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Estimation of solar irradiance for PV--ECS based distributed power generation.


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)


[EPV.sub.(min)] minimum daily output of PV panel (Wh)

[P.sub.load] average value of the load (W).


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)


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.


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].



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.



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.


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.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)


[] 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)


[1] Kaplanis S. N, 2006 "New methodologies to estimate the hourly global solar radiation; comparison with existing models," Renewable Energy, vol. 31, pp. 781-90.

[2] Madkour M. A. and Hamed A. B., 2006, "Comparative study on different models for estimation of solar radiation," Renewable Energy, vol. 31, pp. 361-82.

[3] Hottel, H. C., 1976, "A simple model for estimating the transmittance of direct solar radiation through clear atmosphere," Solar Energy, vol. 18, pp. 129-34.

[4] Power H. C., 2001, "Estimating atmospheric turbidity from climate data," Atmospheric Environment, vol. 35 pp. 125-34.

[5] Yamashiro S. and Rahman M. H., 2007, "Novel distributed power generating system of PV-ECaSS using solar energy estimation," IEEE transactions on Energy Conversion, vol. 22 (2), pp. 358- 67.

[6] Duffie J. A. and Beckman W. A., 1997, Solar Engineering of Thermal Processes, John Willey and Sons, New York, pp 6-65.

[7] Muneer T. and Asif M., 2005, "Sustainable production of solar electricity with particular reference to the Indian economy," Renewable and Sustainable Energy Reviews, vol. 9, pp. 444-73.

[8] Mani A. 1980, Handbook of Solar Radiation Data for India, 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:, 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
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Title Annotation:photovoltaic energy capacitor system
Author:Rizwan, M.; Jamil, Majid
Publication:International Journal of Applied Engineering Research
Article Type:Report
Date:Jun 1, 2008
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