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A Statistical Analysis of Wind Pump Performance in the Sahel
A Statistical Analysis of Wind
Pump Performance
in the Sahel
R.G. Carothers and G.M. Bragg Department of Mechanical Engineering University of Waterloo Waterloo, Ontario, Canada N2L 301
Abstract A statistical analysis procedure has been developed to improve predictions of performance and cost effectiveness for wind pumps operating in low to moderate wind regimes. The method requires m i n i m a l m e t e o r 1 ogica 1 data and can provide for the o p t i m a l matching of reciprocating pumps and wind rotors. The predicted pumping outputs are compared with field measurements from the Projet Tapis Vert site in the Sahelian region of Niger. Keyword s wind, pump, energy, prediction, matching, optimization, Sahel Inst ant aneous Wind Pump Characteristics Torque c o e f f i c i e n t v e r s u s tip speed ratio c h a r a c t e r i s t i c s for typical c o m m e r c i a l rotors have been used along with p u m p and transmission parameters to describe the instantaneous wind pump system performance and these results have been checked against s t e a d y - s t a t e e x p e r i m e n t a l data from Niger. This s i m p l i f i e d analysis provides reasonably good agreement with the Niger data shown in Fig. 1. A m o r e thorough d y n a m i c a n a l y s i s as outlined in (1) can provide a better e s t i m a t i o n of the low start-up windspeed often observed but this requires a detailed knowledge of the wind history just prior to s t a r t - u p and is t h e r e f o r e difficult to use in practice. The a n a l y s i s procedure a p p r o x i m a t e s the A m e r i c a η - f a r m rotor torque c o e f f i c i e n t as a linearly d e c r e a s i n g function of tip speed ratio. This is c o n s i s t e n t with the wind tunnel tests of (2) as well as the field m e a s u r e m e n t s from Niger but would not c h a r a c t e r i z e the low solidity rotors d e s c r i b e d in ( 3 ) . Rotor torque output can then be specified as a function of rotational 2107
2108
I N T E R S O L 85
speed w h i l e the p u m p torque r e q u i r e m e n t w h i c h includes both h y d r a u l i c and m e c h a n i c a l c o m p o n e n t s is a s s u m e d to v a r y sinusoidally on the up stroke and to be zero on the down stroke. The a s s u m p t i o n s g o v e r n i n g the system o p e r a t i o n are that the starting torque output of the rotor equals the peak pump torque r e q u i r e m e n t but that once s t a r t e d , the rotor output torque equals the mean pump torque due to the averaging effects of the rotor's m o m e n t of i n e r t i a . The stopping v e l o c i t y v^ is then equal to the cut-in velocity v^¿ over y/^T . It is p o s s i b l e to obtain a system power c o e f f i c i e n t and to d e t e r m i n e overall system e f f i c i e n c y as a function of non d i m e n s i o n a l w i n d s p e e d ( w i n d s p e e d ν over v ^ ^ ) . Figure 2 s h o w s that the maximum system efficiency occurs between the cut-in and stopping windspeeds and therefore the contribution to total pump output from this band can be m o r e s i g n i f i c a n t than would be expected given the c o m p a r a t i v e l y low e n e r g y content of these wind s peed s. Wind Regimes To predict the wind pump output for an extended time period the instantaneous wind pump characteristics must be combined with a s t a t i s t i c a l d e s c r i p t i o n of the wind r e g i m e . A l t h o u g h this is best done from extensive wind measurements at the proposed site, the high costs involved often make it impractical particularly for wind p u m p i n g a p p l i c a t i o n s . Since frequently the only m e t e o r o l o g i c a l data a v a i l a b l e are m e a s u r e m e n t s of daily wind run, a t w o - ρ a r a m e t e r W e i b u l l function is g e n e r a l l y c o n s i d e r e d suitable for d e s c r i b i n g the d i s t r i b u t i o n of w i n d s p e e d s on a m o n t h l y or yearly b a s i s . This may be s i m p l i f i e d to a single parameter Rayleigh distribution when mean windspeeds are above 3.5 m / s , ( 4 ) . A typical Weibull distribution of windspeeds is illustrated in Fig. 3 which s h o w s four ranges affecting the o p e r a t i o n of the wind p u m p . The system will not operate b e l o w v^ or above the cut-out v e l o c i t y and will be in c o n t i n u o u s o p e r a t i o n for windspeeds between v^¿ and ν ^. However for windspeeds between V g and v^¿ the wind pump will operate only if the windspeed has entered this range from a b o v e . Thus the c o n t r i b u t i o n to pump output arising from this v e l o c i t y interval will depend on the the detailed c h a r a c t e r i s t i c s of the wind r e g i m e . In the calculation procedure it has been assumed that the probability of the windspeed entering this region from above is equal to the fraction of the total time that the w i n d s p e e d s are above v ^ ¿ . A l t h o u g h this a s s u m e s zero a u t o c o r r e l a t i o n for s h o r t - t e r m windspeed fluctuations, the errors introduced are expected to be small. This is supported by (5). The Weibull shape factor as well as the mean windspeed can have a s i g n i f i c a n t effect on the non d i m e n s i o n a l system output as shown in Fig. 4. Due to the effects of the cut-out w i n d s p e e d low m e a n w i n d s p e e d s s h o w an increase in p u m p output with d e c r e a s i n g 'k' while the reverse is true for the higher m e a n wind speeds.
