria s / n, 28040 Madrid, Spain Instituto de Energıa Received 1 December 1998; revised version accepted 31 May 1999 Communicated by JOACHIM LUTHER
Abstract—PV pump manufacturers usually provide standardized graphic tools relating water output with PV array power, under given radiation conditions and for constant pumping head. This paper proposes a simple procedure allowing the use of such graphics for the design of boreholes showing significant water level variations with the water flow rate, which lead to important pumping head variations during the day. The procedure requires a knowledge of three parameters widely used for borehole characterization: ‘static level’, ‘dynamic level’ and ‘maximum flow rate’, and is based on a very simple analytical description of results from a simulation exercise. 1999 Elsevier Science Ltd. All rights reserved.
electric power to the input of the motor-pump unit, PEL , is given by
1. INTRODUCTION
Since the first installations in 1978 (Barlow et al., 1991), the PV-pumping market has being consistently growing; some studies indicate more than 10,000 PV pumps in operation up to 1994 and predict about fifty times this figure for 2010 (Commission of the European Communities, 1995). Many of them will be devoted to the supply of water to rural villages from medium head boreholes of 15 to 50 metres (Kabore, 1994; Lorenzo, 1997). A typical scheme of a PV-pumping system, comprising PV-array, power conditioning unit, motor-pump unit, as well as piping system and storage reservoir, is depicted in Fig. 1. The hydraulic power, PH , required to pump water is a function of both the apparent vertical head, HV , and the water flow rate, Q (numerically equal to mass-flow rate since the specific gravity of water is unity), as it is indicated by the formula PH 5 gQHV , where g is the acceleration due to gravity. This can be written as follows, if Q is expressed in (m 3 h 21 ), HV in (m), and PH in (W): PH 5 2.725 ? Q ? HV
PH 1 Pf PEL 5 ]]] hMP
where hMP is the efficiency of the motor-pump unit. The value of PH 1Pf is, in fact, the mechanical power at the output of the pump. Usually, it is considered as equivalent to the hydraulic power required to pump water at the flow rate Q, with a total head, HT , given by HT 5 HV 1 Hf
(3)
where Pf Hf 5 HV ? ] PH
(4)
On the other hand, the electric power from a PV system which is composed of a PV-array and an inverter is given by G PEL 5 PNOM ? ]] ? h A ? hI GREF
(1)
(5)
where PNOM is the power of the PV-array under Standard Test Conditions (STC: irradiance51000 W/ m 2 , AM 1.5, cell temperature5258C), G is the on plane irradiance, GREF is the irradiance at STC, h A is an array performance factor considering cell temperature, wiring and mismatch losses, and hI is the inverter efficiency. The volume of water pumped throughout the day is given by
Assuming that the pumped water emerges from the outlet at an insignificant velocity, the output power from the pump needs to cover PH plus the friction losses in the pipes, Pf . Consequently, the
†
(2)
Author to whom correspondence should be addressed. Tel.: 134-91-549-5700; fax: 134-91-544-6341; e-mail: [email protected] 49
50
L. Narvarte et al.
Fig. 1. Typical scheme of a PV water pumping system for drinking water supply. HV is the vertical head from the outlet of the water to water level, and HOT is the vertical height from the outlet of the water to the ground.
P ? G ?h ?h E ]]]]]] dt 2.725 ? G ? H NOM
Qd 5
day
A
REF
MPI
(6)
T
where
hMPI 5 hMP ? hI
(7)
Because of irradiance and ambient temperature variations, and also due to the dynamic of the wells, all the above mentioned parameters (G, h A , hMPI , HV and HT ) vary with time, so that to directly solve Eq. (6) is far from being a straightforward task. To help designers, PV pump manufacturers usually test the performance of their PV pumps under various conditions and provide graphic tools allowing to solve Eq. (6) under given conditions of radiation and ambient temperature, and under the specific assumption of constant total head. Fig. 2 shows performance curves for a
particular power conditioning–motor pump combination, based on an 11 hour Standard Solar Day (International Standard IEC 61725, 1997), SSD, and constant ambient temperature of 308C. Note that this graph helps to determine the value of PNOM for given Q d , HT and Gd values. In other words, it allows to size the PV pump for a given water requirement. Because of its intrinsic simplicity, the use of the Standard Solar Day and constant total head has been extensively adopted in the past (IT Power, 1984), to the extent of it becoming a standard serving as technical reference in the procurement procedures for the most important PV pumping projects (CILSS, 1989). There is a wide consensus that SSD adequately represents daily irradiance distributions on a mean monthly basis. However, constant total heads occur only when friction losses are negligible and the water level is maintained constant inside the
PV pumping analytical design and characteristics of boreholes
51
Fig. 2. Graphic tool provided by a PV pump manufacturer.
borehole. The first can be assured by using relatively large diameter pipes, which is usually the case, because costly pumping systems, like PV driven units, should only be considered in conjunction with efficient conveyance and field distribution techniques. Head friction losses below 5% must be a general requirement for optimal PV systems (that is to say, HF ,0.05 HT ) (IES, 1995). However, the constancy of the water level requires pumping rates well below the maximum capacity of the borehole. This means under-use of water extraction possibilities and is far from being the optimal case. This paper proposes a simple procedure to extend the use of the above-mentioned graphic tools to the general case of boreholes showing large water level variations with flow rate. 2. DYNAMICS OF BOREHOLES
When pumping, the water level in the borehole tends to drop until the inflow of water flowing ‘downhill’ from the surrounding water table balances the rate at which water is being extracted (see Fig. 3). Consequently, the greater the rate of
extraction, the greater the drop in the water level. The actual drop of the level in a given borehole depends on a number of factors including soil permeability, type and the wetted surface area of the borehole below the water table, and the phenomenon obeys the general diffusion laws (Gibson and Singer, 1979). A pumping test to characterize the draw-down in boreholes is normally done by extracting water with a portable engine-pump, and measuring the drop in level at a certain pumping rate, after the water level has stabilized. Then, three data characterize a borehole after the test: the static level, HST , the dynamic level, HDT , and the test flow rate, Q T (see Fig. 3). Fortunately, in many countries, boreholes are normally pumped as a matter of routine to test their draw-down, so that the information from pumping tests are commonly logged and stored in official records and can be later obtained by potential users. However, it must be taken into consideration that excessive extraction rates on boreholes can damage the internal surface below the water table and cause voids to be formed which then lead to an eventual collapse of the bore. Consequently, a
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L. Narvarte et al.
