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Wind energy potential at Palkalainagar
RenewableEnergyVol. 1. No. 5/6, pp. 815-821. 1991 Printed in Great Britain.
0960-1481/91 $3.00+,00 Pergamon Press pie
TECHNICAL NOTE Wind energy potential at Palkalainagar T. V. CHINNASAMY*and T. M. HARIDASAN School of Energy, Environment and Natural Resources, Madurai Kamaraj University, Palkalainagar, Madurai 625 021, India (Received 20 April 1990 ; accepted 10 July 1990)
Abstract--This paper uses the Weibull's distribution function to describe the wind speed frequency distribution at Palkalalnagar (geographical co-ordinates N : 9°54 ', E : 78°54'), Madurai, India using the one year data available. Weibull's parameters are used to estimate the wind data parameters for the site. Of the wind data parameters the most important one is the annual specific output (TA), This is used in determining the annual energy output of a Wind Energy Conversion System (WECS) and in conducting cost-benefit analysis of wind-electricity generation. The parameter is used in evaluating the efficiency of WECS in the same site. Results show the possibilities of harnessing wind energy towards electricity generation.
1. INTRODUCTION Wind energy is one of the indirect sources of solar energy and it is directly proportional to the cube of the wind speed at a particular site. Therefore, the site location is an important factor when installing a WECS. There are several methods to describe the wind speed frequency distribution and hence the wind data for a particular site. Out of the various methods, Weibull distribution has been given more attention since it gives a good fit to experimental data as indicated in a number of published papers [1--4]. Hennessey [5] compared Rayleigh distribution and Weibull distribution and found that the maximum error in energy output of WECS would be about 10% of full rated power when the Rayleigh distribution is used instead of the Weibulrs. Peterson et al. [6] found that Weibull distribution gave an excellent fit to the wind speed distribution prevailing in Denmark. Gupta [7] applied the Weibull distribution to data for 37 stations in India, published by Mani and Mooley [8], and concluded that Weibull distribution matches well with the observed frequency distribution. He also found that Rayleigh distribution predicts a lower specific output for typical WECS, as compared to that calculated from observed frequency distribution in all the 37 cases. Ishwar Chand et al. [9] applied the Weibull distribution for their study on wind energy for natural ventilation in buildings in India. In this paper Weibull's parameters for the Palkalainagar site (University township) have been estimated from the available wind speed data. The Weibull's parameters are used to estimate the other parameters of wind energy for the same site. 2. DATA USED FOR COMPUTATION The available hourly wind speed data, for the year 1980, which was recorded at the meteorological station, Madurai Kamaraj University, Palkalainagar, are used for the analysis of wind energy potential at the site concerned. The data used
for the computation are for 11 months, except January, for which data were not available. Hence all the calculations presented in this paper are based on a total number of 7830 hours. 3. FREQUENCY DISTRIBUTION It is important to know the number of hours per month or per year during which the given wind speeds occurred, To arrive at this frequency distribution we must first divide the entire wind speed domain into a number of intervals, mostly of equal width of 0.5 m s-~. Then, starting at first interval of 0-0.5 m s- t, the number of hours is counted in the period concerned that the wind speed was in this interval as shown in Table 1. When the number of hours in each interval is plotted against the wind speed, the frequency distribution emerges as a histogram for a month or a year (Figs 1 and 2). 4. THE WEIBULL'S PARAMETERS The Weibull probability distribution for wind speed V is given by K V -i f(V) = ( ~ ) ( C ) K exp [ -
(~fJ;
(1)
where K and C are the Weibull's parameters. K = dimensionless shape parameter and C = scale parameter with unit of speed. The cumulative probability function for a speed Vt is given by
Equation (2) may be written in the linear form as * Rajapalayam Rajus' College, Rajapalayam 626 117, India.
Y = a+bX
where 815
(3)
816
Technical Note Table 1. Wind speed duration at Palkalainagar for the year 1980 Range (m s - ' )
Jan
Jul
Aug
Sep
Oct
Nov
Dec
Annual (h)
0 16 19 43 74 85 73 88 72 55 44 39 31 22 21 15 13 5 2 3
0 9 8 35 50 84 116 117 73 72 41 40 29 15 14 16 9 6 5 1
0 3 23 38 60 108 116 112 87 68 42 36 10 13 8 9 1 4 2 1
4 27 55 59 95 78 71 98 54 53 45 20 9 1 0 0 0 0 0 0
10 88 100 167 113 I00 60 37 35 8 2 0 0 0 0 0 0 0 0 0
8 63 85 178 179 117 34 25 16 6 2 1 1 0 0 0 0 0 0 0
6 79 90 141 133 148 59 45 12 18 4 0 0 0 0 0 0 0 0 0
52 679 761 1128 1181 1067 819 683 457 327 226 158 90 57 46 45 23 15 11 5
720
740
741
669
720
715
735
7830
Feb
Mar
Apr
May
Jun
0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 4.5-5.0 5.0-5.5 5.5-6.0 6.0--6.5 6.5-7.0 7.0-7.5 7.5-8.0 8.0-8.5 8.5-9.0 9.0-9.5 9.5-10.0
2 65 95 55 131 100 113 38 25 2 3 0 0 0 0 0 0 0 0 0
11 126 110 121 149 105 59 17 11 6 2 2 0 0 0 0 0 0 0 0
6 121 92 173 105 70 48 34 22 4 12 8 1 0 1 I 0 0 0 0
5 82 84 118 92 72 70 72 50 35 29 12 9 6 2 4 0 0 2 0
Total
629
719
698
744
Y = In [ - l n . ( l -
F(V))]
X = In V~
(4)
K=b C = exp [-a/b].