INTERSOL 85
2109
Long-Term Output Pred ic tIons Tne predicted flow results have been c o m p a r e d with field measurements taken at the Projet Tapis Vert site over a two year period (Fig. 5 ) . While a R a y l e i g h d i s t r i b u t i o n (k«2) p r o v i d e s reasonable agreement for Sahelian conditions at mean windspeeds above 3.5 m / s , a low 'k* W e i b u l l d i s t r i b u t i o n is m o r e s u i t a b l e for the low w i n d s p e e d c a s e . A v a r i a b l e k as suggested in (6) would then be required to provide general a g r e e m e n t over the range of velocities from 2 to 5 m / s . Match ing o f Rotors with Ree iproc at ing Pumps Although it is t e c h n i c a l l y possible to m a t c h wind rotors to a variety of pump t y p e s , with existing c o m m e r c i a l rotors the choice is usually limited to matching a particular rotor with a properly-sized, positive-displacement piston pump. The pumping head and pump d i s c h a r g e can be d e s c r i b e d together in t e r m s of the torque loading placed on the rotor and it is the choice of the torque loading which d e t e r m i n e s the degree to which the windpump is optimally matched to a given wind regime. A longterm system e f f i c i e n c y can be defined as the predicted energy output of the wind pump over the available energy for a Weibull distribution of windspeeds (7). Figures 6(a) and 6(b) show the effects of varying torque loading on the 3 meter diameter Projet Tapis Vert rotor and how this can affect the l o n g - t e r m system effic iency . In Fig. 7 the shape factor k is a function of m e a n w i n d s p e e d . Under such c i r c u m s t a n c e s the choice of o p t i m a l torque loading can be confined to a m o r e limited range than for the cases w h e r e shape factor or mean windspeed are constant. This suggests that in real wind r e g i m e s an o p t i m a l m a t c h i n g of a rotor and pump combination will be valid for a range of windspeeds. Storage Aspect s The o b s e r v e d v a r i a b i l i t y in p u m p o u t p u t s for p a r t i c u l a r windspeeds at the Projet Tapis Vert site will require increased storage f a c i l i t i e s to a c c o m o d a t e u n c e r t a i n t i e s in p r e d i c t i n g daily p u m p i n g r a t e s . This may be further c o m p l i c a t e d w h e r e there is an a u t o c o r r e l a t i o n in daily m e a n w i n d s p e e d s as this implies that calm periods will occur sequentially. Preliminary data suggest that autocorrelations may be significant for lags of 2 to 4 d a y s . The study of the storage a s p e c t s for wind pumping forms the basis of on-going work.
I N T E R S O L 85
2110
Re ferences 1.
E.H. L y s e n , I n t r o d u c t i o n to Wind E n e r g y , Steering C o m m i t t e e on Wind Energy for D e v e l o p i n g C o u n t r i e s , the N e t h e r l a n d s , 1982
2.
J.A.C. K e n t f i e l d , A P e r f o r m a n c e C o m p a r i s o n of Various Wind Turbine Types for P o w e r i n g W a t e r P u m p s , 17th lECEC C H 1 7 8 9 7/82/0000-2082, 1982
3.
H.J.M. B e u r s k e n s , A.J.F.K. H a g e m a n , C D . H o s p e r s , A. K r a g t e n , E.H. L y s e n , Low Speed W a t e r P u m p i n g W i n d m i l l s : Rotor Tests and Overall Performance, Proceedings of the Third I n t e r n a t i o n a l S y m p o s i u m on Wind Energy S y s t e m s ' , D e n m a r k , 1980 W.C. C l i f f , G e n e r a l i z e d Wind Effect on Wind Turbine Output, 2, No 1 & 2, 1976
C h a r a c t e r i s t i c s and Their Wind Technology Journal, Vol
5.