Fig. 3. Water level variations: diffusion profiles around the borehole.
Table 1. Examples of real boreholes Location Angola Rotunda Simoes de Abreu Chamaco Nongiue Lupale Mimue Morocco Oum Erromane Abdi Iferd Ourika Ait Mersid
Static level HST (m)
Dynamic level HDT (m)
Maximum flow rate Q M AX (m 3 / h)
20 11 12 20 20 16
45 49 32 24 44 53
7.2 8.3 6.9 13 5 8.5
10.8 12.7 9.8 16.4 7.9
25 35 60 18.2 35
17.3 21.6 36 10.8 15.5
maximum flow rate, Q M AX (m 3 / h), exists for each borehole. Information from borehole pumping tests, mentioned above, is usually referred to as the maximum flow rate at which water can be extracted from it (Q T 5Q M AX ). As a particular example, Table 1 shows the characteristic parameters of the boreholes included in some projects designed at the I.E.S 1 . 1
Data provided by the Boureau Technique de Ouarzazate, Ministere de L’Interieur, Royaume du Maroc, and by the ´ Direc¸ao Geral de Aguas do Ministerio da Energia e Petroleos de Angola.
In addition to the usual design parameters, we also compute a parameter g, defined as: HDT 2 HST Q d g 5 ]]] ? ]] HST 5 ? QT
(8)
where Q d is expressed in (m 3 ) and Q T in (m 3 h 21 ). Factor 5, expressed in hours, is empirical and makes g easier to use. Note that g depends on the borehole characteristics and also on the PV pumping rate, and can be understood as a measurement of the extent of the water drop when pumping. Such a drop may
PV pumping analytical design and characteristics of boreholes Table 2. Values of the parameter g for different boreholes and Qd Location Angola Rotunda Simoes de Abreu Chamaco Nongiue Lupale Mimue Morocco Oun Erromane Abdi Iferd Ourika Ait Mersid
g (Q d 515 m 3 )
g (Q d 540 m 3 )
0.52 1.25 0.72 0.04 0.72 0.82
1.39 3.33 1.93 0.12 1.92 2.18
0.23 0.24 0.42 0.03 0.67
0.61 0.65 1.13 0.08 1.78
be insignificant either because the borehole is very stable, ((HDT 2HST ) /HST )→0, or because the pumping rate is well below the borehole capacity, Q d / 5.Q T →0. To give a quick idea, we can establish that g ,0.2 means that water drop can be neglected for designs, which is not the general case, as Table 2 shows. It is worth pointing out that for a daily water demand of 40 m 3 , this happens only in two cases. That is to say, the common approach relying on using the static level together with graphic tools is not, in general, a correct practise. 3. PV PUMPING DESIGN
Because irradiance varies with the time of day, the power available for the pump, the consequential flow rate, and total head imposed on the PV pump also vary with the time. To analyse precisely the relation between irradiance and flow rate, and to generally determine the volume of water pumped during a certain period of time are rather complex tasks. Software tools (Mayer et al., 1992) are available to help with these calculations, but they are sometimes complex to work with, and they need rarely available information like internal motor parameters, etc. On the other hand, it should be taken into account that the task of selecting a proper PV pump and PV array for a particular application is always done with a certain degree of uncertainty which is associated with the variability in solar radiation, which means that, the water output of a PV pump can be predicted only with relatively low accuracy. Typically, monthly irradiation values have a variation of 630% over the long-term mean. Keeping this idea in mind, the use of the above-described graphic tools corresponding to the constant total head idealization can be extended to general boreholes. Returning once more to Eq. (6), an ‘equivalent total head’, HTE , can be
53
defined as the hypothetical constant value leading to the same volume of water, that is: PNOM Q d 5 ]]]]] ? 2.725 ? GREF ? HTE
E G ?h ?h A
MPI
? dt
(9)
day
Note that, for a given HTE , Eq. (9) depends neither on borehole nor on pipe characteristics, but only on climatological conditions and on PV pump characteristics. In order to explore the possibilities of quick HTE calculations, we performed a simulation exercise, using the well-proven DASTPVPS software tool 2 (Baumeister et al., 1993), consisting of: 1. To determine Q d from Gd (0), HOT , HST , HTE , Q T and PNOM (where HOT is the vertical head from the outlet of the water to the ground). All the boreholes described in Table 1 have been simulated for Gd (0)54000 Wh / m 2 , PNOM 5 1810 Wp and HOT 50. We have used two different daily irradiance profiles, respectively corresponding to the SSD and to the Typical Meteorological Year contained in the DASTPVPS database. It is worth mentioning that the differences between the results from these two irradiance profiles are insignificant in all the cases, which confirms the above mentioned validity of the SSD, at least for design purposes. 2. To determine the HTE value leading to the same Q d . This was done by simulating a hypothetical well with an infinite permeability coefficient, so that the draw-down is always zero, and testing different HTE values until the Q d calculated in the previous steps is reached. The analysis of a wide collection of simulated situations leads us to propose the general use of the simple formula: HDT 2 HST HTE 5 HOT 1 HST 1 ( ]]] ) ? Q AP QT 1 HF (Q AP )
(10)
with Q AP 5 a ? Q d 2
(11)
It should be noted that DASTPVPS includes a very precise description of the performance of the motor-pumps, based on a rather large number of experimental tests. Furthermore, DASTPVPS models the dynamic of boreholes by using the Daray’s law, which relates the drawdown with the water output through the radius of well and the permeability coefficient of the aquifer. Because of that we believe that DASTPVPS results can be considered as a proper reference for other calculation exercises.