(5)
The coefficients a and b of the equation (3) were computed using the least square method. To perform this, cumulative frequencies F(Iz) for various speeds were determined from the frequencies in Table 1. Hence with the help of the eqs (4)
and (5), the values K and C can be determined. The values K and C thus obtained are based on the records of an anemometer mounted at a 7 m height. Then the values of Weibull's parameters were converted to the standard anemometer height of 10 m or at any height above the ground by eqs (9). C10
=
Ca[(10/Za)]
(6)
a
K,0 = Ka[1-0.088 In (Z,/10)] and
AnnuoL 1900 ~ = P_86 me-' 1200 r -
K = 1.84
,oL.
LI.
Z~
•
O. I0
5 O I
l
(~
"
1~5
"
"
2.2o
"
3~
4.~
~2~
~
7.~
¢~
~
--
O
Velocity (ms-') Fig. I. Actual and fitted wind speed frequency distribution at Palkalainagar.
(7)
817
Technical Note June 1980 : 4.09 ms-' K : 2.24 90 -
eo
....-1
C = 4.32
....J
-
m s -)
-
25
f I Act.°t 2o
7o 6o
~0 20
I0 0
J
/
40
.d0.~,~
I.~
5
2.~
3.2~
4.2S
~
6.~
7.~
e.2~
9.~'J
O
Vel,.ocit,y I ms-')
Fig. 2. Actual and fitted wind speed frequency distribution at Palkalainagar.
n = [0.37-0.088 In C~I/[1-0.088 In (Z,/10)]
(8)
where Ca and K, are the Weibull's parameters at Za metre, C)0 and Kt 0 are the Weibull's parameters at 10 m and n = the power law exponent. The annual results and also the results for 11 months data are summarised in Table 2. The values K and C at anemometric height are used to find the probability of the distribution for various wind speeds using the eq. (1). The calculated values are plotted in the same graph of the histograms. The agreement between the histograms and the fitted Weibull distributions may be noted (Figs 1 and 2). Hence the Weibull distribution expression can be used to determine the wind characteristics at Palkalainagar.
5. D E R I V E D
FACTORS TO ESTIMATE CHARACTERISTICS
WIND
Equation (1) can be used to find the following factors [9]. Average wind speed 17=CF(I+ 1)
(ms-')
(9)
where F = gamma function. Most probable wind speed
Vmp c I K - - I I 'Ix ( m s - ' ) .
= L~ j
(10)
Time during which wind speed >t Vmp T = exp [ -
(V,,p/C)•].
(11)
Energy pattern factor Table 2. Weibull's parameters at Palkalainagar for the year 1980
EPF = F1 + 3K/(FI + 1/3) 3.
(12)
Energy density At anemometer height 7 m K C (kmph) Jan
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ann
.
2.42 1.93 1.85 1.81 2.24 2.59 2.80 2.25 1.94 2.10 2.14 1.84
.
.
8.39 7.10 8.24 10.55 15.55 16.13 15.34 11.59 7.60 7.78 8.06 10.87
At standard anemometer Power law height 10 m coefficient K C (kmph) n .
2.50 1.99 1.91 1.87 2.31 2.67 2.89 2.32 2.00 2.17 2.21 1.90
E~=0.00031(P)3xEPF
(kWhm-2day -1)
(13)
where I7 = average calculated speed in kmph. All such values calculated from the above stated relations are listed in Tables 3 and 4.
.
8,94 7.60 8,78 11.16 16.28 16.84 16.05 12.23 8.12 8.31 8.60 11.49
0.177 0.192 0.179 0.158 0.129 0.121 0.126 0.150 0.186 0.184 0.181 0.155
6. ESTIMATION OF ANNUAL OR MONTHLY SPECIFIC OUTPUT (TA OR T . ) OF WIND POWER Following the procedure mentioned by Gupta [7], the specific output TA or Tmo is given by TA = PLF x 8760 Tmo = PLF x (no.ofhoursinthemonth),
(14) (15)
where PLF is plant load factor for the corresponding year or month calculated using the Weibull's parameters Kand C at anemometric height. The values so obtained are also tabulated in Table 5.
818
Technical Note Table 3. Wind data at Palkalainagar for the anemometer height 7 m
(actual) (m s- ~)
(calculated) (m s- ')
Vmp (m s- ~)
T (%)
EPF
Ed (kWh m - ~ day-~)
2.27 2.09 2.17 2.71 4.09 4.30 3.77 3.07 2.32 2.32 2.37 2.86
2.06 1.75 2.03 2.61 3.82 3.98 3.80 2.85 1.88 1.91 1.98 2.68
1.87 1.35 1.50 1.88 3.32 3.71 3.64 2.48 1.45 1.59 1.64 1.97
56 62 63 64 57 54 53 57 62 59 59 63
1.62 1.98 2.07 2.13 1.72 1.54 1.46 1.71 1.97 1.82 1.79 2.09
0.21 0.15 0.25 0.54 1.39 1.40 1.16 0.58 0.19 0.19 0.20 0.58
Jail
Feb Mar Apr May Juil Jul Aug Sep Oct Nov Dec Ann
Table 4. Wind data at Palkalainagar for the standard anemometer height I0 m
(actual) (m s- i) Jail
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ann
.
