Estimation of solar irradiance for PV--ECS based distributed power generation.
Rizwan, M. ; Jamil, Majid
Introduction
Renewable energy sources have enormous potential and can meet many
times the present world energy demand. They can enhance diversity in
energy supply markets, secure long-term sustainable energy supplies, and
reduce local and global atmospheric emissions. They can also provide
commercially attractive options to meet specific needs for energy
services (particularly in developing countries and rural areas), create
new employment opportunities, and offer possibilities for local
manufacturing of equipment. Major types of renewable energy sources
include solar, wind, hydro and biomass, all of which have huge potential
to meet future energy challenges. Solar power is one of the most
promising and more predictable than other renewable sources and less
vulnerable to changes in seasonal weather. Whereas generation of power
from other renewable sources is limited to sites where these resources
exist in sufficient quantities and can be harnessed, solar energy can
produce power at the point of demand in both rural and urban areas [1].
Solar PV electricity is an equally significant energy option for
developed and developing countries because of the cost of transmission
lines and the difficulty of transporting fuel to remote areas,
developing countries are increasingly turning to solar energy as a
cost-effective way to supply electricity. Usage of solar PV modules will
increase significantly as the demand for electricity spreads throughout
the world. Solar energy has the potential, not only, to play a very
important role in providing most of the heating, cooling and electricity
needs of the world, but also to solve our environmental problems. Solar
energy can be exploited through the solar thermal and solar photovoltaic
(SPV) routes for various applications. SPV technology enables direct
conversion of sunlight into electricity through semi-conductor devices
called solar cells. Solar cells are interconnected and hermetically
sealed to constitute a photovoltaic module. The photovoltaic modules are
integrated with other components such as storage batteries to constitute
SPV systems and power plants. Photovoltaic systems and power plants are
highly reliable and modular in nature [1,2,3].
However the proper estimation of potential of any renewable energy
source is essential for planning and promotion of the technology. The
measurement of solar irradiance is difficult at different places because
of high instrument cost, limited spatial coverage and limited length of
record. So there is a need of theoretical models based on the measured
solar data on specific locations, which can be used to get the
information on solar data for other places where measurements have not
been done [1, 2]. Various theoretical models have been proposed in the
literature to estimate the solar irradiance for photovoltaic power
generation. Modified Hottel's model [3, 5] has been used to
calculate the beam radiation and Liu-Jordan's model [5] to
calculate the diffuse radiation. But in these models the atmospheric
turbidity and N[O.sub.2] absorbance have not been considered [4]. These
factors are important for accurate estimation at different locations.
In the proposed study a broadband-based REST model is used to
calculate the solar irradiance that takes into account the atmospheric
turbidity and N[O.sub.2] absorbance too. Obtained solar irradiance from
REST model is used to generate the solar output power for PV based
distributed power generation. Now a days the use of the distributed
power generating systems, especially those using photovoltaic (PV), is
increasing due to the maintenance free, long lasting, and environment
friendly nature of PV. For the intermittent nature of the PV output,
some storage devices or backup systems are necessary to accommodate the
luctuations. Batteries are used most commonly as storage devices. But,
as usually known, a major problem of batteries is in their durability,
i.e., the lack of long lasting [7]. So, in this context, we have
proposed a distributed power generating system by using a PV panel and a
new storage device called energy capacitor system (ECS). The ECS is a
combination of electric double layer capacitors (EDLC) and electronic
circuits, and has long lifetime, high efficiency, and power density [5].
Rest Model
This newly proposed model called ' Reference Evaluation of
Solar Transmittance' Model (REST) is a direct spin- off the
intermediate calculations performed for this study. Its basic functional
form is similar to others models, except that the total N[O.sub.2]
absorption is taken into account through a specific transmittance. A New
and highly accurate parameterizations for each of the extinction
processes have been obtained here by fitting the reference calculations.
The complete mathematical model is presented in Appendix A.
Brief Description of the PV-ECS System
A simplified block diagram of the PV-ECS system shown in Fig. 1 is
designed with an aim to meet a residential load of 1 kW peak, and the
load pattern is assumed to have an average value of 530 W witha load
form factor (LFF: the ratio of the total energy above the average power
to the daily total energy) of 18%. Here, it is considered that the PV
panel should be enough size to supply the peak power of the load. Its
capacity is calculated using the following equation:
[EPV.sub.(min)] = [P.sub.load] x LFF x 24 (1)
where
[EPV.sub.(min)] minimum daily output of PV panel (Wh)
[P.sub.load] average value of the load (W).