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L. Narvarte et al.
Table 3. Comparison between the HTE values obtained by the simplification of Eq. (10) and by simulations. The simulation input parameters are: Gd (0)54000 Wh / m 2 ; PNOM 51810 Wp, HOT 50 m Location
Qd 3 (m )
HTE (m) from DASTPVPS
HTE (m) from Eq. (10)
Error (%)
Rotunda Simoes de Abreu Chamaco Nongiue Lupale Mimue Oum Erromane Abdi Iferd Ourika Ait Mersid
33.3 42.2 45.0 41.0 32.3 36.3 53.3 49.8 54.1 47.2 54.6
26.3 20 18 20.5 27 24 12.8 15 12.2 16.5 12
25.4 20.1 18.1 20.6 27.3 23.4 13.1 15.3 13.5 16.4 12.6
3.1 20.3 20.7 20.4 21.0 2.4 22.4 22.2 10.4 0.6 5.1
where a 50.047 (h 21 ) when Q d is expressed in m 3 , and HF (Q AP ) is the head loss in the pipes corresponding to Q AP . Note that Q AP , called ‘apparent flow rate’, is an average flow rate. Table 3 shows some particular results. The low error associated with Eq. (10), despite its simplicity, merits underlining. The validity of Eq. (10) was later confirmed using simulations with different motor-pumps, radiation levels, array powers, and different vertical heights. The precise description of all the cases would be tedious and of little value. Instead, we will only mention that they cover all the range of possibilities we have been able to imagine, even comprising DC pumps without maximum
power tracking facilities, and non-optimised pumps, i.e., having the wrong number of impellers. The mean error for all the cases is around 2%, which clearly shows that Eq. (10) allows us to overcome the complexity associated with the dynamics of boreholes on PV-pumping design, by reducing the problem to a hypothetical static one leading to similar water output. Moreover, in order to explore further the practical usefulness of Eq. (10), we have used it in combination with the graphic tools provided by the manufacturers of the pumps, in order to size the PV array, and again, we have contrasted the results against simulation values. For each borehole described in Table 1, we have used DASTPVPS to determine the Q d and the HTE values corresponding to the four combinations of Gd 54000 and 6000 Wh / m 2 and PNOM 5905 and 1810 Wp (see columns 4 and 5 of Table 4). Then, such Q d and HTE values have been used as input for the graphic tools to obtain a new PNOM value (PNOM (2) in column 6 of Table 4), which ideally must be equal to the one used as DASTPVPS input. As a matter of fact, deviations between both PNOM values can be understood as a measure of the validity of the graphic tools. A mere glance at column 7 of Table 4 leads us to suspect that PV manufacturers generally tend to overestimate the performance of their motor-pumps. Finally, we have used again the graphic tools, this time
Table 4. Comparison between the resultant array peak powers when HTE is used in graphic tools, and the initial array peak power used as input in the simulation tool. The reduction of boreholes with respect to Table 1 serves to reduce the size of this paper Location
Simoes
Rotunda
Nongiue
Oum Erroman Abdi
Iferd
Input
From DASTPVPS
From PV manufacturer graphic tools
From PV manufacturer graphic tools1Eq. (10)
Gd (Wh / m 2 )
PNOM (1) (Wp)
Qd (m 3 / d)
HTE (m)
PNOM (2) (Wp)
Error (P1 2 P2 ) /P1 (%)
PNOM (3) (Wp)
Error (P2 2 P3 ) /P2 (%)
6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000
1810 1810 905 905 1810 1810 905 905 1810 1810 905 905 1810 1810 905 905 1810 1810 905 905 1810 1810 905 905
54.3 42.2 34.2 23.1 46.0 33.3 24.8 13.5 57.1 41.0 30.3 15.9 68.3 53.3 43.5 29.2 65.0 49.8 39.9 25.5 68.9 54.1 44.6 30.6
23 20 18 15 30.0 26.3 24.5 22.3 21.0 20.5 20.5 20.3 13.0 12.8 12.5 12.0 15.5 15.0 14.5 14.0 13.0 12.3 12.0 11.0
1800 1750 850 800 1850 1725 850 775 1750 1725 850 775 1775 1750 900 850 1750 1775 900 825 1825 1800 900 875
0.55 3.31 6.08 11.6 22.21 4.70 6.08 14.36 3.31 4.70 6.08 14.36 1.93 3.31 0.55 6.08 3.31 1.93 0.55 8.84 20.83 0.55 0.55 3.31
1800 1750 850 825 1700 1675 850 775 1750 1725 850 775 1800 1750 900 850 1775 1775 900 825 1900 1850 950 900
0 0 0 23.13 8.12 2.90 0 0 0 0 0 0 21.41 0 0 0 21.43 0 0 0 24.11 22.78 25.55 2.86
PV pumping analytical design and characteristics of boreholes
considering HTE values given by Eq. (10). The values of PNOM (3) presented in column 8 of Table 4 confirm that errors associated with such an equation are virtually negligible. As an example of the difference of using HTE instead of HST , it is possible to calculate with graphic tools the required PV size with these two heights for Simoes de Abreu in the case of Gd (0)56000 Wh / m 2 and Q d 554 m 3 . The result is a nominal peak power of 1800 and 1200 W respectively. On the other hand, compatibility between a borehole and a PV pump requires us to be sure that the flow rate is always below the limit given by Q M AX . PV pump manufacturers also usually provide graphic information about instantaneous output from the pump for given DC power and total head, as Fig. 4 shows. As a rule of thumb, such compatibility is assured if the output from the pump, corresponding to DC power50.8 PNOM and HT 5 HDT 1 HOT , is lower than Q M AX . This condition reflects the fact that the nominal power of the PV array, PNOM , is given under STC, which are rarely reached in real operation. Note that HTE should not be considered here. Finally, one danger if large pumps are used in small boreholes is to draw the water down to the pump intake level, at which stage the pump starts to ‘snore’, that is, it draws a mixture of air and
55
water. A ‘snoring’ pump can be soon damaged, and therefore should be avoided by using any of the technical solutions whose efficacy has been already demonstrated, such as maximum frequency stop capabilities of inverters, level switches incorporated in the inverter, etc. Nevertheless, one good practice is to place the pump intake at the dynamic level of the borehole, so that the pump will not ‘snore’ for outputs smaller than Q M AX . 4. CONCLUSIONS
PV manufacturers usually provide standardised graphic information about the performance of their systems, that allows to directly design the proper PV pump for a given water requirement under the specific assumption of a constant water level. This paper has presented a simple method to extend such graphic tools to the more general case of boreholes showing significant water level variations with water flow rate. Real situations, characterized by pumping head variations along the day, are conceptually assimilated to the constant head case, by defining an ‘equivalent total head’ as the hypothetical constant value leading to the same volume of pumped water. Furthermore, a simulation exercise, by using a well proven
Fig. 4. Instantaneous PV pump output for various DC powers and total heads.