(calculated) (m s- i) .
2.27 2.09 2.17 2.71 4.09 4.30 3.77 3.07 2.32 2.32 2.37 2.86
.
Vmp (m s- a) .
2.02 1.87 2.16 2.75 4.01 4.16 3.98 3.01 2.00 2.04 2.12 2.83
T (%) .
2.03 1.49 1.66 2.06 3.54 3.93 3.85 2.66 1.59 1.74 1.82 2.15
7. COMPARISON OF SPECIFIC OUTPUT AND ENERGY DENSITY The annual specific output and energy density at t0 m height are compared with that of the selected stations in India [7]. These values are listed in Table 6.
Month
The annual specific output TA for different hub-heights and wind characteristics such as cut-in-speed (Vc), rated speed (Vr), cut-off speed (Vf) can be determined using the Weibull's parameters K and C with the help of eq. (14). The energy output can be calculated using the following equation:
Apr May Jun Jul Aug Sep Oct Nov
(rated)
(16)
1.58 1.92 2.00 2.05 1.68 1.51 1.43 1.67 1.91 1.77 1.74 2.01
0.24 0.18 0.29 0.62 1.56 1.57 1.30 0.66 0.22 0.22 0.24 0.66
Table 5. Specific outputs at Palkalainagar for typical WECS (Vc = 9 kmph; Vr = 29 kmph; Vr = 45 kmph)
Jan Feb Mar
Eg = TA × Pr
Ed (kWh m - 2 day- 1)
.
55 61 62 63 57 54 52 57 61 58 58 62
8. VARIATION OF ANNUAL SPECIFIC OUTPUT WITH VARIOUS HUB-HEIGHT AND WIND CHARACTERISTICS OF WECS
where Eg is the annual generated energy in kWh, TA is the annual specific output in kWh/kW (rated) and Pr is the rated power in kW of the WECS.
EPF
Dec Ann
K
2.42 1.93 1.85 1.81 2.24 2.59 2.80 2.25 1.94 2.10 2,14 1.84
C (kmph)
8.39 7.10 8.24 10.55 15.55 16.13 15.35 11.59 7.61 7.78 8.06 10.87
PLF
0.0107 0.0077 0.0189 0.0556 0.1625 0.1684 0.1358 0.0570 0.0108 0.0100 0.0116 0.0606
Specific output (kWh kW- ~monthor year- ~)
7.2 5.7 13.6 41.4 117.0 125.3 I01.0 41.0 8.0 7.2 8.6 531.0
Technical Note
819
Table 6. Comparison of annual specific output and energy density at Palkalainagar with other stations
Station
Annual specific output (kWh kW -I year -~)
Energy density at height 10 m ( k W h m -2 day -I)
531 1972 3300 2168 1347 3230 1640
0.662 1.316 3.438 I. 140 0.864 2.625 1.248
Palkalainagar Tiruchirappalli Airport Tuticorin Harbour Madras Harbour Kodaikanal Indore Airport Bangalore Airport
A graph is drawn between the specific output versus different rated speed, for various cut-in-speeds at different heights (Fig. 3). From Fig. 3 we can conclude that (a) the lower the rated and cut-in speeds of the WECS for the same height, the higher will be the specific output ; (b) the specific output increases with height; (c) we can easily obtain the annual energy output for different machines using the eq. (16).
I = the initial cost of WECS per kW (rated) in Rs/kW (rated) O M C = the operation and maintenance cost in Rs/kW (rated)/year TA = the annual specific output in kWh/kW (rated) P R F = present worth factor which is given by P R F = 1/DR[I 1/(1 +DR) u] (18) D R = the discount rate N = the life of WECS in years. - -
9. ECONOMIC ANALYSIS
The data used in eq. (17) and (18) to determine the C O E by wind energy are the following :
Following Anani et al. [10] the cost of 1 kWh in Rupees (15 = Rs. 16/-), generated by WECS is given by the following formula. C O E = I + ( P R F x OMC) (I 7)
I = 5000; 10,000; 15,000; 20,000; 25,000; 30,000. O M C = 2% of L
P R F × TA
TA = 200; 400; 600; 800; 1000; 1200. D R = 0.08
where
N = 15 years.
COE = the cost of electricity generated by WECS in
Rs/kWh
The cost of energy generated by WECS is calculated and
V, - ~ l d
lmmd m ~
o - VC=7
kmph
v c - C u t In speed
•
II
-
H - Height.
&-Vc-
13
M
V~ - 4 5 kin1)11
cl - V c =
15
-
-Vc=
~12
IO
m
2
I
I
I
I
I
I
I
I
I
I
I
I
25 27 29 31 33"3!5 37 25 27 29 31 33 ~
V,
V,
I
I
I
I
I
I
I
I
37 25 27 29 31 33 ~ , 37
V,
Fig. 3. Variation of specific output for different WECS and height.