[FIGURE 1 OMITTED]
For 1 kW load [EPV.sub.(min)] is 2.29 kWh.
As the load is ac, dividing this value by the efficiency of the
inverter =90% we get, EPV(min) = 2.54 kWh. To be on safer side, we have
considered this value to be 3 kWh. The modules are connected in series
that can produce a peak output of 1296 W at MPP ([I.sub.m] = 7.2A,
[V.sub.m] = 180 V). Again, it is considered that the ECS should be big
enough to supply the peak energy even in rainy/snowy days. So, its size
is calculated using the following equation:
EECS = EPV (min)--EPV (2)
Where
EECS capacity of the ECS (Wh)
EPV daily PV output in rainy/snowy days (Wh)
For the same load, considering EPV = 0.5 kWh gives EECS = 1.79 kWh.
Dividing this value by the efficiency of the ECS =85% and that of
inverter =90% we get, EECS = 2.3 kWh. To construct an ECS of this size,
four capacitor modules have been taken. Each module has 252 EDLCs and a
total capacitance of 505.5 F at 90 V. So, four such modules have a total
storage capacity of 2.27 kW x h. To increase the storage capacity and to
yield a large energy output, electronic circuits have been used with the
EDLC. To match the peak power of the PV panel, a 1000 W maximum power
point tracker (MPPT) has been used. In order to supply the dc output of
the MPPT and the EDLC to the load and to charge the EDLC by grid power,
a bi-directional error tracking mode-pulse width modulation (ETM-PWM)
power conversion system (PCS) has been used. Its maximum capacity, dc
input/output range, and ac input/output range are 1000 W, 90-180 V, and
90-110 V, respectively. To keep the capacitor voltage within the dc
range of the PCS, charging/discharging is performed by connecting the
modules in two combinations. Combination-I is the parallel connection of
two strings, where each string contains two modules in series. On the
other hand, combination-II is the series connection of the four modules.
During discharging, the capacitor modules remain in combination-I first,
then in combination-II, and vice versa during charging. The control
system consists of a microcomputer, a data acquisition unit, and its
necessary interfacing circuits. To simulate different load patterns, a
resistive room heater of variable power is used. Its value is 50-1150 W,
but within this range the value can be set to any integer multiple of
50W.
In this work, the ECS has been used to overcome some difficulties
of conventional batteries. The superiority of the ECS compared to the
popular batteries is given in Table 1. As shown in this table, the ECS
has very longer lifetime, higher efficiency, and lower charging time
than the lead acid and NiCd batteries. All of these properties have
encouraged the use of ECS in spite of its higher price.
Results
The estimated and measured values has been calculated for all the
months of the year, but due to paucity of space it is shown only for the
month of January in this paper is shown in table II and III. The
presented data in table II and III is taken by using pyranometer at IIT
Delhi in 2007.
A computer program in MAT LAB language is written and the measured
data is given as the input along with hourly values of relative humidity
and ambient temperature. By using REST model, hourly values of global
and diffuse radiation have been computed. It is seen that global &
diffuse radiation estimated by REST model is very close to measured
values.
Figure 2 and 3 shows the comparison of computed and measured values
of global and diffuse radiation respectively using REST model. It is
seen that in this model computed values are lower than the measured one,
same trend is also seen in diffuse radiation. It is clearly seen from
the graph and table, both the measured values and computed values are
very close to each other during sunshine hours, while it gives more than
5% error during morning and evening hours. Hence the study of two
important atmospheric factors is very important in the estimation of
solar irradiance [2].
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
The figure 4 and 5 shows the comparison of computed and measured
values of global and diffuse radiation respectively for the month of
July 2007. It is clearly seen from the graphs, the value of solar
irradiance in the month of July is more than the other months of the
year and are very close to each other. Thus the output power of the PV
panel is more. So it is necessary to calculate the output power
generated from PV panel throughout the year, but the power shown in the
results is the average power generated in the year.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
Since, the efficiency of the PV panel, cp is calculated by
considering the average temperature of the day, the estimated PPV gives
the temperature compensated value. Powers is generated by PV panels from
beam radiation and diffuse radiation. To calculate the beam and diffuse
radiation REST model has been used.