J.C. D i x o n , Load M a t c h i n g E f f e c t s on Wind Energy Performance, lEE C o n f e r e n c e on Future Energy London, 1979
6.
W. F r o s t , B.H. Long, R.E. T u r n e r , E n g i n e e r i n g Handbook on the A t m o s p h e r i c E n v i r o n m e n t a l G u i d e l i n e s for Use in Wind Turbine G e n e r a t o r D e v e l o p m e n t , NASA Technical Paper 1359, 197b
7.
M.J.M. S t e v e n s , P.T. S m u l d e r s , The E s t i m a t i o n of the P a r a m e t e r s of the W e i b u l l W i n d s p e e d D i s t r i b u t i o n for Wind Energy Utilization Purposes, Wind Engineering, Vol.3, No.2, 1979
Ε
1
5|
V. (PTV field me o$uremenf$)
Fit
UTUAUNTOUT •T
VIADIPEED.
OUTPM
Fit.
2
SYTUA
OYTPM
perrorMftAG*.
Converter Concepts,
2111
INTERSOL 85
Instonloneous Wind Pump Output
ν
V · 5.0 m/»
y \/
s /
/ /
' /
\
V
o|~:
\
/ \ f \ / \i ' '/
· 10 m/»
^Typicol Weibull Distribution of Windspeeds
ν „ · 20mA
'
1
1 'CO
Fit.
Operfttittg wittdtpMd for a wind pusp.
3
ψ
raAt«t
^
mtx of l i i i p « fftctor k OS p U B p o u t p u t .
Mfon Windtpfe d
Ϊ > 2 m/t
-j 10 Ooily Mton Windspfid ol 2m Elt»Olion .ϊ ( m / t )
Fig. 5
Dwly puap output vi dailV ••aa vindipood.
Fit.
20 30 Tofque Looding Nm)
40
50
mti or tkap« factor k oa optiaal torqu« loadiat for lont-tora iytus «rricioAqr.
_JjlOm/h.k»20 ^ 3 0 m/h. k« 15
20 30 Tofqu« Loodinq |Nm
Fit.
'^'*^ ^ windtpood OB optiaal torqu« loadiM for loat-tora lysua •rricioacy.
Torque Loodin« (Nm)
Fit. 7
last« of optimal torqu« loadittt for hypotli«ücal coapoiit« wiad ritie«.
Pump Performance
in the Sahel
R.G. Carothers and G.M. Bragg Department of Mechanical Engineering University of Waterloo Waterloo, Ontario, Canada N2L 301
Abstract A statistical analysis procedure has been developed to improve predictions of performance and cost effectiveness for wind pumps operating in low to moderate wind regimes. The method requires m i n i m a l m e t e o r 1 ogica 1 data and can provide for the o p t i m a l matching of reciprocating pumps and wind rotors. The predicted pumping outputs are compared with field measurements from the Projet Tapis Vert site in the Sahelian region of Niger. Keyword s wind, pump, energy, prediction, matching, optimization, Sahel Inst ant aneous Wind Pump Characteristics Torque c o e f f i c i e n t v e r s u s tip speed ratio c h a r a c t e r i s t i c s for typical c o m m e r c i a l rotors have been used along with p u m p and transmission parameters to describe the instantaneous wind pump system performance and these results have been checked against s t e a d y - s t a t e e x p e r i m e n t a l data from Niger. This s i m p l i f i e d analysis provides reasonably good agreement with the Niger data shown in Fig. 1. A m o r e thorough d y n a m i c a n a l y s i s as outlined in (1) can provide a better e s t i m a t i o n of the low start-up windspeed often observed but this requires a detailed knowledge of the wind history just prior to s t a r t - u p and is t h e r e f o r e difficult to use in practice. The a n a l y s i s procedure a p p r o x i m a t e s the A m e r i c a η - f a r m rotor torque c o e f f i c i e n t as a linearly d e c r e a s i n g function of tip speed ratio. This is c o n s i s t e n t with the wind tunnel tests of (2) as well as the field m e a s u r e m e n t s from Niger but would not c h a r a c t e r i z e the low solidity rotors d e s c r i b e d in ( 3 ) . Rotor torque output can then be specified as a function of rotational 2107
2108
I N T E R S O L 85
speed w h i l e the p u m p torque r e q u i r e m e n t w h i c h includes both h y d r a u l i c and m e c h a n i c a l c o m p o n e n t s is a s s u m e d to v a r y sinusoidally on the up stroke and to be zero on the down stroke. The a s s u m p t i o n s g o v e r n i n g the system o p e r a t i o n are that the starting torque output of the rotor equals the peak pump torque r e q u i r e m e n t but that once s t a r t e d , the rotor output torque equals the mean pump torque due to the averaging effects of the rotor's m o m e n t of i n e r t i a . The stopping v e l o c i t y v^ is then equal to the cut-in velocity v^¿ over y/^T . It is p o s s i b l e to obtain a system power c o e f f i c i e n t and to d e t e r m i n e overall system e f f i c i e n c y as a function of non d i m e n s i o n a l w i n d s p e e d ( w i n d s p e e d ν over v ^ ^ ) . Figure 2 s h o w s that the maximum system efficiency occurs between the cut-in and stopping windspeeds and therefore the contribution to total pump output from this band can be m o r e s i g n i f i c a n t than would be expected given the c o m p a r a t i v e l y low e n e r g y content of these wind s peed s. Wind Regimes To predict the wind pump output for an extended time period the instantaneous wind pump characteristics must be