Comparison between Regenerator Model and the Instantaneous Direct Solar Radiation for Port Harcourt

This paper compares the result generated by the Regenerator technique and the Ideriah’s method for instantaneous solar radiation. It considered the generation of the actual power input from the regenerator. The actual power input to the photovoltaic panel was calculated from a power model derived from the regenerator’s standard power that is nominally provided, regenerator material and reflectivity of the material. The amount of visible radiation absorbable by photovoltaic plates was further derived in the model and a value of 0.386Pi was obtained. The Ideriah’s model was used to calculate global solar radiation from extraterrestrial solar radiation. It utilized the concept of transmittance to arrive at the amount of insolation received locally (i.e. at the point of interest). It also calculated the amount of insolation at optical thicknesses (Air mass values) representing top of the hour from 5.0am to 7.0pm. Comparison & result showed that the regenerator model gave 84% to 97% correctness or an approximated average correctness of 94% when compared to the Ideriah’s model. Chi-square was used to test the relationship between the results. Chi-square results showed a high level of significance in the similarity of the results obtained. Python software was used to simulate the results and graph presentation.


I. INTRODUCTION
The ever growing desire to divert the utilization of energy by man and equipment to be derived from an amazing point of nature which has been found to be free and in relative abundancethe solar energycannot be over emphasized.This solar energy has been found to vary from place to place on the earth's surface and according to environmental provision has a value of up to (4.0 -6.5) Wh/m 2 /day in Nigeria [1].The design of any solar equipment and utilization of solar energy requires a proper knowledge of the amount of radiation in a particular location, environment [2], [3].The amount of radiation at a particular point in time, specifically, at the top of the hour (noon day) is utilized in this work as a basis of assessment.The assessment is done for Port Harcourt on Longitude 7.05 0 E and Latitude 4.82 0 N on the 11 th of November, 2017.
The regenerator or solar recharger is a component unit which has the ability to generate radiation from energy stored in deep cells (solar batteries) and then project this radiation onto photovoltaic panels which can be used to properly re-charge the solar battery in a seemingly cyclic manner.It makes use of geometric modeling to properly design and fabricate the regenerator casing.[4] conceived that a geometric model is central to any tool product cycle in a manufacturing environment and in schematic representation, showed that the ideas, design analysis and production are central in a geometric model [5].In his geometric modeling described shapes as representations, which are symbol structures that correspond to mathematical models.The Regenerator model, utilizes the power model to calculate the amount of radiation actually absorbed by the photovoltaic panel and then takes a record of the output of each of those absorbed energy since the power provided at the regenerator are standard power and then posits that when the same panel is exposed to solar radiation, the panel output would generate the same value as it would, when the regenerator was in position [6].The regenerator model could be used to calculate the absorbed radiation by the photovoltaic panel and invariably the amount of available direct radiation.

II. MATERIALS AND METHODS
Analytical method was used to derive the actual power input from the regenerator.

A. Assumptions
i. Neglect distance of thermal source from all surfaces ii.Thermal source conforms to standard ratings in watts.
iii.Radiation on regenerator surface losses no energy This model tells us the amount of radiation released by the regenerator (Actual) and the amount of this radiation absorbed by the Photovoltaic panel (Absorbed) Let power input =  , total reflectivity = , and Let power = .Given that Average Reflectivity of aluminum metal = 92% [7].Then, Actual amount of input wattage (i.e.incident radiation): If % Actual amount of radiation in the visible bandwidth be ; Actual absorbed power by PV cell or Panel absorbed power: (i.e.Actual   = 0.92 Since   and  are standards Then Comparison between Regenerator Model and the Instantaneous Direct Solar Radiation for Port Harcourt Rex K. C. Amadi, F. J. K. Ideriah, and B. Nkoi