56
L. Narvarte et al.
software tool, has led us to propose a simple equation linking the value of HTE with the standard information usually available for boreholes. Compatibility between PV pumps and boreholes has also been commented on. The proposed method allows the complete design of a PV pump (to select a motor-pump– power conditioning unit, and to size the PV array) for any given water requirement, and in particular solar radiation conditions. Although water needs are not considered in this paper, it is worth emphasising that they usually represent the largest source of uncertainties in real situations. References (Kabore, 1994; IT Power, 1984; Malbranche et al., 1994; Burgess and Prymm, 1985; Doorenbos and Pruit, 1977) are particularly suggested for useful further reading on that.
NOMENCLATURE hA hI hMP hMPI g G (W/ m 2 ) Gd (Wh / m 2 ) Gd (0) (Wh / m 2 ) GREF (W/ m 2 ) HDT (m) Hf (m) HF ( Q AP ) (m) HOT (m) HST (m) HT (m) HTE (m) HV (m) PEL (W) Pf (W) PH (W) PNOM (W) Q (m 3 / h) Q AP (m 3 / h) Q d (m 3 ) Q M AX (m 3 / h)
Array performance factor Inverter efficiency Motor-pump efficiency Motor-pump and inverter efficiency Relevance of water drop On plane irradiance Irradiation on a tilted surface Horizontal daily irradiation Irradiance at Standard Test Conditions Dynamic level Head loss Head loss in the pipes corresponding to Q AP Vertical head from the water outlet to the ground Static level Total head Equivalent total head Vertical head Electrical power to the input of the motorpump Power to cover friction losses Hydraulic power PV array power under Standard Test Conditions Water flow rate Apparent flow rate Volume of water pumped throughout a day Maximum flow rate
Q T (m 3 / h) SSD
Test flow rate Standard Solar Day
Acknowledgements—This work has been in part supported by contract JOU2-CT92-0161 in the context of the JOULE II project. We would like to thank the helpful collaboration of Mr. Oliver Mayer, who gave us every facility to use the PV-pumping software tool DASTPVPS.
REFERENCES Barlow R., McNelis B. and Derrick A. (1991) Status and Experience of Solar PV Pumping in Developing Countries. In Proc. 10 th Europ. PV Solar Energy Conf., Lisbon, Portugal, pp. 1143–1146. Baumeister A., Festl T. and Mayer O. (1993) DASTPVPS, Manual. Commission of the European Communities, JOULE Project: JOUL-0048-P. Brussels. Burgess P. and Prymm P. (1985). Solar Pumping in the Future: A Socio-Economic Assesment, CSP Economic Publications, U.K. CILSS (1989) Appel d’Offres Restreint. In Programme Re¨ gional d’ utilisation de l’ energie solaire Photovoltaıque dans les pays du Sahel, CR-VI FED, Ouagadougou, Burkina Faso The world PV Market to 2010, Directorate Generale for Energy, Brussels. Doorenbos J. and Pruit W. O. (1977). Crop Water Requirements, FAO, Rome. Gibson U. and Singer R. (1979). Manual de los Pozos ˜ Pequenos, Limusa, Mexico. IES (1995) (compiled by) PV Pump Optimization. A Manual to Advise on the Optimization of PV Centrifugal Pump Systems. JOULE II Project: JOU2-CT92-0161. Brussels. International Standard IEC 61725: 1997. Analytical Expression for Daily Solar Profiles. IT Power in association with Sir William Halcrow and Partners (1984) Handbook on Solar Water Pumping. UNDP-World Bank project GLO / 80 / 003, pp. 36–49. Washington. Kabore F. (1994) PV energy for a sustained and social development in the Sahelian region. The Regional Solar Program. In The Yearbook of Renewable Energies, James and James, London. Lorenzo E. (1997) Photovoltaic rural electrification. Progress in Photovoltaics 5, 3–27. ¨ Malbranche Ph., Servant J. M., Hanel A. and Helm P. (1994) Recent Developments in PV Pumping Applications and Research in the European Community. In Proc. 12 th Europ. PV Solar Energy Conf., Amsterdam, The Netherlands, pp 476–481. Mayer O., Baumeister A. and Ferstl T. (1992) A Novel PC Software Tool for Simulation and Design of Photovoltaic th Pumping System. In Proc. 11 Europ. PV Solar Energy Conf., Montreux, Switzerland, pp. 1395–1398.