820
Technical Note Init~l cost I
~! 1,1 .c m 20 [-/
n5 -0 0 0IO000 Rs/kW(r°ted)o-
+
•
\
- 15000
x-
ooo
"F x\\
ii" 4
C
Specific output kwh/kw (roted) Fig. 4. Cost of electricity generated for different specific output.
a graph drawn for these results (Fig. 4). From Fig. 4 we can infer the following: (a) as the specific output increases for the same initial cost, the cost of electricity generated decreases ; (b) as the initial cost increases for the same specific output the cost of electricity increases ; (c) in our judgement all the machines which fall under line 'c' (Rs. 1-10), are possible for the Palkalainagar site,
4. 5. 6.
10. CONCLUSIONS The Weibull frequency distribution has been applied to study the wind speed distribution at the Palkalainagar site at the Madurai Kamaraj University, India. The estimated Weibull's parameters are used to calculate all the parameters related to wind characteristics and also the cost of electricity generated. The conclusions arrived at are as follows : 1. As pointed out in a number of published papers, the Weibull distribution matches well with the observed wind speed frequency distribution for the Palkalainagar site. 2. The availability of wind energy is poor in this site when compared to other stations like Tuticorin and Madras (coastal areas) and Kodaikanal (Hill area). 3. The possible WECS that can be installed in this site should have initial cost less than Rs. 5000/kW (rated) with wind characteristics that can produce specific output between 600 and 1200 kWh/kW (rated). 4. It is not possible to tap wind energy in this site continuously throughout the year, since in some months the energy density in the wind is quite small.
REFERENCES 1. J. P. Hennessey, Some aspects of wind power statistics. J. Appl. Meteorology 16(2), (1977). 2. C. G. Justus, W. R. Hargraves, A. Mikhail and D. Graber, Methods for estimating wind speed frequency distribution. J. Appl. Meteorology 17(3), (1978). 3. M. J. M. Stevens and P. T. Smulders, The estimation of
7.
8. 9.
10.
the parameters of the Weibull wind distribution for wind energy utilisation purposes. Wind Engineering 3(2), (1979). A. N. Elgammal, Estimating wind energy potential using statistical model. Proceedings of the Second International Conference, Sept. 1981. J. P. Hennessey Jr, A comparison of the Weibull and Rayleigh distribution for estimating wind power potential. Wind Engineerin 9 2, 156-164 (1978). E, L. Peterson, I. Troen, S. Frandsen and K. Hedegaard, Windatlasfor Denmark. RIS, Denmark (1981). B, K. Gupta, Estimates of the Weibull Parameters and Specific Wind Energy for Thirtyseven Locations in India. Institute for Development of Energy and Society, India (1985). A. Mani and D. A. Mooley, WindEneryy Data for India. Allied Publishers, India (1983). I. Chand and P. K. Bhargava, Estimation of Weibull's parameters and evaluation of wind data for utilisation of wind energy for natural ventilation in building in India. Indian Journal o f Power and River Valley Development (1985). A. Anani, S. Zuamot, F. Abu-Allan and Z. Jibril, Evaluation of wind energy as a power generation source in a selected site in Jordan. Solar Wind Technol. 59, 67-74 (1988).
APPENDIX Mathematical analysis to obtain the formula for PLF mentioned in Section 6 The analytical expression for power P(V) for a wind machine, by taking into account of losses such as power available at the shaft, losses in the transmission and generator etc., can be taken as P(V) = 0 V < Vc =A+BV+CV 2 V¢<~V
Vf< V
Technical Note where
821
eLF = L f"
P~ Vc = V~ = Vr = P~ =
is the is the is the is the
hub height cut-in speed, hub height rated speed, hub height cut-off speed, rated power.
1 r V,
f(V)P(V) d V + EJVr .f(V)P~ dV V~
)) K
The coefficients A, B and C are determined by solutions of the following set of simultaneous equations. K
A +Bvc+cv~ = o A+BVr+CV~ = Pr
V x-~
Vx fV,{K\/V'?~-'
f~,
F {v'vq
where
( V,'~3 A+BV,+CV~ = P ~ \ ~ ]
Vx y(V) = VX- ' e x p [ - (C) I(A + BV+CV2).
where V~ = (Vc+ Vr)/2. The equations are solved to get expressions for A, B and C. They are given by
The first integration may be performed numerically using Simpson's one third rule. Therefore on integration
v,},
B=P~
~
(Vr--Vc)(Vr--V,)(V,--Vc) V¢)l/(V:,-v~) A = -BVo-CV:.
c = [P,- B(v,-
HK PLF= 3~c~ {Y(V~) + y( V~)+4[y(V~ + K,H)]
v~)-(v:,-vl) (A2)
(A3) (A4)
where H
Knowing the Weibull's parameters K and C for the site under consideration and the power wind speed characteristics of the proposed WECS, the PLF is obtained as follows : The PLF is defined as the ratio between the actual power available in wind and the rated power of the WECS. i.e.
=
V~-V~ N
KL = 1,3 . . . . , ( N - - l ) ,
K2 = 2, 4 . . . . , (N-- 2). N is chosen such that V, - Vc is divided in equal even number of intervals which is assumed as 20 in this calculation.