B. The Instantaneous Radiation Model (Ideriah's Model)
This model is used as a validation tool for the hourly radiation estimation carried out with the photovoltaic panel.The global solar radiation E is usually lower in value than the extraterrestrial radiation Es.
Mathematically, E or ELocal<ESolar or Es (7) Where Extraterrestrial radiation (Es) also known as solar constant reduces to global solar radiation (E) which is absorbed and scattered as it traverses the atmosphere and reduces to local radiation called the instantaneous radiation [8].
Considering that optical thickness is a function of the zenith angle which varies accordingly with the time of the day (ti), then for all time (11) The instantaneous value represents all radiation bandwidth.The Actual amount of solar radiation available for use is 46% of the radiation [9].The results from the application of the models are presented in tabular form as follows: A. Models Table I is used as a validation tool, to show clearly the relationship between Ideriah's model (the validator) and the hourly experimental result obtained for the photovoltaic panel.The model did not give any radiation value at 5.00am, 6.00am, 6.00pm and 7.00pm since (m) value was infinite, however Photovoltaic panel gave 14.08 W/m2.statistical mean result for the regenerator model gave a percentage correctness of 89% to 97% with an average value of 94% close to the Ideriah's model.
The inference drawn from this is that the Regenerator model results highly adapts the Ideriah's model to 94% which validates the experimental model used.The instantaneous result as shown in Table II is given for the available optical thickness as obtained practically.The Table II also gives the result of hourly instantaneous radiation for Longitude 7.05 O E and Latitude 4.81 O Non the 11 th day of November 2017 and represents values from 7am to 12pm which is a half day cycle since the other half part is a mirror image of the other half (i.e.1pm to 5pm).Evidently, 6:00am and 6pm have no representation here due to the inability to obtain an optical thickness value at that time.The trend shows that as m reduces from 6:00am to 11am, troughs at 12.00pm and increases again from 1pm to 6pm, the total instantaneous radiation as well as actual radiation for PV consumption increases from 107W/m 2 6.00am, peaks at 12.00pm and reduces 50 to 107 at 6.pm using the Ideriah's model.

B. Instantaneous Radiation Calculation
For transmittance, ( 1 ) =   −   ,  = 0.1, and P = 0.794 when m = 1.07.Where:  For each repetition the summation then gives the overall chi-square value for the test.
To test whether the observed value agree with expected value, Then utilize  2 (chi) square.I.e.Fig. 2 is the graphical trend establishing Tables (I and II) which is used as a validation, to show clearly the relationship between Ideriah's model (the validator) and the hourly experimental result obtained for the photovoltaic panel by using the regenerator model.The model could not be used at 6.00am and 6.00pm since (m) value was infinite, however PV panel gave 14.08w/m 2 .Low values comparable to the PV panel were however obtained at 6.30 am and 5.30pm.The regenerator model has a percentage correctness of 89% to 97%(average value of 94%) close to the Ideriah's model.That is, the photovoltaic result highly agrees to within 94% of Ideriah's model which validates the experimental model used.

IV. CONCLUSION
The results obtained showed that the regenerator model was able to capture the required design parameters since it gave values that were correct up to 94% of the Ideriah's model.The calculated chi-square value which was less than the tabulated chi-square showed a significant relationship between both models.The regenerator model highly adapts the Ideriah's instantaneous solar radiation model and hence, applicable for instantaneous solar radiation measurement.

2 ;
accept or fail to reject   and conclude that experimental value did not differ from instantaneous model.

Fig. 1 .
Fig. 1.Software Version of Relationship Between Hourly Instantaneous Radiation and Ideriah's Model with Python's Environmental Calculator.

Fig. 1
Fig. 1 is the python environmental calculator, it consists of an interface where for the various input variables for the instantaneous radiation model.It also has the value of the constants provided by the instantaneous model it then has a calculator which calculates and the software tabulates the result as is shown.

Fig. 2 .
Fig. 2. Relationship Between the Photovoltaic Power Model and Ideriah's Model for Instantaneous Radiation

TABLE III
Table III is the chi-Square table.It gives the value for the ratio of variation of the square observed and expected values to the expected value.