PII: S0038 – 092X( 99 )00050 – X
Solar Energy Vol. 68, No. 1, pp. 49–56, 2000 1999 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X / 00 / $ - see front matter
www.elsevier.com / locate / solener
PV PUMPING ANALYTICAL DESIGN AND CHARACTERISTICS OF BOREHOLES ˜ L. NARVARTE†, E. LORENZO and E. CAAMANO ´ Solar, ETSI Telecomunicacion, ´ Ciudad Universitaria s / n, 28040 Madrid, Spain Instituto de Energıa Received 1 December 1998; revised version accepted 31 May 1999 Communicated by JOACHIM LUTHER
Abstract—PV pump manufacturers usually provide standardized graphic tools relating water output with PV array power, under given radiation conditions and for constant pumping head. This paper proposes a simple procedure allowing the use of such graphics for the design of boreholes showing significant water level variations with the water flow rate, which lead to important pumping head variations during the day. The procedure requires a knowledge of three parameters widely used for borehole characterization: ‘static level’, ‘dynamic level’ and ‘maximum flow rate’, and is based on a very simple analytical description of results from a simulation exercise. 1999 Elsevier Science Ltd. All rights reserved.
electric power to the input of the motor-pump unit, PEL , is given by
1. INTRODUCTION
Since the first installations in 1978 (Barlow et al., 1991), the PV-pumping market has being consistently growing; some studies indicate more than 10,000 PV pumps in operation up to 1994 and predict about fifty times this figure for 2010 (Commission of the European Communities, 1995). Many of them will be devoted to the supply of water to rural villages from medium head boreholes of 15 to 50 metres (Kabore, 1994; Lorenzo, 1997). A typical scheme of a PV-pumping system, comprising PV-array, power conditioning unit, motor-pump unit, as well as piping system and storage reservoir, is depicted in Fig. 1. The hydraulic power, PH , required to pump water is a function of both the apparent vertical head, HV , and the water flow rate, Q (numerically equal to mass-flow rate since the specific gravity of water is unity), as it is indicated by the formula PH 5 gQHV , where g is the acceleration due to gravity. This can be written as follows, if Q is expressed in (m 3 h 21 ), HV in (m), and PH in (W): PH 5 2.725 ? Q ? HV
PH 1 Pf PEL 5 ]]] hMP
where hMP is the efficiency of the motor-pump unit. The value of PH 1Pf is, in fact, the mechanical power at the output of the pump. Usually, it is considered as equivalent to the hydraulic power required to pump water at the flow rate Q, with a total head, HT , given by HT 5 HV 1 Hf
(3)
where Pf Hf 5 HV ? ] PH
(4)
On the other hand, the electric power from a PV system which is composed of a PV-array and an inverter is given by G PEL 5 PNOM ? ]] ? h A ? hI GREF
(1)
(5)
where PNOM is the power of the PV-array under Standard Test Conditions (STC: irradiance51000 W/ m 2 , AM 1.5, cell temperature5258C), G is the on plane irradiance, GREF is the irradiance at STC, h A is an array performance factor considering cell temperature, wiring and mismatch losses, and hI is the inverter efficiency. The volume of water pumped throughout the day is given by
Assuming that the pumped water emerges from the outlet at an insignificant velocity, the output power from the pump needs to cover PH plus the friction losses in the pipes, Pf . Consequently, the
†
(2)
Author to whom correspondence should be addressed. Tel.: 134-91-549-5700; fax: 134-91-544-6341; e-mail: [email protected] 49
50
L. Narvarte et al.
Fig. 1. Typical scheme of a PV water pumping system for drinking water supply. HV is the vertical head from the outlet of the water to water level, and HOT is the vertical height from the outlet of the water to the ground.
P ? G ?h ?h E ]]]]]] dt 2.725 ? G ? H NOM
Qd 5
day
A
REF
MPI
(6)
T
where
hMPI 5 hMP ? hI
(7)
Because of irradiance and ambient temperature variations, and also due to the dynamic of the wells, all the above mentioned parameters (G, h A , hMPI , HV and HT ) vary with time, so that to directly solve Eq. (6) is far from being a straightforward task. To help designers, PV pump manufacturers usually test the performance of their PV pumps under various conditions and provide graphic tools allowing to solve Eq. (6) under given conditions of radiation and ambient temperature, and under the specific assumption of constant total head. Fig. 2 shows performance curves for a
particular power conditioning–motor pump combination, based on an 11 hour Standard Solar Day (International Standard IEC 61725, 1997), SSD, and constant ambient temperature of 308C. Note that this graph helps to determine the value of PNOM for given Q d , HT and Gd values. In other words, it allows to size the PV pump for a given water requirement. Because of its intrinsic simplicity, the use of the Standard Solar Day and constant total head has been extensively adopted in the past (IT Power, 1984), to the extent of it becoming a standard serving as technical reference in the procurement procedures for the most important PV pumping projects (CILSS, 1989). There is a wide consensus that SSD adequately represents daily irradiance distributions on a mean monthly basis. However, constant total heads occur only when friction losses are negligible and the water level is maintained constant inside the
PV pumping analytical design and characteristics of boreholes
51
Fig. 2. Graphic tool provided by a PV pump manufacturer.