0960-1481/91 $3.00+,00 Pergamon Press pie
TECHNICAL NOTE Wind energy potential at Palkalainagar T. V. CHINNASAMY*and T. M. HARIDASAN School of Energy, Environment and Natural Resources, Madurai Kamaraj University, Palkalainagar, Madurai 625 021, India (Received 20 April 1990 ; accepted 10 July 1990)
Abstract--This paper uses the Weibull's distribution function to describe the wind speed frequency distribution at Palkalalnagar (geographical co-ordinates N : 9°54 ', E : 78°54'), Madurai, India using the one year data available. Weibull's parameters are used to estimate the wind data parameters for the site. Of the wind data parameters the most important one is the annual specific output (TA), This is used in determining the annual energy output of a Wind Energy Conversion System (WECS) and in conducting cost-benefit analysis of wind-electricity generation. The parameter is used in evaluating the efficiency of WECS in the same site. Results show the possibilities of harnessing wind energy towards electricity generation.
1. INTRODUCTION Wind energy is one of the indirect sources of solar energy and it is directly proportional to the cube of the wind speed at a particular site. Therefore, the site location is an important factor when installing a WECS. There are several methods to describe the wind speed frequency distribution and hence the wind data for a particular site. Out of the various methods, Weibull distribution has been given more attention since it gives a good fit to experimental data as indicated in a number of published papers [1--4]. Hennessey [5] compared Rayleigh distribution and Weibull distribution and found that the maximum error in energy output of WECS would be about 10% of full rated power when the Rayleigh distribution is used instead of the Weibulrs. Peterson et al. [6] found that Weibull distribution gave an excellent fit to the wind speed distribution prevailing in Denmark. Gupta [7] applied the Weibull distribution to data for 37 stations in India, published by Mani and Mooley [8], and concluded that Weibull distribution matches well with the observed frequency distribution. He also found that Rayleigh distribution predicts a lower specific output for typical WECS, as compared to that calculated from observed frequency distribution in all the 37 cases. Ishwar Chand et al. [9] applied the Weibull distribution for their study on wind energy for natural ventilation in buildings in India. In this paper Weibull's parameters for the Palkalainagar site (University township) have been estimated from the available wind speed data. The Weibull's parameters are used to estimate the other parameters of wind energy for the same site. 2. DATA USED FOR COMPUTATION The available hourly wind speed data, for the year 1980, which was recorded at the meteorological station, Madurai Kamaraj University, Palkalainagar, are used for the analysis of wind energy potential at the site concerned. The data used
for the computation are for 11 months, except January, for which data were not available. Hence all the calculations presented in this paper are based on a total number of 7830 hours. 3. FREQUENCY DISTRIBUTION It is important to know the number of hours per month or per year during which the given wind speeds occurred, To arrive at this frequency distribution we must first divide the entire wind speed domain into a number of intervals, mostly of equal width of 0.5 m s-~. Then, starting at first interval of 0-0.5 m s- t, the number of hours is counted in the period concerned that the wind speed was in this interval as shown in Table 1. When the number of hours in each interval is plotted against the wind speed, the frequency distribution emerges as a histogram for a month or a year (Figs 1 and 2). 4. THE WEIBULL'S PARAMETERS The Weibull probability distribution for wind speed V is given by K V -i f(V) = ( ~ ) ( C ) K exp [ -
(~fJ;
(1)
where K and C are the Weibull's parameters. K = dimensionless shape parameter and C = scale parameter with unit of speed. The cumulative probability function for a speed Vt is given by
Equation (2) may be written in the linear form as * Rajapalayam Rajus' College, Rajapalayam 626 117, India.
Y = a+bX
where 815
(3)
816
Technical Note Table 1. Wind speed duration at Palkalainagar for the year 1980 Range (m s - ' )
Jan
Jul
Aug
Sep
Oct
Nov
Dec
Annual (h)
0 16 19 43 74 85 73 88 72 55 44 39 31 22 21 15 13 5 2 3
0 9 8 35 50 84 116 117 73 72 41 40 29 15 14 16 9 6 5 1
0 3 23 38 60 108 116 112 87 68 42 36 10 13 8 9 1 4 2 1
4 27 55 59 95 78 71 98 54 53 45 20 9 1 0 0 0 0 0 0
10 88 100 167 113 I00 60 37 35 8 2 0 0 0 0 0 0 0 0 0
8 63 85 178 179 117 34 25 16 6 2 1 1 0 0 0 0 0 0 0
6 79 90 141 133 148 59 45 12 18 4 0 0 0 0 0 0 0 0 0
52 679 761 1128 1181 1067 819 683 457 327 226 158 90 57 46 45 23 15 11 5
720
740
741
669
720
715
735
7830
Feb
Mar
Apr
May
Jun
0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 4.5-5.0 5.0-5.5 5.5-6.0 6.0--6.5 6.5-7.0 7.0-7.5 7.5-8.0 8.0-8.5 8.5-9.0 9.0-9.5 9.5-10.0
2 65 95 55 131 100 113 38 25 2 3 0 0 0 0 0 0 0 0 0
11 126 110 121 149 105 59 17 11 6 2 2 0 0 0 0 0 0 0 0
6 121 92 173 105 70 48 34 22 4 12 8 1 0 1 I 0 0 0 0
5 82 84 118 92 72 70 72 50 35 29 12 9 6 2 4 0 0 2 0
Total
629
719
698
744
Y = In [ - l n . ( l -
F(V))]
X = In V~
(4)
K=b C = exp [-a/b].