combined with a s t a t i s t i c a l d e s c r i p t i o n of the wind r e g i m e . A l t h o u g h this is best done from extensive wind measurements at the proposed site, the high costs involved often make it impractical particularly for wind p u m p i n g a p p l i c a t i o n s . Since frequently the only m e t e o r o l o g i c a l data a v a i l a b l e are m e a s u r e m e n t s of daily wind run, a t w o - ρ a r a m e t e r W e i b u l l function is g e n e r a l l y c o n s i d e r e d suitable for d e s c r i b i n g the d i s t r i b u t i o n of w i n d s p e e d s on a m o n t h l y or yearly b a s i s . This may be s i m p l i f i e d to a single parameter Rayleigh distribution when mean windspeeds are above 3.5 m / s , ( 4 ) . A typical Weibull distribution of windspeeds is illustrated in Fig. 3 which s h o w s four ranges affecting the o p e r a t i o n of the wind p u m p . The system will not operate b e l o w v^ or above the cut-out v e l o c i t y and will be in c o n t i n u o u s o p e r a t i o n for windspeeds between v^¿ and ν ^. However for windspeeds between V g and v^¿ the wind pump will operate only if the windspeed has entered this range from a b o v e . Thus the c o n t r i b u t i o n to pump output arising from this v e l o c i t y interval will depend on the the detailed c h a r a c t e r i s t i c s of the wind r e g i m e . In the calculation procedure it has been assumed that the probability of the windspeed entering this region from above is equal to the fraction of the total time that the w i n d s p e e d s are above v ^ ¿ . A l t h o u g h this a s s u m e s zero a u t o c o r r e l a t i o n for s h o r t - t e r m windspeed fluctuations, the errors introduced are expected to be small. This is supported by (5). The Weibull shape factor as well as the mean windspeed can have a s i g n i f i c a n t effect on the non d i m e n s i o n a l system output as shown in Fig. 4. Due to the effects of the cut-out w i n d s p e e d low m e a n w i n d s p e e d s s h o w an increase in p u m p output with d e c r e a s i n g 'k' while the reverse is true for the higher m e a n wind speeds.
INTERSOL 85
2109
Long-Term Output Pred ic tIons Tne predicted flow results have been c o m p a r e d with field measurements taken at the Projet Tapis Vert site over a two year period (Fig. 5 ) . While a R a y l e i g h d i s t r i b u t i o n (k«2) p r o v i d e s reasonable agreement for Sahelian conditions at mean windspeeds above 3.5 m / s , a low 'k* W e i b u l l d i s t r i b u t i o n is m o r e s u i t a b l e for the low w i n d s p e e d c a s e . A v a r i a b l e k as suggested in (6) would then be required to provide general a g r e e m e n t over the range of velocities from 2 to 5 m / s . Match ing o f Rotors with Ree iproc at ing Pumps Although it is t e c h n i c a l l y possible to m a t c h wind rotors to a variety of pump t y p e s , with existing c o m m e r c i a l rotors the choice is usually limited to matching a particular rotor with a properly-sized, positive-displacement piston pump. The pumping head and pump d i s c h a r g e can be d e s c r i b e d together in t e r m s of the torque loading placed on the rotor and it is the choice of the torque loading which d e t e r m i n e s the degree to which the windpump is optimally matched to a given wind regime. A longterm system e f f i c i e n c y can be defined as the predicted energy output of the wind pump over the available energy for a Weibull distribution of windspeeds (7). Figures 6(a) and 6(b) show the effects of varying torque loading on the 3 meter diameter Projet Tapis Vert rotor and how this can affect the l o n g - t e r m system effic iency . In Fig. 7 the shape factor k is a function of m e a n w i n d s p e e d . Under such c i r c u m s t a n c e s the choice of o p t i m a l torque loading can be confined to a m o r e limited range than for the cases w h e r e shape factor or mean windspeed are constant. This suggests that in real wind r e g i m e s an o p t i m a l m a t c h i n g of a rotor and pump combination will be valid for a range of windspeeds. Storage Aspect s The o b s e r v e d v a r i a b i l i t y in p u m p o u t p u t s for p a r t i c u l a r windspeeds at the Projet Tapis Vert site will require increased storage f a c i l i t i e s to a c c o m o d a t e u n c e r t a i n t i e s in p r e d i c t i n g daily p u m p i n g r a t e s . This may be further c o m p l i c a t e d w h e r e there is an a u t o c o r r e l a t i o n in daily m e a n w i n d s p e e d s as this implies that calm periods will occur sequentially. Preliminary data suggest that autocorrelations may be significant for lags of 2 to 4 d a y s . The study of the storage a s p e c t s for wind pumping forms the basis of on-going work.