borehole. The first can be assured by using relatively large diameter pipes, which is usually the case, because costly pumping systems, like PV driven units, should only be considered in conjunction with efficient conveyance and field distribution techniques. Head friction losses below 5% must be a general requirement for optimal PV systems (that is to say, HF ,0.05 HT ) (IES, 1995). However, the constancy of the water level requires pumping rates well below the maximum capacity of the borehole. This means under-use of water extraction possibilities and is far from being the optimal case. This paper proposes a simple procedure to extend the use of the above-mentioned graphic tools to the general case of boreholes showing large water level variations with flow rate. 2. DYNAMICS OF BOREHOLES
When pumping, the water level in the borehole tends to drop until the inflow of water flowing ‘downhill’ from the surrounding water table balances the rate at which water is being extracted (see Fig. 3). Consequently, the greater the rate of
extraction, the greater the drop in the water level. The actual drop of the level in a given borehole depends on a number of factors including soil permeability, type and the wetted surface area of the borehole below the water table, and the phenomenon obeys the general diffusion laws (Gibson and Singer, 1979). A pumping test to characterize the draw-down in boreholes is normally done by extracting water with a portable engine-pump, and measuring the drop in level at a certain pumping rate, after the water level has stabilized. Then, three data characterize a borehole after the test: the static level, HST , the dynamic level, HDT , and the test flow rate, Q T (see Fig. 3). Fortunately, in many countries, boreholes are normally pumped as a matter of routine to test their draw-down, so that the information from pumping tests are commonly logged and stored in official records and can be later obtained by potential users. However, it must be taken into consideration that excessive extraction rates on boreholes can damage the internal surface below the water table and cause voids to be formed which then lead to an eventual collapse of the bore. Consequently, a
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Fig. 3. Water level variations: diffusion profiles around the borehole.
Table 1. Examples of real boreholes Location Angola Rotunda Simoes de Abreu Chamaco Nongiue Lupale Mimue Morocco Oum Erromane Abdi Iferd Ourika Ait Mersid
Static level HST (m)
Dynamic level HDT (m)
Maximum flow rate Q M AX (m 3 / h)
20 11 12 20 20 16
45 49 32 24 44 53
7.2 8.3 6.9 13 5 8.5
10.8 12.7 9.8 16.4 7.9
25 35 60 18.2 35
17.3 21.6 36 10.8 15.5
maximum flow rate, Q M AX (m 3 / h), exists for each borehole. Information from borehole pumping tests, mentioned above, is usually referred to as the maximum flow rate at which water can be extracted from it (Q T 5Q M AX ). As a particular example, Table 1 shows the characteristic parameters of the boreholes included in some projects designed at the I.E.S 1 . 1
Data provided by the Boureau Technique de Ouarzazate, Ministere de L’Interieur, Royaume du Maroc, and by the ´ Direc¸ao Geral de Aguas do Ministerio da Energia e Petroleos de Angola.
In addition to the usual design parameters, we also compute a parameter g, defined as: HDT 2 HST Q d g 5 ]]] ? ]] HST 5 ? QT
(8)
where Q d is expressed in (m 3 ) and Q T in (m 3 h 21 ). Factor 5, expressed in hours, is empirical and makes g easier to use. Note that g depends on the borehole characteristics and also on the PV pumping rate, and can be understood as a measurement of the extent of the water drop when pumping. Such a drop may
PV pumping analytical design and characteristics of boreholes Table 2. Values of the parameter g for different boreholes and Qd Location Angola Rotunda Simoes de Abreu Chamaco Nongiue Lupale Mimue Morocco Oun Erromane Abdi Iferd Ourika Ait Mersid
g (Q d 515 m 3 )
g (Q d 540 m 3 )
0.52 1.25 0.72 0.04 0.72 0.82
1.39 3.33 1.93 0.12 1.92 2.18
0.23 0.24 0.42 0.03 0.67
0.61 0.65 1.13 0.08 1.78
be insignificant either because the borehole is very stable, ((HDT 2HST ) /HST )→0, or because the pumping rate is well below the borehole capacity, Q d / 5.Q T →0. To give a quick idea, we can establish that g ,0.2 means that water drop can be neglected for designs, which is not the general case, as Table 2 shows. It is worth pointing out that for a daily water demand of 40 m 3 , this happens only in two cases. That is to say, the common approach relying on using the static level together with graphic tools is not, in general, a correct practise. 3. PV PUMPING DESIGN
Because irradiance varies with the time of day, the power available for the pump, the consequential flow rate, and total head imposed on the PV pump also vary with the time. To analyse precisely the relation between irradiance and flow rate, and to generally determine the volume of water pumped during a certain period of time are rather complex tasks. Software tools (Mayer et al., 1992) are available to help with these calculations, but they are sometimes complex to work with, and they need rarely available information like internal motor parameters, etc. On the other hand, it should be taken into account that the task of selecting a proper PV pump and PV array for a particular application is always done with a certain degree of uncertainty which is associated with the variability in solar radiation, which means that, the water output of a PV pump can be predicted only with relatively low accuracy. Typically, monthly irradiation values have a variation of 630% over the long-term mean. Keeping this idea in mind, the use of the above-described graphic tools corresponding to the constant total head idealization can be extended to general boreholes. Returning once more to Eq. (6), an ‘equivalent total head’, HTE , can be
53
defined as the hypothetical constant value leading to the same volume of water, that is: PNOM Q d 5 ]]]]] ? 2.725 ? GREF ? HTE
E G ?h ?h A
MPI
? dt
(9)
day
Note that, for a given HTE , Eq. (9) depends neither on borehole nor on pipe characteristics, but only on climatological conditions and on PV pump characteristics. In order to explore the possibilities of quick HTE calculations, we performed a simulation exercise, using the well-proven DASTPVPS software tool 2 (Baumeister et al., 1993), consisting of: 1. To determine Q d from Gd (0), HOT , HST , HTE , Q T and PNOM (where HOT is the vertical head from the outlet of the water to the ground). All the boreholes described in Table 1 have been simulated for Gd (0)54000 Wh / m 2 , PNOM 5 1810 Wp and HOT 50. We have used two different daily irradiance profiles, respectively corresponding to the SSD and to the Typical Meteorological Year contained in the DASTPVPS database. It is worth mentioning that the differences between the results from these two irradiance profiles are insignificant in all the cases, which confirms the above mentioned validity of the SSD, at least for design purposes. 2. To determine the HTE value leading to the same Q d . This was done by simulating a hypothetical well with an infinite permeability coefficient, so that the draw-down is always zero, and testing different HTE values until the Q d calculated in the previous steps is reached. The analysis of a wide collection of simulated situations leads us to propose the general use of the simple formula: HDT 2 HST HTE 5 HOT 1 HST 1 ( ]]] ) ? Q AP QT 1 HF (Q AP )
(10)
with Q AP 5 a ? Q d 2
(11)
It should be noted that DASTPVPS includes a very precise description of the performance of the motor-pumps, based on a rather large number of experimental tests. Furthermore, DASTPVPS models the dynamic of boreholes by using the Daray’s law, which relates the drawdown with the water output through the radius of well and the permeability coefficient of the aquifer. Because of that we believe that DASTPVPS results can be considered as a proper reference for other calculation exercises.