(5)
The coefficients a and b of the equation (3) were computed using the least square method. To perform this, cumulative frequencies F(Iz) for various speeds were determined from the frequencies in Table 1. Hence with the help of the eqs (4)
and (5), the values K and C can be determined. The values K and C thus obtained are based on the records of an anemometer mounted at a 7 m height. Then the values of Weibull's parameters were converted to the standard anemometer height of 10 m or at any height above the ground by eqs (9). C10
=
Ca[(10/Za)]
(6)
a
K,0 = Ka[1-0.088 In (Z,/10)] and
AnnuoL 1900 ~ = P_86 me-' 1200 r -
K = 1.84
,oL.
LI.
Z~
•
O. I0
5 O I
l
(~
"
1~5
"
"
2.2o
"
3~
4.~
~2~
~
7.~
¢~
~
--
O
Velocity (ms-') Fig. I. Actual and fitted wind speed frequency distribution at Palkalainagar.
(7)
817
Technical Note June 1980 : 4.09 ms-' K : 2.24 90 -
eo
....-1
C = 4.32
....J
-
m s -)
-
25
f I Act.°t 2o
7o 6o
~0 20
I0 0
J
/
40
.d0.~,~
I.~
5
2.~
3.2~
4.2S
~
6.~
7.~
e.2~
9.~'J
O
Vel,.ocit,y I ms-')
Fig. 2. Actual and fitted wind speed frequency distribution at Palkalainagar.
n = [0.37-0.088 In C~I/[1-0.088 In (Z,/10)]
(8)
where Ca and K, are the Weibull's parameters at Za metre, C)0 and Kt 0 are the Weibull's parameters at 10 m and n = the power law exponent. The annual results and also the results for 11 months data are summarised in Table 2. The values K and C at anemometric height are used to find the probability of the distribution for various wind speeds using the eq. (1). The calculated values are plotted in the same graph of the histograms. The agreement between the histograms and the fitted Weibull distributions may be noted (Figs 1 and 2). Hence the Weibull distribution expression can be used to determine the wind characteristics at Palkalainagar.
5. D E R I V E D
FACTORS TO ESTIMATE CHARACTERISTICS
WIND
Equation (1) can be used to find the following factors [9]. Average wind speed 17=CF(I+ 1)
(ms-')
(9)
where F = gamma function. Most probable wind speed
Vmp c I K - - I I 'Ix ( m s - ' ) .
= L~ j
(10)
Time during which wind speed >t Vmp T = exp [ -
(V,,p/C)•].
(11)
Energy pattern factor Table 2. Weibull's parameters at Palkalainagar for the year 1980
EPF = F1 + 3K/(FI + 1/3) 3.
(12)
Energy density At anemometer height 7 m K C (kmph) Jan
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ann
.
2.42 1.93 1.85 1.81 2.24 2.59 2.80 2.25 1.94 2.10 2.14 1.84
.
.
8.39 7.10 8.24 10.55 15.55 16.13 15.34 11.59 7.60 7.78 8.06 10.87
At standard anemometer Power law height 10 m coefficient K C (kmph) n .
2.50 1.99 1.91 1.87 2.31 2.67 2.89 2.32 2.00 2.17 2.21 1.90
E~=0.00031(P)3xEPF
(kWhm-2day -1)
(13)
where I7 = average calculated speed in kmph. All such values calculated from the above stated relations are listed in Tables 3 and 4.
.
8,94 7.60 8,78 11.16 16.28 16.84 16.05 12.23 8.12 8.31 8.60 11.49
0.177 0.192 0.179 0.158 0.129 0.121 0.126 0.150 0.186 0.184 0.181 0.155
6. ESTIMATION OF ANNUAL OR MONTHLY SPECIFIC OUTPUT (TA OR T . ) OF WIND POWER Following the procedure mentioned by Gupta [7], the specific output TA or Tmo is given by TA = PLF x 8760 Tmo = PLF x (no.ofhoursinthemonth),
(14) (15)
where PLF is plant load factor for the corresponding year or month calculated using the Weibull's parameters Kand C at anemometric height. The values so obtained are also tabulated in Table 5.
818
Technical Note Table 3. Wind data at Palkalainagar for the anemometer height 7 m
(actual) (m s- ~)
(calculated) (m s- ')
Vmp (m s- ~)
T (%)
EPF
Ed (kWh m - ~ day-~)
2.27 2.09 2.17 2.71 4.09 4.30 3.77 3.07 2.32 2.32 2.37 2.86
2.06 1.75 2.03 2.61 3.82 3.98 3.80 2.85 1.88 1.91 1.98 2.68
1.87 1.35 1.50 1.88 3.32 3.71 3.64 2.48 1.45 1.59 1.64 1.97
56 62 63 64 57 54 53 57 62 59 59 63
1.62 1.98 2.07 2.13 1.72 1.54 1.46 1.71 1.97 1.82 1.79 2.09
0.21 0.15 0.25 0.54 1.39 1.40 1.16 0.58 0.19 0.19 0.20 0.58
Jail
Feb Mar Apr May Juil Jul Aug Sep Oct Nov Dec Ann
Table 4. Wind data at Palkalainagar for the standard anemometer height I0 m
(actual) (m s- i) Jail
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ann
.