I N T E R S O L 85
2110
Re ferences 1.
E.H. L y s e n , I n t r o d u c t i o n to Wind E n e r g y , Steering C o m m i t t e e on Wind Energy for D e v e l o p i n g C o u n t r i e s , the N e t h e r l a n d s , 1982
2.
J.A.C. K e n t f i e l d , A P e r f o r m a n c e C o m p a r i s o n of Various Wind Turbine Types for P o w e r i n g W a t e r P u m p s , 17th lECEC C H 1 7 8 9 7/82/0000-2082, 1982
3.
H.J.M. B e u r s k e n s , A.J.F.K. H a g e m a n , C D . H o s p e r s , A. K r a g t e n , E.H. L y s e n , Low Speed W a t e r P u m p i n g W i n d m i l l s : Rotor Tests and Overall Performance, Proceedings of the Third I n t e r n a t i o n a l S y m p o s i u m on Wind Energy S y s t e m s ' , D e n m a r k , 1980 W.C. C l i f f , G e n e r a l i z e d Wind Effect on Wind Turbine Output, 2, No 1 & 2, 1976
C h a r a c t e r i s t i c s and Their Wind Technology Journal, Vol
5.
J.C. D i x o n , Load M a t c h i n g E f f e c t s on Wind Energy Performance, lEE C o n f e r e n c e on Future Energy London, 1979
6.
W. F r o s t , B.H. Long, R.E. T u r n e r , E n g i n e e r i n g Handbook on the A t m o s p h e r i c E n v i r o n m e n t a l G u i d e l i n e s for Use in Wind Turbine G e n e r a t o r D e v e l o p m e n t , NASA Technical Paper 1359, 197b
7.
M.J.M. S t e v e n s , P.T. S m u l d e r s , The E s t i m a t i o n of the P a r a m e t e r s of the W e i b u l l W i n d s p e e d D i s t r i b u t i o n for Wind Energy Utilization Purposes, Wind Engineering, Vol.3, No.2, 1979
Ε
1
5|
V. (PTV field me o$uremenf$)
Fit
UTUAUNTOUT •T
VIADIPEED.
OUTPM
Fit.
2
SYTUA
OYTPM
perrorMftAG*.
Converter Concepts,
2111
INTERSOL 85
Instonloneous Wind Pump Output
ν
V · 5.0 m/»
y \/
s /
/ /
' /
\
V
o|~:
\
/ \ f \ / \i ' '/
· 10 m/»
^Typicol Weibull Distribution of Windspeeds
ν „ · 20mA
'
1
1 'CO
Fit.
Operfttittg wittdtpMd for a wind pusp.
3
ψ
raAt«t
^
mtx of l i i i p « fftctor k OS p U B p o u t p u t .
Mfon Windtpfe d
Ϊ > 2 m/t
-j 10 Ooily Mton Windspfid ol 2m Elt»Olion .ϊ ( m / t )
Fig. 5
Dwly puap output vi dailV ••aa vindipood.
Fit.
20 30 Tofque Looding Nm)
40
50
mti or tkap« factor k oa optiaal torqu« loadiat for lont-tora iytus «rricioAqr.
_JjlOm/h.k»20 ^ 3 0 m/h. k« 15
20 30 Tofqu« Loodinq |Nm
Fit.
'^'*^ ^ windtpood OB optiaal torqu« loadiM for loat-tora lysua •rricioacy.
Torque Loodin« (Nm)
Fit. 7
last« of optimal torqu« loadittt for hypotli«ücal coapoiit« wiad ritie«.