Once the insolation, incident on a PV panel, is known, its output
power (PPV) can easily be estimated by the following equation:
PPV = [tau] x cos [theta] x [[eta].sub.m] x [A.sub.p] x
[[eta].sub.p] (3)
Where: [tau]- Solar radiation (W/[m.sup.2]);
[theta]- Angle of incidence calculated by considering [beta] =
45[degrees]. (declination of our panel);
[[eta].sub.m]--efficiency of the MPPT = 90%
[A.sub.p]--area of the PV panel ([m.sup.2]) = 27 [m.sup.2]
[[eta].sub.p]--efficiency of the PV panel = 9%
Considering the given values of the above parameters, the PV output
on a typical sunny day has been estimated and the actual output on the
same day has been measured for comparison. The integrated energy of the
estimated PPV is 7.36 kWh and that of the practically obtained one is
7.21 kWh, i.e., the error in the estimation is 2.1%. While it goes upto
10%, if we have not considered the atmospheric factors and the
estimation has been done by modified Hottel's equation and
Liu-Jordan equations [1]. Although the estimated PV output is smooth,
the practically obtained one has many fluctuations due to the tracking
action of the MPPT. However, these fluctuations do not hamper the system
operation. As the ECS can be charged and discharged quickly, it absorbs
these variations and provides a steady output.
Conclusion
In this paper, the effect of two important atmospheric factors,
variation of turbidity and N[O.sub.2] absorbance is studied in
estimating the solar irradiance. The proposed system has an excellent
overall efficiency and is expected to be durable, as we have proposed
the ECS that has longer lifetime than conventional batteries. Although
the price of the ECS is very high, but it is gradually decreasing. If
the ECS is produced on a large scale, the manufacturers would be able to
sell it at a cheaper price, and then, hopefully the PV-ECS system would
be cost effective.
The percentage error in the output power of the PV panel obtained
from the proposed study is found only 2.1%, whereas in the other studies
it is upto 10%. The proposed system has also become reliable and durable
after including ECS system.
Appendix A: Equations for the REST Model
[E.sub.bn] = [E.sub.on] [T.sub.r] [T.sub.g] [T.sub.o] [T.sub.n]
[T.sub.w] [T.sub.a] (A.1)
[T.sub.r] = exp (-[m'.sub.r] [[tau].sub.r]) (A.2)
[T.sub.g] = exp (-[m'.sub.r] [[tau].sub.g]) (A.3)
[T.sub.o] = exp (-[m'.sub.r] [[tau].sub.o]) (A.4)
[T.sub.n] = exp (-[m'.sub.w]s [[tau].sub.n]) (A.5)
[T.sub.w] = exp (-[m'.sub.r] [[tau].sub.w]) (A.6)
[T.sub.a] = exp (-[m'.sub.r] [[tau].sub.a]) (A.7)
[m'.sub.r] = (1-q) [[cos[[theta].sub.z] + 0.48353
[[theta].sup.0.095846.sub.z] /[(96.741-
[[theta].sub.z]).sup.1.754]].sup.-1] (A.8)
[m.sub.o] = [[cos[[theta].sub.z] + 1.0651 [[theta].sup.06379.sub.z]
/[(101.8 - [[theta].sub.z]).sup.2.2694]].sup.-1] (A.9)
[m.sub.n] = [[cos[[theta].sub.z] + 1.1212
[[theta].sup.1.6131.sub.z] /[(111.55 -
[[theta].sub.z]).sup.3.2629]].sup.-1] (A.10)
[m.sub.w] = [[cos[[theta].sub.z] + 0.10648
[[theta].sup.0.11423.sub.z] /[(93.781 - [theta]z).sup.1.9203]].sup.-1]
(A.11)
[m.sub.a] = [[cos[[theta].sub.z] + 0.16851
[[theta].sup.0.18198.sub.z] /[(95.318 - [theta]z).sup.1.9542]].sup.-1]
(A.12)
[[tau].sub.r] = (0.11005 + 0.014758 [m'.sub.r] + 0.000051409
[m'.sup.2.sub.r]) /(1 +0.3269 [m'.sub.r] + 0.012374
[m'.sup.2.sub.r]) (A.13)
[[tau].sub.g] = (0.028786 + 0.019308 [m'.sub.r] + 0.00046277
[m'.sup.2.sub.r]) /(1 + 1.9068 [m'.sub.r] + 0.23897
[m'.sup.2.sub.r]) (A.14)
[[tau].sub.o] = [u.sub.o] ([C.sub.o] + [C.sub.1][m.sub.o] +