(calculated) (m s- i) .
2.27 2.09 2.17 2.71 4.09 4.30 3.77 3.07 2.32 2.32 2.37 2.86
.
Vmp (m s- a) .
2.02 1.87 2.16 2.75 4.01 4.16 3.98 3.01 2.00 2.04 2.12 2.83
T (%) .
2.03 1.49 1.66 2.06 3.54 3.93 3.85 2.66 1.59 1.74 1.82 2.15
7. COMPARISON OF SPECIFIC OUTPUT AND ENERGY DENSITY The annual specific output and energy density at t0 m height are compared with that of the selected stations in India [7]. These values are listed in Table 6.
Month
The annual specific output TA for different hub-heights and wind characteristics such as cut-in-speed (Vc), rated speed (Vr), cut-off speed (Vf) can be determined using the Weibull's parameters K and C with the help of eq. (14). The energy output can be calculated using the following equation:
Apr May Jun Jul Aug Sep Oct Nov
(rated)
(16)
1.58 1.92 2.00 2.05 1.68 1.51 1.43 1.67 1.91 1.77 1.74 2.01
0.24 0.18 0.29 0.62 1.56 1.57 1.30 0.66 0.22 0.22 0.24 0.66
Table 5. Specific outputs at Palkalainagar for typical WECS (Vc = 9 kmph; Vr = 29 kmph; Vr = 45 kmph)
Jan Feb Mar
Eg = TA × Pr
Ed (kWh m - 2 day- 1)
.
55 61 62 63 57 54 52 57 61 58 58 62
8. VARIATION OF ANNUAL SPECIFIC OUTPUT WITH VARIOUS HUB-HEIGHT AND WIND CHARACTERISTICS OF WECS
where Eg is the annual generated energy in kWh, TA is the annual specific output in kWh/kW (rated) and Pr is the rated power in kW of the WECS.
EPF
Dec Ann
K
2.42 1.93 1.85 1.81 2.24 2.59 2.80 2.25 1.94 2.10 2,14 1.84
C (kmph)
8.39 7.10 8.24 10.55 15.55 16.13 15.35 11.59 7.61 7.78 8.06 10.87
PLF
0.0107 0.0077 0.0189 0.0556 0.1625 0.1684 0.1358 0.0570 0.0108 0.0100 0.0116 0.0606
Specific output (kWh kW- ~monthor year- ~)
7.2 5.7 13.6 41.4 117.0 125.3 I01.0 41.0 8.0 7.2 8.6 531.0
Technical Note
819
Table 6. Comparison of annual specific output and energy density at Palkalainagar with other stations
Station
Annual specific output (kWh kW -I year -~)
Energy density at height 10 m ( k W h m -2 day -I)
531 1972 3300 2168 1347 3230 1640
0.662 1.316 3.438 I. 140 0.864 2.625 1.248
Palkalainagar Tiruchirappalli Airport Tuticorin Harbour Madras Harbour Kodaikanal Indore Airport Bangalore Airport
A graph is drawn between the specific output versus different rated speed, for various cut-in-speeds at different heights (Fig. 3). From Fig. 3 we can conclude that (a) the lower the rated and cut-in speeds of the WECS for the same height, the higher will be the specific output ; (b) the specific output increases with height; (c) we can easily obtain the annual energy output for different machines using the eq. (16).
I = the initial cost of WECS per kW (rated) in Rs/kW (rated) O M C = the operation and maintenance cost in Rs/kW (rated)/year TA = the annual specific output in kWh/kW (rated) P R F = present worth factor which is given by P R F = 1/DR[I 1/(1 +DR) u] (18) D R = the discount rate N = the life of WECS in years. - -
9. ECONOMIC ANALYSIS
The data used in eq. (17) and (18) to determine the C O E by wind energy are the following :
Following Anani et al. [10] the cost of 1 kWh in Rupees (15 = Rs. 16/-), generated by WECS is given by the following formula. C O E = I + ( P R F x OMC) (I 7)
I = 5000; 10,000; 15,000; 20,000; 25,000; 30,000. O M C = 2% of L
P R F × TA
TA = 200; 400; 600; 800; 1000; 1200. D R = 0.08
where
N = 15 years.
COE = the cost of electricity generated by WECS in
Rs/kWh
The cost of energy generated by WECS is calculated and
V, - ~ l d
lmmd m ~
o - VC=7
kmph
v c - C u t In speed
•
II
-
H - Height.
&-Vc-
13
M
V~ - 4 5 kin1)11
cl - V c =
15
-
-Vc=
~12
IO
m
2
I
I
I
I
I
I
I
I
I
I
I
I
25 27 29 31 33"3!5 37 25 27 29 31 33 ~
V,
V,
I
I
I
I
I
I
I
I
37 25 27 29 31 33 ~ , 37
V,
Fig. 3. Variation of specific output for different WECS and height.