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Table 3. Comparison between the HTE values obtained by the simplification of Eq. (10) and by simulations. The simulation input parameters are: Gd (0)54000 Wh / m 2 ; PNOM 51810 Wp, HOT 50 m Location
Qd 3 (m )
HTE (m) from DASTPVPS
HTE (m) from Eq. (10)
Error (%)
Rotunda Simoes de Abreu Chamaco Nongiue Lupale Mimue Oum Erromane Abdi Iferd Ourika Ait Mersid
33.3 42.2 45.0 41.0 32.3 36.3 53.3 49.8 54.1 47.2 54.6
26.3 20 18 20.5 27 24 12.8 15 12.2 16.5 12
25.4 20.1 18.1 20.6 27.3 23.4 13.1 15.3 13.5 16.4 12.6
3.1 20.3 20.7 20.4 21.0 2.4 22.4 22.2 10.4 0.6 5.1
where a 50.047 (h 21 ) when Q d is expressed in m 3 , and HF (Q AP ) is the head loss in the pipes corresponding to Q AP . Note that Q AP , called ‘apparent flow rate’, is an average flow rate. Table 3 shows some particular results. The low error associated with Eq. (10), despite its simplicity, merits underlining. The validity of Eq. (10) was later confirmed using simulations with different motor-pumps, radiation levels, array powers, and different vertical heights. The precise description of all the cases would be tedious and of little value. Instead, we will only mention that they cover all the range of possibilities we have been able to imagine, even comprising DC pumps without maximum
power tracking facilities, and non-optimised pumps, i.e., having the wrong number of impellers. The mean error for all the cases is around 2%, which clearly shows that Eq. (10) allows us to overcome the complexity associated with the dynamics of boreholes on PV-pumping design, by reducing the problem to a hypothetical static one leading to similar water output. Moreover, in order to explore further the practical usefulness of Eq. (10), we have used it in combination with the graphic tools provided by the manufacturers of the pumps, in order to size the PV array, and again, we have contrasted the results against simulation values. For each borehole described in Table 1, we have used DASTPVPS to determine the Q d and the HTE values corresponding to the four combinations of Gd 54000 and 6000 Wh / m 2 and PNOM 5905 and 1810 Wp (see columns 4 and 5 of Table 4). Then, such Q d and HTE values have been used as input for the graphic tools to obtain a new PNOM value (PNOM (2) in column 6 of Table 4), which ideally must be equal to the one used as DASTPVPS input. As a matter of fact, deviations between both PNOM values can be understood as a measure of the validity of the graphic tools. A mere glance at column 7 of Table 4 leads us to suspect that PV manufacturers generally tend to overestimate the performance of their motor-pumps. Finally, we have used again the graphic tools, this time
Table 4. Comparison between the resultant array peak powers when HTE is used in graphic tools, and the initial array peak power used as input in the simulation tool. The reduction of boreholes with respect to Table 1 serves to reduce the size of this paper Location
Simoes
Rotunda
Nongiue
Oum Erroman Abdi
Iferd
Input
From DASTPVPS
From PV manufacturer graphic tools
From PV manufacturer graphic tools1Eq. (10)
Gd (Wh / m 2 )
PNOM (1) (Wp)
Qd (m 3 / d)
HTE (m)
PNOM (2) (Wp)
Error (P1 2 P2 ) /P1 (%)
PNOM (3) (Wp)
Error (P2 2 P3 ) /P2 (%)
6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000 6000 4000
1810 1810 905 905 1810 1810 905 905 1810 1810 905 905 1810 1810 905 905 1810 1810 905 905 1810 1810 905 905
54.3 42.2 34.2 23.1 46.0 33.3 24.8 13.5 57.1 41.0 30.3 15.9 68.3 53.3 43.5 29.2 65.0 49.8 39.9 25.5 68.9 54.1 44.6 30.6
23 20 18 15 30.0 26.3 24.5 22.3 21.0 20.5 20.5 20.3 13.0 12.8 12.5 12.0 15.5 15.0 14.5 14.0 13.0 12.3 12.0 11.0
1800 1750 850 800 1850 1725 850 775 1750 1725 850 775 1775 1750 900 850 1750 1775 900 825 1825 1800 900 875
0.55 3.31 6.08 11.6 22.21 4.70 6.08 14.36 3.31 4.70 6.08 14.36 1.93 3.31 0.55 6.08 3.31 1.93 0.55 8.84 20.83 0.55 0.55 3.31
1800 1750 850 825 1700 1675 850 775 1750 1725 850 775 1800 1750 900 850 1775 1775 900 825 1900 1850 950 900
0 0 0 23.13 8.12 2.90 0 0 0 0 0 0 21.41 0 0 0 21.43 0 0 0 24.11 22.78 25.55 2.86
PV pumping analytical design and characteristics of boreholes
considering HTE values given by Eq. (10). The values of PNOM (3) presented in column 8 of Table 4 confirm that errors associated with such an equation are virtually negligible. As an example of the difference of using HTE instead of HST , it is possible to calculate with graphic tools the required PV size with these two heights for Simoes de Abreu in the case of Gd (0)56000 Wh / m 2 and Q d 554 m 3 . The result is a nominal peak power of 1800 and 1200 W respectively. On the other hand, compatibility between a borehole and a PV pump requires us to be sure that the flow rate is always below the limit given by Q M AX . PV pump manufacturers also usually provide graphic information about instantaneous output from the pump for given DC power and total head, as Fig. 4 shows. As a rule of thumb, such compatibility is assured if the output from the pump, corresponding to DC power50.8 PNOM and HT 5 HDT 1 HOT , is lower than Q M AX . This condition reflects the fact that the nominal power of the PV array, PNOM , is given under STC, which are rarely reached in real operation. Note that HTE should not be considered here. Finally, one danger if large pumps are used in small boreholes is to draw the water down to the pump intake level, at which stage the pump starts to ‘snore’, that is, it draws a mixture of air and
55
water. A ‘snoring’ pump can be soon damaged, and therefore should be avoided by using any of the technical solutions whose efficacy has been already demonstrated, such as maximum frequency stop capabilities of inverters, level switches incorporated in the inverter, etc. Nevertheless, one good practice is to place the pump intake at the dynamic level of the borehole, so that the pump will not ‘snore’ for outputs smaller than Q M AX . 4. CONCLUSIONS
PV manufacturers usually provide standardised graphic information about the performance of their systems, that allows to directly design the proper PV pump for a given water requirement under the specific assumption of a constant water level. This paper has presented a simple method to extend such graphic tools to the more general case of boreholes showing significant water level variations with water flow rate. Real situations, characterized by pumping head variations along the day, are conceptually assimilated to the constant head case, by defining an ‘equivalent total head’ as the hypothetical constant value leading to the same volume of pumped water. Furthermore, a simulation exercise, by using a well proven
Fig. 4. Instantaneous PV pump output for various DC powers and total heads.