[C.sub.2][m.sup.2.sub.o])/(1 + [C.sub.3][m.sub.o]) (A.15)
[[tau].sub.w] = w' ([D.sub.o] + [D.sub.1][m.sub.w])/(1 +
[D.sub.2][m.sub.w]) (A.16)
[[tau].sub.a] = [beta](1.6933 + [E.sub.1] [m.sub.a])/(1 +
[E.sub.2][m.sub.a]) (A.17)
Nomenclature
[E.sub.bn] Beam solar irradiance at normal surface (W/[m.sup.2])
[E.sub.on]s Extraterrestrial solar irradiance (W/[m.sup.2])
[T.sub.r] Rayleigh transmittance (dimensionless)
[T.sub.g] Transmittance due to mixed gases (dimensionless)
[T.sub.o] Transmittance of ozone (dimensionless)
[T.sub.w] Transmittance of water vapor (dimensionless)
[T.sub.a] Transmittance of aerosols (dimensionless)
[[tau].subr] Fraction of incident energy transmitted after
scattering by clean, dry air molecules i.e. atmospheric transmittance
due to Rayleigh scattering (dimensionless)
[[tau].sub.g] Fraction of incident energy transmitted after
absorption by uniformly mixed gases (dimensionless)
[[tau].sub.o] Fraction of incident energy transmitted after
absorption by ozone (dimensionless)
[[tau].sub.n] Fraction of incident energy transmitted
(dimensionless)
[[tau].sub.w] Fraction of incident energy transmitted after
absorption by water vapor (dimensionless)
[[tau].sub.a] Fraction of incident energy transmitted after
scattering effect of aerosol (dimensionless)
[m'.sub.r] Relative air mass or air mass at standard
atmospheric pressure (dimensionless)
[m.sub.o] Optical mass for ozone (dimensionless)
[m.sub.n] Optical mass (dimensionless)
[m.sub.w] Optical mass for water vapor (dimensionless)
[m.sub.a] Pressure corrected relative air mass or air mass at
actual pressure (dimensionless)
[u.sub.o] Total ozone abundance (atm-cm)
w' Precitable water thickness (cm)
[beta] Angstrom turbidity cofficient (dimensionless)
[[theta].sub.z] Solar zenith angle (degree)
Co, [C.sub.1], [C.sub.2], [C.sub.3], [D.sub.o], [D.sub.1],
[D.sub.2], [E.sub.0], [E.sub.1] and [E.sub.2] Constants (dimensionless)
References
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Allied Publishers, New Delhi.
M. Rizwan* and Majid Jamil (#)
* Department of Electrical Engineering,
G. L. Bajaj Institute of Tech. & Mgt., Gr. Noida (U.P) 201306
Email: rizwaniit@yahoo.co.in, Mobile No. 09891558821
(#) Department of Electrical Engineering,
Jamia Millia Islamia, New Delhi- 110025, India
Table I : Comparison between ECS and popular storage batteries
Parameters ECS Lead-Acid NiCd
Power density 400 10 ~ 30 100 ~ 160
Energy density 6.5 40 ~ 45 45 ~ 53
Depth of discharge 95 50 ~ 70 80 ~ 100
Efficiency ~90 ~ 80 ~ 75
Charging time 1 min 5- 10 h 15 min ~ 8 h
Life cycle ~3000000 300 ~ 1000 300 ~ 500
Price/ Rs.Kwh 200 10 ~ 40 40 ~ 75
Table II : Percentage RMSE for Computed Global Radiation Comparison to
Measured Global Radiation for New Delhi, by using REST Model.
Global Radiation Global Radiation
Time Measured Computed January 2007
(hrs.) (W/[m.saup.2]) (W/[m.saup.2]) % Error
9:00 294.12 280.68 4.57
10:00 523.20 512.75 2.10
11:00 614.35 605.42 1.45
12:00 678.72 669.45 1.37
1:00 682.44 672.50 1.46
2:00 542.65 532.72 1.83
3:00 490.72 480.75 2.03
4:00 319.75 310.55 2.87
5:00 138.20 130.40 5.64
Table III : Percentage RMSE for Computed Diffuse Radiation
Comparison to Measured Diffuse Radiation for New Delhi,
by using REST Model.
January 2007
Diffuse Diffuse
Radiation Radiation
Time Measured Computed
(hrs.) (W/[m.sup.2]) (W/[m.sup.2]) % Error
9:00 86.52 81.24 6.10
10:00 104.56 99.54 4.80
11:00 121.10 114.80 5.20
12:00 116.58 110.80 4.96
1:00 122.65 118.32 3.53
2:00 112.55 108.92 3.23
3:00 102.50 98.78 3.63
4:00 76.85 73.95 3.78
5:00 27.58 25.90 6.10