820
Technical Note Init~l cost I
~! 1,1 .c m 20 [-/
n5 -0 0 0IO000 Rs/kW(r°ted)o-
+
•
\
- 15000
x-
ooo
"F x\\
ii" 4
C
Specific output kwh/kw (roted) Fig. 4. Cost of electricity generated for different specific output.
a graph drawn for these results (Fig. 4). From Fig. 4 we can infer the following: (a) as the specific output increases for the same initial cost, the cost of electricity generated decreases ; (b) as the initial cost increases for the same specific output the cost of electricity increases ; (c) in our judgement all the machines which fall under line 'c' (Rs. 1-10), are possible for the Palkalainagar site,
4. 5. 6.
10. CONCLUSIONS The Weibull frequency distribution has been applied to study the wind speed distribution at the Palkalainagar site at the Madurai Kamaraj University, India. The estimated Weibull's parameters are used to calculate all the parameters related to wind characteristics and also the cost of electricity generated. The conclusions arrived at are as follows : 1. As pointed out in a number of published papers, the Weibull distribution matches well with the observed wind speed frequency distribution for the Palkalainagar site. 2. The availability of wind energy is poor in this site when compared to other stations like Tuticorin and Madras (coastal areas) and Kodaikanal (Hill area). 3. The possible WECS that can be installed in this site should have initial cost less than Rs. 5000/kW (rated) with wind characteristics that can produce specific output between 600 and 1200 kWh/kW (rated). 4. It is not possible to tap wind energy in this site continuously throughout the year, since in some months the energy density in the wind is quite small.
REFERENCES 1. J. P. Hennessey, Some aspects of wind power statistics. J. Appl. Meteorology 16(2), (1977). 2. C. G. Justus, W. R. Hargraves, A. Mikhail and D. Graber, Methods for estimating wind speed frequency distribution. J. Appl. Meteorology 17(3), (1978). 3. M. J. M. Stevens and P. T. Smulders, The estimation of
7.
8. 9.
10.
the parameters of the Weibull wind distribution for wind energy utilisation purposes. Wind Engineering 3(2), (1979). A. N. Elgammal, Estimating wind energy potential using statistical model. Proceedings of the Second International Conference, Sept. 1981. J. P. Hennessey Jr, A comparison of the Weibull and Rayleigh distribution for estimating wind power potential. Wind Engineerin 9 2, 156-164 (1978). E, L. Peterson, I. Troen, S. Frandsen and K. Hedegaard, Windatlasfor Denmark. RIS, Denmark (1981). B, K. Gupta, Estimates of the Weibull Parameters and Specific Wind Energy for Thirtyseven Locations in India. Institute for Development of Energy and Society, India (1985). A. Mani and D. A. Mooley, WindEneryy Data for India. Allied Publishers, India (1983). I. Chand and P. K. Bhargava, Estimation of Weibull's parameters and evaluation of wind data for utilisation of wind energy for natural ventilation in building in India. Indian Journal o f Power and River Valley Development (1985). A. Anani, S. Zuamot, F. Abu-Allan and Z. Jibril, Evaluation of wind energy as a power generation source in a selected site in Jordan. Solar Wind Technol. 59, 67-74 (1988).
APPENDIX Mathematical analysis to obtain the formula for PLF mentioned in Section 6 The analytical expression for power P(V) for a wind machine, by taking into account of losses such as power available at the shaft, losses in the transmission and generator etc., can be taken as P(V) = 0 V < Vc =A+BV+CV 2 V¢<~V
Vf< V
Technical Note where
821
eLF = L f"
P~ Vc = V~ = Vr = P~ =
is the is the is the is the
hub height cut-in speed, hub height rated speed, hub height cut-off speed, rated power.
1 r V,
f(V)P(V) d V + EJVr .f(V)P~ dV V~
)) K
The coefficients A, B and C are determined by solutions of the following set of simultaneous equations. K
A +Bvc+cv~ = o A+BVr+CV~ = Pr
V x-~
Vx fV,{K\/V'?~-'
f~,
F {v'vq
where
( V,'~3 A+BV,+CV~ = P ~ \ ~ ]
Vx y(V) = VX- ' e x p [ - (C) I(A + BV+CV2).
where V~ = (Vc+ Vr)/2. The equations are solved to get expressions for A, B and C. They are given by
The first integration may be performed numerically using Simpson's one third rule. Therefore on integration
v,},
B=P~
~
(Vr--Vc)(Vr--V,)(V,--Vc) V¢)l/(V:,-v~) A = -BVo-CV:.
c = [P,- B(v,-
HK PLF= 3~c~ {Y(V~) + y( V~)+4[y(V~ + K,H)]
v~)-(v:,-vl) (A2)
(A3) (A4)
where H
Knowing the Weibull's parameters K and C for the site under consideration and the power wind speed characteristics of the proposed WECS, the PLF is obtained as follows : The PLF is defined as the ratio between the actual power available in wind and the rated power of the WECS. i.e.
=
V~-V~ N
KL = 1,3 . . . . , ( N - - l ) ,
K2 = 2, 4 . . . . , (N-- 2). N is chosen such that V, - Vc is divided in equal even number of intervals which is assumed as 20 in this calculation.