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L. Narvarte et al.
software tool, has led us to propose a simple equation linking the value of HTE with the standard information usually available for boreholes. Compatibility between PV pumps and boreholes has also been commented on. The proposed method allows the complete design of a PV pump (to select a motor-pump– power conditioning unit, and to size the PV array) for any given water requirement, and in particular solar radiation conditions. Although water needs are not considered in this paper, it is worth emphasising that they usually represent the largest source of uncertainties in real situations. References (Kabore, 1994; IT Power, 1984; Malbranche et al., 1994; Burgess and Prymm, 1985; Doorenbos and Pruit, 1977) are particularly suggested for useful further reading on that.
NOMENCLATURE hA hI hMP hMPI g G (W/ m 2 ) Gd (Wh / m 2 ) Gd (0) (Wh / m 2 ) GREF (W/ m 2 ) HDT (m) Hf (m) HF ( Q AP ) (m) HOT (m) HST (m) HT (m) HTE (m) HV (m) PEL (W) Pf (W) PH (W) PNOM (W) Q (m 3 / h) Q AP (m 3 / h) Q d (m 3 ) Q M AX (m 3 / h)
Array performance factor Inverter efficiency Motor-pump efficiency Motor-pump and inverter efficiency Relevance of water drop On plane irradiance Irradiation on a tilted surface Horizontal daily irradiation Irradiance at Standard Test Conditions Dynamic level Head loss Head loss in the pipes corresponding to Q AP Vertical head from the water outlet to the ground Static level Total head Equivalent total head Vertical head Electrical power to the input of the motorpump Power to cover friction losses Hydraulic power PV array power under Standard Test Conditions Water flow rate Apparent flow rate Volume of water pumped throughout a day Maximum flow rate
Q T (m 3 / h) SSD
Test flow rate Standard Solar Day
Acknowledgements—This work has been in part supported by contract JOU2-CT92-0161 in the context of the JOULE II project. We would like to thank the helpful collaboration of Mr. Oliver Mayer, who gave us every facility to use the PV-pumping software tool DASTPVPS.
REFERENCES Barlow R., McNelis B. and Derrick A. (1991) Status and Experience of Solar PV Pumping in Developing Countries. In Proc. 10 th Europ. PV Solar Energy Conf., Lisbon, Portugal, pp. 1143–1146. Baumeister A., Festl T. and Mayer O. (1993) DASTPVPS, Manual. Commission of the European Communities, JOULE Project: JOUL-0048-P. Brussels. Burgess P. and Prymm P. (1985). Solar Pumping in the Future: A Socio-Economic Assesment, CSP Economic Publications, U.K. CILSS (1989) Appel d’Offres Restreint. In Programme Re¨ gional d’ utilisation de l’ energie solaire Photovoltaıque dans les pays du Sahel, CR-VI FED, Ouagadougou, Burkina Faso The world PV Market to 2010, Directorate Generale for Energy, Brussels. Doorenbos J. and Pruit W. O. (1977). Crop Water Requirements, FAO, Rome. Gibson U. and Singer R. (1979). Manual de los Pozos ˜ Pequenos, Limusa, Mexico. IES (1995) (compiled by) PV Pump Optimization. A Manual to Advise on the Optimization of PV Centrifugal Pump Systems. JOULE II Project: JOU2-CT92-0161. Brussels. International Standard IEC 61725: 1997. Analytical Expression for Daily Solar Profiles. IT Power in association with Sir William Halcrow and Partners (1984) Handbook on Solar Water Pumping. UNDP-World Bank project GLO / 80 / 003, pp. 36–49. Washington. Kabore F. (1994) PV energy for a sustained and social development in the Sahelian region. The Regional Solar Program. In The Yearbook of Renewable Energies, James and James, London. Lorenzo E. (1997) Photovoltaic rural electrification. Progress in Photovoltaics 5, 3–27. ¨ Malbranche Ph., Servant J. M., Hanel A. and Helm P. (1994) Recent Developments in PV Pumping Applications and Research in the European Community. In Proc. 12 th Europ. PV Solar Energy Conf., Amsterdam, The Netherlands, pp 476–481. Mayer O., Baumeister A. and Ferstl T. (1992) A Novel PC Software Tool for Simulation and Design of Photovoltaic th Pumping System. In Proc. 11 Europ. PV Solar Energy Conf., Montreux, Switzerland, pp. 1395–1398.